Mathematical model of two-phase flow in accelerator channel
Directory of Open Access Journals (Sweden)
О.Ф. Нікулін
2010-01-01
Full Text Available The problem of two-phase flow composed of energy-carrier phase (Newtonian liquid and solid fine-dispersed phase (particles in counter jet mill accelerator channel is considered. The mathematical model bases goes on the supposition that the phases interact with each other like independent substances by means of aerodynamics’ forces in conditions of adiabatic flow. The mathematical model in the form of system of differential equations of order 11 is represented. Derivations of equations by base physical principles for cross-section-averaged quantity are produced. The mathematical model can be used for estimation of any kinematic and thermodynamic flow characteristics for purposely parameters optimization problem solving and transfer functions determination, that take place in counter jet mill accelerator channel design.
Mathematical modeling of disperse two-phase flows
Morel, Christophe
2015-01-01
This book develops the theoretical foundations of disperse two-phase flows, which are characterized by the existence of bubbles, droplets or solid particles finely dispersed in a carrier fluid, which can be a liquid or a gas. Chapters clarify many difficult subjects, including modeling of the interfacial area concentration. Basic knowledge of the subjects treated in this book is essential to practitioners of Computational Fluid Dynamics for two-phase flows in a variety of industrial and environmental settings. The author provides a complete derivation of the basic equations, followed by more advanced subjects like turbulence equations for the two phases (continuous and disperse) and multi-size particulate flow modeling. As well as theoretical material, readers will discover chapters concerned with closure relations and numerical issues. Many physical models are presented, covering key subjects including heat and mass transfers between phases, interfacial forces and fluid particles coalescence and breakup, a...
Mathematical models for two-phase stratified pipe flow
Energy Technology Data Exchange (ETDEWEB)
Biberg, Dag
2005-06-01
The simultaneous transport of oil, gas and water in a single multiphase flow pipe line has for economical and practical reasons become common practice in the gas and oil fields operated by the oil industry. The optimal design and safe operation of these pipe lines require reliable estimates of liquid inventory, pressure drop and flow regime. Computer simulations of multiphase pipe flow have thus become an important design tool for field developments. Computer simulations yielding on-line monitoring and look ahead predictions are invaluable in day-to-day field management. Inaccurate predictions may have large consequences. The accuracy and reliability of multiphase pipe flow models are thus important issues. Simulating events in large pipelines or pipeline systems is relatively computer intensive. Pipe-lines carrying e.g. gas and liquefied gas (condensate) may cover distances of several hundred km in which transient phenomena may go on for months. The evaluation times associated with contemporary 3-D CFD models are thus not compatible with field applications. Multiphase flow lines are therefore normally simulated using specially dedicated 1-D models. The closure relations of multiphase pipe flow models are mainly based on lab data. The maximum pipe inner diameter, pressure and temperature in a multiphase pipe flow lab is limited to approximately 0.3 m, 90 bar and 60{sup o}C respectively. The corresponding field values are, however, much higher i.e.: 1 m, 1000 bar and 200{sup o}C respectively. Lab data does thus not cover the actual field conditions. Field predictions are consequently frequently based on model extrapolation. Applying field data or establishing more advanced labs will not solve this problem. It is in fact not practically possible to acquire sufficient data to cover all aspects of multiphase pipe flow. The parameter range involved is simply too large. Liquid levels and pressure drop in three-phase flow are e.g. determined by 13 dimensionless parameters
Mathematical modeling of a gas jet impinging on a two phase bath
Delgado-Álvárez, J.; Ramírez-Argáez, Marco A.; González-Rivera, C.
2012-09-01
In this work a three phase 3D mathematical model was developed using the Volume Of Fluid (VOF) algorithm, which is able to accurately describe the cavity geometry and size as well as the liquid flow patterns created when a gas jet impinges on a two phase liquid free surface. These phenomena are commonly found in steelmaking operations such as in the Electric Arc Furnace (EAF) and the Basic Oxygen Furnace (BOF) where oxygen jets impinge on a steel bath and they control heat, momentum and mass transfer. The cavity formed in the liquids by the impinging jet depends on a force balance at the free surface where the inertial force of the jet governs these phenomena. The inertial force of the jet and its angle play important roles, being the lowest angle the best choice to shear the bath and promote stronger circulation and better mixing in the liquids.
Mathematical modeling and numerical simulation of two-phase flow problems at pore scale
Directory of Open Access Journals (Sweden)
Paula Luna
2015-11-01
Full Text Available Mathematical modeling and numerical simulation of two-phase flow through porous media is a very active field of research, because of its relevancy in a wide range of physical and technological applications. Some outstanding applications concern reservoir simulation and oil and gas recovery, fields in which a great effort is being paid in the development of efficient numerical methods. The mathematical model used in this work is written as a system comprising an elliptic equation for pressure and a hyperbolic one for saturation. Our aim is to obtain the numerical solution of this model by combining finite element and finite volume techniques, with a second-order non-oscillatory reconstruction procedure to build the values of the velocities at the cell interfaces of the FV mesh from pointwise values of the pressure at the FE nodes. The numerical results are compared to those obtained using the commercial code ECLIPSE showing an appropriate behavior from a qualitative point of view. The use of this FE-FV procedure is not the usual numerical method in petroleum reservoir simulation, since the techniques most frequently used are based on finite differences, even in standard commercial tools.
Mathematical Model of Two Phase Flow in Natural Draft Wet-Cooling Tower Including Flue Gas Injection
Directory of Open Access Journals (Sweden)
Hyhlík Tomáš
2016-01-01
Full Text Available The previously developed model of natural draft wet-cooling tower flow, heat and mass transfer is extended to be able to take into account the flow of supersaturated moist air. The two phase flow model is based on void fraction of gas phase which is included in the governing equations. Homogeneous equilibrium model, where the two phases are well mixed and have the same velocity, is used. The effect of flue gas injection is included into the developed mathematical model by using source terms in governing equations and by using momentum flux coefficient and kinetic energy flux coefficient. Heat and mass transfer in the fill zone is described by the system of ordinary differential equations, where the mass transfer is represented by measured fill Merkel number and heat transfer is calculated using prescribed Lewis factor.
Institute of Scientific and Technical Information of China (English)
邓英尔; 刘慈群
2003-01-01
A mathematical model of two-phase fluid nonlinear flow in the direction ofnormal of ellipse through low-permeability porous media was established according to anonlinear flow law expressed in a continuous function with three parameters, a massconservation law and a concept of turbulent ellipses. A solution to the model was obtainedby using a finite difference method and an extrapolation method. Formulas of calculatingdevelopment index not only before but also after water breaks through an oil well in thecondition of two-phase fluid nonlinear flow in the media were derived. An example wasdiscussed. Water saturation distribution was presented. The moving law of drainage frontwas found. Laws of change of pressure difference with time were recognized. Results showthat there is much difference of water saturation distribution between nonlinear flow andlinear flow; that drainage front by water moves faster, water breaks through sooner and theindex gets worse because of the nonlinear flow ; and that dimensionless pressure differencegets larger at the same dimensionless time and difficulty of oil development becomes biggerby the nonlinear flow . Thus, it is necessary that influence of nonlinear flow on developmentindexes of the oil fields be taken into account. The results provide water-floodingdevelopment of the oil fields with scientific basis.
DEFF Research Database (Denmark)
Petkov, K.P.; Puton, M; Madsen, Søren Peder
2014-01-01
A model based on a homogeneous formulation of the governing differential equations (Navier-Stokes equations) describing the process of pressure drop in a simplified geometry of an expansion valve is investigated and simulated. Numerical solutions are compared to experimental results. The model...... is a one dimensional formulation in space and the equations incorporates the change in tubes and orifice diameter as formulated in (S. Madsen et.al., Dynamic Modeling of Phase Crossings in Two-Phase Flow, Communications in Computational Physics 12 (4), 1129-1147). The pressure changes in the flow...
Musakaev, N. G.; Borodin, S. L.
2016-05-01
The mathematical model of the two-phase flow in a vertical well with an electric centrifugal pump located in the permafrost region is presented. The comparison of the calculation's results with experimental data, the results of numerical experiments by determining the flow structure, the temperature distribution in a well, influence of the temperature distribution on paraffin deposition and change in time of the radius of thawing in the frozen ground are presented.
Energy Technology Data Exchange (ETDEWEB)
Cabezas Gomez, Luben; Milioli, Fernando Eduardo [Sao Paulo Univ., Sao Carlos, SP (Brazil). Escola de Engenharia. Nucleo de Engenharia Termica e Fluidos]. E-mails: lubencg@sc.usp.br; milioli@sc.usp.br
2001-06-01
A mathematical model is developed for gas-solids flows in circulating fluidized beds. An Eulerian formulation is followed based on the two-fluids model approach where both the fluid and the particulate phases are treated as a continuum. The physical modelling is discussed, including the formulation of boundary conditions and the description of the numerical methodology. Results of numerical simulation are presented and discussed. The model is validated through comparison to experiment, and simulation is performed to investigate the effects on the flow hydrodynamics of the solids viscosity. (author)
Conder, J. R.; Gunn, D. J.; Shaikh, M. A.
1982-08-01
A mathematical model is presented for the vaporisation of liquid from a laminar film flowing down the inside surface of a smooth tube into a countercurrent laminar flow of gas. The partial differential equations that describe temperature and composition distributions are integrated across the tube to give a set of four coupled ordinary differential equations. A numerical method for the solution of the equations is proposed and examined; the method is posed to solve the transient response for heat and mass transfer. A satisfactory solution is found for a range of space and time intervals. The mathematical model has been validated by experimental measurements on a falling film evaporator with evaporation occurring at sub-boiling temperatures from a laminar liquid film into a laminar gas stream. The performance of the evaporator is assessed.
Carrara, Mark David
2006-04-01
The overall objective of this dissertation is the development of a modeling and simulation approach for turbulent two-phase chemically reacting flows. A new full velocity-scalar filtered mass density function (FMDF) formulation for large eddy simulation (LES) of a separated two-phase flow is developed. In this formulation several terms require modeling that include important conditionally averaged phase-coupling terms (PCT). To close the PCT a new derivation of the local instantaneous two-phase equations is presented and important identities are derived relating the PCT to surface averages. The formulation is then applied for two particle laden flow cases and solved using a full particle based Monte-Carlo numerical solution procedure. The first case is a temporally developing counter-current mixing layer dilutely seeded with evaporating water droplets. Validation studies reveal excellent agreement of the full particle method to previous hybrid FDF studies and direct numerical simulations for single-phase flows. One-way coupled simulations reveal that the overall dispersion is maximized with unity Stokes number droplets. Two-way coupled simulations reveal the advantages of two FDF approaches where the subgrid variation of droplet properties are explicitly taken into account. Comparisons of the fully-coupled FDF approach are compared to more approximate means of determining phase-coupling based on filtered properties and local and compounded global errors are assessed. The second case considered is the combustion aluminum particles. A new mechanistic model for the ignition and combustion of aluminum particulate is developed that accounts for unsteady heating, melting, heterogeneous surface reactions (HSR) and quasi-steady burning. Results of this model agree well with experimental data for overall burn rates and ignition times. Two-phase simulations of aluminum particulate seeded mixing layer reveal the variations in flame radius resulting in local extinguishment
A mechanical erosion model for two-phase mass flows
Pudasaini, Shiva P
2016-01-01
Erosion, entrainment and deposition are complex and dominant, but yet poorly understood, mechanical processes in geophysical mass flows. Here, we propose a novel, process-based, two-phase, erosion-deposition model capable of adequately describing these complex phenomena commonly observed in landslides, avalanches, debris flows and bedload transport. The model is based on the jump in the momentum flux including changes of material and flow properties along the flow-bed interface and enhances an existing general two-phase mass flow model (Pudasaini, 2012). A two-phase variably saturated erodible basal morphology is introduced and allows for the evolution of erosion-deposition-depths, incorporating the inherent physical process including momentum and rheological changes of the flowing mixture. By rigorous derivation, we show that appropriate incorporation of the mass and momentum productions or losses in conservative model formulation is essential for the physically correct and mathematically consistent descript...
Directory of Open Access Journals (Sweden)
Leonardo Neves
2015-03-01
Full Text Available Continuous casting is a solidification process, in which the knowledge about its variables is very important in order to produce steel with good quality. The tundish distributes the steel coming from the ladle to the metallurgical mold as the traditional function, besides, it also has some other important functions. Because of its importance in the process, this work aim to carry out studies on the steel flow in the tundish with two different configurations, with and without inert gas injection. A Computational Fluid Dynamic (CFD software were used to make the mathematical simulations making possible to note the difference in terms of the Residence Time Distribution curves (RTD curves, levels of turbulence and velocity profiles with or without inert gas injection
Microgravity two-phase flow regime modeling
Energy Technology Data Exchange (ETDEWEB)
Lee, D.; Best, F.R.; Faget, N.
1987-01-01
A flow pattern or flow regime is the characteristics spatial distribution of the phases of fluid in a duct. Since heat transfer and pressure drop are dependent on the characteristic distribution of the phases, it is necessary to describe flow patterns in an appropriate manner so that a hydrodynamic or heat transfer theory applicable to that pattern can be chosen. The objective of the present analysis is to create a flow regime map based on physical modeling of vapor/liquid interaction phenomena in a microgravity environment. In the present work, four basic flow patterns are defined: dispersed flow, stratified flow, slug flow, and annular flow. Fluid properties, liquid and vapor flow rates, and pipe size were chosen as the principal parameters. It is assumed that a transition from one flow pattern to another will occur when there is a change in the dominant force which controls that flow pattern. The forces considered in this modeling are surface tension force, both force, inertial force, friction, and turbulent fluctuations.
Modelling two-phase transport of 3H/3He
Visser, A.; Schaap, J.D.; Leijnse, T.; Broers, H.P.; Bierkens, M.F.P.
2008-01-01
Degassing of groundwater by excess denitrification of agricultural pollution complicates the interpretation of 3H/3He data and hinders the estimation of travel times in nitrate pollution studies. In this study we used a two-phase flow and transport model (STOMP) to evaluate the method presented by
Modelling two-phase transport of 3H/3He
Visser, A.; Schaap, J.D.; Leijnse, T.; Broers, H.P.; Bierkens, M.F.P.
2008-01-01
Degassing of groundwater by excess denitrification of agricultural pollution complicates the interpretation of 3H/3He data and hinders the estimation of travel times in nitrate pollution studies. In this study we used a two-phase flow and transport model (STOMP) to evaluate the method presented by V
Two-phase relative permeability models in reservoir engineering calculations
Energy Technology Data Exchange (ETDEWEB)
Siddiqui, S.; Hicks, P.J.; Ertekin, T.
1999-01-15
A comparison of ten two-phase relative permeability models is conducted using experimental, semianalytical and numerical approaches. Model predicted relative permeabilities are compared with data from 12 steady-state experiments on Berea and Brown sandstones using combinations of three white mineral oils and 2% CaCl1 brine. The model results are compared against the experimental data using three different criteria. The models are found to predict the relative permeability to oil, relative permeability to water and fractional flow of water with varying degrees of success. Relative permeability data from four of the experimental runs are used to predict the displacement performance under Buckley-Leverett conditions and the results are compared against those predicted by the models. Finally, waterflooding performances predicted by the models are analyzed at three different viscosity ratios using a two-dimensional, two-phase numerical reservoir simulator. (author)
A phenomenological model of two-phase (air/fuel droplet developing and breakup
Directory of Open Access Journals (Sweden)
Pavlović Radomir R.
2013-01-01
Full Text Available Effervescent atomization namely the air-filled liquid atomization comprehends certain complex two-phase phenomenon that are difficult to be modeled. Just a few researchers have found the mathematical expressions for description of the complex atomization model of the two-phase mixture air/diesel fuel. In the following review, developing model of twophase (air/fuel droplet of Cummins spray pump-injector is shown. The assumption of the same diameters of the droplet and the opening of the atomizer is made, while the air/fuel mass ratio inside the droplet varies.
Approaches to myosin modelling in a two-phase flow model for cell motility
Kimpton, L. S.; Whiteley, J. P.; Waters, S. L.; Oliver, J. M.
2016-04-01
A wide range of biological processes rely on the ability of cells to move through their environment. Mathematical models have been developed to improve our understanding of how cells achieve motion. Here we develop models that explicitly track the cell's distribution of myosin within a two-phase flow framework. Myosin is a small motor protein which is important for contracting the cell's actin cytoskeleton and enabling cell motion. The two phases represent the actin network and the cytosol in the cell. We start from a fairly general description of myosin kinetics, advection and diffusion in the two-phase flow framework, then identify a number of sub-limits of the model that may be relevant in practice, two of which we investigate further via linear stability analyses and numerical simulations. We demonstrate that myosin-driven contraction of the actin network destabilizes a stationary steady state leading to cell motion, but that rapid diffusion of myosin and rapid unbinding of myosin from the actin network are stabilizing. We use numerical simulation to investigate travelling-wave solutions relevant to a steadily gliding cell and we consider a reduction of the model in which the cell adheres strongly to the substrate on which it is crawling. This work demonstrates that a number of existing models for the effect of myosin on cell motility can be understood as different sub-limits of our two-phase flow model.
A new two-phase erosion-deposition model for mass flows
Pudasaini, Shiva P.; Fischer, Jan-Thomas
2016-04-01
Erosion, entrainment and deposition are complex and dominant, but yet poorly understood, mechanical processes in geophysical mass flows. Here, we propose a novel, two-phase, erosion-deposition model capable of adequately describing these complex phenomena commonly observed in landslides, avalanches, debris flows and bedload transports. The model enhances an existing general two-phase mass flow model (Pudasaini, 2012) by introducing a two-phase variably saturated erodible basal morphology. The adaptive basal morphology allows for the evolution of erosion-deposition-depths, incorporating the inherent physical process and rheological changes of the flowing mixture. With rigorous derivation, we show that appropriate incorporation of the mass and momentum productions and losses in conservative model formulation is essential for the physically correct and mathematically consistent description of erosion-entrainment-deposition processes. Simulation indicates a sharp erosion-front and steady-state-rear erosion depth. The model appropriately captures the emergence and propagation of complex frontal surge dynamics associated with the frontal ambient-drag which is a new hypothesis associated with erosion. The novel enhanced real two-phase model also allows for simulating fluid-run-off during the deposition process. The model resembles laboratory experiments for particle-fluid mixture flows and reveals some major aspects of the mechanics associated with erosion, entrainment and deposition. Reference: Shiva P. Pudasaini (2012): A general two-phase debris flow model. J. Geophys. Res., 117, F03010, doi: 10.1029/2011JF002186.
Modeling and simulation of nanoparticles transport in a two-phase flow in porous media
El-Amin, Mohamed
2012-01-01
In the current paper, a mathematical model to describe the nanoparticles transport carried by a two-phase flow in a porous medium is presented. Both capillary forces as well as Brownian diffusion are considered in the model. A numerical example of countercurrent water-oil imbibition is considered. We monitor the changing of the fluid and solid properties due to the addition of the nanoparticles using numerical experiments. Variation of water saturation, nanoparticles concentration and porosity ratio are investigated.
Transient thermohydraulic modeling of two-phase fluid systems
Blet, N.; Delalandre, N.; Ayel, V.; Bertin, Y.; Romestant, C.; Platel, V.
2012-11-01
This paper presents a transient thermohydraulic modeling, initially developed for a capillary pumped loop in gravitational applications, but also possibly suitable for all kinds of two-phase fluid systems. Using finite volumes method, it is based on Navier-Stokes equations for transcribing fluid mechanical aspects. The main feature of this 1D-model is based on a network representation by analogy with electrical. This paper also proposes a parametric study of a counterflow condenser following the sensitivity to inlet mass flow rate and cold source temperature. The comparison between modeling results and experimental data highlights a good numerical evaluation of temperatures. Furthermore, the model is able to represent a pretty good dynamic evolution of hydraulic variables.
Supporting universal prevention programs: a two-phased coaching model.
Becker, Kimberly D; Darney, Dana; Domitrovich, Celene; Keperling, Jennifer Pitchford; Ialongo, Nicholas S
2013-06-01
Schools are adopting evidence-based programs designed to enhance students' emotional and behavioral competencies at increasing rates (Hemmeter et al. in Early Child Res Q 26:96-109, 2011). At the same time, teachers express the need for increased support surrounding implementation of these evidence-based programs (Carter and Van Norman in Early Child Educ 38:279-288, 2010). Ongoing professional development in the form of coaching may enhance teacher skills and implementation (Noell et al. in School Psychol Rev 34:87-106, 2005; Stormont et al. 2012). There exists a need for a coaching model that can be applied to a variety of teacher skill levels and one that guides coach decision-making about how best to support teachers. This article provides a detailed account of a two-phased coaching model with empirical support developed and tested with coaches and teachers in urban schools (Becker et al. 2013). In the initial universal coaching phase, all teachers receive the same coaching elements regardless of their skill level. Then, in the tailored coaching phase, coaching varies according to the strengths and needs of each teacher. Specifically, more intensive coaching strategies are used only with teachers who need additional coaching supports, whereas other teachers receive just enough support to consolidate and maintain their strong implementation. Examples of how coaches used the two-phased coaching model when working with teachers who were implementing two universal prevention programs (i.e., the PATHS curriculum and PAX Good Behavior Game [PAX GBG]) provide illustrations of the application of this model. The potential reach of this coaching model extends to other school-based programs as well as other settings in which coaches partner with interventionists to implement evidence-based programs.
Well-posed Euler model of shock-induced two-phase flow in bubbly liquid
Tukhvatullina, R. R.; Frolov, S. M.
2017-07-01
A well-posed mathematical model of non-isothermal two-phase two-velocity flow of bubbly liquid is proposed. The model is based on the two-phase Euler equations with the introduction of an additional pressure at the gas bubble surface, which ensures the well-posedness of the Cauchy problem for a system of governing equations with homogeneous initial conditions, and the Rayleigh-Plesset equation for radial pulsations of gas bubbles. The applicability conditions of the model are formulated. The model is validated by comparing one-dimensional calculations of shock wave propagation in liquids with gas bubbles with a gas volume fraction of 0.005-0.3 with experimental data. The model is shown to provide satisfactory results for the shock propagation velocity, pressure profiles, and the shock-induced motion of the bubbly liquid column.
DEFF Research Database (Denmark)
Blomhøj, Morten
2004-01-01
Developing competences for setting up, analysing and criticising mathematical models are normally seen as relevant only from and above upper secondary level. The general belief among teachers is that modelling activities presuppose conceptual understanding of the mathematics involved. Mathematical...... modelling, however, can be seen as a practice of teaching that place the relation between real life and mathematics into the centre of teaching and learning mathematics, and this is relevant at all levels. Modelling activities may motivate the learning process and help the learner to establish cognitive...... roots for the construction of important mathematical concepts. In addition competences for setting up, analysing and criticising modelling processes and the possible use of models is a formative aim in this own right for mathematics teaching in general education. The paper presents a theoretical...
A splitting technique for analytical modelling of two-phase multicomponent flow in porous media
DEFF Research Database (Denmark)
Pires, A.P.; Bedrikovetsky, P.G.; Shapiro, Alexander
2006-01-01
In this paper we discuss one-dimensional models for two-phase Enhanced Oil Recovery (EOR) floods (oil displacement by gases, polymers, carbonized water, hot water, etc.). The main result presented here is the splitting of the EOR mathematical model into thermodynamical and hydrodynamical parts....... The introduction of a potential associated with one of the conservation laws and its use as a new independent coordinate reduces the number of equations by one. The (n)x(n) conservation law model for two-phase n-component EOR flows in new coordinates is transformed into a reduced (n-1)x(n-1) auxiliary system...... containing just thermodynamical variables (equilibrium fractions of components, sorption isotherms) and one lifting equation containing just hydrodynamical parameters (phase relative permeabilities and viscosities). The algorithm to solve analytically the problem includes solution of the reduced auxiliary...
MODELING TWO-PHASE FLOW IN PULSED FLUIDIZED BED
Institute of Scientific and Technical Information of China (English)
Dayou Liu; Guodong Jin
2003-01-01
Mathematical models for pulsed fluidization are systematically discussed. Several undetermined constitutive relationships are included in the General Two-Fluid Model (GTFM), the adjustable parameters of which are always chosen at will to some extent. Although there are no adjustable parameters in the Basic Two-Fluid Model (BTFM), its eigenvalues are complex numbers and it is ill-posed for initial-value problems. The Local Equilibrium Model (LEM), a further simplification of BTFM, is discussed at length. Although the model is very simple, it is highly capable of simulating complex processes in pulsed fluidization over a broad range of operating parameters, and its numerical results well fit experimental results in both the variation of bed height and the distribution of particle concentration as fluidizing velocity varies.
Simulation and modeling of two-phase bubbly flows
Energy Technology Data Exchange (ETDEWEB)
Sylvain L Pigny; Pierre F Coste [DEN/DER/SSTH, CEA/Grenoble, 38054 Grenoble Cedex 9 (France)
2005-07-01
Full text of publication follows: Phenomena related to bubbles in two-phase recirculating flows are investigated, via the computational code SIMMER, concerning an experiment in which air is injected in the lower part of a tank filled of water and initially at rest. Averaged mass and momentum transport equations are solved for air and water. Close to the injector, the formation of individual large bubbles is represented in the calculations, via direct simulation. Small scale phenomena, related to small bubbles behavior or turbulence in the liquid continuous phase, are modeled, in a statistical way, via classical closure laws. In a first calculation, the splitting of large bubbles is not represented. It is shown that this phenomenon, the space scale of which is close to the cell size, cannot be simulated, in view of the present computational resources. Nevertheless, relatively fine meshes are used, for an accurate description of hydrodynamical phenomena, and the splitting phenomenon is too large to be modeled via closure laws. A specific approach for the intermediate scales is therefore developed to represent it. (authors)
TWO PHASE FLOW SPLIT MODEL FOR PARALLEL CHANNELS
African Journals Online (AJOL)
Ifeanyichukwu Onwuka
The equations are solved using the Broyden'smethod ... channel system subjected to a two-phase flow transient, and the results have been very .... system pressure, the heat addition rates inside ... three dimensional flows in the LP.
Diagnosing Traffic Anomalies Using a Two-Phase Model
Institute of Scientific and Technical Information of China (English)
Bin Zhang; Jia-Hai Yang; Jian-Ping Wu; Ying-Wu Zhu
2012-01-01
Network traffic anomalies are unusual changes in a network,so diagnosing anomalies is important for network management.Feature-based anomaly detection models (ab)normal network traffic behavior by analyzing packet header features. PCA-subspace method (Principal Component Analysis) has been verified as an efficient feature-based way in network-wide anomaly detection.Despite the powerful ability of PCA-subspace method for network-wide traffic detection,it cannot be effectively used for detection on a single link.In this paper,different from most works focusing on detection on flow-level traffic,based on observations of six traffc features for packet-level traffic,we propose a new approach B6SVM to detect anomalies for packet-level traffic on a single link.The basic idea of B6-SVM is to diagnose anomalies in a multi-dimensional view of traffic features using Support Vector Machine (SVM).Through two-phase classification,B6-SVM can detect anomalies with high detection rate and low false alarm rate.The test results demonstrate the effectiveness and potential of our technique in diagnosing anomalies.Further,compared to previous feature-based anomaly detection approaches,B6-SVM provides a framework to automatically identify possible anomalous types.The framework of B6-SVM is generic and therefore,we expect the derived insights will be helpful for similar future research efforts.
Dynamic Modeling of Phase Crossings in Two-Phase Flow
DEFF Research Database (Denmark)
Madsen, Søren; Veje, Christian; Willatzen, Morten
2012-01-01
of the variables and are usually very slow to evaluate. To overcome these challenges, we use an interpolation scheme with local refinement. The simulations show that the method handles crossing of the saturation lines for both liquid to two-phase and two-phase to gas regions. Furthermore, a novel result obtained...... in this work, the method is stable towards dynamic transitions of the inlet/outlet boundaries across the saturation lines. Results for these cases are presented along with a numerical demonstration of conservation of mass under dynamically varying boundary conditions. Finally we present results...
2016-01-01
This book provides a thorough introduction to the challenge of applying mathematics in real-world scenarios. Modelling tasks rarely involve well-defined categories, and they often require multidisciplinary input from mathematics, physics, computer sciences, or engineering. In keeping with this spirit of modelling, the book includes a wealth of cross-references between the chapters and frequently points to the real-world context. The book combines classical approaches to modelling with novel areas such as soft computing methods, inverse problems, and model uncertainty. Attention is also paid to the interaction between models, data and the use of mathematical software. The reader will find a broad selection of theoretical tools for practicing industrial mathematics, including the analysis of continuum models, probabilistic and discrete phenomena, and asymptotic and sensitivity analysis.
Eck, Christof; Knabner, Peter
2017-01-01
Mathematical models are the decisive tool to explain and predict phenomena in the natural and engineering sciences. With this book readers will learn to derive mathematical models which help to understand real world phenomena. At the same time a wealth of important examples for the abstract concepts treated in the curriculum of mathematics degrees are given. An essential feature of this book is that mathematical structures are used as an ordering principle and not the fields of application. Methods from linear algebra, analysis and the theory of ordinary and partial differential equations are thoroughly introduced and applied in the modeling process. Examples of applications in the fields electrical networks, chemical reaction dynamics, population dynamics, fluid dynamics, elasticity theory and crystal growth are treated comprehensively.
A two-phase model of plantar tissue: a step toward prediction of diabetic foot ulceration.
Sciumè, G; Boso, D P; Gray, W G; Cobelli, C; Schrefler, B A
2014-11-01
A new computational model, based on the thermodynamically constrained averaging theory, has been recently proposed to predict tumor initiation and proliferation. A similar mathematical approach is proposed here as an aid in diabetic ulcer prevention. The common aspects at the continuum level are the macroscopic balance equations governing the flow of the fluid phase, diffusion of chemical species, tissue mechanics, and some of the constitutive equations. The soft plantar tissue is modeled as a two-phase system: a solid phase consisting of the tissue cells and their extracellular matrix, and a fluid one (interstitial fluid and dissolved chemical species). The solid phase may become necrotic depending on the stress level and on the oxygen availability in the tissue. Actually, in diabetic patients, peripheral vascular disease impacts tissue necrosis; this is considered in the model via the introduction of an effective diffusion coefficient that governs transport of nutrients within the microvasculature. The governing equations of the mathematical model are discretized in space by the finite element method and in time domain using the θ-Wilson Method. While the full mathematical model is developed in this paper, the example is limited to the simulation of several gait cycles of a healthy foot.
A Numerical Simulation of Gas-Particle Two-Phase Flow in a Suspension Bed Using Diffusion Flux Model
Institute of Scientific and Technical Information of China (English)
尚智; 杨瑞昌; FUKUDAKenji; 钟勇; 巨泽建
2003-01-01
A mathematical model of two-dimensional turbulent gas-particle two-phase flow based on the modified diffusion flux model (DFM) and a numerical simulation method to analyze the gas-particle flow structures are developed. The modified diffusion flux model, in which the acceleration due to various forces is taken into account for the calculation of the diffusion velocity of particles, is applicable to the analysis of multi-dimensional gas-particle two-phase turbulent flow. In order to verify its accuracy and efficiency, the numerical simulation by DFM is compared with experimental studies and the prediction by κ-ε-κp two-fluid model, which shows a reasonable agreement. It is confirmed that the modified diffusion flux model is suitable for simulating the multi-dimensional gas-particle two-phase flow.
Meso-Scale Modeling of Spall in a Heterogeneous Two-Phase Material
Energy Technology Data Exchange (ETDEWEB)
Springer, Harry Keo [Univ. of California, Davis, CA (United States)
2008-07-11
The influence of the heterogeneous second-phase particle structure and applied loading conditions on the ductile spall response of a model two-phase material was investigated. Quantitative metallography, three-dimensional (3D) meso-scale simulations (MSS), and small-scale spall experiments provided the foundation for this study. Nodular ductile iron (NDI) was selected as the model two-phase material for this study because it contains a large and readily identifiable second- phase particle population. Second-phase particles serve as the primary void nucleation sites in NDI and are, therefore, central to its ductile spall response. A mathematical model was developed for the NDI second-phase volume fraction that accounted for the non-uniform particle size and spacing distributions within the framework of a length-scale dependent Gaussian probability distribution function (PDF). This model was based on novel multiscale sampling measurements. A methodology was also developed for the computer generation of representative particle structures based on their mathematical description, enabling 3D MSS. MSS were used to investigate the effects of second-phase particle volume fraction and particle size, loading conditions, and physical domain size of simulation on the ductile spall response of a model two-phase material. MSS results reinforce existing model predictions, where the spall strength metric (SSM) logarithmically decreases with increasing particle volume fraction. While SSM predictions are nearly independent of applied load conditions at lower loading rates, which is consistent with previous studies, loading dependencies are observed at higher loading rates. There is also a logarithmic decrease in SSM for increasing (initial) void size, as well. A model was developed to account for the effects of loading rate, particle size, matrix sound-speed, and, in the NDI-specific case, the probabilistic particle volume fraction model. Small-scale spall experiments were designed
Mathematical Modeling and Pure Mathematics
Usiskin, Zalman
2015-01-01
Common situations, like planning air travel, can become grist for mathematical modeling and can promote the mathematical ideas of variables, formulas, algebraic expressions, functions, and statistics. The purpose of this article is to illustrate how the mathematical modeling that is present in everyday situations can be naturally embedded in…
Numerical modeling of two-phase binary fluid mixing using mixed finite elements
Sun, Shuyu
2012-07-27
Diffusion coefficients of dense gases in liquids can be measured by considering two-phase binary nonequilibrium fluid mixing in a closed cell with a fixed volume. This process is based on convection and diffusion in each phase. Numerical simulation of the mixing often requires accurate algorithms. In this paper, we design two efficient numerical methods for simulating the mixing of two-phase binary fluids in one-dimensional, highly permeable media. Mathematical model for isothermal compositional two-phase flow in porous media is established based on Darcy\\'s law, material balance, local thermodynamic equilibrium for the phases, and diffusion across the phases. The time-lag and operator-splitting techniques are used to decompose each convection-diffusion equation into two steps: diffusion step and convection step. The Mixed finite element (MFE) method is used for diffusion equation because it can achieve a high-order and stable approximation of both the scalar variable and the diffusive fluxes across grid-cell interfaces. We employ the characteristic finite element method with moving mesh to track the liquid-gas interface. Based on the above schemes, we propose two methods: single-domain and two-domain methods. The main difference between two methods is that the two-domain method utilizes the assumption of sharp interface between two fluid phases, while the single-domain method allows fractional saturation level. Two-domain method treats the gas domain and the liquid domain separately. Because liquid-gas interface moves with time, the two-domain method needs work with a moving mesh. On the other hand, the single-domain method allows the use of a fixed mesh. We derive the formulas to compute the diffusive flux for MFE in both methods. The single-domain method is extended to multiple dimensions. Numerical results indicate that both methods can accurately describe the evolution of the pressure and liquid level. © 2012 Springer Science+Business Media B.V.
A two phase harmonic model for left ventricular function
Dubi, S; Dubi, Y
2006-01-01
A minimal model for mechanical motion of the left ventricle is proposed. The model assumes the left ventricle to be a harmonic oscillator with two distinct phases, simulating the systolic and diastolic phases, at which both the amplitude and the elastic constant of the oscillator are different. Taking into account the pressure within the left ventricle, the model shows qualitative agreement with functional parameters of the left ventricle. The model allows for a natural explanation of heart failure with preserved systolic left ventricular function, also termed diastolic heart failure. Specifically, the rise in left ventricular filling pressures following increased left-ventricular wall stiffness is attributed to a mechanism aimed at preserving heart rate and cardiac output.
A MODEL FOR PREDICTING PHASE INVERSION IN OIL-WATER TWO-PHASE PIPE FLOW
Institute of Scientific and Technical Information of China (English)
GONG Jing; LI Qing-ping; YAO Hai-yuan; YU Da
2006-01-01
Experiments of phase inversion characteristics for horizontal oil-water two-phase flow in a stainless steel pipe loop (25.7 mm inner diameter,52 m long) are conducted. A new viewpoint is brought forward about the process of phase inversion in oil-water two-phase pipe flow. Using the relations between the total free energies of the pre-inversion and post-inversion dispersions, a model for predicting phase inversion in oil-water two-phase pipe flow has been developed that considers the characteristics of pipe flow. This model is compared against other models with relevant data of phase inversion in oil-water two-phase pipe flow. Results indicate that this model is better than other models in terms of calculation precision and applicability. The model is useful for guiding the design for optimal performance and safety in the operation of oil-water two-phase pipe flow in oil fields.
Two-Phase Flow Modeling in a Single Closed Loop Pulsating Heat Pipes
Institute of Scientific and Technical Information of China (English)
YANG Hong-hai; Sameer Khandekar; Sanka V. V. S. N. S. Manyam; Manfred Groll
2007-01-01
Mathematical modeling of pulsating heat pipes through 'first’ principles is a contemporary problem which remains quite elusive. Simplifications and assumptions made in all the modeling approaches developed so far render them unsuitable for engineering design. In this paper, a more realistic modeling scheme is presented which provides considerable try for thought toward the next progressive step. At high enough heat flux level, closed loop pulsating heat pipes experience a bulk internal unidirectional fluid circulation. Under such a condition, conventional two-phaseflow modeling in capillary tubes may be applied. This has been attempted for single-loop PHPs. A homogeneous model and a separated two-fluid flow model based on simultaneous conservation of mass, momentum and energy, have been developed for an equivalent 'open flow' system. The model allows prediction of two-phase flow parameters in each subsection of the device thereby providing important insights into its operation. The concept of 'void fraction constraint'in pulsating heat pipe operation is introduced and its relevance to future modeling attempts is outlined.
Two-phase flow experimental studies in micro-models (Utrecht Studies in Earth Sciences 034)
Karadimitriou, N.K.
2013-01-01
The aim of this research project was to put more physics into theories of two-phase flow. The significance of including interfacial area as a separate variable in two-phase flow and transport models was investigated. In order to investigate experimentally the significance of the inclusion of interfa
The effect of membrane-regulated actin polymerization on a two-phase flow model for cell motility
Kimpton, L. S.
2014-07-23
Two-phase flow models have been widely used to model cell motility and we have previously demonstrated that even the simplest, stripped-down, 1D model displays many observed features of cell motility [Kimpton, L.S., Whiteley, J.P., Waters, S.L., King, J.R. & Oliver, J.M. (2013) Multiple travelling-wave solutions in a minimal model for cell motility. Math. Med. Biol. 30, 241 - 272]. In this paper, we address a limitation of the previous model.We show that the two-phase flow framework can exhibit travelling-wave solutions with biologically plausible actin network profiles in two simple models that enforce polymerization or depolymerization of the actin network at the ends of the travelling, 1D strip of cytoplasm. © 2014 The authors 2014. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.
Institute of Scientific and Technical Information of China (English)
章明川; 吕勇; 王峻晔; 范浩杰; 李德贵; 陈启峰
2000-01-01
In accordance with the results of previous experimental investigations,and starting from the formulation of conservation equations of mass ,momentum and energy for the gas ,the liquid and the interaction of them,including the normal stress action at the curved liquid stream head in the mixing chamber ,the heat transfer and the work done by the shear stress at the parallel part of the interface of the two phases ,a mathematical model for the gas-liquid two-phase flow in the Y-jet nozzle was established by the authors. Furthermore,based on the theory of unsteady surface vibration and the theory of aerodynamic atomization in the literature ,the two-stage breakup process of the liquid film from the exit of the nozzle was modeled. Thus a complete mathematical modeling system for the performance prediction and the design optimization of Y-jet nozzles has been formed. And judged by the practice,the modeling system is very effective.%根据前人实验观察结果所得的流动结构，从气液两相各自的质量、动量、能量平衡及其相互作用方程的构造人手，包括混合孔内油流端部界面上的正应力传递，两相平行界面上的剪应力作功及传热等，建立了Y型喷嘴内部流动过程的数学模型。进而，依据不稳定表面波理论及空气动力破碎理论，分别对Y型喷嘴出口油膜的初级破碎及二次雾化过程作了进一步的模化，建立了一套较为完整的Y型喷嘴性能预测及设计优化的数学方法。经检验，实际使用效果良好。
Tomei, M Concetta; Annesini, M Cristina; Rita, Sara; Daugulis, Andrew J
2008-10-01
The objectives of this work were to demonstrate the potential of a two-phase sequencing batch reactor in degrading xenobiotics and to evaluate the kinetic parameters leading to a mathematical model of the system. 4-Nitrophenol (4NP), a typical representative of substituted phenols, was selected as the target xenobiotic; this compound has never been remediated in a two-phase bioreactor before. Partition tests were conducted to determine the most appropriate partitioning solvent, and among the three investigated solvents (1-undecanol, 2-undecanone and oleyl alcohol), 2-undecanone was chosen because of its favourable partition coefficient and its negligible emulsion-forming tendencies. Moreover, the selected solvent showed satisfactory biocompatibility characteristics with respect to the biomass, with only minor effects on the intrinsic microbial kinetics. Kinetic tests were then performed in a sequencing batch reactor (2-l volume) operated in both conventional one- and two-phase configurations, with the two-phase system showing a significant improvement in the process kinetics in terms of reduced inhibition and increased maximum removal rate. The obtained kinetic parameters suggest that the two-phase sequencing batch system may find full-scale application, as the maximum removal rate k(max) (approximately 3 mg 4NP mgVSS(-1) day(-1)) is of the same order of magnitude of heterotrophic bacteria operating in wastewater treatment plants.
Institute of Scientific and Technical Information of China (English)
张小斌; 姚蕾; 邱利民; 张学军
2013-01-01
Characterizing the complex two-phase hydrodynamics in structured packed columns requires a power-ful modeling tool. The traditional two-dimensional model exhibits limitations when one attempts to model the de-tailed two-phase flow inside the columns. The present paper presents a three-dimensional computational fluid dy-namics (CFD) model to simulate the two-phase flow in a representative unit of the column. The unit consists of an entire corrugation channel and describes well the real liquid flow conditions. The detailed unsteady two-phase 3D CFD calculations on column packed with Flexipak 1Y were implemented within the volume of fluid (VOF) mathe-matical framework. The CFD model was validated by comparing the calculated thickness of liquid film with the available experimental data. Special attention was given to quantitative analysis of the effects of gravity on the hy-drodynamics. Fluctuations in the liquid mass flow rate and the calculated pressure drop loss were found to be quali-tatively in agreement with the experimental observations.
IMPROVED SUBGRID SCALE MODEL FOR DENSE TURBULENT SOLID-LIQUID TWO-PHASE FLOWS
Institute of Scientific and Technical Information of China (English)
TANG Xuelin; QIAN Zhongdong; WU Yulin
2004-01-01
The dense solid-phase governing equations for two-phase flows are obtained by using the kinetic theory of gas molecules. Assuming that the solid-phase velocity distributions obey the Maxwell equations, the collision term for particles under dense two-phase flow conditions is also derived.In comparison with the governing equations of a dilute two-phase flow, the solid-particle's governing equations are developed for a dense turbulent solid-liquid flow by adopting some relevant terms from the dilute two-phase governing equations. Based on Cauchy-Helmholtz theorem and Smagorinsky model,a second-order dynamic sub-grid-scale (SGS) model, in which the sub-grid-scale stress is a function of both the strain-rate tensor and the rotation-rate tensor, is proposed to model the two-phase governing equations by applying dimension analyses. Applying the SIMPLEC algorithm and staggering grid system to the two-phase discretized governing equations and employing the slip boundary conditions on the walls, the velocity and pressure fields, and the volumetric concentration are calculated. The simulation results are in a fairly good agreement with experimental data in two operating cases in a conduit with a rectangular cross-section and these comparisons imply that these models are practical.
Mathematical Analysis for Peristaltic Flow of Two Phase Nanofluid in a Curved Channel
Nadeem, S.; Iqra, Shahzadi
2015-11-01
This paper describes the theoretical analysis for peristaltic motion of water base nanofluid containing distinct types of the nanoparticles like Cu, TiO2, and Al2O3. Equations of nano fluid are modelled and simplified by constructing the suppositions of low Reynolds number as well as long wave length. The reduced equations are solved exactly. Solutions are represented through graphs. Outcomes for the velocity, temperature, pressure rise and stream lines are analyzed graphically. The work presented here is based on the fictitious values, however some other values can be tested experimentally.
DYNAMIC MODELING STRATEGY FOR FLOW REGIME TRANSITION IN GAS-LIQUID TWO-PHASE FLOWS
Energy Technology Data Exchange (ETDEWEB)
X. Wang; X. Sun; H. Zhao
2011-09-01
In modeling gas-liquid two-phase flows, the concept of flow regime has been used to characterize the global interfacial structure of the flows. Nearly all constitutive relations that provide closures to the interfacial transfers in two-phase flow models, such as the two-fluid model, are often flow regime dependent. Currently, the determination of the flow regimes is primarily based on flow regime maps or transition criteria, which are developed for steady-state, fully-developed flows and widely applied in nuclear reactor system safety analysis codes, such as RELAP5. As two-phase flows are observed to be dynamic in nature (fully-developed two-phase flows generally do not exist in real applications), it is of importance to model the flow regime transition dynamically for more accurate predictions of two-phase flows. The present work aims to develop a dynamic modeling strategy for determining flow regimes in gas-liquid two-phase flows through the introduction of interfacial area transport equations (IATEs) within the framework of a two-fluid model. The IATE is a transport equation that models the interfacial area concentration by considering the creation and destruction of the interfacial area, such as the fluid particle (bubble or liquid droplet) disintegration, boiling and evaporation; and fluid particle coalescence and condensation, respectively. For the flow regimes beyond bubbly flows, a two-group IATE has been proposed, in which bubbles are divided into two groups based on their size and shape (which are correlated), namely small bubbles and large bubbles. A preliminary approach to dynamically identifying the flow regimes is provided, in which discriminators are based on the predicted information, such as the void fraction and interfacial area concentration of small bubble and large bubble groups. This method is expected to be applied to computer codes to improve their predictive capabilities of gas-liquid two-phase flows, in particular for the applications in
Chen, Zhaobo; Hu, Dongxue; Zhang, Zhenpeng; Ren, Nanqi; Zhu, Haibo
2009-10-01
The aim of the study was to implement a mathematical model to simulate two-phase anaerobic digestion (TPAD) process which consisted of an anaerobic continuous stirred tank reactor (CSTR) and an upflow anaerobic sludge blanket (UASB) reactor in series treating traditional Chinese medicine (TCM) wastewater. A model was built on the basis of Anaerobic Digestion Model No. 1 (ADM1) while considering complete mixing model for the CSTR, and axial direction discrete model and mixed series connection model for the UASB. The mathematical model was implemented with the simulation software package MATLABTM/Simulinks. System performance, in terms of COD removal, volatile fatty acids (VFA) accumulation and pH fluctuation, was simulated and compared with the measured values. The simulation results indicated that the model built was able to well predict the COD removal rate (-4.8-5.0%) and pH variation (-2.9-1.4%) of the UASB reactor, while failed to simulate the CSTR performance. Comparing to the measured results, the simulated acetic acid concentration of the CSTR effluent was underpredicted with a deviation ratios of 13.8-23.2%, resulting in an underprediction of total VFA and COD concentrations despite good estimation of propionic acid, butyric acid and valeric acid. It is presumed that ethanol present in the raw wastewater was converted into acetic acid during the acidification process, which was not considered by the model. Additionally, due to the underprediction of acetic acid the pH of CSTR effluent was overestimated.
Preliminary Two-Phase Terry Turbine Nozzle Models for RCIC Off-Design Operation Conditions
Energy Technology Data Exchange (ETDEWEB)
Zhao, Haihua [Idaho National Lab. (INL), Idaho Falls, ID (United States); O' Brien, James [Idaho National Lab. (INL), Idaho Falls, ID (United States)
2017-06-12
This report presents the effort to extend the single-phase analytical Terry turbine model to cover two-phase off-design conditions. The work includes: (1) adding well-established two-phase choking models – the Isentropic Homogenous Equilibrium Model (IHEM) and Moody’s model, and (2) theoretical development and implementation of a two-phase nozzle expansion model. The two choking models provide bounding cases for the two-phase choking mass flow rate. The new two-phase Terry turbine model uses the choking models to calculate the mass flow rate, the critical pressure at the nozzle throat, and steam quality. In the divergent stage, we only consider the vapor phase with a similar model for the single-phase case by assuming that the liquid phase would slip along the wall with a much slower speed and will not contribute the impulse on the rotor. We also modify the stagnation conditions according to two-phase choking conditions at the throat and the cross-section areas for steam flow at the nozzle throat and at the nozzle exit. The new two-phase Terry turbine model was benchmarked with the same steam nozzle test as for the single-phase model. Better agreement with the experimental data is observed than from the single-phase model. We also repeated the Terry turbine nozzle benchmark work against the Sandia CFD simulation results with the two-phase model for the pure steam inlet nozzle case. The RCIC start-up tests were simulated and compared with the single-phase model. Similar results are obtained. Finally, we designed a new RCIC system test case to simulate the self-regulated Terry turbine behavior observed in Fukushima accidents. In this test, a period inlet condition for the steam quality varying from 1 to 0 is applied. For the high quality inlet period, the RCIC system behaves just like the normal operation condition with a high pump injection flow rate and a nominal steam release rate through the turbine, with the net addition of water to the primary system; for
Mixed Model for Silt-Laden Solid-Liquid Two-Phase Flows
Institute of Scientific and Technical Information of China (English)
唐学林; 徐宇; 吴玉林
2003-01-01
The kinetic theory of molecular gases was used to derive the governing equations for dense solid-liquid two-phase flows from a microscopic flow characteristics viewpoint by multiplying the Boltzmann equation for each phase by property parameters and integrating over the velocity space. The particle collision term was derived from microscopic terms by comparison with dilute two-phase flow but with consideration of the collisions between particles for dense two-phase flow conditions and by assuming that the particle-phase velocity distribution obeys the Maxwell equations. Appropriate terms from the dilute two-phase governing equations were combined with the dense particle collision term to develop the governing equations for dense solid-liquid turbulent flows. The SIMPLEC algorithm and a staggered grid system were used to solve the discretized two-phase governing equations with a Reynolds averaged turbulence model. Dense solid-liquid turbulent two-phase flows were simulated for flow in a duct. The simulation results agree well with experimental data.
A Dual-Stage Two-Phase Model of Selective Attention
Hubner, Ronald; Steinhauser, Marco; Lehle, Carola
2010-01-01
The dual-stage two-phase (DSTP) model is introduced as a formal and general model of selective attention that includes both an early and a late stage of stimulus selection. Whereas at the early stage information is selected by perceptual filters whose selectivity is relatively limited, at the late stage stimuli are selected more efficiently on a…
THE LINEAR HOMOGENEOUS FLOW MODEL FOR TWO-PHASE FLOW INSTABILITY IN BOILING CHANNELS
Institute of Scientific and Technical Information of China (English)
无
2002-01-01
This paper presents liner homogeneous model describing two-phase flow instability. Dimensionless parameter η was derived by using the linear homogeneous model. Using parameter η the stability of a system could be easily judged. The calculated results agree with the experimental data well.
Entropy analysis on non-equilibrium two-phase flow models
Energy Technology Data Exchange (ETDEWEB)
Karwat, H.; Ruan, Y.Q. [Technische Universitaet Muenchen, Garching (Germany)
1995-09-01
A method of entropy analysis according to the second law of thermodynamics is proposed for the assessment of a class of practical non-equilibrium two-phase flow models. Entropy conditions are derived directly from a local instantaneous formulation for an arbitrary control volume of a structural two-phase fluid, which are finally expressed in terms of the averaged thermodynamic independent variables and their time derivatives as well as the boundary conditions for the volume. On the basis of a widely used thermal-hydraulic system code it is demonstrated with practical examples that entropy production rates in control volumes can be numerically quantified by using the data from the output data files. Entropy analysis using the proposed method is useful in identifying some potential problems in two-phase flow models and predictions as well as in studying the effects of some free parameters in closure relationships.
Numerical simulation of the two-phase flows in a hydraulic coupling by solving VOF model
Luo, Y.; Zuo, Z. G.; Liu, S. H.; Fan, H. G.; Zhuge, W. L.
2013-12-01
The flow in a partially filled hydraulic coupling is essentially a gas-liquid two-phase flow, in which the distribution of two phases has significant influence on its characteristics. The interfaces between the air and the liquid, and the circulating flows inside the hydraulic coupling can be simulated by solving the VOF two-phase model. In this paper, PISO algorithm and RNG k-ɛ turbulence model were employed to simulate the phase distribution and the flow field in a hydraulic coupling with 80% liquid fill. The results indicate that the flow forms a circulating movement on the torus section with decreasing speed ratio. In the pump impeller, the air phase mostly accumulates on the suction side of the blades, while liquid on the pressure side; in turbine runner, air locates in the middle of the flow passage. Flow separations appear near the blades and the enclosing boundaries of the hydraulic coupling.
A state-of-the-art report on two-phase critical flow modelling
Energy Technology Data Exchange (ETDEWEB)
Jung, Jae Joon; Jang, Won Pyo; Kim, Dong Soo [Korea Atomic Energy Research Institute, Taejon (Korea, Republic of)
1993-09-01
This report reviews and analyses two-phase, critical flow models. The purposes of the report are (1) to make a knowledge base for the full understanding and best-estimate of two-phase, critical flow, (2) to analyse the model development trend and to derive the direction of further studies. A wide range of critical flow models are reviewed. Each model, in general, predicts critical flow well only within specified conditions. The critical flow models of best-estimate codes are special process model included in the hydrodynamic model. The results of calculations depend on the nodalization, discharge coefficient, and other user`s options. The following topics are recommended for continuing studies: improvement of two-fluid model, development of multidimensional model, data base setup and model error evaluation, and generalization of discharge coefficients. 24 figs., 5 tabs., 80 refs. (Author).
Estimation of flow velocity for a debris flow via the two-phase fluid model
Directory of Open Access Journals (Sweden)
S. Guo
2014-06-01
Full Text Available The two-phase fluid model is applied in this study to calculate the steady velocity of a debris flow along a channel bed. By using the momentum equations of the solid and liquid phases in the debris flow together with an empirical formula to describe the interaction between two phases, the steady velocities of the solid and liquid phases are obtained theoretically. The comparison of those velocities obtained by the proposed method with the observed velocities of two real-world debris flows shows that the proposed method can estimate accurately the velocity for a debris flow.
Comparison of Experimental and Numerical Two-Phase Flows in a Porous Micro-Model
Directory of Open Access Journals (Sweden)
Dustin Crandall
2009-12-01
Full Text Available Characterizing two-phase flow in porous media is important to provide estimates of sweep efficiency in enhanced oil recovery and storage estimates in potential geological CO2 sequestration repositories. To further the current understanding of two-phase flow in porous media a micro-model of interconnected channels was designed and fabricated using stereolithography to experimentally study gas-liquid flows. This flowcell was created with a wide variability of throat dimensions to represent naturally occurring porous media. Low flow rate experiments of immiscible two-phase drainage were performed within this cell. Additionally, a computational model for analyzing two-phase flows in the same flowcell was developed and used to simulate conditions not possible with our laboratory settings. The computational model was first tested for the identical conditions used in the experimental studies, and was shown to be in good agreement with the experimentally determined fractal dimension of the invading gas structure, time until breakthrough, and fluid saturation. The numerical model was then used to study two-phase air-water flows in flowcells with the same geometry and different gas-liquid-solid contact angles. The percent saturation of air and the motion of the fluids through the cell were found to vary with changes in these parameters. Finally, to simulate flows expected during geologic carbon sequestration, the fluid properties and interface conditions were set to model the flow of CO2 into a brine-saturated porous medium at representative subsurface conditions. The CO2 flows were shown to have larger gas saturations than the previous air into water studies. Thus the accuracy of the computational model was supported by the flowcell experiments, and the computational model extended the laboratory results to conditions not possible with the apparatus used in the experiments.
Lattice-Boltzmann-based two-phase thermal model for simulating phase change
Kamali, M.R.; Gillissen, J.J.J.; Van den Akker, H.E.A.; Sundaresan, S.
2013-01-01
A lattice Boltzmann (LB) method is presented for solving the energy conservation equation in two phases when the phase change effects are included in the model. This approach employs multiple distribution functions, one for a pseudotemperature scalar variable and the rest for the various species. A
Model description of bactrial 3-methylcatechol production in one- and two-phase systems
Husken, L.E.; Hoogakker, J.; Bont, de J.A.M.; Tramper, J.; Beeftink, H.H.
2003-01-01
Pseudomonas putida MC2 produces 3-methylcatechol from toluene in aqueous medium. A second phase of 1-octanol may improve total product accumulation. To optimise the design of such a biphasic process, a process model was developed, both for one- and two-phase applications. The insights obtained by th
Lattice-Boltzmann-based two-phase thermal model for simulating phase change
Kamali, M.R.; Gillissen, J.J.J.; Van den Akker, H.E.A.; Sundaresan, S.
2013-01-01
A lattice Boltzmann (LB) method is presented for solving the energy conservation equation in two phases when the phase change effects are included in the model. This approach employs multiple distribution functions, one for a pseudotemperature scalar variable and the rest for the various species. A
A two-phase solid/fluid model for dense granular flows including dilatancy effects
Mangeney, Anne; Bouchut, Francois; Fernandez-Nieto, Enrique; Koné, El-Hadj; Narbona-Reina, Gladys
2016-04-01
Describing grain/fluid interaction in debris flows models is still an open and challenging issue with key impact on hazard assessment [{Iverson et al.}, 2010]. We present here a two-phase two-thin-layer model for fluidized debris flows that takes into account dilatancy effects. It describes the velocity of both the solid and the fluid phases, the compression/dilatation of the granular media and its interaction with the pore fluid pressure [{Bouchut et al.}, 2016]. The model is derived from a 3D two-phase model proposed by {Jackson} [2000] based on the 4 equations of mass and momentum conservation within the two phases. This system has 5 unknowns: the solid and fluid velocities, the solid and fluid pressures and the solid volume fraction. As a result, an additional equation inside the mixture is necessary to close the system. Surprisingly, this issue is inadequately accounted for in the models that have been developed on the basis of Jackson's work [{Bouchut et al.}, 2015]. In particular, {Pitman and Le} [2005] replaced this closure simply by imposing an extra boundary condition at the surface of the flow. When making a shallow expansion, this condition can be considered as a closure condition. However, the corresponding model cannot account for a dissipative energy balance. We propose here an approach to correctly deal with the thermodynamics of Jackson's model by closing the mixture equations by a weak compressibility relation following {Roux and Radjai} [1998]. This relation implies that the occurrence of dilation or contraction of the granular material in the model depends on whether the solid volume fraction is respectively higher or lower than a critical value. When dilation occurs, the fluid is sucked into the granular material, the pore pressure decreases and the friction force on the granular phase increases. On the contrary, in the case of contraction, the fluid is expelled from the mixture, the pore pressure increases and the friction force diminishes. To
Modelling of two-phase flow based on separation of the flow according to velocity
Energy Technology Data Exchange (ETDEWEB)
Narumo, T. [VTT Energy, Espoo (Finland). Nuclear Energy
1997-12-31
The thesis concentrates on the development work of a physical one-dimensional two-fluid model that is based on Separation of the Flow According to Velocity (SFAV). The conventional way to model one-dimensional two-phase flow is to derive conservation equations for mass, momentum and energy over the regions occupied by the phases. In the SFAV approach, the two-phase mixture is divided into two subflows, with as distinct average velocities as possible, and momentum conservation equations are derived over their domains. Mass and energy conservation are treated equally with the conventional model because they are distributed very accurately according to the phases, but momentum fluctuations follow better the flow velocity. Submodels for non-uniform transverse profile of velocity and density, slip between the phases within each subflow and turbulence between the subflows have been derived. The model system is hyperbolic in any sensible flow conditions over the whole range of void fraction. Thus, it can be solved with accurate numerical methods utilizing the characteristics. The characteristics agree well with the used experimental data on two-phase flow wave phenomena Furthermore, the characteristics of the SFAV model are as well in accordance with their physical counterparts as of the best virtual-mass models that are typically optimized for special flow regimes like bubbly flow. The SFAV model has proved to be applicable in describing two-phase flow physically correctly because both the dynamics and steady-state behaviour of the model has been considered and found to agree well with experimental data This makes the SFAV model especially suitable for the calculation of fast transients, taking place in versatile form e.g. in nuclear reactors. 45 refs. The thesis includes also five previous publications by author.
Two-phase SPH modelling of waves caused by dam break over a movable bed
Institute of Scientific and Technical Information of China (English)
Seyedeh Leila RAZAVITOOSI; Seyed Ali AYYOUBZADEH; Alireza VALIZADEH
2014-01-01
This paper describes the application of the Smoothed Particle Hydrodynamics (SPH) method for modeling two dimensional waves caused by dam break over a movable bed in two dimensions. The two phase SPH method is developed to solve the Navier-Stokes equations. Both fluid and sediment phases are described by particles as weakly compressible fluids and the incompressibility is achieved by the equation of state. The sediment phase is modeled as a non-Newtonian fluid using three alternative approaches of artificial viscosity and Bingham Model. In this paper, the new formulations for two-phase flows are proposed. The numerical results obtained from the developed SPH model show acceptable accuracy with comparison to experimental data.
Modeling the behavior of a two-phase flow apparatus in microgravity
Baker, Eric W.; Tuttle, Ronald F.
1992-01-01
There are many unknown parameters in two-phase flow in microgravity environment. The database is incomplete and therefore correlations are unknown. This has prompted theoretical and experimental work in the area. A Phillips Laboratory program is currently exploring this area. The Phillips Laboratory experiment is a closed loop rankine cycle with a boiler, condenser/subcooler, accumulator and a pump. The work reported herein attempts to model the Phillips Laboratory Apparatus using a thermal-hydraulic software modeling system called Sim-Tool, developed by Mainstream Engineering. This work also explores the limitations of software modeling a microgravity environment. Results of this modeling effort indicate that Sim-Tool needs further development in order to correctly predict two-phase flow in a microgravity environment.
Performance Prediction of Two-Phase Geothermal Reservoir using Lumped Parameter Model
Nurlaela, F.; Sutopo
2016-09-01
Many studies have been conducted to simulate performance of low-temperature geothermal reservoirs using lumped parameter method. Limited work had been done on applying non-isothermal lumped parameter models to higher temperature geothermal reservoirs. In this study, the lumped parameter method was applied to high-temperature two phase geothermal reservoirs. The model couples both energy and mass balance equations thus can predict temperature, pressure and fluid saturation changes in the reservoir as a result of production, reinjection of water, and/or natural recharge. This method was validated using reservoir simulation results of TOUGH2. As the results, the two phase lumped parameter model simulation without recharge shows good matching, however reservoir model with recharge condition show quite good conformity.
Lattice-Boltzmann-based two-phase thermal model for simulating phase change
Kamali, M.R.; Gillissen, J.J.J.; Van den Akker, H.E.A.; Sundaresan, S.
2013-01-01
A lattice Boltzmann (LB) method is presented for solving the energy conservation equation in two phases when the phase change effects are included in the model. This approach employs multiple distribution functions, one for a pseudotemperature scalar variable and the rest for the various species. A nonideal equation of state (EOS) is introduced by using a pseudopotential LB model. The evolution equation for the pseudotemperature variable is constructed in such a manner that in the continuum l...
Multiphysics modeling of two-phase film boiling within porous corrosion deposits
Energy Technology Data Exchange (ETDEWEB)
Jin, Miaomiao, E-mail: mmjin@mit.edu; Short, Michael, E-mail: hereiam@mit.edu
2016-07-01
Porous corrosion deposits on nuclear fuel cladding, known as CRUD, can cause multiple operational problems in light water reactors (LWRs). CRUD can cause accelerated corrosion of the fuel cladding, increase radiation fields and hence greater exposure risk to plant workers once activated, and induce a downward axial power shift causing an imbalance in core power distribution. In order to facilitate a better understanding of CRUD's effects, such as localized high cladding surface temperatures related to accelerated corrosion rates, we describe an improved, fully-coupled, multiphysics model to simulate heat transfer, chemical reactions and transport, and two-phase fluid flow within these deposits. Our new model features a reformed assumption of 2D, two-phase film boiling within the CRUD, correcting earlier models' assumptions of single-phase coolant flow with wick boiling under high heat fluxes. This model helps to better explain observed experimental values of the effective CRUD thermal conductivity. Finally, we propose a more complete set of boiling regimes, or a more detailed mechanism, to explain recent CRUD deposition experiments by suggesting the new concept of double dryout specifically in thick porous media with boiling chimneys. - Highlights: • A two-phase model of CRUD's effects on fuel cladding is developed and improved. • This model eliminates the formerly erroneous assumption of wick boiling. • Higher fuel cladding temperatures are predicted when accounting for two-phase flow. • Double-peaks in thermal conductivity vs. heat flux in experiments are explained. • A “double dryout” mechanism in CRUD is proposed based on the model and experiments.
A Variational Model for Two-Phase Immiscible Electroosmotic Flow at Solid Surfaces
Shao, Sihong
2012-01-01
We develop a continuum hydrodynamic model for two-phase immiscible flows that involve electroosmotic effect in an electrolyte and moving contact line at solid surfaces. The model is derived through a variational approach based on the Onsager principle of minimum energy dissipation. This approach was first presented in the derivation of a continuum hydrodynamic model for moving contact line in neutral two-phase immiscible flows (Qian, Wang, and Sheng, J. Fluid Mech. 564, 333-360 (2006)). Physically, the electroosmotic effect can be formulated by the Onsager principle as well in the linear response regime. Therefore, the same variational approach is applied here to the derivation of the continuum hydrodynamic model for charged two-phase immiscible flows where one fluid component is an electrolyte exhibiting electroosmotic effect on a charged surface. A phase field is employed to model the diffuse interface between two immiscible fluid components, one being the electrolyte and the other a nonconductive fluid, both allowed to slip at solid surfaces. Our model consists of the incompressible Navier-Stokes equation for momentum transport, the Nernst-Planck equation for ion transport, the Cahn-Hilliard phase-field equation for interface motion, and the Poisson equation for electric potential, along with all the necessary boundary conditions. In particular, all the dynamic boundary conditions at solid surfaces, including the generalized Navier boundary condition for slip, are derived together with the equations of motion in the bulk region. Numerical examples in two-dimensional space, which involve overlapped electric double layer fields, have been presented to demonstrate the validity and applicability of the model, and a few salient features of the two-phase immiscible electroosmotic flows at solid surface. The wall slip in the vicinity of moving contact line and the Smoluchowski slip in the electric double layer are both investigated. © 2012 Global-Science Press.
Zhou, J. X.; Shen, X.; Yin, Y. J.; Guo, Z.; Wang, H.
2015-06-01
In this paper, Gas-liquid two phase flow mathematic models of incompressible fluid were proposed to explore the feature of fluid under certain centrifugal force in vertical centrifugal casting (VCC). Modified projection-level-set method was introduced to solve the mathematic models. To validate the simulation results, two methods were used in this study. In the first method, the simulation result of basic VCC flow process was compared with its analytic solution. The relationship between the numerical solution and deterministic analytic solution was presented to verify the correctness of numerical algorithms. In the second method, systematic water simulation experiments were developed. In this initial experiment, special experimental vertical centrifugal device and casting shapes were designed to describe typical mold-filling processes in VCC. High speed camera system and data collection devices were used to capture flow shape during the mold-filling process. Moreover, fluid characteristic at different rotation speed (from 40rpm, 60rpmand 80rpm) was discussed to provide comparative resource for simulation results. As compared with the simulation results, the proposed mathematical models could be proven and the experimental design could help us advance the accuracy of simulation and further studies for VCC.
Two-phase flow modelling of sediment suspension in the Ems/Dollard estuary
Xu, Chunyang; Dong, Ping
2017-05-01
Understanding and quantifying mud suspension and sediment transport processes are of great importance for effective exploitation and sustainable management of estuarine environments. Event-based predictive models are widely used to identify the key interactions and mechanisms that govern the dynamics involved and to provide the essential parameterisation for assessing the long-term morphodynamic evolution of the estuaries. This study develops a one-dimensional-vertical (1DV) Reynolds averaged two-phase model for cohesive sediments resuspension driven by tidal flows. To capture the time-dependent flocculation process more accurately, a new drag force closure which relates empirically to settling velocity of mud flocs with suspended sediment concentration (SSC) is incorporated into the two-phase model. The model is then applied to simulate mud suspension in the Ems/Dollard estuary during two periods (June and August 1996) of tidal forcing. Numerical predictions of bed shear stresses and sediment concentrations at different elevations above the bed are compared with measured variations. The results confirm the importance of including flocculation effects in calculating the settling velocity of mud flocs and demonstrates the sensitivity of prediction with the settling velocity in terms of flocs concentration. Although the two-phase modelling approach can in principle better capture the essential interactions between fluid and sediment phases, its practical advantages over the simpler single phase approach cannot be confirmed for the data periods simulated, partly because the overall suspended sediment concentration measured is rather low and the interaction between the two phases is weak and also because the uncertainties in the relationship between the settling velocity and flocs concentration.
Central upwind scheme for a compressible two-phase flow model.
Directory of Open Access Journals (Sweden)
Munshoor Ahmed
Full Text Available In this article, a compressible two-phase reduced five-equation flow model is numerically investigated. The model is non-conservative and the governing equations consist of two equations describing the conservation of mass, one for overall momentum and one for total energy. The fifth equation is the energy equation for one of the two phases and it includes source term on the right-hand side which represents the energy exchange between two fluids in the form of mechanical and thermodynamical work. For the numerical approximation of the model a high resolution central upwind scheme is implemented. This is a non-oscillatory upwind biased finite volume scheme which does not require a Riemann solver at each time step. Few numerical case studies of two-phase flows are presented. For validation and comparison, the same model is also solved by using kinetic flux-vector splitting (KFVS and staggered central schemes. It was found that central upwind scheme produces comparable results to the KFVS scheme.
A Novel Hyperbolization Procedure for The Two-Phase Six-Equation Flow Model
Energy Technology Data Exchange (ETDEWEB)
Samet Y. Kadioglu; Robert Nourgaliev; Nam Dinh
2011-10-01
We introduce a novel approach for the hyperbolization of the well-known two-phase six equation flow model. The six-equation model has been frequently used in many two-phase flow applications such as bubbly fluid flows in nuclear reactors. One major drawback of this model is that it can be arbitrarily non-hyperbolic resulting in difficulties such as numerical instability issues. Non-hyperbolic behavior can be associated with complex eigenvalues that correspond to characteristic matrix of the system. Complex eigenvalues are often due to certain flow parameter choices such as the definition of inter-facial pressure terms. In our method, we prevent the characteristic matrix receiving complex eigenvalues by fine tuning the inter-facial pressure terms with an iterative procedure. In this way, the characteristic matrix possesses all real eigenvalues meaning that the characteristic wave speeds are all real therefore the overall two-phase flowmodel becomes hyperbolic. The main advantage of this is that one can apply less diffusive highly accurate high resolution numerical schemes that often rely on explicit calculations of real eigenvalues. We note that existing non-hyperbolic models are discretized mainly based on low order highly dissipative numerical techniques in order to avoid stability issues.
An acoustic-convective splitting-based approach for the Kapila two-phase flow model
ten Eikelder, M. F. P.; Daude, F.; Koren, B.; Tijsseling, A. S.
2017-02-01
In this paper we propose a new acoustic-convective splitting-based numerical scheme for the Kapila five-equation two-phase flow model. The splitting operator decouples the acoustic waves and convective waves. The resulting two submodels are alternately numerically solved to approximate the solution of the entire model. The Lagrangian form of the acoustic submodel is numerically solved using an HLLC-type Riemann solver whereas the convective part is approximated with an upwind scheme. The result is a simple method which allows for a general equation of state. Numerical computations are performed for standard two-phase shock tube problems. A comparison is made with a non-splitting approach. The results are in good agreement with reference results and exact solutions.
An acoustic-convective splitting-based approach for the Kapila two-phase flow model
Energy Technology Data Exchange (ETDEWEB)
Eikelder, M.F.P. ten, E-mail: m.f.p.teneikelder@tudelft.nl [EDF R& D, AMA, 7 boulevard Gaspard Monge, 91120 Palaiseau (France); Eindhoven University of Technology, Department of Mathematics and Computer Science, P.O. Box 513, 5600 MB Eindhoven (Netherlands); Daude, F. [EDF R& D, AMA, 7 boulevard Gaspard Monge, 91120 Palaiseau (France); IMSIA, UMR EDF-CNRS-CEA-ENSTA 9219, Université Paris Saclay, 828 Boulevard des Maréchaux, 91762 Palaiseau (France); Koren, B.; Tijsseling, A.S. [Eindhoven University of Technology, Department of Mathematics and Computer Science, P.O. Box 513, 5600 MB Eindhoven (Netherlands)
2017-02-15
In this paper we propose a new acoustic-convective splitting-based numerical scheme for the Kapila five-equation two-phase flow model. The splitting operator decouples the acoustic waves and convective waves. The resulting two submodels are alternately numerically solved to approximate the solution of the entire model. The Lagrangian form of the acoustic submodel is numerically solved using an HLLC-type Riemann solver whereas the convective part is approximated with an upwind scheme. The result is a simple method which allows for a general equation of state. Numerical computations are performed for standard two-phase shock tube problems. A comparison is made with a non-splitting approach. The results are in good agreement with reference results and exact solutions.
Numerical Fractional-Calculus Model for Two-Phase Flow in Fractured Media
Directory of Open Access Journals (Sweden)
Wenwen Zhong
2013-01-01
Full Text Available Numerical simulation of two-phase flow in fractured porous media is an important topic in the subsurface flow, environmental problems, and petroleum reservoir engineering. The conventional model does not work well in many cases since it lacks the memory property of fracture media. In this paper, we develop a new numerical formulation with fractional time derivative for two-phase flow in fractured porous media. In the proposed formulation, the different fractional time derivatives are applied to fracture and matrix regions since they have different memory properties. We further develop a two-level time discrete method, which uses a large time step for the pressure and a small time step size for the saturation. The pressure equation is solved implicitly in each large time step, while the saturation is updated by an explicit fractional time scheme in each time substep. Finally, the numerical tests are carried out to demonstrate the effectiveness of the proposed numerical model.
On modeling shape memory polymers as elastic two-phase composite materials
Gilormini, Pierre; Diani, Julie
2012-01-01
International audience; A model has been proposed recently, which describes the experimentally observed mechanical behavior of some shape memory polymers. It considers a purely thermoelastic behavior, without strain rate effects, and assumes essentially that the polymer can be considered as a two-phase composite, with glassy and rubbery phases having volume fractions that depend on temperature only. Since a uniform stress hypothesis was used in the original formulation, with an inconsistency ...
Numerical modelling of the temperature distribution in a two-phase closed thermosyphon
Fadhl, B; Wrobel, LC; Jouhara, H
2013-01-01
Interest in the use of heat pipe technology for heat recovery and energy saving in a vast range of engineering applications has been on the rise in recent years. Heat pipes are playing a more important role in many industrial applications, particularly in improving the thermal performance of heat exchangers and increasing energy savings in applications with commercial use. In this paper, a comprehensive CFD modelling was built to simulate the details of the two-phase flow and heat transfer ph...
A Lagrangian-Lagrangian Model for Two-Phase Bubbly Flow around Circular Cylinder
Directory of Open Access Journals (Sweden)
M. Shademan
2014-06-01
Full Text Available A Lagrangian-Lagrangian model is developed using an in-house code to simulate bubble trajectory in two-phase bubbly flow around circular cylinder. Random Vortex Method (RVM which is a Lagrangian approach is used for solving the liquid phase. The significance of RVM relative to other RANS/LES methods is its capability in directly modelling the turbulence. In RVM, turbulence is modeled by solving the vorticity transport equation and there is no need to use turbulence closure models. Another advantage of RVM relative to other CFD approaches is its independence from mesh generation. For the bubbles trajectory, equation of motion of bubbles which takes into account effect of different forces are coupled with the RVM. Comparison of the results obtained from current model with the experimental data confirms the validity of the model. Effect of different parameters including flow Reynolds number, bubble diameter and injection point on the bubbles' trajectory are investigated. Results show that increase in the Reynolds number reduces the rising velocity of the bubbles. Similar behavior is observed for the bubbles when their diameter was decreased. According to the analysis carried out, present Lagrangian-Lagrangian model solves the issues of mesh generation and turbulence modelling which exist in common two phase flow modelling schemes.
On a regularized family of models for homogeneous incompressible two-phase flows
Gal, Ciprian G
2014-01-01
We consider a general family of regularized models for incompressible two-phase flows based on the Allen-Cahn formulation in n-dimensional compact Riemannian manifolds for n=2,3. The system we consider consists of a regularized family of Navier-Stokes equations (including the Navier-Stokes-{\\alpha}-like model, the Leray-{\\alpha} model, the Modified Leray-{\\alpha} model, the Simplified Bardina model, the Navier-Stokes-Voight model and the Navier-Stokes model) for the fluid velocity suitably coupled with a convective Allen-Cahn equation for the (phase) order parameter. We give a unified analysis of the entire three-parameter family of two-phase models using only abstract mapping properties of the principal dissipation and smoothing operators, and then use assumptions about the specific form of the parametrizations, leading to specific models, only when necessary to obtain the sharpest results. We establish existence, stability and regularity results, and some results for singular perturbations, which as special...
Duc, Linh Do; Horák, Vladimír; Kulish, Vladimir; Lukáč, Tomáš
2017-01-01
Carbon dioxide is widely used as the power gas in the gas guns community due to its ease of handling, storability at room temperature, and high vapor pressure depending only upon temperature, but not a tank size, as long as some liquid carbon dioxide remains in the tank. This high vapor pressure can be used as the pressurant, making it what is referred to as a self-pressurising propellant. However, as a two-phase substance, carbon dioxide does have its drawbacks: (1) vaporization of liquefied CO2 inside a tank when shooting rapidly or a lot causes the tank to get cool, resulting in pressure fluctuations that makes the gun's performance and accuracy worse, (2) solid carbon dioxide that is also known as dry ice can appear on the output valve of the tank while shooting and it can cause damage or slow the gun's performance down, if it works its way into some control components, including the barrel of the gun. Hence, it is crucial to obtain a scientific understanding of carbon dioxide behavior and further the discharge characteristics of a wide range of pressure-tank configurations. For the purpose of satisfying this goal, a comprehensive discharge mathematical model for carbon dioxide tank dynamics is required. In this paper, the possibility to develop an advanced non-equilibrium model of depressurization in two-phase fluids is discussed.
Prediction of shear bands in sand based on granular flow model and two-phase equilibrium
Institute of Scientific and Technical Information of China (English)
张义同; 齐德瑄; 杜如虚; 任述光
2008-01-01
In contrast to the traditional interpretation of shear bands in sand as a bifurcation problem in continuum mechanics,shear bands in sand are considered as high-strain phase(plastic phase) of sand and the materials outside the bands are still in low-strain phase(elastic phase),namely,the two phases of sand can coexist under certain condition.As a one-dimensional example,the results show that,for materials with strain-softening behavior,the two-phase solution is a stable branch of solutions,but the method to find two-phase solutions is very different from the one for bifurcation analysis.The theory of multi-phase equilibrium and the slow plastic flow model are applied to predict the formation and patterns of shear bands in sand specimens,discontinuity of deformation gradient and stress across interfaces between shear bands and other regions is considered,the continuity of displacements and traction across interfaces is imposed,and the Maxwell relation is satisfied.The governing equations are deduced.The critical stress for the formation of a shear band,both the stresses and strains inside the band and outside the band,and the inclination angle of the band can all be predicted.The predicted results are consistent with experimental measurements.
El-Amin, M F; Sun, Shuyu; Salama, Amgad
2013-01-01
In this paper, we introduce a mathematical model to describe the nanoparticles transport carried by a two-phase flow in a porous medium including gravity, capillary forces and Brownian diffusion. Nonlinear iterative IMPES scheme is used to solve the flow equation, and saturation and pressure are calculated at the current iteration step and then the transport equation is soved implicitly. Therefore, once the nanoparticles concentration is computed, the two equations of volume of the nanoparticles available on the pore surfaces and the volume of the nanoparticles entrapped in pore throats are solved implicitly. The porosity and the permeability variations are updated at each time step after each iteration loop. Two numerical examples, namely, regular heterogeneous permeability and random permeability are considered. We monitor the changing of the fluid and solid properties due to adding the nanoparticles. Variation of water saturation, water pressure, nanoparticles concentration and porosity are presented graph...
Multi-Scale Computational Modeling of Two-Phased Metal Using GMC Method
Moghaddam, Masoud Ghorbani; Achuthan, A.; Bednacyk, B. A.; Arnold, S. M.; Pineda, E. J.
2014-01-01
A multi-scale computational model for determining plastic behavior in two-phased CMSX-4 Ni-based superalloys is developed on a finite element analysis (FEA) framework employing crystal plasticity constitutive model that can capture the microstructural scale stress field. The generalized method of cells (GMC) micromechanics model is used for homogenizing the local field quantities. At first, GMC as stand-alone is validated by analyzing a repeating unit cell (RUC) as a two-phased sample with 72.9% volume fraction of gamma'-precipitate in the gamma-matrix phase and comparing the results with those predicted by finite element analysis (FEA) models incorporating the same crystal plasticity constitutive model. The global stress-strain behavior and the local field quantity distributions predicted by GMC demonstrated good agreement with FEA. High computational saving, at the expense of some accuracy in the components of local tensor field quantities, was obtained with GMC. Finally, the capability of the developed multi-scale model linking FEA and GMC to solve real life sized structures is demonstrated by analyzing an engine disc component and determining the microstructural scale details of the field quantities.
Development of two-phase pipeline hydraulic analysis model based on Beggs-Brill correlation
Waluyo, Joko; Hermawan, Achilleus; Indarto
2016-06-01
The hydraulic analysis is an important stage in a reliable pipeline design. In the implementation, fluid distribution from a source to the sinks often occurs on parallel pipeline networks. The solution to the problem is complicated because of the iterative technique requirement. Regarding its solution effectiveness, there is a need for analysis related to the model and the solution method. This study aims to investigate pipeline hydraulic analysis on distributing of two-phase fluids flow. The model uses Beggs-Brill correlation to converse mass flow rates into pressure drops. In the solution technique, the Newton-Raphson iterative method is utilized. The iterative technique is solved using a computer program. The study is carried out using a certain pipeline network. The model is validated by comparing between Beggs-Brill towards Mukherjee-Brill correlation. The result reveals that the computer program enables solving of iterative calculation on the parallel pipeline hydraulic analysis. Convergence iteration is achieved by 50 iterations. The main results of the model are mass flow rate and pressure drop. The mass flow rate is obtained in the deviation up to 2.06%, between Beggs-Brill and Mukherjee-Brill correlation. On the other hand, the pressure gradient deviation is achieved on a higher deviation due to the different approach of the two correlations. The model can be further developed in the hydraulic pipeline analysis for two-phase flow.
A Hydrodynamic Model for Slug Frequency in Horizontal Gas-Liquid Two-Phase Flow
Institute of Scientific and Technical Information of China (English)
刘磊; 孙贺东; 胡志华; 周芳德
2003-01-01
The prediction of slug frequency has important significance on gas-liquid two-phase flow. A hydrodynamic model was put forward to evaluate slug frequency for horizontal two-phase flow, based on the dependence of slug frequency on the frequency of unstable interfacial wave. Using air and water, experimental verification of the model was carried out in a large range of flow parameters. Six electrical probes were installed at different positions of a horizontal plexiglass pipe to detect slug frequency development. The pipe is 30 m long and its inner diameter is 24 ram. It is observed experimentally that the interracial wave frequency at the inlet is about i to 3 times the frequency of stable slug. The slug frequencies predicted by the model fit well with Tronconi (1990) model and the experimental data. The combination of the hydrodynamic model and the experimental data results in a conclusion that the frequency of equilibrium liquid slug is approximately half the minimum frequency of interfacial wave.
Multiphysics modeling of two-phase film boiling within porous corrosion deposits
Jin, Miaomiao; Short, Michael
2016-07-01
Porous corrosion deposits on nuclear fuel cladding, known as CRUD, can cause multiple operational problems in light water reactors (LWRs). CRUD can cause accelerated corrosion of the fuel cladding, increase radiation fields and hence greater exposure risk to plant workers once activated, and induce a downward axial power shift causing an imbalance in core power distribution. In order to facilitate a better understanding of CRUD's effects, such as localized high cladding surface temperatures related to accelerated corrosion rates, we describe an improved, fully-coupled, multiphysics model to simulate heat transfer, chemical reactions and transport, and two-phase fluid flow within these deposits. Our new model features a reformed assumption of 2D, two-phase film boiling within the CRUD, correcting earlier models' assumptions of single-phase coolant flow with wick boiling under high heat fluxes. This model helps to better explain observed experimental values of the effective CRUD thermal conductivity. Finally, we propose a more complete set of boiling regimes, or a more detailed mechanism, to explain recent CRUD deposition experiments by suggesting the new concept of double dryout specifically in thick porous media with boiling chimneys.
Numerical Investigation of Nanofluid Thermocapillary Convection Based on Two-Phase Mixture Model
Jiang, Yanni; Xu, Zelin
2017-08-01
Numerical investigation of nanofluid thermocapillary convection in a two-dimensional rectangular cavity was carried out, in which the two-phase mixture model was used to simulate the nanoparticles-fluid mixture flow, and the influences of volume fraction of nanoparticles on the flow characteristics and heat transfer performance were discussed. The results show that, with the increase of nanoparticle volume fraction, thermocapillary convection intensity weakens gradually, and the heat conduction effect strengthens; meanwhile, the temperature gradient at free surface increases but the free surface velocity decreases gradually. The average Nusselt number of hot wall and the total entropy generation decrease with nanoparticle volume fraction increasing.
Energy Technology Data Exchange (ETDEWEB)
Mérigoux, Nicolas, E-mail: nicolas.merigoux@edf.fr; Laviéville, Jérôme; Mimouni, Stéphane; Guingo, Mathieu; Baudry, Cyril
2016-04-01
Highlights: • NEPTUNE-CFD is used to model two-phase PTS. • k-ε model did produce some satisfactory results but also highlights some weaknesses. • A more advanced turbulence model has been developed, validated and applied for PTS. • Coupled with LIM, the first results confirmed the increased accuracy of the approach. - Abstract: Nuclear power plants are subjected to a variety of ageing mechanisms and, at the same time, exposed to potential pressurized thermal shock (PTS) – characterized by a rapid cooling of the internal Reactor Pressure Vessel (RPV) surface. In this context, NEPTUNE-CFD is used to model two-phase PTS and give an assessment on the structural integrity of the RPV. The first available choice was to use standard first order turbulence model (k-ε) to model high-Reynolds number flows encountered in Pressurized Water Reactor (PWR) primary circuits. In a first attempt, the use of k-ε model did produce some satisfactory results in terms of condensation rate and temperature field distribution on integral experiments, but also highlights some weaknesses in the way to model highly anisotropic turbulence. One way to improve the turbulence prediction – and consequently the temperature field distribution – is to opt for more advanced Reynolds Stress turbulence Model. After various verification and validation steps on separated effects cases – co-current air/steam-water stratified flows in rectangular channels, water jet impingements on water pool free surfaces – this Reynolds Stress turbulence Model (R{sub ij}-ε SSG) has been applied for the first time to thermal free surface flows under industrial conditions on COSI and TOPFLOW-PTS experiments. Coupled with the Large Interface Model, the first results confirmed the adequacy and increased accuracy of the approach in an industrial context.
Modeling of fluidelastic instability in tube bundle subjected to two-phase cross-flow
Energy Technology Data Exchange (ETDEWEB)
Sawadogo, T.P.; Mureithi, N.W.; Azizian, R.; Pettigrew, M.J. [Ecole Polytechnique, Dept. of Mechanical Engineering, BWC/AECL/NSERC Chair of Fluid-Structure Interaction, Montreal, Quebec (Canada)
2009-07-01
Tube arrays in steam generators and heat exchangers operating in two-phase cross-flow are subjected sometimes to strong vibration due mainly to turbulence buffeting and fluidelastic forces. This can lead to tube damage by fatigue or fretting wear. A computer implementation of a fluidelastic instability model is proposed to determine with improved accuracy the fluidelastic forces and hence the critical instability flow velocity. Usually the fluidelastic instability is 'predicted', using the Connors relation with K=3. While the value of K can be determined experimentally to get an accurate prediction of the instability, the Connors relation does not allow good estimation of the fluid forces. Consequently the RMS value of the magnitude of vibration of the tube bundle, necessary to evaluate the work rate and the tube wear is only poorly estimated. The fluidelastic instability analysis presented here is based on the quasi-steady model, originally developed for single phase flow. The fluid forces are expressed in terms of the quasi-static drag and lift force coefficients and their derivatives which are determined experimentally. The forces also depend on the tube displacement and velocity. In the computer code ABAQUS, the fluid forces are provided in the user subroutines VDLOAD or VUEL. A typical simulation of the vibration of a single flexible tube within an array in two phase cross-flow is done in ABAQUS and the results are compared with the experimental measurements for a tube with similar physical properties. For a cantilever tube, in two phase cross-flow of void fraction 60%, the numerical critical flow velocity was 2.0 m/s compared to 1.8 m/s obtained experimentally. The relative error was 5% compared to 26.6% for the Connors relation with K=3. The simulation of the vibration of a typical tube in a steam generator is also presented. The numerical results show good agreement with experimental measurements. (author)
A complete two-phase model of a porous cathode of a PEM fuel cell
Hwang, J. J.
This paper has developed a complete two-phase model of a proton exchange membrane (PEM) fuel cell by considering fluid flow, heat transfer and current simultaneously. In fluid flow, two momentum equations governing separately the gaseous-mixture velocity (u g) and the liquid-water velocity (u w) illustrate the behaviors of the two-phase flow in a porous electrode. Correlations for the capillary pressure and the saturation level connect the above two-fluid transports. In heat transfer, a local thermal non-equilibrium (LTNE) model accounting for intrinsic heat transfer between the reactant fluids and the solid matrices depicts the interactions between the reactant-fluid temperature (T f) and the solid-matrix temperature (T s). The irreversibility heating due to electrochemical reactions, Joule heating arising from Ohmic resistance, and latent heat of water condensation/evaporation are considered in the present non-isothermal model. In current, Ohm's law is applied to yield the conservations in ionic current (i m) and electronic current (i s) in the catalyst layer. The Butler-Volmer correlation describes the relation of the potential difference (overpotential) and the transfer current between the electrolyte (such as Nafion™) and the catalyst (such as Pt/C).
Validation of NEPTUNE-CFD Two-Phase Flow Models Using Experimental Data
Directory of Open Access Journals (Sweden)
Jorge Pérez Mañes
2014-01-01
Full Text Available This paper deals with the validation of the two-phase flow models of the CFD code NEPTUNEC-CFD using experimental data provided by the OECD BWR BFBT and PSBT Benchmark. Since the two-phase models of CFD codes are extensively being improved, the validation is a key step for the acceptability of such codes. The validation work is performed in the frame of the European NURISP Project and it was focused on the steady state and transient void fraction tests. The influence of different NEPTUNE-CFD model parameters on the void fraction prediction is investigated and discussed in detail. Due to the coupling of heat conduction solver SYRTHES with NEPTUNE-CFD, the description of the coupled fluid dynamics and heat transfer between the fuel rod and the fluid is improved significantly. The averaged void fraction predicted by NEPTUNE-CFD for selected PSBT and BFBT tests is in good agreement with the experimental data. Finally, areas for future improvements of the NEPTUNE-CFD code were identified, too.
Teaching Mathematical Modeling in Mathematics Education
Saxena, Ritu; Shrivastava, Keerty; Bhardwaj, Ramakant
2016-01-01
Mathematics is not only a subject but it is also a language consisting of many different symbols and relations. Taught as a compulsory subject up the 10th class, students are then able to choose whether or not to study mathematics as a main subject. The present paper discusses mathematical modeling in mathematics education. The article provides…
The difficult challenge of a two-phase CFD modelling for all flow regimes
Energy Technology Data Exchange (ETDEWEB)
Bestion, D., E-mail: dominique.bestion@cea.fr
2014-11-15
Highlights: • The theoretical difficulties for modelling all flow regimes at CFD scale are identified. • The choice of the number of fields and of the time and space averaging or filtering are discussed and clarified. • Closure issues related to an all flow regime CFD model are listed and the main difficulties are identified. - Abstract: System thermalhydraulic codes model all two-phase flow regimes but they are limited to a macroscopic description. Two-phase CFD tools predict two-phase flow with a much finer space resolution but the current modelling capabilities are limited to dispersed bubbly or droplet flow and separate-phase flow. Much less experience exists on more complex flow regimes which combine the existence of dispersed fields with the presence of large interfaces such as a free surface or a film surface. A list of possible reactor issues which might benefit from an “all flow regime CFD model” is given. The first difficulty is to identify the various types of local flow configuration. It is shown that a 4-field model has much better capabilities than a two-fluid approach to identify most complex regimes. Then the choice between time averaging, space averaging, or even ensemble averaging is discussed. It is shown that only the RANS-2-fluid and a space-filtered 4-field model may be reasonably envisaged. The latter has the capabilities to identify all types of interfaces and should be privileged if a good accuracy is expected or if time fluctuations in intermittent flow have to be predicted while the former may be used when a high accuracy is not necessary and if time fluctuations in intermittent flow are not of interest. Finally the closure issue is presented including wall transfers, interfacial transfers, mass transfers between dispersed and continuous fields, and turbulent transfers. An important effort is required to model all interactions between sub-filter phenomena and the transfers from the sub-filter domain to the simulated domain. The
Magnetohydrodynamic two-phase dusty fluid flow and heat model over deforming isothermal surfaces
Turkyilmazoglu, Mustafa
2017-01-01
This paper is devoted to the mathematical analysis of a magnetohydrodynamic viscous two-phase dusty fluid flow and heat transfer over permeable stretching or shrinking bodies. The wall boundary is subjected to a linear deformation as well as to a quadratic surface temperature. Such a highly nonlinear phenomenon, for the first time in the literature, is attacked to search for occurrence of exact solutions, whose numerical correspondences are already available for limited wall transpiration velocities. The obtained analytical solutions are found be in perfect line with the numerical computations. Besides this, exact solutions point to the existence of dual solutions for both permeable stretching and shrinking cases, which were not detected from the numerical studies up to date. The existence of such exact solutions and their parameter domain particularly depending on the wall suction or injection are successfully analyzed. The physical outcomes concerning the effects of suspended particles on the momentum and thermal boundary layers well-documented in the open literature can be best understood from the presented exact solutions.
A two phase field model for tracking vesicle-vesicle adhesion.
Gu, Rui; Wang, Xiaoqiang; Gunzburger, Max
2016-11-01
A multi-phase-field model for simulating the adhesion between two vesicles is constructed. Two phase field functions are introduced to simulate each of the two vesicles. An energy model is defined which accounts for the elastic bending energy of each vesicle and the contact potential energy between the two vesicles; the vesicle volume and surface area constraints are imposed using a penalty method. Numerical results are provided to verify the efficacy of our model and to provide visual illustrations of the different types of contact. The method can be adjusted to solve endocytosis problems by modifying the bending rigidity coefficients of the two elastic bending energies. The method can also be extended to simulate multi-cell adhesions, one example of which is erythrocyte rouleaux. A comparison with laboratory observations demonstrates the effectiveness of the multi-phase field approach.
EFFECTS OF PHASE CONTINUITY ON RHEOLOGY OF TWO-PHASE ROCKS:A CONTINUUM MECHANICL MODEL
Institute of Scientific and Technical Information of China (English)
JI Shao-cheng
2001-01-01
Based on continuum mechanics,we have developed a model for semi-quantitative estimating effects of phase continuity on flow strength of two-phase rocks including partially melted or crystallized rocks.Calculations of the bulk flow strength of composite rocks as functions of the volume fraction,geometrical shape and continuity of the constitutive phases involve in numerically solving two non-linear equations and thus are easy to be performed.The model has been justified by a good agreement between the predicted and measured results on diabase (64% clinopyroxene and 36% plagioclase) in the range of experimental temperatures and strain-rates.It is believed that the present model could provide an approximate estimate for the rheological evolution of magmatic rocks during their life cycle of melting-crystallization-deformation.
Modeling and Simulation of Two-Phase Two-Component Flow with Disappearing Nonwetting Phase
Neumann, Rebecca; Ippisch, Olaf
2012-01-01
Carbon Capture and Storage (CCS) is a recently discussed new technology, aimed at allowing an ongoing use of fossil fuels while preventing the produced CO2 to be released to the atmosphere. CSS can be modeled with two components (water and CO2) in two phases (liquid and CO2). To simulate the process, a multiphase flow equation with equilibrium phase exchange is used. One of the big problems arising in two-phase two-component flow simulations is the disappearance of the nonwetting phase, which leads to a degeneration of the equations satisfied by the saturation. A standard choice of primary variables, which is the pressure of one phase and the saturation of the other phase, cannot be applied here. We developed a new approach using the pressure of the nonwetting phase and the capillary pressure as primary variables. One important advantage of this approach is the fact that we have only one set of primary variables that can be used for the biphasic as well as the monophasic case. We implemented this new choice o...
Directory of Open Access Journals (Sweden)
Xuemiao Xu
2016-04-01
Full Text Available Exterior orientation parameters’ (EOP estimation using space resection plays an important role in topographic reconstruction for push broom scanners. However, existing models of space resection are highly sensitive to errors in data. Unfortunately, for lunar imagery, the altitude data at the ground control points (GCPs for space resection are error-prone. Thus, existing models fail to produce reliable EOPs. Motivated by a finding that for push broom scanners, angular rotations of EOPs can be estimated independent of the altitude data and only involving the geographic data at the GCPs, which are already provided, hence, we divide the modeling of space resection into two phases. Firstly, we estimate the angular rotations based on the reliable geographic data using our proposed mathematical model. Then, with the accurate angular rotations, the collinear equations for space resection are simplified into a linear problem, and the global optimal solution for the spatial position of EOPs can always be achieved. Moreover, a certainty term is integrated to penalize the unreliable altitude data for increasing the error tolerance. Experimental results evidence that our model can obtain more accurate EOPs and topographic maps not only for the simulated data, but also for the real data from Chang’E-1, compared to the existing space resection model.
Two Phase Analysis of Ski Schools Customer Satisfaction: Multivariate Ranking and Cub Models
Directory of Open Access Journals (Sweden)
Rosa Arboretti
2014-06-01
Full Text Available Monitoring tourists' opinions is an important issue also for companies providing sport services. The aim of this paper was to apply CUB models and nonparametric permutation methods to a large customer satisfaction survey performed in 2011 in the ski schools of Alto Adige (Italy. The two-phase data processing was mainly aimed to: establish a global ranking of a sample of five ski schools, on the basis of satisfaction scores for several specific service aspects; to estimate specific components of the respondents’ evaluation process (feeling and uncertainty and to detect if customers’ characteristics affected these two components. With the application of NPC-Global ranking we obtained a ranking of the evaluated ski schools simultaneously considering satisfaction scores of several service’s aspects. CUB models showed which aspects and subgroups were less satisfied giving tips on how to improve services and customer satisfaction.
Unified constitutive modelling for two-phase lamellar titanium alloys at hot forming conditions
Directory of Open Access Journals (Sweden)
Yang Lei
2016-01-01
Full Text Available In this paper, a set of mechanism based unified viscoplastic constitutive equations have been established for two-phase titanium alloys with initial lamellar microstructure, which models the softening mechanisms of the alloys in hot forming conditions. The dislocation density, rotation and globularization of lamellar α-phase and their effects on flow behaviour can also be modelled. The values of material constants in the equation set have been calibrated, according to stress-strain curves and globularization fractions of lamellar α-phase obtained from compression tests at a range of temperatures and strain rates, using a genetic algorithm (GA based optimisation method. Based on the determined constitutive equations, flow stress and globularization evolution of Ti-17 and TA15 alloys at different temperatures and strain rates were predicted. Good agreements between the experimental and computed results were obtained.
An accurate two-phase approximate solution to the acute viral infection model
Energy Technology Data Exchange (ETDEWEB)
Perelson, Alan S [Los Alamos National Laboratory
2009-01-01
During an acute viral infection, virus levels rise, reach a peak and then decline. Data and numerical solutions suggest the growth and decay phases are linear on a log scale. While viral dynamic models are typically nonlinear with analytical solutions difficult to obtain, the exponential nature of the solutions suggests approximations can be found. We derive a two-phase approximate solution to the target cell limited influenza model and illustrate the accuracy using data and previously established parameter values of six patients infected with influenza A. For one patient, the subsequent fall in virus concentration was not consistent with our predictions during the decay phase and an alternate approximation is derived. We find expressions for the rate and length of initial viral growth in terms of the parameters, the extent each parameter is involved in viral peaks, and the single parameter responsible for virus decay. We discuss applications of this analysis in antiviral treatments and investigating host and virus heterogeneities.
A two-dimensional parabolic model for vertical annular two-phase flow
Energy Technology Data Exchange (ETDEWEB)
Fernandez, F.M.; Toledo, A. Alvarez; Paladino, E.E. [Graduate Program in Mechanical Engineering, Universidade Federal de Rio Grande do Norte, Natal, RN (Brazil)], e-mail: emilio@ct.ufrn.br
2010-07-01
This work presents a solution algorithm for predicting hydrodynamic parameters for developing and equilibrium, adiabatic, annular, vertical two-phase flow. It solves mass and momentum transport differential equations for both the core and the liquid film across their entire domains. Thus, the velocity and shear stress distributions from the tube center to the wall are obtained, together with the average film thickness and the pressure gradient, making no use of empirical closure relations nor assuming any known velocity profile to solve the triangular relationship in the liquid film. The model was developed using the Finite Volume Method and an iterative procedure is proposed to solve all flow variables for given phase superficial velocities. The procedure is validated against the analytical solution for laminar flow and experimental data for gas-liquid turbulent flow with entrainment. For the last case, an algebraic turbulence model is used for turbulent viscosity calculation for both, liquid film and gas core. (author)
Simulation of horizontal pipe two-phase slug flows using the two-fluid model
Energy Technology Data Exchange (ETDEWEB)
Ortega Malca, Arturo J. [Pontificia Univ. Catolica do Rio de Janeiro, RJ (Brazil). Dept. de Engenharia Mecanica. Nucleo de Simulacao Termohidraulica de Dutos (SIMDUT); Nieckele, Angela O. [Pontificia Univ. Catolica do Rio de Janeiro, RJ (Brazil). Dept. de Engenharia Mecanica
2005-07-01
Slug flow occurs in many engineering applications, mainly in the transport of hydrocarbon fluids in pipelines. The intermittency of slug flow causes severe unsteady loading on the pipelines carrying the fluids, which gives rise to design problems. Therefore, it is important to be able to predict the onset and development of slug flow as well as slug characteristics. The present work consists in the simulation of two-phase flow in slug pattern through horizontal pipes using the two-fluid model in its transient and one-dimensional form. The advantage of this model is that the flow field is allowed to develop naturally from a given initial conditions as part of the transient calculation; the slug evolves automatically as a product of the computed flow development. Simulations are then carried out for a large number of flow conditions that lead a slug flow. (author)
A phenomenological two-phase constitutive model for porous shape memory alloys
El Sayed, Tamer S.
2012-07-01
We present a two-phase constitutive model for pseudoelastoplastic behavior of porous shape memory alloys (SMAs). The model consists of a dense SMA phase and a porous plasticity phase. The overall response of the porous SMA is obtained by a weighted average of responses of individual phases. Based on the chosen constitutive model parameters, the model incorporates the pseudoelastic and pseudoplastic behavior simultaneously (commonly reported for porous SMAs) as well as sequentially (i.e. dense SMAs; pseudoelastic deformation followed by the pseudoplastic deformation until failure). The presented model also incorporates failure due to the deviatoric (shear band formation) and volumetric (void growth and coalescence) plastic deformation. The model is calibrated by representative volume elements (RVEs) with different sizes of spherical voids that are solved by unit cell finite element calculations. The overall response of the model is tested against experimental results from literature. Finally, application of the presented constitutive model has been presented by performing finite element simulations of the deformation and failure in unaixial dog-bone shaped specimen and compact tension (CT) test specimen. Results show a good agreement with the experimental data reported in the literature. © 2012 Elsevier B.V. All rights reserved.
Two-Phase Fluid Simulation Using a Diffuse Interface Model with Peng--Robinson Equation of State
Qiao, Zhonghua
2014-01-01
In this paper, two-phase fluid systems are simulated using a diffusive interface model with the Peng-Robinson equation of state (EOS), a widely used realistic EOS for hydrocarbon fluid in the petroleum industry. We first utilize the gradient theory of thermodynamics and variational calculus to derive a generalized chemical equilibrium equation, which is mathematically a second-order elliptic partial differential equation (PDE) in molar density with a strongly nonlinear source term. To solve this PDE, we convert it to a time-dependent parabolic PDE with the main interest in its final steady state solution. A Lagrange multiplier is used to enforce mass conservation. The parabolic PDE is then solved by mixed finite element methods with a semi-implicit time marching scheme. Convex splitting of the energy functional is proposed to construct this time marching scheme, where the volume exclusion effect of an EOS is treated implicitly while the pairwise attraction effect of EOS is calculated explicitly. This scheme is proved to be unconditionally energy stable. Our proposed algorithm is able to solve successfully the spatially heterogeneous two-phase systems with the Peng-Robinson EOS in multiple spatial dimensions, the first time in the literature. Numerical examples are provided with realistic hydrocarbon components to illustrate the theory. Furthermore, our computational results are compared with laboratory experimental data and verified with the Young-Laplace equation with good agreement. This work sets the stage for a broad extension of efficient convex-splitting semi-implicit schemes for numerical simulation of phase field models with a realistic EOS in complex geometries of multiple spatial dimensions.
A two-phase model for chronic disease processes under intermittent inspection.
Wu, Ying; Cook, Richard J
2017-06-15
A model is developed for chronic diseases with an indolent phase that is followed by a phase with more active disease resulting in progression and damage. The time scales for the intensity functions for the active phase are more naturally based on the time since the start of the active phase, corresponding to a semi-Markov formulation. This two-phase model enables one to fit a separate regression model for the duration of the indolent phase and intensity-based models for the more active second phase. In cohort studies for which the disease status is only known at a series of clinical assessment times, transition times are interval-censored, which means the time origin for phase II is interval-censored. Weakly parametric models with piecewise constant baseline hazard and rate functions are specified, and an expectation-maximization algorithm is described for model fitting. Simulation studies examining the performance of the proposed model show good performance under maximum likelihood and two-stage estimation. An application to data from the motivating study of disease progression in psoriatic arthritis illustrates the procedure and identifies new human leukocyte antigens associated with the duration of the indolent phase. Copyright © 2017 John Wiley & Sons, Ltd. Copyright © 2017 John Wiley & Sons, Ltd.
Modeling of Two-Phase Immiscible Flow with Moving Contact Lines
Abu Alsaud, Moataz; Soulaine, Cyprien; Riaz, Amir; Tchelepi, Hamdi; Stanford University Collaboration; University of Maryland, College Park Collaboration
2015-11-01
A new numerical method based on the implicit interface approach on Cartesian grids is proposed for modeling two-phase immiscible flow with moving contact lines. The reinitialization of level-set function by computing the minimum distance to linearly reconstructed interface to obtain signed distance function is extended to include the contact angle boundary condition. The physics of contact line dynamics is implemented using the Cox-Voinov hydrodynamic theory that efficiently captures the effect of the microscopic contact line region. The numerical method is validated through various examples. Parasitic currents are studied in the case of static and constantly advected parabolic interface intersecting the domain boundary with an imposed contact angle. Moving contact line in the viscous dominated regime is studied and verified through comparison with experiments.
Modelling of transient two-phase heat transfer for spacecraft thermal management
Shyy, W.
1994-01-01
A computational method for predicting the two-phase transient fluid flow and heat transfer characteristics within a reservoir of the capillary-pumped-loop, intended to be used for spacecraft thermal management, has been developed. The model is based on the enthalpy formulation in an axisymmetric configuration. The reservoir operates under a constant thermodynamic pressure by allowing mass exchange between the reservoir and the outside loop. Both 1 g and 0 g environments have been considered to assess the effects of gravity on the reservoir performance. Depending on the gravity level, the power input and the reservoir orientation, three different convection modes have been identified, namely, the thermocapillary mode, the buoyancy mode, and the rapid-expansion mode (caused by interface movement). The impact of these modes on the performance of the reservoir and the associated physical phenomena have been discussed.
Dividing phases in two-phase flow and modeling of interfacial drag
Energy Technology Data Exchange (ETDEWEB)
Narumo, T.; Rajamaeki, M. [VTT Energy (Finland)
1997-07-01
Different models intended to describe one-dimensional two-phase flow are considered in this paper. The following models are introduced: conventional six-equation model, conventional model equipped with terms taking into account nonuniform transverse velocity distribution of the phases, several virtual mass models and a model in which the momentum equations have been derived by using the principles of Separation of the Flow According to Velocity (SFAV). The dynamics of the models have been tested by comparing their characteristic velocities to each other and against experimental data. The results show that the SFAV-model makes a hyperbolic system and predicts the propagation velocities of disturbances with the same order of accuracy as the best tested virtual mass models. Furthermore, the momentum interaction terms for the SFAV-model are considered. These consist of the wall friction terms and the interfacial friction term. The authors model wall friction with two independent terms describing the effect of each fluid on the wall separately. In the steady state, a relationship between the slip velocity and friction coefficients can be derived. Hence, the friction coefficients for the SFAV-model can be calculated from existing correlations, viz. from a drift-flux correlation and a wall friction correlation. The friction model was tested by searching steady-state distributions in a partial BWR fuel channel and comparing the relaxed values with the drift-flux correlation, which agreed very well with each other. In addition, response of the flow to a sine-wave disturbance in the water inlet flux was calculated as function of frequency. The results of the models differed from each other already with frequency of order 5 Hz, while the time constant for the relaxation, obtained from steady-state distribution calculation, would have implied significant differences appear not until with frequency of order 50 Hz.
A Two-Phase Model of Resource Allocation in Visual Working Memory.
Ye, Chaoxiong; Hu, Zhonghua; Li, Hong; Ristaniemi, Tapani; Liu, Qiang; Liu, Taosheng
2017-03-02
Two broad theories of visual working memory (VWM) storage have emerged from current research, a discrete slot-based theory and a continuous resource theory. However, neither the discrete slot-based theory or continuous resource theory clearly stipulates how the mental commodity for VWM (discrete slot or continuous resource) is allocated. Allocation may be based on the number of items via stimulus-driven factors, or it may be based on task demands via voluntary control. Previous studies have obtained conflicting results regarding the automaticity versus controllability of such allocation. In the current study, we propose a two-phase allocation model, in which the mental commodity could be allocated only by stimulus-driven factors in the early consolidation phase. However, when there is sufficient time to complete the early phase, allocation can enter the late consolidation phase, where it can be flexibly and voluntarily controlled according to task demands. In an orientation recall task, we instructed participants to store either fewer items at high-precision or more items at low-precision. In 3 experiments, we systematically manipulated memory set size and exposure duration. We did not find an effect of task demands when the set size was high and exposure duration was short. However, when we either decreased the set size or increased the exposure duration, we found a trade-off between the number and precision of VWM representations. These results can be explained by a two-phase model, which can also account for previous conflicting findings in the literature. (PsycINFO Database Record
SECOND-ORDER MOMENT MODEL FOR DENSE TWO-PHASE TURBULENT FLOW OF BINGHAM FLUID WITH PARTICLES
Institute of Scientific and Technical Information of China (English)
ZENG Zhuo-xiong; ZHOU Li-xing; LIU Zhi-he
2006-01-01
The USM-θ model of Bingham fluid for dense two-phase turbulent flow was developed, which combines the second-order moment model for two-phase turbulence with the particle kinetic theory for the inter-particle collision. In this model, phases interaction and the extra term of Bingharn fluid yield stress are taken into account. An algorithm for USM-θ model in dense two-phase flow was proposed, in which the influence of particle volume fraction is accounted for. This model was used to simulate turbulent flow of Bingham fluid single-phase and dense liquid-particle two-phase in pipe. It is shown USM-θ model has better prediction result than the five-equation model, in which the particle-particle collision is modeled by the particle kinetic theory, while the turbulence of both phase is simulated by the two-equation turbulence model. The USM-θ model was then used to simulate the dense two-phase turbulent up flow of Bingham fluid with particles. With the increasing of the yield stress, the velocities of Bingham and particle decrease near the pipe centre. Comparing the two-phase flow of Bingham-particle with that of liquid-particle, it is found the source term of yield stress has significant effect on flow.
Modeling of annular two-phase flow using a unified CFD approach
Energy Technology Data Exchange (ETDEWEB)
Li, Haipeng, E-mail: haipengl@kth.se; Anglart, Henryk, E-mail: henryk@kth.se
2016-07-15
Highlights: • Annular two-phase flow has been modeled using a unified CFD approach. • Liquid film was modeled based on a two-dimensional thin film assumption. • Both Eulerian and Lagrangian methods were employed for the gas core flow modeling. - Abstract: A mechanistic model of annular flow with evaporating liquid film has been developed using computational fluid dynamics (CFD). The model is employing a separate solver with two-dimensional conservation equations to predict propagation of a thin boiling liquid film on solid walls. The liquid film model is coupled to a solver of three-dimensional conservation equations describing the gas core, which is assumed to contain a saturated mixture of vapor and liquid droplets. Both the Eulerian–Eulerian and the Eulerian–Lagrangian approach are used to describe the droplet and vapor motion in the gas core. All the major interaction phenomena between the liquid film and the gas core flow have been accounted for, including the liquid film evaporation as well as the droplet deposition and entrainment. The resultant unified framework for annular flow has been applied to the steam-water flow with conditions typical for a Boiling Water Reactor (BWR). The simulation results for the liquid film flow rate show good agreement with the experimental data, with the potential to predict the dryout occurrence based on criteria of critical film thickness or critical film flow rate.
Prediction of Three-Phase Capillary Pressure using a Network Model Anchored to Two-Phase Data
Dale, Elisabeth Iren; Dijke, Marinus I. J. van; Skauge, Arne
2008-01-01
Three-phase capillary pressure is difficult to measure experimentally and therefore has to be estimated by other methods. In this work a network model was applied to generate a consistent set of two-phase and three-phase capillary pressure curves. Experimental data for two-phase, gas-oil and oil-water, capillary pressure from a North Sea reservoir was used in this study. The network model was anchored to the measured two-phase data, and three-phase capillary pressure was constr...
Developing mathematical modelling competence
DEFF Research Database (Denmark)
Blomhøj, Morten; Jensen, Tomas Højgaard
2003-01-01
In this paper we introduce the concept of mathematical modelling competence, by which we mean being able to carry through a whole mathematical modelling process in a certain context. Analysing the structure of this process, six sub-competences are identified. Mathematical modelling competence...... cannot be reduced to these six sub-competences, but they are necessary elements in the development of mathematical modelling competence. Experience from the development of a modelling course is used to illustrate how the different nature of the sub-competences can be used as a tool for finding...... the balance between different kinds of activities in a particular educational setting. Obstacles of social, cognitive and affective nature for the students' development of mathematical modelling competence are reported and discussed in relation to the sub-competences....
Teaching Mathematical Modelling.
Jones, Mark S.
1997-01-01
Outlines a course at the University of Glamorgan in the United Kingdom in which a computer algebra system (CAS) teaches mathematical modeling. The format is based on continual assessment of group and individual work stating the problem, a feature list, and formulation of the models. No additional mathematical word processing package is necessary.…
Kou, Jisheng
2015-07-16
In this paper, we consider an interface model for multicomponent two-phase fluids with geometric mean influence parameters, which is popularly used to model and predict surface tension in practical applications. For this model, there are two major challenges in theoretical analysis and numerical simulation: the first one is that the influence parameter matrix is not positive definite; the second one is the complicated structure of the energy function, which requires us to find out a physically consistent treatment. To overcome these two challenging problems, we reduce the formulation of the energy function by employing a linear transformation and a weighted molar density, and furthermore, we propose a local minimum grand potential energy condition to establish the relation between the weighted molar density and mixture compositions. From this, we prove the existence of the solution under proper conditions and prove the maximum principle of the weighted molar density. For numerical simulation, we propose a modified Newton\\'s method for solving this nonlinear model and analyze its properties; we also analyze a finite element method with a physical-based adaptive mesh-refinement technique. Numerical examples are tested to verify the theoretical results and the efficiency of the proposed methods.
Indian Academy of Sciences (India)
Jagjiwanram; Ramvir Singh
2004-08-01
A theoretical model has been developed for real two-phase system assuming linear flow of heat flux lines having ellipsoidal particles arranged in a three-dimensional cubic array. The arrangement has been divided into unit cells, each of which contains an ellipsoid. The resistor model has been applied to determine the effective thermal conductivity (ETC) of the unit cell. To take account of random packing of the phases, non-uniform shape of the particles and non-linear flow of heat flux lines in real systems, incorporating an empirical correction factor in place of physical porosity modifies an expression for ETC. An effort is made to correlate it in terms of the ratio of thermal conductivities of the constituents and the physical porosity. Theoretical expression so obtained has been tested on a large number of samples cited in the literature and found that the values predicted are quite close to the experimental results. Comparison of our model with different models cited in the literature has also been made.
Institute of Scientific and Technical Information of China (English)
P.A.Nikrityuk; K.Eckert; R.Grundmann; B.Willers; S.Eckert
2003-01-01
The main aim of this work is to study numerically the influence of an external magnetic field on the solidification processes of two-component materials. Based on the continuum model of two-phase flow a mathematical model for the directional solidification of a binary alloy in a magnetic field is presented. The model includes mass,momentum, energy and species mass conservation equations written in compressible form and additional relationships describing the temperature-solute coupling. The geometry under study is a cylindrical mold with adiabatic walls and cooled bottom. The macroscale transport in the solidification of alloys is governed by the progress of the two-phase mushy zone, which is treated by means of a porous medium approach. The volume fraction of liquid and solid phases, respectively, is calculated from a 2D approximation of the phase diagram. The results of calculation are compared with experimental data.
Nikrityuk, P. A.; Eckert, K.; Grundmann, R.; Willers, B.; Eckert, S.
2003-11-01
The main aim of this work is to study numerically the influence of an external magnetic field on the solidification processes of two-component materials. Based on the continuum model of two-phase flow a mathematical model for the directional solidification of a binary alloy in a magnetic field is presented. The model includes mass, momentum, energy and species mass conservation equations written in compressible form and additional relationships describing the temperature-solute coupling. The geometry under study is a cylindrical mold with adiabatic walls and cooled bottom. The macroscale transport in the solidification of alloys is governed by the progress of the two-phase mushy zone, which is treated by means of a porous medium approach. The volume fraction of liquid and solid phases, respectively, is calculated from a 2D approximation of the phase diagram. The results of calculation are compared with experimental data.
Study of colloids transport during two-phase flow using a novel polydimethylsiloxane micro-model.
Zhang, Qiulan; Karadimitriou, N K; Hassanizadeh, S M; Kleingeld, P J; Imhof, A
2013-07-01
As a representation of a porous medium, a closed micro-fluidic device made of polydimethylsiloxane (PDMS), with uniform wettability and stable hydrophobic properties, was designed and fabricated. A flow network, with a mean pore size of 30 μm, was formed in a PDMS slab, covering an area of 1 mm × 10 mm. The PDMS slab was covered and bonded with a 120-μm-thick glass plate to seal the model. The glass plate was first spin-coated with a thin layer, roughly 10 μm, of PDMS. The micro-model was treated with silane in order to make it uniformly and stably hydrophobic. Fluorescent particles of 300 μm in diameter were used as colloids. It is known that more removal of colloids occurs under unsaturated conditions, compared to saturated flow in soil. At the same time, the change of saturation has been observed to cause remobilization of attached colloids. The mechanisms for these phenomena are not well understood. This is the first time that a closed micro-model, made of PDMS with uniform and stable wettability, has been used in combination with confocal microscopy to study colloid transport under transient two-phase flow conditions. With confocal microscopy, the movement of fluorescent particles and flow of two liquids within the pores can be studied. One can focus at different depths within the pores and thus determine where the particles exactly are. Thus, remobilization of attached colloids by moving fluid-fluid interfaces was visualized. In order to allow for the deposition and subsequent remobilization of colloids during two-phase flow, three micro-channels for the injection of liquids with and without colloids were constructed. An outlet channel was designed where effluent concentration breakthrough curves can be quantified by measuring the fluorescence intensity. A peak concentration also indicated in the breakthrough curve with the drainage event. The acquired images and breakthrough curve successfully confirmed the utility of the combination of such a PDMS
Mathematical modelling techniques
Aris, Rutherford
1995-01-01
""Engaging, elegantly written."" - Applied Mathematical ModellingMathematical modelling is a highly useful methodology designed to enable mathematicians, physicists and other scientists to formulate equations from a given nonmathematical situation. In this elegantly written volume, a distinguished theoretical chemist and engineer sets down helpful rules not only for setting up models but also for solving the mathematical problems they pose and for evaluating models.The author begins with a discussion of the term ""model,"" followed by clearly presented examples of the different types of mode
An implicit numerical model for multicomponent compressible two-phase flow in porous media
Zidane, Ali; Firoozabadi, Abbas
2015-11-01
We introduce a new implicit approach to model multicomponent compressible two-phase flow in porous media with species transfer between the phases. In the implicit discretization of the species transport equation in our formulation we calculate for the first time the derivative of the molar concentration of component i in phase α (cα, i) with respect to the total molar concentration (ci) under the conditions of a constant volume V and temperature T. The species transport equation is discretized by the finite volume (FV) method. The fluxes are calculated based on powerful features of the mixed finite element (MFE) method which provides the pressure at grid-cell interfaces in addition to the pressure at the grid-cell center. The efficiency of the proposed model is demonstrated by comparing our results with three existing implicit compositional models. Our algorithm has low numerical dispersion despite the fact it is based on first-order space discretization. The proposed algorithm is very robust.
Homogenized Model of Two-Phase Flow with Local Nonequilibrium in Double Porosity Media
Directory of Open Access Journals (Sweden)
Brahim Amaziane
2016-01-01
Full Text Available We consider two-phase flow in a heterogeneous porous medium with highly permeable fractures and low permeable periodic blocks. The flow in the blocks is assumed to be in local capillary disequilibrium and described by Barenblatt’s relaxation relationships for the relative permeability and capillary pressure. It is shown that the homogenization of such equations leads to a new macroscopic model that includes two kinds of long-memory effects: the mass transfer between the blocks and fractures and the memory caused by the microscopic Barenblatt disequilibrium. We have obtained a general relationship for the double nonequilibrium capillary pressure which represents great interest for applications. Due to the nonlinear coupling and the nonlocality in time, the macroscopic model remains incompletely homogenized in general case. The completely homogenized model was obtained for two different regimes. The first case corresponds to a linearized flow in the blocks. In the second case, we assume a low contrast in the block-fracture permeability. Numerical results for the two-dimensional problem are presented for two test cases to demonstrate the effectiveness of the methodology.
Computing Debris-flow Mobilization and Run-out with a Two-phase Depth-averaged Model
George, D. L.; Iverson, R. M.
2011-12-01
Large-scale, shallow earth-surface flows, such as river flows, overland flooding, and tsunami propagation and inundation, are commonly modeled with depth-averaged equations for the evolution of mass and momentum distributions. Depth-averaging three-dimensional conservation equations results in a tractable two-dimensional model that predicts macroscopic flow features with reasonable accuracy. For example, the simplest of the depth-averaged models---the shallow water equations---has proven to accurately describe water flooding and inundation. We have developed a depth-averaged, two-phase model applicable to granular-fluid mixtures such as landslides and debris flows. While the model relies on relatively simple assumptions for Coulomb frictional stress, the governing equations are more complex than those for shallow water flow. Our new equations include important feedback effects due to coupled evolution of the solid volume fraction and pore-fluid pressure, which mediates frictional stress. While pore-fluid pressure has long been known to be an important factor influencing debris-flow mobility, previous models lacked explicit coupling between pressure and granular dilation. Consequently, traditional models have also lacked the ability to account for the quasi-static transition of a stable mass of water-laden sediment into a debris flow. These models must be initialized by assuming a force balance far from equilibrium, ignoring the important transition to instability. By explicitly tracking the coupled pore-fluid pressure and solid volume fraction, our model captures this important transition and therefore can be used to investigate stability and mobility in addition to flow routing and deposition. Our model equations are a nonlinear hyperbolic system similar in mathematical structure to the shallow water equations, but having two additional equations for the solid volume fraction and pore-fluid pressure. Because of the mathematical similarities, numerical techniques
Modeling of Immiscible, Two-Phase Flows in a Natural Rock Fracture
Energy Technology Data Exchange (ETDEWEB)
Crandall, Dustin; Ahmadi, Goodarz; Smith, Duane H
2009-01-01
One potential method of geologically sequestering carbon dioxide (CO2) is to inject the gas into brine-filled, subsurface formations. Within these low-permeability rocks, fractures exist that can act as natural fluid conduits. Understanding how a less viscous fluid moves when injected into an initially saturated rock fracture is important for the prediction of CO2 transport within fractured rocks. Our study examined experimentally and numerically the motion of immiscible fluids as they were transported through models of a fracture in Berea sandstone. The natural fracture geometry was initially scanned using micro-computerized tomography (CT) at a fine volume-pixel (voxel) resolution by Karpyn et al. [1]. This CT scanned fracture was converted into a numerical mesh for two-phase flow calculations using the finite-volume solver FLUENT® and the volume-of-fluid method. Additionally, a translucent experimental model was constructed using stereolithography. The numerical model was shown to agree well with experiments for the case of a constant rate injection of air into the initially water-saturated fracture. The invading air moved intermittently, quickly invading large-aperture regions of the fracture. Relative permeability curves were developed to describe the fluid motion. These permeability curves can be used in reservoir-scale discrete fracture models for predictions of fluid motion within fractured geological formations. The numerical model was then changed to better mimic the subsurface conditions at which CO2 will move into brine saturated fractures. The different fluid properties of the modeled subsurface fluids were shown to increase the amount of volume the less-viscous invading gas would occupy while traversing the fracture.
Numerical Simulations of Two-Phase Flow in a Dorr-Oliver Flotation Cell Model
Directory of Open Access Journals (Sweden)
Hassan Fayed
2013-08-01
Full Text Available Two-phase (water and air flow in the forced-air mechanically-stirred Dorr-Oliver machine has been investigated using computational fluid dynamics (CFD. A 6 m3 model is considered. The flow is modeled by the Euler-Euler approach, and transport equations are solved using software ANSYS-CFX5. Unsteady simulations are conducted in a 180-degree sector with periodic boundary conditions. Air is injected into the rotor at the rate of 2.63 m3/min, and a uniform bubble diameter is specified. The effects of bubble diameter on velocity field and air volume fraction are determined by conducting simulations for three diameters of 0.5, 1.0, and 2.0 mm. Air volume fraction contours, velocity profiles, and turbulent kinetic energy profiles in different parts of the machine are presented and discussed. Results have been compared to experimental data, and good agreement is obtained for the mean velocity and turbulent kinetic energy profiles in the rotor-stator gap and in the jet region outside stator blades.
Modeling and testing of two-phase flow in manifolds under microgravity conditions
Best, Frederick; Kurwitz, Cable
2001-02-01
Previous work relating to two-phase flow in manifolds has dealt primarily with 1-g phase distribution at each junction. Understanding the redistribution of gas and liquid at each junction in microgravity allows the investigator to calculate specific thermal-hydraulic phenomena in each branch or run. A model was developed at Texas A&M to determine the phasic distribution in an arbitrary manifold. Previously developed phase distribution equations are used to describe the redistribution at a dividing T-junction (Young et al., 1999). Mass flow rate, void fraction, and pressure drop are calculated iteratively for the entire manifold. Output from the model was compared to data taken from tests aboard NASA's KC-135. The test manifold consisted of a run with three branches. The system allowed the output to be directed to a phase separator or to collection bags. The distribution of liquid and gas in each collection bag could be used to determine the mass fraction in each branch and run. Results show good agreement between predicted mass fraction and flight data. .
Non-equilibrium model of two-phase porous media flow with phase change
Cueto-Felgueroso, L.; Fu, X.; Juanes, R.
2014-12-01
The efficient simulation of multi-phase multi-component flow through geologic porous media is challenging and computationally intensive, yet quantitative modeling of these processes is essential in engineering and the geosciences. Multiphase flow with phase change and complex phase behavior arises in numerous applications, including enhanced oil recovery, steam injection in groundwater remediation, geologic CO2 storage and enhanced geothermal energy systems. A challenge of multiphase compositional simulation is that the number of existing phases varies with position and time, and thus the number of state variables in the saturation-based conservation laws is a function of space and time. The tasks of phase-state identification and determination of the composition of the different phases are performed assuming local thermodynamic equilibrium. Here we investigate a thermodynamically consistent formulation for non-isothermal two-phase flow, in systems where the hypothesis of instantaneous local equilibrium does not hold. Non-equilibrium effects are important in coarse-scale simulations where the assumption of complete mixing in each gridblock is not realistic. We apply our model to steam injection in water-saturated porous media.
Lattice-Boltzmann-based two-phase thermal model for simulating phase change.
Kamali, M R; Gillissen, J J J; van den Akker, H E A; Sundaresan, Sankaran
2013-09-01
A lattice Boltzmann (LB) method is presented for solving the energy conservation equation in two phases when the phase change effects are included in the model. This approach employs multiple distribution functions, one for a pseudotemperature scalar variable and the rest for the various species. A nonideal equation of state (EOS) is introduced by using a pseudopotential LB model. The evolution equation for the pseudotemperature variable is constructed in such a manner that in the continuum limit one recovers the well known macroscopic energy conservation equation for the mixtures. Heats of reaction, the enthalpy change associated with the phase change, and the diffusive transport of enthalpy are all taken into account; but the dependence of enthalpy on pressure, which is usually a small effect in most nonisothermal flows encountered in chemical reaction systems, is ignored. The energy equation is coupled to the LB equations for species transport and pseudopotential interaction forces through the EOS by using the filtered local pseudotemperature field. The proposed scheme is validated against simple test problems for which analytical solutions can readily be obtained.
Modeling the macroscopic behavior of two-phase nonlinear composites by infinite-rank laminates
Idiart, Martín I.
A new approach is proposed for estimating the macroscopic behavior of two-phase nonlinear composites with random, particulate microstructures. The central idea is to model composites by sequentially laminated constructions of infinite rank whose macroscopic behavior can be determined exactly. The resulting estimates incorporate microstructural information up to the two-point correlation functions, and require the solution to a Hamilton-Jacobi equation with the inclusion concentration and the macroscopic fields playing the role of 'time' and 'spatial' variables, respectively. Because they are realizable, by construction, these estimates are guaranteed to be convex, to satisfy all pertinent bounds, to exhibit no duality gap, and to be exact to second order in the heterogeneity contrast. Sample results are provided for two- and three-dimensional power-law composites, and are compared with other homogenization estimates, as well as with numerical simulations available from the literature. The estimates are found to give physically sensible predictions for all the cases considered, even for extreme values of the nonlinearity and heterogeneity contrast. Interestingly, in the case of isotropic porous materials under hydrostatic loadings, the estimates agree exactly with standard Gurson-type models for viscoplastic porous media.
A Unified Detail-Preserving Liquid Simulation by Two-Phase Lattice Boltzmann Modeling.
Guo, Yulong; Liu, Xiaopei; Xu, Xuemiao
2016-02-19
Traditional methods in graphics to simulate liquid-air dynamics under different scenarios usually employ separate approaches with sophisticated interface tracking/reconstruction techniques. In this paper, we propose a novel unified approach which is easy and effective to produce a variety of liquid-air interface phenomena. These phenomena, such as complex surface splashes, bubble interactions, as well as surface tension effects, can co-exist in one single simulation, and are created within the same computational framework. Such a framework is unique in that it is free from any complicated interface tracking/reconstruction procedures. Our approach is developed from the two-phase lattice Boltzmann method with the mean field model, which provides a unified framework for interface dynamics but is numerically unstable under turbulent conditions. Considering the drawbacks of the existing approaches, we propose techniques to suppress oscillation for significant stability enhancement, as well as derive a new subgrid-scale model to further improve stability, faithfully preserving liquid-air interface details without excessive diffusion by taking into account the density variation. The whole framework is highly parallel, enabling very efficient implementation. Comparisons to the related approaches show superiority on stable simulation with detail preservation and multiphase phenomena simultaneously involved. A set of animation results demonstrate the effectiveness of our method.
Numerical simulation of two-phase flow around flatwater competition kayak design-evolution models.
Mantha, Vishveshwar R; Silva, António J; Marinho, Daniel A; Rouboa, Abel I
2013-06-01
The aim of the current study was to analyze the hydrodynamics of three kayaks: 97-kg-class, single-rower, flatwater sports competition, full-scale design evolution models (Nelo K1 Vanquish LI, LII, and LIII) of M.A.R. Kayaks Lda., Portugal, which are among the fastest frontline kayaks. The effect of kayak design transformation on kayak hydrodynamics performance was studied by the application of computational fluid dynamics (CFD). The steady-state CFD simulations where performed by application of the k-omega turbulent model and the volume-of-fluid method to obtain two-phase flow around the kayaks. The numerical result of viscous, pressure drag, and coefficients along with wave drag at individual average race velocities was obtained. At an average velocity of 4.5 m/s, the reduction in drag was 29.4% for the design change from LI to LII and 15.4% for the change from LII to LIII, thus demonstrating and reaffirming a progressive evolution in design. In addition, the knowledge of drag hydrodynamics presented in the current study facilitates the estimation of the paddling effort required from the athlete during progression at different race velocities. This study finds an application during selection and training, where a coach can select the kayak with better hydrodynamics.
Numerical modelling of two phase flow with hysteresis in heterogeneous porous media
Energy Technology Data Exchange (ETDEWEB)
Abreu, E. [Instituto Nacional de Matematica Pura e Aplicada (IMPA), Rio de Janeiro, RJ (Brazil); Furtado, F.; Pereira, F. [University of Wyoming, Laramie, WY (United States). Dept. of Mathematicsatics; Souza, G. [Universidade do Estado do Rio de Janeiro (UERJ), RJ (Brazil)
2008-07-01
Numerical simulators are necessary for the understanding of multiphase flow in porous media in order to optimize hydrocarbon recovery. In this work, the immiscible flow of two incompressible phases, a problem very common in waterflooding of petroleum reservoirs, is considered and numerical simulation techniques are presented. The system of equations which describe this type of flow form a coupled, highly nonlinear system of time-dependent partial differential equations (PDEs). The equation for the saturation of the invading fluid is a convection-dominated, degenerate parabolic PDE whose solutions typically exhibit sharp fronts (i.e., internal layers with strong gradients) and is very difficult to approximate numerically. It is well known that accurate modeling of convective and diffusive processes is one of the most daunting tasks in the numerical approximation of PDEs. Particularly difficult is the case where convection dominates diffusion. Specifically, we consider the injection problem for a model of two-phase (water/oil) flow in a core sample of porous rock, taking into account hysteresis effects in the relative permeability of the oil phase. (author)
Microtomography and pore-scale modeling of two-phase Fluid Distribution
Energy Technology Data Exchange (ETDEWEB)
Silin, D.; Tomutsa, L.; Benson, S.; Patzek, T.
2010-10-19
Synchrotron-based X-ray microtomography (micro CT) at the Advanced Light Source (ALS) line 8.3.2 at the Lawrence Berkeley National Laboratory produces three-dimensional micron-scale-resolution digital images of the pore space of the reservoir rock along with the spacial distribution of the fluids. Pore-scale visualization of carbon dioxide flooding experiments performed at a reservoir pressure demonstrates that the injected gas fills some pores and pore clusters, and entirely bypasses the others. Using 3D digital images of the pore space as input data, the method of maximal inscribed spheres (MIS) predicts two-phase fluid distribution in capillary equilibrium. Verification against the tomography images shows a good agreement between the computed fluid distribution in the pores and the experimental data. The model-predicted capillary pressure curves and tomography-based porosimetry distributions compared favorably with the mercury injection data. Thus, micro CT in combination with modeling based on the MIS is a viable approach to study the pore-scale mechanisms of CO{sub 2} injection into an aquifer, as well as more general multi-phase flows.
CHOOSING STRUCTURE-DEPENDENT DRAG COEFFICIENT IN MODELING GAS-SOLID TWO-PHASE FLOW
Institute of Scientific and Technical Information of China (English)
Ning Yang; Wei Wang; Wei Ge; Jinghai Li
2003-01-01
@@ Introduction Gas-solid two-phase flow is often encountered in chemical reactors for the process industry. For industrial users, design, scale-up, control and optimization for these reactors require a good understanding of the hydrodynamics of gas-solid two-phase flow. For researchers, exploration and prediction of the complex phenomena call for a good comprehension of the heterogeneous structure and of the dominant mechanisms of gas-solid and solid-solid interactions.
Development of two-phase Flow Model, 'SOBOIL', for Sodium
Energy Technology Data Exchange (ETDEWEB)
Hahn, Do Hee; Chang, Won Pyo; Kim, In Chul; Kwon, Young Min; Lee, Yong Bum
2000-03-01
The objective of this research is to develop a sodium two-phase flow analysis model, 'SOBOIL', for the assessment of the initial stage of the KALIMER HCDA (Hypotherical Core Disruptive Accident). The 'SOBOIL' is basically similar to the multi-bubble slug ejection model used in SAS2A[1]. When a bubble is formed within the liquid slug, the bubble fills the whole cross section of the coolant channel except for a film left on the cladding or on the structure. Up to nine bubbles, separated by the liquid slugs, are allowed in the channel at any time. Each liquid slug flow rate in the model is performed in 2 steps. In the first step, the preliminary flow rate in the liquid slug is calculated neglecting the effect of changes in the vapor bubble pressures over the time step. The temperature and pressure distributions, and interface velocity at the interface between the liquid slug and vapor bubble are also calculated during this process. The new vapor temperature and pressure are then determined from the balance between the net energy transferred into the vapor and the change of the vapor energy. The liquid flow is finally calculated considering the change of the vapor pressure over a time step and the calculation is repeated until specified elapsed time is met. Continuous effort, therefore, must be made on the examination and improvement for the model to become reliable. To this end, much interest must be concentrated in the relevant international collaborations for access to a reference model or test data for the verification.
Directory of Open Access Journals (Sweden)
Clive R McMahon
Full Text Available Generally, sigmoid curves are used to describe the growth of animals over their lifetime. However, because growth rates often differ over an animal's lifetime a single curve may not accurately capture the growth. Broken-stick models constrained to pass through a common point have been proposed to describe the different growth phases, but these are often unsatisfactory because essentially there are still two functions that describe the lifetime growth. To provide a single, converged model to age animals with disparate growth phases we developed a smoothly joining two-phase nonlinear function (SJ2P, tailored to provide a more accurate description of lifetime growth of the macropod, the Tasmanian pademelon Thylogale billardierii. The model consists of the Verhulst logistic function, which describes pouch-phase growth--joining smoothly to the Brody function, which describes post-pouch growth. Results from the model demonstrate that male pademelons grew faster and bigger than females. Our approach provides a practical means of ageing wild pademelons for life history studies but given the high variability of the data used to parametrise the second growth phase of the model, the accuracy of ageing of post-weaned animals is low: accuracy might be improved with collection of longitudinal growth data. This study provides a unique, first robust method that can be used to characterise growth over the lifespan of pademelons. The development of this method is relevant to collecting age-specific vital rates from commonly used wildlife management practices to provide crucial insights into the demographic behaviour of animal populations.
Intermediate scales between simulation and modeling of two-phase flows
Energy Technology Data Exchange (ETDEWEB)
Pigny, Sylvain L., E-mail: sylvain.pigny@cea.f [CEA/DEN, 17 rue des Martyrs, 38054 Grenoble Cedex 9 (France)
2011-03-15
Research highlights: Simulation and modeling of bubbles are done at high Reynolds number. Intermediate scales between simulation and modeling are of importance. Specific approaches can be envisaged in accurate multiphase codes. An attempt leads to agreement with experimental data. We establish a link between multiphase codes and DNS ones. - Abstract: Phenomena related to two-phase flows in an experiment in which air is injected in the lower part of a tank filled with water are investigated, via the SIMMER-IV software. The Reynolds and Weber numbers of the bubbly flow have high values. Small scale phenomena, related to small bubbles behavior or turbulence in the liquid continuous phase, are modeled via classical closure laws. An attempt to represent the formation of individual large bubbles, close to the injector, via direct simulation is done. In a first calculation, the large bubbles break-up is not represented. This phenomenon, the space scale of which is close to the cell size, cannot be simulated, with the present computational resources. Nevertheless, relatively fine meshes are used, for an accurate description of hydrodynamical phenomena, and these phenomena are too large to be modeled via closure laws. The case is therefore useful to underline some basic limits in the potentialities of direct simulation and modeling and to propose an attempt to face the problem. The breakup of bubbles is now represented. Finally the validity of the approach is checked directly by simulating a single bubble experiment. The problem of the convergence between multiphase codes and direct simulation ones is pointed.
Investigation of Two-Phase Flow in AxialCentrifugal Impeller by Hydrodynamic Modeling Methods
Directory of Open Access Journals (Sweden)
V. O. Lomakin
2014-01-01
Full Text Available The article provides a methodology to study the flow in the wet part of the pump with fundamentally new axial-centrifugal impeller by methods of hydrodynamic modeling in the software package STAR CCM +. The objective of the study was to determine the normal and cavitation characteristics of the pump with a new type of wet part, as well as optimization of the geometrical parameters of the pump. Authors solved this problem using an example of the hot coolant pump, which should meet high requirements for cavitation quality and efficiency (hydraulic efficiency up to 87%, critical value of NPSH to 2.2 m.Also, the article focuses on the methods of numerical solution of two-phase flow simulation in a pump that are needed for a more accurate simulation of cavitation in the pump and research work in liquids with high gas content.Hydrodynamic modeling was performed on a computing cluster at the department E-10 of BMSTU for pump flow simulation in unsteady statement of problem using the computational grid size to 1.5 million cells. Simultaneously, the experimental model of the pump was made by 3D printing and tested at the stand in the BMSTU. Test results, which were compared with the calculated data are also given in the article. Inaccuracy of the calculation of pump head does not exceed 5%.The simulation results may be of interest to specialists in the field of hydrodynamic modeling, and for designers of such pumps. The authors also report production of a full-length prototype of the pump in order to conduct further testing for the verification of the data in the article, primarily in terms of cavitation characteristics.
Applied impulsive mathematical models
Stamova, Ivanka
2016-01-01
Using the theory of impulsive differential equations, this book focuses on mathematical models which reflect current research in biology, population dynamics, neural networks and economics. The authors provide the basic background from the fundamental theory and give a systematic exposition of recent results related to the qualitative analysis of impulsive mathematical models. Consisting of six chapters, the book presents many applicable techniques, making them available in a single source easily accessible to researchers interested in mathematical models and their applications. Serving as a valuable reference, this text is addressed to a wide audience of professionals, including mathematicians, applied researchers and practitioners.
A splitting method for the isentropic Baer-Nunziato two-phase flow model
Directory of Open Access Journals (Sweden)
Coquel Frédéric
2013-01-01
Full Text Available In the present work, we propose a fractional step method for computing approximate solutions of the isentropic Baer-Nunziato two-phase flow model. The scheme relies on an operator splitting method corresponding to a separate treatment of fast propagation phenomena due to the acoustic waves on the one hand and slow propagation phenomena due to the fluid motion on the other. The scheme is proved to preserve positive values of the statistical fractions and densities. We also provide two test-cases that assess the convergence of the method. Nous proposons ici une méthode à pas fractionnaires pour le calcul de solutions approchées pour la version isentropique du modèle diphasique de Baer-Nunziato. Le schéma s’appuie sur un splitting de l’opérateur temporel correspondant à la prise en compte différenciée des phéno-mènes de propagation rapide dus aux ondes acoustiques et des phénomènes de propagation lente dus aux ondes matérielles. On prouve que le schéma permet de préserver des valeurs positives pour les taux statistiques de présence des phases ainsi que pour les densités. Deux cas tests numériques permettent d’illustrer la convergence de la méthode.
Evaluation Of Two Phase Flow Characteristics In A Pipeline Homogenous Model Approach
Directory of Open Access Journals (Sweden)
Okoye Obuora A.
2015-08-01
Full Text Available The motion of a multi-fluid flow is of interest in the oil and gas industry. The flow characteristics aid or impede production rate. This study analyses two phase fluid flow characteristics consisting of crude oil and natural gas in straight pipes of the same internal diameter using homogenous model. Flow values were obtained from a Niger Delta flow station and predetermined experimental flow equations were used to determine the pressure drop in order to comprehend the flow characteristics in the pipeline. An average total pressure loss amp8710PT of 0.075 MPa was obtained in the laminar flow category at 0.006228 MPam and an average total pressure amp8710PT of 27.896 MPa in turbulent flow category at 2.325 MPam in a pipe length of 12 metres. Graphs were plotted to show the influence of the calculated flow parameters on the fluid flow. The graphs aided in depicting the flow regimes in the pipeline. These are universally dominant parameters in the oil and gas industry as they significantly impact on the transportation of crude oil from oil wells or reservoirs to the process plants. These results may be used as a baseline and guide to compare realistic measurements in similar flows.
Numerical modeling of immiscible two-phase flow in micro-models using a commercial CFD code
Energy Technology Data Exchange (ETDEWEB)
Crandall, Dustin; Ahmadia, Goodarz; Smith, Duane H.
2009-01-01
Off-the-shelf CFD software is being used to analyze everything from flow over airplanes to lab-on-a-chip designs. So, how accurately can two-phase immiscible flow be modeled flowing through some small-scale models of porous media? We evaluate the capability of the CFD code FLUENT{trademark} to model immiscible flow in micro-scale, bench-top stereolithography models. By comparing the flow results to experimental models we show that accurate 3D modeling is possible.
Directory of Open Access Journals (Sweden)
Michal Prazenica
2011-01-01
Full Text Available This paper deals with the two-stage two-phase electronic systems with orthogonal output voltages and currents - DC/AC/AC. Design of two-stage DC/AC/AC high frequency converter with two-phase orthogonal output using single-phase matrix converter is also introduced. Output voltages of them are strongly nonharmonic ones, so they must be pulse-modulated due to requested nearly sinusoidal currents with low total harmonic distortion. Simulation experiment results of matrix converter for both steady and transient states for IM motors are given in the paper, also experimental verification under R-L load, so far. The simulation results confirm a very good time-waveform of the phase current and the system seems to be suitable for low-cost application in automotive/aerospace industries and application with high frequency voltage sources.
Coupled Hydromechanical Model of Two-Phase Fluid Flow in Deformable Porous Media
Directory of Open Access Journals (Sweden)
You-Seong Kim
2013-01-01
Full Text Available A model of solid-water-air coupling in triphasic mixtures is compared with solid-water coupling in biphasic mixtures with an application to partially saturated porous media. Based on thermodynamics, the mathematical framework governing the behavior of a partially saturated soil is derived using balance equations, and the numerical implementation and drainage tests of a soil column are carried out to validate the obtained formulations. The role of the air phase in the hydro-mechanical behavior of triphasic mixtures can be analyzed from the interactions among multiple phases for the constitutive behavior of a solid skeleton, and the triphasic mixture model can be applied in geotechnical engineering problems, such as CO2 sequestration and air storage in aquifers.
Analysis of two-phase sampling data with semiparametric additive hazards models.
Sun, Yanqing; Qian, Xiyuan; Shou, Qiong; Gilbert, Peter B
2017-07-01
Under the case-cohort design introduced by Prentice (Biometrica 73:1-11, 1986), the covariate histories are ascertained only for the subjects who experience the event of interest (i.e., the cases) during the follow-up period and for a relatively small random sample from the original cohort (i.e., the subcohort). The case-cohort design has been widely used in clinical and epidemiological studies to assess the effects of covariates on failure times. Most statistical methods developed for the case-cohort design use the proportional hazards model, and few methods allow for time-varying regression coefficients. In addition, most methods disregard data from subjects outside of the subcohort, which can result in inefficient inference. Addressing these issues, this paper proposes an estimation procedure for the semiparametric additive hazards model with case-cohort/two-phase sampling data, allowing the covariates of interest to be missing for cases as well as for non-cases. A more flexible form of the additive model is considered that allows the effects of some covariates to be time varying while specifying the effects of others to be constant. An augmented inverse probability weighted estimation procedure is proposed. The proposed method allows utilizing the auxiliary information that correlates with the phase-two covariates to improve efficiency. The asymptotic properties of the proposed estimators are established. An extensive simulation study shows that the augmented inverse probability weighted estimation is more efficient than the widely adopted inverse probability weighted complete-case estimation method. The method is applied to analyze data from a preventive HIV vaccine efficacy trial.
Petrological and two-phase flow modelling of deep arc crust: insights on continental crust formation
Riel, Nicolas; Bouilhol, Pierre; van Hunen, Jeroen; Cornet, Julien
2017-04-01
The genesis of felsic crust is generally attributed to two main processes: the differentiation of primary magmas by crystallization within the crust or uppermost mantle and the partial melting of older crustal rocks. The Mixing/Assimilation/Hybridization of these magmas in the deep crust (MASH zone) and their subsequent segregation constitutes the principal process by which continents have become differentiated into a more mafic, residual lower crust and a more felsic and hydrated upper crust. Although this model describes qualitatively how continental crust forms, little is known on the physical and chemical mechanisms occurring at the root of volcanic arcs. To assess the dynamics of partial melting, melt injection and hybridization in the deep crust, a new 2-D two-phase flow code using finite volume method has been developed. The formulation takes into account: (i) melt flow through porosity waves/channels, (ii) heat transfer, assuming local thermal equilibrium between solid and liquid, (iii) thermodynamic modelling of stable phases and (iv) injection of mantle-derived melt at the Moho. Our parametric study shows that pressure, heat influx and melt:rock ratio are the main parameters controlling the volume and composition of differentiated magma. Overall the composition of segregated products scatters in two groups: felsic (80-68% SiO2) and intermediate (60-52% SiO2), with an average andesitic composition. The bimodal distribution is controlled by amphibole which buffer the composition of segregated products to high SiO2-content when stable. As the amphibole-out melting reaction is crossed segregated products become intermediate. When compared to available geological evidence, the liquid line of descent of mantle-derived magma do not fit the Mg# versus silica trends of exposed volcanic arcs. Instead our modelling results show that reactive flow of those same magma through a mafic crust is able to reproduce such trends.
A two-phase restricted equilibrium model for combustion of metalized solid propellants
Sabnis, J. S.; Dejong, F. J.; Gibeling, H. J.
1992-01-01
An Eulerian-Lagrangian two-phase approach was adopted to model the multi-phase reacting internal flow in a solid rocket with a metalized propellant. An Eulerian description was used to analyze the motion of the continuous phase which includes the gas as well as the small (micron-sized) particulates, while a Lagrangian description is used for the analysis of the discrete phase which consists of the larger particulates in the motor chamber. The particulates consist of Al and Al2O3 such that the particulate composition is 100 percent Al at injection from the propellant surface with Al2O3 fraction increasing due to combustion along the particle trajectory. An empirical model is used to compute the combustion rate for agglomerates while the continuous phase chemistry is treated using chemical equilibrium. The computer code was used to simulate the reacting flow in a solid rocket motor with an AP/HTPB/Al propellant. The computed results show the existence of an extended combustion zone in the chamber rather than a thin reaction region. The presence of the extended combustion zone results in the chamber flow field and chemical being far from isothermal (as would be predicted by a surface combustion assumption). The temperature in the chamber increases from about 2600 K at the propellant surface to about 3350 K in the core. Similarly the chemical composition and the density of the propellant gas also show spatially non-uniform distribution in the chamber. The analysis developed under the present effort provides a more sophisticated tool for solid rocket internal flow predictions than is presently available, and can be useful in studying apparent anomalies and improving the simple correlations currently in use. The code can be used in the analysis of combustion efficiency, thermal load in the internal insulation, plume radiation, etc.
Two-phase plate-fin heat exchanger modeling for waste heat recovery systems in diesel engines
Feru, E.; de Jager, B.; Willems, F.; Steinbuch, M.
2014-01-01
This paper presents the modeling and model validation for a modular two-phase heat exchanger that recovers energy in heavy-duty diesel engines. The model is developed for temperature and vapor quality prediction and for control design of the waste heat recovery system. In the studied waste heat reco
Energy Technology Data Exchange (ETDEWEB)
Lebensohn, Ricardo A [Los Alamos National Laboratory; Lee, Sukbin [CMU; Rollett, Anthony D [CMU
2009-01-01
A viscoplastic approach using the Fast Fourier Transform (FFT) method for obtaining local mechanical response is utilized to study microstructure-property relationships in composite materials. Specifically, three-dimensional, two-phase digital materials containing isotropically coarsened particles surrounded by a matrix phase, generated through a Kinetic Monte Carlo Potts model for Ostwald ripening, are used as instantiations in order to calculate the stress and strain rate fields under uniaxial tension. The effects of the morphology of the matrix phase, the volume fraction and the contiguity of particles, and the polycrystallinity of matrix phase, on the stress and strain rate fields under uniaxial tension are examined. It is found that the first moments of the stress and strain rate fields have a different dependence on the particle volume fraction and the particle contiguity from their second moments. The average stresses and average strain rates of both phases and of the overall composite have rather simple relationships with the particle volume fraction whereas their standard deviations vary strongly, especially when the particle volume fraction is high, and the contiguity of particles has a noticeable effect on the mechanical response. It is also found that the shape of stress distribution in the BCC hard particle phase evolves as the volume fraction of particles in the composite varies, such that it agrees with the stress field in the BCC polycrystal as the volume of particles approaches unity. Finally, it is observed that the stress and strain rate fields in the microstructures with a polycrystalline matrix are less sensitive to changes in volume fraction and contiguity of particles.
The Deep Crust Magmatic Refinery, Part 1: A Coupled Thermodynamic and Two-phase Flow Model
Riel, N., Jr.; Bouilhol, P.; Van Hunen, J.; Velic, M.; Magni, V.
2016-12-01
Metamorphic and magmatic processes occurring in the deep crust ultimately control the chemical and physical characteristic of the continental crust. A complex interplay between magma intrusion, crystallization, and reaction with the pre-existing crust provide a wide range of differentiated magma and cumulates (and / or restites) that will feed the upper crustal levels with evolved melt while constructing the lower crust. With growing evidence from field and experimental studies, it becomes clearer that crystallization and melting processes are non-exclusive but should be considered together. Incoming H2O bearing mantle melts will start to fractionate to a certain extent, forming cumulates but also releasing heat and H2O to the intruded host-rock allowing it to melt in saturated conditions. The end-result of such dynamic system is a function of the amount and composition of melt input, and extent of reaction with the host which is itself dependent on the migration mode of the melts. To assess the dynamics of this deep magmatic system we developed a new 2-D two-phase flow code using finite volume method. Our formulation takes into account: (i) melt flow through a viscous porous matrix with temperature- and melt-content dependent host-rock viscosity, (ii) heat transfer, assuming local thermal equilibrium between solid and liquid, (iii) thermodynamic modelling of stable phases, (iv) injection of fractionated melt from crystallizing basalt at the Moho and (v) chemical advection of both the solid and liquid compositions. Here we present the core of our modelling approach, especially the petrological implementation. We show in details that our thermodynamic model can reproduce well both the sub- and supra solidus phase relationship and composition of the host-rock. We apply our method to an idealized amphibolite lower crust that is affected by a magmatic event represented by the intrusion of a wet mantle melt into the crust at Moho depth. The models [see Bouilhol et al
Numerical Simulation of Hydrodynamic Wave Loading by a Compressible Two-Phase Model
Wemmenhove, R.; Loots, G.E.; Veldman, A.E.P.
2006-01-01
The numerical simulation of hydrodynamic wave loading on different types of offshore structures is important to predict forces on and water motion around these structures. This paper presents a numerical study of the effects of two-phase flow on an offshore structure subject to breaking waves. The
Xu, Xianmin
2010-01-01
In this paper, the equilibrium behavior of an immiscible two phase fluid on a rough surface is studied from a phase field equation derived from minimizing the total free energy of the system. When the size of the roughness becomes small, we derive the effective boundary condition for the equation by the multiple scale expansion homogenization technique. The Wenzel and Cassie equations for the apparent contact angles on the rough surfaces are then derived from the effective boundary condition. The homogenization results are proved rigorously by the F-convergence theory. © 2010 Society for Industrial and Applied Mathematics.
Energy Technology Data Exchange (ETDEWEB)
Lorentzen, Rolf Johan
2002-04-01
The main objective of this thesis is to develop methods which can be used to improve predictions of two-phase flow (liquid and gas) in pipelines and wells. More reliable predictions are accomplished by improvements of numerical methods, and by using measured data to tune the mathematical model which describes the two-phase flow. We present a way to extend simple numerical methods to second order spatial accuracy. These methods are implemented, tested and compared with a second order Godunov-type scheme. In addition, a new (and faster) version of the Godunov-type scheme utilizing primitive (observable) variables is presented. We introduce a least squares method which is used to tune parameters embedded in the two-phase flow model. This method is tested using synthetic generated measurements. We also present an ensemble Kalman filter which is used to tune physical state variables and model parameters. This technique is tested on synthetic generated measurements, but also on several sets of full-scale experimental measurements. The thesis is divided into an introductory part, and a part consisting of four papers. The introduction serves both as a summary of the material treated in the papers, and as supplementary background material. It contains five sections, where the first gives an overview of the main topics which are addressed in the thesis. Section 2 contains a description and discussion of mathematical models for two-phase flow in pipelines. Section 3 deals with the numerical methods which are used to solve the equations arising from the two-phase flow model. The numerical scheme described in Section 3.5 is not included in the papers. This section includes results in addition to an outline of the numerical approach. Section 4 gives an introduction to estimation theory, and leads towards application of the two-phase flow model. The material in Sections 4.6 and 4.7 is not discussed in the papers, but is included in the thesis as it gives an important validation
Review:Liquid film dryout model for predicting critical heat flux in annular two-phase flow
Institute of Scientific and Technical Information of China (English)
Bo JIAO; Li-min QIU; Jun-liang LU; Zhi-hua GAN
2009-01-01
Gas-liquid two-phase flow and heat transfer can be encountered in numerous fields, such as chemical engineering, refrigeration, nuclear power reactor, metallurgical industry, spaceflight. Its critical heat flux (CHF) is one of the most important factors for the system security of engineering applications. Since annular flow is the most common flow pattern in gas-liquid two-phase flow, predicting CHF of annular two-phase flow is more significant. Many studies have shown that the liquid film dryout model is successful for that prediction, and determining the following parameters will exert predominant effects on the accuracy of this model: onset of annular flow, inception criterion for droplets entrainment, entrainment fraction, droplets deposi-tion and entrainment rates. The main theoretical results achieved on the above five parameters are reviewed; also, limitations in the existing studies and problems for further research are discussed.
Cherevko, A. A.; Gologush, T. S.; Ostapenko, V. V.; Petrenko, I. A.; Chupakhin, A. P.
2016-06-01
Arteriovenous malformation is a chaotic disordered interlacement of very small diameter vessels, performing reset of blood from the artery into the vein. In this regard it can be adequately modeled using porous medium. In this model process of embolization described as penetration of non-adhesive substance ONYX into the porous medium, filled with blood, both of these fluids are not mixed with each other. In one-dimensional approximation such processes are well described by Buckley-Leverett equation. In this paper Buckley-Leverett equation is solved numerically by using a new modification of Cabaret scheme. The results of numerical modeling process of embolization of AVM are shown.
Mathematical models of morphogenesis
Directory of Open Access Journals (Sweden)
Dilão Rui
2015-01-01
Full Text Available Morphogenesis is the ensemble of phenomena that generates the form and shape of organisms. Organisms are classified according to some of its structural characteristics, to its metabolism and to its form. In particular, the empirical classification associated with the phylum concept is related with the form and shape of organisms. In the first part of this talk, we introduce the class of mathematical models associated the Turing approach to pattern formation. In the Turing approach, morphogenesis models are described by reaction-diffusion parabolic partial differential equations. Based on this formalism, we present a mathematical model describing the first two hours of development of the fruit fly Drosophila. In the second part of this talk, we present results on Pareto optimality to calibrate and validate mathematical models.
Mathematical modelling of metabolism
DEFF Research Database (Denmark)
Gombert, Andreas Karoly; Nielsen, Jens
2000-01-01
Mathematical models of the cellular metabolism have a special interest within biotechnology. Many different kinds of commercially important products are derived from the cell factory, and metabolic engineering can be applied to improve existing production processes, as well as to make new processes...... available. Both stoichiometric and kinetic models have been used to investigate the metabolism, which has resulted in defining the optimal fermentation conditions, as well as in directing the genetic changes to be introduced in order to obtain a good producer strain or cell line. With the increasing...... availability of genomic information and powerful analytical techniques, mathematical models also serve as a tool for understanding the cellular metabolism and physiology....
El-Amin, Mohamed
2017-08-28
In this paper, the magnetic nanoparticles are injected into a water-oil, two-phase system under the influence of an external permanent magnetic field. We lay down the mathematical model and provide a set of numerical exercises of hypothetical cases to show how an external magnetic field can influence the transport of nanoparticles in the proposed two-phase system in porous media. We treat the water-nanoparticles suspension as a miscible mixture, whereas it is immiscible with the oil phase. The magnetization properties, the density, and the viscosity of the ferrofluids are obtained based on mixture theory relationships. In the mathematical model, the phase pressure contains additional term to account for the extra pressures due to fluid magnetization effect and the magnetostrictive effect. As a proof of concept, the proposed model is applied on a countercurrent imbibition flow system in which both the displacing and the displaced fluids move in opposite directions. Physical variables, including waternanoparticles suspension saturation, nanoparticles concentration, and pore wall/throat concentrations of deposited nanoparticles, are investigated under the influence of the magnetic field. Two different locations of the magnet are studied numerically, and variations in permeability and porosity are considered.
A numerical method for a model of two-phase flow in a coupled free flow and porous media system
Chen, Jie
2014-07-01
In this article, we study two-phase fluid flow in coupled free flow and porous media regions. The model consists of coupled Cahn-Hilliard and Navier-Stokes equations in the free fluid region and the two-phase Darcy law in the porous medium region. We propose a Robin-Robin domain decomposition method for the coupled Navier-Stokes and Darcy system with the generalized Beavers-Joseph-Saffman condition on the interface between the free flow and the porous media regions. Numerical examples are presented to illustrate the effectiveness of this method. © 2014 Elsevier Inc.
Principles of mathematical modeling
Dym, Clive
2004-01-01
Science and engineering students depend heavily on concepts of mathematical modeling. In an age where almost everything is done on a computer, author Clive Dym believes that students need to understand and "own" the underlying mathematics that computers are doing on their behalf. His goal for Principles of Mathematical Modeling, Second Edition, is to engage the student reader in developing a foundational understanding of the subject that will serve them well into their careers. The first half of the book begins with a clearly defined set of modeling principles, and then introduces a set of foundational tools including dimensional analysis, scaling techniques, and approximation and validation techniques. The second half demonstrates the latest applications for these tools to a broad variety of subjects, including exponential growth and decay in fields ranging from biology to economics, traffic flow, free and forced vibration of mechanical and other systems, and optimization problems in biology, structures, an...
Well-posedness and asynchronous exponential growth of solutions of a two-phase cell division model
Directory of Open Access Journals (Sweden)
Meng Bai
2010-04-01
Full Text Available In this article we study a two-phase cell division model. The cells of the two different phases have different growth rates. We mainly consider the model of equal mitosis. By using the semigroup theory, we prove that this model is well-posed in suitable function spaces and its solutions have the property of asynchronous exponential growth as time approaches infinity. The corresponding model of asymmetric mitosis is also studied and similar results are obtained.
Institute of Scientific and Technical Information of China (English)
ZENG Zhuo-xiong
2008-01-01
A new second-order moment two- phase turbulence model accounting for particle wake effect was established and used to simulate gas-particle flow in a horizontal channel for different values of wall roughness. The results show that compared with the model without considering the particle wake effect, the present model gives simulation results agreeing much better with the experimental results for the gas turbulence modulation, but the predicted results for particle motion with the two kinds of models are quite close.
A novel Deep Reactive Ion Etched (DRIE) glass micro-model for two-phase flow experiments
Karadimitriou, N.K.; Joekar-Niasar, V.; Hassanizadeh, S.M.; Kleingeld, P.J.; Pyrak-Nolte, L.J.
2012-01-01
In the last few decades, micro-models have become popular experimental tools for two-phase flow studies. In this work, the design and fabrication of an innovative, elongated, glass-etched micromodel with dimensions of 5 6 35 mm2 and constant depth of 43 microns is described. This is the first time t
Institute of Scientific and Technical Information of China (English)
M.M.RASHIDI; A.HOSSEINI; I.POP; S.KUMAR; N.FREIDOONIMEHR
2014-01-01
The main purpose of this study is to survey numerically comparison of two-phase and single phase of heat transfer and flow field of copper-water nanofluid in a wavy channel. The computational fluid dynamics (CFD) prediction is used for heat transfer and flow prediction of the single phase and three different two-phase models (mixture, volume of fluid (VOF), and Eulerian). The heat transfer coefficient, temperature, and velocity distributions are investigated. The results show that the differences between the temperature field in the single phase and two-phase models are greater than those in the hydrodynamic field. Also, it is found that the heat transfer coefficient predicted by the single phase model is enhanced by increasing the volume fraction of nanoparticles for all Reynolds numbers; while for the two-phase models, when the Reynolds number is low, increasing the volume fraction of nanoparticles will enhance the heat transfer coefficient in the front and the middle of the wavy channel, but gradually decrease along the wavy channel.
Application of the CE/SE Method to a Two-Phase Detonation Model in Porous Media
Institute of Scientific and Technical Information of China (English)
DONG He-Fei; HONG Tao; ZHANG De-Liang
2011-01-01
We extend the conservation-element and solution-element method to simulate a two-phase detonation model in porous media. The accuracy of the method is validated by calculating an inert compaction problem. The main characteristics of piston-driven detonation phenomena, including the compaction wave, the onset of combustion,and the transition to detonation, could be predicted successfully.
Concepts of mathematical modeling
Meyer, Walter J
2004-01-01
Appropriate for undergraduate and graduate students, this text features independent sections that illustrate the most important principles of mathematical modeling, a variety of applications, and classic models. Students with a solid background in calculus and some knowledge of probability and matrix theory will find the material entirely accessible. The range of subjects includes topics from the physical, biological, and social sciences, as well as those of operations research. Discussions cover related mathematical tools and the historical eras from which the applications are drawn. Each sec
See, Evan J.
Proton Exchange Membrane Fuel Cells (PEMFCs) have been an area of focus as an alternative for internal combustion engines in the transportation sector. Water and thermal management techniques remain as one of the key roadblocks in PEMFC development. The ability to model two-phase flow and pressure drop in PEMFCs is of significant importance to the performance and optimization of PEMFCs. This work provides a perspective on the numerous factors that affect the two-phase flow in the gas channels and presents a comprehensive pressure drop model through an extensive in situ fuel cell investigation. The study focused on low current density and low temperature operation of the cell, as these conditions present the most challenging scenario for water transport in the PEMFC reactant channels. Tests were conducted using two PEMFCs that were representative of the actual full scale commercial automotive geometry. The design of the flow fields allowed visual access to both cathode and anode sides for correlating the visual observations to the two-phase flow patterns and pressure drop. A total of 198 tests were conducted varying gas diffusion layer (GDL), inlet humidity, current density, and stoichiometry; this generated over 1500 average pressure drop measurements to develop and validate two-phase models. A two-phase 1+1 D modeling scheme is proposed that incorporates an elemental approach and control volume analysis to provide a comprehensive methodology and correlation for predicting two-phase pressure drop in PEMFC conditions. Key considerations, such as condensation within the channel, consumption of reactant gases, water transport across the membrane, and thermal gradients within the fuel cell, are reviewed and their relative importance illustrated. The modeling scheme is shown to predict channel pressure drop with a mean error of 10% over the full range of conditions and with a mean error of 5% for the primary conditions of interest. The model provides a unique and
Modeling two-phase flow with stochastic coalescence/breakage model
Park, Ki Sun
Gas-particle flows were modeled to account for coalescence and breakup of liquid metal oxide droplets dispersed within the gas phase. The one-way coupled population balance equation (PBE) describing the evolution of number concentration due to particle-particle interactions and aerodynamic forces was solved using the direct quadrature method of moments (DQMOM) along with Reynolds averaged Navier-Stokes equation (RANS). The turbulent feature was assessed by Wilcox's k-ω equations. The fast Eulerian method was used to assess the slip velocity of the dispersed phase which holds a significant inertia. Orthokinetic collision was considered under laminar and turbulent flow where the radial component of relative velocity between two colliding particles is a source of collision. Hydrodynamic and aerodynamic collision frequency functions for turbulent flow were obtained from prior studies and modified to take into account inertia of particles. For a general laminar movement of flow, hydrodynamic and aerodynamic collision frequency functions were derived for spherical particles. The laminar hydrodynamic collision frequency kernel was derived for application to high speed (high Reynolds number) flows. The inclusion of influence of multidimensional and mean flow behavior permits application to flows in which shear layers are present and high Reynolds number flow which necessitates inclusion of compressibility effects. The new model agrees well with prior incompressible formulations. Results indicate that the compressible part of new shearing collision frequency has a significant effect on the collision kernel due to the contraction and dilatation effects of a fluid element. The model was validated using historical data from particle collection experiments (and a correlation based on these data) in solid rocket motors. Considering the error bounds of correlation, the predicted mass mean diameter was in agreement with the measurements/correlation. Further validations performed
A Diffuse Interface Model for Incompressible Two-Phase Flow with Large Density Ratios
Xie, Yu
2016-10-04
In this chapter, we explore numerical simulations of incompressible and immiscible two-phase flows. The description of the fluid–fluid interface is introduced via a diffuse interface approach. The two-phase fluid system is represented by a coupled Cahn–Hilliard Navier–Stokes set of equations. We discuss challenges and approaches to solving this coupled set of equations using a stabilized finite element formulation, especially in the case of a large density ratio between the two fluids. Specific features that enabled efficient solution of the equations include: (i) a conservative form of the convective term in the Cahn–Hilliard equation which ensures mass conservation of both fluid components; (ii) a continuous formula to compute the interfacial surface tension which results in lower requirement on the spatial resolution of the interface; and (iii) a four-step fractional scheme to decouple pressure from velocity in the Navier–Stokes equation. These are integrated with standard streamline-upwind Petrov–Galerkin stabilization to avoid spurious oscillations. We perform numerical tests to determine the minimal resolution of spatial discretization. Finally, we illustrate the accuracy of the framework using the analytical results of Prosperetti for a damped oscillating interface between two fluids with a density contrast.
A two-scale second-order moment two-phase turbulence model for simulating dense gas-particle flows
Institute of Scientific and Technical Information of China (English)
Zhuoxiong Zeng; Lixing Zhou; Jian Zhang; Keren Wang
2005-01-01
A two-scale second-order moment two-phase turbulence model accounting for inter-particle collision is developed, based on the concepts of particle large-scale fluctuation due to turbulence and particle small-scale fluctuation due to collision and through a unified treatment of these two kinds of fluctuations. The proposed model is used to simulate gas-particle flows in a channel and in a downer. Simulation results are in agreement with the experimental results reported in references and are near the results obtained using the single-scale second-order moment two-phase turbulence model superposed with a particle collision model (USM-θ model)in most regions.
Sert, İsmail Ozan; Sezer-Uzol, Nilay
2016-09-01
Computational fluid dynamics simulations for initially hydro-dynamically fully developed laminar flow with nanofluids in a circular duct under constant wall temperature condition are performed with two-phase mixture model by using Fluent software. Thermal behaviors of the system are investigated for constant wall temperature condition for Al2O3/water nanofluid. Hamilton-Crosser model and the Brownian motion effect are used for the thermal conductivity model of nanofluid instead of the Fluent default model for mixtures which gives extraordinary high thermal conductivity values and is valid for macro systems. Also, thermal conductivity and viscosity of the base fluid are taken as temperature dependent. The effects of nanoparticle volume fraction, nanoparticle size, and inlet Peclet number on the heat transfer enhancement are investigated. The results are compared with single-phase results which give slightly lower heat transfer coefficient values than the results of two-phase mixture model.
Energy Technology Data Exchange (ETDEWEB)
Rascle, P.; El Amine, K. [Electricite de France (EDF), Direction des Etudes et Recherches, 92 - Clamart (France)
1997-12-31
We are interested in the numerical approximation of two-fluid models of nonequilibrium two-phase flows described by six balance equations. We introduce an original splitting technique of the system of equations. This technique is derived in a way such that single phase Riemann solvers may be used: moreover, it allows a straightforward extension to various and detailed exchange source terms. The properties of the fluids are first approached by state equations of ideal gas type and then extended to real fluids. For the construction of numerical schemes , the hyperbolicity of the full system is not necessary. When based on suitable kinetic unwind schemes, the algorithm can compute flow regimes evolving from mixture to single phase flows and vice versa. The whole scheme preserves the physical features of all the variables which remain in the set of physical states. Several stiff numerical tests, such as phase separation and phase transition are displayed in order to highlight the efficiency of the proposed method. The document is a PhD thesis divided in 6 chapters and two annexes. They are entitled: 1. - Introduction (in French), 2. - Two-phase flow, modelling and hyperbolicity (in French), 3. - A numerical method using upwind schemes for the resolution of two-phase flows without exchange terms (in English), 4. - A numerical scheme for one-phase flow of real fluids (in English), 5. - An upwind numerical for non-equilibrium two-phase flows (in English), 6. - The treatment of boundary conditions (in English), A.1. The Perthame scheme (in English) and A.2. The Roe scheme (in English). 136 refs. This document represents a PhD thesis in the speciality Applied Mathematics presented par Khalid El Amine to the Universite Paris 6.
Mathematical modeling in psychological researches
Directory of Open Access Journals (Sweden)
Aleksandra Zyolko
2013-04-01
Full Text Available The author considers the nature of mathematical modeling and its significance in psychological researches. The author distinguishes the types of mathematical models: deterministic, stochastic models and synergetic models. The system approach is proposed as an instrument of implementation of mathematical modelling in psychological research.
Mathematical models of hysteresis
Energy Technology Data Exchange (ETDEWEB)
NONE
1998-08-01
The ongoing research has largely been focused on the development of mathematical models of hysteretic nonlinearities with nonlocal memories. The distinct feature of these nonlinearities is that their current states depend on past histories of input variations. It turns out that memories of hysteretic nonlinearities are quite selective. Indeed, experiments show that only some past input extrema (not the entire input variations) leave their marks upon future states of hysteretic nonlinearities. Thus special mathematical tools are needed in order to describe nonlocal selective memories of hysteretic nonlinearities. The origin of such tools can be traced back to the landmark paper of Preisach. Their research has been primarily concerned with Preisach-type models of hysteresis. All these models have a common generic feature; they are constructed as superpositions of simplest hysteretic nonlinearities-rectangular loops. During the past four years, the study has been by and large centered around the following topics: (1) further development of Scalar and vector Preisach-type models of hysteresis; (2) experimental testing of Preisach-type models of hysteresis; (3) development of new models for viscosity (aftereffect) in hysteretic systems; (4) development of mathematical models for superconducting hysteresis in the case of gradual resistive transitions; (5) software implementation of Preisach-type models of hysteresis; and (6) development of new ideas which have emerged in the course of the research work. The author briefly describes the main scientific results obtained in the areas outlined above.
A two-phase fuzzy programming model for a complex bi-objective no-wait flow shop scheduling
Directory of Open Access Journals (Sweden)
Reza Tavakkoli-Moghaddam
2012-08-01
Full Text Available In this paper, we study no-wait flow shop problem where setup times depend on sequence of operations. The proposed problem considers sequence-independent removal times, release date with an additional assumption that there are some preliminary setup times. There are two objectives of weighted mean tardiness and makespan associated with the proposed model of this paper. We formulate the resulted problem as a mixed integer programming, where a two-phase fuzzy programming is implemented to solve the model. To examine the performance of the proposed model, we generate several sample data, randomly and compare the results with other methods. The preliminary results indicate that the proposed two-phase model of this paper performed relatively better than Zimmerman's single-phase fuzzy method.
Directory of Open Access Journals (Sweden)
Shamiria Ahmad
2013-01-01
Full Text Available A comparative study describing gas-phase propylene polymerization in fluidized-bed reactors using Ziegler-Natta catalyst is presented. The reactor behavior was explained using a two-phase model (which is based on principles of fluidization as well as simulation using the Aspen Polymers process simulator. The two-phase reactor model accounts for the emulsion and bubble phases which contain different portions of catalysts with the polymerization occurring in both phases. Both models predict production rate, molecular weight, polydispersity index (PDI and melt flow index (MFI of the polymer. We used both models to investigate the effect of important polymerization parameters, namely catalyst feed rate and hydrogen concentration, on the product polypropylene properties, such as production rate, molecular weight, PDI and MFI. Both the two-phase model and Aspen Polymers simulator showed good agreement in terms of production rate. However, the models differed in their predictions for weight-average molecular weight, PDI and MFI. Based on these results, we propose incorporating the missing hydrodynamic effects into Aspen Polymers to provide a more realistic understanding of the phenomena encountered in fluidized bed reactors for polyolefin production.
Finite mathematics models and applications
Morris, Carla C
2015-01-01
Features step-by-step examples based on actual data and connects fundamental mathematical modeling skills and decision making concepts to everyday applicability Featuring key linear programming, matrix, and probability concepts, Finite Mathematics: Models and Applications emphasizes cross-disciplinary applications that relate mathematics to everyday life. The book provides a unique combination of practical mathematical applications to illustrate the wide use of mathematics in fields ranging from business, economics, finance, management, operations research, and the life and social sciences.
Wang, W.; Zehner, B.; Böttcher, N.; Goerke, U.; Kolditz, O.
2013-12-01
Numerical modeling of the two-phase flow process in porous media for real applications, e.g. CO2 storage processes in saline aquifers, is computationally expensive due to the complexity and the non-linearity of the observed physical processes. In such modeling, a fine discretization of the considered domain is normally needed for a high degree of accuracy, and it leads to the requirement of extremely high computational resources. This work focuses on the parallel simulation of the two-phase flow process in porous media. The Galerkin finite element method is used to solve the governing equations. Based on the overlapping domain decomposition approach, the PETSc package is employed to parallelize the global equation assembly and the linear solver, respectively. A numerical model based on the real test site Ketzin in Germany is adopted for parallel computing. The model domain is discretized with more than four million tetrahedral elements. The parallel simulations are carried out on a Linux cluster with different number of cores. The obtained speedup shows a good scalability of the current parallel finite element approach of the two-phase flow modeling in geological CO2 storage applications.
Multi-scale diffuse interface modeling of multi-component two-phase flow with partial miscibility
Kou, Jisheng
2016-05-10
In this paper, we introduce a diffuse interface model to simulate multi-component two-phase flow with partial miscibility based on a realistic equation of state (e.g. Peng-Robinson equation of state). Because of partial miscibility, thermodynamic relations are used to model not only interfacial properties but also bulk properties, including density, composition, pressure, and realistic viscosity. As far as we know, this effort is the first time to use diffuse interface modeling based on equation of state for modeling of multi-component two-phase flow with partial miscibility. In numerical simulation, the key issue is to resolve the high contrast of scales from the microscopic interface composition to macroscale bulk fluid motion since the interface has a nanoscale thickness only. To efficiently solve this challenging problem, we develop a multi-scale simulation method. At the microscopic scale, we deduce a reduced interfacial equation under reasonable assumptions, and then we propose a formulation of capillary pressure, which is consistent with macroscale flow equations. Moreover, we show that Young-Laplace equation is an approximation of this capillarity formulation, and this formulation is also consistent with the concept of Tolman length, which is a correction of Young-Laplace equation. At the macroscopical scale, the interfaces are treated as discontinuous surfaces separating two phases of fluids. Our approach differs from conventional sharp-interface two-phase flow model in that we use the capillary pressure directly instead of a combination of surface tension and Young-Laplace equation because capillarity can be calculated from our proposed capillarity formulation. A compatible condition is also derived for the pressure in flow equations. Furthermore, based on the proposed capillarity formulation, we design an efficient numerical method for directly computing the capillary pressure between two fluids composed of multiple components. Finally, numerical tests
Su, Qian; Tan, Chao; Dong, Feng
2017-03-01
When measuring the phase fraction of oil–water two-phase flow with the ultrasound attenuation, the phase distribution and fraction have direct influence on the attenuation coefficient. Therefore, the ultrasound propagation at various phase fractions and distributions were investigated. Mechanism models describing phase fraction with the ultrasound attenuation coefficient were established by analyzing the interaction between ultrasound and two-phase flow by considering the scattering, absorption and diffusion effect. Experiments were performed to verify the theoretical analysis, and the test results gave good agreement with the theoretical analysis. When the dispersed phase fraction is low, the relationship between ultrasound attenuation coefficient and phase fraction is of monotonic linearity; at higher dispersed phase fraction, ultrasound attenuation coefficient presents an irregular response to the dispersed phase fraction. The presented mechanism models give reasonable explanations about the trend of ultrasound attenuation.
Drift flux modelling for a two-phase system in a flotation column
Energy Technology Data Exchange (ETDEWEB)
Vandenberghe, J.; Choung, J.; Xu, Z.; Masliyah, J. [Alberta Univ., Edmonton, AB (Canada). Dept. of Chemical and Materials Engineering
2005-04-01
Mineral and coal industries use flotation columns to improve recovery, upgrade products, save energy and reduce scale. Flotation columns are a proven process equipment that are adaptable to computer process control and offer flexible operation. Once gas is introduced to the bottom of the flotation column, bubbles form and rise throughout the pulp. Hydrophobic particles in the pulp attache to the bubbles, making the density of the bubble particle aggregates less than that of the medium. The bubble zone and the froth zone are the 2 main zones of a flotation column. This study applied the drift flux analysis to a wide range of operating conditions of a two-phase system column in order develop a better empirical relation that can predict the bubbly and froth zone characteristics. Tests were performed with process water taken from a bitumen extraction process at Syncrude Canada Limited with aqueous solutions having low concentrations of methyl isobutyl carbinol at 7.8 or 15.5 ppm. A new correlation for the drift flux system characteristic curve was discovered in this study. The new correlation is applicable for a bubble Reynolds number range of 5 to 70. The numerical equation for this correlation was presented. The bubble and froth zones have different hydrodynamics. Therefore, the method for calculating the Reynolds number in the bubble zone may not be suitable for the froth zone. Therefore, a new equation was proposed to accommodate a wider operating range. 16 refs., 1 tab., 13 figs.
One-Dimensional, Two-Phase Flow Modeling Toward Interpreting Motor Slag Expulsion Phenomena
Kibbey, Timothy P.
2012-01-01
Aluminum oxide slag accumulation and expulsion was previously shown to be a player in various solid rocket motor phenomena, including the Space Shuttle's Reusable Solid Rocket Motor (RSRM) pressure perturbation, or "blip," and phantom moment. In the latter case, such un ]commanded side accelerations near the end of burn have also been identified in several other motor systems. However, efforts to estimate the mass expelled during a given event have come up short. Either bulk calculations are performed without enough physics present, or multiphase, multidimensional Computational Fluid Dynamic analyses are performed that give a snapshot in time and space but do not always aid in grasping the general principle. One ]dimensional, two ]phase compressible flow calculations yield an analytical result for nozzle flow under certain assumptions. This can be carried further to relate the bulk motor parameters of pressure, thrust, and mass flow rate under the different exhaust conditions driven by the addition of condensed phase mass flow. An unknown parameter is correlated to airflow testing with water injection where mass flow rates and pressure are known. Comparison is also made to full ]scale static test motor data where thrust and pressure changes are known and similar behavior is shown. The end goal is to be able to include the accumulation and flow of slag in internal ballistics predictions. This will allow better prediction of the tailoff when much slag is ejected and of mass retained versus time, believed to be a contributor to the widely-observed "flight knockdown" parameter.
Authenticity of Mathematical Modeling
Tran, Dung; Dougherty, Barbara J.
2014-01-01
Some students leave high school never quite sure of the relevancy of the mathematics they have learned. They fail to see links between school mathematics and the mathematics of everyday life that requires thoughtful decision making and often complex problem solving. Is it possible to bridge the gap between school mathematics and the mathematics in…
Energy Technology Data Exchange (ETDEWEB)
Sharma, Subash L., E-mail: sharma55@purdue.edu [School of Nuclear Engineering, Purdue University, West Lafayette, IN 47907-1290 (United States); Hibiki, Takashi; Ishii, Mamoru [School of Nuclear Engineering, Purdue University, West Lafayette, IN 47907-1290 (United States); Brooks, Caleb S. [Department of Nuclear, Plasma, and Radiological Engineering, University of Illinois, Urbana, IL 61801 (United States); Schlegel, Joshua P. [Nuclear Engineering Program, Missouri University of Science and Technology, Rolla, MO 65409 (United States); Liu, Yang [Nuclear Engineering Program, Department of Mechanical Engineering, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061 (United States); Buchanan, John R. [Bechtel Marine Propulsion Corporation, Bettis Laboratory, West Mifflin, PA 15122 (United States)
2017-02-15
Highlights: • Void distribution in narrow rectangular channel with various non-uniform inlet conditions. • Modeling of void diffusion due to bubble collision force. • Validation of new modeling in adiabatic air–water two-phase flow in a narrow channel. - Abstract: The prediction capability of the two-fluid model for gas–liquid dispersed two-phase flow depends on the accuracy of the closure relations for the interfacial forces. In previous studies of two-phase flow Computational Fluid Dynamics (CFD), interfacial force models for a single isolated bubble has been extended to disperse two-phase flow assuming the effect in a swarm of bubbles is similar. Limited studies have been performed investigating the effect of the bubble concentration on the lateral phase distribution. Bubbles, while moving through the liquid phase, may undergo turbulence-driven random collision with neighboring bubbles without significant coalescence. The rate of these collisions depends upon the bubble approach velocity and bubble spacing. The bubble collision frequency is expected to be higher in locations with higher bubble concentrations, i.e., volume fraction. This turbulence-driven random collision causes the diffusion of the bubbles from high concentration to low concentration. Based on experimental observations, a phenomenological model has been developed for a “turbulence-induced bubble collision force” for use in the two-fluid model. For testing the validity of the model, two-phase flow data measured at Purdue University are utilized. The geometry is a 10 mm × 200 mm cross section channel. Experimentally, non-uniform inlet boundary conditions are applied with different sparger combinations to vary the volume fraction distribution across the wider dimension. Examining uniform and non-uniform inlet data allows for the influence of the volume fraction to be studied as a separate effect. The turbulence-induced bubble collision force has been implemented in ANSYS CFX. The
Wang, Lei; Sun, Jianglong
2017-08-01
An axisymmetric two-phase lattice Boltzmann method is applied to simulate the dewetting dynamics of a thin liquid film on a substrate. Initially, a circular dry spot exists in the center of the liquid film. A contact line forms around the dry spot and expands outwards. The liquid films dewetting on smooth and rough substrates are investigated. For a smooth substrate, the effects of the contact angle (θeq), Ohnesorge number (Oh), and viscosity ratio (λμ) are studied. It is observed that the contact line recedes with a constant velocity V and that if θeq > 45°, V has a linear relationship with θeq, which has never been mentioned in previous literatures. For a rough substrate, well-distributed pillars are set up to represent the roughness. There are two states for the liquid film dewetting on a rough substrate: Cassie and Wenzel states. By comparison, it is found that the speed of the liquid film dewetting on the rough substrate of the Cassie state is slightly faster than that on the smooth substrate but much faster than that on the rough substrate of the Wenzel state, i.e., Wenzel state can obviously hold back the movement of the receding contact line. The corresponding mechanism is analyzed. The effect of the geometric factors of the pillars on the dewetting speed is discussed in detail. It is indicated that both the width and the depth of the grooves in roughness can significantly affect the dewetting speed. The results are helpful to design structured substrates for controlling the dewetting process of the liquid film.
Examples of Mathematical Modeling
Johnston, Matthew D.; Edwards, Carina M.; Bodmer, Walter F.; Maini, Philip K.; Chapman, S. Jonathan
2008-01-01
Mathematical modeling is being increasingly recognized within the biomedical sciences as an important tool that can aid the understanding of biological systems. The heavily regulated cell renewal cycle in the colonic crypt provides a good example of how modeling can be used to find out key features of the system kinetics, and help to explain both the breakdown of homeostasis and the initiation of tumorigenesis. We use the cell population model by Johnston et al.5 to illustrate the power of mathematical modeling by considering two key questions about the cell population dynamics in the colonic crypt. We ask: how can a model describe both homeostasis and unregulated growth in tumorigenesis; and to which parameters in the system is the model most sensitive? In order to address these questions, we discuss what type of modeling approach is most appropriate in the crypt. We use the model to argue why tumorigenesis is observed to occur in stages with long lag phases between periods of rapid growth, and we identify the key parameters. PMID:17873520
Bourgeat, Alain; Smaï, Farid
2008-01-01
We derive a compositional compressible two-phase, liquid and gas, flow model for numerical simulations of hydrogen migration in deep geological repository for radioactive waste. This model includes capillary effects and the gas high diffusivity. Moreover, it is written in variables (total hydrogen mass density and liquid pressure) chosen in order to be consistent with gas appearance or disappearance. We discuss the well possedness of this model and give some computational evidences of its adequacy to simulate gas generation in a water saturated repository.
Moving Boudary Models for Dynamic Simulations of Two-phase Flows
DEFF Research Database (Denmark)
Jensen, Jakob Munch; Tummelscheit, H.
2002-01-01
-model and a discretized homogeneous model and the two responses are compared as well as the simulation time. The closed loop response of the evaporator controlled by a PID controller is shown using the MB model, and the control parameters are found. Finally some discussions are given on limitations and advantages of MB-models....
Numerical Simulations of Two-Phase Flow in a Self-Aerated Flotation Machine and Kinetics Modeling
Fayed, Hassan E.
2015-03-30
A new boundary condition treatment has been devised for two-phase flow numerical simulations in a self-aerated minerals flotation machine and applied to a Wemco 0.8 m3 pilot cell. Airflow rate is not specified a priori but is predicted by the simulations as well as power consumption. Time-dependent simulations of two-phase flow in flotation machines are essential to understanding flow behavior and physics in self-aerated machines such as the Wemco machines. In this paper, simulations have been conducted for three different uniform bubble sizes (db = 0.5, 0.7 and 1.0 mm) to study the effects of bubble size on air holdup and hydrodynamics in Wemco pilot cells. Moreover, a computational fluid dynamics (CFD)-based flotation model has been developed to predict the pulp recovery rate of minerals from a flotation cell for different bubble sizes, different particle sizes and particle size distribution. The model uses a first-order rate equation, where models for probabilities of collision, adhesion and stabilization and collisions frequency estimated by Zaitchik-2010 model are used for the calculation of rate constant. Spatial distributions of dissipation rate and air volume fraction (also called void fraction) determined by the two-phase simulations are the input for the flotation kinetics model. The average pulp recovery rate has been calculated locally for different uniform bubble and particle diameters. The CFD-based flotation kinetics model is also used to predict pulp recovery rate in the presence of particle size distribution. Particle number density pdf and the data generated for single particle size are used to compute the recovery rate for a specific mean particle diameter. Our computational model gives a figure of merit for the recovery rate of a flotation machine, and as such can be used to assess incremental design improvements as well as design of new machines.
Mathematical Modelling in European Education
Ferri, Rita Borromeo
2013-01-01
Teaching and learning of mathematical modelling has become a key competence within school curricula and educational standards in many countries of the world. The term mathematical modelling, its meaning, and how it can be implemented in mathematics lessons have been intensively discussed during several Conferences of the European Society for…
Institute of Scientific and Technical Information of China (English)
无
2002-01-01
A full second-order moment (FSM) model and an algebraic stress (ASM) two-phase turbulence modelare proposed and applied to predict turbulent bubble-liquid flows in a 2D rectangular bubble column. Predictiongives the bubble and liquid velocities, bubble volume fraction, bubble and liquid Reynolds stresses and bubble-liquidvelocity correlation. For predicted two-phase velocities and bubble volume fraction there is only slight differencebetween these two models, and the simulation results using both two models are in good agreement with the particleimage velocimetry (PIV) measurements. Although the predicted two-phase Reynolds stresses using the FSM are insomewhat better agreement with the PIV measurements than those predicted using the ASM, the Reynolds stressespredicted using both two models are in general agreement with the experiments. Therefore, it is suggested to usethe ASM two-phase turbulence model in engineering application for saving the computation time.
Two-phase flow with surfactants: Diffuse interface models and their analysis
Abels, Helmut; Lam, Kei Fong; Weber, Josef
2016-01-01
New diffuse interface and sharp interface models for soluble and insoluble surfactants fulfilling energy inequalities are introduced. We discuss their relation with the help of asymptotic analysis and present an existence result for a particular diffuse interface model.
Kou, Jisheng
2016-01-01
A general diffuse interface model with a realistic equation of state (e.g. Peng-Robinson equation of state) is proposed to describe the multi-component two-phase fluid flow based on the principles of the NVT-based framework which is a latest alternative over the NPT-based framework to model the realistic fluids. The proposed model uses the Helmholtz free energy rather than Gibbs free energy in the NPT-based framework. Different from the classical routines, we combine the first law of thermodynamics and related thermodynamical relations to derive the entropy balance equation, and then we derive a transport equation of the Helmholtz free energy density. Furthermore, by using the second law of thermodynamics, we derive a set of unified equations for both interfaces and bulk phases that can describe the partial miscibility of two fluids. A relation between the pressure gradient and chemical potential gradients is established, and this relation leads to a new formulation of the momentum balance equation, which dem...
Validation of Wall Friction Model in SPACE-3D Module with Two-Phase Cross Flow Experiment
Energy Technology Data Exchange (ETDEWEB)
Choi, Chi-Jin; Yang, Jin-Hwa; Cho, Hyoung-Kyu; Park, Goon-Cher [Seoul National University, Seoul (Korea, Republic of); Euh, Dong-Jin [Korea Atomic Energy Research Institute, Daejeon (Korea, Republic of)
2015-10-15
In this study, SPACE-3D was used to simulate the Yang's experiment, and obtained the local variables. Then, the wall friction model used in SPACE-3D was validated by comparing the two-phase cross flow experimental results with the calculated local variables. In this study, the two-phase cross flow experiment was modeled by SPACE-3D to validate the wall friction model in multi-dimensional module. Considering the realistic phenomena in the reactor, however, recent trends in safety analysis codes have tended to adopt multi-dimensional module to simulate the complex flow more accurately. Even though the module was applied to deal the multi-dimensional phenomena, implemented models in that are one-dimensional empirical models. Therefore, prior to applying the multi-dimensional module, the constitutive models implemented in the codes need to be validated. In the downcomer of Advanced Power Reactor 1400 (APR1400) which has direct vessel injection (DVI) lines as an emergency core cooling system, multi-dimensional two-phase flow may occur due to the Loss-of-Coolant-Accident (LOCA). The accurate prediction about that is high relevance to evaluation of the integrity of the reactor core. For this reason, Yang performed an experiment that was to investigate the two-dimensional film flow which simulated the two-phase cross flow in the upper downcomer, and obtained the local liquid film velocity and thickness data. From these data, it could be possible to validate the friction models in multi-dimensional module of system analysis codes. Compared with the experiment, SPACE-3D underestimated the liquid film velocity and overestimated the liquid film thickness. From these results, it was clarified that the Wallis correlation which is used as a wall friction model in SPACE-3D overestimates the wall friction. On the other hand, H.T.F.S. correlation which is used as the wall friction in MARS-multiD underestimates the wall friction.
Directory of Open Access Journals (Sweden)
R.A.G. Sé
2002-04-01
Full Text Available The NRTL (nonrandom, two-liquid model, expressed in mass fraction instead of mole fraction, was used to correlate liquid-liquid equilibria for aqueous two-phase polymer-salt solutions. New interaction energy parameters for this model were determined using reported data on the water + poly(ethylene glycol + salt systems, with different molecular masses for PEG and the salts potassium phosphate, sodium sulfate, sodium carbonate and magnesium sulfate. The correlation of liquid-liquid equilibrium is quite satisfactory.
Institute of Scientific and Technical Information of China (English)
王经明; 李竞生; 高智联; 杨保禹
1998-01-01
This study is concerned with developing a two-dimensional two-phase model thatsimulate the movement of non-aqueous phase liquid (NAPL) in a fracture-rock matrix system. Theintrinsic permeability and the fracture aperture are represented in the model via its Karhunen-Loeve expansion. Other parameters and the nodal unknowns, water saturations and waterpressures, are represented by their stochastic spectral expanions. The errors resulting fromtruncation of Karhunen - Loeve and polynomial chaos expansions to a finite number of terms areanalyzed. The eigenvalues of stochastic process is found out for any point in the special domain ofthe problem at any instant in time.
Directory of Open Access Journals (Sweden)
Zheng Miao
2014-04-01
Full Text Available The transport phenomena in a passive direct methanol fuel cell (DMFC were numerically simulated by the proposed two-dimensional two-phase nonisothermal mass transport model. The anisotropic transport characteristic and deformation of the gas diffusion layer (GDL were considered in this model. The natural convection boundary conditions were adopted for the transport of methanol, oxygen, and heat at the GDL outer surface. The effect of methanol concentration in the reservoir on cell performance was examined. The distribution of multiphysical fields in the membrane electrode assembly (MEA, especially in the catalyst layers (CLs, was obtained and analyzed. The results indicated that transport resistance for the methanol mainly existed in the MEA while that for oxygen and heat was primarily due to natural convection at the GDL outer surface. Because of the relatively high methanol concentration, the local reaction rate in CLs was mainly determined by the overpotential. Methanol concentration between 3 M and 4 M was recommended for passive liquid feed DMFC in order to achieve a balance between the cell performance and the methanol crossover.
Weigand, T. M.; Miller, C. T.; Dye, A. L.; Gray, W. G.; McClure, J. E.; Rybak, I.
2015-12-01
The thermodynamically constrained averaging theory (TCAT) has been usedto formulate general classes of porous medium models, including newmodels for two-fluid-phase flow. The TCAT approach provides advantagesthat include a firm connection between the microscale, or pore scale,and the macroscale; a thermodynamically consistent basis; explicitinclusion of factors such as interfacial areas, contact angles,interfacial tension, and curvatures; and dynamics of interface movementand relaxation to an equilibrium state. In order to render the TCATmodel solvable, certain closure relations are needed to relate fluidpressure, interfacial areas, curvatures, and relaxation rates. In thiswork, we formulate and solve a TCAT-based two-fluid-phase flow model. We detail the formulation of the model, which is a specific instancefrom a hierarchy of two-fluid-phase flow models that emerge from thetheory. We show the closure problem that must be solved. Using recentresults from high-resolution microscale simulations, we advance a set ofclosure relations that produce a closed model. Lastly, we solve the model using a locally conservative numerical scheme and compare the TCAT model to the traditional model.
A Multiscale Diffuse-Interface Model for Two-Phase Flow in Porous Media
Roudbari, Mahnaz Shokrpour; Verhoosel, Clemens V
2016-01-01
In this paper we consider a multiscale phase-field model for capillarity-driven flows in porous media. The presented model constitutes a reduction of the conventional Navier-Stokes-Cahn-Hilliard phase-field model, valid in situations where interest is restricted to dynamical and equilibrium behavior in an aggregated sense, rather than a precise description of microscale flow phenomena. The model is based on averaging of the equation of motion, thereby yielding a significant reduction in the complexity of the underlying Navier-Stokes-Cahn-Hilliard equations, while retaining its macroscopic dynamical and equilibrium properties. Numerical results are presented for the representative 2-dimensional capillary-rise problem pertaining to two closely spaced vertical plates with both identical and disparate wetting properties. Comparison with analytical solutions for these test cases corroborates the accuracy of the presented multiscale model. In addition, we present results for a capillary-rise problem with a non-triv...
Arbogast, Todd
2012-01-01
Motivated by possible generalizations to more complex multiphase multicomponent systems in higher dimensions, we develop an Eulerian-Lagrangian numerical approximation for a system of two conservation laws in one space dimension modeling a simplified two-phase flow problem in a porous medium. The method is based on following tracelines, so it is stable independent of any CFL constraint. The main difficulty is that it is not possible to follow individual tracelines independently. We approximate tracing along the tracelines by using local mass conservation principles and self-consistency. The two-phase flow problem is governed by a system of equations representing mass conservation of each phase, so there are two local mass conservation principles. Our numerical method respects both of these conservation principles over the computational mesh (i.e., locally), and so is a fully conservative traceline method. We present numerical results that demonstrate the ability of the method to handle problems with shocks and rarefactions, and to do so with very coarse spatial grids and time steps larger than the CFL limit. © 2012 Society for Industrial and Applied Mathematics.
Marrone, Salvatore; Colagrossi, Andrea; Di Mascio, Andrea; Le Touzé, David
2016-05-01
The study of energetic free-surface flows is challenging because of the large range of interface scales involved due to multiple fragmentations and reconnections of the air-water interface with the formation of drops and bubbles. Because of their complexity the investigation of such phenomena through numerical simulation largely increased during recent years. Actually, in the last decades different numerical models have been developed to study these flows, especially in the context of particle methods. In the latter a single-phase approximation is usually adopted to reduce the computational costs and the model complexity. While it is well known that the role of air largely affects the local flow evolution, it is still not clear whether this single-phase approximation is able to predict global flow features like the evolution of the global mechanical energy dissipation. The present work is dedicated to this topic through the study of a selected problem simulated with both single-phase and two-phase models. It is shown that, interestingly, even though flow evolutions are different, energy evolutions can be similar when including or not the presence of air. This is remarkable since, in the problem considered, with the two-phase model about half of the energy is lost in the air phase while in the one-phase model the energy is mainly dissipated by cavity collapses.
Li, Jianying; Li, Haiyan; Fok, Alex S L; Watts, David C
2012-09-01
The aim of this study was to numerically evaluate the effects of filler contents and resin properties on the material properties of dental composites utilizing realistic 3D micromechanical finite element models. 3D micromechanical finite element models of dental composites containing irregular fillers with non-uniform sizes were created based on a large-scale, surrogate mixture fabricated from irregularly shaped stones and casting resin. The surrogate mixture was first scanned with a micro-CT scanner, and the images reassembled to produce a 3D finite element model. Different filler fractions were achieved by adjusting the matrix volume while keeping the fillers unchanged. Polymerization shrinkage, Young's modulus, Poisson's ratio and viscosity of the model composites were predicted using the finite element models, and their dependence on the filler fraction and material properties of the resin matrix were considered. Comparison of the numerical predictions with available experimental data and analytical models from the literature was performed. Increased filler fraction resulted in lower material shrinkage, higher Young's modulus, lower Poisson's ratio and higher viscosity in the composite. Predicted shrinkage and Young's modulus agreed well with the experimental data and analytical predictions. The McGee-McCullough model best fit the shrinkage and Young's modulus predicted by the finite element method. However, a new parameter, used as the exponent of the filler fraction, had to be introduced to the McGee-McCullough model to better match the predicted viscosity and Poisson's ratio with those from the finite element analysis. Realistic micro-structural finite element models were successfully applied to study the effects of filler fraction and matrix properties on a wide range of mechanical properties of dental composites with irregular fillers. The results can be used to direct the design of such materials to achieve the desired mechanical properties. Published by
Two-phase flow modeling for low concentration spherical particle motion through a Newtonian fluid
CSIR Research Space (South Africa)
Smit GJF
2010-11-01
Full Text Available number is given by Re ? qf eds l kv f � v sk; ?9? and a = 2.65[10]; a = 2.70[11]; a = 2.78[9]. The equation developed by Lewis et al. [10] is usually adopted as a default correlation in commercial CFD codes when the void fraction of the suspension... with the Ergun equation, as illustrated in Fig. 8. As expected, the model of Lewis et al. [10], over-predicts the momentum transfer coefficient as the particular void fraction falls outside the model?s range of applicability. Fig. 9 shows that the predicted...
A thermodynamically consistent phase-field model for two-phase flows with thermocapillary effects
Guo, Zhenlin
2014-01-01
In this paper, we develop a phase-field model for binary incompressible fluid with thermocapillary effects, which allows the different properties (densities, viscosities and heat conductivities) for each component and meanwhile maintains the thermodynamic consistency. The governing equations of the model including the Navier-Stokes equations, Cahn-Hilliard equations and energy balance equation are derived together within a thermodynamic framework based on the entropy generation, which guarantees the thermodynamic consistency. The sharp-interface limit analysis is carried out to show that the interfacial conditions of the classical sharp-interface models can be recovered from our phase-field model. Moreover, some numerical examples including thermocapillary migration of a bubble and thermocapillary convections in a two- layer fluid system are computed by using a continuous finite element method. The results are compared to the existing analytical solutions and theoretical predictions as validations for our mod...
Modeling Two-Phase Flow and Vapor Cycles Using the Generalized Fluid System Simulation Program
Smith, Amanda D.; Majumdar, Alok K.
2017-01-01
This work presents three new applications for the general purpose fluid network solver code GFSSP developed at NASA's Marshall Space Flight Center: (1) cooling tower, (2) vapor-compression refrigeration system, and (3) vapor-expansion power generation system. These systems are widely used across engineering disciplines in a variety of energy systems, and these models expand the capabilities and the use of GFSSP to include fluids and features that are not part of its present set of provided examples. GFSSP provides pressure, temperature, and species concentrations at designated locations, or nodes, within a fluid network based on a finite volume formulation of thermodynamics and conservation laws. This paper describes the theoretical basis for the construction of the models, their implementation in the current GFSSP modeling system, and a brief evaluation of the usefulness of the model results, as well as their applicability toward a broader spectrum of analytical problems in both university teaching and engineering research.
Teague, J. W., II
1981-08-01
The code was designed to calculate mass fluxes and mass flux standard deviations, as well as certain other fluid physical properties. Several models are used to compute mass fluxes and uncertainties since some models provide more reliable results than others under certain flow situations. The program was specifically prepared to compute these variables using data gathered from spoolpiece instrumentation on the Thermal-Hydraulic Test Facility (THTF) and written to an Engineering Units (EU) data set.
Phase-field model for the two-phase lithiation of silicon
Gao, Fangliang; Hong, Wei
2016-09-01
As an ideal anode material, silicon has the highest lithium-ion capacity in theory, but the broader application is limited by the huge volumetric strain caused by lithium insertion and extraction. To better understand the physical process and to resolve the related reliability issue, enormous efforts have been made. Recent experiments observed sharp reaction fronts in both crystalline and amorphous silicon during the first lithiation half-cycle. Such a concentration profile indicates that the process is likely to be reaction limited. Based on this postulation, a phase-field model is developed and implemented into a finite-element code to simulate the coupled large inelastic deformation and motion of the reaction front in a silicon electrode. In contrast to most existing models, the model treats both volumetric and deviatoric inelastic deformation in silicon as a direct consequence of the lithiation at the reaction front. The amount of deviatoric deformation is determined by using the recently developed kinetic model of stress-induced anisotropic reaction. By considering the role of stress in the lithiation process, this model successfully recovers the self-limiting phenomenon of silicon electrodes, and relates it to the local geometry of electrodes. The model is also used to evaluate the energy-release rate of the surface crack on a spherical electrode, and the result suggests a critical size of silicon nanoparticles to avert fracture. As examples, the morphology evolution of a silicon disk and a Si nanowire during lithiation are also investigated.
Two-phase numerical model for thermal conductivity and convective heat transfer in nanofluids.
Kondaraju, Sasidhar; Lee, Joon Sang
2011-03-21
Due to the numerous applications of nanofluids, investigating and understanding of thermophysical properties of nanofluids has currently become one of the core issues. Although numerous theoretical and numerical models have been developed by previous researchers to understand the mechanism of enhanced heat transfer in nanofluids; to the best of our knowledge these models were limited to the study of either thermal conductivity or convective heat transfer of nanofluids. We have developed a numerical model which can estimate the enhancement in both the thermal conductivity and convective heat transfer in nanofluids. It also aids in understanding the mechanism of heat transfer enhancement. The study reveals that the nanoparticle dispersion in fluid medium and nanoparticle heat transport phenomenon are equally important in enhancement of thermal conductivity. However, the enhancement in convective heat transfer was caused mainly due to the nanoparticle heat transport mechanism. Ability of this model to be able to understand the mechanism of convective heat transfer enhancement distinguishes the model from rest of the available numerical models.
Cheng, Z.; Hsu, T. J.; Chauchat, J.; Revil-Baudard, T.
2016-12-01
Coastal morphological evolution is caused by a wide range of coupled cross-shore and alongshore sediment transport processes associated with short waves, infragravity waves and wave-induced currents. However, the fundamental transport mechanisms occur within the thin bottom boundary layer and are dictated by turbulence-sediment interaction and inter-granular interactions. Recently, a turbulence-averaged two-phase Eulerian sediment transport model, called sedFoam, was developed and validated for U-tube sheet flows (Cheng et al., 2016). With closures of particle stresses and fluid-particle interactions, the model is able to resolve full profiles of sediment transport from the immobile bed, to the concentrated near-bed transport layer and up to dilute transport without conventional bedload/suspended load assumptions. In this study, we further extend this model with a 3D large eddy simulation (LES) approach, where substantial amount of the turbulence-sediment interaction is directly resolved. In the present LES model, a dynamic Smagorinsky sub-grid stress closure is adopted for both fluid and sediment phases, and the sub-grid contribution to the fluid-particle interactions is included by a sub-grid drift velocity in drag model (Ozel et al., 2013). The model is validated with high-resolution measurements in a unidirectional steady sheet flow experiment (Revil-Baudard et al. 2015). We further apply the LES Eulerian two-phase model to medium and fine sand in oscillatory sheet flows (O'Donoghue & Wright, 2004). The LES model performance for the medium sand is similar to the turbulence-averaged model, except that the LES model seems to be superior to the turbulence-averaged model during acceleration and decelerating phases. In addition, the LES model is able to capture the enhanced transport layer thickness for fine sand, which may be related to the burst events near the flow reversal. We further confirm that this phenomenon is absent for medium sand.
Bottoni, M.; Struwe, D.
The theoretical background of the BLOW-3A program is reported, including the basic equations used to determine temperature fields in the fuel, clad, coolant and structure material as well as the coolant dynamics in single and two-phase flow conditions. The two-phase flow model assumes an annular flow regime. Special aspects to calculate two-phase pressure drops for these conditions are discussed. Examples of the experimental validation of the program are given.
A Well-Posed Two Phase Flow Model and its Numerical Solutions for Reactor Thermal-Fluids Analysis
Energy Technology Data Exchange (ETDEWEB)
Kadioglu, Samet Y. [Idaho National Lab. (INL), Idaho Falls, ID (United States); Berry, Ray [Idaho National Lab. (INL), Idaho Falls, ID (United States); Martineau, Richard [Idaho National Lab. (INL), Idaho Falls, ID (United States)
2016-08-01
A 7-equation two-phase flow model and its numerical implementation is presented for reactor thermal-fluids applications. The equation system is well-posed and treats both phases as compressible flows. The numerical discretization of the equation system is based on the finite element formalism. The numerical algorithm is implemented in the next generation RELAP-7 code (Idaho National Laboratory (INL)’s thermal-fluids code) built on top of an other INL’s product, the massively parallel multi-implicit multi-physics object oriented code environment (MOOSE). Some preliminary thermal-fluids computations are presented.
Deng, Hongling; Koyi, Hemin A.; Nilfouroushan, Faramarz
2016-02-01
Orogens may suffer more than one phase shortening resulting in superposition of structures of different generations. Superimposition of orthogonal or oblique shortening is studied using sandbox and centrifuge modelling. Results of sand models show that in orthogonal superimposition, the two resulting structural trends are approximately orthogonal to each other. In oblique superimposition, structures trend obliquely to each other in the relatively thin areas of the model (foreland), and mutually orthogonal in areas where the model is thickened during the first phase of shortening (i.e. the hinterland). Thrusts formed during the first shortening phase may be reactivated during the later shortening phase. Spacing of the later phase structures is not as wide as expected, considering they across the pre-existing thickened wedge. Superposition of structures results in formation of type 1 fold interference pattern. Bedding is curved outwards both in the dome and basin structures. Folded layers are dipping and plunging outwards in a dome, while they are dipping and plunging inwards in a basin. In the areas between two adjacent domes or basins (i.e. where an anticline is superimposed by a syncline or a syncline is superimposed by an anticline), bedding is curved inwards, and the anticlines plunge inwards and the synclines outwards. The latter feature could be helpful to determine the age relationship for type 2 fold interference pattern. In tectonic regions where multiple phases of shortening have occurred, the orogenic-scale dome-and-basin and arrowhead-shaped interference patterns are commonly formed, as in the models. However, in some areas, the fold interference pattern might be modified by a later phase of thrusting. Similar to models results, superimposition of two and/or even more deformation phases may not be recorded by structures all over the tectonic area.
DAM-BREAK SHOCK WAVES WITH FLOATING DEBRIS: EXPERIMENTALANALYSIS AND TWO-PHASE MODELLING
Stefano Mambretti; Daniele De Wrachien; Enrico Larcan
2008-01-01
To predict floods and debris flow dynamics a numerical model, based on 1D De Saint Venant (SV) equations, was developed. The McCormack – Jameson shock capturing scheme was employed for the solution of the equations, written in a conservative law form. This technique was applied to determine both the propagation and the profile of a two – phase debris flow resulting from the instantaneous and complete collapse of a storage dam. To validate the model, comparisons have been made between its pred...
Mathematical modeling with multidisciplinary applications
Yang, Xin-She
2013-01-01
Features mathematical modeling techniques and real-world processes with applications in diverse fields Mathematical Modeling with Multidisciplinary Applications details the interdisciplinary nature of mathematical modeling and numerical algorithms. The book combines a variety of applications from diverse fields to illustrate how the methods can be used to model physical processes, design new products, find solutions to challenging problems, and increase competitiveness in international markets. Written by leading scholars and international experts in the field, the
DAM-BREAK SHOCK WAVES WITH FLOATING DEBRIS: EXPERIMENTALANALYSIS AND TWO-PHASE MODELLING
Directory of Open Access Journals (Sweden)
Stefano Mambretti
2008-06-01
Full Text Available To predict floods and debris flow dynamics a numerical model, based on 1D De Saint Venant (SV equations, was developed. The McCormack – Jameson shock capturing scheme was employed for the solution of the equations, written in a conservative law form. This technique was applied to determine both the propagation and the profile of a two – phase debris flow resulting from the instantaneous and complete collapse of a storage dam. To validate the model, comparisons have been made between its predictions and laboratory measurements concerning flows of water and homogeneous granular mixtures in a uniform geometry flume reproducing dam – break waves. Agreements between computational and experimental results are considered very satisfactory for mature (non – stratified debris flows, which embrace most real cases. To better predict immature (stratified flows, the model should be improved in order to feature, in a more realistic way, the distribution of the particles of different size within the mixture. On the whole, the model proposed can easily be extended to channels with arbitrary cross sections for debris flow routing, as well as for solving different problems of unsteady flow in open channels by incorporating the appropriate initial and boundary conditions.
Three-dimensional lattice Boltzmann model for immiscible two-phase flow simulations.
Liu, Haihu; Valocchi, Albert J; Kang, Qinjun
2012-04-01
We present an improved three-dimensional 19-velocity lattice Boltzmann model for immisicible binary fluids with variable viscosity and density ratios. This model uses a perturbation step to generate the interfacial tension and a recoloring step to promote phase segregation and maintain surfaces. A generalized perturbation operator is derived using the concept of a continuum surface force together with the constraints of mass and momentum conservation. A theoretical expression for the interfacial tension is determined directly without any additional analysis and assumptions. The recoloring algorithm proposed by Latva-Kokko and Rothman is applied for phase segregation, which minimizes the spurious velocities and removes lattice pinning. This model is first validated against the Laplace law for a stationary bubble. It is found that the interfacial tension is predicted well for density ratios up to 1000. The model is then used to simulate droplet deformation and breakup in simple shear flow. We compute droplet deformation at small capillary numbers in the Stokes regime and find excellent agreement with the theoretical Taylor relation for the segregation parameter β=0.7. In the limit of creeping flow, droplet breakup occurs at a critical capillary number 0.35Droplet breakup can also be promoted by increasing the Reynolds number. Finally, we numerically investigate a single bubble rising under buoyancy force in viscous fluids for a wide range of Eötvös and Morton numbers. Numerical results are compared with theoretical predictions and experimental results, and satisfactory agreement is shown.
Mesoscopic modeling of a two-phase flow in the presence of boundaries: The contact angle
Benzi, R.; Biferale, L.; Sbragaglia, M.; Succi, S.; Toschi, F.
2006-01-01
We present a mesoscopic model, based on the Boltzmann equation, for the interaction between a solid wall and a nonideal fluid. We present an analytic derivation of the contact angle in terms of the surface tension between the liquid-gas, the liquid-solid, and the gas-solid phases. We study the depen
Pore-scale modeling of moving contact line problems in immiscible two-phase flow
Kucala, Alec; Noble, David; Martinez, Mario
2016-11-01
Accurate modeling of moving contact line (MCL) problems is imperative in predicting capillary pressure vs. saturation curves, permeability, and preferential flow paths for a variety of applications, including geological carbon storage (GCS) and enhanced oil recovery (EOR). Here, we present a model for the moving contact line using pore-scale computational fluid dynamics (CFD) which solves the full, time-dependent Navier-Stokes equations using the Galerkin finite-element method. The MCL is modeled as a surface traction force proportional to the surface tension, dependent on the static properties of the immiscible fluid/solid system. We present a variety of verification test cases for simple two- and three-dimensional geometries to validate the current model, including threshold pressure predictions in flows through pore-throats for a variety of wetting angles. Simulations involving more complex geometries are also presented to be used in future simulations for GCS and EOR problems. Sandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the United States Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000.
Two-phase air-water flows:Scale effects in physical modeling
Institute of Scientific and Technical Information of China (English)
PFISTER Michael; CHANSON Hubert
2014-01-01
Physical modeling represents probably the oldest design tool in hydraulic engineering together with analytical approaches. In free surface flows, the similitude based upon a Froude similarity allows for a correct representation of the dominant forces, namely gravity and inertia. As a result fluid flow properties such as the capillary forces and the viscous forces might be incorrectly reproduced, affecting the air entrainment and transport capacity of a high-speed model flow. Small physical models operating under a Froude similitude systematically underestimate the air entrainment rate and air-water interfacial properties. To limit scale effects, minimal values of Reynolds or Weber number have to be respected. The present article summarizes the physical background of such limitations and their combination in terms of the Morton number. Based upon a literature review, the existing limits are presented and discussed, resulting in a series of more conservative recommendations in terms of air concentration scaling. For other air-water flow parameters, the selection of the criteria to assess scale effects is critical because some parameters (e.g., bubble sizes, turbulent scales) can be affected by scale effects, even in relatively large laboratory models.
Flow past a permeable stretching/shrinking sheet in a nanofluid using two-phase model.
Directory of Open Access Journals (Sweden)
Khairy Zaimi
Full Text Available The steady two-dimensional flow and heat transfer over a stretching/shrinking sheet in a nanofluid is investigated using Buongiorno's nanofluid model. Different from the previously published papers, in the present study we consider the case when the nanofluid particle fraction on the boundary is passively rather than actively controlled, which make the model more physically realistic. The governing partial differential equations are transformed into nonlinear ordinary differential equations by a similarity transformation, before being solved numerically by a shooting method. The effects of some governing parameters on the fluid flow and heat transfer characteristics are graphically presented and discussed. Dual solutions are found to exist in a certain range of the suction and stretching/shrinking parameters. Results also indicate that both the skin friction coefficient and the local Nusselt number increase with increasing values of the suction parameter.
CFD Modeling of Wall Steam Condensation: Two-Phase Flow Approach versus Homogeneous Flow Approach
Directory of Open Access Journals (Sweden)
S. Mimouni
2011-01-01
Full Text Available The present work is focused on the condensation heat transfer that plays a dominant role in many accident scenarios postulated to occur in the containment of nuclear reactors. The study compares a general multiphase approach implemented in NEPTUNE_CFD with a homogeneous model, of widespread use for engineering studies, implemented in Code_Saturne. The model implemented in NEPTUNE_CFD assumes that liquid droplets form along the wall within nucleation sites. Vapor condensation on droplets makes them grow. Once the droplet diameter reaches a critical value, gravitational forces compensate surface tension force and then droplets slide over the wall and form a liquid film. This approach allows taking into account simultaneously the mechanical drift between the droplet and the gas, the heat and mass transfer on droplets in the core of the flow and the condensation/evaporation phenomena on the walls. As concern the homogeneous approach, the motion of the liquid film due to the gravitational forces is neglected, as well as the volume occupied by the liquid. Both condensation models and compressible procedures are validated and compared to experimental data provided by the TOSQAN ISP47 experiment (IRSN Saclay. Computational results compare favorably with experimental data, particularly for the Helium and steam volume fractions.
Energy Technology Data Exchange (ETDEWEB)
Lage, Antonio C.V.M. [PETROBRAS, Rio de Janeiro, RJ (Brazil); Froyen, Johnny; Saevareid, Ove; Fjelde, Kjell K. [RF-Rogaland Research, Stavanger (Norway)
2000-07-01
A dynamic model, based on the drift-flux formulation, is presented for treating transient phenomena in UBD operations. A set of mechanistic steady state procedures for dealing with the definition of flow patterns, pressure drops, gas volumetric fractions, and in-situ velocities completes the model. The iteration between those mechanistic laws and the conservation equations is discussed. Two distinct strategies for solving numerically the resultant set of partial differential equations are presented. The first numerical approach is based on the use of a composite explicit scheme that consists of combining the second order McCormick and the first order Lax-Friedrichs methods while the other one is an improved form of the classical semi-implicit formulation. Both computer codes are validated through comparison to full-scale experimental data in transient scenarios. First, the model simulates the injection of a high velocity single pulse of a gas-liquid mixture. Further, a typical unloading scenario in an under balanced operation is studied. Measured variables as pressure and returning liquid and gas rates at surface are compared to the predicted ones. Finally, the study addresses a comparison between the performances of the numerical methods based on some relevant variables such as the grid refinement, the required computational time and the accuracy of the numerical approximation. (author)
Afrizal, Irfan Mufti; Dachlan, Jarnawi Afghani
2017-05-01
The aim of this study was to determine design of mathematical models of teaching materials to improve students' mathematical connection ability and mathematical disposition in middle school through experimental studies. The design in this study was quasi-experimental with non-equivalent control group type. This study consisted of two phases, the first phase was identify students' learning obstacle on square and rectangle concepts to obtain the appropriate design of teaching materials, beside that there were internalization of the values or characters expected to appear on students through the teaching materials. Second phase was experiments on the effectiveness and efficiency of mathematical models of teaching materials to improve students' mathematical connection ability and mathematical disposition. The result of this study are 1) Students' learning obstacle that have identified was categorized as an epistemological obstacle. 2) The improvement of students' mathematical connection ability and mathematical disposition who used mathematical teaching materials is better than the students who used conventional learning.
Bieliński, Henryk
2016-09-01
The current paper presents the experimental validation of the generalized model of the two-phase thermosyphon loop. The generalized model is based on mass, momentum, and energy balances in the evaporators, rising tube, condensers and the falling tube. The theoretical analysis and the experimental data have been obtained for a new designed variant. The variant refers to a thermosyphon loop with both minichannels and conventional tubes. The thermosyphon loop consists of an evaporator on the lower vertical section and a condenser on the upper vertical section. The one-dimensional homogeneous and separated two-phase flow models were used in calculations. The latest minichannel heat transfer correlations available in literature were applied. A numerical analysis of the volumetric flow rate in the steady-state has been done. The experiment was conducted on a specially designed test apparatus. Ultrapure water was used as a working fluid. The results show that the theoretical predictions are in good agreement with the measured volumetric flow rate at steady-state.
Mathematical modeling in chronobiology.
Bordyugov, G; Westermark, P O; Korenčič, A; Bernard, S; Herzel, H
2013-01-01
Circadian clocks are autonomous oscillators entrained by external Zeitgebers such as light-dark and temperature cycles. On the cellular level, rhythms are generated by negative transcriptional feedback loops. In mammals, the suprachiasmatic nucleus (SCN) in the anterior part of the hypothalamus plays the role of the central circadian pacemaker. Coupling between individual neurons in the SCN leads to precise self-sustained oscillations even in the absence of external signals. These neuronal rhythms orchestrate the phasing of circadian oscillations in peripheral organs. Altogether, the mammalian circadian system can be regarded as a network of coupled oscillators. In order to understand the dynamic complexity of these rhythms, mathematical models successfully complement experimental investigations. Here we discuss basic ideas of modeling on three different levels (1) rhythm generation in single cells by delayed negative feedbacks, (2) synchronization of cells via external stimuli or cell-cell coupling, and (3) optimization of chronotherapy.
A Dynamic Two-Phase Pore-Scale Model of Imbibition
DEFF Research Database (Denmark)
Mogensen, Kristian; Stenby, Erling Halfdan
1998-01-01
We present a dynamic pore-scale network model of imbibition, capable of calculating residual oil saturation for any given capillary number, viscosity ratio, contact angle, and aspect ratio. Our goal is not to predict the outcome of core floods, but rather to perform a sensitivity analysis...... of the above-mentioned parameters, except from the viscosity ratio. We find that contact angle, aspect ratio, and capillary number all have a significant influence on the competition between piston-lice advance, leading to high recovery, and snap-off, causing oil entrapment. Due to significant CPU...
CTH Implementation of a Two-Phase Material Model With Strength: Application to Porous Materials
2012-07-01
The idea of fitting constants τ0 and D0 in [13] is based on an approximation of the stationary solution of the viscoelastic model equations [17]. It...limit is Y = σ11 and 11 xu . Therefore, the stationary point of (16) after index summation can be found from .2 YG The last...concentration c (CMS variable); iii) scalar volume concentration θ ( TET variable); iv) scalar entropy disequilibrium χ (XI variable); v) symmetric strain
Local existence and stability for a hyperbolic-elliptic system modeling two-phase reservoir flow
Directory of Open Access Journals (Sweden)
H. J. Schroll
2000-01-01
Full Text Available A system arising in the modeling of oil-recovery processes is analyzed. It consists of a hyperbolic conservation law governing the saturation and an elliptic equation for the pressure. By an operator splitting approach, an approximate solution is constructed. For this approximation appropriate a-priori bounds are derived. Applying the Arzela-Ascoli theorem, local existence and uniqueness of a classical solution for the original hyperbolic-elliptic system is proved. Furthermore, convergence of the approximation generated by operator splitting towards the unique solution follows. It is also proved that the unique solution is stable with respect to perturbations of the initial data.
Aniszewski, Wojciech
2016-01-01
In this paper, a specific subgrid term occurring in Large Eddy Simulation (LES) of two-phase flows is investigated. This and other subgrid terms are presented, we subsequently elaborate on the existing models for those and re-formulate the ADM-{\\tau} model for sub-grid surface tension previously published by these authors. This paper presents a substantial, conceptual simplification over the original model version, accompanied by a decrease in its computational cost. At the same time, it addresses the issues the original model version faced, e.g. introduces non-isotropic applicability criteria based on resolved interface's principal curvature radii. Additionally, this paper introduces more throughout testing of the ADM-{\\tau}, in both simple and complex flows.
Two Phase Flow Models and Numerical Methods of the Commercial CFD Codes
Energy Technology Data Exchange (ETDEWEB)
Bae, Sung Won; Jeong, Jae Jun; Chang, Seok Kyu; Cho, Hyung Kyu
2007-11-15
The use of commercial CFD codes extend to various field of engineering. The thermal hydraulic analysis is one of the promising engineering field of application of the CFD codes. Up to now, the main application of the commercial CFD code is focused within the single phase, single composition fluid dynamics. Nuclear thermal hydraulics, however, deals with abrupt pressure changes, high heat fluxes, and phase change heat transfer. In order to overcome the CFD limitation and to extend the capability of the nuclear thermal hydraulics analysis, the research efforts are made to collaborate the CFD and nuclear thermal hydraulics. To achieve the final goal, the current useful model and correlations used in commercial CFD codes should be reviewed and investigated. This report gives the summary information about the constitutive relationships that are used in the FLUENT, STAR-CD, and CFX. The brief information of the solution technologies are also enveloped.
Tecklenburg, Jan; Neuweiler, Insa; Carrera, Jesus; Dentz, Marco
2016-05-01
We study modeling of two-phase flow in highly heterogeneous fractured and porous media. The flow behaviour is strongly influenced by mass transfer between a highly permeable (mobile) fracture domain and less permeable (immobile) matrix blocks. We quantify the effective two-phase flow behavior using a multirate rate mass transfer (MRMT) approach. We discuss the range of applicability of the MRMT approach in terms of the pertinent viscous and capillary diffusion time scales. We scrutinize the linearization of capillary diffusion in the immobile regions, which allows for the formulation of MRMT in the form of a non-local single equation model. The global memory function, which encodes mass transfer between the mobile and the immobile regions, is at the center of this method. We propose two methods to estimate the global memory function for a fracture network with given fracture and matrix geometry. Both employ a scaling approach based on the known local memory function for a given immobile region. With the first method, the local memory function is calculated numerically, while the second one employs a parametric memory function in form of truncated power-law. The developed concepts are applied and tested for fracture networks of different complexity. We find that both physically based parameter estimation methods for the global memory function provide predictive MRMT approaches for the description of multiphase flow in highly heterogeneous porous media.
Ludwig, A.; Vakhrushev, A.; Holzmann, T.; Wu, M.; Kharicha, A.
2015-06-01
During many industrial solidification processes equiaxed crystals form, grow and move. When those crystals are small they are carried by the melt, whereas when getting larger they sediment. As long as the volume fraction of crystals is below the packing limit, they are able to move relatively free. Crystals being backed in a so called packed bed form a semi-solid slurry, which may behave like a visco-plastic material. In addition, cooling-induced density increase of both, liquid and solid phases might lead to shrinkage of the whole casting domain. So deformation happens and gaps between casting and mold occur. In the present work, a two-phase Eulerian-Eulerian volume averaging model for describing the motion of equiaxed crystals in the melt is combined with a similar two-phase model for describing the dynamic of the packed bed. As constitutive equation for the solid skeleton in the packed bed Norton-Hoff law is applied. Shrinkage induced by density changes in the liquid or the solid phase is explicitly taken into account and handled by remeshing the calculation domain accordantly.
Tecklenburg, Jan; Carrera, Jesus; Dentz, Marco
2016-01-01
We study modeling of two-phase flow in highly heterogeneous fractured and porous media. The flow behaviour is strongly influenced by mass transfer between a highly permeable (mobile) fracture domain and less permeable (immobile) matrix blocks. We quantify the effective two-phase flow behaviour using a multirate rate mass transfer (MRMT) approach. We discuss the range of applicability of the MRMT approach in terms of the pertinent viscous and capillary diffusion time scales. We scrutinize the linearization of capillary diffusion in the immobile regions, which allows for the formulation of MRMT in the form of a non-local single equation model. The global memory function, which encodes mass transfer between the mobile and the immobile regions, is at the center of this method. We propose two methods to estimate the global memory function for a fracture network with given fracture and matrix geometry. Both employ a scaling approach based on the known local memory function for a given immobile region. With the firs...
Development of a Two-Phase Model for the Hot Deformation of Highly-Alloyed Aluminum
Energy Technology Data Exchange (ETDEWEB)
A. J. Beaudoin; J. A. Dantzig; I. M. Robertson; B. E. Gore; S. F. Harnish; H. A. Padilla
2005-10-31
Conventional processing methods for highly alloyed aluminum consist of ingot casting, followed by hot rolling and thermal treatments. Defects result in lost productivity and wasted energy through the need to remelt and reprocess the material. This research centers on developing a fundamental understanding for deformation of wrought 705X series alloys, a key alloy system used in structural airframe applications. The development of damage at grain boundaries is characterized through a novel test that provides initiation of failure while preserving a controlled deformation response. Data from these mechanical tests are linked to computer simulations of the hot rolling process through a critical measure of damage. Transmission electron microscopy provides fundamental insight into deformation at these high working temperatures, and--in a novel link between microscale and macroscale response--the evolution of microstructure (crystallographic orientation) provides feedback for tuning of friction in the hot rolling process. The key product of this research is a modeling framework for the analysis of industrial hot rolling.
Chattopadhyay, Soma; Kelly, S. D.; Shibata, Tomohiro; Balasubramanian, M.; Srinivasan, S. G.; Du, Jincheng; Banerjee, Rajarshi; Ayyub, Pushan
2016-02-01
We report a detailed study of the local composition and structure of a model, bi-phasic nanoglass with nominal stoichiometry Cu55Nb45. Three dimensional atom probe data suggest a nanoscale-phase-separated glassy structure having well defined Cu-rich and Nb-rich regions with a characteristic length scale of ≈3 nm. However, extended x-ray absorption fine structure analysis indicates subtle differences in the local environments of Cu and Nb. While the Cu atoms displayed a strong tendency to cluster and negligible structural order beyond the first coordination shell, the Nb atoms had a larger fraction of unlike neighbors (higher chemical order) and a distinctly better-ordered structural environment (higher topological order). This provides the first experimental indication that metallic glass formation may occur due to frustration arising from the competition between chemical ordering and clustering. These observations are complemented by classical as well as ab initio molecular dynamics simulations. Our study indicates that these nanoscale phase-separated glasses are quite distinct from the single phase nanoglasses (studied by Gleiter and others) in the following three respects: (i) they contain at least two structurally and compositionally distinct, nanodispersed, glassy phases, (ii) these phases are separated by comparatively sharp inter-phase boundaries, and (iii) thermally induced crystallization occurs via a complex, multi-step mechanism. Such materials, therefore, appear to constitute a new class of disordered systems that may be called a composite nanoglass.
Energy Technology Data Exchange (ETDEWEB)
Chattopadhyay, Soma; Shibata, Tomohiro [CSRRI-IIT, MRCAT, Sector 10, Advanced Photon Source, Argonne National Laboratory, Argonne, Illinois 60439 (United States); Kelly, S. D. [EXAFS Analysis, Bolingbrook, Illinois 60440 (United States); Balasubramanian, M. [Sector 20 XOR, Advanced Photon Source, Argonne National Laboratory, Argonne, Illinois 60439 (United States); Srinivasan, S. G.; Du, Jincheng; Banerjee, Rajarshi [Department of Materials Science and Engineering, University of North Texas, Denton, Texas 76203-5017 (United States); Ayyub, Pushan, E-mail: pushan@tifr.res.in [Department of Condensed Matter Physics and Materials Science, Tata Institute of Fundamental Research, Mumbai 400005 (India)
2016-02-14
We report a detailed study of the local composition and structure of a model, bi-phasic nanoglass with nominal stoichiometry Cu{sub 55}Nb{sub 45}. Three dimensional atom probe data suggest a nanoscale-phase-separated glassy structure having well defined Cu-rich and Nb-rich regions with a characteristic length scale of ≈3 nm. However, extended x-ray absorption fine structure analysis indicates subtle differences in the local environments of Cu and Nb. While the Cu atoms displayed a strong tendency to cluster and negligible structural order beyond the first coordination shell, the Nb atoms had a larger fraction of unlike neighbors (higher chemical order) and a distinctly better-ordered structural environment (higher topological order). This provides the first experimental indication that metallic glass formation may occur due to frustration arising from the competition between chemical ordering and clustering. These observations are complemented by classical as well as ab initio molecular dynamics simulations. Our study indicates that these nanoscale phase-separated glasses are quite distinct from the single phase nanoglasses (studied by Gleiter and others) in the following three respects: (i) they contain at least two structurally and compositionally distinct, nanodispersed, glassy phases, (ii) these phases are separated by comparatively sharp inter-phase boundaries, and (iii) thermally induced crystallization occurs via a complex, multi-step mechanism. Such materials, therefore, appear to constitute a new class of disordered systems that may be called a composite nanoglass.
Directory of Open Access Journals (Sweden)
Markatos N. C.
2006-11-01
Full Text Available Many key issuesin design for the process industries are related to the behaviour of fluids in turbulent flow, often involving more than one phase, chemical reaction or heat transfer. Computational-Fluid-Dynamics (CFD techniques have great potential for analysing these processes and can be of great help to the designer, by reducing the need to resort to cut and try : approaches to the design of complex equipment. The paper presents the fundamental principles of CFD within the context of the so-called finite-domain technique. The procedure can handle one-, two-, and three-dimensional distributions of the variables in space, steady or transient processes, multi-phase processes, and effects such as turbulence, compressibility of phases, buoyancy, phase-change, chemical reactions, gravity stratification, etc. Demonstrations are made of the application of the procedure to the numerical computation of some process industry situations, such as those occurring in adsorbers/regenerators, combustors, cement kilns, and heat - exchangers. It is concluded that :- The finite - domain versions of the differential equations are soluble, with modest computer costs;- The solutions are always physically plausible; and,- There is a need for extensive evaluation and validation of CFD physical and chemical sub-models, particularly those concerning turbulence, chemical kinetics and interphase-transport processes. Bon nombre de difficultés de conception des procédés industriels sont liés au comportement des fluides en écoulement turbulent, qui font souvent intervenir plusieurs phases, réactions chimiques ou transferts thermiques. Les techniques de dynamique des fluides assistée par ordinateur (CFD permettent d'analyser ces procédés et peuvent apporter une aide considérable à la conception en éliminant le recours aux méthodes expérimentales pour l'étude d'équipements complexes. Cette communication présente les principes fondamentaux de la CFD dans le
Mathematical problems in meteorological modelling
Csomós, Petra; Faragó, István; Horányi, András; Szépszó, Gabriella
2016-01-01
This book deals with mathematical problems arising in the context of meteorological modelling. It gathers and presents some of the most interesting and important issues from the interaction of mathematics and meteorology. It is unique in that it features contributions on topics like data assimilation, ensemble prediction, numerical methods, and transport modelling, from both mathematical and meteorological perspectives. The derivation and solution of all kinds of numerical prediction models require the application of results from various mathematical fields. The present volume is divided into three parts, moving from mathematical and numerical problems through air quality modelling, to advanced applications in data assimilation and probabilistic forecasting. The book arose from the workshop “Mathematical Problems in Meteorological Modelling” held in Budapest in May 2014 and organized by the ECMI Special Interest Group on Numerical Weather Prediction. Its main objective is to highlight the beauty of the de...
Mathematical Modeling of Thermal Modes of Closed Two-Phase Thermosyphons with Refrigerant R600A
Directory of Open Access Journals (Sweden)
Krasnoshlykov A.S.
2016-01-01
Full Text Available Numerical analysis using the software package ANSYS FLUENT has been carried out. Characteristic temperature distribution, streamlines and velocity vectors for various heat loads have been obtained. The study found the possibility of using the software package for analysis of the energy transfer processes at high thermal loads.
MATHEMATICAL MODELING OF NEAR-WALL FLOWS OF TWO-PHASE MIXTURE WITH EVAPORATING DROPLETS
Institute of Scientific and Technical Information of China (English)
WANG Bo-yi(王柏懿); A.N.Osiptsov
2002-01-01
In the framework of the two-continuum approach, using the matched asymptotic expansion method, the equations of a laminar boundary layer in mist flows with evaporating droplets were derived and solved. The similarity criteria controlling the mist flows were determined. For the flow along a curvilinear surface, the forms of the boundary layer equations differ from the regimes of presence and absence of the droplet inertia deposition.The numerical results were presented for the vapor-droplet boundary layer in the neighborhood of a stagnation point of a hot blunt body. It is demonstrated that, due to evaporation, a droplet-free region develops near the wall inside the boundary layer. On the upper edge of this region, the droplet radius tends to zero and the droplet number density becomes much higher than that in the free stream. The combined effect of the droplet evaporation and accumulation results in a significant enhancement of the heat transfer on the surface even for small mass concentration of the droplets in the free stream.
Directory of Open Access Journals (Sweden)
B. Panic
2013-04-01
Full Text Available The results of experimental investigations concerning radial distribution of powder accumulation in bed and static pressure were presented in this paper. To realize this research physical model of gas-powder two phase flow with descending bed was projected and constructed. Amounts of “dynamic” and “static” powder accumulated in bed, in dependence on gas velocity and of bed particles were investigated. In 3D model “static” powder (with its radial distribution at the tuyere level and in the higher part of bed was measured. The influence of bed particles, powder and gas radial distribution on values of interaction forces between flow phases in investigated system was defined.
Energy Technology Data Exchange (ETDEWEB)
Mohammadi, M. [Petroleum Univ. of Technology, Ahwaz (Iran, Islamic Republic of). Gas Engineering Dept.
2006-07-01
Liquid holdup in pipelines refers to the fraction of pipe that is occupied by liquid. Accurate prediction of liquid holdup associated with multiphase flow is important for the design and operation of modern petroleum production systems. Multiphase flow refers to the concurrent flow of 2 or more phases, liquid, solid or gas, where motion affects the interface between the phases. The ability to predict liquid holdup makes it possible to calculate a pressure gradient based on a two-phase friction factor. However, this approach is dependent on the accuracy of flow pattern predictions and is subject to discontinuities in predictions made across flow pattern transition boundaries. Artificial neural networks (ANN) are computing tools that can recognize complex patterns within available data. ANN has been used successfully to solve many difficult engineering problems including multiphase flow problems that involve pressure drop, flow pattern identification and liquid holdup. This study used a 3-layer backpropagation ANN model for predicting the liquid holdup in gas-liquid two-phase flow at all ranges of pipe inclinations. Five independent sets of experimental data were used, covering a wide range of variables such as inclination from horizontal, pipe diameter, gas and liquid superficial velocity, liquid viscosity, density and surface tension. The model is independent of flow pattern determination and uses an individual method for all conditions. Experimental results have shown that the newly developed model can accurately predict liquid holdup in terms of the lowest absolute average percent error, the lowest standard deviation and the highest correlation coefficient. This study confirmed the power of ANN models in solving complicated engineering problems. 28 refs., 5 tabs., 4 figs., 1 appendix.
Institute of Scientific and Technical Information of China (English)
SantiagoLain; RicardoAliod
2000-01-01
A statistical formalism overcoming some conceptual and practical difficulties arising in existing two-phase flow (2PHF) mathematical modelling has been applied to propose a model for dilute 2PHF turbulent flows.Phase interaction terms with a clear physical meaning enter the equations and the formalism provides some guidelines for the avoidance of closure assumptions or the rational approximation of these terms. Continuous phase averaged continuity, momentum, turbulent kinetic energy and turbulence dissipation rate equations have been rigorously and systematically obtained in a single step. These equations display a structure similar to that for single-phase flows.It is also assumed that dispersed phase dynamics is well described by a probability density function (pdf) equation and Eulerian continuity, momentum and fluctuating kinetic energy equations for the dispersed phase are deduced.An extension of the standard k-c turbulence model for the continuous phase is used. A gradient transport model is adopted for the dispersed phase fluctuating fluxes of momentum and kinetic energy at the non-colliding, large inertia limit. This model is then used to predict the behaviour of three axisymmetric turbulent jets of air laden with solid particles varying in size and concentration. Qualitative and quantitative numerical predictions compare reasonably well with the three different sets of experimental results, studying the influence of particle size, loading ratio and flow confinement velocity.
Wang, Lijuan; Yan, Yong; Wang, Xue; Wang, Tao
2017-03-01
Input variable selection is an essential step in the development of data-driven models for environmental, biological and industrial applications. Through input variable selection to eliminate the irrelevant or redundant variables, a suitable subset of variables is identified as the input of a model. Meanwhile, through input variable selection the complexity of the model structure is simplified and the computational efficiency is improved. This paper describes the procedures of the input variable selection for the data-driven models for the measurement of liquid mass flowrate and gas volume fraction under two-phase flow conditions using Coriolis flowmeters. Three advanced input variable selection methods, including partial mutual information (PMI), genetic algorithm-artificial neural network (GA-ANN) and tree-based iterative input selection (IIS) are applied in this study. Typical data-driven models incorporating support vector machine (SVM) are established individually based on the input candidates resulting from the selection methods. The validity of the selection outcomes is assessed through an output performance comparison of the SVM based data-driven models and sensitivity analysis. The validation and analysis results suggest that the input variables selected from the PMI algorithm provide more effective information for the models to measure liquid mass flowrate while the IIS algorithm provides a fewer but more effective variables for the models to predict gas volume fraction.
Mathematical Modeling and Computational Thinking
Sanford, John F.; Naidu, Jaideep T.
2017-01-01
The paper argues that mathematical modeling is the essence of computational thinking. Learning a computer language is a valuable assistance in learning logical thinking but of less assistance when learning problem-solving skills. The paper is third in a series and presents some examples of mathematical modeling using spreadsheets at an advanced…
Jin, Shi; Shu, Ruiwen
2017-04-01
In this paper we consider a kinetic-fluid model for disperse two-phase flows with uncertainty. We propose a stochastic asymptotic-preserving (s-AP) scheme in the generalized polynomial chaos stochastic Galerkin (gPC-sG) framework, which allows the efficient computation of the problem in both kinetic and hydrodynamic regimes. The s-AP property is proved by deriving the equilibrium of the gPC version of the Fokker-Planck operator. The coefficient matrices that arise in a Helmholtz equation and a Poisson equation, essential ingredients of the algorithms, are proved to be positive definite under reasonable and mild assumptions. The computation of the gPC version of a translation operator that arises in the inversion of the Fokker-Planck operator is accelerated by a spectrally accurate splitting method. Numerical examples illustrate the s-AP property and the efficiency of the gPC-sG method in various asymptotic regimes.
Glass, Robert J.; Yarrington, Lane
2003-03-01
Fingering, nonmonotonicity, fragmentation, and pulsation within gravity/buoyant destabilized two-phase/unsaturated flow systems has been widely observed with examples in homogeneous to heterogeneous porous media, in single fractures to fracture networks, and for both wetting and nonwetting invasion. To model this phenomena, we consider a mechanistic approach based on forms of modified invasion percolation (MIP) that include gravity, the influence of the local interfacial curvature along the phase-phase interface, and the simultaneous invasion and reinvasion of both wetting and nonwetting fluids. We present example simulations and compare them to experimental data for three very different situations: (1) downward gravity-driven fingering of water into a dry, homogeneous, water-wettable, porous medium; (2) upward buoyancy-driven migration of gas within a water saturated, heterogeneous, water-wettable, porous medium; and (3) downward gravity-driven fingering of water into a dry, water-wettable, rough-walled fracture.
Energy Technology Data Exchange (ETDEWEB)
Jin, Shi, E-mail: sjin@wisc.edu [Department of Mathematics, University of Wisconsin–Madison, Madison, WI 53706 (United States); Institute of Natural Sciences, School of Mathematical Science, MOELSEC and SHL-MAC, Shanghai Jiao Tong University, Shanghai 200240 (China); Shu, Ruiwen, E-mail: rshu2@math.wisc.edu [Department of Mathematics, University of Wisconsin–Madison, Madison, WI 53706 (United States)
2017-04-15
In this paper we consider a kinetic-fluid model for disperse two-phase flows with uncertainty. We propose a stochastic asymptotic-preserving (s-AP) scheme in the generalized polynomial chaos stochastic Galerkin (gPC-sG) framework, which allows the efficient computation of the problem in both kinetic and hydrodynamic regimes. The s-AP property is proved by deriving the equilibrium of the gPC version of the Fokker–Planck operator. The coefficient matrices that arise in a Helmholtz equation and a Poisson equation, essential ingredients of the algorithms, are proved to be positive definite under reasonable and mild assumptions. The computation of the gPC version of a translation operator that arises in the inversion of the Fokker–Planck operator is accelerated by a spectrally accurate splitting method. Numerical examples illustrate the s-AP property and the efficiency of the gPC-sG method in various asymptotic regimes.
Balasubramaniam, R.; Rame, E.; Kizito, J.; Kassemi, M.
2006-01-01
The purpose of this report is to provide a summary of state-of-the-art predictions for two-phase flows relevant to Advanced Life Support. We strive to pick out the most used and accepted models for pressure drop and flow regime predictions. The main focus is to identify gaps in predictive capabilities in partial gravity for Lunar and Martian applications. Following a summary of flow regimes and pressure drop correlations for terrestrial and zero gravity, we analyze the fully developed annular gas-liquid flow in a straight cylindrical tube. This flow is amenable to analytical closed form solutions for the flow field and heat transfer. These solutions, valid for partial gravity as well, may be used as baselines and guides to compare experimental measurements. The flow regimes likely to be encountered in the water recovery equipment currently under consideration for space applications are provided in an appendix.
Naphon, P.; Arisariyawong, T.; Nualboonrueng, T.
2017-07-01
A computation fluid dynamics study has been performed to analyze the nanofluids heat transfer and flow characteristics in the spirally coiled tubes. Eulerian two-phase turbulent model is applied to simulate the heat transfer and flow characteristics in the vertical spirally coiled tube. The spirally coiled tubes are fabricated by bending a 8.50 mm inner diameter straight copper tube into a spiral-coil with two different curvature ratios of 0.035, 0.060. The predicted results are verified with the present measured data. Reasonable agreement is obtained from the comparison between the measured data and the predicted results. In addition, due to the centrifugal force, the induced secondary flow has significant effect on the heat transfer enhancement as flowing through the spirally coiled tube. Effects of curvature, nanofluids concentration and hot water temperature on the nanofluids heat transfer characteristics and pressure drop are considered.
Modeling and controlling the two-phase dynamics of the p53 network: a Boolean network approach
Lin, Guo-Qiang; Ao, Bin; Chen, Jia-Wei; Wang, Wen-Xu; Di, Zeng-Ru
2014-12-01
Although much empirical evidence has demonstrated that p53 plays a key role in tumor suppression, the dynamics and function of the regulatory network centered on p53 have not yet been fully understood. Here, we develop a Boolean network model to reproduce the two-phase dynamics of the p53 network in response to DNA damage. In particular, we map the fates of cells into two types of Boolean attractors, and we find that the apoptosis attractor does not exist for minor DNA damage, reflecting that the cell is reparable. As the amount of DNA damage increases, the basin of the repair attractor shrinks, accompanied by the rising of the apoptosis attractor and the expansion of its basin, indicating that the cell becomes more irreparable with more DNA damage. For severe DNA damage, the repair attractor vanishes, and the apoptosis attractor dominates the state space, accounting for the exclusive fate of death. Based on the Boolean network model, we explore the significance of links, in terms of the sensitivity of the two-phase dynamics, to perturbing the weights of links and removing them. We find that the links are either critical or ordinary, rather than redundant. This implies that the p53 network is irreducible, but tolerant of small mutations at some ordinary links, and this can be interpreted with evolutionary theory. We further devised practical control schemes for steering the system into the apoptosis attractor in the presence of DNA damage by pinning the state of a single node or perturbing the weight of a single link. Our approach offers insights into understanding and controlling the p53 network, which is of paramount importance for medical treatment and genetic engineering.
Directory of Open Access Journals (Sweden)
. Dr. S. Rawat
2014-01-01
Full Text Available A mathematical model is presented for the steady, two-dimensional magneto-convection heat transfer of a two-phase, electrically-conducting, particle-suspension in a channel containing a non-Darcian porous medium intercalated between two parallel plates, in the presence of a transverse magnetic field. The channel walls are assumed to be isothermal but at different temperatures. The governing equations for the one-dimensional steady flow are formulated following Marble (1970 and extended to include the influence of Darcian porous drag, Forcheimmer quadratic drag, buoyancy effects, Lorentz body force (hydromagnetic retardation force and particle-phase viscous stresses. Special boundary conditions for the particle-phase wall conditions are implemented. The governing coupled, non-linear differential equations are reduced from an (x,y coordinate system to a one-dimensional (y coordinate system. A series of transformations is then employed to non-dimensionalize the model in terms of a single independent variable, , yielding a quartet of coupled ordinary differential equations which are solved numerically using the finite element method, under appropriate transformed boundary conditions. The influence of for example Grashof free convection number (Gr, Hartmann hydromagnetic number (Ha, inverse Stokes number (Skm, Darcy number (Da, Forcheimmer number (Fs,particle loading parameter (PL, buoyancy parameter (B on the fluid-phase velocity and particle-phase velocity are presented graphically. A number of special cases of the transformed model are also studied. The mathematical model finds applications in solar collector devices, electronic fabrication, jet nozzle flows, industrial materials processing transport phenomena, MHD energy generator systems etc.
Liu, Xunliang; Lou, Guofeng; Wen, Zhi
A non-isothermal, steady-state, three-dimensional (3D), two-phase, multicomponent transport model is developed for proton exchange membrane (PEM) fuel cell with parallel gas distributors. A key feature of this work is that a detailed membrane model is developed for the liquid water transport with a two-mode water transfer condition, accounting for the non-equilibrium humidification of membrane with the replacement of an equilibrium assumption. Another key feature is that water transport processes inside electrodes are coupled and the balance of water flux is insured between anode and cathode during the modeling. The model is validated by the comparison of predicted cell polarization curve with experimental data. The simulation is performed for water vapor concentration field of reactant gases, water content distribution in the membrane, liquid water velocity field and liquid water saturation distribution inside the cathode. The net water flux and net water transport coefficient values are obtained at different current densities in this work, which are seldom discussed in other modeling works. The temperature distribution inside the cell is also simulated by this model.
Hubert, Olivier; Lazreg, Said
2017-02-01
A growing interest of automotive industry in the use of high performance steels is observed. These materials are obtained thanks to complex manufacturing processes whose parameters fluctuations lead to strong variations of microstructure and mechanical properties. The on-line magnetic non-destructive monitoring is a relevant response to this problem but it requires fast models sensitive to different parameters of the forming process. The plastic deformation is one of these important parameters. Indeed, ferromagnetic materials are known to be sensitive to stress application and especially to plastic strains. In this paper, a macroscopic approach using the kinematic hardening is proposed to model this behavior, considering a plastic strained material as a two phase system. Relationship between kinematic hardening and residual stress is defined in this framework. Since stress fields are multiaxial, an uniaxial equivalent stress is calculated and introduced inside the so-called magneto-mechanical multidomain modeling to represent the effect of plastic strain. The modeling approach is complemented by many experiments involving magnetic and magnetostrictive measurements. They are carried out with or without applied stress, using a dual-phase steel deformed at different levels. The main interest of this material is that the mechanically hard phase, soft phase and the kinematic hardening can be clearly identified thanks to simple experiments. It is shown how this model can be extended to single phase materials.
Three-dimensional radiative transfer modeling of AGN dusty tori as a clumpy two-phase medium
Stalevski, Marko; Baes, Maarten; Nakos, Theodoros; Popovic, Luka C
2011-01-01
We investigate the emission of active galactic nuclei (AGN) dusty tori in the infrared domain. Following theoretical predictions coming from hydrodynamical simulations, we model the dusty torus as a 3D two-phase medium with high-density clumps and low-density medium filling the space between the clumps. Spectral energy distributions (SED) and images of the torus at different wavelengths are obtained using 3D Monte Carlo radiative transfer code SKIRT. Our approach of generating clumpy structure allows us to model tori with single clumps, complex structures of merged clumps or interconnected sponge-like structure. A corresponding set of clumps-only models and models with smooth dust distribution is calculated for comparison. We found that dust distribution, optical depth, clump size and their actual arrangement in the innermost region, all have an impact on the shape of near- and mid-infrared SED. The 10 micron silicate feature can be suppressed for some parameters, but models with smooth dust distribution are ...
Shaw, Sachin; Murthy, P V S N
2010-09-01
The present investigation deals with finding the trajectories of the drug dosed magnetic carrier particle in a microvessel with two-phase fluid model which is subjected to the external magnetic field. The radius of the microvessel is divided into the endothelial glycocalyx layer in which the blood is assumed to obey Newtonian character and a core and plug regions where the blood obeys the non-Newtonian Herschel-Bulkley character which is suitable for the microvessel of radius 50 microm. The carrier particles, bound with nanoparticles and drug molecules are injected into the vascular system upstream from malignant tissue, and captured at the tumor site using a local applied magnetic field. The applied magnetic field is produced by a cylindrical magnet positioned outside the body and near the tumor position. The expressions for the fluidic force for the carrier particle traversing in the two-phase fluid in the microvessel and the magnetic force due to the external magnetic field are obtained. Several factors that influence the magnetic targeting of the carrier particles in the microvasculature, such as the size of the carrier particle, the volume fraction of embedded magnetic nanoparticles, and the distance of separation of the magnet from the axis of the microvessel are considered in the present problem. An algorithm is given to solve the system of coupled equations for trajectories of the carrier particle in the invasive case. The trajectories of the carrier particle are found for both invasive and noninvasive targeting systems. A comparison is made between the trajectories in these cases. Also, the present results are compared with the data available for the impermeable microvessel with single-phase fluid flow. Also, a prediction of the capture of therapeutic magnetic nanoparticle in the impermeable microvasculature is made for different radii, distances and volume fractions in both the invasive and noninvasive cases.
The 2005 Vazcun Valley Lahar: Evaluation of the TITAN2D Two-Phase Flow Model Using an Actual Event.
Williams, R.; Stinton, A. J.; Sheridan, M. F.
2005-12-01
TITAN2D is a depth-averaged, thin-layer computational fluid dynamics (CFD) code, suitable for simulating a variety of geophysical mass flows. TITAN2D output data include pile thickness and flow momentum at each time step for all cells traversed by the flow during the simulation. From this the flow limit, run-out path, pile velocity, deposit thickness, and travel time can be calculated. Results can be visualized in the open source GRASS GIS software or with the built-in TITAN2D viewer. A new two-phase TITAN2D version allows simulation of flows containing various mixtures of water and solids. The purpose of this study is to compare simulations by the two-phase flow version of TITAN2D with an actual event. The chosen natural flow is a small ash-rich lahar (volume approximately 60,000 m3) that occurred on 12 February 2005 in the Vazcún Valley, located on the north-east flank of Volcán Tungurahua, Ecuador. Lahars and pyroclastic flows along this valley could potentially threaten the 20,000 inhabitants living in and near the city of Baños. A variety of data sources exist for this lahar, including: pre- and post-event meter-scale topography, and photographic, video, seismic and acoustic flow monitoring (AFM) records from during the event. These data permit detailed comparisons between the dynamics of the actual lahar and those of the TITAN2D simulated flow. In particular, detailed comparisons are made between run-up heights, flow velocity, inundation area, and deposit area and thickness. Simulations utilize a variety of data derived from field observations such as lahar volume, solid to pore-fluid ratio and pre-event topography. TITAN2D is important in modeling lahars because it allows assessment of the impact of the flows on buildings and infrastructure lifelines located near drainages that descend from volcanoes.
Mathematical Model for Hit Phenomena
Ishii, Akira; Hayashi, Takefumi; Matsuda, Naoya; Nakagawa, Takeshi; Arakaki, Hisashi; Yoshida, Narihiko
2010-01-01
The mathematical model for hit phenomena in entertainments is presented as a nonlinear, dynamical and non-equilibrium phenomena. The purchase intention for each person is introduced and direct and indirect communications are expressed as two-body and three-body interaction in our model. The mathematical model is expressed as coupled nonlinear differential equations. The important factor in the model is the decay time of rumor for the hit. The calculated results agree very well with revenues of recent 25 movies.
An introduction to mathematical modeling
Bender, Edward A
2000-01-01
Employing a practical, ""learn by doing"" approach, this first-rate text fosters the development of the skills beyond the pure mathematics needed to set up and manipulate mathematical models. The author draws on a diversity of fields - including science, engineering, and operations research - to provide over 100 reality-based examples. Students learn from the examples by applying mathematical methods to formulate, analyze, and criticize models. Extensive documentation, consisting of over 150 references, supplements the models, encouraging further research on models of particular interest. The
Schmeling, Harro; Maruqart, Gabriele; Weinberg, Roberto; Cruden, Sandy
2017-04-01
Melting within the lower continental crust with and without extension and subsequent ascent of silicic melts is modelled by a thermo-mechanical two-phase flow approach. The approach is based on the conservation equations of mass, momentum, and energy for melt and solid, respectively, and includes a simplified binary melting model, as well as compaction / decompaction of the solid matrix. The rheology is based on dislocation creep of quartzite or granite, and includes plasticity. 2D models are carried out for cases without and with differential melt-matrix flow. As control parameter the heat flow is varied between 75 and 90 mW m-2 at the base of a thickened continental crust. In the case of no differential flow (batch melting) the model predicts episodic melting, rise and freezing of partially molten magmatic bodies. The recurrence time inversely scales with the bottom heat flux. In the case of allowing for melt migration, no such episodicity is observed anymore. Melt accumulates within melt rich layers and bodies, which subsequently rise through the crust by a combination of diapirism and decompaction related sinking of solid material through the melt rich layer. Final emplacement depths are between 30 and 15 km, shapes of the resulting plutons are visualized by the evolved enrichment and depletion fields. They show a strong dependence on the applied bottom heat fluxes.
García-Salaberri, Pablo A.; Vera, Marcos; Iglesias, Immaculada
2014-01-01
An isothermal two-phase 2D/1D across-the-channel model for the anode of a liquid-feed Direct Methanol Fuel Cell (DMFC) is presented. The model takes into account the effects of the inhomogeneous assembly compression of the Gas Diffusion Layer (GDL), including the spatial variations of porosity, diffusivity, permeability, capillary pressure, and electrical conductivity. The effective anisotropic properties of the GDL are evaluated from empirical data reported in the literature corresponding to Toray carbon paper TGP-H series. Multiphase transport is modeled according to the classical theory of porous media (two-fluid model), considering the effect of non-equilibrium evaporation and condensation of methanol and water. The numerical results evidence that the hydrophobic Leverett J-function approach is physically inconsistent to describe capillary transport in the anode of a DMFC when assembly compression effects are considered. In contrast, more realistic results are obtained when GDL-specific capillary pressure curves reflecting the mixed-wettability characteristics of GDLs are taken into account. The gas coverage factor at the GDL/channel interface also exhibits a strong influence on the gas-void fraction distribution in the GDL, which in turn depends on the relative importance between the capillary resistance induced by the inhomogeneous compression, Rc(∝ ∂pc / ∂ ε) , and the capillary diffusivity, Dbarc(∝ ∂pc / ∂ s) .
Ohtaki, Megu; Tonda, Tetsuji; Aihara, Kazuyuki
2015-10-01
We consider a two-phase Poisson process model where only early successive transitions are assumed to be sensitive to exposure. In the case where intensity transitions are low, we derive analytically an approximate formula for the distribution of time to event for the excess hazard ratio (EHR) due to a single point exposure. The formula for EHR is a polynomial in exposure dose. Since the formula for EHR contains no unknown parameters except for the number of total stages, number of exposure-sensitive stages, and a coefficient of exposure effect, it is applicable easily under a variety of situations where there exists a possible latency time from a single point exposure to occurrence of event. Based on the multistage hypothesis of cancer, we formulate a radiation carcinogenesis model in which only some early consecutive stages of the process are sensitive to exposure, whereas later stages are not affected. An illustrative analysis using the proposed model is given for cancer mortality among A-bomb survivors.
Energy Technology Data Exchange (ETDEWEB)
Abu Saleem, Rabie A., E-mail: raabusaleem@just.edu.jo [Nuclear Engineering Department, Jordan University of Science and Technology, P.O. Box 3030, Irbid 22110 (Jordan); Kozlowski, Tomasz, E-mail: txk@illinois.edu [Department of Nuclear, Plasma and Radiological Engineering, University of Illinois at Urbana-Champaign, 216 Talbot Laboratory, 104 S. Wright St., Urbana, IL 61801 (United States); Shrestha, Rijan, E-mail: rijan.shrestha@intel.com [Portland Technology Development, Intel Corporation, 2501 NW 229th Ave Hillsboro OR 97124 (United States)
2016-05-15
Highlights: • The two-fluid model and the challenges associated with its numerical modeling are investigated. • A high-order solver based on flux limiter schemes and the theta method was developed. • The solver was compared to existing thermal hydraulics codes used in nuclear industry. • The solver was shown to handle fast transients with discontinuities and phase change. - Abstract: Finite volume techniques with staggered mesh are used to develop a new numerical solver for the one-dimensional two-phase two-fluid model using a high-resolution, Total Variation Diminishing (TVD) scheme. The solver is implemented to analyze numerical benchmark problems for verification and testing its abilities to handle discontinuities and fast transients with phase change. Convergence rates are investigated by comparing numerical results to analytical solutions available in literature for the case of the faucet flow problem. The solver based on a new TVD scheme is shown to exhibit higher-order of accuracy compared to other numerical schemes. Mass errors are also examined when phase change occurs for the shock tube problem, and compared to those of the 1st-order upwind scheme implemented in the nuclear thermal-hydraulics code TRACE. The solver is shown to exhibit numerical stability when applied to problems with discontinuous solutions and results of the new solver are free of spurious oscillations.
Mathematical Models of Biochemical Oscillations
Conrad, Emery David
1999-01-01
The goal of this paper is to explain the mathematics involved in modeling biochemical oscillations. We first discuss several important biochemical concepts fundamental to the construction of descriptive mathematical models. We review the basic theory of differential equations and stability analysis as it relates to two-variable models exhibiting oscillatory behavior. The importance of the Hopf Bifurcation will be discussed in detail for the central role it plays in limit cycle behavior and...
Energy Technology Data Exchange (ETDEWEB)
Seidel, Tobias; Vallee, Christophe; Lucas, Dirk; Beyer, Matthias; Deendarlianto
2011-09-15
In order to investigate the two-phase flow behaviour in a complex reactor-typical geometry and to supply suitable data for CFD code validation, a model of the hot leg of a pressurised water reactor was built at FZD. The hot leg model is operated in the pressure chamber of the TOPFLOW test facility, which is used to perform high-pressure experiments under pressure equilibrium with the inside atmosphere of the chamber. This technique makes it possible to visualise the two-phase flow through large windows, also at reactor-typical pressure levels. In order to optimise the optical observation possibilities, the test section was designed with a rectangular cross-section. Experiments were performed with air and water at 1.5 and 3.0 bar at room temperature as well as with steam and water at 15, 30 and 50 bar and the corresponding saturation temperature (i.e. up to 264 C). The total of 194 runs are divided into 4 types of experiments covering stationary co-current flow, counter-current flow, flow without water circulation and transient counter-current flow limitation (CCFL) experiments. This report provides a detailed documentation of the experiments including information on the experimental setup, experimental procedure, test matrix and on the calibration of the measuring devices. The available data is described and data sheets were arranged for each experiment in order to give an overview of the most important parameters. For the cocurrent flow experiments, water level histograms were arranged and used to characterise the flow in the hot leg. In fact, the form of the probability distribution was found to be sensitive to the boundary conditions and, therefore, is useful for the CFD comparison. Furthermore, the flooding characteristics of the hot leg model plotted in terms of the classical Wallis parameter or Kutateladze number were found to fail to properly correlate the data of the air/water and steam/water series. Therefore, a modified Wallis parameter is proposed, which
Symmetrical components and power analysis for a two-phase microgrid system
DEFF Research Database (Denmark)
Alibeik, M.; Santos Jr., E. C. dos; Blaabjerg, Frede
2014-01-01
This paper presents a mathematical model for the symmetrical components and power analysis of a new microgrid system consisting of three wires and two voltages in quadrature, which is designated as a two-phase microgrid. The two-phase microgrid presents the following advantages: 1) constant power...
Energy Technology Data Exchange (ETDEWEB)
Fichman, Sergio [Universidade Federal, Rio de Janeiro, RJ (Brazil). Coordenacao dos Programas de Pos-graduacao de Engenharia. Lab. de Metodos Computacionais em Engenharia (LAMCE)]. E-mail: fichman@brfree.com.br; Soares Filho, Djalma M. [PETROBRAS, Rio de Janeiro, RJ (Brazil). Centro de Pesquisas (CENPES)]. E-mail: djalma@cenpes.petrobras.com.br
2003-07-01
This work was based on porous-elastic equation proposed by Biot (1962). We developed an algorithm for modeling the seismic wave propagation in two phases heterogeneous media. At Biot equation the media is a porous elastic solid filled by fluid. The porous-elastic equation is closer to the geological reality than acoustic equation that is largely used for processing of seismic data in the petroleum industry. The methodology employed to solve the equations was the finite difference method, with second order approximations in time and fourth order approximations in space, and the introduction of parameters was through staggered grid generalizing then the technique introduced by Virieux (1986). An non-reflexive boundary condition was used at the sides and bottom of model, where were used absorbing borders A1 proposed by Clayton and Engquist (1977), added progressively attenuating borders proposed by Cerjan, Kosloff et al. (1985), and in upper border was used free-surface condition proposed by por Zhu and McMechan (1991)
Kim, Jinyong; Luo, Gang; Wang, Chao-Yang
2017-10-01
3D fine-mesh flow-fields recently developed by Toyota Mirai improved water management and mass transport in proton exchange membrane (PEM) fuel cell stacks, suggesting their potential value for robust and high-power PEM fuel cell stack performance. In such complex flow-fields, Forchheimer's inertial effect is dominant at high current density. In this work, a two-phase flow model of 3D complex flow-fields of PEMFCs is developed by accounting for Forchheimer's inertial effect, for the first time, to elucidate the underlying mechanism of liquid water behavior and mass transport inside 3D complex flow-fields and their adjacent gas diffusion layers (GDL). It is found that Forchheimer's inertial effect enhances liquid water removal from flow-fields and adds additional flow resistance around baffles, which improves interfacial liquid water and mass transport. As a result, substantial improvements in high current density cell performance and operational stability are expected in PEMFCs with 3D complex flow-fields, compared to PEMFCs with conventional flow-fields. Higher current density operation required to further reduce PEMFC stack cost per kW in the future will necessitate optimizing complex flow-field designs using the present model, in order to efficiently remove a large amount of product water and hence minimize the mass transport voltage loss.
Energy Technology Data Exchange (ETDEWEB)
Rosa, M.P. [Instituto de Estudos Avancados - CTA, Sao Paolo (Brazil); Podowski, M.Z. [Rensselaer Polytechnic Institute, Troy, NY (United States)
1995-09-01
This paper is concerned with the analysis of dynamics and stability of boiling channels and systems. The specific objectives are two-fold. One of them is to present the results of a study aimed at analyzing the effects of various modeling concepts and numerical approaches on the transient response and stability of parallel boiling channels. The other objective is to investigate the effect of closed-loop feedback on stability of a boiling water reactor (BWR). Various modeling and computational issues for parallel boiling channels are discussed, such as: the impact of the numerical discretization scheme for the node containing the moving boiling boundary on the convergence and accuracy of computations, and the effects of subcooled boiling and other two-phase flow phenomena on the predictions of marginal stability conditions. Furthermore, the effects are analyzed of local loss coefficients around the recirculation loop of a boiling water reactor on stability of the reactor system. An apparent paradox is explained concerning the impact of changing single-phase losses on loop stability. The calculations have been performed using the DYNOBOSS computer code. The results of DYNOBOSS validation against other computer codes and experimental data are shown.
Mathematical Models of Waiting Time.
Gordon, Sheldon P.; Gordon, Florence S.
1990-01-01
Considered are several mathematical models that can be used to study different waiting situations. Problems involving waiting at a red light, bank, restaurant, and supermarket are discussed. A computer program which may be used with these problems is provided. (CW)
Ahmad, Zahoor; Hanif, Muhammad
2013-01-01
The development of estimators of population parameters based on two-phase sampling schemes has seen a dramatic increase in the past decade. Various authors have developed estimators of population using either one or two auxiliary variables. The present volume is a comprehensive collection of estimators available in single and two phase sampling. The book covers estimators which utilize information on single, two and multiple auxiliary variables of both quantitative and qualitative nature. Th...
Drift flux model as approximation of two fluid model for two phase dispersed and slug flow in tube
Energy Technology Data Exchange (ETDEWEB)
Nigmatulin, R.I.
1995-09-01
The analysis of one-dimensional schematizing for non-steady two-phase dispersed and slug flow in tube is presented. Quasi-static approximation, when inertia forces because of the accelerations of the phases may be neglected, is considered. Gas-liquid bubbly and slug vertical upward flows are analyzed. Non-trivial theoretical equations for slip velocity for these flows are derived. Juxtaposition of the derived equations for slip velocity with the famous Zuber-Findlay correlation as cross correlation coefficients is criticized. The generalization of non-steady drift flux Wallis theory taking into account influence of wall friction on the bubbly or slug flows for kinematical waves is considered.
Numerical modelling of the impact of a liquid drop on the surface of a two-phase fluid system
Sochan, Agata; Lamorski, Krzysztof; Bieganowski, Andrzej; Ryżak, Magdalena
2014-05-01
The aim of the study was validation of a numerical model of the impact of a liquid drop on the surface of a two-phase system of immiscible fluids. The drop impact phenomenon was recorded using a high-speed camera (Vision Research MIRO M310) and the data were recorded at 2000 frames per second. The numerical calculations were performed with the Finite Volume Method (FVM) solving the three-dimensional Navier-Stokes equations for three phases: air and two selected immiscible fluids. The Volume of Fluid (VOF) technique was employed for modelling of the boundaries between the phases. Numerical modelling was done with the Finite Volume Method using an available OpenFOAM software. The experiment was based on three variables: • the height from which the drop of the selected fluids fell (the speed of the drop), • the thickness of the layers of the two selected immiscible fluids (a thin layer of the fluid with a lower density was spread over the higher-density fluid), • the size of the fluid droplet. The velocity and radius of the falling drop was calculated based on the recorded images. The used parameters allowed adequate projection of the impact of fluid droplets on a system of two immiscible liquids. Development of the numerical model of splash may further have practical applications in environmental protection (spraying of hazardous fluids, spread of fuels and other hazardous substances as a result of disasters, spraying (water cooling) of hot surfaces), and in agriculture (prevention of soil erosion). The study was partially funded from the National Science Centre (Poland) based on the decision no. DEC-2012/07/N/ST10/03280.
Directory of Open Access Journals (Sweden)
Safikhani Hamed
2016-01-01
Full Text Available In this article, the laminar mixed convection of Al2O3-Water nanofluid flow in a horizontal flat tube has been numerically simulated. The two-phase mixture model has been employed to solve the nanofluid flow, and constant heat flux has been considered as the wall boundary condition. The effects of different and important parameters such as the Reynolds number (Re, Grashof number (Gr, nanoparticles volume fraction (Φ and nanoparticle diameter (dp on the thermal and hydrodynamic performances of nanofluid flow have been analyzed. The results of numerical simulation were compared with similar existing data and good agreement is observed between them. It will be demonstrated that the Nusselt number (Nu and the friction factor (Cf are different for each of the upper, lower, left and right walls of the flat tube. The increase of Re, Gr and f and the reduction of dp lead to the increase of Nu. Similarly, the increase of Re and f results in the increase of Cf. Therefore, the best way to increase the amount of heat transfer in flat tubes using nanofluids is to increase the Gr and reduce the dp.
Hatami, M.; Mosayebidorcheh, S.; Jing, D.
2017-01-01
In this paper, two-phase Nanofluid condensation and heat transfer analysis over a vertical plate under gravity and between two parallel plates under magnetic force are investigated respectively using Least Square Method (LSM) and numerical method. After presenting the governing equations and solving them by LSM, the accuracy of results is examined by fourth order Runge-Kutta numerical method. Modeling results show that the condensate film thickness after condensation is reduced and therefore, the rate of heat transfer is enhanced by the addition of nanoparticles to the regular fluid. Effect of different nanoparticles and constant numbers on the temperature/velocity/concentration profiles as well as Nusselt number and boundary layer thickness, are also investigated. For instance, it was found that TiO2 and Ag have maximum boundary layer thicknesses and Nusselt number, respectively. By considering the magnetic field effect, it is also found that nanoparticles concentration can be controlled by changing the Hartmann number which, in turn, leads to different condensation and heat transfer properties.
Phase-Field and Korteweg-Type Models for the Time-Dependent Flow of Compressible Two-Phase Fluids
Freistühler, Heinrich; Kotschote, Matthias
2016-11-01
Various versions of the Navier-Stokes-Allen-Cahn (NSAC), the Navier-Stokes-Cahn-Hilliard (NSCH), and the Navier-Stokes-Korteweg (NSK) equations have been used in the literature to model the dynamics of two-phase fluids. One main purpose of this paper consists in (re-)deriving NSAC, NSCH and NSK from first principles, in the spirit of rational mechanics, for fluids of very general constitutive laws. For NSAC, this deduction confirms and extends a proposal of Blesgen. Regarding NSCH, it continues work of Lowengrub and Truskinovsky and provides the apparently first justified formulation in the non-isothermal case. For NSK, it yields a most natural correction to the formulation by Dunn and Serrin. The paper uniformly recovers as examples various classes of fluids, distinguished according to whether none, one, or both of the phases are compressible, and according to the nature of their co-existence. The latter is captured not only by the mixing energy, but also by a `mixing rule'—a constitutive law that characterizes the type of the mixing. A second main purpose of the paper is to communicate the apparently new observation that in the case of two immiscible incompressible phases of different temperature-independent specific volumes, NSAC reduces literally to NSK. This finding may be considered as an independent justification of NSK. An analogous fact is shown for NSCH, which under the same assumption reduces to a new non-local version of NSK.
Bashtani, Farzad; Maini, Brij; Kantzas, Apostolos
2016-08-01
3D random networks are constructed in order to represent the tight Mesaverde formation which is located in north Wyoming, USA. The porous-space is represented by pore bodies of different shapes and sizes which are connected to each other by pore throats of varying length and diameter. Pore bodies are randomly distributed in space and their connectivity varies based on the connectivity number distribution which is used in order to generate the network. Network representations are then validated using publicly available mercury porosimetry experiments. The network modeling software solves the fundamental equations of two-phase immiscible flow incorporating wettability and contact angle variability. Quasi-static displacement is assumed. Single phase macroscopic properties (porosity, permeability) are calculated and whenever possible are compared to experimental data. Using this information drainage and imbibition capillary pressure, and relative permeability curves are predicted and (whenever possible) compared to experimental data. The calculated information is grouped and compared to available literature information on typical behavior of tight formations. Capillary pressure curve for primary drainage process is predicted and compared to experimental mercury porosimetry in order to validate the virtual porous media by history matching. Relative permeability curves are also calculated and presented.
Berejnov, Viatcheslav; Sinton, David; Djilali, Ned
2009-01-01
Experimental two-phase invasion percolation flow patterns were observed in hydrophobic micro-porous networks designed to model fuel cell specific porous media. In order to mimic the operational conditions encountered in the porous electrodes of polymer electrolyte membrane fuel cells (PEMFCs), micro-porous networks were fabricated with corresponding microchannel size distributions. The inlet channels were invaded homogeneously with flow rates corresponding to fuel cell current densities of 1.0 to 0.1 A/cm2 (Ca 10e-7-10e-8). A variety of fractal breakthrough patterns were observed and analyzed to quantify flooding density and geometrical diversity in terms of the total saturation, St, local saturations, s, and fractal dimension, D. It was found that St increases monotonically during the invasion process until the breakthrough point is reached, and s profiles indicate the dynamic distribution of the liquid phase during the process. Fractal analysis confirmed that the experiments fall within the flow regime of i...
Hoermann, Astrid; Cicin-Sain, Damjan; Jaeger, Johannes
2016-03-15
Understanding eukaryotic transcriptional regulation and its role in development and pattern formation is one of the big challenges in biology today. Most attempts at tackling this problem either focus on the molecular details of transcription factor binding, or aim at genome-wide prediction of expression patterns from sequence through bioinformatics and mathematical modelling. Here we bridge the gap between these two complementary approaches by providing an integrative model of cis-regulatory elements governing the expression of the gap gene giant (gt) in the blastoderm embryo of Drosophila melanogaster. We use a reverse-engineering method, where mathematical models are fit to quantitative spatio-temporal reporter gene expression data to infer the regulatory mechanisms underlying gt expression in its anterior and posterior domains. These models are validated through prediction of gene expression in mutant backgrounds. A detailed analysis of our data and models reveals that gt is regulated by domain-specific CREs at early stages, while a late element drives expression in both the anterior and the posterior domains. Initial gt expression depends exclusively on inputs from maternal factors. Later, gap gene cross-repression and gt auto-activation become increasingly important. We show that auto-regulation creates a positive feedback, which mediates the transition from early to late stages of regulation. We confirm the existence and role of gt auto-activation through targeted mutagenesis of Gt transcription factor binding sites. In summary, our analysis provides a comprehensive picture of spatio-temporal gene regulation by different interacting enhancer elements for an important developmental regulator.
Annual Perspectives in Mathematics Education 2016: Mathematical Modeling and Modeling Mathematics
Hirsch, Christian R., Ed.; McDuffie, Amy Roth, Ed.
2016-01-01
Mathematical modeling plays an increasingly important role both in real-life applications--in engineering, business, the social sciences, climate study, advanced design, and more--and within mathematics education itself. This 2016 volume of "Annual Perspectives in Mathematics Education" ("APME") focuses on this key topic from a…
The Spectrum of Mathematical Models.
Karplus, Walter J.
1983-01-01
Mathematical modeling problems encountered in many disciplines are discussed in terms of the modeling process and applications of models. The models are classified according to three types of abstraction: continuous-space-continuous-time, discrete-space-continuous-time, and discrete-space-discrete-time. Limitations in different kinds of modeling…
Mathematical models of magnetite desliming for automated quality control systems
Olevska, Yu.; Mishchenko, V.; Olevskyi, V.
2016-10-01
The aim of the study is to provide multifactor mathematical models suitable for use in automatic control systems of desliming process. For this purpose we described the motion of a two-phase environment regard to the shape the desliming machine and technological parameters of the enrichment process. We created the method for preparation of dependences of the enrichment process quality from the technological and design parameters. To automate the process we constructed mathematical models to justify intensive technological modes and optimal parameters for design of desliming machine.
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
When there exists anisotropy in underground media, elastic parameters of the observed coordinate possibly do not coincide with that of the natural coordinate. According to the theory that the density of potential energy, dissipating energy is independent of the coordinate, the relationship of elastic parameters between two coordinates is derived for two-phase anisotropic media. Then, pseudospectral method to solve wave equations of two-phase anisotropic media is derived. At last, we use this method to simulate wave propagation in two-phase anisotropic media, four types of waves are observed in the snapshots, i.e., fast P wave and slow P wave, fast S wave and slow S wave. Shear wave splitting, SV wave cusps and elastic wave reflection and transmission are also observed.
Mathematics Teachers' Ideas about Mathematical Models: A Diverse Landscape
Bautista, Alfredo; Wilkerson-Jerde, Michelle H.; Tobin, Roger G.; Brizuela, Bárbara M.
2014-01-01
This paper describes the ideas that mathematics teachers (grades 5-9) have regarding mathematical models of real-world phenomena, and explores how teachers' ideas differ depending on their educational background. Participants were 56 United States in-service mathematics teachers. We analyzed teachers' written responses to three open-ended…
Chauchat, J.; Revil-Baudard, T.; Hurther, D.
2014-12-01
Sheet flow is believed to be a major process for morphological evolution of natural systems. An important research effort has been dedicated to laboratory and numerical studies of sheet flow regime that have allowed to make some progress in the understanding of the underlying physical processes. Recent advances made in high resolution measurement techniques allows to give new insights into the small scale physical processes. In this contribution, a novel uniform and steady sheet flow dataset based on an Acoustic Concentration and Velocity Profiler (ACVP) is presented. Profile of colocated velocities (streamwise and wall-normal) and sediment concentration has been measured at high-resolution (3 mm ; 78 Hz for the velocities and 4.9 Hz for the concentration). The measured profiles extend over the whole water column, from the free surface down to the fixed bed and an ensemble averaging over eleven realisations of the same experimental conditions has been used to obtain mean profiles of streamwise velocity, concentration, sediment flux and turbulent shear stress. The present experiment corresponds to a Shields number of θ=0.44 and a suspension number of ws/u*=1.1 corresponding to the lower limit of the no-suspension sheet flow regime. The analysis of the mixing length profile allows to identify two layers, a dilute suspension layer dominated by turbulence and a dense moving bed layer dominated by granular interactions. Our measurements show that the Von Karman parameter is reduced by a factor of more than two and that the Schmidt number is almost constant with a mean value of σs=0.44. Frictional and collisional interactions are encountered in the bed layer. Frictional interactions dominate close to the fixed bed interface whereas collisional interactions seems to control the flow at the transition between the dense and dilute layers. The relevancy of different constitutive laws for two-phase flow models are discussed.
Energy Technology Data Exchange (ETDEWEB)
Wang, J.A.
1996-05-01
Ultrasonic methods used in the study of radiation damage and recovery in single crystals appear to also be useful for similar studies on polycrystalline alloys. Ultrasonic methods have demonstrated a sensitivity to radiation damage as affected by neutron fluence, irradiation temperature, large changes in composition, and possibly, as well, by neutron energy spectrum. On the microstructure defect evolution, only the residual defects created through the radiation event will contribute to the final macroscopic material property change. From a microstructure point, it is generally accepted that radiation hardening and embrittlement in metals are caused by clusters of vacancies, interstitial, and solute atoms that impede the motion of slip dislocations. Although vacancy-type defects are a major contributor to the material hardening, they also indicate the presence of other interstitial defects. Thus the total volume change of vacancy-type defects before and after irradiation can serve as a direct index to the final material property changes. The volume change of the vacancy-type defects can be determined by utilizing the two -phase composite model (matrix and void-type inclusion) to interpret wave velocities of baseline and irradiated specimens that are obtained from the ultrasonic wave experiment. This is a relatively economic and straightforward procedure. The correlation of the volume change of the vacancy-type defects with the existing destructive mechanical test results may play an important role in the future for the prediction of the radiation embrittlement and remaining plant lifetime, especially for the older plants on the verge of exhausting all the available mechanical test specimens loaded in the surveillance capsules. The above hypothesis was supported by the limited irradiated data analyzed and presented in his paper. The proposed ultrasonic methodology also has a potential application to assess creep damage in fossil power plants.
Delil, A. A. M.
2001-02-01
Earlier publications extensively describe NLR research on thermal-gravitational modeling and scaling of two-phase heat transport systems for spacecraft applications. These publications on mechanically and capillary pumped two-phase loops discuss pure geometric scaling, pure fluid to fluid scaling, and combined (hybrid) scaling of a prototype system by a model at the same gravity level, and of a prototype in micro-gravity environment by a scale-model on earth. More recent publications include the scaling aspects of prototype two-phase loops for Moon or Mars applications by scale-models on earth. Recent work, discussed here, concerns extension of thermal-gravitational scaling to super-g acceleration levels. This turned out to be necessary, since a very promising super-g application for (two-phase) heat transport systems will be cooling of high-power electronics in spinning satellites and in military combat aircraft. In such aircraft, the electronics can be exposed during maneuvres to transient accelerations up to 120 m/s2. The discussions focus on ``conventional'' (capillary) pumped two-phase loops. It can be considered as introduction to the accompanying article, which focuses on pulsating and oscillating devices. .
Liu, Haihu; Ju, Yaping; Wang, Ningning; Xi, Guang; Zhang, Yonghao
2015-09-01
Contact angle hysteresis is an important physical phenomenon omnipresent in nature and various industrial processes, but its effects are not considered in many existing multiphase flow simulations due to modeling complexity. In this work, a multiphase lattice Boltzmann method (LBM) is developed to simulate the contact-line dynamics with consideration of the contact angle hysteresis for a broad range of kinematic viscosity ratios. In this method, the immiscible two-phase flow is described by a color-fluid model, in which the multiple-relaxation-time collision operator is adopted to increase numerical stability and suppress unphysical spurious currents at the contact line. The contact angle hysteresis is introduced using the strategy proposed by Ding and Spelt [Ding and Spelt, J. Fluid Mech. 599, 341 (2008)JFLSA70022-112010.1017/S0022112008000190], and the geometrical wetting boundary condition is enforced to obtain the desired contact angle. This method is first validated by simulations of static contact angle and dynamic capillary intrusion process on ideal (smooth) surfaces. It is then used to simulate the dynamic behavior of a droplet on a nonideal (inhomogeneous) surface subject to a simple shear flow. When the droplet remains pinned on the surface due to hysteresis, the steady interface shapes of the droplet quantitatively agree well with the previous numerical results. Four typical motion modes of contact points, as observed in a recent study, are qualitatively reproduced with varying advancing and receding contact angles. The viscosity ratio is found to have a notable impact on the droplet deformation, breakup, and hysteresis behavior. Finally, this method is extended to simulate the droplet breakup in a microfluidic T junction, with one half of the wall surface ideal and the other half nonideal. Due to the contact angle hysteresis, the droplet asymmetrically breaks up into two daughter droplets with the smaller one in the nonideal branch channel, and the
Liu, Haihu; Ju, Yaping; Wang, Ningning; Xi, Guang; Zhang, Yonghao
2015-09-01
Contact angle hysteresis is an important physical phenomenon omnipresent in nature and various industrial processes, but its effects are not considered in many existing multiphase flow simulations due to modeling complexity. In this work, a multiphase lattice Boltzmann method (LBM) is developed to simulate the contact-line dynamics with consideration of the contact angle hysteresis for a broad range of kinematic viscosity ratios. In this method, the immiscible two-phase flow is described by a color-fluid model, in which the multiple-relaxation-time collision operator is adopted to increase numerical stability and suppress unphysical spurious currents at the contact line. The contact angle hysteresis is introduced using the strategy proposed by Ding and Spelt [Ding and Spelt, J. Fluid Mech. 599, 341 (2008), 10.1017/S0022112008000190], and the geometrical wetting boundary condition is enforced to obtain the desired contact angle. This method is first validated by simulations of static contact angle and dynamic capillary intrusion process on ideal (smooth) surfaces. It is then used to simulate the dynamic behavior of a droplet on a nonideal (inhomogeneous) surface subject to a simple shear flow. When the droplet remains pinned on the surface due to hysteresis, the steady interface shapes of the droplet quantitatively agree well with the previous numerical results. Four typical motion modes of contact points, as observed in a recent study, are qualitatively reproduced with varying advancing and receding contact angles. The viscosity ratio is found to have a notable impact on the droplet deformation, breakup, and hysteresis behavior. Finally, this method is extended to simulate the droplet breakup in a microfluidic T junction, with one half of the wall surface ideal and the other half nonideal. Due to the contact angle hysteresis, the droplet asymmetrically breaks up into two daughter droplets with the smaller one in the nonideal branch channel, and the behavior of
Patel, Sonal; Wilding, W Vincent; Rowley, Richard L
2011-01-14
Molecular dynamics simulations were performed to determine two-phase configurations of model propane molecules below the critical point and in the near-critical, two-phase region. A postprocessor that uses a Monte Carlo method for determination of volumes attributable to each molecule was used to obtain density histograms of the particles from which the bulk coexisting equilibrium vapor and liquid densities were determined. This method of analyzing coexisting densities in a two-phase simulation is straightforward and can be easily implemented for complex, multisite models. Various degrees of internal flexibility in the propane models have little effect on the coexisting densities at temperatures 40 K or more below the critical point, but internal flexibility (angle bending and bond vibrations) does affect the saturated liquid densities in the near-critical region, changing the critical temperature by approximately 20 K. Shorter cutoffs were also found to affect the phase dome and the location of the critical point.
Representations used by mathematics student teachers in mathematical modeling process
Directory of Open Access Journals (Sweden)
Aytuğ Özaltun
2014-02-01
Full Text Available The purpose of this study is to determine representations used by mathematics student teachers in steps of mathematical modeling process based on their solutions of problems formed in the context of different classification of modeling. The study was conducted with fifteen secondary mathematics student teachers given a Mathematical Modeling course. The participants were separated into five collaboration groups of three students. Data were collected with the detailed written papers given by the groups for the problems and GeoGebra solution files. The groups benefited from verbal, algebraic, figural, tabular and dynamic representations while they were solving the problems. Considering all steps of the process, groups at most used verbal and algebraic representations. While they used only verbal representation in analyzing the problem, they benefited from at most verbal representation and then figural representation in establishing the systematic structure. The most used is algebraic and then verbal representations in the steps of mathematization, meta-mathematization, and mathematical analysis. In the steps of interpretation/evaluation and the model verification, the groups mainly benefited from verbal and then algebraic representations. Further researches towards why representations are preferred in the specific steps of the mathematical modeling process are suggested.Key Words: Mathematical modeling, modeling problems, mathematics student teachers, representations.
The 24-Hour Mathematical Modeling Challenge
Galluzzo, Benjamin J.; Wendt, Theodore J.
2015-01-01
Across the mathematics curriculum there is a renewed emphasis on applications of mathematics and on mathematical modeling. Providing students with modeling experiences beyond the ordinary classroom setting remains a challenge, however. In this article, we describe the 24-hour Mathematical Modeling Challenge, an extracurricular event that exposes…
Shock wave of vapor-liquid two-phase flow
Institute of Scientific and Technical Information of China (English)
Liangju ZHAO; Fei WANG; Hong GAO; Jingwen TANG; Yuexiang YUAN
2008-01-01
The shock wave of vapor-liquid two-phase flow in a pressure-gain steam injector is studied by build-ing a mathematic model and making calculations. The results show that after the shock, the vapor is nearly com-pletely condensed. The upstream Mach number and the volume ratio of vapor have a great effect on the shock. The pressure and Mach number of two-phase shock con-form to the shock of ideal gas. The analysis of available energy shows that the shock is an irreversible process with entropy increase.
Modeling interdisciplinary activities involving Mathematics
DEFF Research Database (Denmark)
Iversen, Steffen Møllegaard
2006-01-01
In this paper a didactical model is presented. The goal of the model is to work as a didactical tool, or conceptual frame, for developing, carrying through and evaluating interdisciplinary activities involving the subject of mathematics and philosophy in the high schools. Through the terms...... domains (Michelsen, 2001, 2005a, 2005b). Furthermore the theoretical description rest on a series of qualitative interviews with teachers from the Danish high school (grades 9-11) conducted recently. The special case of concrete interdisciplinary activities between mathematics and philosophy is also...
DEFF Research Database (Denmark)
Jakobsen, Arne; Antonius, Jesper; Knudsen, Hans Jørgen Høgaard
1999-01-01
Distributed dynamic models of a simple coaxial-type evaporator are implemented in the simulation tool Sinda/Fluint. In order to obtain data for model validation an experimental set-up is built, where dynamic responses to changes in inflow and/or outflow of refrigerant are recorded. Model validation...
Mathematical modelling of membrane separation
DEFF Research Database (Denmark)
Vinther, Frank
This thesis concerns mathematical modelling of membrane separation. The thesis consists of introductory theory on membrane separation, equations of motion, and properties of dextran, which will be the solute species throughout the thesis. Furthermore, the thesis consist of three separate mathemat......This thesis concerns mathematical modelling of membrane separation. The thesis consists of introductory theory on membrane separation, equations of motion, and properties of dextran, which will be the solute species throughout the thesis. Furthermore, the thesis consist of three separate....... It is found that the probability of entering the pore is highest when the largest of the radii in the ellipse is equal to half the radius of the pore, in case of molecules with circular radius less than the pore radius. The results are directly related to the macroscopic distribution coefficient...
Mathematical Modelling of Silica Scaling Deposition in Geothermal Wells
Nizami, M.; Sutopo
2016-09-01
Silica scaling is widely encountered in geothermal wells in which produce two-phase geothermal fluid. Silica scaling could be formed due to chemical reacting by mixing a geothermal fluid with other geothermal fluid in different compositions, or also can be caused by changes in fluid properties due to changes pressure and temperature. One of method to overcome silica scaling which is occurred around geothermal well is by workover operation. Modelling of silica deposition in porous medium has been modeled in previously. However, the growth of silica scaling deposition in geothermal wells has never been modeled. Modelling of silica deposition through geothermal is important aspects to determine depth of silica scaling growth and best placing for workover device to clean silica scaling. This study is attempted to develop mathematical models for predicting silica scaling through geothermal wells. The mathematical model is developed by integrating the solubility-temperature correlation and two-phase pressure drop coupled wellbore fluid temperature correlation in a production well. The coupled model of two-phase pressure drop and wellbore fluid temperature correlation which is used in this paper is Hasan-Kabir correlation. This modelling is divided into two categories: single and two phase fluid model. Modelling of silica deposition is constrained in temperature distribution effect through geothermal wells by solubility correlation for silica. The results of this study are visualizing the growth of silica scaling thickness through geothermal wells in each segment of depth. Sensitivity analysis is applied in several parameters, such as: bottom-hole pressure, temperature, and silica concentrations. Temperature is most impact factor for silica scaling through geothermal wellbore and depth of flash point. In flash point, silica scaling thickness has reached maximum because reducing of mole in liquid portion.
Full status two phase turbulent combustion model%全状态两相湍流燃烧模型及其检验
Institute of Scientific and Technical Information of China (English)
王方; 黄勇
2012-01-01
在欧拉-拉氏体系中在传统点源两相湍流燃烧模型（TM）中考虑液滴带火燃烧状态，提出全状态两相湍流燃烧模型（FSM），并用甲醇-空气两相湍流射流火焰实验数据对两种模型进行检验，对比结果表明：FSM模型能够给出平均温度的双峰分布，得到更合理的预报结果.%In Euler-Lagrange frame,the individual droplet burning behavior was added into the traditional point source two phase turbulent combustion model(TM),and then a full status two phase turbulent combustion model(FSM) was presented.The two kinds of two phase turbulent combustion models were tested by a set of methanol air two phase turbulent spray jet flame experimental data.The comparison results between the computational prediction results and the experimental data show that the FSM model can give two peaks in the averaged temperature profile,as well as more reasonable predictions.
Mathematical modeling of biological processes
Friedman, Avner
2014-01-01
This book on mathematical modeling of biological processes includes a wide selection of biological topics that demonstrate the power of mathematics and computational codes in setting up biological processes with a rigorous and predictive framework. Topics include: enzyme dynamics, spread of disease, harvesting bacteria, competition among live species, neuronal oscillations, transport of neurofilaments in axon, cancer and cancer therapy, and granulomas. Complete with a description of the biological background and biological question that requires the use of mathematics, this book is developed for graduate students and advanced undergraduate students with only basic knowledge of ordinary differential equations and partial differential equations; background in biology is not required. Students will gain knowledge on how to program with MATLAB without previous programming experience and how to use codes in order to test biological hypothesis.
Yilmaz, Suha; Tekin-Dede, Ayse
2016-01-01
Mathematization competency is considered in the field as the focus of modelling process. Considering the various definitions, the components of the mathematization competency are determined as identifying assumptions, identifying variables based on the assumptions and constructing mathematical model/s based on the relations among identified…
Energy Technology Data Exchange (ETDEWEB)
Touma, Rony [Department of Computer Science & Mathematics, Lebanese American University, Beirut (Lebanon); Zeidan, Dia [School of Basic Sciences and Humanities, German Jordanian University, Amman (Jordan)
2016-06-08
In this paper we extend a central finite volume method on nonuniform grids to the case of drift-flux two-phase flow problems. The numerical base scheme is an unstaggered, non oscillatory, second-order accurate finite volume scheme that evolves a piecewise linear numerical solution on a single grid and uses dual cells intermediately while updating the numerical solution to avoid the resolution of the Riemann problems arising at the cell interfaces. We then apply the numerical scheme and solve a classical drift-flux problem. The obtained results are in good agreement with corresponding ones appearing in the recent literature, thus confirming the potential of the proposed scheme.
Bai, Meng; Xu, Shihe
2014-01-01
In this paper we study the two-phase size-structured population model with infinite states-at-birth and distributed delay in birth process. The model distinguishes individuals by two different status: the ‘reproductive’ stage and the ‘nonreproductive’ stage. We establish the well-posedness for this model and show that the solution of this model exhibits asynchronous exponential growth by means of semigroups. We also consider a special case in which the individuals in the ‘reproductive’ stage and the ‘nonreproductive’ stage have the same growth rates and give a comparison between this two-phase model with the classical one-phase model. PMID:24963976
Modeling interdisciplinary activities involving Mathematics
DEFF Research Database (Denmark)
Iversen, Steffen Møllegaard
2006-01-01
In this paper a didactical model is presented. The goal of the model is to work as a didactical tool, or conceptual frame, for developing, carrying through and evaluating interdisciplinary activities involving the subject of mathematics and philosophy in the high schools. Through the terms...... of Horizontal Intertwining, Vertical Structuring and Horizontal Propagation the model consists of three phases, each considering different aspects of the nature of interdisciplinary activities. The theoretical modelling is inspired by work which focuses on the students abilities to concept formation in expanded...... domains (Michelsen, 2001, 2005a, 2005b). Furthermore the theoretical description rest on a series of qualitative interviews with teachers from the Danish high school (grades 9-11) conducted recently. The special case of concrete interdisciplinary activities between mathematics and philosophy is also...
Computational methods for two-phase flow and particle transport
Lee, Wen Ho
2013-01-01
This book describes mathematical formulations and computational methods for solving two-phase flow problems with a computer code that calculates thermal hydraulic problems related to light water and fast breeder reactors. The physical model also handles the particle and gas flow problems that arise from coal gasification and fluidized beds. The second part of this book deals with the computational methods for particle transport.
Lee, Cheng-Hsien; Low, Ying Min; Chiew, Yee-Meng
2016-05-01
Sediment transport is fundamentally a two-phase phenomenon involving fluid and sediments; however, many existing numerical models are one-phase approaches, which are unable to capture the complex fluid-particle and inter-particle interactions. In the last decade, two-phase models have gained traction; however, there are still many limitations in these models. For example, several existing two-phase models are confined to one-dimensional problems; in addition, the existing two-dimensional models simulate only the region outside the sand bed. This paper develops a new three-dimensional two-phase model for simulating sediment transport in the sheet flow condition, incorporating recently published rheological characteristics of sediments. The enduring-contact, inertial, and fluid viscosity effects are considered in determining sediment pressure and stresses, enabling the model to be applicable to a wide range of particle Reynolds number. A k - ɛ turbulence model is adopted to compute the Reynolds stresses. In addition, a novel numerical scheme is proposed, thus avoiding numerical instability caused by high sediment concentration and allowing the sediment dynamics to be computed both within and outside the sand bed. The present model is applied to two classical problems, namely, sheet flow and scour under a pipeline with favorable results. For sheet flow, the computed velocity is consistent with measured data reported in the literature. For pipeline scour, the computed scour rate beneath the pipeline agrees with previous experimental observations. However, the present model is unable to capture vortex shedding; consequently, the sediment deposition behind the pipeline is overestimated. Sensitivity analyses reveal that model parameters associated with turbulence have strong influence on the computed results.
Energy Technology Data Exchange (ETDEWEB)
Lee, Cheng-Hsien [Centre for Offshore Research and Engineering, Department of Civil and Environmental Engineering, National University of Singapore, 1 Engineering Drive 2, Singapore 117576 (Singapore); Department of Water Resources and Environmental Engineering, Tamkang University, New Taipei City 25137, Taiwan (China); Low, Ying Min, E-mail: ceelowym@nus.edu.sg [Centre for Offshore Research and Engineering, Department of Civil and Environmental Engineering, National University of Singapore, 1 Engineering Drive 2, Singapore 117576 (Singapore); Chiew, Yee-Meng [School of Civil and Environmental Engineering, Nanyang Technological University (Singapore)
2016-05-15
Sediment transport is fundamentally a two-phase phenomenon involving fluid and sediments; however, many existing numerical models are one-phase approaches, which are unable to capture the complex fluid-particle and inter-particle interactions. In the last decade, two-phase models have gained traction; however, there are still many limitations in these models. For example, several existing two-phase models are confined to one-dimensional problems; in addition, the existing two-dimensional models simulate only the region outside the sand bed. This paper develops a new three-dimensional two-phase model for simulating sediment transport in the sheet flow condition, incorporating recently published rheological characteristics of sediments. The enduring-contact, inertial, and fluid viscosity effects are considered in determining sediment pressure and stresses, enabling the model to be applicable to a wide range of particle Reynolds number. A k − ε turbulence model is adopted to compute the Reynolds stresses. In addition, a novel numerical scheme is proposed, thus avoiding numerical instability caused by high sediment concentration and allowing the sediment dynamics to be computed both within and outside the sand bed. The present model is applied to two classical problems, namely, sheet flow and scour under a pipeline with favorable results. For sheet flow, the computed velocity is consistent with measured data reported in the literature. For pipeline scour, the computed scour rate beneath the pipeline agrees with previous experimental observations. However, the present model is unable to capture vortex shedding; consequently, the sediment deposition behind the pipeline is overestimated. Sensitivity analyses reveal that model parameters associated with turbulence have strong influence on the computed results.
Mathematical modelling in solid mechanics
Sofonea, Mircea; Steigmann, David
2017-01-01
This book presents new research results in multidisciplinary fields of mathematical and numerical modelling in mechanics. The chapters treat the topics: mathematical modelling in solid, fluid and contact mechanics nonconvex variational analysis with emphasis to nonlinear solid and structural mechanics numerical modelling of problems with non-smooth constitutive laws, approximation of variational and hemivariational inequalities, numerical analysis of discrete schemes, numerical methods and the corresponding algorithms, applications to mechanical engineering numerical aspects of non-smooth mechanics, with emphasis on developing accurate and reliable computational tools mechanics of fibre-reinforced materials behaviour of elasto-plastic materials accounting for the microstructural defects definition of structural defects based on the differential geometry concepts or on the atomistic basis interaction between phase transformation and dislocations at nano-scale energetic arguments bifurcation and post-buckling a...
Opinions of Secondary School Mathematics Teachers on Mathematical Modelling
Tutak, Tayfun; Güder, Yunus
2013-01-01
The aim of this study is to identify the opinions of secondary school mathematics teachers about mathematical modelling. Qualitative research was used. The participants of the study were 40 secondary school teachers working in the Bingöl Province in Turkey during 2012-2013 education year. Semi-structured interview form prepared by the researcher…
Opinions of Secondary School Mathematics Teachers on Mathematical Modelling
Tutak, Tayfun; Güder, Yunus
2013-01-01
The aim of this study is to identify the opinions of secondary school mathematics teachers about mathematical modelling. Qualitative research was used. The participants of the study were 40 secondary school teachers working in the Bingöl Province in Turkey during 2012-2013 education year. Semi-structured interview form prepared by the researcher…
Raeini, Ali Q.; Bijeljic, Branko; Blunt, Martin J.
2015-09-01
We study capillary trapping in porous media using direct pore-scale simulation of two-phase flow on micro-CT images of a Berea sandstone and a sandpack. The trapped non-wetting phase saturations are predicted by solving the full Navier-Stokes equations using a volume-of-fluid based finite-volume framework to simulate primary drainage followed by water injection. Using these simulations, we analyse the effects of initial non-wetting-phase saturation, capillary number and flow direction on the residual saturation. The predictions from our numerical method are in agreement with published experimental measurements of capillary trapping curves. This shows that our direct simulation method can be used to elucidate the effect of pore structure and flow pattern of capillary trapping and provides a platform to study the physics of multiphase flow at the pore scale.
Directory of Open Access Journals (Sweden)
Rauch Ł.
2015-09-01
Full Text Available The coupled finite element multiscale simulations (FE2 require costly numerical procedures in both macro and micro scales. Attempts to improve numerical efficiency are focused mainly on two areas of development, i.e. parallelization/distribution of numerical procedures and simplification of virtual material representation. One of the representatives of both mentioned areas is the idea of Statistically Similar Representative Volume Element (SSRVE. It aims at the reduction of the number of finite elements in micro scale as well as at parallelization of the calculations in micro scale which can be performed without barriers. The simplification of computational domain is realized by transformation of sophisticated images of material microstructure into artificially created simple objects being characterized by similar features as their original equivalents. In existing solutions for two-phase steels SSRVE is created on the basis of the analysis of shape coefficients of hard phase in real microstructure and searching for a representative simple structure with similar shape coefficients. Optimization techniques were used to solve this task. In the present paper local strains and stresses are added to the cost function in optimization. Various forms of the objective function composed of different elements were investigated and used in the optimization procedure for the creation of the final SSRVE. The results are compared as far as the efficiency of the procedure and uniqueness of the solution are considered. The best objective function composed of shape coefficients, as well as of strains and stresses, was proposed. Examples of SSRVEs determined for the investigated two-phase steel using that objective function are demonstrated in the paper. Each step of SSRVE creation is investigated from computational efficiency point of view. The proposition of implementation of the whole computational procedure on modern High Performance Computing (HPC
Mathematical models of human behavior
DEFF Research Database (Denmark)
Møllgaard, Anders Edsberg
data set, along with work on other behavioral data. The overall goal is to contribute to a quantitative understanding of human behavior using big data and mathematical models. Central to the thesis is the determination of the predictability of different human activities. Upper limits are derived......, thereby implying that interactions between spreading processes are driving forces of attention dynamics. Overall, the thesis contributes to a quantitative understanding of a wide range of different human behaviors by applying mathematical modeling to behavioral data. There can be no doubt......During the last 15 years there has been an explosion in human behavioral data caused by the emergence of cheap electronics and online platforms. This has spawned a whole new research field called computational social science, which has a quantitative approach to the study of human behavior. Most...
Continuum mechanics the birthplace of mathematical models
Allen, Myron B
2015-01-01
Continuum mechanics is a standard course in many graduate programs in engineering and applied mathematics as it provides the foundations for the various differential equations and mathematical models that are encountered in fluid mechanics, solid mechanics, and heat transfer. This book successfully makes the topic more accessible to advanced undergraduate mathematics majors by aligning the mathematical notation and language with related courses in multivariable calculus, linear algebra, and differential equations; making connections with other areas of applied mathematics where parial differe
Simsek, Gorkem; Roudbari, Mahnaz Shokrpour; van Brummelen, E Harald
2016-01-01
We derive a new form of a thermodynamically consistent quasi-incompressible diffuse-interface Navier-Stokes Cahn-Hilliard model for a two-phase-flow of incompressible fluids with different densities. The derivation is based on mixture theory by invoking the second law of thermodynamics and Coleman-Noll procedure. In addition, we develop a linear and unconditionally energy stable time-integration scheme for the derived model. Such a scheme is nontrivial, because it has to suitably deal with all nonlinear terms in the model. Our proposed scheme is the first linear method satisfying a discrete energy law for quasi-incompressible two-phase flows. The scheme also preserves mass. Numerical experiments verify the suitability of the scheme for high density ratios and for large time step sizes by considering the coalescence and break-up dynamics of droplets including pinching due to gravity.
Mathematical models of granular matter
Mariano, Paolo; Giovine, Pasquale
2008-01-01
Granular matter displays a variety of peculiarities that distinguish it from other appearances studied in condensed matter physics and renders its overall mathematical modelling somewhat arduous. Prominent directions in the modelling granular flows are analyzed from various points of view. Foundational issues, numerical schemes and experimental results are discussed. The volume furnishes a rather complete overview of the current research trends in the mechanics of granular matter. Various chapters introduce the reader to different points of view and related techniques. New models describing granular bodies as complex bodies are presented. Results on the analysis of the inelastic Boltzmann equations are collected in different chapters. Gallavotti-Cohen symmetry is also discussed.
A mathematical model for preflush treatment in an oil reservoir using a fully miscible fluid
F.J. Vermolen; G.-J. Pieters; P.L.J. Zitha; J. Bruining
1999-01-01
textabstractIn this paper we propose and analyse a mathematical model for preflush treatment in an oil reservoir. The model is based on two phase flow in which both phases are fully miscible. For the case of constant injection rate condition, fully implicit solutions can be constructed. Saturation p
Institute of Scientific and Technical Information of China (English)
尚智; 杨瑞昌; FUKUDA Kenji; 钟勇; 巨泽建
2003-01-01
A mathematical model of two-dimensional turbulent gas-particle two-phase flow based on the modified diffusion flux model (DFM) and a numerical simulation method to analyze the gas-particle flow structures are developed. The modified diffusion flux model, in which the acceleration due to various forces is taken into account for the calculation of the diffusion velocity of particles, is applicable to the analysis of multi-dimensional gas-particle two-phase turbulent flow. In order to verify its accuracy and efficiency, the numerical simulation by DFM is compared with experimental studies and the prediction by κ-ε-κp two-fluid model, which shows a reasonable agreement. It is confirmed that the modified diffusion flux model is suitable for simulating the multi-dimensional gas-particle two-phase flow.
Mathematical modeling of laser lipolysis
Directory of Open Access Journals (Sweden)
Reynaud Jean
2008-02-01
Full Text Available Abstract Background and Objectives Liposuction continues to be one of the most popular procedures performed in cosmetic surgery. As the public's demand for body contouring continues, laser lipolysis has been proposed to improve results, minimize risk, optimize patient comfort, and reduce the recovery period. Mathematical modeling of laser lipolysis could provide a better understanding of the laser lipolysis process and could determine the optimal dosage as a function of fat volume to be removed. Study design/Materials and Methods An Optical-Thermal-Damage Model was formulated using finite-element modeling software (Femlab 3.1, Comsol Inc. The general model simulated light distribution using the diffusion approximation of the transport theory, temperature rise using the bioheat equation and laser-induced injury using the Arrhenius damage model. Biological tissue was represented by two homogenous regions (dermis and fat layer with a nonlinear air-tissue boundary condition including free convection. Video recordings were used to gain a better understanding of the back and forth movement of the cannula during laser lipolysis in order to consider them in our mathematical model. Infrared video recordings were also performed in order to compare the actual surface temperatures to our calculations. The reduction in fat volume was determined as a function of the total applied energy and subsequently compared to clinical data reported in the literature. Results In patients, when using cooled tumescent anesthesia, 1064 nm Nd:YAG laser or 980 nm diode laser: (6 W, back and forth motion: 100 mm/s give similar skin surface temperature (max: 41°C. These measurements are in accordance with those obtained by mathematical modeling performed with a 1 mm cannula inserted inside the hypodermis layer at 0.8 cm below the surface. Similarly, the fat volume reduction observed in patients at 6-month follow up can be determined by mathematical modeling. This fat reduction
Computer simulation of two-phase flow in nuclear reactors
Energy Technology Data Exchange (ETDEWEB)
Wulff, W.
1992-09-01
Two-phase flow models dominate the economic resource requirements for development and use of computer codes for analyzing thermohydraulic transients in nuclear power plants. Six principles are presented on mathematical modeling and selection of numerical methods, along with suggestions on programming and machine selection, all aimed at reducing the cost of analysis. Computer simulation is contrasted with traditional computer calculation. The advantages of run-time interactive access operation in a simulation environment are demonstrated. It is explained that the drift-flux model is better suited for two-phase flow analysis in nuclear reactors than the two-fluid model, because of the latter`s closure problem. The advantage of analytical over numerical integration is demonstrated. Modeling and programming techniques are presented which minimize the number of needed arithmetical and logical operations and thereby increase the simulation speed, while decreasing the cost.
Computer simulation of two-phase flow in nuclear reactors
Energy Technology Data Exchange (ETDEWEB)
Wulff, W.
1992-01-01
Two-phase flow models dominate the economic resource requirements for development and use of computer codes for analyzing thermohydraulic transients in nuclear power plants. Six principles are presented on mathematical modeling and selection of numerical methods, along with suggestions on programming and machine selection, all aimed at reducing the cost of analysis. Computer simulation is contrasted with traditional computer calculation. The advantages of run-time interactive access operation in a simulation environment are demonstrated. It is explained that the drift-flux model is better suited for two-phase flow analysis in nuclear reactors than the two-fluid model, because of the latter's closure problem. The advantage of analytical over numerical integration is demonstrated. Modeling and programming techniques are presented which minimize the number of needed arithmetical and logical operations and thereby increase the simulation speed, while decreasing the cost.
Siripatana, Chairat; Thongpan, Hathaikarn; Promraksa, Arwut
2017-03-01
This article explores a volumetric approach in formulating differential equations for a class of engineering flow problems involving component transfer within or between two phases. In contrast to conventional formulation which is based on linear velocities, this work proposed a slightly different approach based on volumetric flow-rate which is essentially constant in many industrial processes. In effect, many multi-dimensional flow problems found industrially can be simplified into multi-component or multi-phase but one-dimensional flow problems. The formulation is largely generic, covering counter-current, concurrent or batch, fixed and fluidized bed arrangement. It was also intended to use for start-up, shut-down, control and steady state simulation. Since many realistic and industrial operation are dynamic with variable velocity and porosity in relation to position, analytical solutions are rare and limited to only very simple cases. Thus we also provide a numerical solution using Crank-Nicolson finite difference scheme. This solution is inherently stable as tested against a few cases published in the literature. However, it is anticipated that, for unconfined flow or non-constant flow-rate, traditional formulation should be applied.
Gu, Rui
Vapor compression cycles are widely used in heating, refrigerating and air-conditioning. A slight performance improvement in the components of a vapor compression cycle, such as the compressor, can play a significant role in saving energy use. However, the complexity and cost of these improvements can block their application in the market. Modifying the conventional cycle configuration can offer a less complex and less costly alternative approach. Economizing is a common modification for improving the performance of the refrigeration cycle, resulting in decreasing the work required to compress the gas per unit mass. Traditionally, economizing requires multi-stage compressors, the cost of which has restrained the scope for practical implementation. Compressors with injection ports, which can be used to inject economized refrigerant during the compression process, introduce new possibilities for economization with less cost. This work focuses on computationally investigating a refrigeration system performance with two-phase fluid injection, developing a better understanding of the impact of injected refrigerant quality on refrigeration system performance as well as evaluating the potential COP improvement that injection provides based on refrigeration system performance provided by Copeland.
Mathematical modeling of kidney transport.
Layton, Anita T
2013-01-01
In addition to metabolic waste and toxin excretion, the kidney also plays an indispensable role in regulating the balance of water, electrolytes, nitrogen, and acid-base. In this review, we describe representative mathematical models that have been developed to better understand kidney physiology and pathophysiology, including the regulation of glomerular filtration, the regulation of renal blood flow by means of the tubuloglomerular feedback mechanisms and of the myogenic mechanism, the urine concentrating mechanism, epithelial transport, and regulation of renal oxygen transport. We discuss the extent to which these modeling efforts have expanded our understanding of renal function in both health and disease.
Mathematical Modeling in Combustion Science
Takeno, Tadao
1988-01-01
An important new area of current research in combustion science is reviewed in the contributions to this volume. The complicated phenomena of combustion, such as chemical reactions, heat and mass transfer, and gaseous flows, have so far been studied predominantly by experiment and by phenomenological approaches. But asymptotic analysis and other recent developments are rapidly changing this situation. The contributions in this volume are devoted to mathematical modeling in three areas: high Mach number combustion, complex chemistry and physics, and flame modeling in small scale turbulent flow combustion.
A mathematical model of inheritance
Institute of Scientific and Technical Information of China (English)
瞿裕忠; 王志坚; 徐家福
1996-01-01
Inheritance is regarded as the hallmark of object-oriented programming languages.A mathematical model of inheritance is presented.In this model,the graph-sorted signature is introduced to represent the algebraic structure of the program,and an extension function on the graph-sorted signatures is used to formally describe the semantics of inheritance.The program’s algebraic structure reflects the syntactic constraints of the language and the corresponding extension function exposes the character of the language’s inheritance.
Institute of Scientific and Technical Information of China (English)
Zhen WANG; Hui ZHANG
2014-01-01
In this work, we obtain the global existence and uniqueness of classical solu-tions to a viscous liquid-gas two-phase model with mass-dependent viscosity and vacuum in one dimension, where the initial vacuum is allowed. We get the upper and lower bounds of gas and liquid masses n and m by the continuity methods which we use to study the compressible Navier-Stokes equations.
Noguchi, Yuki; Yamamoto, Takashi; Yamada, Takayuki; Izui, Kazuhiro; Nishiwaki, Shinji
2017-09-01
This papers proposes a level set-based topology optimization method for the simultaneous design of acoustic and structural material distributions. In this study, we develop a two-phase material model that is a mixture of an elastic material and acoustic medium, to represent an elastic structure and an acoustic cavity by controlling a volume fraction parameter. In the proposed model, boundary conditions at the two-phase material boundaries are satisfied naturally, avoiding the need to express these boundaries explicitly. We formulate a topology optimization problem to minimize the sound pressure level using this two-phase material model and a level set-based method that obtains topologies free from grayscales. The topological derivative of the objective functional is approximately derived using a variational approach and the adjoint variable method and is utilized to update the level set function via a time evolutionary reaction-diffusion equation. Several numerical examples present optimal acoustic and structural topologies that minimize the sound pressure generated from a vibrating elastic structure.
Energy Technology Data Exchange (ETDEWEB)
Hibiki, T. [Kyoto University, Research Reactor Institute, Osaka (Japan); Takamasa, T. [Tokyo University of Marine Science and Technology, Faculty of Marine Science, Tokyo (Japan); Ishii, M. [Purdue University, School of Nuclear Engineering, West Lafayette IN (United States)
2004-07-01
In view of the practical importance of the drift-flux model for two-phase flow analyses at microgravity conditions, the constitutive equations for distribution parameter and drift velocity have been developed for various two-phase flow regimes at microgravity conditions. A comparison of the model with various experimental data over various flow regimes and a wide range of flow parameters taken at microgravity conditions shows a satisfactory agreement. The newly developed drift-flux model has been applied to reduced gravity conditions such as 1.62 and 3.71 cm/s{sup 2}, which correspond to the Lunar and Martian surface gravities, respectively, and the effect of the gravity on the void fraction in two-phase flow systems has been discussed. It appears that the effect of the gravity on the void fraction in 2-phase flow systems is more pronounced for low liquid flow conditions, whereas the gravity effect may be ignored for high liquid velocity conditions.
Directory of Open Access Journals (Sweden)
Chao Si
2015-01-01
Full Text Available Water transport and the corresponding water management strategy in proton exchange membrane (PEM fuel cells are quite critical for the improvement of the cell performance. Accuracy modeling of water transport in porous electrodes strongly depends on the appropriate constitutive relationship for capillary pressure which is referred to as pc-s correlation, where pc is the capillary pressure and s is the fraction of saturation in the pores. In the present PEM fuel cell two-phase models, the Leverett-Udell pc-s correlation is widely utilized which is proposed based on fitting the experimental data for packed sands. However, the size and structure of pores for the commercial porous electrodes used in PEM fuel cells differ from those for the packed sands significantly. As a result, the Leverett-Udell correlation should be improper to characterize the two-phase transport in the porous electrodes. In the recent decade, many efforts were devoted to measuring the capillary pressure data and developing new pc-s correlations. The objective of this review is to review the most significant developments in recent years concerning the capillary pressure measurements and the developed pc-s correlations. It is expected that this review will be beneficial to develop the improved PEM fuel cell two-phase model.
Institute of Scientific and Technical Information of China (English)
Shuyuan Jiang∗and Hao Wang
2016-01-01
Aiming at the characteristics of the long tubular powder, a one⁃dimensional discrete group gas⁃solid two-phase flow model was established for the large caliber high speed Davis gun with a tubular modular charge. In this model, the tubular modules were described by the Lagrangian system without being assumed as pseudo⁃fluid, whereas the gas field is described by Eulerian system. The new model was used to simulate a 480 mm Davis gun. The simulation results were compared with test results, and the model was verified to be feasibility. This study provides a new method to research the interior ballistic performance of Davis guns.
A Mathematical Model of Mechanotransduction
Roth, Bradley J
2016-01-01
This article reviews the mechanical bidomain model, a mathematical description how the extracellular matrix and intracellular cytoskeleton are coupled by integrin proteins. The fundamental hypothesis is that differences between intracellular and extracellular displacements drive mechanotransduction. A one-dimensional example illustrates the model, which is then extended to two dimensions. In several cases the equations are solved analytically, illustrating how displacements divide into two parts: monodomain displacements are identical in both spaces and therefore do not contribute to mechanotransduction, whereas bidomain displacements cause mechanotransduction. A new length constant depends on the intracellular and extracellular shear moduli and the integrin spring constant, and bidomain effects often occur within a few length constants of the tissue edge. Numerical methods for solving the model equations are being developed. Precursors to the model and potential applications are discussed. The bidomain model...
Directory of Open Access Journals (Sweden)
B. D. Castro
2005-09-01
Full Text Available Liquid-liquid extraction using aqueous two-phase systems is a highly efficient technique for separation and purification of biomolecules due to the mild properties of both liquid phases. Reliable data on the phase behavior of these systems are essential for the design and operation of new separation processes; several authors reported phase diagrams for polymer-polymer systems, but data on polymer-salt systems are still relatively scarce. In this work, experimental liquid-liquid equilibrium data on water + polyethylene glycol 8000 + magnesium sulfate and water + polyethylene glycol 8000 + sodium sulfate aqueous two-phase systems were obtained at 35°C. Both equilibrium phases were analyzed by lyophilization and ashing. Experimental results were correlated with a mass-fraction-based NRTL activity coefficient model. New interaction parameters were estimated with the Simplex method. The mean deviations between the experimental and calculated compositions in both equilibrium phases is about 2%.
Explorations in Elementary Mathematical Modeling
Directory of Open Access Journals (Sweden)
Mazen Shahin
2010-06-01
Full Text Available In this paper we will present the methodology and pedagogy of Elementary Mathematical Modeling as a one-semester course in the liberal arts core. We will focus on the elementary models in finance and business. The main mathematical tools in this course are the difference equations and matrix algebra. We also integrate computer technology and cooperative learning into this inquiry-based learning course where students work in small groups on carefully designed activities and utilize available software to support problem solving and understanding of real life situations. We emphasize the use of graphical and numerical techniques, rather than theoretical techniques, to investigate and analyze the behavior of the solutions of the difference equations.As an illustration of our approach, we will show a nontraditional and efficient way of introducing models from finance and economics. We will also present an interesting model of supply and demand with a lag time, which is called the cobweb theorem in economics. We introduce a sample of a research project on a technique of removing chaotic behavior from a chaotic system.
Mathematical Modelling Plant Signalling Networks
Muraro, D.
2013-01-01
During the last two decades, molecular genetic studies and the completion of the sequencing of the Arabidopsis thaliana genome have increased knowledge of hormonal regulation in plants. These signal transduction pathways act in concert through gene regulatory and signalling networks whose main components have begun to be elucidated. Our understanding of the resulting cellular processes is hindered by the complex, and sometimes counter-intuitive, dynamics of the networks, which may be interconnected through feedback controls and cross-regulation. Mathematical modelling provides a valuable tool to investigate such dynamics and to perform in silico experiments that may not be easily carried out in a laboratory. In this article, we firstly review general methods for modelling gene and signalling networks and their application in plants. We then describe specific models of hormonal perception and cross-talk in plants. This mathematical analysis of sub-cellular molecular mechanisms paves the way for more comprehensive modelling studies of hormonal transport and signalling in a multi-scale setting. © EDP Sciences, 2013.
Mathematical model of induction heating
Rak, Josef
2017-07-01
One of mathematical models of induction heating can be described by a parabolic differential equation with the specific Joule looses in the body. Advantage of this method is that the detailed knowledge of the 3D-magnetic field is not necessary and move of the body or the inductor can be easily implemented. The specific Joule looses can computed by solving the Fredholm integral equation of the second kind for the eddy current of density by the Nyström method with the singularity subtraction.
Mathematical modeling courses for Media technology students
DEFF Research Database (Denmark)
Timcenko, Olga
2009-01-01
This paper addresses curriculum development for Mathematical Modeling course at Medialogy education. Medialogy as a study line was established in 2002 at Faculty for Engineering and Natural Sciences at Aalborg University, and mathematics curriculum has already been revised three times, Mathematic...
A Generative Model of Mathematics Learning
Wittrock, M. C.
1974-01-01
The learning of mathematics is presented as a cognitive process rather than as a behavioristic one. A generative model of mathematics learning is described. Learning with understanding can occur with discovery or reception treatments. Relevant empirical research is discussed and implications for teaching mathematics as a generative process are…
Energy Technology Data Exchange (ETDEWEB)
Fraser, D.W.H. [Univ. of British Columbia (Canada); Abdelmessih, A.H. [Univ. of Toronto, Ontario (Canada)
1995-09-01
A general unified model is developed to predict one-component critical two-phase pipe flow. Modelling of the two-phase flow is accomplished by describing the evolution of the flow between the location of flashing inception and the exit (critical) plane. The model approximates the nonequilibrium phase change process via thermodynamic equilibrium paths. Included are the relative effects of varying the location of flashing inception, pipe geometry, fluid properties and length to diameter ratio. The model predicts that a range of critical mass fluxes exist and is bound by a maximum and minimum value for a given thermodynamic state. This range is more pronounced at lower subcooled stagnation states and can be attributed to the variation in the location of flashing inception. The model is based on the results of an experimental study of the critical two-phase flow of saturated and subcooled water through long tubes. In that study, the location of flashing inception was accurately controlled and adjusted through the use of a new device. The data obtained revealed that for fixed stagnation conditions, the maximum critical mass flux occurred with flashing inception located near the pipe exit; while minimum critical mass fluxes occurred with the flashing front located further upstream. Available data since 1970 for both short and long tubes over a wide range of conditions are compared with the model predictions. This includes test section L/D ratios from 25 to 300 and covers a temperature and pressure range of 110 to 280{degrees}C and 0.16 to 6.9 MPa. respectively. The predicted maximum and minimum critical mass fluxes show an excellent agreement with the range observed in the experimental data.
2002-01-01
Solid/liquid extraction is performed on raw plant substrate with a modified twin-screw extruder (TSE) used as a thermo-mecanochemical reactor. Visual observations and experimental residence time distributions (RTD) are used to develop a solid transport model based on classical chemical engineering method. Modeled and experimental residence times are compared. The transport model is then coupled with a reactive extraction model in order to predict extraction yields.
Numerical Simulation for Two-Phase Water Hammer Flows in Pipe by Quasi-Two-Dimensional Model
Institute of Scientific and Technical Information of China (English)
Tae Uk Jang; Yuebin Wu; Ying Xu; Qiang Sun
2016-01-01
The features of a quasi⁃two⁃dimensional ( quasi⁃2D) model for simulating two⁃phase water hammer flows with vaporous cavity in a pipe are investigated. The quasi⁃2D model with discrete vaporous cavity in the pipe is proposed in this paper. This model uses the quasi⁃2D model for pure liquid zone and one⁃dimensional ( 1D ) discrete vapor cavity model for vaporous cavity zone. The quasi⁃2D model solves two⁃dimensional equations for both axial and radial velocities and 1D equations for both pressure head and discharge by the method of characteristics. The 1D discrete vapor cavity model is used to simulate the vaporous cavity occurred when the pressure in the local pipe is lower than the vapor pressure of the liquid. The proposed model is used to simulate two⁃phase water flows caused by the rapid downstream valve closure in a reservoir⁃pipe⁃valve system. The results obtained by the proposed model are compared with those by the corresponding 1D model and the experimental ones provided by the literature, respectively. The comparison shows that the maximum pressure heads simulated by the proposed model are more accurate than those by the corresponding 1D model.
Mathematical models in biological discovery
Walter, Charles
1977-01-01
When I was asked to help organize an American Association for the Advancement of Science symposium about how mathematical models have con tributed to biology, I agreed immediately. The subject is of immense importance and wide-spread interest. However, too often it is discussed in biologically sterile environments by "mutual admiration society" groups of "theoreticians", many of whom have never seen, and most of whom have never done, an original scientific experiment with the biolog ical materials they attempt to describe in abstract (and often prejudiced) terms. The opportunity to address the topic during an annual meeting of the AAAS was irresistable. In order to try to maintain the integrity ;,f the original intent of the symposium, it was entitled, "Contributions of Mathematical Models to Biological Discovery". This symposium was organized by Daniel Solomon and myself, held during the 141st annual meeting of the AAAS in New York during January, 1975, sponsored by sections G and N (Biological and Medic...
Bachrata, A.; Fichot, F.; Quintard, M.; Repetto, G.; Fleurot, J.
2012-05-01
A generalized non local-equilibrium, three-equation model was developed for the macroscopic description of two-phase flow heat and mass transfer in porous media subjected to phase change. Six pore-scale closure problems were proposed to determine all the effective transport coefficients for representative unit cells. An improved model is presented in this paper with the perspective of application to intense boiling phenomena. The objective of this paper is to present application of this model to the simulation of reflooding of severely damaged nuclear reactor cores. In case of accident at a nuclear power plant, water sources may not be available for a long period of time and the core heats up due to the residual power. Any attempt to inject water during core degradation can lead to quenching and further fragmentation of the core material. The fragmentation of fuel rods and melting of reactor core materials may result in the formation of a "debris bed". The typical particle size in a debris bed might reach few millimeters (characteristic length-scale: 1 to 5 mm), which corresponds to a high permeability porous medium. The proposed two-phase flow model is implemented in the ICARECATHARE code, developed by IRSN to study severe accident scenarios in pressurized water reactors. Currently, the French IRSN has set up two experimental facilities to study debris bed reflooding, PEARL and PRELUDE, with the objective to validate safety models. The PRELUDE program studies the complex two phase flow of water and steam in a porous medium (diameter 180 mm, height 200 mm), initially heated to a high temperature (400°C or 700°C). The series of PRELUDE experiments achieved in 2010 constitute a significant complement to the database of high temperature bottom reflood experimental data. They provide relevant data to understand the progression of the quench front and the intensity of heat transfer. Modeling accurately these experiments required improvements to the reflooding model
Energy Technology Data Exchange (ETDEWEB)
Bachrata, A.; Fichot, F.; Quintard, M.; Repetto, G.; Fleurot, J. [Institut de Radioprotection et de Surete Nucleaire, Cadarache (France); Universite de Toulouse (France); INPT, UPS (France); IMFT - Institut de Mecanique des Fluides de Toulouse, Allee Camille Soula, F-31400 Toulouse (France) and CNRS (France); IMFT, F-31400 Toulouse (France); Institut de Radioprotection et de Surete Nucleaire, Cadarache (France)
2012-05-15
A generalized non local-equilibrium, three-equation model was developed for the macroscopic description of two-phase flow heat and mass transfer in porous media subjected to phase change. Six pore-scale closure problems were proposed to determine all the effective transport coefficients for representative unit cells. An improved model is presented in this paper with the perspective of application to intense boiling phenomena. The objective of this paper is to present application of this model to the simulation of reflooding of severely damaged nuclear reactor cores. In case of accident at a nuclear power plant, water sources may not be available for a long period of time and the core heats up due to the residual power. Any attempt to inject water during core degradation can lead to quenching and further fragmentation of the core material. The fragmentation of fuel rods and melting of reactor core materials may result in the formation of a {sup d}ebris bed{sup .} The typical particle size in a debris bed might reach few millimeters (characteristic length-scale: 1 to 5 mm), which corresponds to a high permeability porous medium. The proposed two-phase flow model is implemented in the ICARECATHARE code, developed by IRSN to study severe accident scenarios in pressurized water reactors. Currently, the French IRSN has set up two experimental facilities to study debris bed reflooding, PEARL and PRELUDE, with the objective to validate safety models. The PRELUDE program studies the complex two phase flow of water and steam in a porous medium (diameter 180 mm, height 200 mm), initially heated to a high temperature (400 deg. C or 700 deg. C). The series of PRELUDE experiments achieved in 2010 constitute a significant complement to the database of high temperature bottom reflood experimental data. They provide relevant data to understand the progression of the quench front and the intensity of heat transfer. Modeling accurately these experiments required improvements to the
Córdoba, G.; Villarosa, G.; Sheridan, M. F.; Viramonte, J. G.; Beigt, D.; Salmuni, G.
2015-04-01
This paper presents the results of lahar modelling in the town of Villa La Angostura (Neuquén-Argentina) based on the Two-Phase-Titan modelling computer code. The purpose of this exercise is to provide decision makers with a useful tool to assess lahar hazard during the 2011 Puyehue-Cordón Caulle Volcanic Complex eruption. The possible occurrence of lahars mobilized from recent ash falls that could reach the city was analysed. The performance of the Two-Phase-Titan model using 15 m resolution digital elevation models (DEMs) developed from optical satellite images and from radar satellite images was evaluated. The output of these modellings showed inconsistencies that, based on field observations, were attributed to bad adjustment of the DEMs to real topography. Further testing of results using more accurate radar-based 10 m DEM, provided more realistic predictions. This procedure allowed us to simulate the path of flows from Florencia, Las Piedritas and Colorado creeks, which are the most hazardous streams for debris flows in Villa La Angostura. The output of the modelling is a valuable tool for city planning and risk management especially considering the glacial geomorphic features of the region, the strong urban development growth and the land occupation that has occurred in the last decade in Villa La Angostura and its surroundings.
The two-phase issue in the O(n) non-linear $\\sigma$-model: A Monte Carlo study
Alles, B.; Buonanno, A.; Cella, G.
1996-01-01
We have performed a high statistics Monte Carlo simulation to investigate whether the two-dimensional O(n) non-linear sigma models are asymptotically free or they show a Kosterlitz- Thouless-like phase transition. We have calculated the mass gap and the magnetic susceptibility in the O(8) model with standard action and the O(3) model with Symanzik action. Our results for O(8) support the asymptotic freedom scenario.
Building fire zone model with symbolic mathematics
Institute of Scientific and Technical Information of China (English)
武红梅; 郜冶; 周允基
2009-01-01
To apply the fire modelling for the fire engineer with symbolic mathematics,the key equations of a zone model were demonstrated. There were thirteen variables with nine constraints,so only four ordinary differential equations (ODEs) were required to solve. A typical fire modelling with two-room structure was studied. Accordingly,the source terms included in the ODEs were simplified and modelled,and the fourth Runge-Kutta method was used to solve the ordinary differential equations (ODEs) with symbolic mathematics. Then a zone model could be used with symbolic mathematics. It is proposed that symbolic mathematics is possible for use by fire engineer.
Mathematical modeling in biomedical imaging
2012-01-01
This volume reports on recent mathematical and computational advances in optical, ultrasound, and opto-acoustic tomographies. It outlines the state-of-the-art and future directions in these fields and provides readers with the most recently developed mathematical and computational tools. It is particularly suitable for researchers and graduate students in applied mathematics and biomedical engineering.
Analysis of the two-fluid model and the drift-flux model for numerical calculation of two-phase flow
Energy Technology Data Exchange (ETDEWEB)
Munkejord, Svend Tollak
2006-05-11
This thesis analyses models for two-phase flows and methods for the numerical resolution of these models. It is therefore one contribution to the development of reliable design tools for multiphase applications. Such tools are needed and expected by engineers in a range of fields, including in the oil and gas industry. The approximate Riemann solver of Roe has been studied. Roe schemes for three different two-phase flow models have been implemented in the framework of a standard numerical algorithm for the solution of hyperbolic conservation laws. The schemes have been analysed by calculation of benchmark tests from the literature, and by comparison with each other. A Roe scheme for the four-equation one-pressure two-fluid model has been implemented, and a second-order extension based on wave decomposition and flux-difference splitting was shown to work well and to give improved results compared to the first-order scheme. The convergence properties of the scheme were tested on smooth and discontinuous solutions. A Roe scheme has been proposed for a five-equation two-pressure two-fluid model with pressure relaxation. The use of analogous numerical methods for the five-equation and four-equation models allowed for a direct comparison of a method with and without pressure relaxation. Numerical experiments demonstrated that the two approaches converged to the same results, but that the five-equation pressure-relaxation method was significantly more dissipative, particularly for contact discontinuities. Furthermore, even though the five-equation model with instantaneous pressure relaxation has real eigenvalues, the calculations showed that it produced oscillations for cases where the four-equation model had complex eigenvalues. A Roe scheme has been constructed for the drift-flux model with general closure laws. For the case of the Zuber-Findlay slip law describing bubbly flows, the Roe matrix is completely analytical. Hence the present Roe scheme is more efficient than
Yohan, D.; Gerald, D.; Magali, G.; Michel, Q.
2008-12-01
The general problem of transport and reaction in multiphase porous media has been a subject of extensive studies during the last decades. For example, biologically mediated porous media have seen a long history of research from the environmental engineering point of view. Biofilms (aggregate of microorganisms coated in a polymer matrix generated by bacteria) have been particularly examined within the context of bioremediation in the subsurface zone. Five types of models may be used to describe these kinds of physical system: 1) one-equation local mass equilibrium models when the assumption of local mass equilibrium is valid 2) two equations models when the assumption of local mass equilibrium is not valid 3) one equation non-equilibrium models 4) mixed models coupling equations solved at two different scales 5) one equation time-asymptotic models. In this presentation, we use the method of volume averaging with closure to extend the time- asymptotic model at the Darcy scale to the reactive case. Closure problems are solved for simple unit cells, and the macro-scale model is validated against pore-scale simulations.
Two-phase viscoelastic jetting
Energy Technology Data Exchange (ETDEWEB)
Yu, J-D; Sakai, S.; Sethian, J.A.
2008-12-10
A coupled finite difference algorithm on rectangular grids is developed for viscoelastic ink ejection simulations. The ink is modeled by the Oldroyd-B viscoelastic fluid model. The coupled algorithm seamlessly incorporates several things: (1) a coupled level set-projection method for incompressible immiscible two-phase fluid flows; (2) a higher-order Godunov type algorithm for the convection terms in the momentum and level set equations; (3) a simple first-order upwind algorithm for the convection term in the viscoelastic stress equations; (4) central difference approximations for viscosity, surface tension, and upper-convected derivative terms; and (5) an equivalent circuit model to calculate the inflow pressure (or flow rate) from dynamic voltage.
Doyle, Timothy E; Robinson, David A.; Scott B. Jones; Warnick, Keith H.; Carruth, Brent L.
2007-01-01
A numerical modeling approach was developed to predict the dielectric properties of heterogeneous particulate materials with arbitrary microstructures. To test the method, simulation and experimental data were acquired for the effective permittivities of various glass sphere suspensions. Both ordered lattices and random microstructures of up to 3600 spheres were modeled for volume fractions of 0.025–0.60. The electric fields in the suspensions were computed using an iterative multipole method...
Mathematical models for plant-herbivore interactions
Feng, Zhilan; DeAngelis, Donald L.
2017-01-01
Mathematical Models of Plant-Herbivore Interactions addresses mathematical models in the study of practical questions in ecology, particularly factors that affect herbivory, including plant defense, herbivore natural enemies, and adaptive herbivory, as well as the effects of these on plant community dynamics. The result of extensive research on the use of mathematical modeling to investigate the effects of plant defenses on plant-herbivore dynamics, this book describes a toxin-determined functional response model (TDFRM) that helps explains field observations of these interactions. This book is intended for graduate students and researchers interested in mathematical biology and ecology.
THE STOCHASTIC DISCRETE MODEL FOR SIMULATING GAS-SOLID TWO-PHASE FLOW%气固两相流模拟的随机离散模型
Institute of Scientific and Technical Information of China (English)
欧阳洁; 孙国刚; 李静海
2003-01-01
A stochastic discrete model is proposed for simulating the dynamic behaviors of gas-solid systems. In the model, the motions of solid phase are obtained by calcu-lating individual particle motions while gas flow is obtained by solving the Navier-Stokes equation including two-phase interaction. For the calculation of solid phase,the motion process of each particle is decomposed into the collision process and suspension process. Momentum conservation of collision mechanics controls the interaction between colliding particles, while the state of each suspended particle is fully dominated by the equation of force balance over that particle. Inaddition to gravity, drag force and pressure, other unclear factors are described as random force in the suspension process. As a result, the proposed model has given some nu-merical simulations of gas-solid systems, in which different random forces are used.It indicates that the stochastic discrete model can be used to simulate qualitatively the dynamic behaviors of gas-solid two-phase flow.
Qian, Tiezheng
2009-10-29
This paper starts with an introduction to the Onsager principle of minimum energy dissipation which governs the optimal paths of deviation and restoration to equilibrium. Then there is a review of the variational approach to moving contact line hydrodynamics. To demonstrate the validity of our continuum hydrodynamic model, numerical results from model calculations and molecular dynamics simulations are presented for immiscible Couette and Poiseuille flows past homogeneous solid surfaces, with remarkable overall agreement. Our continuum model is also used to study the contact line motion on surfaces patterned with stripes of different contact angles (i.e. surfaces of varying wettability). Continuum calculations predict the stick-slip motion for contact lines moving along these patterned surfaces, in quantitative agreement with molecular dynamics simulation results. This periodic motion is tunable through pattern period (geometry) and contrast in wetting property (chemistry). The consequence of stick-slip contact line motion on energy dissipation is discussed. © 2009 IOP Publishing Ltd.
Energy Technology Data Exchange (ETDEWEB)
Qian Tiezheng; Wu Congmin; Lei Siu Long; Wang Xiaoping [Department of Mathematics, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon (Hong Kong); Sheng Ping, E-mail: maqian@ust.h [Department of Physics and William Mong Institute of Nano Science and Technology, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon (Hong Kong)
2009-11-18
This paper starts with an introduction to the Onsager principle of minimum energy dissipation which governs the optimal paths of deviation and restoration to equilibrium. Then there is a review of the variational approach to moving contact line hydrodynamics. To demonstrate the validity of our continuum hydrodynamic model, numerical results from model calculations and molecular dynamics simulations are presented for immiscible Couette and Poiseuille flows past homogeneous solid surfaces, with remarkable overall agreement. Our continuum model is also used to study the contact line motion on surfaces patterned with stripes of different contact angles (i.e. surfaces of varying wettability). Continuum calculations predict the stick-slip motion for contact lines moving along these patterned surfaces, in quantitative agreement with molecular dynamics simulation results. This periodic motion is tunable through pattern period (geometry) and contrast in wetting property (chemistry). The consequence of stick-slip contact line motion on energy dissipation is discussed.
Qian, Tiezheng; Wu, Congmin; Lei, Siu Long; Wang, Xiao-Ping; Sheng, Ping
2009-11-18
This paper starts with an introduction to the Onsager principle of minimum energy dissipation which governs the optimal paths of deviation and restoration to equilibrium. Then there is a review of the variational approach to moving contact line hydrodynamics. To demonstrate the validity of our continuum hydrodynamic model, numerical results from model calculations and molecular dynamics simulations are presented for immiscible Couette and Poiseuille flows past homogeneous solid surfaces, with remarkable overall agreement. Our continuum model is also used to study the contact line motion on surfaces patterned with stripes of different contact angles (i.e. surfaces of varying wettability). Continuum calculations predict the stick-slip motion for contact lines moving along these patterned surfaces, in quantitative agreement with molecular dynamics simulation results. This periodic motion is tunable through pattern period (geometry) and contrast in wetting property (chemistry). The consequence of stick-slip contact line motion on energy dissipation is discussed.
Mathematical model for bone mineralization
Directory of Open Access Journals (Sweden)
Svetlana V Komarova
2015-08-01
Full Text Available Defective bone mineralization has serious clinical manifestations, including deformities and fractures, but the regulation of this extracellular process is not fully understood. We have developed a mathematical model consisting of ordinary differential equations that describe collagen maturation, production and degradation of inhibitors, and mineral nucleation and growth. We examined the roles of individual processes in generating normal and abnormal mineralization patterns characterized using two outcome measures: mineralization lag time and degree of mineralization. Model parameters describing the formation of hydroxyapatite mineral on the nucleating centers most potently affected the degree of mineralization, while the parameters describing inhibitor homeostasis most effectively changed the mineralization lag time. Of interest, a parameter describing the rate of matrix maturation emerged as being capable of counter-intuitively increasing both the mineralization lag time and the degree of mineralization. We validated the accuracy of model predictions using known diseases of bone mineralization such as osteogenesis imperfecta and X-linked hypophosphatemia. The model successfully describes the highly non-linear mineralization dynamics, which includes an initial lag phase when osteoid is present but no mineralization is evident, then fast primary mineralization, followed by secondary mineralization characterized by a continuous slow increase in bone mineral content. The developed model can potentially predict the function for a mutated protein based on the histology of pathologic bone samples from mineralization disorders of unknown etiology.
Directory of Open Access Journals (Sweden)
Furmański Piotr
2014-09-01
Full Text Available Heat flow in heterogeneous media with complex microstructure follows tortuous path and therefore determination of temperature distribution in them is a challenging task. Two-scales, micro-macro model of heat conduction with phase change in such media was considered in the paper. A relation between temperature distribution on the microscopic level, i.e., on the level of details of microstructure, and the temperature distribution on the macroscopic level, i.e., on the level where the properties were homogenized and treated as effective, was derived. The expansion applied to this relation allowed to obtain its more simplified, approximate form corresponding to separation of micro- and macro-scales. Then the validity of this model was checked by performing calculations for 2D microstructure of a composite made of two constituents. The range of application of the proposed micro-macro model was considered in transient states of heat conduction both for the case when the phase change in the material is present and when it is absent. Variation of the effective thermal conductivity with time was considered and a criterion was found for which application of the considered model is justified.
Escher, Joachim; Matioc, Bogdan-Vasile
2011-01-01
We prove global existence of nonnegative weak solutions to a degenerate parabolic system which models the interaction of two thin fluid films in a porous medium. Furthermore, we show that these weak solutions converge at an exponential rate towards flat equilibria.
Energy Technology Data Exchange (ETDEWEB)
Minier, Jean-Pierre, E-mail: Jean-Pierre.Minier@edf.fr [EDF R and D, Mécanique des Fluides, Energie et Environnement, 6 quai Watier, 78400 Chatou (France); Chibbaro, Sergio [Sorbonne Universités, Institut Jean Le Rond d’Alembert, UPMC Univ Paris 06, CNRS, UMR7190, F-75005 Paris (France); Pope, Stephen B. [Sibley School of Mechanical and Aerospace Engineering, Cornell University, 254 Upson Hall, Ithaca, New York 14853 (United States)
2014-11-15
In this paper, we establish a set of criteria which are applied to discuss various formulations under which Lagrangian stochastic models can be found. These models are used for the simulation of fluid particles in single-phase turbulence as well as for the fluid seen by discrete particles in dispersed turbulent two-phase flows. The purpose of the present work is to provide guidelines, useful for experts and non-experts alike, which are shown to be helpful to clarify issues related to the form of Lagrangian stochastic models. A central issue is to put forward reliable requirements which must be met by Lagrangian stochastic models and a new element brought by the present analysis is to address the single- and two-phase flow situations from a unified point of view. For that purpose, we consider first the single-phase flow case and check whether models are fully consistent with the structure of the Reynolds-stress models. In the two-phase flow situation, coming up with clear-cut criteria is more difficult and the present choice is to require that the single-phase situation be well-retrieved in the fluid-limit case, elementary predictive abilities be respected and that some simple statistical features of homogeneous fluid turbulence be correctly reproduced. This analysis does not address the question of the relative predictive capacities of different models but concentrates on their formulation since advantages and disadvantages of different formulations are not always clear. Indeed, hidden in the changes from one structure to another are some possible pitfalls which can lead to flaws in the construction of practical models and to physically unsound numerical calculations. A first interest of the present approach is illustrated by considering some models proposed in the literature and by showing that these criteria help to assess whether these Lagrangian stochastic models can be regarded as acceptable descriptions. A second interest is to indicate how future
Mathematical models of human behavior
DEFF Research Database (Denmark)
Møllgaard, Anders Edsberg
During the last 15 years there has been an explosion in human behavioral data caused by the emergence of cheap electronics and online platforms. This has spawned a whole new research field called computational social science, which has a quantitative approach to the study of human behavior. Most...... studies have considered data sets with just one behavioral variable such as email communication. The Social Fabric interdisciplinary research project is an attempt to collect a more complete data set on human behavior by providing 1000 smartphones with pre-installed data collection software to students...... data set, along with work on other behavioral data. The overall goal is to contribute to a quantitative understanding of human behavior using big data and mathematical models. Central to the thesis is the determination of the predictability of different human activities. Upper limits are derived...
A two-phase charge-density real-space-pairing model of high-T{sub c} superconductivity
Energy Technology Data Exchange (ETDEWEB)
Humphreys, C.J. [Cambridge Univ. (United Kingdom). Dept. of Metallurgy and Materials Science
1999-03-01
It is usually assumed that high-T{sub c} superconductors have a periodic band structure and a periodic charge density, although amorphous low-T{sub c} superconductors are known. In this paper, it is suggested that the CuO{sub 2} conduction planes of cuprate superconductors consist of regions of two different charge densities which do not normally repeat periodically. It is suggested that the pairing of holes occurs in real space in cuprate superconductors. It is proposed that the hole-pairing mechanism is magnetic exchange coupling and the pairing force is strong, the pairing energy being greater than kT at room temperature. The bound hole pair is essentially a bipolaron. A real-space model is very tentatively suggested in which the CuO{sub 2} planes of YBa{sub 2}Cu{sub 3}O{sub 7} contain nanodomains of a 3 x 3 hole lattice surrounded by interfaces one unit cell wide in which the holes are paired. In the superconducting state in this model, the existing hole pairs condense and move coherently and collectively around the insulating nanodomains, like trams running around blocks of houses, with one hole on each tramline. The hole pairs move in an elegant manner with hole pairs hopping from oxygen to oxygen via adjacent copper sites. The model explains the superconducting current being in the ab plane and it also explains the very short coherence lengths. Because the pairing force is strong, the model suggests that room-temperature superconductivity might be possible in carefully designed new oxide materials. (orig.) 22 refs.
A two-phase charge-density real-space-pairing model of high-Tc superconductivity.
Humphreys
1999-03-01
It is usually assumed that high-T(c) superconductors have a periodic band structure and a periodic charge density, although amorphous low-T(c) superconductors are known. In this paper, it is suggested that the CuO(2) conduction planes of cuprate superconductors consist of regions of two different charge densities which do not normally repeat periodically. It is suggested that the pairing of holes occurs in real space in cuprate superconductors. It is proposed that the hole-pairing mechanism is magnetic exchange coupling and the pairing force is strong, the pairing energy being greater than kT at room temperature. The bound hole pair is essentially a bipolaron. A real-space model is very tentatively suggested in which the CuO(2) planes of YBa(2)Cu(3)O(7) contain nanodomains of a 3 x 3 hole lattice surrounded by interfaces one unit cell wide in which the holes are paired. In the superconducting state in this model, the existing hole pairs condense and move coherently and collectively around the insulating nanodomains, like trams running around blocks of houses, with one hole on each tramline. The hole pairs move in an elegant manner with hole pairs hopping from oxygen to oxygen via adjacent copper sites. The model explains the superconducting current being in the ab plane and it also explains the very short coherence lengths. Because the pairing force is strong, the model suggests that room-temperature superconductivity might be possible in carefully designed new oxide materials.
Zhang, Hong
2016-01-01
Saturation overshoot and pressure overshoot are studied by incorporating dynamic capillary pressure, capillary pressure hysteresis and hysteretic dynamic coefficient with a traditional fractional flow equation. Using the method of lines, the discretizations are constructed by applying Castillo-Grone's mimetic operators in the space direction and explicit trapezoidal integrator in the time direction. Convergence tests and conservation property of the schemes are presented. Computed profiles capture both the saturation overshoot and pressure overshoot phenomena. Comparisons between numerical results and experiments illustrate the effectiveness and different features of the models.
Computacional-representantional model of mathematics (crmmath)
Toro Carvajal, Luis Alberto
2016-01-01
This paper presents the so-called computational representational model of mathematics (MCRMATH), its theoretical importance for mathematics education and its relation with the use of technology tools in mathematics teaching. To do this, from a cognitive point of view, we conduct a research study of representations and we explain the computational-representational model of mind (CRMM).
Directory of Open Access Journals (Sweden)
Xiangwei Kong
2014-01-01
Full Text Available Investigation of surge pressure is of great significance to the circulation loss problem caused by unsteady operations in management pressure drilling (MPD operations. With full consideration of the important factors such as wave velocity, gas influx rate, pressure, temperature, and well depth, a new surge pressure model has been proposed based on the mass conservation equations and the momentum conservation equations during MPD operations. The finite-difference method, the Newton-Raphson iterative method, and the fourth-order explicit Runge-Kutta method (R-K4 are adopted to solve the model. Calculation results indicate that the surge pressure has different values with respect to different drill pipe tripping speeds and well parameters. In general, the surge pressure tends to increase with the increases of drill pipe operating speed and with the decrease of gas influx rate and wellbore diameter. When the gas influx occurs, the surge pressure is weakened obviously. The surge pressure can cause a significant lag time if the gas influx occurs at bottomhole, and it is mainly affected by pressure wave velocity. The maximum surge pressure may occur before drill pipe reaches bottomhole, and the surge pressure is mainly affected by drill pipe operating speed and gas influx rate.
Fiorentino, Eve-Agnès; Toussaint, Renaud; Jouniaux, Laurence
2017-02-01
The streaming potential phenomenon is an electrokinetic effect that occurs in porous media. It is characterized by an electrokinetic (EK) coefficient. The aim of this paper is to simulate the EK coefficient in unsaturated conditions using the Lattice Boltzmann method in a 2-D capillary channel. The multiphase flow is simulated with the model of Shan & Chen. The Poisson-Boltzmann equation is solved by implementing the model of Chai & Shi. The streaming potential response shows a non-monotonous behaviour due to the combination of the increase of charge density and decrease of flow velocity with decreasing water saturation. Using a ζ potential of -20 mV at the air-water interface, an enhancement of a factor 5-30 of the EK coefficient, compared to the saturated state, can be observed due to the positive charge excess at this interface which is magnified by the fluid velocity away from the rock surface. This enhancement is correlated to the fractioning of the bubbles, and to the dynamic state of these bubbles, moving or entrapped in the crevices of the channel.
Minier, J P; Chibbaro, S
2010-01-01
The aim of the paper is to discuss the main characteristics of a complete theoretical and numerical model for turbulent polydispersed two-phase flows, pointing out some specific issues. The theoretical details of the model have already been presented [Minier and Peirano, Physics Reports, Vol. 352/1-3, 2001 ]. Consequently, the present work is mainly focused on complementary aspects, that are often overlooked and that require particular attention. In particular, the following points are analysed : the necessity to add an extra term in the equation for the velocity of the fluid seen in the case of twoway coupling, the theoretical and numerical evaluations of particle averages and the fulfilment of the particle mass-continuity constraint. The theoretical model is developed within the PDF formalism. The important-physical choice of the state vector variables is first discussed and the model is then expressed as a stochastic differential equation (SDE) written in continuous time (Langevin equations) for the veloci...
Institute of Scientific and Technical Information of China (English)
杨慧霞; 李然; 梁瑞峰; 魏娟; 张沁
2016-01-01
A high concentration of the total dissolved gas (TDG) in a flow downstream high dams may cause the gas bubble disease in fishes. To better understand the spatial distribution of a supersaturated TDG, a numerical simulation approach for determining the TDG concentration is shown to be effective and convenient; however, the determination of the model parameters relies to a great extent on the observed field data, which are scarce but are very sensitive to the accuracy of the simulation. In this regard, determining the source parameter in the TDG transport equation is the primary concern of this paper. Observed field data from six different spillways in China are used to calibrate the source parameter. A relationship between the source parameter and the hydrodynamic characteristics is established. The inclusion of this relationship in the predictive relationship will enable an accurate and rapid estimation of the source parameter and may help in developing mitigation measures for the TDG supersaturation downstream the spillways.
Energy Technology Data Exchange (ETDEWEB)
R. A. Berry; S. Y. Kadioglu
2012-05-01
The numerical simulation of multiphase flows in Light Water (Nuclear) Reactors, LWRs, for normal, accident, and off-normal operation, and for operational optimization must cover a huge disparity of transient time durations, from milliseconds to years. In addition, our recent work has shown that the application of classical Riemann approaches, which pervade modern computational fluid dynamics (CFD), suffer numerical accuracy degradation, especially for compressible liquid flows. In this setting, all-speed or Mach uniform methods are need which can be accurately and efficiently integrated over a very large range of time scales. Thus we need a multi-time-scale integration approach to compliment our previously documented multi-spatial-scale approach to multiphase flow modeling [1]. This report briefly summarizes our efforts in these areas.
Abu-Al-Saud, Moataz O.; Riaz, Amir; Tchelepi, Hamdi A.
2017-03-01
We developed a multiscale sharp-interface level-set method for immiscible two-phase flow with a pre-existing thin film on solid surfaces. The lubrication approximation theory is used to model the thin-film equation efficiently. The incompressible Navier-Stokes, level-set, and thin-film evolution equations are coupled sequentially to capture the dynamics occurring at multiple length scales. The Hamilton-Jacobi level-set reinitialization is employed to construct the signed-distance function, which takes into account the deposited thin-film on the solid surface. The proposed multiscale method is validated and shown to match the augmented Young-Laplace equation for a static meniscus in a capillary tube. Viscous bending of the advancing interface over the precursor film is captured by the proposed level-set method and agrees with the Cox-Voinov theory. The advancing bubble surrounded by a wetting film inside a capillary tube is considered, and the predicted film thickness compares well with both theory and experiments. We also demonstrate that the multiscale level-set approach can model immiscible two-phase flow with a capillary number as low as 10-6.
Mathematical Model for Photovoltaic Cells
Directory of Open Access Journals (Sweden)
Wafaa ABD EL-BASIT
2013-11-01
Full Text Available The study of photovoltaic systems in an efficient manner requires a precise knowledge of the (I-V and (P-V characteristic curves of photovoltaic modules. So, the aim of the present paper is to estimate such characteristics based on different operating conditions. In this concern, a simple one diode mathematical model was implemented using MATLAB script. The output characteristics of PV cell depend on the environmental conditions. For any solar cell, the model parameters are function of the irradiance and the temperature values of the site where the panel is placed. In this paper, the numerical values of the equivalent circuit parameters are generated by the program. As well, the dependence of the cells electrical parameters are analyzed under the influence of different irradiance and temperature levels. The variation of slopes of the (I–V curves of a cell at short-circuit and open-circuit conditions with intensity of illumination in small span of intensity and different temperature levels have been applied to determine the cell parameters, shunt resistance, series resistance. The results show that the efficiency of solar cells has an inverse relationship with temperature, irradiance levels are affected by the change of the photo-generation current and the series resistance in the single diode model.
Energy Technology Data Exchange (ETDEWEB)
Sheikholeslami, Mohsen; Domiri Ganji, Davood [Department of Mechanical Engineering, Babol University of Technology, Babol (Iran, Islamic Republic of); Younus Javed, M. [National University of Sciences and Technology, College of Electrical and Mechanical Engineering Islamabad (Pakistan); Ellahi, R., E-mail: rellahi@engr.ucr.edu [Department of Mechanical Engineering, University of California Riverside, Bourns Hall A373 (United States); Department of Mathematics and Statistics, FBAS, IIUI, H-10 Sector, Islamabad (Pakistan)
2015-01-15
In this study, effect of thermal radiation on magnetohydrodynamics nanofluid flow between two horizontal rotating plates is studied. The significant effects of Brownian motion and thermophoresis have been included in the model of nanofluid. By using the appropriate transformation for the velocity, temperature and concentration, the basic equations governing the flow, heat and mass transfer are reduced to a set of ordinary differential equations. These equations, subjected to the associated boundary conditions are solved numerically using the fourth-order Runge–Kutta method. The effects of Reynolds number, magnetic parameter, rotation parameter, Schmidt number, thermophoretic parameter, Brownian parameter and radiation parameter on heat and mass characteristics are examined. Results show that Nusselt number has direct relationship with radiation parameter and Reynolds number while it has reverse relationship with other active parameters. It can also be found that concentration boundary layer thickness decreases with the increase of radiation parameter. - Highlights: • This paper analyses thermal radiation on magnetohydrodynamic nanofluid. • Fourth-order Runge–Kutta method is used. • The effects of Reynolds number, magnetic parameter, rotation parameter, Schmidt number thermophoretic parameter, Brownian parameter and radiation parameter on heat and mass characteristics are examined. • Comparison is also made with the existing literature.
Náraigh, L Ó; Matar, O; Zaki, T
2009-01-01
We investigate the linear stability of a flat interface that separates a liquid layer from a fully-developed turbulent gas flow. In this context, linear-stability analysis involves the study of the dynamics of a small-amplitude wave on the interface, and we develop a model that describes wave-induced perturbation turbulent stresses (PTS). We demonstrate the effect of the PTS on the stability properties of the system in two cases: for a laminar thin film, and for deep-water waves. In the first case, we find that the PTS have little effect on the growth rate of the waves, although they do affect the structure of the perturbation velocities. In the second case, the PTS enhance the maximum growth rate, although the overall shape of the dispersion curve is unchanged. Again, the PTS modify the structure of the velocity field, especially at longer wavelengths. Finally, we demonstrate a kind of parameter tuning that enables the production of the thin-film (slow) waves in a deep-water setting.
Energy Technology Data Exchange (ETDEWEB)
Richardson, D. [NeoCorr Engineering Ltd., Calgary, Alberta (Canada); Bich, N.N. [Shell Canada Ltd., Calgary, Alberta (Canada)
1997-08-01
Pipeline failures attributed to internal corrosion in the oil and gas producing industry have not been decreasing despite the many corrosion mitigation, monitoring and inspection programs implemented. This paper describes how preliminary investigations for evaluating the susceptibility of internal corrosion for wet sour gas pipelines have been based on integrating the latest knowledge in fluid flow and sour gas corrosion mechanisms. It is anticipated future efforts to correlate the onset of slug flow regime with historical corrosion and inspection data may lead to development of an improved criteria for predicting the onset of corrosive water traps and for triggering appropriate maintenance activities. This paper provides details of two corrosion failure Case Studies where application of flow modeling has improved the understanding of the operating hazards that contributed to the formation of a corrosive environment leading to high-rate initiation and growth of localized pitting corrosion. Preliminary analysis indicates slug flow pattern, and long water residence time of water within stagnant traps increases the likelihood of pitting corrosion.
Directory of Open Access Journals (Sweden)
E.M. Matos
2002-07-01
Full Text Available This work presents a model to predict the behavior of velocity, gas holdup and local concentration fields in a pseudo-two-phase gas-liquid column reactor applied for thermal hydrocracking of petroleum heavy fractions. The model is based on the momentum and mass balances for the system, using an Eulerian-Eulerian approach. Using the k-epsilon model,fluid dynamics accounts for both laminar and turbulent flows, with discrete small bubbles (hydrogen flowing in a continuous pseudohomogeneous liquid phase (oil and catalyst particles. The petroleum is assumed to be a mixture of pseudocomponents, grouped by similar chemical structural properties, and the thermal hydrocracking is taken into account using a kinetic network based on these pseudocomponents.
Energy Technology Data Exchange (ETDEWEB)
Majta, J; Zurek, A.K.; Pietrzyk, M.
1999-07-13
The differences in microstructure development of hot deformed steels in the austenite and two-phase region have been effectively described using an integrated computer modeling process. In general, the complete model presented here takes into account kinetics of recrystallization, precipitation, phase transformation, recrystallized austenite grain size, ferrite grain size, and the resulting mechanical properties. The transformation submodel of niobium-microalloyed steels is based on the nucleation and grain growth theory and additivity rule. The thermomechanical part of the modeling process was effectively carried out using the finite element method. Results were obtained in different temperatures, strain rates, and range of deformation. The thermomechanical treatments are different for two grades of niobium-steels to make possible analysis of the resulting structure and properties for different histories of deformation and chemical composition.
Modelling and Optimizing Mathematics Learning in Children
Käser, Tanja; Busetto, Alberto Giovanni; Solenthaler, Barbara; Baschera, Gian-Marco; Kohn, Juliane; Kucian, Karin; von Aster, Michael; Gross, Markus
2013-01-01
This study introduces a student model and control algorithm, optimizing mathematics learning in children. The adaptive system is integrated into a computer-based training system for enhancing numerical cognition aimed at children with developmental dyscalculia or difficulties in learning mathematics. The student model consists of a dynamic…
Scaffolding Mathematical Modelling with a Solution Plan
Schukajlow, Stanislaw; Kolter, Jana; Blum, Werner
2015-01-01
In the study presented in this paper, we examined the possibility to scaffold mathematical modelling with strategies. The strategies were prompted using an instrument called "solution plan" as a scaffold. The effects of this step by step instrument on mathematical modelling competency and on self-reported strategies were tested using…
Mathematical Model of Gravitational and Electrostatic Forces
Krouglov, Alexei
2006-01-01
Author presents mathematical model for acting-on-a-distance attractive and repulsive forces based on propagation of energy waves that produces Newton expression for gravitational and Coulomb expression for electrostatic forces. Model uses mathematical observation that difference between two inverse exponential functions of the distance asymptotically converges to function proportional to reciprocal of distance squared.
Mathematical Modelling as a Professional Task
Frejd, Peter; Bergsten, Christer
2016-01-01
Educational research literature on mathematical modelling is extensive. However, not much attention has been paid to empirical investigations of its scholarly knowledge from the perspective of didactic transposition processes. This paper reports from an interview study of mathematical modelling activities involving nine professional model…
Mineral potential mapping with mathematical geological models
Porwal, A.K.
2006-01-01
Mathematical geological models are being increasingly used by natural resources delineation and planning agencies for mapping areas of mineral potential in order to optimize land use in accordance with socio-economic needs of the society. However, a key problem in spatial-mathematical-model-based mi
Mathematical Modeling of the Agriculture Crop Technology
Directory of Open Access Journals (Sweden)
D. Drucioc
1999-02-01
Full Text Available The organized structure of computer system for economic and ecological estimation of agriculture crop technologies is described. The system is composed of six interconnected blocks. The linear, non-linear and stochastic mathematical models for machinery sizing and selection in farm-level cropping system is presented in the mathematical model block of computer system.
Mineral potential mapping with mathematical geological models
Porwal, A.K.
2006-01-01
Mathematical geological models are being increasingly used by natural resources delineation and planning agencies for mapping areas of mineral potential in order to optimize land use in accordance with socio-economic needs of the society. However, a key problem in spatial-mathematical-model-based
Mathematical Modeling of Cellular Metabolism.
Berndt, Nikolaus; Holzhütter, Hermann-Georg
2016-01-01
Cellular metabolism basically consists of the conversion of chemical compounds taken up from the extracellular environment into energy (conserved in energy-rich bonds of organic phosphates) and a wide array of organic molecules serving as catalysts (enzymes), information carriers (nucleic acids), and building blocks for cellular structures such as membranes or ribosomes. Metabolic modeling aims at the construction of mathematical representations of the cellular metabolism that can be used to calculate the concentration of cellular molecules and the rates of their mutual chemical interconversion in response to varying external conditions as, for example, hormonal stimuli or supply of essential nutrients. Based on such calculations, it is possible to quantify complex cellular functions as cellular growth, detoxification of drugs and xenobiotic compounds or synthesis of exported molecules. Depending on the specific questions to metabolism addressed, the methodological expertise of the researcher, and available experimental information, different conceptual frameworks have been established, allowing the usage of computational methods to condense experimental information from various layers of organization into (self-) consistent models. Here, we briefly outline the main conceptual frameworks that are currently exploited in metabolism research.
Mathematical modelling of scour: A review
DEFF Research Database (Denmark)
Sumer, B. Mutlu
2007-01-01
A review is presented of mathematical modelling of scour around hydraulic and marine structures. Principal ideas, general features and procedures are given. The paper is organized in three sections: the first two sections deal with the mathematical modelling of scour around piers/piles and pipeli......A review is presented of mathematical modelling of scour around hydraulic and marine structures. Principal ideas, general features and procedures are given. The paper is organized in three sections: the first two sections deal with the mathematical modelling of scour around piers....../piles and pipelines, respectively, the two benchmark cases, while the third section deals with the mathematical modelling of scour around other structures such as groins, breakwaters and sea walls. A section is also added to discuss potential future research areas. Over one hundred references are included...
Time dependent two phase flows in Magnetohydrodynamics: A ...
African Journals Online (AJOL)
Journal of the Nigerian Association of Mathematical Physics ... Open Access DOWNLOAD FULL TEXT Subscription or Fee Access. Time dependent two phase flows in Magnetohydrodynamics: A Greens function approach. BK Jha, HM Jibril ...
Energy Technology Data Exchange (ETDEWEB)
Deendarlianto, E-mail: deendarlianto@ugm.ac.id [Helmholtz-Zentrum Dresden-Rossendorf e.V., Institute of Safety Research, P.O. Box 510 119, D-01314 Dresden (Germany); Department of Mechanical and Industrial Engineering, Faculty of Engineering, Gadjah Mada University, Jalan Grafika No. 2, Yogyakarta 55281 (Indonesia); Hoehne, Thomas; Lucas, Dirk; Vallee, Christophe [Helmholtz-Zentrum Dresden-Rossendorf e.V., Institute of Safety Research, P.O. Box 510 119, D-01314 Dresden (Germany); Zabala, Gustavo Adolfo Montoya [Department of Chemical Engineering, Simon Bolivar University, Valle of Sartenejas, Caracas 1080 (Venezuela, Bolivarian Republic of)
2011-12-15
Highlights: Black-Right-Pointing-Pointer We modelled CCFL in a PWR hot leg using Algebraic Interfacial Area Density model. Black-Right-Pointing-Pointer The model is able to distinguish the local flow morphologies. Black-Right-Pointing-Pointer Test fluids are air-water and steam-water. Black-Right-Pointing-Pointer Calculated CCFL and water level are in good agreement with experimental data. - Abstract: In order to improve the understanding of counter-current two-phase flow and to validate new physical models, CFD simulations of a 1/3rd scale model of the hot leg of a German Konvoi pressurized water reactor (PWR) with rectangular cross section were performed. Selected counter-current flow limitation (CCFL) experiments conducted at Helmholtz-Zentrum Dresden-Rossendorf (HZDR) were calculated with ANSYS CFX using the multi-fluid Euler-Euler modelling approach. The transient calculations were carried out using a gas/liquid inhomogeneous multiphase flow model coupled with a shear stress transport (SST) turbulence model. In the simulation, the drag law was approached by a newly developed correlation of the drag coefficient in the Algebraic Interfacial Area Density (AIAD) model. The model can distinguish the bubbles, droplets and the free surface using the local liquid phase volume fraction value. A comparison with the high-speed video observations shows a good qualitative agreement. The results indicate also a quantitative agreement between calculations and experimental data for the CCFL characteristics and the water level inside the hot leg channel.
Mathematical modeling in soil science
Tarquis, Ana M.; Gasco, Gabriel; Saa-Requejo, Antonio; Méndez, Ana; Andina, Diego; Sánchez, M. Elena; Moratiel, Rubén; Antón, Jose Manuel
2015-04-01
Teaching in context can be defined as teaching a mathematical idea or process by using a problem, situation, or data to enhance the teaching and learning process. The same problem or situation may be used many times, at different mathematical levels to teach different objectives. A common misconception exists that assigning/teaching applications is teaching in context. While both use problems, the difference is in timing, in purpose, and in student outcome. In this work, one problem situation is explored thoroughly at different levels of understanding and other ideas are suggested for classroom explorations. Some teachers, aware of the difficulties some students have with mathematical concepts, try to teach quantitative sciences without using mathematical tools. Such attempts are not usually successful. The answer is not in discarding the mathematics, but in finding ways to teach mathematically-based concepts to students who need them but who find them difficult. The computer is an ideal tool for this purpose. To this end, teachers of the Soil Science and Mathematics Departments of the UPM designed a common practice to teach to the students the role of soil on the carbon sequestration. The objective of this work is to explain the followed steps to the design of the practice. Acknowledgement Universidad Politécnica de Madrid (UPM) for the Projects in Education Innovation IE12_13-02009 and IE12_13-02012 is gratefully acknowledge.
Institute of Scientific and Technical Information of China (English)
姜俊泽; 张伟明; 李正阳
2013-01-01
Based on the deeply analyzing the simulation method, VOF model was employed to research gas-liquid two-phase flow of the pipe pigging process, taking surface tension, wall adhesion, the viscosity of the liquid, the wall's roughness and the gas compressibility into consideration. The simulation took unobstructed mesh and mesh decipherment technology to trace the gas-liquid interface and the gas-liquid interface mixture and variation processes were obtained. Then, The pressure distribution, gas volume percentage, two-phase flow friction and the energy transformation at different moment were analyzed.The results show that VOF model could be used to the numerical simulation of non-free surface two phase flow.%为了获得管道充气排液过程的两相流动状态,采用VOF模型对管道充气排液工况进行了数值模拟研究.模型考虑了液体表面张力、壁面粘附力,流体粘度,管壁粗糙度以及气体可压缩性效应,并采用结构化网格和自适应网格加密技术,对两相界面进行了跟踪,观察了这一工况下的气液两相混合及界面变化过程,分析了充气过程中不同时刻的管道内压力分布、气相体积分数、管流摩阻和能量交换情况,得到了这一工况下气液两相的流动特征.模拟结果也表明,在进行适当的网格划分和参数设置,VOF模型可以用于非自由表面的有压流动的数值模拟.
A Seminar in Mathematical Model-Building.
Smith, David A.
1979-01-01
A course in mathematical model-building is described. Suggested modeling projects include: urban problems, biology and ecology, economics, psychology, games and gaming, cosmology, medicine, history, computer science, energy, and music. (MK)
Directory of Open Access Journals (Sweden)
S. Mimouni
2009-01-01
Full Text Available In our work in 2008, we evaluated the aptitude of the code Neptune_CFD to reproduce the incidence of a structure topped by vanes on a boiling layer, within the framework of the Neptune project. The objective was to reproduce the main effects of the spacer grids. The turbulence of the liquid phase was modeled by a first-order K-ε model. We show in this paper that this model is unable to describe the turbulence of rotating flows, in accordance with the theory. The objective of this paper is to improve the turbulence modeling of the liquid phase by a second turbulence model based on a Rij-ε approach. Results obtained on typical single-phase cases highlight the improvement of the prediction for all computed values. We tested the turbulence model Rij-ε implemented in the code versus typical adiabatic two-phase flow experiments. We check that the simulations with the Reynolds stress transport model (RSTM give satisfactory results in a simple geometry as compared to a K-ε model: this point is crucial before calculating rod bundle geometries where the K-ε model may fail.
Huang, Y.; Shao, H.; Thullner, M.; Kolditz, O.
2014-12-01
In applications of Deep Geothermal reservoirs, thermal recovery processes, and contaminated groundwater sites, the multiphase multicomponent flow and transport processes are often considered the most important underlying physical process. In particular, the behavior of phase appearance and disappearance is the critical to the performance of many geo-reservoirs, and great interests exit in the scientific community to simulate this coupled process. This work is devoted to the modeling and simulation of two-phase, two components flow and transport in the porous medium, whereas the phase change behavior in non-isothermal conditions is considered. In this work, we have implemented the algorithm developed by Marchand, et al., into the open source scientific software OpenGeoSys. The governing equation is formulated in terms of molar fraction of the light component and mean pressure as the persistent primary variables, which leads to a fully coupled nonlinear PDE system. One of the important advantages of this approach is avoiding the primary variables switching between single phase and two phase zones, so that this uniform system can be applied to describe the behavior of phase change. On the other hand, due to the number of unkown variables closure relationships are also formulated to close the whole equation system by using the approach of complementarity constrains. For the numerical technical scheme: The standard Galerkin Finite element method is applied for space discretization, while a fully implicit scheme for the time discretization, and Newton-Raphson method is utilized for the global linearization, as well as the closure relationship. This model is verified based on one test case developed to simulate the heat pipe problem. This benchmark involves two-phase two-component flow in saturated/unsaturated porous media under non-isothermal condition, including phase change and mineral-water geochemical reactive transport processes. The simulation results will be
MATHEMATICAL MODEL OF GRAIN MICRONIZATION
Directory of Open Access Journals (Sweden)
V. A. Afanas’ev
2014-01-01
Full Text Available Summary. During micronisation grain moisture evaporates mainly in decreasing drying rate period. Grain layer located on the surface of the conveyor micronisers will be regarded as horizontal plate. Due to the fact that the micronisation process the surface of the grain evaporates little moisture (within 2-7 % is assumed constant plate thickness. Because in the process of micronization grain structure is changing, in order to achieve an exact solution of the equations necessary to take into account changes thermophysical, optical and others. Equation of heat transfer is necessary to add a term that is responsible for the infrared heating. Because of the small thickness of the grain, neglecting the processes occurring at the edge of the grain, that is actually consider the problem of an infinite plate. To check the adequacy of the mathematical model of the process of micronisation of wheat grain moisture content must be comparable to the function of time, obtained by solving the system of equations with the measured experimental data of experience. Numerical solution of a system of equations for the period of decreasing drying rate is feasible with the help of the Maple 14, substituting the values of the constants in the system. Calculation of the average relative error does not exceed 7- 10 %, and shows a good agreement between the calculated data and the experimental values.
Applications of mathematical models of road cycling
Dahmen, Thorsten; Saupe, Dietmar; Wolf, Stefan
2012-01-01
This contribution discusses several use cases of mathematical models for road cycling. A mechanical model for the pedaling forces is the basis for an accurate indoor ergometer simulation of road cycling on real-world tracks. Together with a simple physiological model for the exertion of the athlete as a function of his/her accumulated power output, an optimal riding strategy for time trials on mountain ascents is computed. A combination of the two models leads to a mathematical optimization p...
The mathematics of cancer: integrating quantitative models.
Altrock, Philipp M; Liu, Lin L; Michor, Franziska
2015-12-01
Mathematical modelling approaches have become increasingly abundant in cancer research. The complexity of cancer is well suited to quantitative approaches as it provides challenges and opportunities for new developments. In turn, mathematical modelling contributes to cancer research by helping to elucidate mechanisms and by providing quantitative predictions that can be validated. The recent expansion of quantitative models addresses many questions regarding tumour initiation, progression and metastases as well as intra-tumour heterogeneity, treatment responses and resistance. Mathematical models can complement experimental and clinical studies, but also challenge current paradigms, redefine our understanding of mechanisms driving tumorigenesis and shape future research in cancer biology.
Zhan, Shuiqing; Yang, Jianhong; Wang, Zhentao; Zhao, Ruijie; Zheng, Jun; Wang, Junfeng
2017-09-01
Numerical simulations of gas-liquid two-phase flows in aluminum electrolysis cells using the Euler-Euler approach were presented. The attempt was made to assess the performance and applicability of different interphase forces (drag, lift, wall lubrication, and turbulent dispersion forces) and turbulence models (standard k- ɛ, renormalization group k- ɛ, standard k- ω, shear stress transport k- ω, and Reynolds stress models). Moreover, three different bubble-induced turbulence models have been also analyzed. The simulated electrolyte velocity profiles were discussed by comparing with each other and against published experimental data. Based on the results of the validation of different interphase forces and turbulence models, a set consisting of the dispersed standard k- ɛ model, Grace drag coefficient model, Simonin turbulent dispersion force model, and Sato et al.'s bubble-induced effective viscosity model was found to provide the best agreement with the experimental data. The prediction results showed that the contributions of the lift force and the wall lubrication force can be neglected for the present bubbly flows.
Zhan, Shuiqing; Yang, Jianhong; Wang, Zhentao; Zhao, Ruijie; Zheng, Jun; Wang, Junfeng
2017-03-01
Numerical simulations of gas-liquid two-phase flows in aluminum electrolysis cells using the Euler-Euler approach were presented. The attempt was made to assess the performance and applicability of different interphase forces (drag, lift, wall lubrication, and turbulent dispersion forces) and turbulence models (standard k-ɛ, renormalization group k-ɛ, standard k-ω, shear stress transport k-ω, and Reynolds stress models). Moreover, three different bubble-induced turbulence models have been also analyzed. The simulated electrolyte velocity profiles were discussed by comparing with each other and against published experimental data. Based on the results of the validation of different interphase forces and turbulence models, a set consisting of the dispersed standard k-ɛ model, Grace drag coefficient model, Simonin turbulent dispersion force model, and Sato et al.'s bubble-induced effective viscosity model was found to provide the best agreement with the experimental data. The prediction results showed that the contributions of the lift force and the wall lubrication force can be neglected for the present bubbly flows.
Mathematical Programming Models in Educational Planning.
McNamara, James F.
This document begins by defining and discussing educational planning. A brief overview of mathematical programing with an explanation of the general linear programing model is then provided. Some recent applications of mathematical programing techniques to educational planning problems are reviewed, and their implications for educational research…
Directory of Open Access Journals (Sweden)
Y. B. Wang
2016-08-01
Full Text Available Though widely used in modelling nano- and micro- structures, Eringen’s differential model shows some inconsistencies and recent study has demonstrated its differences between the integral model, which then implies the necessity of using the latter model. In this paper, an analytical study is taken to analyze static bending of nonlocal Euler-Bernoulli beams using Eringen’s two-phase local/nonlocal model. Firstly, a reduction method is proved rigorously, with which the integral equation in consideration can be reduced to a differential equation with mixed boundary value conditions. Then, the static bending problem is formulated and four types of boundary conditions with various loadings are considered. By solving the corresponding differential equations, exact solutions are obtained explicitly in all of the cases, especially for the paradoxical cantilever beam problem. Finally, asymptotic analysis of the exact solutions reveals clearly that, unlike the differential model, the integral model adopted herein has a consistent softening effect. Comparisons are also made with existing analytical and numerical results, which further shows the advantages of the analytical results obtained. Additionally, it seems that the once controversial nonlocal bar problem in the literature is well resolved by the reduction method.
Mu, Yaoming; Sungkorn, Radompon; Toelke, Jonas
2016-09-01
In this paper, we extend pore-morphology-based methods proposed by Hazlett (1995) and Hilpert and Miller (2001) to simulate drainage and imbibition in uniformly wetting porous media and add an (optional) entrapment of the (non-)wetting phase. By improving implementation, this method allows us to identify the statistical representative elementary volume and estimate uncertainty by computing fluid flow properties and saturation distributions of hundreds of subsamples within a reasonable time-frame. The method was utilized to study three different porous medium systems and results demonstrate that morphology-based pore-scale modeling is a viable approach to assess the representative elementary volume with respect to capillary dominated two-phase flow. The focus of this paper is the determination of the representative elementary volume for multiphase-flow properties for a digital representation of a rock.
Directory of Open Access Journals (Sweden)
Pessôa Filho P. A.
2004-01-01
Full Text Available Mixtures containing compounds that undergo hydrogen bonding show large deviations from ideal behavior. These deviations can be accounted for through chemical theory, according to which the formation of a hydrogen bond can be treated as a chemical reaction. This chemical equilibrium needs to be taken into account when applying stability criteria and carrying out phase equilibrium calculations. In this work, we illustrate the application of the stability criteria to establish the conditions under which a liquid-phase split may occur and the subsequent calculation of liquid-liquid equilibrium using a chemical-theory-modified Flory-Huggins equation to describe the non ideality of aqueous two-phase systems composed of poly(ethylene glycol and dextran. The model was found to be able to correlate ternary liquid-liquid diagrams reasonably well by simple adjustment of the polymer-polymer binary interaction parameter.
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
A statistical formalism overcoming some conceptualand practical difficulties arising in existing two-phase flow (2PHF)mathematical modelling has been applied to propose a model for dilute2PHF turbulent flows. Phase interaction terms with a clear physical meaning enterthe equations andthe formalism provides some guidelines for the avoidance of closure assumptions orthe rational approximation of these terms. Continuous phase averaged continuity,momentum, turbulent kinetic energy and turbulencedissipation rate equations have been rigorously andsystematically obtained in a single step.These equations display a structure similar to that forsingle-phase flows. It is also assumed thatdispersed phase dynamics is well described by a probability densityfunction (pdf) equation and Eulerian continuity,momentum and fluctuating kinetic energy equations for the dispersedphase are deduced. Anextension of the standard k- turbulencemodel for the continuous phase is used. A gradient transport model is adopted forthe dispersedphase fluctuating fluxes of momentum and kinetic energy at the non-colliding, largeinertia limit. This model is thenused to predict the behaviour of three axisymmetric turbulent jets of air laden withsolid particlesvarying in size and concentration. Qualitative and quantitative numericalpredictions comparereasonably well with the three different sets of experimental results, studying theinfluence ofparticle size, loading ratio and flow confinement velocity.
Sweijen, Thomas; Hartog, Niels; Marsman, Annemieke; Keijzer, Thomas J. S.
2014-06-01
Mercury is a contaminant of global concern. The use of elemental mercury in various (former) industrial processes, such as chlorine production at chlor-alkali plants, is known to have resulted in soil and groundwater contaminations worldwide. However, the subsurface transport behaviour of elemental mercury as an immiscible dense non-aqueous phase liquid (DNAPL) in porous media has received minimal attention to date. Even though, such insight would aid in the remediation effort of mercury contaminated sites. Therefore, in this study a detailed field characterization of elemental mercury DNAPL distribution with depth was performed together with two-phase flow modelling, using STOMP. This is to evaluate the dynamics of mercury DNAPL migration and the controls on its distribution in saturated porous media. Using a CPT-probe mounted with a digital camera, in-situ mercury DNAPL depth distribution was obtained at a former chlor-alkali-plant, down to 9 m below ground surface. Images revealing the presence of silvery mercury DNAPL droplets were used to quantify its distribution, characteristics and saturation, using an image analysis method. These field-observations with depth were compared with results from a one-dimensional two-phase flow model simulation for the same transect. Considering the limitations of this approach, simulations reasonably reflected the variability and range of the mercury DNAPL distribution. To further explore the impact of mercury's physical properties in comparison with more common DNAPLs, the migration of mercury and PCE DNAPL in several typical hydrological scenarios was simulated. Comparison of the simulations suggest that mercury's higher density is the overall controlling factor in controlling its penetration in saturated porous media, despite its higher resistance to flow due to its higher viscosity. Based on these results the hazard of spilled mercury DNAPL to cause deep contamination of groundwater systems seems larger than for any other
Mathematical models in biology bringing mathematics to life
Ferraro, Maria; Guarracino, Mario
2015-01-01
This book presents an exciting collection of contributions based on the workshop “Bringing Maths to Life” held October 27-29, 2014 in Naples, Italy. The state-of-the art research in biology and the statistical and analytical challenges facing huge masses of data collection are treated in this Work. Specific topics explored in depth surround the sessions and special invited sessions of the workshop and include genetic variability via differential expression, molecular dynamics and modeling, complex biological systems viewed from quantitative models, and microscopy images processing, to name several. In depth discussions of the mathematical analysis required to extract insights from complex bodies of biological datasets, to aid development in the field novel algorithms, methods and software tools for genetic variability, molecular dynamics, and complex biological systems are presented in this book. Researchers and graduate students in biology, life science, and mathematics/statistics will find the content...
A mathematical model of symmetry based on mathematical definition
Institute of Scientific and Technical Information of China (English)
无
2002-01-01
Tolerance is imperative for seamless integration of CAD/CAM(Computer Aided Disign/Computer Aided Manufacture) which is just a text attribute and has no semantics in present CAD systems. There are many tolerance types, the relations between which are very complicated. In addition, the different principles of tolerance make study of tolerance difficult; and there may be various meanings or interpretation for the same type of tolerance because of the literal definition. In this work, latest unambiguous mathematical definition was applied to study, explain and clarify: (1) the formation and representation of tolerance zone, and (2) the formation and representation of variational elements; after which, the mathematical models of symmetry of different tolerance principles and different interpretations were derived. An example is given to illustrate the application of these models in tolerance analysis.
A mathematical model of symmetry based on mathematical definition
Institute of Scientific and Technical Information of China (English)
刘玉生; 杨将新; 吴昭同; 高曙明
2002-01-01
Tolerance is imperative for seamless integration of CAD/CAM(Computer Aided Disignd/Computer Aided Manufacture) which is just a text attribute and has no semantics in present CAD systems. There are many tolerance types, the relations between which are very complicated. In addition, the different principles of tolerance make study of tolerance difficult; and there may be various meanings or interpretation for the same type of tolerance beeanse of the literal definition. In this work, latest unambiguous mathematical definition was applied to study, explain and clarify: ( 1 ) the formation and representation of tolerance zone, and (2) the formation and representation of variational elements ; after which, the mathematical models of syrmmetry of different tolerance principles and different interpretations were derived. An example is given to illustrate the application of these models in tolerance analysis.
Study of Photovoltaic Cells Engineering Mathematical Model
Zhou, Jun; Yu, Zhengping; Lu, Zhengyi; Li, Chenhui; Zhang, Ruilan
2016-11-01
The characteristic curve of photovoltaic cells is the theoretical basis of PV Power, which simplifies the existing mathematical model, eventually, obtains a mathematical model used in engineering. The characteristic curve of photovoltaic cells contains both exponential and logarithmic calculation. The exponential and logarithmic spread out through Taylor series, which includes only four arithmetic and use single chip microcontroller as the control center. The result shows that: the use of single chip microcontroller for calculating exponential and logarithmic functions, simplifies mathematical model of PV curve, also can meet the specific conditions’ requirement for engineering applications.
Mathematical modeling a chemical engineer's perspective
Rutherford, Aris
1999-01-01
Mathematical modeling is the art and craft of building a system of equations that is both sufficiently complex to do justice to physical reality and sufficiently simple to give real insight into the situation. Mathematical Modeling: A Chemical Engineer's Perspective provides an elementary introduction to the craft by one of the century's most distinguished practitioners.Though the book is written from a chemical engineering viewpoint, the principles and pitfalls are common to all mathematical modeling of physical systems. Seventeen of the author's frequently cited papers are reprinted to illus
Energy Technology Data Exchange (ETDEWEB)
Han, L.H., E-mail: Luhui.Han@tum.de; Hu, X.Y., E-mail: Xiangyu.Hu@tum.de; Adams, N.A., E-mail: Nikolaus.Adams@tum.de
2015-01-01
In this paper we present a scale separation approach for multi-scale modeling of free-surface and two-phase flows with complex interface evolution. By performing a stimulus-response operation on the level-set function representing the interface, separation of resolvable and non-resolvable interface scales is achieved efficiently. Uniform positive and negative shifts of the level-set function are used to determine non-resolvable interface structures. Non-resolved interface structures are separated from the resolved ones and can be treated by a mixing model or a Lagrangian-particle model in order to preserve mass. Resolved interface structures are treated by the conservative sharp-interface model. Since the proposed scale separation approach does not rely on topological information, unlike in previous work, it can be implemented in a straightforward fashion into a given level set based interface model. A number of two- and three-dimensional numerical tests demonstrate that the proposed method is able to cope with complex interface variations accurately and significantly increases robustness against underresolved interface structures.
Pressure Loss across Tube Bundles in Two-phase Flow
Energy Technology Data Exchange (ETDEWEB)
Sim, Woo Gun; Banzragch, Dagdan [Hannam Univ., Daejon (Korea, Republic of)
2016-03-15
An analytical model was developed by Sim to estimate the two-phase damping ratio for upward two-phase flow perpendicular to horizontal tube bundles. The parameters of two-phase flow, such as void fraction and pressure loss evaluated in the model, were calculated based on existing experimental formulations. However, it is necessary to implement a few improvements in the formulations for the case of tube bundles. For the purpose of the improved formulation, we need more information about the two-phase parameters, which can be found through experimental test. An experiment is performed with a typical normal square array of cylinders subjected to the two-phase flow of air-water in the tube bundles, to calculate the two-phase Euler number and the two-phase friction multiplier. The pitch-to-diameter ratio is 1.35 and the diameter of cylinder is 18mm. Pressure loss along the flow direction in the tube bundles is measured with a pressure transducer and data acquisition system to calculate the two-phase Euler number and the two-phase friction multiplier. The void fraction model by Feenstra et al. is used to estimate the void fraction of the two-phase flow in tube bundles. The experimental results of the two phase friction multiplier and two-phase Euler number for homogeneous and non-homogeneous two-phase flows are compared and evaluated against the analytical results given by Sim's model.
Mathematical Modelling and Parameter Optimization of Pulsating Heat Pipes
Yang, Xin-She; Luan, Tao; Koziel, Slawomir
2014-01-01
Proper heat transfer management is important to key electronic components in microelectronic applications. Pulsating heat pipes (PHP) can be an efficient solution to such heat transfer problems. However, mathematical modelling of a PHP system is still very challenging, due to the complexity and multiphysics nature of the system. In this work, we present a simplified, two-phase heat transfer model, and our analysis shows that it can make good predictions about startup characteristics. Furthermore, by considering parameter estimation as a nonlinear constrained optimization problem, we have used the firefly algorithm to find parameter estimates efficiently. We have also demonstrated that it is possible to obtain good estimates of key parameters using very limited experimental data.
Mathematical Modelling as Problem Solving for Children in the Singapore Mathematics Classrooms
Eric, Chan Chun Ming
2009-01-01
The newly revised mathematics curriculum in Singapore has recently factored Applications and Modelling to be part of the teaching and learning of mathematics. Its implication is that even children should now be involved in works of mathematical modelling. However, to be able to implement modelling activities in the primary mathematics classroom,…
Institute of Scientific and Technical Information of China (English)
LIU Cheng; SHEN YongMing
2009-01-01
A three-dimensional k-ε-Ap solid-liquid two-phase two-fluid model with the effect of vegetation Is solved numerically with a finite-volume method on an adaptive grid to study water-sediment movements and bed evolution in vegetated channels. The additional drag force and additional turbulence generation due to vegetation are added to the relevant control equations for simulating the interaction between vegetation and flow. The flow structure and the bed-topography changes in a 60° partly vegetated channel bend are calculated by the model. The numerical results agree well with the measured ones. Calculated and measured results show that the primary flow velocity reduces much in the vegetation zone and increases in the non-vegetation zone, the secondary flow velocity weakens in the vegetation zone and strengthens in the non-vegetation zone, the sediment movement and bed-topography change also weaken in the vegetation zone and strengthen in the non-vegetation zone, a well-planed vegetation arrangement can improve bank stabilization program, and the k-ε-Ap model can deal with bed-load transport with a more reasonable method than the one-fluid model.
Institute of Scientific and Technical Information of China (English)
无
2009-01-01
A three-dimensional k-ε-Ap solid-liquid two-phase two-fluid model with the effect of vegetation is solved numerically with a finite-volume method on an adaptive grid to study water-sediment movements and bed evolution in vegetated channels. The additional drag force and additional turbulence generation due to vegetation are added to the relevant control equations for simulating the interaction between vegetation and flow. The flow structure and the bed-topography changes in a 60° partly vegetated channel bend are calculated by the model. The numerical results agree well with the measured ones. Calculated and measured results show that the primary flow velocity reduces much in the vegetation zone and increases in the non-vegetation zone, the secondary flow velocity weakens in the vegetation zone and strengthens in the non-vegetation zone, the sediment movement and bed-topography change also weaken in the vegetation zone and strengthen in the non-vegetation zone, a well-planed vegetation arrangement can improve bank stabilization program, and the k-ε-Ap model can deal with bed-load transport with a more reasonable method than the one-fluid model.
Energy Technology Data Exchange (ETDEWEB)
Jaeger, Wadim; Manes, Jorge Perez; Imke, Uwe; Escalante, Javier Jimenez; Espinoza, Victor Sanchez, E-mail: victor.sanchez@kit.edu
2013-10-15
Highlights: • Simulation of BFBT turbine and pump transients at multiple scales. • CFD, sub-channel and system codes are used for the comparative study. • Heat transfer models are compared to identify difference between the code predictions. • All three scales predict results in good agreement to experiment. • Sub cooled boiling models are identified as field for future research. -- Abstract: The Institute for Neutron Physics and Reactor Technology (INR) at the Karlsruhe Institute of Technology (KIT) is involved in the validation and qualification of modern thermo hydraulic simulations tools at various scales. In the present paper, the prediction capabilities of four codes from three different scales – NEPTUNE{sub C}FD as fine mesh computational fluid dynamics code, SUBCHANFLOW and COBRA-TF as sub channels codes and TRACE as system code – are assessed with respect to their two-phase flow modeling capabilities. The subject of the investigations is the well-known and widely used data base provided within the NUPEC BFBT benchmark related to BWRs. Void fraction measurements simulating a turbine and a re-circulation pump trip are provided at several axial levels of the bundle. The prediction capabilities of the codes for transient conditions with various combinations of boundary conditions are validated by comparing the code predictions with the experimental data. In addition, the physical models of the different codes are described and compared to each other in order to explain the different results and to identify areas for further improvements.
Mathematical modelling of cucumber (cucumis sativus) drying
Shahari, N.; Hussein, S. M.; Nursabrina, M.; Hibberd, S.
2014-07-01
This paper investigates the applicability of using an experiment based mathematical model (empirical model) and a single phase mathematical model with shrinkage to describe the drying curve of cucumis sativus (cucumber). Drying experiments were conducted using conventional air drying and data obtained from these experiments were fitted to seven empirical models using non-linear least square regression based on the Levenberg Marquardt algorithm. The empirical models were compared according to their root mean square error (RMSE), sum of square error (SSE) and coefficient of determination (R2). A logarithmic model was found to be the best empirical model to describe the drying curve of cucumber. The numerical result of a single phase mathematical model with shrinkage was also compared with experiment data for cucumber drying. A good agreement was obtained between the model predictions and the experimental data.
Mathematical modelling of the calcination process | Olayiwola ...
African Journals Online (AJOL)
Mathematical modelling of the calcination process. ... High quality lime is an essential raw material for Electric Arc Furnaces and Basic Oxygen Furnaces ... From the numerical simulation, it is observed that the gas temperature increases as the ...
Teaching mathematical modelling through project work
DEFF Research Database (Denmark)
Blomhøj, Morten; Kjeldsen, Tinne Hoff
2006-01-01
are reported in manners suitable for internet publication for colleagues. The reports and the related discussions reveal interesting dilemmas concerning the teaching of mathematical modelling and how to cope with these through “setting the scene” for the students modelling projects and through dialogues...... in their own classes, evaluate and report a project based problem oriented course in mathematical modelling. The in-service course runs over one semester and includes three seminars of 3, 1 and 2 days. Experiences show that the course objectives in general are fulfilled and that the course projects......The paper presents and analyses experiences from developing and running an in-service course in project work and mathematical modelling for mathematics teachers in the Danish gymnasium, e.g. upper secondary level, grade 10-12. The course objective is to support the teachers to develop, try out...
Applied mathematics: Models, Discretizations, and Solvers
Institute of Scientific and Technical Information of China (English)
D.E. Keyes
2007-01-01
@@ Computational plasma physicists inherit decades of developments in mathematical models, numerical algorithms, computer architecture, and software engineering, whose recent coming together marks the beginning of a new era of large-scale simulation.
Teaching mathematical modelling through project work
DEFF Research Database (Denmark)
Blomhøj, Morten; Kjeldsen, Tinne Hoff
2006-01-01
The paper presents and analyses experiences from developing and running an in-service course in project work and mathematical modelling for mathematics teachers in the Danish gymnasium, e.g. upper secondary level, grade 10-12. The course objective is to support the teachers to develop, try out...... in their own classes, evaluate and report a project based problem oriented course in mathematical modelling. The in-service course runs over one semester and includes three seminars of 3, 1 and 2 days. Experiences show that the course objectives in general are fulfilled and that the course projects...... are reported in manners suitable for internet publication for colleagues. The reports and the related discussions reveal interesting dilemmas concerning the teaching of mathematical modelling and how to cope with these through “setting the scene” for the students modelling projects and through dialogues...
Cooking Potatoes: Experimentation and Mathematical Modeling.
Chen, Xiao Dong
2002-01-01
Describes a laboratory activity involving a mathematical model of cooking potatoes that can be solved analytically. Highlights the microstructure aspects of the experiment. Provides the key aspects of the results, detailed background readings, laboratory procedures and data analyses. (MM)
Mathematical Modeling of Chemical Stoichiometry
Croteau, Joshua; Fox, William P.; Varazo, Kristofoland
2007-01-01
In beginning chemistry classes, students are taught a variety of techniques for balancing chemical equations. The most common method is inspection. This paper addresses using a system of linear mathematical equations to solve for the stoichiometric coefficients. Many linear algebra books carry the standard balancing of chemical equations as an…
Mathematical modeling in biomedical imaging
2009-01-01
This volume gives an introduction to a fascinating research area to applied mathematicians. It is devoted to providing the exposition of promising analytical and numerical techniques for solving challenging biomedical imaging problems, which trigger the investigation of interesting issues in various branches of mathematics.
Mathematical Modeling of Chemical Stoichiometry
Croteau, Joshua; Fox, William P.; Varazo, Kristofoland
2007-01-01
In beginning chemistry classes, students are taught a variety of techniques for balancing chemical equations. The most common method is inspection. This paper addresses using a system of linear mathematical equations to solve for the stoichiometric coefficients. Many linear algebra books carry the standard balancing of chemical equations as an…
Zeytun, Aysel Sen; Cetinkaya, Bulent; Erbas, Ayhan Kursat
2017-01-01
This paper investigates how prospective teachers develop mathematical models while they engage in modeling tasks. The study was conducted in an undergraduate elective course aiming to improve prospective teachers' mathematical modeling abilities, while enhancing their pedagogical knowledge for the integrating of modeling tasks into their future…
Energy Technology Data Exchange (ETDEWEB)
Guillemaud, V
2007-03-15
This thesis is devoted to the modelling and numerical simulation of liquid-vapor flows. In order to describe these phase transition flows, a two-fluid two-pressure approach is considered. This description of the liquid-vapor mixing is associated to the seven-equation model introduced by Baer and Nunziato. This work investigates the properties of this model in order to simulate the phase transition flows occurring in nuclear engineering. First, a theoretical thermodynamic framework is constructed to describe the liquid-vapor mixing. Provided with this framework, various modelling choices are suggested for the interaction terms between the phases. These closure laws comply with an entropy inequality. The mathematical properties of this model are thereafter examined. The convective part is associated to a nonconservative hyperbolic system. First, we focus on the definition of its weak solutions. Several flow regimes for the two-phase mixing derive from this analysis. Such regimes for the two-phase flows are analogous to the torrential and fluvial regimes for the shallow-water equations. Furthermore, we establish the linear and nonlinear stabilities of the liquid-vapor equilibrium. Finally, the implementation of a turbulence model and the introduction of a reconstruction process for the interfacial area are investigated in order to refine the description of the interfacial transfers. Using a fractional step approach, a Finite Volume method is at last constructed to simulate this model. First, various nonconservative adaptations of standard Riemann solvers are developed to approach the convective part. Unlike the classic nonconservative framework, these schemes converge towards the same solution. Furthermore, a new relaxation scheme is proposed to approach the interfacial transfers. Provided with these schemes, the whole numerical method preserves the liquid-vapor equilibria. Using this numerical method, a careful comparison between the one- and two-pressure two
Energy Technology Data Exchange (ETDEWEB)
Sharma, S.L., E-mail: sharma55@purdue.edu [School of Nuclear Engineering, Purdue University, West Lafayette, IN (United States); Hibiki, T.; Ishii, M. [School of Nuclear Engineering, Purdue University, West Lafayette, IN (United States); Schlegel, J.P. [Department of Mining and Nuclear Engineering, Missouri University of Science and Technology, Rolla, MO (United States); Buchanan, J.R.; Hogan, K.J. [Bettis Laboratory, Naval Nuclear Laboratory, West Mifflin, PA (United States); Guilbert, P.W. [ANSYS UK Ltd, Oxfordshire (United Kingdom)
2017-02-15
Highlights: • Closure form of the interfacial shear term in three-dimensional form is investigated. • Assessment against adiabatic upward bubbly air–water flow data using CFD. • Effect of addition of the interfacial shear term on the phase distribution. - Abstract: In commercially available Computational Fluid Dynamics (CFD) codes such as ANSYS CFX and Fluent, the interfacial shear term is missing in the field momentum equations. The derivation of the two-fluid model (Ishii and Hibiki, 2011) indicates the presence of this term as a momentum source in the right hand side of the field momentum equation. The inclusion of this term is considered important for proper modeling of the interfacial momentum coupling between phases. For separated flows, such as annular flow, the importance of the shear term is understood in the one-dimensional (1-D) form as the major mechanism by which the wall shear is transferred to the gas phase (Ishii and Mishima, 1984). For gas dispersed two-phase flow CFD simulations, it is important to assess the significance of this term in the prediction of phase distributions. In the first part of this work, the closure of this term in three-dimensional (3-D) form in a CFD code is investigated. For dispersed gas–liquid flow, such as bubbly or churn-turbulent flow, bubbles are dispersed in the shear layer of the continuous phase. The continuous phase shear stress is mainly due to the presence of the wall and the modeling of turbulence through the Boussinesq hypothesis. In a 3-D simulation, the continuous phase shear stress can be calculated from the continuous fluid velocity gradient, so that the interfacial shear term can be closed using the local values of the volume fraction and the total stress of liquid phase. This form also assures that the term acts as an action-reaction force for multiple phases. In the second part of this work, the effect of this term on the volume fraction distribution is investigated. For testing the model two-phase
Students’ mathematical learning in modelling activities
DEFF Research Database (Denmark)
Kjeldsen, Tinne Hoff; Blomhøj, Morten
2013-01-01
Ten years of experience with analyses of students’ learning in a modelling course for first year university students, led us to see modelling as a didactical activity with the dual goal of developing students’ modelling competency and enhancing their conceptual learning of mathematical concepts...... involved. We argue that progress in students’ conceptual learning needs to be conceptualised separately from that of progress in their modelling competency. Findings are that modelling activities open a window to the students’ images of the mathematical concepts involved; that modelling activities can...... create and help overcome hidden cognitive conflicts in students’ understanding; that reflections within modelling can play an important role for the students’ learning of mathematics. These findings are illustrated with a modelling project concerning the world population....
Kou, Jisheng
2015-03-01
In this paper, we consider multi-component dynamic two-phase interface models, which are formulated by the Cahn-Hilliard system with Peng-Robinson equation of state and various boundary conditions. These models can be derived from the minimum problems of Helmholtz free energy or grand potential in the realistic thermodynamic systems. The resulted Cahn-Hilliard systems with various boundary conditions are fully coupled and strongly nonlinear. A linear transformation is introduced to decouple the relations between different components, and as a result, the models are simplified. From this, we further propose a semi-implicit unconditionally stable time discretization scheme, which allows us to solve the Cahn-Hilliard system by a decoupled way, and thus, our method can significantly reduce the computational cost and memory requirements. The mixed finite element methods are employed for the spatial discretization, and the approximate errors are also analyzed for both space and time. Numerical examples are tested to demonstrate the efficiency of our proposed methods. © 2015 Elsevier B.V.
Investigation on two-phase flow instability in steam generator of integrated nuclear reactor
Institute of Scientific and Technical Information of China (English)
无
1996-01-01
In the pressure range of 3-18MPa,high pressure steam-water two-phase flow density wave instability in vertical upward parallel pipes with inner diameter of 12mm is studied experimentally.The oscillation curves of two-phase flow instability and the effects of several parameters on the oscillation threshold of the system are obtained.Based on the small pertubation linearization method and the stability principles of automatic control system,a mathematical model is developed to predict the characteristics of density wave instability threshold.The predictions of the model are in good agreement with the experimental results.
Energy Technology Data Exchange (ETDEWEB)
Zakarian, E.
2000-03-10
Recent estimations predict that over half the remaining offshore oil and gas reserves are located in deep water and marginal fields. For such reserves, economic recovery methods are required. Then, multiphase flows are transported within pipelines and separated on treatment platforms built in shallow water or processed in onshore facilities. Unfortunately, hydrodynamic instabilities may occur whenever gas and liquid flow in a pipeline, generating serious operating problems. This dissertation presents a new way to model two-phase flows in pipelines such as pipeline-riser systems. Equations are algebraic and differential. Their smoothness depends on the closure laws of the problem such as slip or friction laws. Smooth forms of these closure laws are presented for the first time in this dissertation. Therefore, a mathematical analysis of our model fits into a classical frame: a linear analysis leads to an analytical expression of the boundary between stable and unstable flows. A nonlinear analysis provides for the first time, the bifurcation curves of gas-liquid flows in pipe-riser systems, locally round their stability boundary. (author)
Mathematical model of cylindrical form tolerance
Institute of Scientific and Technical Information of China (English)
蔡敏; 杨将新; 吴昭同
2004-01-01
Tolerance is essential for integration of CAD and CAM. Unfortunately, the meaning of tolerances in the national standard is expressed in graphical and language forms and is not adaptable for expression, processing and data transferring with computers. How to interpret its semantics is becoming a focus of relevant studies. This work based on the mathematical definition of form tolerance in ANSI Y 14.5.1 M-1994, established the mathematical model of form tolerance for cylindrical feature. First, each tolerance in the national standard was established by vector equation. Then on the foundation of toler-ance's mathematical definition theory, each tolerance zone's mathematical model was established by inequality based on degrees of feature. At last the variance area of each tolerance zone is derived. This model can interpret the semantics of form tolerance exactly and completely.
Mathematical model of cylindrical form tolerance
Institute of Scientific and Technical Information of China (English)
蔡敏; 杨将新; 吴昭同
2004-01-01
Tolerance is essential for integration of CAD and CAM.Unfortunately,the meaning of tolerances in the national standard is expressed in graphical and language forms and is not adaptable for expression,processing and data transferring with computers.How to interpret its semantics is becoming a focus of relevant studies.This work based on the mathematical definition of form tolerance in ANSI Y 14.5.1 M-1994,established the mathematical model of form tolerance for cylindrical feature.First,each tolerance in the national standard was established by vector equation.Then on the foundation of tolerance's mathematical definition theory,each tolerance zone's mathematical model was established by inequality based on degrees of feature.At last the variance area of each tolerance zone is derived.This model can interpret the semantics of form tolerance exactly and completely.
Directory of Open Access Journals (Sweden)
Edwin Musdi
2016-02-01
Full Text Available This research aims to develop a mathematics instructional model based realistic mathematics education (RME to promote students' problem-solving abilities. The design research used Plomp models, which consists of preliminary phase, development or proto-typing phase and assessment phase. At this study, only the first two phases conducted. The first phase, a preliminary investigation, carried out with a literature study to examine the theory-based instructional learning RME model, characteristics of learners, learning management descriptions by junior high school mathematics teacher and relevant research. The development phase is done by developing a draft model (an early prototype model that consists of the syntax, the social system, the principle of reaction, support systems, and the impact and effects of instructional support. Early prototype model contain a draft model, lesson plans, worksheets, and assessments. Tesssmer formative evaluation model used to revise the model. In this study only phase of one to one evaluation conducted. In the ppreliminary phase has produced a theory-based learning RME model, a description of the characteristics of learners in grade VIII Junior High School Padang and the description of teacher teaching in the classroom. The result showed that most students were still not be able to solve the non-routine problem. Teachers did not optimally facilitate students to develop problem-solving skills of students. It was recommended that the model can be applied in the classroom.
Directory of Open Access Journals (Sweden)
Edwin Musdi
2016-02-01
Full Text Available This research aims to develop a mathematics instructional model based realistic mathematics education (RME to promote students' problem-solving abilities. The design research used Plomp models, which consists of preliminary phase, development or proto-typing phase and assessment phase. At this study, only the first two phases conducted. The first phase, a preliminary investigation, carried out with a literature study to examine the theory-based instructional learning RME model, characteristics of learners, learning management descriptions by junior high school mathematics teacher and relevant research. The development phase is done by developing a draft model (an early prototype model that consists of the syntax, the social system, the principle of reaction, support systems, and the impact and effects of instructional support. Early prototype model contain a draft model, lesson plans, worksheets, and assessments. Tesssmer formative evaluation model used to revise the model. In this study only phase of one to one evaluation conducted. In the ppreliminary phase has produced a theory-based learning RME model, a description of the characteristics of learners in grade VIII Junior High School Padang and the description of teacher teaching in the classroom. The result showed that most students were still not be able to solve the non-routine problem. Teachers did not optimally facilitate students to develop problem-solving skills of students. It was recommended that the model can be applied in the classroom.
Thermo-fluid dynamics of two-phase flow
Ishii, Mamoru; Ishii, Mamoru; Ishii, M
2006-01-01
Provides a very systematic treatment of two phase flow problems from a theoretical perspectiveProvides an easy to follow treatment of modeling and code devlopemnt of two phase flow related phenomenaCovers new results of two phase flow research such as coverage of fuel cells technology.
Kartal, Ozgul; Dunya, Beyza Aksu; Diefes-Dux, Heidi A.; Zawojewski, Judith S.
2016-01-01
Critical to many science, technology, engineering, and mathematics (STEM) career paths is mathematical modeling--specifically, the creation and adaptation of mathematical models to solve problems in complex settings. Conventional standardized measures of mathematics achievement are not structured to directly assess this type of mathematical…
Abu AlSaud, M.; Riaz, A.; Tchelepi, H.
2016-12-01
We developed a multiscale sharp interface method based on the level-set for two-phase immiscible flow with pre-existing thin-films on solid surfaces. The lubrication approximation theory is used to model the thin-film equation efficiently. The incompressible Navier-Stokes, level-set, and thin-film evolution equation are coupled sequentially to capture the physics occurring at multiple length scales. The proposed multiscale method is validated through comparison with the augmented Young-Laplace equation that includes the Van der Waals intermolecular force for a static meniscus in a capillary tube. The viscous bending in the advancing interface over precursor film problem is captured by the numerical method and agrees with the Cox-Voinov theory. The problem of a moving-bubble inside a capillary tube is modeled, and the results compare well with both theory and experiments. In addition, the performance of the new approach is assessed by studying the spurious currents for capillary-dominated flows at low capillary numbers. The method is applicable for flows with a capillary number as low as Ca10-6.
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
The dual-inlet liquid-spray-fuelled sudden-expansion combustors are frequently adopted in ramjet engines. The original combustors with swirlers in the inlet tubes frequently suffer from poor ignition, low flame stabilization and poor combustion performance due to insufficient sizes of recirculation zones in the head part of the combustor. There are only very small recirculation zones behind the swirlers. To improve the performance of the combustors, a new configuration is proposed by the authors, in which a small central tube instead of the original swirler is mounted in the inlet tube of the combustor with a tangential angle for creating swirling flows and enlarging the recirculation zones. So, it is expected to know the gas-droplet flow behavior after mounting the central tube. The turbulent swirling and recirculating gas-droplet flows in a dual-inlet sudden-expansion combustor are very complex. In the head part of the combustor there are recirculating flows. In the whole combustor there are swirling flows with a Rankine-vortex structure (solid-body rotation plus free vortex) of tangential velocity profiles. There should be obvious velocity slip between the gas and droplet phases due to the differences in inertia and centrifugal forces. The recirculating and swirling gas-particle flows were previously measured using LDV or PDPA［1～3］. In this paper the experimental studies on two-phase flows were carried out in a cold model of the combustor, and the motion of solid particles is used to simulate that of liquid droplets. The gas and particle (simulating the droplets) velocities were measured using a 2-D LDV system and the particle (simulating the droplet) concentration distribution is measured using a laser optic fiber system and a sampling probe. The purpose of this experimental study is not to simulate the real combustion regime, but to understand the features of the improved two-phase flow field using a central tube in the inlet tube and to provide the data
Czocher, Jennifer A.
2016-01-01
This study contributes a methodological tool to reconstruct the cognitive processes and mathematical activities carried out by mathematical modelers. Represented as Modeling Transition Diagrams (MTDs), individual modeling routes were constructed for four engineering undergraduate students. Findings stress the importance and limitations of using…
NUMERICAL SIMULATION ON 2-D WATER-AIR TWO-PHASE FLOW OVER TOP OUTLET
Institute of Scientific and Technical Information of China (English)
无
2002-01-01
Flood discharge over top outlet of dam is simu-lated by 2-dimension water-air two-phase mathematical model.Distribution of dynamic pressure, turbulent kinetic energy (k), turbulent dissipation rate (ε) , free water surface and veloci-ty field have been obtained. The simulated results were testedby physical model, which shows that the computed results areidentical with that of the physical model.
Controllability, Observability, and Stability of Mathematical Models
Iggidr, Abderrahman
2004-01-01
International audience; This article presents an overview of three fundamental concepts in Mathematical System Theory: controllability, stability and observability. These properties play a prominent role in the study of mathematical models and in the understanding of their behavior. They constitute the main research subject in Control Theory. Historically the tools and techniques of Automatic Control have been developed for artificial engineering systems but nowadays they are more and more ap...
Williams, R.; Stinton, A. J.; Sheridan, M. F.
2008-11-01
Titan2D is a depth-averaged, thin-layer computational fluid dynamics (CFD) code, suitable for simulating a variety of geophysical mass flows. Titan2D output data include flow thickness and flow momentum at each time step for all cells traversed by the flow during the simulation. From this information the flow limit, run-out path, flow velocity, deposit thickness, and travel time can be calculated. Results can be visualized in the open-source GRASS GIS software or with the built-in Titan2D viewer. A new two-phase Titan2D version allows simulation of flows containing various mixtures of water and solids. The purpose of this study is to compare simulations by the two-phase flow version of Titan2D with an actual event. The chosen natural flow is a small ash-rich lahar (volume 50,000 m 3-70,000 m 3) that occurred on 12 February 2005 in the Vazcún Valley, located on the north-east flank of Volcán Tungurahua, Ecuador. Lahars and pyroclastic flows along this valley could potentially threaten the 20,000 inhabitants living in and near the city of Baños. A variety of data sources exist for this lahar, including: post-event meter-scale topography, and photographic, video, seismic and acoustic flow monitoring (AFM) records from during the event. These data permit detailed comparisons between the dynamics of the actual lahar and those of the Titan2D simulated flow. In particular, detailed comparisons are made between run-up heights, flow velocity, inundation area, and flow thickness. Simulations utilize a variety of data derived from field observations such as lahar volume, solid to pore-fluid ratio and pre-event topography. Titan2D is important in modeling lahars because it allows assessment of the impact of the flows on buildings and infrastructure lifelines located near drainages that descend from volcanoes.
On the mathematical modeling of aeolian saltation
DEFF Research Database (Denmark)
Jensen, Jens Ledet; Sørensen, Michael
1983-01-01
The development of a mathematical model for aeolian saltation is a promising way of obtaining further progress in the field of wind-blown sand. Interesting quantities can be calculated from a model defined in general terms, and a specific model is defined and compared to previously published data...
Energy Technology Data Exchange (ETDEWEB)
Okazaki, Motoaki [Japan Atomic Energy Research Inst., Tokai, Ibaraki (Japan). Tokai Research Establishment
1997-11-01
A new numerical method to achieve a rigorous numerical calculation of each phase using a simple explicit method with volume-junction model is proposed. For this purpose, difference equations for numerical use are carefully derived so as to preserve the physical meaning of the basic equations. Specifically, momentum equations for the flow in the volume are newly derived to keep strict conservation of energy within the volume. To prove the validity of the numerical method and of previously proposed basic equations, including the original phase change equations, which were rigorously derived, some numerical calculations were made for each phase independently to examine the correctness of calculated results. The numerical calculation is advanced by simple integration of an explicitly obtained solution of difference equations without any special treatment. Calculated results of density and specific internal energy of each phase for saturated two-phase blowdown behavior are consistent for two different solution scheme as described below. Further, no accumulation of error in mass or energy was found. These results prove the consistency among basic equations, including phase change equations, and the correctness of numerical calculation method. The two different solution schemes used were: (1) solutions of pressure and void fraction in saturated condition were obtained by using mass conservation equation of each phase simultaneously, and (2) fluid properties were calculated directly from mass and energy conservation equation of each phase. (author)
Chalons, Christophe; Girardin, Mathieu; Kokh, Samuel
2017-04-01
We propose an all regime Lagrange-Projection like numerical scheme for 2D homogeneous models for two-phase flows. By all regime, we mean that the numerical scheme is able to compute accurate approximate solutions with an under-resolved discretization, i.e. a mesh size and time step much bigger than the Mach number M of the mixture. The key idea is to decouple acoustic, transport and phase transition phenomenon using a Lagrange-Projection decomposition in order to treat implicitly (fast) acoustic and phase transition phenomenon and explicitly the (slow) transport phenomena. Then, extending a strategy developed in the case of the usual gas dynamics equations, we alter the numerical flux in the acoustic approximation to obtain a uniform truncation error in terms of M. This modified scheme is conservative and endowed with good stability properties with respect to the positivity of the density and preserving the mass fraction within the interval (0 , 1). Numerical evidences are proposed and show the ability of the scheme to deal with cases where the flow regime may vary from low to high Mach values.
Directory of Open Access Journals (Sweden)
Annamaris Olmo Velázquez
2015-01-01
Full Text Available El flujo simultáneo de líquido y gas es una de las combinaciones más complejas de flujo bifásico. Para este estudio se seleccionaron como fluidos de trabajo Glicerina en solución con agua al 80 % y Gel industrial. Estos por sus viscosidades permiten establecer los sistemas deseados para el estudio, con valores de Reynolds menor a 15. Fueron desarrollados experimentos para la determinación de las propiedades hidrodinámicas del los fluidos y los parámetros que caracterizan este tipo de flujo en un canal vertical. Fue obtenido a partir del análisis físico matemático de losexperimentos realizados, un modelo teórico experimental capaz de evaluar las fuerzas y coeficientes de arrastre para una burbuja aislada y un tren de burbujas. Se realizaron modelaciones computacionales de los distintos regímenes de trabajo, validadas con los resultados experimentales. Obteniéndose simulaciones y resultados que permiten visualizar y analizar el comportamiento real del sistema.Palabras claves: flujo bifásico, número de Reynolds, burbuja aislada, tren de burbujas, coeficientes de arrastre, fuerzas de arrastre._________________________________________________________________________________AbstractThe study of simultaneous flow of liquid and gas over a conduit is two phases flow combinations more complex that exist. For the study we select fluid (glycerin in solution with water (80 % and industrial gel that establish flow models necessary for the investigation the desired systems. And is obtained from physical-mathematical analysis of obtained results made experiment for different configurations, a theorys experimental model have evaluate the drag coefficient and force acting on only bubble and train bubbles in job regimen for Reynolds value less and equal to 15. In the present study was performed computational modeling of different patterns, validated with experimental results.Simulations and results obtained for visualizing and analyzing the actual
Mathematical and Computational Modeling of Polymer Exchange Membrane Fuel Cells
Ulusoy, Sehribani
In this thesis a comprehensive review of fuel cell modeling has been given and based on the review, a general mathematical fuel cell model has been developed in order to understand the physical phenomena governing the fuel cell behavior and in order to contribute to the efforts investigating the optimum performance at different operating conditions as well as with different physical parameters. The steady state, isothermal model presented here accounts for the combined effects of mass and species transfer, momentum conservation, electrical current distribution through the gas channels, the electrodes and the membrane, and the electrochemical kinetics of the reactions in the anode and cathode catalyst layers. One of the important features of the model is that it proposes a simpler modified pseudo-homogeneous/agglomerate catalyst layer model which takes the advantage of the simplicity of pseudo-homogenous modeling while taking into account the effects of the agglomerates in the catalyst layer by using experimental geometric parameters published. The computation of the general mathematical model can be accomplished in 3D, 2D and 1D with the proper assumptions. Mainly, there are two computational domains considered in this thesis. The first modeling domain is a 2D Membrane Electrode Assembly (MEA) model including the modified agglomerate/pseudo-homogeneous catalyst layer modeling with consistent treatment of water transport in the MEA while the second domain presents a 3D model with different flow filed designs: straight, stepped and tapered. COMSOL Multiphysics along with Batteries and Fuel Cell Module have been used for 2D & 3D model computations while ANSYS FLUENT PEMFC Module has been used for only 3D two-phase computation. Both models have been validated with experimental data. With 2D MEA model, the effects of temperature and water content of the membrane as well as the equivalent weight of the membrane on the performance have been addressed. 3D COMSOL simulation
A New Two-phase Flow Model Applied to the 2007 Crater Lake Break-out Lahar, Mt. Ruapehu, New Zealand
Sheridan, M. F.; Cordoba, G.; Pitman, E.; Cronin, S. J.; Procter, J.
2010-12-01
The 2007 Crater Lake break-out lahar, Mt. Ruapehu, New Zealand, is a complex but well-characterized natural debris flow that follows an intricate course over an array of topographic features (see Manville et al., this conference). Detailed digital terrain data (DEM) and accurate flow characterization allow us to test our computational model with an unusually high level of control for such a large natural flood wave. The new two-phase flow code is imbedded within the TITAN2D framework (Patra et al. 2005) that is widely used in hazard assessment for both dry (granular) and wet (debris flow) flows (Murcia et al., 2010). Because TITAN2D is actually valid for dry flows (avalanches) we developed a new two-phase model based on balance laws for mass and momentum for each phase. The granular material is assumed to obey a Coulomb constitutive relation and the fluid is assumed to be inviscid. The Darcy-Weisbach formulation is used to account for bed friction, and a phenomenological drag coefficient mediates the momentum exchange between phases. The resulting system of 6 partial differential equations are depth averaged and correspond to the Savage and Hutter model in the limit of no fluid, and to the typical shallow water solutions (Ortiz, et al., 2005) for pure water. This model is capable of simulating particle volumetric fractions as dilute as 0.001 and as concentrated as 0.55. To confirm the usefulness of the new code for complex flows we used data from four observation stations at Ruapehu located at runout distances of 2 km, 5 km, 7 km and 9 km. The specific flow data that we compare with the model outcomes include: 1) arrival time of the flood front, 2) maximum flood depth, and 3) flow velocity. The computed values for these flow characteristics are all within about ± 10% of the observed figures. References: Manville, V., et al., 2010, Anatomy of a basin break-out flood: The 2007 Crater Lake break-out lahar, Mt. Ruapehu, New Zealand, this conference. Murcia, H
Mathematical modeling and applications in nonlinear dynamics
Merdan, Hüseyin
2016-01-01
The book covers nonlinear physical problems and mathematical modeling, including molecular biology, genetics, neurosciences, artificial intelligence with classical problems in mechanics and astronomy and physics. The chapters present nonlinear mathematical modeling in life science and physics through nonlinear differential equations, nonlinear discrete equations and hybrid equations. Such modeling can be effectively applied to the wide spectrum of nonlinear physical problems, including the KAM (Kolmogorov-Arnold-Moser (KAM)) theory, singular differential equations, impulsive dichotomous linear systems, analytical bifurcation trees of periodic motions, and almost or pseudo- almost periodic solutions in nonlinear dynamical systems. Provides methods for mathematical models with switching, thresholds, and impulses, each of particular importance for discontinuous processes Includes qualitative analysis of behaviors on Tumor-Immune Systems and methods of analysis for DNA, neural networks and epidemiology Introduces...
Mathematical Properties Relevant to Geomagnetic Field Modeling
DEFF Research Database (Denmark)
Sabaka, Terence J.; Hulot, Gauthier; Olsen, Nils
2010-01-01
properties of those spatial mathematical representations are also discussed, especially in view of providing a formal justification for the fact that geomagnetic field models can indeed be constructed from ground-based and satellite-born observations, provided those reasonably approximate the ideal......Geomagnetic field modeling consists in converting large numbers of magnetic observations into a linear combination of elementary mathematical functions that best describes those observations.The set of numerical coefficients defining this linear combination is then what one refers...... be directly measured. In this chapter, the mathematical foundation of global (as opposed to regional) geomagnetic field modeling is reviewed, and the spatial modeling of the field in spherical coordinates is focussed. Time can be dealt with as an independent variable and is not explicitly considered...
Mathematical Properties Relevant to Geomagnetic Field Modeling
DEFF Research Database (Denmark)
Sabaka, Terence J.; Hulot, Gauthier; Olsen, Nils
2014-01-01
properties of those spatial mathematical representations are also discussed, especially in view of providing a formal justification for the fact that geomagnetic field models can indeed be constructed from ground-based and satellite-born observations, provided those reasonably approximate the ideal situation......Geomagnetic field modeling consists in converting large numbers of magnetic observations into a linear combination of elementary mathematical functions that best describes those observations. The set of numerical coefficients defining this linear combination is then what one refers...... be directly measured. In this chapter, the mathematical foundation of global (as opposed to regional) geomagnetic field modeling is reviewed, and the spatial modeling of the field in spherical coordinates is focused. Time can be dealt with as an independent variable and is not explicitly considered...
Mathematical Models of Tuberculosis Reactivation and Relapse
Directory of Open Access Journals (Sweden)
Robert Steven Wallis
2016-05-01
Full Text Available The natural history of human infection with Mycobacterium tuberculosis (Mtb is highly variable, as is the response to treatment of active tuberculosis. There is presently no direct means to identify individuals in whom Mtb infection has been eradicated, whether by a bactericidal immune response or sterilizing antimicrobial chemotherapy. Mathematical models can assist in such circumstances by measuring or predicting events that cannot be directly observed. The 3 models discussed in this review illustrate instances in which mathematical models were used to identify individuals with innate resistance to Mtb infection, determine the etiology of tuberculosis in patients treated with tumor necrosis factor antagonists, and predict the risk of relapse in persons undergoing tuberculosis treatment. These examples illustrate the power of various types of mathematic models to increase knowledge and thereby inform interventions in the present global tuberculosis epidemic.
Interfacial Fluid Mechanics A Mathematical Modeling Approach
Ajaev, Vladimir S
2012-01-01
Interfacial Fluid Mechanics: A Mathematical Modeling Approach provides an introduction to mathematical models of viscous flow used in rapidly developing fields of microfluidics and microscale heat transfer. The basic physical effects are first introduced in the context of simple configurations and their relative importance in typical microscale applications is discussed. Then,several configurations of importance to microfluidics, most notably thin films/droplets on substrates and confined bubbles, are discussed in detail. Topics from current research on electrokinetic phenomena, liquid flow near structured solid surfaces, evaporation/condensation, and surfactant phenomena are discussed in the later chapters. This book also: Discusses mathematical models in the context of actual applications such as electrowetting Includes unique material on fluid flow near structured surfaces and phase change phenomena Shows readers how to solve modeling problems related to microscale multiphase flows Interfacial Fluid Me...
Mathematical modeling and optimization of complex structures
Repin, Sergey; Tuovinen, Tero
2016-01-01
This volume contains selected papers in three closely related areas: mathematical modeling in mechanics, numerical analysis, and optimization methods. The papers are based upon talks presented on the International Conference for Mathematical Modeling and Optimization in Mechanics, held in Jyväskylä, Finland, March 6-7, 2014 dedicated to Prof. N. Banichuk on the occasion of his 70th birthday. The articles are written by well-known scientists working in computational mechanics and in optimization of complicated technical models. Also, the volume contains papers discussing the historical development, the state of the art, new ideas, and open problems arising in modern continuum mechanics and applied optimization problems. Several papers are concerned with mathematical problems in numerical analysis, which are also closely related to important mechanical models. The main topics treated include: * Computer simulation methods in mechanics, physics, and biology; * Variational problems and methods; minimiz...
Mathematical models and methods for planet Earth
Locatelli, Ugo; Ruggeri, Tommaso; Strickland, Elisabetta
2014-01-01
In 2013 several scientific activities have been devoted to mathematical researches for the study of planet Earth. The current volume presents a selection of the highly topical issues presented at the workshop “Mathematical Models and Methods for Planet Earth”, held in Roma (Italy), in May 2013. The fields of interest span from impacts of dangerous asteroids to the safeguard from space debris, from climatic changes to monitoring geological events, from the study of tumor growth to sociological problems. In all these fields the mathematical studies play a relevant role as a tool for the analysis of specific topics and as an ingredient of multidisciplinary problems. To investigate these problems we will see many different mathematical tools at work: just to mention some, stochastic processes, PDE, normal forms, chaos theory.
SIMULATION OF LOW-CONCENTRATION SEDIMENT-LADEN FLOW BASED ON TWO-PHASE FLOW THEORY
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
Low concentration sediment-laden flow is usually involved in water conservancy, environmental protection, navigation and so on. In this article, a mathematical model for low-concentration sediment-laden flow was suggested based on the two-phase flow theory, and a solving scheme for the mathematical model in curvilinear grids was worked out. The observed data in the Zhang River in China was used for the verification of the model, and the calculated results of the water level, velocity and river bed deformation are in agreement with the observed ones.
Numerical and experimental investigation of two-phase flow in an electrochemical cell
Energy Technology Data Exchange (ETDEWEB)
Aldas, Kemal; Pehlivanoglu, Nur [Mechanical Engineering Department, Aksaray University, Aksaray (Turkey); Mat, Mahmut D. [Mechanical Engineering Department, Nigde University, 51100 Nigde (Turkey)
2008-07-15
In this study, a two-phase mathematical model is adapted to study void fraction distribution, flow field and characteristics of electrolysis process. The model involves transport equations for both liquid and gaseous phases. An experimental set-up is established to collect data to validate and improve the mathematical model. The void fraction is determined from measurement of resistivity changes in the system due to the presence of bubbles. It is observed that there is a good agreement between the numerical results and the experimental data. (author)
On the well-posedness of a mathematical model describing water-mud interaction
Escher, Joachim
2012-01-01
In this paper we consider a mathematical model describing the two-phase interaction between water and mud in a water canal when the width of the canal is small compared to its depth. The mud is treated as a non-Netwonian fluid and the interface between the mud and fluid is allowed to move under the influence of gravity and surface tension. We reduce the mathematical formulation, for small boundary and initial data, to a fully nonlocal and nonlinear problem and prove its local well-posedness by using abstract parabolic theory.
Mathematical model in economic environmental problems
Energy Technology Data Exchange (ETDEWEB)
Nahorski, Z. [Polish Academy of Sciences, Systems Research Inst. (Poland); Ravn, H.F. [Risoe National Lab. (Denmark)
1996-12-31
The report contains a review of basic models and mathematical tools used in economic regulation problems. It starts with presentation of basic models of capital accumulation, resource depletion, pollution accumulation, and population growth, as well as construction of utility functions. Then the one-state variable model is discussed in details. The basic mathematical methods used consist of application of the maximum principle and phase plane analysis of the differential equations obtained as the necessary conditions of optimality. A summary of basic results connected with these methods is given in appendices. (au) 13 ills.; 17 refs.
Mathematical modeling of complex noise barriers
Energy Technology Data Exchange (ETDEWEB)
Hayek, S.I.
1982-01-01
Mathematical modeling of the noise reduction efficiency of highway noise barriers depends on the shape and absorptivity of the barrier, the influence of the impedance of the ground under the receiver, the atmospheric conditions as well as traffic details. The mathematical model for a barrier's noise reduction requires the knowledge of point-to-point acoustic diffraction models. In many instances, the shape of the barrier is simple; such as thin wall (edge), sharp wedge, and cylindrically topped berms. However, new designs of more efficient barriers have been investigated recently.
Energy Technology Data Exchange (ETDEWEB)
Trabold, T.A.; Kumar, R. [Lockheed Martin Corp., Schenectady, NY (United States)
1999-07-01
In Part 1, detailed measurements were made in a high pressure, adiabatic (boiled at the inlet) annular flow in a narrow, high aspect ratio duct using a gamma densitometer, hot-film anemometer and high-speed video photography. Measurements of void fraction, droplet frequency, velocity, drop size, and interfacial area concentration have been made to support the three field computational capability. An important aspect of this testing is the use of a modeling fluid (R-134a) in a vertical duct which permits visual access in annular flow. This modeling fluid accurately simulates the low liquid-to-vapor density ratio of steam-water flows at high pressures. These measurements have been taken in a narrow duct of hydraulic diameter 4.85 mm, and a cross-section aspect ratio of 22.5. However, the flow displays profiles of various shapes not only in the narrow dimension, but also in the width dimension. In particular, the shape of the droplet profiles depends on the entrained droplet flux from the edges in the vapor core. The average diameter from these profiles compare well with the models developed in the literature. Interfacial area concentration for these low density ratio flows is higher than the highest concentration reported for air-water flows. Video records show that along with the bow-shaped waves, three-dimensional {lambda}-shaped waves appear in annular flows for high flow rates. Part 2 outlines the development of a three-field modeling approach in annular flow and the predictive capability of an analysis code. Models have been developed here or adapted from the literature for the thin film near the wall as well as the droplets in the vapor core, and have been locally applied in a fully developed, two-phase adiabatic boiling annular flow in a duct heated at the inlet at high pressure. Numerical results have been obtained using these models that are required for the closure of the continuity and momentum equations. The two-dimensional predictions are compared with
Mathematical Modeling in Continuum Mechanics
Temam, Roger; Miranville, Alain
2005-06-01
Temam and Miranville present core topics within the general themes of fluid and solid mechanics. The brisk style allows the text to cover a wide range of topics including viscous flow, magnetohydrodynamics, atmospheric flows, shock equations, turbulence, nonlinear solid mechanics, solitons, and the nonlinear Schrödinger equation. This second edition will be a unique resource for those studying continuum mechanics at the advanced undergraduate and beginning graduate level whether in engineering, mathematics, physics or the applied sciences. Exercises and hints for solutions have been added to the majority of chapters, and the final part on solid mechanics has been substantially expanded. These additions have now made it appropriate for use as a textbook, but it also remains an ideal reference book for students and anyone interested in continuum mechanics.
Kharin, Stanislav N.; Sarsengeldin, Merey M.; Nouri, Hassan
2016-08-01
On the base of the Holm model, we represent two phase spherical Stefan problem and its analytical solution, which can serve as a mathematical model for diverse thermo-physical phenomena in electrical contacts. Suggested solution is obtained from integral error function and its properties which are represented in the form of series whose coefficients have to be determined. Convergence of solution series is proved.
Mathematical modeling of polymer electrolyte fuel cells
Sousa, Ruy; Gonzalez, Ernesto R.
Fuel cells with a polymer electrolyte membrane have been receiving more and more attention. Modeling plays an important role in the development of fuel cells. In this paper, the state-of-the-art regarding modeling of fuel cells with a polymer electrolyte membrane is reviewed. Modeling has allowed detailed studies concerning the development of these cells, e.g. in discussing the electrocatalysis of the reactions and the design of water-management schemes to cope with membrane dehydration. Two-dimensional models have been used to represent reality, but three-dimensional models can cope with some important additional aspects. Consideration of two-phase transport in the air cathode of a proton exchange membrane fuel cell seems to be very appropriate. Most fuel cells use hydrogen as a fuel. Besides safety concerns, there are problems associated with production, storage and distribution of this fuel. Methanol, as a liquid fuel, can be the solution to these problems and direct methanol fuel cells (DMFCs) are attractive for several applications. Mass transport is a factor that may limit the performance of the cell. Adsorption steps may be coupled to Tafel kinetics to describe methanol oxidation and methanol crossover must also be taken into account. Extending the two-phase approach to the DMFC modeling is a recent, important point.
About a mathematical model of market
Kulikov, D. A.
2017-01-01
In the paper a famous mathematical model of macroeconomics, which is called “market model” was considered. Traditional versions of this model have no periodic solutions and, therefore, they cannot describe a cyclic recurrence of the market economy. In the paper for the corresponding equation a delay was added. It allows obtaining sufficient conditions for existence of the stable cycles.
Mathematical human modelling for impact loading
Happee, R.; Hoof, J.F.A.M. van; Lange, R. de
2001-01-01
Mathematical modeling of the human body is widely used for automotive crash-safety research and design. Simulations have contributed to a reduction of injury numbers by optimization of vehicle structures and restraint systems. Currently, such simulations are largely performed using occupant models b
Mathematical Modeling of Viral Zoonoses in Wildlife
2011-01-01
Zoonoses are a worldwide public health concern, accounting for approximately 75% of human infectious diseases. In addition, zoonoses adversely affect agricultural production and wildlife. We review some mathematical models developed for the study of viral zoonoses in wildlife and identify areas where further modeling efforts are needed.
Mathematical modelling of magnetically targeted drug delivery
Energy Technology Data Exchange (ETDEWEB)
Grief, Andrew D. [Theoretical Mechanics, School of Mathematical Sciences, University of Nottingham, University Park, Nottingham NG7 2RD (United Kingdom)]. E-mail: andrew.grief@nottingham.ac.uk; Richardson, Giles [Theoretical Mechanics, School of Mathematical Sciences, University of Nottingham, University Park, Nottingham NG7 2RD (United Kingdom)]. E-mail: giles.richardson@nottingham.ac.uk
2005-05-15
A mathematical model for targeted drug delivery using magnetic particles is developed. This includes a diffusive flux of particles arising from interactions between erythrocytes in the microcirculation. The model is used to track particles in a vessel network. Magnetic field design is discussed and we show that it is impossible to specifically target internal regions using an externally applied field.
Mathematical models of cell self-organization
Directory of Open Access Journals (Sweden)
Benoît Perthame
2011-04-01
More recently nonlinear hyperbolic and kinetic models also have been used to describe the phenomena at a smaller scale. We explain here some motivations for ‘microscopic’ descriptions, the mathematical difficulties arising in their analysis and how kinetic models can help in understanding the unity of these descriptions.
Mathematical human modelling for impact loading
Happee, R.; Hoof, J.F.A.M. van; Lange, R. de
2001-01-01
Mathematical modeling of the human body is widely used for automotive crash-safety research and design. Simulations have contributed to a reduction of injury numbers by optimization of vehicle structures and restraint systems. Currently, such simulations are largely performed using occupant models
Mathematical human body modelling for impact loading
Happee, R.; Morsink, P.L.J.; Wismans, J.S.H.M.
1999-01-01
Mathematical modelling of the human body is widely used for automotive crash safety research and design. Simulations have contributed to a reduction of injury numbers by optimisation of vehicle structures and restraint systems. Currently such simulations are largely performed using occupant models
Mathematical model of electrotaxis in osteoblastic cells
Vanegas-Acosta, J.C.; Garzón-Alvarado, D.A.; Zwamborn, A.P.M.
2012-01-01
Electrotaxis is the cell migration in the presence of an electric field (EF). This migration is parallel to the EF vector and overrides chemical migration cues. In this paper we introduce a mathematical model for the electrotaxis in osteoblastic cells. The model is evaluated using different EF stren
A mathematical model of forgetting and amnesia
Murre, J.M.J.; Chessa, A.G.; Meeter, M.
2013-01-01
We describe a mathematical model of learning and memory and apply it to the dynamics of forgetting and amnesia. The model is based on the hypothesis that the neural systems involved in memory at different time scales share two fundamental properties: (1) representations in a store decline in strengt
Building Mathematical Models Of Solid Objects
Randall, Donald P.; Jones, Kennie H.; Von Ofenheim, William H.; Gates, Raymond L.; Matthews, Christine G.
1989-01-01
Solid Modeling Program (SMP) version 2.0 provides capability to model complex solid objects mathematically through aggregation of geometric primitives (parts). System provides designer with basic set of primitive parts and capability to define new primitives. Six primitives included in present version: boxes, cones, spheres, paraboloids, tori, and trusses. Written in VAX/VMS FORTRAN 77.
Mathematical human body modelling for impact loading
Happee, R.; Morsink, P.L.J.; Wismans, J.S.H.M.
1999-01-01
Mathematical modelling of the human body is widely used for automotive crash safety research and design. Simulations have contributed to a reduction of injury numbers by optimisation of vehicle structures and restraint systems. Currently such simulations are largely performed using occupant models b
Energy Technology Data Exchange (ETDEWEB)
Labois, M
2008-10-15
This thesis deals with hyperbolic models for the simulation of compressible two-phase flows, to find alternatives to the classical bi-fluid model. We first establish a hierarchy of two-phase flow models, obtained according to equilibrium hypothesis between the physical variables of each phase. The use of Chapman-Enskog expansions enables us to link the different existing models to each other. Moreover, models that take into account small physical unbalances are obtained by means of expansion to the order one. The second part of this thesis focuses on the simulation of flows featuring velocity unbalances and pressure balances, in two different ways. First, a two-velocity two-pressure model is used, where non-instantaneous velocity and pressure relaxations are applied so that a balancing of these variables is obtained. A new one-velocity one-pressure dissipative model is then proposed, where the arising of second-order terms enables us to take into account unbalances between the phase velocities. We develop a numerical method based on a fractional step approach for this model. (author)
Coupling two-phase fluid flow with two-phase darcy flow in anisotropic porous media
Chen, J.
2014-06-03
This paper reports a numerical study of coupling two-phase fluid flow in a free fluid region with two-phase Darcy flow in a homogeneous and anisotropic porous medium region. The model consists of coupled Cahn-Hilliard and Navier-Stokes equations in the free fluid region and the two-phase Darcy law in the anisotropic porous medium region. A Robin-Robin domain decomposition method is used for the coupled Navier-Stokes and Darcy system with the generalized Beavers-Joseph-Saffman condition on the interface between the free flow and the porous media regions. Obtained results have shown the anisotropic properties effect on the velocity and pressure of the two-phase flow. 2014 Jie Chen et al.
A mathematical model for Neanderthal extinction
Flores, J C
1997-01-01
A simple mathematical homogeneous model of competition is used to describe Neanderthal extinction in Europe. It considers two interacting species, Neanderthals and Early Modern Men, in the same ecological niche. Using paleontological data we claim that the parameter of similarity, between both species, fluctuates between 0.992 and 0.997. An extension of the model including migration (diffusion) is also discussed nevertheless, extinction of Neanderthal seems unavoidable. Numerical analysis of travelling wave solution (fronts) comfirms the extinction. The wave-front-velocity is estimated from linear analysis and numerical simulations confirm this estimation. We conjecture a mathematical formulation for the principle of exclusion between competitive interacting species (Gause).
On the mathematical modeling of memristors
Radwan, Ahmed G.
2012-10-06
Since the fourth fundamental element (Memristor) became a reality by HP labs, and due to its huge potential, its mathematical models became a necessity. In this paper, we provide a simple mathematical model of Memristors characterized by linear dopant drift for sinusoidal input voltage, showing a high matching with the nonlinear SPICE simulations. The frequency response of the Memristor\\'s resistance and its bounding conditions are derived. The fundamentals of the pinched i-v hysteresis, such as the critical resistances, the hysteresis power and the maximum operating current, are derived for the first time.
Two-phase microfluidics: thermophysical fundamentals and engineering concepts
Kuznetsov, V. V.
2016-10-01
Thermophysical fundamentals and engineering concepts of the two-phase microfluidic devises based on controlled liquid decay are discussed in this paper. The results of an experimental study of the explosive evaporation at a thin film heater of the MEMS devise in application to thermal inkjet printing are presented. The peculiarities of homogeneous nucleation and bubble growth in the liquid subjected to pulse heating are discussed. Using experimental data a simple equation suitable for predicting the growth rate of a vapor bubble in a non-uniformly superheated liquid was obtained and used to complete a mathematical model of the self-consistent nucleation and vapor bubbles growth in the induced pressure field. The results of numerical calculations according to the proposed model showed good agreement with the experimental data on a time of nucleation and duration of the initial stage of an explosive evaporation of water.
Two-Phase Cavitating Flow in Turbomachines
Directory of Open Access Journals (Sweden)
Sandor I. Bernad
2012-11-01
Full Text Available Cavitating flows are notoriously complex because they are highly turbulent and unsteady flows involving two species (liquid/vapor with a large density difference. These features pose a unique challenge to numerical modeling works. The study briefly reviews the methodology curently employed for industrial cavitating flow simulations using the two-phase mixture model. The two-phase mixture model is evaluated and validated using benchmark problem where experimental data are available. A 3D cavitating flow computation is performed for the GAMM Francis runner. The model is able to qualitatively predict the location and extent of the 3D cavity on the blade, but further investigation are needed to quatitatively assess the accuracy for real turbomachinery cavitating flows.
Dynamics of mathematical models in biology bringing mathematics to life
Zazzu, Valeria; Guarracino, Mario
2016-01-01
This volume focuses on contributions from both the mathematics and life science community surrounding the concepts of time and dynamicity of nature, two significant elements which are often overlooked in modeling process to avoid exponential computations. The book is divided into three distinct parts: dynamics of genomes and genetic variation, dynamics of motifs, and dynamics of biological networks. Chapters included in dynamics of genomes and genetic variation analyze the molecular mechanisms and evolutionary processes that shape the structure and function of genomes and those that govern genome dynamics. The dynamics of motifs portion of the volume provides an overview of current methods for motif searching in DNA, RNA and proteins, a key process to discover emergent properties of cells, tissues, and organisms. The part devoted to the dynamics of biological networks covers networks aptly discusses networks in complex biological functions and activities that interpret processes in cells. Moreover, chapters i...
Mathematical Modelling of Unmanned Aerial Vehicles
Directory of Open Access Journals (Sweden)
Saeed Sarwar
2013-04-01
Full Text Available UAVs (Unmanned Arial Vehicleis UAVs are emerging as requirement of time and it is expected that in next five to ten years, complete air space will be flooded with UAVs, committed in varied assignments ranging from military, scientific and commercial usage. Non availability of human pilot inside UAV necessitates the requirement of an onboard autopilot in order to maintain desired flight profile against any unexpected disturbance and/or parameter variations. Design of such an autopilot requires an accurate mathematical model of UAV. The aim of this paper is to present a consolidated picture of UAV model. This paper first consolidates complete 6 DOF Degree of Freedom equations of motion into a nonlinear mathematical model and its simulation using model parameters of a real UAV. Model is then linearized into longitudinal and lateral modes. State space models of linearized modes are simulated and analyzed for stability parameters. The developed model can be used to design autopilot for UAV
Applied Mathematics, Modelling and Computational Science
Kotsireas, Ilias; Makarov, Roman; Melnik, Roderick; Shodiev, Hasan
2015-01-01
The Applied Mathematics, Modelling, and Computational Science (AMMCS) conference aims to promote interdisciplinary research and collaboration. The contributions in this volume cover the latest research in mathematical and computational sciences, modeling, and simulation as well as their applications in natural and social sciences, engineering and technology, industry, and finance. The 2013 conference, the second in a series of AMMCS meetings, was held August 26–30 and organized in cooperation with AIMS and SIAM, with support from the Fields Institute in Toronto, and Wilfrid Laurier University. There were many young scientists at AMMCS-2013, both as presenters and as organizers. This proceedings contains refereed papers contributed by the participants of the AMMCS-2013 after the conference. This volume is suitable for researchers and graduate students, mathematicians and engineers, industrialists, and anyone who would like to delve into the interdisciplinary research of applied and computational mathematics ...
Next steps in two-phase flow: executive summary
Energy Technology Data Exchange (ETDEWEB)
DiPippo, R.
1980-09-01
The executive summary includes the following topics of discussion: the state of affairs; the fundamental governing equations; the one-dimensional mixture model; the drift-flux model; the Denver Research Institute two-phase geothermal flow program; two-phase flow pattern transition criteria; a two-fluid model under development; the mixture model as applied to geothermal well flow; DRI downwell instrumentation; two-phase flow instrumentation; the Sperry Research Corporation downhole pump and gravity-head heat exchanger systems; and the Brown University two-phase flow experimental program. (MHR)
The (mathematical modelling process in biosciences
Directory of Open Access Journals (Sweden)
Nestor V. Torres
2015-12-01
Full Text Available In this communication we introduce a general framework and discussion on the role of models and the modelling process within the scientific activity in the biosciences realm. The objective is sum up the common procedure during the formalization and analysis of a biological problem under the foundations of Systems Biology, which approach the study of biological systems as a whole.We begin by presenting the definitions of (biological system and model. Particular attention is given to the meaning of mathematical model within the context of the biology. Then, we present the modelization and analysis process of biological systems. Three stages are described in detail: conceptualization of the biological system into a model, mathematical formalization of the previous conceptual model and optimization and system management derived from the analysis of the mathematical model.All along this presentation the main features and shortcomings of the process are developed together with a set of rules that could help in the modelling endeavour of any biological system. Special regard is given to the formative requirements and the interdisciplinary nature of this approach. We conclude with some general considerations on the challenges that the modelling are currently posing to the current biology.
Mathematical Modelling of Bridges with SAP2000
Maraž, Miha
2006-01-01
The present work describes a relatively new programme module, which is enhanced in the recently released versions of SAP2000 software. The new module, called Bridge Modeler, is intended for simple, parametric mathematical modelling of bridges. The modelling procedure is explained on a test case through the steps of a user-friendly Bridge Wizard. For each step, we described the basic principles and the application possibilities as well as some limitations. We also explained two types of analys...
Mathematical Modeling of Circadian and Homeostatic Interaction
2011-11-16
Williams and C. Diniz Behn. A Hodgkin- Huxley -type model orexin neuron. SLEEP 32, A25, 2009. 4) C. Diniz Behn, D. Pal, G. Vanini, R. Lydic, G. A. Mashour...Switzerland, September 2009. 11) K. Williams, “A Hodgkin- Huxley -type model orexin neuron”, Associated Professional Sleep Societies Annual Meeting...Seattle, WA, June 2009. 12) K. Williams, “Dynamics in a Hodgkin- Huxley -type model orexin neuron”, Society for Industrial and Applied Mathematics Annual
Mathematical System Theory and System Modeling
1980-01-01
Choosing models related effectively to the questions to be addressed is a central issue in the craft of systems analysis. Since the mathematical description the analyst chooses constrains the types of issues he candeal with, it is important for these models to be selected so as to yield limitations that are acceptable in view of the questions the systems analysis seeks to answer. In this paper, the author gives an overview of the central issues affecting the question of model choice. To ...
Energy Technology Data Exchange (ETDEWEB)
Zhou Tao [Department of Thermal Engineering, Tsinghua University, Beijing 100084 (China)]. E-mail: zhoutao@mail.tsinghua.edu.cn; Wang Zenghui [Department of Engineering Mechanics, Tsinghua University, Beijing 100084 (China); Yang Ruichang [Department of Thermal Engineering, Tsinghua University, Beijing 100084 (China)
2005-10-01
Experiment data got from onset of nucleate boiling (ONB) in natural circulation is analyzed using unascertained mathematics. Unitary mathematics model of the relation between the temperature and onset of nucleate boiling is built up to analysis ONB. Multiple unascertained mathematics models are also built up with the onset of natural circulation boiling equation based on the experiment. Unascertained mathematics makes that affirmative results are a range of numbers that reflect the fluctuation of experiment data more truly. The fluctuating value with the distribution function F(x) is the feature of unascertained mathematics model and can express fluctuating experimental data. Real status can be actually described through using unascertained mathematics. Thus, for calculation of ONB point, the description of unascertained mathematics model is more precise than common mathematics model. Based on the unascertained mathematics, a new ONB model is developed, which is important for advanced reactor safety analysis. It is conceivable that the unascertained mathematics could be applied to many other two-phase measurements as well.
Pedagogical Content Knowledge in Mathematical Modelling Instruction
Tan, Liang Soon; Ang, Keng Cheng
2012-01-01
This paper posits that teachers' pedagogical content knowledge in mathematical modelling instruction can be demonstrated in the crafting of action plans and expected teaching and learning moves via their lesson images (Schoenfeld, 1998). It can also be developed when teachers shape appropriate teaching moves in response to students' learning…
Optimization and mathematical modeling in computer architecture
Sankaralingam, Karu; Nowatzki, Tony
2013-01-01
In this book we give an overview of modeling techniques used to describe computer systems to mathematical optimization tools. We give a brief introduction to various classes of mathematical optimization frameworks with special focus on mixed integer linear programming which provides a good balance between solver time and expressiveness. We present four detailed case studies -- instruction set customization, data center resource management, spatial architecture scheduling, and resource allocation in tiled architectures -- showing how MILP can be used and quantifying by how much it outperforms t
Modeling life the mathematics of biological systems
Garfinkel, Alan; Guo, Yina
2017-01-01
From predator-prey populations in an ecosystem, to hormone regulation within the body, the natural world abounds in dynamical systems that affect us profoundly. This book develops the mathematical tools essential for students in the life sciences to describe these interacting systems and to understand and predict their behavior. Complex feedback relations and counter-intuitive responses are common in dynamical systems in nature; this book develops the quantitative skills needed to explore these interactions. Differential equations are the natural mathematical tool for quantifying change, and are the driving force throughout this book. The use of Euler’s method makes nonlinear examples tractable and accessible to a broad spectrum of early-stage undergraduates, thus providing a practical alternative to the procedural approach of a traditional Calculus curriculum. Tools are developed within numerous, relevant examples, with an emphasis on the construction, evaluation, and interpretation of mathematical models ...
Mathematical modeling of the flash converting process
Energy Technology Data Exchange (ETDEWEB)
Sohn, H.Y.; Perez-Tello, M.; Riihilahti, K.M. [Utah Univ., Salt Lake City, UT (United States)
1996-12-31
An axisymmetric mathematical model for the Kennecott-Outokumpu flash converting process for converting solid copper matte to copper is presented. The model is an adaptation of the comprehensive mathematical model formerly developed at the University of Utah for the flash smelting of copper concentrates. The model incorporates the transport of momentum, heat, mass, and reaction kinetics between gas and particles in a particle-laden turbulent gas jet. The standard k-{epsilon} model is used to describe gas-phase turbulence in an Eulerian framework. The particle-phase is treated from a Lagrangian viewpoint which is coupled to the gas-phase via the source terms in the Eulerian gas-phase governing equations. Matte particles were represented as Cu{sub 2}S yFeS, and assumed to undergo homogeneous oxidation to Cu{sub 2}O, Fe{sub 3}O{sub 4}, and SO{sub 2}. A reaction kinetics mechanism involving both external mass transfer of oxygen gas to the particle surface and diffusion of oxygen through the porous oxide layer is proposed to estimate the particle oxidation rate Predictions of the mathematical model were compared with the experimental data collected in a bench-scale flash converting facility. Good agreement between the model predictions and the measurements was obtained. The model was used to study the effect of different gas-injection configurations on the overall fluid dynamics in a commercial size flash converting shaft. (author)