Effects of salt stress imposed during two growth phases on cauliflower production and quality.

Science.gov (United States)

Giuffrida, Francesco; Cassaniti, Carla; Malvuccio, Angelo; Leonardi, Cherubino

2017-03-01

Cultivation of cauliflower is diffused in Mediterranean areas where water salinity results in the need to identify alternative irrigation sources or management strategies. Using saline water during two growth phases (from transplanting to visible appearance of inflorescence or from appearance of inflorescence to head harvest), the present study aimed to identify the growth period that is more suitable for irrigation with low quality water in relation to cauliflower production and quality. Salinity affected cauliflower growth mainly when imposed in the first growth phase. The growth reduction depended mainly on ion-specific effects, although slight nutrient imbalances as a result of Na + and Cl - antagonisms were observed. The use of non-saline water in the first or second growth period reduced both the osmotic and toxic effects of salinity. When salinity was applied during inflorescence growth, yield was reduced because of a restriction of water accumulation in the head. The results of the present study demonstrate the possibility of producing marketable cauliflower heads under conditions of salinity by timing the application of the best quality water during the first growth phase to improve fruit quality and during the second phase to reduce the negative effects of salinity on yield. © 2016 Society of Chemical Industry. © 2016 Society of Chemical Industry.

Phase Characterization of Cucumber Growth: A Chemical Gel Model

Directory of Open Access Journals (Sweden)

Bo Li

2016-01-01

Full Text Available Cucumber grows with complex phenomena by changing its volume and shape, which is not fully investigated and challenges agriculture and food safety industry. In order to understand the mechanism and to characterize the growth process, the cucumber is modeled as a hydrogel in swelling and its development is studied in both preharvest and postharvest stages. Based on thermodynamics, constitutive equations, incorporating biological quantities, are established. The growth behavior of cucumber follows the classic theory of continuous or discontinuous phase transition. The mechanism of bulged tail in cucumber is interpreted by phase coexistence and characterized by critical conditions. Conclusions are given for advances in food engineering and novel fabrication techniques in mechanical biology.

Modeling and numerical study of two phase flow

International Nuclear Information System (INIS)

Champmartin, A.

2011-01-01

This thesis describes the modelization and the simulation of two-phase systems composed of droplets moving in a gas. The two phases interact with each other and the type of model to consider directly depends on the type of simulations targeted. In the first part, the two phases are considered as fluid and are described using a mixture model with a drift relation (to be able to follow the relative velocity between the two phases and take into account two velocities), the two-phase flows are assumed at the equilibrium in temperature and pressure. This part of the manuscript consists of the derivation of the equations, writing a numerical scheme associated with this set of equations, a study of this scheme and simulations. A mathematical study of this model (hyperbolicity in a simplified framework, linear stability analysis of the system around a steady state) was conducted in a frame where the gas is assumed baro-tropic. The second part is devoted to the modelization of the effect of inelastic collisions on the particles when the time of the simulation is shorter and the droplets can no longer be seen as a fluid. We introduce a model of inelastic collisions for droplets in a spray, leading to a specific Boltzmann kernel. Then, we build caricatures of this kernel of BGK type, in which the behavior of the first moments of the solution of the Boltzmann equation (that is mass, momentum, directional temperatures, variance of the internal energy) are mimicked. The quality of these caricatures is tested numerically at the end. (author) [fr

Modeling two-phase flow in PEM fuel cell channels

Energy Technology Data Exchange (ETDEWEB)

Wang, Yun; Basu, Suman; Wang, Chao-Yang [Electrochemical Engine Center (ECEC), and Department of Mechanical and Nuclear Engineering, The Pennsylvania State University, University Park, PA 16802 (United States)

2008-05-01

This paper is concerned with the simultaneous flow of liquid water and gaseous reactants in mini-channels of a proton exchange membrane (PEM) fuel cell. Envisaging the mini-channels as structured and ordered porous media, we develop a continuum model of two-phase channel flow based on two-phase Darcy's law and the M{sup 2} formalism, which allow estimate of the parameters key to fuel cell operation such as overall pressure drop and liquid saturation profiles along the axial flow direction. Analytical solutions of liquid water saturation and species concentrations along the channel are derived to explore the dependences of these physical variables vital to cell performance on operating parameters such as flow stoichiometric ratio and relative humility. The two-phase channel model is further implemented for three-dimensional numerical simulations of two-phase, multi-component transport in a single fuel-cell channel. Three issues critical to optimizing channel design and mitigating channel flooding in PEM fuel cells are fully discussed: liquid water buildup towards the fuel cell outlet, saturation spike in the vicinity of flow cross-sectional heterogeneity, and two-phase pressure drop. Both the two-phase model and analytical solutions presented in this paper may be applicable to more general two-phase flow phenomena through mini- and micro-channels. (author)

Parallel two-phase-flow-induced vibrations in fuel pin model

International Nuclear Information System (INIS)

Hara, Fumio; Yamashita, Tadashi

1978-01-01

This paper reports the experimental results of vibrations of a fuel pin model -herein meaning the essential form of a fuel pin from the standpoint of vibration- in a parallel air-and-water two-phase flow. The essential part of the experimental apparatus consisted of a flat elastic strip made of stainless steel, both ends of which were firmly supported in a circular channel conveying the two-phase fluid. Vibrational strain of the fuel pin model, pressure fluctuation of the two-phase flow and two-phase-flow void signals were measured. Statistical measures such as power spectral density, variance and correlation function were calculated. The authors obtained (1) the relation between variance of vibrational strain and two-phase-flow velocity, (2) the relation between variance of vibrational strain and two-phase-flow pressure fluctuation, (3) frequency characteristics of variance of vibrational strain against the dominant frequency of the two-phase-flow pressure fluctuation, and (4) frequency characteristics of variance of vibrational strain against the dominant frequency of two-phase-flow void signals. The authors conclude that there exist two kinds of excitation mechanisms in vibrations of a fuel pin model inserted in a parallel air-and-water two-phase flow; namely, (1) parametric excitation, which occurs when the fundamental natural frequency of the fuel pin model is related to the dominant travelling frequency of water slugs in the two-phase flow by the ratio 1/2, 1/1, 3/2 and so on; and (2) vibrational resonance, which occurs when the fundamental frequency coincides with the dominant frequency of the two-phase-flow pressure fluctuation. (auth.)

A two-dimensional, two-phase mass transport model for liquid-feed DMFCs

International Nuclear Information System (INIS)

Yang, W.W.; Zhao, T.S.

2007-01-01

A two-dimensional, isothermal two-phase mass transport model for a liquid-feed direct methanol fuel cell (DMFC) is presented in this paper. The two-phase mass transport in the anode and cathode porous regions is formulated based on the classical multiphase flow in porous media without invoking the assumption of constant gas pressure in the unsaturated porous medium flow theory. The two-phase flow behavior in the anode flow channel is modeled by utilizing the drift-flux model, while in the cathode flow channel the homogeneous mist-flow model is used. In addition, a micro-agglomerate model is developed for the cathode catalyst layer. The model also accounts for the effects of both methanol and water crossover through the membrane. The comprehensive model formed by integrating those in the different regions is solved numerically using a home-written computer code and validated against the experimental data in the literature. The model is then used to investigate the effects of various operating and structural parameters, such as methanol concentration, anode flow rate, porosities of both anode and cathode electrodes, the rate of methanol crossover, and the agglomerate size, on cell performance

Two kinds of Phase transitions in a Voting model

OpenAIRE

Hisakado, Masato; Mori, Shintaro

2012-01-01

In this paper, we discuss a voting model with two candidates, C_0 and C_1. We consider two types of voters--herders and independents. The voting of independents is based on their fundamental values; on the other hand, the voting of herders is based on the number of previous votes. We can identify two kinds of phase transitions. One is an information cascade transition similar to a phase transition seen in Ising model. The other is a transition of super and normal diffusions. These phase trans...

Two-phase flow models in unbounded two-phase critical flows

International Nuclear Information System (INIS)

Celata, G.P.; Cumo, M.; Farello, G.E.

1985-01-01

With reference to a Loss-of-Coolant Accident in Light Water Reactors, an analysis of the unbounded two-phase critical flow (i.e. the issuing two-phase jet) has been accomplished. Considering jets external shape, obtained by means of photographic pictures; pressure profiles inside the jet, obtained by means of a movable ''Pitot;'' and jet phases distribution information, obtained by means of X-rays pictures; a characterization of the flow pattern in the unbounded region of a two-phase critical flow is given. Jets X-ray pictures show the existence of a central high density ''core'' gradually evaporating all around, which gives place to a characteristic ''dartflow'' the length of which depends on stagnation thermodynamic conditions

Two kinds of phase transitions in a voting model

Science.gov (United States)

Hisakado, M.; Mori, S.

2012-08-01

In this paper, we discuss a voting model with two candidates, C0 and C1. We consider two types of voters—herders and independents. The voting of independents is based on their fundamental values, while the voting of herders is based on the number of previous votes. We can identify two kinds of phase transitions. One is an information cascade transition similar to a phase transition seen in the Ising model. The other is a transition of super and normal diffusions. These phase transitions coexist. We compared our results to the conclusions of experiments and identified the phase transitions in the upper limit of the time t by using the analysis of human behavior obtained from experiments.

The drift-flux asymptotic limit of baro-tropic two-phase two-pressure models

International Nuclear Information System (INIS)

Ambroso, A.; Galie, Th.; Chalons, Ch.; Coquel, F.; Godlewski, E.; Raviart, P.A.; Seguin, N.; Coquel, F.

2008-01-01

We study the asymptotic behavior of the solutions of baro-tropic two-phase two-pressure models, with pressure relaxation, drag force and external forces. Using Chapman-Enskog expansions close to the expected equilibrium, a drift-flux model with a Darcy type closure law is obtained. Also, restricting this closure law to permanent flows (defined as steady flows in some Lagrangian frame), we can obtain a drift-flux model with an algebraic closure law, in the spirit of Zuber-Findlay models. The example of a two-phase flow in a vertical pipe is described. (authors)

Contribution to the theory of the two phase blowdown phenomenon

International Nuclear Information System (INIS)

Hutcherson, M.N.

1975-12-01

In order to accurately model the two phase portion of a pressure vessel blowdown, it becomes necessary to understand the bubble growth mechanism within the vessel during the early period of the decompression, the two phase flow behavior within the vessel, and the applicability of the available two phase critical flow models to the blowdown transient. To aid in providing answers to such questions, a small scale, separate effects, isothermal blowdown experiment has been conducted in a small pressure vessel. The tests simulated a full open, double ended, guillotine break in a large diameter, short exhaust duct from the vessel. The vaporization process at the initiation of the decompression is apparently that of thermally dominated bubble growth originating from the surface cavities inside the system. Thermodynamic equilibrium of the remaining fluid within the vessel existed in the latter portion of the decompression. A nonuniform distribution of fluid quality within the vessel was also detected in this experiment. By comparison of the experimental results from this and other similar transient, two phase critical flow studies with steady state, small duct, two phase critical flow data, it is shown that transient, two phase critical flow in large ducts appears to be similar to steady state, two phase critical flow in small ducts. Analytical models have been developed to predict the blowdown characteristics of a system during subcooled decompression, the bubble growth regime of blowdown, and also in the nearly dispersed period of depressurization. This analysis indicates that the system pressure history early in the blowdown is dependent on the internal vessel surface area, the internal vessel volume, and also on the exhaust flow area from the system. This analysis also illustrates that the later period of decompression can be predicted based on thermodynamic equilibrium

New theoretical model for two-phase flow discharged from stratified two-phase region through small break

International Nuclear Information System (INIS)

Yonomoto, Taisuke; Tasaka, Kanji

1988-01-01

A theoretical and experimental study was conducted to understand two-phase flow discharged from a stratified two-phase region through a small break. This problem is important for an analysis of a small break loss-of-coolant accident (LOCA) in a light water reactor (LWR). The present theoretical results show that a break quality is a function of h/h b , where h is the elevation difference between a bulk water level in the upstream region and break and b the suffix for entrainment initiation. This result is consistent with existing eperimental results in literature. An air-water experiment was also conducted changing a break orientation as an experimental parameter to develop and assess the model. Comparisons between the model and the experimental results show that the present model can satisfactorily predict the flow rate and the quality at the break without using any adjusting constant when liquid entrainment occurs in a stratified two-phase region. When gas entrainment occurs, the experimental data are correlated well by using a single empirical constant. (author)

Macroscopic balance equations for two-phase flow models

International Nuclear Information System (INIS)

Hughes, E.D.

1979-01-01

The macroscopic, or overall, balance equations of mass, momentum, and energy are derived for a two-fluid model of two-phase flows in complex geometries. These equations provide a base for investigating methods of incorporating improved analysis methods into computer programs, such as RETRAN, which are used for transient and steady-state thermal-hydraulic analyses of nuclear steam supply systems. The equations are derived in a very general manner so that three-dimensional, compressible flows can be analysed. The equations obtained supplement the various partial differential equation two-fluid models of two-phase flow which have recently appeared in the literature. The primary objective of the investigation is the macroscopic balance equations. (Auth.)

An algebraic stress/flux model for two-phase turbulent flow

International Nuclear Information System (INIS)

Kumar, R.

1995-12-01

An algebraic stress model (ASM) for turbulent Reynolds stress and a flux model for turbulent heat flux are proposed for two-phase bubbly and slug flows. These mathematical models are derived from the two-phase transport equations for Reynolds stress and turbulent heat flux, and provide C μ , a turbulent constant which defines the level of eddy viscosity, as a function of the interfacial terms. These models also include the effect of heat transfer. When the interfacial drag terms and the interfacial momentum transfer terms are absent, the model reduces to a single-phase model used in the literature

Implicit approximate Riemann solver for two fluid two phase flow models

International Nuclear Information System (INIS)

Raymond, P.; Toumi, I.; Kumbaro, A.

1993-01-01

This paper is devoted to the description of new numerical methods developed for the numerical treatment of two phase flow models with two velocity fields which are now widely used in nuclear engineering for design or safety calculations. These methods are finite volumes numerical methods and are based on the use of Approximate Riemann Solver's concepts in order to define convective flux versus mean cell quantities. The first part of the communication will describe the numerical method for a three dimensional drift flux model and the extensions which were performed to make the numerical scheme implicit and to have fast running calculations of steady states. Such a scheme is now implemented in the FLICA-4 computer code devoted to 3-D steady state and transient core computations. We will present results obtained for a steady state flow with rod bow effect evaluation and for a Steam Line Break calculation were the 3-D core thermal computation was coupled with a 3-D kinetic calculation and a thermal-hydraulic transient calculation for the four loops of a Pressurized Water Reactor. The second part of the paper will detail the development of an equivalent numerical method based on an approximate Riemann Solver for a two fluid model with two momentum balance equations for the liquid and the gas phases. The main difficulty for these models is due to the existence of differential modelling terms such as added mass effects or interfacial pressure terms which make hyperbolic the model. These terms does not permit to write the balance equations system in a conservative form, and the classical theory for discontinuity propagation for non-linear systems cannot be applied. Meanwhile, the use of non-conservative products theory allows the study of discontinuity propagation for a non conservative model and this will permit the construction of a numerical scheme for two fluid two phase flow model. These different points will be detailed in that section which will be illustrated by

Nanoparticle growth by particle-phase chemistry

Science.gov (United States)

Apsokardu, Michael J.; Johnston, Murray V.

2018-02-01

The ability of particle-phase chemistry to alter the molecular composition and enhance the growth rate of nanoparticles in the 2-100 nm diameter range is investigated through the use of a kinetic growth model. The molecular components included are sulfuric acid, ammonia, water, a non-volatile organic compound, and a semi-volatile organic compound. Molecular composition and growth rate are compared for particles that grow by partitioning alone vs. those that grow by a combination of partitioning and an accretion reaction in the particle phase between two organic molecules. Particle-phase chemistry causes a change in molecular composition that is particle diameter dependent, and when the reaction involves semi-volatile molecules, the particles grow faster than by partitioning alone. These effects are most pronounced for particles larger than about 20 nm in diameter. The modeling results provide a fundamental basis for understanding recent experimental measurements of the molecular composition of secondary organic aerosol showing that accretion reaction product formation increases linearly with increasing aerosol volume-to-surface-area. They also allow initial estimates of the reaction rate constants for these systems. For secondary aerosol produced by either OH oxidation of the cyclic dimethylsiloxane (D5) or ozonolysis of β-pinene, oligomerization rate constants on the order of 10-3 to 10-1 M-1 s-1 are needed to explain the experimental results. These values are consistent with previously measured rate constants for reactions of hydroperoxides and/or peroxyacids in the condensed phase.

Two-phase flow model with nonequilibrium and critical flow

International Nuclear Information System (INIS)

Sureau, H.; Houdayer, G.

1976-01-01

The model proposed includes the three conservation equations (mass, momentum, energy) applied to the two phase flows and a fourth partial derivative equation which takes into account the nonequilibriums and describes the mass transfer process. With this model, the two phase critical flow tests performed on the Moby-Dick loop (CENG) with several geometries, are interpreted by a unique law. Extrapolations to industrial dimension problems show that geometry and size effects are different from those obtained with earlier models (Zaloudek, Moody, Fauske) [fr

Regulatory design governing progression of population growth phases in bacteria.

Directory of Open Access Journals (Sweden)

Agustino Martínez-Antonio

Full Text Available It has long been noted that batch cultures inoculated with resting bacteria exhibit a progression of growth phases traditionally labeled lag, exponential, pre-stationary and stationary. However, a detailed molecular description of the mechanisms controlling the transitions between these phases is lacking. A core circuit, formed by a subset of regulatory interactions involving five global transcription factors (FIS, HNS, IHF, RpoS and GadX, has been identified by correlating information from the well- established transcriptional regulatory network of Escherichia coli and genome-wide expression data from cultures in these different growth phases. We propose a functional role for this circuit in controlling progression through these phases. Two alternative hypotheses for controlling the transition between the growth phases are first, a continuous graded adjustment to changing environmental conditions, and second, a discontinuous hysteretic switch at critical thresholds between growth phases. We formulate a simple mathematical model of the core circuit, consisting of differential equations based on the power-law formalism, and show by mathematical and computer-assisted analysis that there are critical conditions among the parameters of the model that can lead to hysteretic switch behavior, which--if validated experimentally--would suggest that the transitions between different growth phases might be analogous to cellular differentiation. Based on these provocative results, we propose experiments to test the alternative hypotheses.

Regulatory design governing progression of population growth phases in bacteria.

Science.gov (United States)

Martínez-Antonio, Agustino; Lomnitz, Jason G; Sandoval, Santiago; Aldana, Maximino; Savageau, Michael A

2012-01-01

It has long been noted that batch cultures inoculated with resting bacteria exhibit a progression of growth phases traditionally labeled lag, exponential, pre-stationary and stationary. However, a detailed molecular description of the mechanisms controlling the transitions between these phases is lacking. A core circuit, formed by a subset of regulatory interactions involving five global transcription factors (FIS, HNS, IHF, RpoS and GadX), has been identified by correlating information from the well- established transcriptional regulatory network of Escherichia coli and genome-wide expression data from cultures in these different growth phases. We propose a functional role for this circuit in controlling progression through these phases. Two alternative hypotheses for controlling the transition between the growth phases are first, a continuous graded adjustment to changing environmental conditions, and second, a discontinuous hysteretic switch at critical thresholds between growth phases. We formulate a simple mathematical model of the core circuit, consisting of differential equations based on the power-law formalism, and show by mathematical and computer-assisted analysis that there are critical conditions among the parameters of the model that can lead to hysteretic switch behavior, which--if validated experimentally--would suggest that the transitions between different growth phases might be analogous to cellular differentiation. Based on these provocative results, we propose experiments to test the alternative hypotheses.

A model for non-equilibrium, non-homogeneous two-phase critical flow

International Nuclear Information System (INIS)

Bassel, Wageeh Sidrak; Ting, Daniel Kao Sun

1999-01-01

Critical two phase flow is a very important phenomena in nuclear reactor technology for the analysis of loss of coolant accident. Several recent papers, Lee and Shrock (1990), Dagan (1993) and Downar (1996) , among others, treat the phenomena using complex models which require heuristic parameters such as relaxation constants or interfacial transfer models. In this paper a mathematical model for one dimensional non equilibrium and non homogeneous two phase flow in constant area duct is developed. The model is constituted of three conservation equations type mass ,momentum and energy. Two important variables are defined in the model: equilibrium constant in the energy equation and the impulse function in the momentum equation. In the energy equation, the enthalpy of the liquid phase is determined by a linear interpolation function between the liquid phase enthalpy at inlet condition and the saturated liquid enthalpy at local pressure. The interpolation coefficient is the equilibrium constant. The momentum equation is expressed in terms of the impulse function. It is considered that there is slip between the liquid and vapor phases, the liquid phase is in metastable state and the vapor phase is in saturated stable state. The model is not heuristic in nature and does not require complex interface transfer models. It is proved numerically that for the critical condition the partial derivative of two phase pressure drop with respect to the local pressure or to phase velocity must be zero.This criteria is demonstrated by numerical examples. The experimental work of Fauske (1962) and Jeandey (1982) were analyzed resulting in estimated numerical values for important parameters like slip ratio, equilibrium constant and two phase frictional drop. (author)

A void fraction model for annular two-phase flow

Energy Technology Data Exchange (ETDEWEB)

Tandon, T.N.; Gupta, C.P.; Varma, H.K.

1985-01-01

An analytical model has been developed for predicting void fraction in two-phase annular flow. In the analysis, the Lockhart-Martinelli method has been used to calculate two-phase frictional pressure drop and von Karman's universal velocity profile is used to represent the velocity distribution in the annular liquid film. Void fractions predicted by the proposed model are generally in good agreement with a available experimental data. This model appears to be as good as Smith's correlation and better than the Wallis and Zivi correlations for computing void fraction.

Examination and modeling of void growth kinetics in modern high strength dual phase steels during uniaxial tensile deformation

Energy Technology Data Exchange (ETDEWEB)

Saeidi, N., E-mail: navidsae@gmail.com [Department of Materials Engineering, Isfahan University of Technology, Isfahan 84156-83111 (Iran, Islamic Republic of); Ashrafizadeh, F.; Niroumand, B. [Department of Materials Engineering, Isfahan University of Technology, Isfahan 84156-83111 (Iran, Islamic Republic of); Forouzan, M.R.; Mohseni mofidi, S. [Department of Mechanical Engineering, Isfahan University of Technology, Isfahan 84156-83111 (Iran, Islamic Republic of); Barlat, F. [Materials Mechanics Laboratory (MML), Graduate Institute of Ferrous Technology (GIFT), Pohang University of Science and Technology - POSTECH, San 31 Hyoja-dong, Nam-gu, Pohang, Gyeongbuk 790-784 (Korea, Republic of)

2016-04-01

Ductile fracture mechanisms during uniaxial tensile testing of two different modern high strength dual phase steels, i.e. DP780 and DP980, were studied. Detailed microstructural characterization of the strained and sectioned samples was performed by scanning electron microscopy as well as EBSD examination. The results revealed that interface decohesion, especially at martensite particles located at ferrite grain boundaries, was the most probable mechanism for void nucleation. It was also revealed that the creation of cellular substructure can reduce stored strain energy and thereby, higher true fracture strain was obtained in DP980 than DP780 steel. Prediction of void growth behavior based on some previously proposed models showed unreliable results. Therefore, a modified model based on Rice-Tracey family models was proposed which showed a very lower prediction error compared with other models. - Highlights: • Damage mechanism in two modern high strength dual phase steels was studied. • Creation of cellular substructures can reduce the stored strain energy within the ferrite grains. • The experimental values were examined by Agrawal as well as RT family models. • A modified model was proposed for prediction of void growth behavior of DP steels.

Phase evolution and dendrite growth in laser cladding of aluminium on zirconium

International Nuclear Information System (INIS)

Yue, T.M.; Xie, H.; Lin, X.; Yang, H.O.

2011-01-01

Research highlights: → Laser cladding of Al on pure Zr. → A series of phase evolutions occurred across the laser-clad coating. → Epitaxial crystal growth, backward dendrite growth and two-phase eutectic dendritic growth. → Phase and microstructure evolution is discussed. - Abstract: Aluminium was laser clad on a pure zirconium substrate using the blown powder method. The microstructure across the laser-clad coating was studied. Starting from the bottom to the top surface of the coating, a series of phase evolutions had occurred: (Zr) → (Zr) + AlZr 2 + AlZr 3 → Al 4 Zr 5 + Al 3 Zr 2 → Al 3 Zr 2 + AlZr 2 → Al 2 Zr → Al 2 Zr + Al 3 Zr. This resulted in an epitaxial columnar crystal growth at the re-melt substrate boundary, a band of backward growth Al 3 Zr 2 dendrites towards the lower half of the coating, and a two-phase eutectic dendritic growth of Al 2 Zr + Al 3 Zr towards the top of the coating. The evolution of the various phases and microstructures is discussed in conjunction with the Al-Zr phase diagram, the criteria for planar interface instability, and the theory of eutectic growth under rapid solidification conditions (the TMK model).

Nanoparticle growth by particle-phase chemistry

Directory of Open Access Journals (Sweden)

M. J. Apsokardu

2018-02-01

Full Text Available The ability of particle-phase chemistry to alter the molecular composition and enhance the growth rate of nanoparticles in the 2–100 nm diameter range is investigated through the use of a kinetic growth model. The molecular components included are sulfuric acid, ammonia, water, a non-volatile organic compound, and a semi-volatile organic compound. Molecular composition and growth rate are compared for particles that grow by partitioning alone vs. those that grow by a combination of partitioning and an accretion reaction in the particle phase between two organic molecules. Particle-phase chemistry causes a change in molecular composition that is particle diameter dependent, and when the reaction involves semi-volatile molecules, the particles grow faster than by partitioning alone. These effects are most pronounced for particles larger than about 20 nm in diameter. The modeling results provide a fundamental basis for understanding recent experimental measurements of the molecular composition of secondary organic aerosol showing that accretion reaction product formation increases linearly with increasing aerosol volume-to-surface-area. They also allow initial estimates of the reaction rate constants for these systems. For secondary aerosol produced by either OH oxidation of the cyclic dimethylsiloxane (D5 or ozonolysis of β-pinene, oligomerization rate constants on the order of 10−3 to 10−1 M−1 s−1 are needed to explain the experimental results. These values are consistent with previously measured rate constants for reactions of hydroperoxides and/or peroxyacids in the condensed phase.

Moving Boudary Models for Dynamic Simulations of Two-phase Flows

DEFF Research Database (Denmark)

Jensen, Jakob Munch; Tummelscheit, H.

2002-01-01

. The Dymola Modelica translator can automatically reduce the DAE index and thus makes efficient simulation possible. Usually the flow entering a dry-expansion evaporator in a refrigeration system is two-phase, and there is thus no liquid region. The general MB model has a number of special cases where only...... model is used. The overall robustness and the simplicity of the MB model, makes it well suited for open loop as well as closed loop simulations of two-phase flows. Simulation results for an evaporator in a refrigeration system are shown. The open loop system is simulated both with the reduced MB...... but is less complex. The reduced MB-model is well suited for control purposes both for determining control parameters and for model based control strategies and examples of a controlled refrigeration system are shown. The general MB model divides the flow into three regions (liquid, two-phase and vapor...

Central upwind scheme for a compressible two-phase flow model.

Science.gov (United States)

Ahmed, Munshoor; Saleem, M Rehan; Zia, Saqib; Qamar, Shamsul

2015-01-01

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.

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.

Heat transfer modelling of two-phase bubbles swarm condensing in three - phase direct - contact condenser

Directory of Open Access Journals (Sweden)

Mahood Hameed B.

2016-01-01

Full Text Available An analytical model for the convective heat transfer coefficient and the two-phase bubble size of a three-phase direct contact heat exchanger was developed. Until the present, there has only been a theoretical model available that deals with a single two-phase bubble and a bubble train condensation in an immiscible liquid. However, to understand the actual heat transfer process within the three-phase direct contact condenser, characteristic models are required. A quasi - steady energy equation in a spherical coordinate system with a potential flow assumption and a cell model configuration has been simplified and solved analytically. The convective heat transfer in terms of Nu number has been derived, and it was found to be a function to Pe number and a system void fraction. In addition, the two-phase bubble size relates to the system void fraction and has been developed by solving a simple energy balance equation and using the derived convective heat transfer coefficient expression. Furthermore, the model correlates well with previous experimental data and theoretical results.

A mathematical model of the growth of uterine myomas.

Science.gov (United States)

Chen, C Y; Ward, J P

2014-12-01

Uterine myomas or fibroids are common, benign smooth muscle tumours that can grow to 10  cm or more in diameter and are routinely removed surgically. They are typically slow- growing, well-vascularised, spherical tumours that, on a macro-scale, are a structurally uniform, hard elastic material. We present a multi-phase mathematical model of a fully vascularised myoma growing within a surrounding elastic tissue. Adopting a continuum approach, the model assumes the conservation of mass and momentum of four phases, namely cells/collagen, extracellular fluid, arterial and venous phases. The cell/collagen phase is treated as a poro-elastic material, based on a linear stress-strain relationship, and Darcy's law is applied to describe flow in the extracellular fluid and the two vascular phases. The supply of extracellular fluid is dependent on the capillary flow rate and mean capillary pressure expressed in terms of the arterial and venous pressures. Cell growth and division is limited to the myoma domain and dependent on the local stress in the material. The resulting model consists of a system of nonlinear partial differential equations with two moving boundaries. Numerical solutions of the model successfully reproduce qualitatively the clinically observed three-phase "fast-slow-fast" growth profile that is typical for myomas. The results suggest that this growth profile requires stress-induced resistance to growth by the surrounding tissue and a switch-like cell growth response to stress. Analysis of large-time solutions reveal that while there is a functioning vasculature throughout the myoma, exponential growth results, otherwise power-law growth is predicted. An extensive survey of the effect of parameters on model solutions is also presented, and in particular, the enhanced growth caused by factors such as oestrogen is predicted by the model.

An investigation of subchannel analysis models for single-phase and two-phase flow

Energy Technology Data Exchange (ETDEWEB)

Hwang, Dae Hyun

1996-01-01

The governing equations and lateral transport modelings of subchannel analysis code, which is the most widely used tool for the analysis of thermal hydraulics fields in reactor cores, have been thoroughly investigated in this study. The procedure for the derivation of subchannel integral balance equations from the local instantaneous phase equations was investigated by stages. The characteristics of governing equations according to the treatment of phase velocity were studies, and the equations based on the drift-flux equilibrium formulation have been derived. Turbulent mixing and void drift modeling, which affect considerably to the accuracy of subchannel analysis code, have been reviewed. In addition, some representative modelings of single-phase and two-phase turbulent mixing models have been introduced. (author). 5 tabs., 4 figs., 16 refs.

Three-dimensional numerical modeling of turbulent single-phase and two-phase flow in curved pipes

International Nuclear Information System (INIS)

Xin, R.C.; Dong, Z.F.; Ebadian, M.A.

1996-01-01

In this study, three-dimensional single-phase and two-phase flows in curved pipes have been investigated numerically. Two different pipe configurations were computed. When the results of the single-phase flow simulation were compared with the experimental data, a fairly good agreement was achieved. A flow-developing process has been suggested in single-phase flow, in which the turbulence is stronger near the outer tube wall than near the inner tube wall. For two-phase flow, the Eulerian multiphase model was used to simulate the phase distribution of a three-dimensional gas-liquid bubble flow in curved pipe. The RNG/κ-ε turbulence model was used to determine the turbulence field. An inlet gas void fraction of 5 percent was simulated. The gas phase effects on the liquid phase flow velocity have been examined by comparing the results of single-phase flow and two-phase flow. The findings show that for the downward flow in the U bend, the gas concentrates at the inner portion of the cross section at φ = π/18 - π/6 in most cases. The results of the phase distribution simulation are compared to experimental observations qualitatively and topologically

Analysis of free-surface flows through energy considerations: Single-phase versus two-phase modeling.

Science.gov (United States)

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.

A New Appraoch to Modeling Immiscible Two-phase Flow in Porous Media

DEFF Research Database (Denmark)

Yuan, Hao; Shapiro, Alexander; Stenby, Erling Halfdan

In this work we present a systematic literature review regarding the macroscopic approaches to modeling immiscible two-phase flow in porous media, the formulation process of the incorporate PDE based on Film Model(viscous coupling), the calculation of saturation profile around the transition zone...... to modeling immiscible two-phase flow in porous media. The suggested approach to immiscible two-phase flow in porous media describes the dispersed mesoscopic fluids’ interfaces which are highly influenced by the injected interfacial energy and the local interfacial energy capacity. It reveals a new...... possibility of modeling two-phase flow through energy balance. The saturation profile generated through the suggested approach is different from those through other approaches....

Phase-field model of eutectic growth

International Nuclear Information System (INIS)

Karma, A.

1994-01-01

A phase-field model which describes the solidification of a binary eutectic alloy with a simple symmetric phase diagram is introduced and the sharp-interface limit of this model is explored both analytically and numerically

Encyclopedia of two-phase heat transfer and flow IV modeling methodologies, boiling of CO₂, and micro-two-phase cooling

CERN Document Server

2018-01-01

Set IV is a new addition to the previous Sets I, II and III. It contains 23 invited chapters from international specialists on the topics of numerical modeling of pulsating heat pipes and of slug flows with evaporation; lattice Boltzmann modeling of pool boiling; fundamentals of boiling in microchannels and microfin tubes, CO2 and nanofluids; testing and modeling of micro-two-phase cooling systems for electronics; and various special topics (flow separation in microfluidics, two-phase sensors, wetting of anisotropic surfaces, ultra-compact heat exchangers, etc.). The invited authors are leading university researchers and well-known engineers from leading corporate research laboratories (ABB, IBM, Nokia Bell Labs). Numerous "must read" chapters are also included here for the two-phase community. Set IV constitutes a "must have" engineering and research reference together with previous Sets I, II and III for thermal engineering researchers and practitioners.

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

Mechanical disequilibria in two-phase flow models: approaches by relaxation and by a reduced model

International Nuclear Information System (INIS)

Labois, M.

2008-10-01

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)

Two-phase wall friction model for the trace computer code

International Nuclear Information System (INIS)

Wang Weidong

2005-01-01

The wall drag model in the TRAC/RELAP5 Advanced Computational Engine computer code (TRACE) has certain known deficiencies. For example, in an annular flow regime, the code predicts an unphysical high liquid velocity compared to the experimental data. To address those deficiencies, a new wall frictional drag package has been developed and implemented in the TRACE code to model the wall drag for two-phase flow system code. The modeled flow regimes are (1) annular/mist, (2) bubbly/slug, and (3) bubbly/slug with wall nucleation. The new models use void fraction (instead of flow quality) as the correlating variable to minimize the calculation oscillation. In addition, the models allow for transitions between the three regimes. The annular/mist regime is subdivided into three separate regimes for pure annular flow, annular flow with entrainment, and film breakdown. For adiabatic two-phase bubbly/slug flows, the vapor phase primarily exists outside of the boundary layer, and the wall shear uses single-phase liquid velocity for friction calculation. The vapor phase wall friction drag is set to zero for bubbly/slug flows. For bubbly/slug flows with wall nucleation, the bubbles are presented within the hydrodynamic boundary layer, and the two-phase wall friction drag is significantly higher with a pronounced mass flux effect. An empirical correlation has been studied and applied to account for nucleate boiling. Verification and validation tests have been performed, and the test results showed a significant code improvement. (authors)

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.

Numerical approach of multi-field two-phase flow models in the OVAP code

International Nuclear Information System (INIS)

Anela Kumbaro

2005-01-01

Full text of publication follows: A significant progress has been made in modeling the complexity of vapor-liquid two-phase flow. Different three-dimensional models exist in order to simulate the evolution of parameters which characterize a two-phase model. These models can be classified into various groups depending on the inter-field coupling. A hierarchy of increasing physical complexity can be defined. The simplest group corresponds to the homogeneous mixture models where no interactions are taken into account. Another group is constituted by the two-fluid models employing physically important interfacial forces between two-phases, liquid, and water. The last group is multi-field modeling where inter-field couplings can be taken into account at different degrees, such as the MUltiple Size Group modeling [2], the consideration of separate equations for the transport and generation of mass and momentum for each field under the assumption of the same energy for all the fields of the same phase, and a full multi-field two-phase model [1]. The numerical approach of the general three-dimensional two-phase flow is by complexity of the phenomena a very challenging task; the ideal numerical method should be at the same time simple in order to apply to any model, from equilibrium to multi-field model and conservative in order to respect the fundamental conservation physical laws. The approximate Riemann solvers have the good properties of conservation of mass, momentum and energy balance and have been extended successfully to two-fluid models [3]- [5]. But, the up-winding of the flux is based on the Eigen-decomposition of the two-phase flow model and the computation of the Eigen-structure of a multi-field model can be a high cost procedure. Our contribution will present a short review of the above two-phase models, and show numerical results obtained for some of them with an approximate Riemann solver and with lower-complexity alternative numerical methods that do not

Modeling and numerical analysis of non-equilibrium two-phase flows

International Nuclear Information System (INIS)

Rascle, P.; El Amine, K.

1997-01-01

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)

Generalized network modeling of capillary-dominated two-phase flow.

Science.gov (United States)

Raeini, Ali Q; Bijeljic, Branko; Blunt, Martin J

2018-02-01

We present a generalized network model for simulating capillary-dominated two-phase flow through porous media at the pore scale. Three-dimensional images of the pore space are discretized using a generalized network-described in a companion paper [A. Q. Raeini, B. Bijeljic, and M. J. Blunt, Phys. Rev. E 96, 013312 (2017)2470-004510.1103/PhysRevE.96.013312]-which comprises pores that are divided into smaller elements called half-throats and subsequently into corners. Half-throats define the connectivity of the network at the coarsest level, connecting each pore to half-throats of its neighboring pores from their narrower ends, while corners define the connectivity of pore crevices. The corners are discretized at different levels for accurate calculation of entry pressures, fluid volumes, and flow conductivities that are obtained using direct simulation of flow on the underlying image. This paper discusses the two-phase flow model that is used to compute the averaged flow properties of the generalized network, including relative permeability and capillary pressure. We validate the model using direct finite-volume two-phase flow simulations on synthetic geometries, and then present a comparison of the model predictions with a conventional pore-network model and experimental measurements of relative permeability in the literature.

Generalized network modeling of capillary-dominated two-phase flow

Science.gov (United States)

Raeini, Ali Q.; Bijeljic, Branko; Blunt, Martin J.

2018-02-01

We present a generalized network model for simulating capillary-dominated two-phase flow through porous media at the pore scale. Three-dimensional images of the pore space are discretized using a generalized network—described in a companion paper [A. Q. Raeini, B. Bijeljic, and M. J. Blunt, Phys. Rev. E 96, 013312 (2017), 10.1103/PhysRevE.96.013312]—which comprises pores that are divided into smaller elements called half-throats and subsequently into corners. Half-throats define the connectivity of the network at the coarsest level, connecting each pore to half-throats of its neighboring pores from their narrower ends, while corners define the connectivity of pore crevices. The corners are discretized at different levels for accurate calculation of entry pressures, fluid volumes, and flow conductivities that are obtained using direct simulation of flow on the underlying image. This paper discusses the two-phase flow model that is used to compute the averaged flow properties of the generalized network, including relative permeability and capillary pressure. We validate the model using direct finite-volume two-phase flow simulations on synthetic geometries, and then present a comparison of the model predictions with a conventional pore-network model and experimental measurements of relative permeability in the literature.

Entropy analysis on non-equilibrium two-phase flow models

International Nuclear Information System (INIS)

Karwat, H.; Ruan, Y.Q.

1995-01-01

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

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.

Three-dimensional two-phase mass transport model for direct methanol fuel cells

International Nuclear Information System (INIS)

Yang, W.W.; Zhao, T.S.; Xu, C.

2007-01-01

A three-dimensional (3D) steady-state model for liquid feed direct methanol fuel cells (DMFC) is presented in this paper. This 3D mass transport model is formed by integrating five sub-models, including a modified drift-flux model for the anode flow field, a two-phase mass transport model for the porous anode, a single-phase model for the polymer electrolyte membrane, a two-phase mass transport model for the porous cathode, and a homogeneous mist-flow model for the cathode flow field. The two-phase mass transport models take account the effect of non-equilibrium evaporation/ condensation at the gas-liquid interface. A 3D computer code is then developed based on the integrated model. After being validated against the experimental data reported in the literature, the code was used to investigate numerically transport behaviors at the DMFC anode and their effects on cell performance

Review on two-phase flow instabilities in narrow spaces

International Nuclear Information System (INIS)

Tadrist, L.

2007-01-01

Instabilities in two-phase flow have been studied since the 1950s. These phenomena may appear in power generation and heat transfer systems where two-phase flow is involved. Because of thermal management in small size systems, micro-fluidics plays an important role. Typical processes must be considered when the channel hydraulic diameter becomes very small. In this paper, a brief review of two-phase flow instabilities encountered in channels having hydraulic diameters greater than 10 mm are presented. The main instability types are discussed according to the existing experimental results and models. The second part of the paper examines two-phase flow instabilities in narrow spaces. Pool and flow boiling cases are considered. Experiments as well as theoretical models existing in the literature are examined. It was found that several experimental works evidenced these instabilities meanwhile only limited theoretical developments exist in the literature. In the last part of the paper an interpretation of the two-phase flow instabilities linked to narrow spaces are presented. This approach is based on characteristic time scales of the two-phase flow and bubble growth in the capillaries

Constructing a unique two-phase compressibility factor model for lean gas condensates

Energy Technology Data Exchange (ETDEWEB)

Moayyedi, Mahmood; Gharesheikhlou, Aliashghar [Research Institute of Petroleum Industry (RIPI), Tehran (Iran, Islamic Republic of); Azamifard, Arash; Mosaferi, Emadoddin [Amirkabir University of Technology (AUT), Tehran (Iran, Islamic Republic of)

2015-02-15

Generating a reliable experimental model for two-phase compressibility factor in lean gas condensate reservoirs has always been demanding, but it was neglected due to lack of required experimental data. This study presents the main results of constructing the first two-phase compressibility factor model that is completely valid for Iranian lean gas condensate reservoirs. Based on a wide range of experimental data bank for Iranian lean gas condensate reservoirs, a unique two-phase compressibility factor model was generated using design of experiments (DOE) method and neural network technique (ANN). Using DOE, a swift cubic response surface model was generated for two-phase compressibility factor as a function of some selected fluid parameters for lean gas condensate fluids. The proposed DOE and ANN models were finally validated using four new independent data series. The results showed that there is a good agreement between experimental data and the proposed models. In the end, a detailed comparison was made between the results of proposed models.

Constructing a unique two-phase compressibility factor model for lean gas condensates

International Nuclear Information System (INIS)

Moayyedi, Mahmood; Gharesheikhlou, Aliashghar; Azamifard, Arash; Mosaferi, Emadoddin

2015-01-01

Generating a reliable experimental model for two-phase compressibility factor in lean gas condensate reservoirs has always been demanding, but it was neglected due to lack of required experimental data. This study presents the main results of constructing the first two-phase compressibility factor model that is completely valid for Iranian lean gas condensate reservoirs. Based on a wide range of experimental data bank for Iranian lean gas condensate reservoirs, a unique two-phase compressibility factor model was generated using design of experiments (DOE) method and neural network technique (ANN). Using DOE, a swift cubic response surface model was generated for two-phase compressibility factor as a function of some selected fluid parameters for lean gas condensate fluids. The proposed DOE and ANN models were finally validated using four new independent data series. The results showed that there is a good agreement between experimental data and the proposed models. In the end, a detailed comparison was made between the results of proposed models

A model for growth of beta-phase particles in zirconium-2.5 wt percent niobium

International Nuclear Information System (INIS)

Chow, C.K.; Liner, Y.; Rigby, G.L.

1984-08-01

The kinetics of the α → β phase change in Zr-2.5 percent Nb pressure-tube material at constant temperature have been studied. The volume-fraction change of the β phase due to diffusion in an infinite α-phase matrix was considered, and a mathematical model with a numerical solution was developed to predict the transient spherical growth of the β-phase region. This model has been applied to Zr-2.5 wt percent Nb, and the calculated results compared to experiment

Modeling and Performance of a Self-Excited Two-Phase Reluctance ...

African Journals Online (AJOL)

A self-excited two-phase reluctance generator (SETPRG) with balanced stator winding is presented. A unique balanced two-phase stator winding was designed with emphasis on obtaining a stator MMF waveform with minimum space harmonics. Then a mathematical model by which the dynamic behavior of the generator ...

Numerical simulation of brain tumor growth model using two-stage ...

African Journals Online (AJOL)

In the recent years, the study of glioma growth to be an active field of research Mathematical models that describe the proliferation and diffusion properties of the growth have been developed by many researchers. In this work, the performance analysis of two-stage Gauss-Seidel (TSGS) method to solve the glioma growth ...

Mathematical modelling of two-phase flows

International Nuclear Information System (INIS)

Komen, E.M.J.; Stoop, P.M.

1992-11-01

A gradual shift from methods based on experimental correlations to methods based on mathematical models to study 2-phase flows can be observed. The latter can be used to predict dynamical behaviour of 2-phase flows. This report discusses various mathematical models for the description of 2-phase flows. An important application of these models can be found in thermal-hydraulic computer codes used for analysis of the thermal-hydraulic behaviour of water cooled nuclear power plants. (author). 17 refs., 7 figs., 6 tabs

RETRAN nonequilibrium two-phase flow model for operational transient analyses

International Nuclear Information System (INIS)

Paulsen, M.P.; Hughes, E.D.

1982-01-01

The field balance equations, flow-field models, and equation of state for a nonequilibrium two-phase flow model for RETRAN are given. The differential field balance model equations are: (1) conservation of mixture mass; (2) conservation of vapor mass; (3) balance of mixture momentum; (4) a dynamic-slip model for the velocity difference; and (5) conservation of mixture energy. The equation of state is formulated such that the liquid phase may be subcooled, saturated, or superheated. The vapor phase is constrained to be at the saturation state. The dynamic-slip model includes wall-to-phase and interphase momentum exchanges. A mechanistic vapor generation model is used to describe vapor production under bulk subcooling conditions. The speed of sound for the mixture under nonequilibrium conditions is obtained from the equation of state formulation. The steady-state and transient solution methods are described

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 two-phase model of aquifer heterogeneity

International Nuclear Information System (INIS)

Moltyaner, G.L.

1994-11-01

A two-phase model of a fluid-saturated geologic medium is developed with groundwater velocity (rather than the hydraulic conductivity) as the primary model parameter. The model describes the groundwater flow, contaminant transport processes, and geologic medium structure at the local-scale of a continuum representation and relates structure to processes quantitatively. In this model, the heterogeneity of a geologic medium is characterized either in terms of the spatial variability in the bulk (local-scale) fluid density and sediment density, or in terms of variability in the local-scale porosity and effective grain diameter. The local-scale continuity equations resulting from these properties are derived for both phases. The effective grain diameter is employed to quantify the geologic structure. Velocity is employed to quantify the transport process. Since structure controls process, a high correlation is observed between the effective grain diameter and velocity. The observed correlation leads to a new formulation of Darcy's law without invoking the concept of a fictitious (Darcy's) velocity. The local-scale groundwater flow equation is developed on the basis of the new formulation. (author). 16 refs., 4 figs

Effects of two-phase flow in a model for nitramine deflagration

International Nuclear Information System (INIS)

Li, S.C.; Williams, F.A.; Margolis, S.B.

1990-01-01

Methods of asymptotic analysis are employed to extend an earlier model for the deflagration of nitramines to account for the presence of bubbles and droplets in a two-phase layer at the propellant surface during combustion. Two zones are identified in the two-phase region: one, at higher liquid volume fractions, maintains evaporative equilibrium, whereas the other, at lower liquid volume fractions, exhibits nonequilibrium vaporization. By introducing the most reasonable estimates for two-phase behavior of nitramines, the steady burning rates are found to be close to those obtained for models with a sharp liquid-gas interface. Good agreement with measured burning rates and pressure and temperature sensitivities are achieved through reasonable approximations concerning overall chemical-kinetic parameters

Mathematical modeling of microbial growth in milk

Directory of Open Access Journals (Sweden)

Jhony Tiago Teleken

2011-12-01

Full Text Available A mathematical model to predict microbial growth in milk was developed and analyzed. The model consists of a system of two differential equations of first order. The equations are based on physical hypotheses of population growth. The model was applied to five different sets of data of microbial growth in dairy products selected from Combase, which is the most important database in the area with thousands of datasets from around the world, and the results showed a good fit. In addition, the model provides equations for the evaluation of the maximum specific growth rate and the duration of the lag phase which may provide useful information about microbial growth.

Lattice Boltzmann model for simulating immiscible two-phase flows

International Nuclear Information System (INIS)

Reis, T; Phillips, T N

2007-01-01

The lattice Boltzmann equation is often promoted as a numerical simulation tool that is particularly suitable for predicting the flow of complex fluids. This paper develops a two-dimensional 9-velocity (D2Q9) lattice Boltzmann model for immiscible binary fluids with variable viscosities and density ratio using a single relaxation time for each fluid. In the macroscopic limit, this model is shown to recover the Navier-Stokes equations for two-phase flows. This is achieved by constructing a two-phase component of the collision operator that induces the appropriate surface tension term in the macroscopic equations. A theoretical expression for surface tension is determined. The validity of this analysis is confirmed by comparing numerical and theoretical predictions of surface tension as a function of density. The model is also shown to predict Laplace's law for surface tension and Poiseuille flow of layered immiscible binary fluids. The spinodal decomposition of two fluids of equal density but different viscosity is then studied. At equilibrium, the system comprises one large low viscosity bubble enclosed by the more viscous fluid in agreement with theoretical arguments of Renardy and Joseph (1993 Fundamentals of Two-Fluid Dynamics (New York: Springer)). Two other simulations, namely the non-equilibrium rod rest and the coalescence of two bubbles, are performed to show that this model can be used to simulate two fluids with a large density ratio

Energy law preserving C0 finite element schemes for phase field models in two-phase flow computations

International Nuclear Information System (INIS)

Hua Jinsong; Lin Ping; Liu Chun; Wang Qi

2011-01-01

Highlights: → We study phase-field models for multi-phase flow computation. → We develop an energy-law preserving C0 FEM. → We show that the energy-law preserving method work better. → We overcome unphysical oscillation associated with the Cahn-Hilliard model. - Abstract: We use the idea in to develop the energy law preserving method and compute the diffusive interface (phase-field) models of Allen-Cahn and Cahn-Hilliard type, respectively, governing the motion of two-phase incompressible flows. We discretize these two models using a C 0 finite element in space and a modified midpoint scheme in time. To increase the stability in the pressure variable we treat the divergence free condition by a penalty formulation, under which the discrete energy law can still be derived for these diffusive interface models. Through an example we demonstrate that the energy law preserving method is beneficial for computing these multi-phase flow models. We also demonstrate that when applying the energy law preserving method to the model of Cahn-Hilliard type, un-physical interfacial oscillations may occur. We examine the source of such oscillations and a remedy is presented to eliminate the oscillations. A few two-phase incompressible flow examples are computed to show the good performance of our method.

Investigations on liquid phase electroepitaxial growth kinetics of GaAs

International Nuclear Information System (INIS)

Mouleeswaran, D.; Dhanasekaran, R.

2004-01-01

This paper presents a model based on solving a two-dimensional diffusion equation incorporating the electromigration effect by numerical simulation method corresponding to liquid phase electroepitaxial (LPEE) growth of GaAs, whose growth is limited by diffusion and electro migration of solute species. Using the numerical simulation method, the concentration profiles of As in Ga rich solution during the electroepitaxial growth of GaAs have been constructed in front of the growing crystal interface. Using the concentration gradient at the interface, the growth rate and thickness of the epitaxial layer of GaAs have been determined for different experimental growth conditions. The proposed model is based on the assumption that there is no convection in the solution. The results are discussed in detail

Interface model coupling in fluid dynamics: application to two-phase flows

International Nuclear Information System (INIS)

Galie, Th.

2009-03-01

This thesis is devoted to the study of interface model coupling problems in space between different models of compressible flows. We consider one-dimensional problems where the interface is sharp, fixed and separating two regions of space corresponding to the two coupled models. Our goal is to define a coupling condition at the interface and to solve numerically the coupling problem with this condition. After a state of art on the interface model coupling of hyperbolic systems of conservation laws, we propose a new coupling condition by adding in the equations of the coupled problem a measure source term at the interface. We first suppose a given constant weight associated to this source term. Two Riemann solvers are developed and one of them is based on a relaxation approach preserving equilibrium solutions of the coupled problem. This relaxation method is then used in an optimization problem, defined by several motivations at the interface, which permits to calculate a time dynamical weight. In a second part, we develop an approached Riemann solver for a two-phase two-pressure model in the particular case of a two-phase isentropic flow. Such a model contains non conservative terms that we write under the form of measure source terms. The previous relaxation method is thus extended to the case of the two-phase two-pressure model with an a priori estimation of the non conservative term contributions. The method allows us to solve, in the next and last chapter, the coupling problem of a two-fluid two-pressure model with a drift-flux model thanks to the father model approach. (authors)

Numerical methods for limit problems in two-phase flow models

International Nuclear Information System (INIS)

Cordier, F.

2011-01-01

Numerical difficulties are encountered during the simulation of two-phase flows. Two issues are studied in this thesis: the simulation of phase transitions on one hand, and the simulation of both compressible and incompressible flows in the other hand. Un asymptotic study has shown that the loss of hyperbolicity of the bi fluid model was responsible for the difficulties encountered by the Roe scheme during the simulation of phase transitions. Robust and accurate polynomial schemes have thus been developed. To tackle the occasional lack of positivity of the solution, a numerical treatment based on adaptive diffusion was proposed and allowed to simulate with accuracy the test-cases of a boiling channel with creation of vapor and a tee-junction with separation of the phases. In a second part, an all-speed scheme for compressible and incompressible flows have been proposed. This pressure-based semi-implicit asymptotic preserving scheme is conservative, solves an elliptic equation on the pressure, and has been designed for general equations of state. The scheme was first developed for the full Euler equations and then extended to the Navier-Stokes equations. The good behaviour of the scheme in both compressible and incompressible regimes have been investigated. An extension of the scheme to the two-phase mixture model was implemented and demonstrated the ability of the scheme to simulate two-phase flows with phase change and a water-steam equation of state. (author) [fr

Theoretical modelling and experimental investigation of single-phase and two-phase flow division at a tee-junction

International Nuclear Information System (INIS)

Lemonnier, H.; Hervieu, E.

1991-01-01

Phase separation in a tee-junction is modelled in the particular case of bubbly-flow. The model is based on a two-dimensional approach and hence, uses local equations. The first step consists in modelling the single-phase flow in the tee-junction. The free streamline theory is used to predict the flow of the continuous phase. The two recirculation zones which are presented in this case are predicted by the model. The second step consists in predicting the gas bubble paths as a result of the actions of the single-phase flow. Finally, the trajectories of gas bubbles are used to predict the separation characteristics of the tee-junction. Each step of the modelling procedure has been carefully tested by an in-depth experimental investigation. Excellent quantitative agreement is obtained between experimental results and model predictions. Moreover, the phase separation phenomenon is found to be clearly described by the model. (orig.)

A positivity preserving and conservative variational scheme for phase-field modeling of two-phase flows

Science.gov (United States)

Joshi, Vaibhav; Jaiman, Rajeev K.

2018-05-01

We present a positivity preserving variational scheme for the phase-field modeling of incompressible two-phase flows with high density ratio. The variational finite element technique relies on the Allen-Cahn phase-field equation for capturing the phase interface on a fixed Eulerian mesh with mass conservative and energy-stable discretization. The mass conservation is achieved by enforcing a Lagrange multiplier which has both temporal and spatial dependence on the underlying solution of the phase-field equation. To make the scheme energy-stable in a variational sense, we discretize the spatial part of the Lagrange multiplier in the phase-field equation by the mid-point approximation. The proposed variational technique is designed to reduce the spurious and unphysical oscillations in the solution while maintaining the second-order accuracy of both spatial and temporal discretizations. We integrate the Allen-Cahn phase-field equation with the incompressible Navier-Stokes equations for modeling a broad range of two-phase flow and fluid-fluid interface problems. The coupling of the implicit discretizations corresponding to the phase-field and the incompressible flow equations is achieved via nonlinear partitioned iterative procedure. Comparison of results between the standard linear stabilized finite element method and the present variational formulation shows a remarkable reduction of oscillations in the solution while retaining the boundedness of the phase-indicator field. We perform a standalone test to verify the accuracy and stability of the Allen-Cahn two-phase solver. We examine the convergence and accuracy properties of the coupled phase-field solver through the standard benchmarks of the Laplace-Young law and a sloshing tank problem. Two- and three-dimensional dam break problems are simulated to assess the capability of the phase-field solver for complex air-water interfaces involving topological changes on unstructured meshes. Finally, we demonstrate the phase

Transient two-phase flow

International Nuclear Information System (INIS)

Hsu, Y.Y.

1974-01-01

The following papers related to two-phase flow are summarized: current assumptions made in two-phase flow modeling; two-phase unsteady blowdown from pipes, flow pattern in Laval nozzle and two-phase flow dynamics; dependence of radial heat and momentum diffusion; transient behavior of the liquid film around the expanding gas slug in a vertical tube; flooding phenomena in BWR fuel bundles; and transient effects in bubble two-phase flow. (U.S.)

Phase-field-based lattice Boltzmann modeling of large-density-ratio two-phase flows

Science.gov (United States)

Liang, Hong; Xu, Jiangrong; Chen, Jiangxing; Wang, Huili; Chai, Zhenhua; Shi, Baochang

2018-03-01

In this paper, we present a simple and accurate lattice Boltzmann (LB) model for immiscible two-phase flows, which is able to deal with large density contrasts. This model utilizes two LB equations, one of which is used to solve the conservative Allen-Cahn equation, and the other is adopted to solve the incompressible Navier-Stokes equations. A forcing distribution function is elaborately designed in the LB equation for the Navier-Stokes equations, which make it much simpler than the existing LB models. In addition, the proposed model can achieve superior numerical accuracy compared with previous Allen-Cahn type of LB models. Several benchmark two-phase problems, including static droplet, layered Poiseuille flow, and spinodal decomposition are simulated to validate the present LB model. It is found that the present model can achieve relatively small spurious velocity in the LB community, and the obtained numerical results also show good agreement with the analytical solutions or some available results. Lastly, we use the present model to investigate the droplet impact on a thin liquid film with a large density ratio of 1000 and the Reynolds number ranging from 20 to 500. The fascinating phenomena of droplet splashing is successfully reproduced by the present model and the numerically predicted spreading radius exhibits to obey the power law reported in the literature.

A Variational Model for Two-Phase Immiscible Electroosmotic Flow at Solid Surfaces

KAUST Repository

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.

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.

Dividing phases in two-phase flow and modeling of interfacial drag

International Nuclear Information System (INIS)

Narumo, T.; Rajamaeki, M.

1997-01-01

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

Identification of two-phase flow regimes by time-series modeling

International Nuclear Information System (INIS)

King, C.H.; Ouyang, M.S.; Pei, B.S.

1987-01-01

The identification of two-phase flow patterns in pipes or ducts is important to the design and operation of thermal-hydraulic systems, especially in the nuclear reactor cores of boiling water reactors or in the steam generators of pressurized water reactors. Basically, two-phase flow shows some fluctuating characteristics even at steady-state conditions. These fluctuating characteristics can be analyzed by statistical methods for obtaining flow signatures. There have been a number of experimental studies conducted that are concerned with the statistical properties of void fraction or pressure pulsation in two-phase flow. In this study, the authors propose a new technique of identifying the patterns of air-water two-phase flow in a vertical pipe. This technique is based on analyzing the statistic characteristics of the pressure signals of the test loop by time-series modeling

Modeling of bubble coalescence and disintegration in confined upward two-phase flow

International Nuclear Information System (INIS)

Sun Xiaodong; Kim, Seungjin; Ishii, Mamoru; Beus, Stephen G.

2004-01-01

This paper presents the modeling of bubble interaction mechanisms in the two-group interfacial area transport equation (IATE) for confined gas-liquid two-phase flow. The transport equation is applicable to bubbly, cap-turbulent, and churn-turbulent flow regimes. In the two-group IATE, bubbles are categorized into two groups: spherical/distorted bubbles as Group 1 and cap/slug/churn-turbulent bubbles as Group 2. Thus, two sets of equations are used to describe the generation and destruction rates of bubble number density, void fraction, and interfacial area concentration for the two groups of bubbles due to bubble expansion and compression, coalescence and disintegration, and phase change. Five major bubble interaction mechanisms are identified for the gas-liquid two-phase flow of interest, and are analytically modeled as the source/sink terms for the transport equation in the confined flow. These models include both intra-group and inter-group bubble interactions

Developing two-phase flow modelling concepts for rock fractures

Energy Technology Data Exchange (ETDEWEB)

Keto, V. (Fortum Nuclear Services Oy, Espoo (Finland))

2010-01-15

The Finnish nuclear waste disposal company, Posiva Oy, is planning an underground repository for spent nuclear fuel to be constructed on the island of Olkiluoto on the south-west coast of Finland. One element of the site investigations conducted at Olkiluoto is the excavation of the underground rock characterisation facility (ONKALO) that will be extended to the final disposal depth (approximately -400 m). The bedrock around the excavated tunnel volume is fully saturated with groundwater, which water commonly contains a mixture of dissolved gases. These gases remain dissolved due to the high hydrostatic pressure. During tunnel excavation work the natural hydrostatic pressure field is disturbed and the water pressure will decrease close to the atmospheric pressure in the immediate vicinity of the tunnel. During this pressure drop two-phase flow conditions (combined flow of both water and gas) may develop in the vicinity of the underground opening, as the dissolved gas is exsoluted under the low pressure (the term exsolution refers here to release of the dissolved gas molecules from the water phase into a separate gas phase). This report steers towards concept development for numerical two-phase flow modeling for fractured rock. The focus is on the description of gas phase formation process under disturbed hydraulic conditions by exsolution of dissolved gases from groundwater, and on understanding the effects of a possibly formed gas phase on groundwater flow conditions in rock fractures. A mathematical model of three mutually coupled nonlinear partial differential equations for two-phase flow is presented and corresponding constitutional relationships are introduced and discussed. Illustrative numerical simulations are performed in a simplified setting using COMSOL Multiphysics 3.5a - software package. Shortcomings and conceptual problems are discussed. (orig.)

Developing two-phase flow modelling concepts for rock fractures

International Nuclear Information System (INIS)

Keto, V.

2010-01-01

The Finnish nuclear waste disposal company, Posiva Oy, is planning an underground repository for spent nuclear fuel to be constructed on the island of Olkiluoto on the south-west coast of Finland. One element of the site investigations conducted at Olkiluoto is the excavation of the underground rock characterisation facility (ONKALO) that will be extended to the final disposal depth (approximately -400 m). The bedrock around the excavated tunnel volume is fully saturated with groundwater, which water commonly contains a mixture of dissolved gases. These gases remain dissolved due to the high hydrostatic pressure. During tunnel excavation work the natural hydrostatic pressure field is disturbed and the water pressure will decrease close to the atmospheric pressure in the immediate vicinity of the tunnel. During this pressure drop two-phase flow conditions (combined flow of both water and gas) may develop in the vicinity of the underground opening, as the dissolved gas is exsoluted under the low pressure (the term exsolution refers here to release of the dissolved gas molecules from the water phase into a separate gas phase). This report steers towards concept development for numerical two-phase flow modeling for fractured rock. The focus is on the description of gas phase formation process under disturbed hydraulic conditions by exsolution of dissolved gases from groundwater, and on understanding the effects of a possibly formed gas phase on groundwater flow conditions in rock fractures. A mathematical model of three mutually coupled nonlinear partial differential equations for two-phase flow is presented and corresponding constitutional relationships are introduced and discussed. Illustrative numerical simulations are performed in a simplified setting using COMSOL Multiphysics 3.5a - software package. Shortcomings and conceptual problems are discussed. (orig.)

Unsteady interfacial coupling of two-phase flow models

International Nuclear Information System (INIS)

Hurisse, O.

2006-01-01

The primary coolant circuit in a nuclear power plant contains several distinct components (vessel, core, pipes,...). For all components, specific codes based on the discretization of partial differential equations have already been developed. In order to obtain simulations for the whole circuit, the interfacial coupling of these codes is required. The approach examined within this work consists in coupling codes by providing unsteady information through the coupling interface. The numerical technique relies on the use of an interface model, which is combined with the basic strategy that was introduced by Greenberg and Leroux in order to compute approximations of steady solutions of non-homogeneous hyperbolic systems. Three different coupling cases have been examined: (i) the coupling of a one-dimensional Euler system with a two-dimensional Euler system; (ii) the coupling of two distinct homogeneous two-phase flow models; (iii) the coupling of a four-equation homogeneous model with the standard two-fluid model. (author)

Stationary two-phase flow evaluation by the dynamic slip model

International Nuclear Information System (INIS)

Stevanovic, D.

1986-01-01

The equations which describe a dynamic slip model for stationary conditions are given in the paper. The basic solving procedure by the code DVOF4 is briefly described. The results are verified on the experiment FRIGG 313014. besides the void fraction and the vapor and liquid phase temperatures, the following parameters are plotted and explained: vapor phase generation rate, vapor and liquid phase velocities, slip between the phases, interfacial surface, friction drag between each phase and the wall, two-phase flow friction multiplier and pressure drop along the channel. (author)

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

Two-phase wall function for modeling of turbulent boundary layer in subcooled boiling flow

International Nuclear Information System (INIS)

Bostjan Koncar; Borut Mavko; Yassin A Hassan

2005-01-01

Full text of publication follows: The heat transfer and phase-change mechanisms in the subcooled flow boiling are governed mainly by local multidimensional mechanisms near the heated wall, where bubbles are generated. The structure of such 'wall boiling flow' is inherently non-homogeneous and is further influenced by the two-phase flow turbulence, phase-change effects in the bulk, interfacial forces and bubble interactions (collisions, coalescence, break-up). In this work the effect of two-phase flow turbulence on the development of subcooled boiling flow is considered. Recently, the modeling of two-phase flow turbulence has been extensively investigated. A notable progress has been made towards deriving reliable models for description of turbulent behaviour of continuous (liquid) and dispersed phase (bubbles) in the bulk flow. However, there is a lack of investigation considering the modeling of two-phase flow boundary layer. In most Eulerian two-fluid models standard single-phase wall functions are used for description of turbulent boundary layer of continuous phase. That might be a good approximation at adiabatic flows, but their use for boundary layers with high concentration of dispersed phase is questionable. In this work, the turbulent boundary layer near the heated wall will be modeled with the so-called 'two-phase' wall function, which is based on the assumption of additional turbulence due to bubble-induced stirring in the boundary layer. In the two-phase turbulent boundary layer the wall function coefficients strongly depend on the void fraction. Moreover, in the turbulent boundary layer with nucleating bubbles, the bubble size variation also has a significant impact on the liquid phase. As a basis, the wall function of Troshko and Hassan (2001), developed for adiabatic bubbly flows will be used. The simulations will be performed by a general-purpose CFD code CFX-4.4 using additional models provided by authors. The results will be compared to the boiling

Modeling and analysis of hydrodynamic instabilities in two-phase flow using two-fluid model

International Nuclear Information System (INIS)

Zhou, J.; Podowski, M.Z.

2001-01-01

Because of the practical importance of two-phase flow instabilities, especially in boiling water nuclear reactor technology, substantial efforts have been made to date to understand the physical phenomena governing such instabilities and to develop computational tools to model the dynamics of marginally-stable/unstable boiling systems. The purpose of this paper is to present an integrated methodology for the analysis of flow-induced instabilities in boiling channels and systems. The major novel aspects of the proposed approach are: (a) it is based on the combined frequency-domain and time-domain methods, the former used to quantify stability margins and to determine the onset of instability conditions, the latter to study the nonlinear system response outside the stability boundaries identified using the nearly-exact results of the frequency-domain analysis; (b) the two-fluid model of two-phase flow has been used for the first time to analytically derive the boiling channel transfer functions for the parallel-channel and channel-to-channel instability modes. In this way, the major characteristics of a boiling system, including the onset-of-instability conditions, can be readily evaluated by using the qualitative frequency-domain approach, whereas the explicit time-domain integration is performed, if necessary, only for the operating conditions that have already been identified as unstable. Both methods use the same physical two-fluid model that, in one case, is linearized and used to derive a rigorous analytical solution in the complex domain, and, in the other case, is solved numerically using an algorithm developed especially for this purpose. The results using both methods have been compared against each other and extensively tested. The testing and validation of the new model included comparisons of the predicted steady-state distributions of major parameters and of the transient channel response against experimental data

A semi-empirical two phase model for rocks

International Nuclear Information System (INIS)

Fogel, M.B.

1993-01-01

This article presents data from an experiment simulating a spherically symmetric tamped nuclear explosion. A semi-empirical two-phase model of the measured response in tuff is presented. A comparison is made of the computed peak stress and velocity versus scaled range and that measured on several recent tuff events

Photosynthetic Entrainment of the Circadian Clock Facilitates Plant Growth under Environmental Fluctuations: Perspectives from an Integrated Model of Phase Oscillator and Phloem Transportation

Directory of Open Access Journals (Sweden)

Takayuki Ohara

2017-10-01

Full Text Available Plants need to avoid carbon starvation and resultant growth inhibition under fluctuating light environments to ensure optimal growth and reproduction. As diel patterns of carbon metabolism are influenced by the circadian clock, appropriate regulation of the clock is essential for plants to properly manage their carbon resources. For proper adjustment of the circadian phase, higher plants utilize environmental signals such as light or temperature and metabolic signals such as photosynthetic products; the importance of the latter as phase regulators has been recently elucidated. A mutant of Arabidopsis thaliana that is deficient in phase response to sugar has been shown, under fluctuating light conditions, to be unable to adjust starch turnover and to realize carbon homeostasis. Whereas, the effects of light entrainment on growth and survival of higher plants are well studied, the impact of phase regulation by sugar remains unknown. Here we show that endogenous sugar entrainment facilitates plant growth. We integrated two mathematical models, one describing the dynamics of carbon metabolism in A. thaliana source leaves and the other growth of sink tissues dependent on sucrose translocation from the source. The integrated model predicted that sugar-sensitive plants grow faster than sugar-insensitive plants under constant as well as changing photoperiod conditions. We found that sugar entrainment enables efficient carbon investment for growth by stabilizing sucrose supply to sink tissues. Our results highlight the importance of clock entrainment by both exogenous and endogenous signals for optimizing growth and increasing fitness.

Spectral Cascade-Transport Turbulence Model Development for Two-Phase Flows

Science.gov (United States)

Brown, Cameron Scott

Turbulence modeling remains a challenging problem in nuclear reactor applications, particularly for the turbulent multiphase flow conditions in nuclear reactor subchannels. Understanding the fundamental physics of turbulent multiphase flows is crucial for the improvement and further development of multiphase flow models used in reactor operation and safety calculations. Reactor calculations with Reynolds-averaged Navier-Stokes (RANS) approach continue to become viable tools for reactor analysis. The on-going increase in available computational resources allows for turbulence models that are more complex than the traditional two-equation models to become practical choices for nuclear reactor computational fluid dynamic (CFD) and multiphase computational fluid dynamic (M-CFD) simulations. Similarly, increased computational capabilities continue to allow for higher Reynolds numbers and more complex geometries to be evaluated using direct numerical simulation (DNS), thus providing more validation and verification data for turbulence model development. Spectral turbulence models are a promising approach to M-CFD simulations. These models resolve mean flow parameters as well as the turbulent kinetic energy spectrum, reproducing more physical details of the turbulence than traditional two-equation type models. Previously, work performed by other researchers on a spectral cascade-transport model has shown that the model behaves well for single and bubbly twophase decay of isotropic turbulence, single and two-phase uniform shear flow, and single-phase flow in a channel without resolving the near-wall boundary layer for relatively low Reynolds number. Spectral models are great candidates for multiphase RANS modeling since bubble source terms can be modeled as contributions to specific turbulence scales. This work focuses on the improvement and further development of the spectral cascadetransport model (SCTM) to become a three-dimensional (3D) turbulence model for use in M

Theory and modeling of microstructural evolution in polycrystalline materials: Solute segregation, grain growth and phase transformations

Science.gov (United States)

Ma, Ning

2005-11-01

To accurately predict microstructure evolution and, hence, to synthesis metal and ceramic alloys with desirable properties involves many fundamental as well as practical issues. In the present study, novel theoretical and phase field approaches have been developed to address some of these issues including solute drag and segregation transition at grain boundaries and dislocations, grain growth in systems of anisotropic boundary properties, and precipitate microstructure development in polycrystalline materials. The segregation model has allowed for the prediction of a first-order segregation transition, which could be related to the sharp transition of solute concentration of grain boundary as a function of temperature. The incorporating of interfacial energy and mobility as functions of misorientation and inclination in the phase field model has allowed for the study of concurrent grain growth and texture evolution. The simulation results were analyzed using the concept of local grain boundary energy density, which simplified significantly the development of governing equations for texture controlled grain growth in Ti-6Al-4V. Quantitative phase field modeling techniques have been developed by incorporating thermodynamic and diffusivity databases. The models have been validated against DICTRA simulations in simple 1D problems and applied to simulate realistic microstructural evolutions in Ti-6Al-4V, including grain boundary a and globular a growth and sideplate development under both isothermal aging and continuous cooling conditions. The simulation predictions agree well with experimental observations.

Analysis of two-phase flow inter-subchannel mass and momentum exchanges by the two-fluid model approach

Energy Technology Data Exchange (ETDEWEB)

Ninokata, H. [Tokyo Institute of Technology (Japan); Deguchi, A. [ENO Mathematical Analysis, Tokyo (Japan); Kawahara, A. [Kumamoto Univ., Kumamoto (Japan)

1995-09-01

A new void drift model for the subchannel analysis method is presented for the thermohydraulics calculation of two-phase flows in rod bundles where the flow model uses a two-fluid formulation for the conservation of mass, momentum and energy. A void drift model is constructed based on the experimental data obtained in a geometrically simple inter-connected two circular channel test sections using air-water as working fluids. The void drift force is assumed to be an origin of void drift velocity components of the two-phase cross-flow in a gap area between two adjacent rods and to overcome the momentum exchanges at the phase interface and wall-fluid interface. This void drift force is implemented in the cross flow momentum equations. Computational results have been successfully compared to experimental data available including 3x3 rod bundle data.

Comprehensive modeling of solid phase epitaxial growth using Lattice Kinetic Monte Carlo

International Nuclear Information System (INIS)

Martin-Bragado, Ignacio

2013-01-01

Damage evolution of irradiated silicon is, and has been, a topic of interest for the last decades for its applications to the semiconductor industry. In particular, sometimes, the damage is heavy enough to collapse the lattice and to locally amorphize the silicon, while in other cases amorphization is introduced explicitly to improve other implanted profiles. Subsequent annealing of the implanted samples heals the amorphized regions through Solid Phase Epitaxial Regrowth (SPER). SPER is a complicated process. It is anisotropic, it generates defects in the recrystallized silicon, it has a different amorphous/crystalline (A/C) roughness for each orientation, leaving pits in Si(1 1 0), and in Si(1 1 1) it produces two modes of recrystallization with different rates. The recently developed code MMonCa has been used to introduce a physically-based comprehensive model using Lattice Kinetic Monte Carlo that explains all the above singularities of silicon SPER. The model operates by having, as building blocks, the silicon lattice microconfigurations and their four twins. It detects the local configurations, assigns microscopical growth rates, and reconstructs the positions of the lattice locally with one of those building blocks. The overall results reproduce the (a) anisotropy as a result of the different growth rates, (b) localization of SPER induced defects, (c) roughness trends of the A/C interface, (d) pits on Si(1 1 0) regrown surfaces, and (e) bimodal Si(1 1 1) growth. It also provides physical insights of the nature and shape of deposited defects and how they assist in the occurrence of all the above effects

A turbulence model for large interfaces in high Reynolds two-phase CFD

International Nuclear Information System (INIS)

Coste, P.; Laviéville, J.

2015-01-01

Highlights: • Two-phase CFD commonly involves interfaces much larger than the computational cells. • A two-phase turbulence model is developed to better take them into account. • It solves k–epsilon transport equations in each phase. • The special treatments and transfer terms at large interfaces are described. • Validation cases are presented. - Abstract: A model for two-phase (six-equation) CFD modelling of turbulence is presented, for the regions of the flow where the liquid–gas interface takes place on length scales which are much larger than the typical computational cell size. In the other regions of the flow, the liquid or gas volume fractions range from 0 to 1. Heat and mass transfer, compressibility of the fluids, are included in the system, which is used at high Reynolds numbers in large scale industrial calculations. In this context, a model based on k and ε transport equations in each phase was chosen. The paper describes the model, with a focus on the large interfaces, which require special treatments and transfer terms between the phases, including some approaches inspired from wall functions. The validation of the model is based on high Reynolds number experiments with turbulent quantities measurements of a liquid jet impinging a free surface and an air water stratified flow. A steam–water stratified condensing flow experiment is also used for an indirect validation in the case of heat and mass transfer

Dynamic Modeling Strategy for Flow Regime Transition in Gas-Liquid Two-Phase Flows

Directory of Open Access Journals (Sweden)

Xia Wang

2012-12-01

Full Text Available In modeling gas-liquid two-phase flows, the concept of flow regimes has been widely 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 flow regime dependent. Current nuclear reactor safety analysis codes, such as RELAP5, classify flow regimes using flow regime maps or transition criteria that were developed for steady-state, fully-developed flows. As two-phase flows are dynamic in nature, it is important to model the flow regime transitions dynamically to more accurately predict the two-phase flows. The present work aims to develop a dynamic modeling strategy to determine flow regimes in gas-liquid two-phase flows through 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 of the interfacial area, fluid particle (bubble or liquid droplet disintegration, boiling and evaporation, and the destruction of the interfacial area, fluid particle coalescence and condensation. For 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 shapes, namely group-1 and group-2 bubbles. A preliminary approach to dynamically identify the flow regimes is discussed, in which discriminators are based on the predicted information, such as the void fraction and interfacial area concentration. The flow regime predicted with this method shows good agreement with the experimental observations.

A Dual-Stage Two-Phase Model of Selective Attention

Science.gov (United States)

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…

Two-phase coolant pump model of pressurized light water nuclear reactors

International Nuclear Information System (INIS)

Santos, G.A. dos; Freitas, R.L.

1990-01-01

The two-phase coolant pump model of pressurized light water nuclear reactors is an important point for the loss of primary coolant accident analysis. The homologous curves set up the complete performance of the pump and are input for accidents analysis thermal-hydraulic codes. This work propose a mathematical model able to predict the two-phase homologous curves where it was incorporated geometric and operational pump condition. The results were compared with the experimental tests data from literature and it has showed a good agreement. (author)

The analysis of two-phase flow and heat transfer using a multidimensional, four field, two-fluid model

International Nuclear Information System (INIS)

Lahey, Richard T.; Drew, Donald A.

2001-01-01

This paper reviews the state-of-the-art in the prediction of multidimensional multiphase flow and heat transfer phenomena using a four field, two-fluid model. It is shown that accurate mechanistic computational fluid dynamic (CFD) predictions are possible for a wide variety of adiabatic and diabatic flows using this computational model. In particular, the model is able to predict the bubbly air/water upflow data of Serizawa (Serizawa, A., 1974. Fluid dynamic characteristics of two-phase flow. Ph.D. thesis, (Nuclear Engineering), Kyoto University, Japan), the downflow data of Wang et al. (Wang, S.K., Lee, S.J., Lahey Jr., R.T., Jones, O.C., 1987. 3-D turbulence structure and phase distribution measurements in bubbly two-phase flows. Int. J. Multiphase Flow 13 (3), 327-343), the isosceles triangle upflow data of Lopez de Bertodano et al. (Lopez de Bertodano, M., Lahey Jr., R.T., Jones, O.C., 1994b. Phase distribution in bubbly two-phase flow in vertical ducts. Int. J. Multiphase Flow 20 (5), 805-818), the heated annular R-113 subcooled boiling data of Velidandala, et al. (Velidandla, V., Pulta, S., Roy, P., Kaira, S.P., 1995. Velocity field in turbulent subcooled boiling flow. ASME Preprint HTD-314, 107-123) and the R-113 CHF data of Hino and Ueda (Hino, R., Ueda, T., 1985. Studies on heat transfer and flow characteristics in subcooled boiling-part 2, flow characteristics. Int. J. Multiphase Flow 11, 283-297). It can also predict external two-phase flows, such as those for spreading two-phase jets (Bonetto, F., Lahey Jr., R.T., 1993. An experimental study on air carryunder due to a plunging liquid jet. Int. J. Multiphase Flow 19 (2), 281-294) and multiphase flows around the hull of naval surface ships (Carrica, P.M., Bonetto, F., Drew, D.A., Lahey, R.T., 1999. A polydispersed model for bubbly two-phase flow around a surface ship. Int. J. Multiphase Flow 25 (2), 257-305)

Simulation of the catalyst layer in PEMFC based on a novel two-phase lattice model

Energy Technology Data Exchange (ETDEWEB)

Zhang Jiejing; Yang Wei; Xu Li [School of Chemical Engineering and Technology, State Key Laboratory of Chemical Engineering, Tianjin Key Laboratory of Membrane Science and Desalination Technology, Tianjin University, Tianjin 300072 (China); Wang Yuxin, E-mail: yxwang@tju.edu.cn [School of Chemical Engineering and Technology, State Key Laboratory of Chemical Engineering, Tianjin Key Laboratory of Membrane Science and Desalination Technology, Tianjin University, Tianjin 300072 (China)

2011-08-01

Highlights: > We propose a novel two phase lattice model of catalyst layer in PEMFC. > The model features a catalyst phase and a mixed ionomer and pores phase. > Transport and electrochemical reaction in the lattice are simulated. > The model enables more accurate results than pore-solid two phase model. > Profiles of oxygen level and reaction rate across catalyst layer vary with cell current. - Abstract: A lattice model of catalyst layer in proton exchange membrane fuel cells (PEMFCs), consisting of randomly distributed catalyst phase (C phase) and mixed ionomer-pore phase (IP phase), was established by means of Monte Carlo method. Transport and electrochemical reactions in the model catalyst layer were calculated. The newly proposed C-IP model was compared with previously established pore-solid two phase model. The variation of oxygen level and reaction rate along the thickness of catalyst layer with cell current was discussed. The effect of ionomer distribution across catalyst layer was studied by comparing profiles of oxygen level, reaction rate and overpotential, as well as corresponding polarization curves.

Modelling of two-phase flow based on separation of the flow according to velocity

International Nuclear Information System (INIS)

Narumo, T.

1997-01-01

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

A method to couple HEM and HRM two-phase flow models

Energy Technology Data Exchange (ETDEWEB)

Herard, J.M.; Hurisse, O. [Elect France, Div Rech and Dev, Dept Mecan Fluides Energies and Environm, F-78401 Chatou (France); Hurisse, O. [Univ Aix Marseille 1, Ctr Math and Informat, Lab Anal Topol and Probabil, CNRS, UMR 6632, F-13453 Marseille 13 (France); Ambroso, A. [CEA Saclay, DEN, DM2S, SFME, LETR, 91 - Gif sur Yvette (France)

2009-04-15

We present a method for the unsteady coupling of two distinct two-phase flow models (namely the Homogeneous Relaxation Model, and the Homogeneous Equilibrium Model) through a thin interface. The basic approach relies on recent works devoted to the interfacial coupling of CFD models, and thus requires to introduce an interface model. Many numerical test cases enable to investigate the stability of the coupling method. (authors)

A method to couple HEM and HRM two-phase flow models

International Nuclear Information System (INIS)

Herard, J.M.; Hurisse, O.; Hurisse, O.; Ambroso, A.

2009-01-01

We present a method for the unsteady coupling of two distinct two-phase flow models (namely the Homogeneous Relaxation Model, and the Homogeneous Equilibrium Model) through a thin interface. The basic approach relies on recent works devoted to the interfacial coupling of CFD models, and thus requires to introduce an interface model. Many numerical test cases enable to investigate the stability of the coupling method. (authors)

Reduced order modeling of flashing two-phase jets

Energy Technology Data Exchange (ETDEWEB)

Gurecky, William, E-mail: william.gurecky@utexas.edu; Schneider, Erich, E-mail: eschneider@mail.utexas.edu; Ballew, Davis, E-mail: davisballew@utexas.edu

2015-12-01

Highlights: • Accident simulation requires ability to quickly predict two-phase flashing jet's damage potential. • A reduced order modeling methodology informed by experimental or computational data is described. • Zone of influence volumes are calculated for jets of various upstream thermodynamic conditions. - Abstract: In the event of a Loss of Coolant Accident (LOCA) in a pressurized water reactor, the escaping coolant produces a highly energetic flashing jet with the potential to damage surrounding structures. In LOCA analysis, the goal is often to evaluate many break scenarios in a Monte Carlo style simulation to evaluate the resilience of a reactor design. Therefore, in order to quickly predict the damage potential of flashing jets, it is of interest to develop a reduced order model that relates the damage potential of a jet to the pressure and temperature upstream of the break and the distance from the break to a given object upon which the jet is impinging. This work presents framework for producing a Reduced Order Model (ROM) that may be informed by measured data, Computational Fluid Dynamics (CFD) simulations, or a combination of both. The model is constructed by performing regression analysis on the pressure field data, allowing the impingement pressure to be quickly reconstructed for any given upstream thermodynamic condition within the range of input data. The model is applicable to both free and fully impinging two-phase flashing jets.

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).

A state-of-the-art report on two-phase critical flow modelling

International Nuclear Information System (INIS)

Jung, Jae Joon; Jang, Won Pyo; Kim, Dong Soo

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)

Three layer model analysis on two-phase critical flow through a converging nozzle

International Nuclear Information System (INIS)

Ochi, J.; Ayukawa, K.

1991-01-01

A three layer model is proposed for a two-phase critical flow through a converging nozzle in this paper. Most previous analyses of the two phase flow have been based on a homogeneous or a separated flow model as the conservation equations. These results were found to have large deviations from the actual measurements for two phase critical flows. The presented model is based on the assumption that a flow consists of three layers with a mixing region between gas and liquid phase layers. The effect of gas and liquid fraction occupied in the mixing layer was made clear from the numerical results. The measurements of the critical flow rate and the pressure profiles through a converging nozzle were made with air-water flow. The calculated results of these models are discussed in comparison with the experimental data for the flow rates and the pressure distributions under critical conditions

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.

Development of a two-phase SPH model for sediment laden flows

Science.gov (United States)

Shi, Huabin; Yu, Xiping; Dalrymple, Robert A.

2017-12-01

A SPH model based on a general formulation for solid-fluid two-phase flows is proposed for suspended sediment motion in free surface flows. The water and the sediment are treated as two miscible fluids, and the multi-fluid system is discretized by a single set of SPH particles, which move with the water velocity and carry properties of the two phases. Large eddy simulation (LES) is introduced to deal with the turbulence effect, and the widely used Smagorinsky model is modified to take into account the influence of sediment particles on the turbulence. The drag force is accurately formulated by including the hindered settling effect. In the model, the water is assumed to be weakly compressible while the sediment is incompressible, and a new equation of state is proposed for the pressure in the sediment-water mixture. Dynamic boundary condition is employed to treat wall boundaries, and a new strategy of Shepard filtering is adopted to damp the pressure oscillation. The developed two-phase SPH model is validated by comparing the numerical results with analytical solutions for idealized cases of still water containing both neutrally buoyant and naturally settling sand and for plane Poiseuille flows carrying neutrally buoyant particles, and is then applied to sand dumping from a line source into a water tank, where the sand cloud settles with a response of the free water surface. It is shown that the numerical results are in good agreement with the experimental data as well as the empirical formulas. The characteristics of the settling sand cloud, the pressure field, and the flow vortices are studied. The motion of the free water surface is also discussed. The proposed two-phase SPH model is proven to be effective for numerical simulation of sand dumping into waters.

Stability of equilibria for a two-phase osmosis model

NARCIS (Netherlands)

Lippoth, F.; Prokert, G.

2012-01-01

For a two-phase moving boundary problem modelling the motion of a semipermeable membrane by osmotic pressure and surface tension, we prove that the manifold of equilibria is locally exponentially attractive. Our method relies on maximal regularity results for parabolic systems with relaxation type

Relations between the kinetic equation and the Langevin models in two-phase flow modelling

International Nuclear Information System (INIS)

Minier, J.P.; Pozorski, J.

1997-05-01

The purpose of this paper is to discuss PDF and stochastic models which are used in two-phase flow modelling. The aim of the present analysis is essentially to try to determine relations and consistency between different models. It is first recalled that different approaches actually correspond to PDF models written either in terms of the process trajectories or in terms of the PDF itself. The main difference lies in the choice of the independent variables which are retained. Two particular models are studied, the Kinetic Equation and the Langevin Equation model. The latter uses a Langevin equation to model the fluid velocities seen along particle trajectories. The Langevin model is more general since it contains an additional variable. It is shown that, in certain cases, this variable can be summed up exactly to retrieve the Kinetic Equation model as a marginal PDF. A joint fluid and solid particle PDF which includes the characteristics of both phases is proposed at the end of the paper. (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.

Diffusion and phase growth in heterophase systems. 1

International Nuclear Information System (INIS)

Mchedlov-Petrosyan, P.O.

1989-01-01

The present paper gives the view of theoretical study of diffusion processes in ternary and more component solid-state systems, caused by chemical reactions and phase growth. Internal oxidation of alloys, nitridation, borating etc. are the well-known and widely investigated processes of such type. Self-consistent theoretical model of such processes must take into account both the effect of concentration macroscopic districutions on new phase precipitation growth and precipitation reaction on concentration distribution; heterophase must be explicitly allowed for. As for binary system, diffusion theory, running into the phase growth, is well developed and completely presented in monographs, the carried out theoretical investigations of ternary systems are explicitly deficient. The first part of the review presents analysis of available theoretical studies approximately up to 1980. Ratios between various analytically solved models are discussed in detail. It is shown that they don't satisfy to full extent the above-given requirements. More consistent, both numerically and analytically solvable models developed for the last years, are considered in the review second part. 119 refs

The questions of liquid metal two-phase flow modelling in the FBR core channels

International Nuclear Information System (INIS)

Martsiniouk, D.Ye.; Sorokin, A.P.

2000-01-01

The two-fluid model representation for calculations of two-phase flow characteristics in the FBR fuel pin bundles with liquid metal cooling is presented and analysed. Two conservation equations systems of the mass, momentum and energy have been written for each phase. Components accounted the mass-, momentum- and heat transfer throughout the interface occur in the macro-field equations after the averaging procedure realisation. The pattern map and correlations for two-fluid model in vertical liquid metal flows are presented. The description of processes interphase mass- and heat exchange and interphase friction is determined by the two-phase flow regime. The opportunity of the liquid metal two-phase flow regime definition is analysed. (author)

Cahn-Hilliard modeling of particles suspended in two-phase flows

NARCIS (Netherlands)

Choi, Y.J.; Anderson, P.D.

2012-01-01

In this paper, we present a model for the dynamics of particles suspended in two-phase flows by coupling the CahnHilliard theory with the extended finite element method (XFEM). In the CahnHilliard model the interface is considered to have a small but finite thickness, which circumvents explicit

Phase field simulation of grain growth in porous uranium dioxide

International Nuclear Information System (INIS)

Ahmed, Karim; Pakarinen, Janne; Allen, Todd; El-Azab, Anter

2014-01-01

Graphical abstract: Display Omitted -- Abstract: A novel phase field model has been developed to investigate grain growth in porous polycrystalline UO 2 . Based on a system of Cahn–Hilliard and Allen–Cahn equations, the model takes into consideration both the curvature driven grain boundary motion and pore migration by surface diffusion. As such, the model accounts for the interaction between pore and grain boundary kinetics, which tends to retard the growth process. The phase field model parameters are found in terms of measurable material properties. Hence, quantitative results that can be compared with experiments were obtained. The model has been used to investigate the effect of porosity on the kinetics of grain growth in UO 2 . It is found that, as the amount of porosity increases, grain growth in UO 2 gradually changes from boundary controlled growth to pore controlled growth. For high porosity levels, the grain growth completely stops after a short evolution time. It is also found that the inhomogeneous distribution of pores leads to abnormal grain growth even without taking into account the anisotropy in grain boundary energy and mobility. The effects of porosity, temperature and initial microstructure on grain growth were thoroughly investigated. The model predictions are in good agreement with published experimental results of grain growth in UO 2

Modeling of two-phase slug flow

International Nuclear Information System (INIS)

Fabre, J.; Line, A.

1992-01-01

When gas and liquid flow in a pipe, over a range of flow rates, a flow pattern results in which sequences of long bubbles, almost filling the pipe cross section, are successively followed by liquid slugs that may contain small bubbles. This flow pattern, usually called slug flow, is encountered in numerous practical situations, such as in the production of hydrocarbons in wells and their transportation in pipelines; the production of steam and water in geothermal power plants; the boiling and condensation in liquid-vapor systems of thermal power plants; emergency core cooling of nuclear reactors; heat and mass transfer between gas and liquid in chemical reactors. This paper provides a review of two phase slug flow modeling

Numerical approximation of a binary fluid-surfactant phase field model of two-phase incompressible flow

KAUST Repository

Zhu, Guangpu

2018-04-17

In this paper, we consider the numerical approximation of a binary fluid-surfactant phase field model of two-phase incompressible flow. The nonlinearly coupled model consists of two Cahn-Hilliard type equations and incompressible Navier-Stokes equations. Using the Invariant Energy Quadratization (IEQ) approach, the governing system is transformed into an equivalent form, which allows the nonlinear potentials to be treated efficiently and semi-explicitly. we construct a first and a second-order time marching schemes, which are extremely efficient and easy-to-implement, for the transformed governing system. At each time step, the schemes involve solving a sequence of linear elliptic equations, and computations of phase variables, velocity and pressure are totally decoupled. We further establish a rigorous proof of unconditional energy stability for the semi-implicit schemes. Numerical results in both two and three dimensions are obtained, which demonstrate that the proposed schemes are accurate, efficient and unconditionally energy stable. Using our schemes, we investigate the effect of surfactants on droplet deformation and collision under a shear flow. The increase of surfactant concentration can enhance droplet deformation and inhibit droplet coalescence.

Numerical approximation of a binary fluid-surfactant phase field model of two-phase incompressible flow

KAUST Repository

Zhu, Guangpu; Kou, Jisheng; Sun, Shuyu; Yao, Jun; Li, Aifen

2018-01-01

In this paper, we consider the numerical approximation of a binary fluid-surfactant phase field model of two-phase incompressible flow. The nonlinearly coupled model consists of two Cahn-Hilliard type equations and incompressible Navier-Stokes equations. Using the Invariant Energy Quadratization (IEQ) approach, the governing system is transformed into an equivalent form, which allows the nonlinear potentials to be treated efficiently and semi-explicitly. we construct a first and a second-order time marching schemes, which are extremely efficient and easy-to-implement, for the transformed governing system. At each time step, the schemes involve solving a sequence of linear elliptic equations, and computations of phase variables, velocity and pressure are totally decoupled. We further establish a rigorous proof of unconditional energy stability for the semi-implicit schemes. Numerical results in both two and three dimensions are obtained, which demonstrate that the proposed schemes are accurate, efficient and unconditionally energy stable. Using our schemes, we investigate the effect of surfactants on droplet deformation and collision under a shear flow. The increase of surfactant concentration can enhance droplet deformation and inhibit droplet coalescence.

A study of critical two-phase flow models

International Nuclear Information System (INIS)

Siikonen, T.

1982-01-01

The existing computer codes use different boundary conditions in the calculation of critical two-phase flow. In the present study these boundary conditions are compared. It is shown that the boundary condition should be determined from the hydraulic model used in the computer code. The use of a correlation, which is not based on the hydraulic model used, leads often to bad results. Usually a good agreement with data is obtained in the calculation as far as the critical mass flux is concerned, but the agreement is not so good in the pressure profiles. The reason is suggested to be mainly in inadequate modeling of non-equilibrium effects. (orig.)

A phase-field model for non-equilibrium solidification of intermetallics

International Nuclear Information System (INIS)

Assadi, H.

2007-01-01

Intermetallics may exhibit unique solidification behaviour-including slow growth kinetics, anomalous partitioning and formation of unusual growth morphologies-because of departure from local equilibrium. A phase-field model is developed and used to illustrate these non-equilibrium effects in solidification of a prototype B2 intermetallic phase. The model takes sublattice compositions as primary field variables, from which chemical long-range order is derived. The diffusive reactions between the two sublattices, and those between each sublattice and the liquid phase are taken as 'internal' kinetic processes, which take place within control volumes of the system. The model can thus capture solute and disorder trapping effects, which are consistent-over a wide range of the solid/liquid interface thickness-with the predictions of the sharp-interface theory of solute and disorder trapping. The present model can also take account of solid-state ordering and thus illustrate the effects of chemical ordering on microstructure formation and crystal growth kinetics

Quantum entanglement and phase transition in a two-dimensional photon-photon pair model

International Nuclear Information System (INIS)

Zhang Jianjun; Yuan Jianhui; Zhang Junpei; Cheng Ze

2013-01-01

We propose a two-dimensional model consisting of photons and photon pairs. In the model, the mixed gas of photons and photon pairs is formally equivalent to a two-dimensional system of massive bosons with non-vanishing chemical potential, which implies the existence of two possible condensate phases. Using the variational method, we discuss the quantum phase transition of the mixed gas and obtain the critical coupling line analytically. Moreover, we also find that the phase transition of the photon gas can be interpreted as enhanced second harmonic generation. We then discuss the entanglement between photons and photon pairs. Additionally, we also illustrate how the entanglement between photons and photon pairs can be associated with the phase transition of the system.

Identification of growth phases and influencing factors in cultivations with AGE1.HN cells using set-based methods.

Directory of Open Access Journals (Sweden)

Steffen Borchers

Full Text Available Production of bio-pharmaceuticals in cell culture, such as mammalian cells, is challenging. Mathematical models can provide support to the analysis, optimization, and the operation of production processes. In particular, unstructured models are suited for these purposes, since they can be tailored to particular process conditions. To this end, growth phases and the most relevant factors influencing cell growth and product formation have to be identified. Due to noisy and erroneous experimental data, unknown kinetic parameters, and the large number of combinations of influencing factors, currently there are only limited structured approaches to tackle these issues. We outline a structured set-based approach to identify different growth phases and the factors influencing cell growth and metabolism. To this end, measurement uncertainties are taken explicitly into account to bound the time-dependent specific growth rate based on the observed increase of the cell concentration. Based on the bounds on the specific growth rate, we can identify qualitatively different growth phases and (in-validate hypotheses on the factors influencing cell growth and metabolism. We apply the approach to a mammalian suspension cell line (AGE1.HN. We show that growth in batch culture can be divided into two main growth phases. The initial phase is characterized by exponential growth dynamics, which can be described consistently by a relatively simple unstructured and segregated model. The subsequent phase is characterized by a decrease in the specific growth rate, which, as shown, results from substrate limitation and the pH of the medium. An extended model is provided which describes the observed dynamics of cell growth and main metabolites, and the corresponding kinetic parameters as well as their confidence intervals are estimated. The study is complemented by an uncertainty and outlier analysis. Overall, we demonstrate utility of set-based methods for analyzing cell

Identification of growth phases and influencing factors in cultivations with AGE1.HN cells using set-based methods.

Science.gov (United States)

Borchers, Steffen; Freund, Susann; Rath, Alexander; Streif, Stefan; Reichl, Udo; Findeisen, Rolf

2013-01-01

Production of bio-pharmaceuticals in cell culture, such as mammalian cells, is challenging. Mathematical models can provide support to the analysis, optimization, and the operation of production processes. In particular, unstructured models are suited for these purposes, since they can be tailored to particular process conditions. To this end, growth phases and the most relevant factors influencing cell growth and product formation have to be identified. Due to noisy and erroneous experimental data, unknown kinetic parameters, and the large number of combinations of influencing factors, currently there are only limited structured approaches to tackle these issues. We outline a structured set-based approach to identify different growth phases and the factors influencing cell growth and metabolism. To this end, measurement uncertainties are taken explicitly into account to bound the time-dependent specific growth rate based on the observed increase of the cell concentration. Based on the bounds on the specific growth rate, we can identify qualitatively different growth phases and (in-)validate hypotheses on the factors influencing cell growth and metabolism. We apply the approach to a mammalian suspension cell line (AGE1.HN). We show that growth in batch culture can be divided into two main growth phases. The initial phase is characterized by exponential growth dynamics, which can be described consistently by a relatively simple unstructured and segregated model. The subsequent phase is characterized by a decrease in the specific growth rate, which, as shown, results from substrate limitation and the pH of the medium. An extended model is provided which describes the observed dynamics of cell growth and main metabolites, and the corresponding kinetic parameters as well as their confidence intervals are estimated. The study is complemented by an uncertainty and outlier analysis. Overall, we demonstrate utility of set-based methods for analyzing cell growth and

Local two-phase modeling of the water-steam flows occurring in steam generators

International Nuclear Information System (INIS)

Denefle, Romain

2013-01-01

The present study is related to the need of modeling the two-phase flows occurring in a steam generator (liquid at inlet and vapour at outlet). The choice is made to investigate a hybrid modeling of the flow, considering the gas phase as two separated fields, each one being modeled with different closure laws. In so doing, the small and spherical bubbles are modeled through a dispersed approach within the two-fluid model, and the distorted bubbles are simulated with an interface locating method. The main outcome is about the implementation, the verification and the validation of the model dedicated to the large and distorted bubbles, as well as the coupling of the two approaches for the gas, allowing the presentation of demonstration calculations using the so-called hybrid approach. (author)

An analytical model for prediction of two-phase (noncondensable) flow pump performance

International Nuclear Information System (INIS)

Furuya, O.

1985-01-01

During operational transients or a hypothetical LOCA (loss of coolant accident) condition, the recirculating coolant of PWR (pressurized water reactor) may flash into steam due to a loss of line pressure. Under such two-phase flow conditions, it is well known that the recirculation pump becomes unable to generate the same head as that of the single-phase flow case. Similar situations also exist in oil well submersible pumps where a fair amount of gas is contained in oil. Based on the one dimensional control volume method, an analytical method has been developed to determine the performance of pumps operating under two-phase flow conditions. The analytical method has incorporated pump geometry, void fraction, flow slippage and flow regime into the basic formula, but neglected the compressibility and condensation effects. During the course of model development, it has been found that the head degradation is mainly caused by higher acceleration on liquid phase and deceleration on gas phase than in the case of single-phase flows. The numerical results for head degradations and torques obtained with the model favorably compared with the air/water two-phase flow test data of Babcock and Wilcox (1/3 scale) and Creare (1/20 scale) pumps

Layered growth model and epitaxial growth structures for SiCAlN alloys

International Nuclear Information System (INIS)

Liu Zhaoqing; Ni Jun; Su Xiaoao; Dai Zhenhong

2009-01-01

Epitaxial growth structures for (SiC) 1-x (AlN) x alloys are studied using a layered growth model. First-principle calculations are used to determine the parameters in the layered growth model. The phase diagrams of epitaxial growth are given. There is a rich variety of the new metastable polytype structures at x=1/6 ,1/5 ,1/4 ,1/3 , and 1/2 in the layered growth phase diagrams. We have also calculated the electronic properties of the short periodical SiCAlN alloys predicted by our layered growth model. The results show that various ordered structures of (SiC) 1-x (AlN) x alloys with the band gaps over a wide range are possible to be synthesized by epitaxial growth.

On a unified presentation of the non-equilibrium two-phase flow models

International Nuclear Information System (INIS)

Boure, J.A.

1975-01-01

If the various existing one-dimensional two-phase flow models are consistent, they must appear as particular cases of more general models. It is shown that such is the case if, and only if, the mathematical form of the laws of the transfers between the phases is sufficiently general. These transfer laws control the non-equilibrium phenomena. A convenient general model is a particular form of the two-fluid model. This particular form involves three equations and three dependent variables characterizing the mixture, and three equations and three dependent variables characterizing the differences between the phases (slip, thermal non-equilibriums). The mathematical expressions of the transfert terms present in the above equations involve first-order partial derivatives of the dependent variables. The other existing models may be deduced from the general model by making assumptions on the fluid evolution. Several examples are given. The resulting unified presentation of the existing model enables a comparison of the implicit assumptions made in these models on the transfer laws. It is therefore, a useful tool for the appraisal of the existing models and for the development of new models [fr

Comparison of Two-Phase Pipe Flow in OpenFOAM with a Mechanistic Model

Science.gov (United States)

Shuard, Adrian M.; Mahmud, Hisham B.; King, Andrew J.

2016-03-01

Two-phase pipe flow is a common occurrence in many industrial applications such as power generation and oil and gas transportation. Accurate prediction of liquid holdup and pressure drop is of vast importance to ensure effective design and operation of fluid transport systems. In this paper, a Computational Fluid Dynamics (CFD) study of a two-phase flow of air and water is performed using OpenFOAM. The two-phase solver, interFoam is used to identify flow patterns and generate values of liquid holdup and pressure drop, which are compared to results obtained from a two-phase mechanistic model developed by Petalas and Aziz (2002). A total of 60 simulations have been performed at three separate pipe inclinations of 0°, +10° and -10° respectively. A three dimensional, 0.052m diameter pipe of 4m length is used with the Shear Stress Transport (SST) k - ɷ turbulence model to solve the turbulent mixtures of air and water. Results show that the flow pattern behaviour and numerical values of liquid holdup and pressure drop compare reasonably well to the mechanistic model.

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.

Silva. EDF two-phase 1D annular model of a CFB boiler furnace

Energy Technology Data Exchange (ETDEWEB)

Montat, D.; Fauquet, Ph. [Electricite de France (EDF), 78 - Chatou (France). Researckh and Development Div.; Lafanechere, L.; Bursi, J.M. [Electricite de France (EDF) (France). Construction Div.

1997-01-01

SILVA computer code is used for the modelling of the thermal-hydraulics and of the combustion of a coal-fired CFBC solid loop. In a first step, only the furnace is considered. The model is based on a 1D annular two phases description of the hydrodynamics. The model is based on particle mass balances and pressure drop calculations. A basic combustion model is incorporated into this model. The coal combustion is divided in two phases, the combustion of volatile matter and the heterogeneous combustion. The model has been developed within LEGO software and can be included into the global model of the solid loop developed by EDF. (author) 26 refs.

Phase-field crystal simulation facet and branch crystal growth

Science.gov (United States)

Chen, Zhi; Wang, Zhaoyang; Gu, Xinrui; Chen, Yufei; Hao, Limei; de Wit, Jos; Jin, Kexin

2018-05-01

Phase-field crystal model with one mode is introduced to describe morphological transition. The relationship between growth morphology and smooth density distribution was investigated. The results indicate that the pattern selection of dendrite growth is caused by the competition between interface energy anisotropy and interface kinetic anisotropy based on the 2D phase diagram. When the calculation time increases, the crystal grows to secondary dendrite at the dimensionless undercooling equal to - 0.4. Moreover, when noise is introduced in the growth progress, the symmetry is broken in the growth mode, and there becomes irregular fractal-like growth morphology. Furthermore, the single crystal shape develops into polycrystalline when the noise amplitude is large enough. When the dimensionless undercooling is less than - 0.3, the noise has a significant effect on the growth shape. In addition, the growth velocity of crystal near to liquid phase line is slow, while the shape far away from the liquid adapts to fast growth. Based on the simulation results, the method was proved to be effective, and it can easily obtain different crystal shapes by choosing the different points in 2D phase diagram.

Anisotropy in wavelet-based phase field models

KAUST Repository

Korzec, Maciek; Mü nch, Andreas; Sü li, Endre; Wagner, Barbara

2016-01-01

When describing the anisotropic evolution of microstructures in solids using phase-field models, the anisotropy of the crystalline phases is usually introduced into the interfacial energy by directional dependencies of the gradient energy coefficients. We consider an alternative approach based on a wavelet analogue of the Laplace operator that is intrinsically anisotropic and linear. The paper focuses on the classical coupled temperature/Ginzburg--Landau type phase-field model for dendritic growth. For the model based on the wavelet analogue, existence, uniqueness and continuous dependence on initial data are proved for weak solutions. Numerical studies of the wavelet based phase-field model show dendritic growth similar to the results obtained for classical phase-field models.

Anisotropy in wavelet-based phase field models

KAUST Repository

Korzec, Maciek

2016-04-01

When describing the anisotropic evolution of microstructures in solids using phase-field models, the anisotropy of the crystalline phases is usually introduced into the interfacial energy by directional dependencies of the gradient energy coefficients. We consider an alternative approach based on a wavelet analogue of the Laplace operator that is intrinsically anisotropic and linear. The paper focuses on the classical coupled temperature/Ginzburg--Landau type phase-field model for dendritic growth. For the model based on the wavelet analogue, existence, uniqueness and continuous dependence on initial data are proved for weak solutions. Numerical studies of the wavelet based phase-field model show dendritic growth similar to the results obtained for classical phase-field models.

Investigation for vertical, two-phase steam-water flow of three turbine models

International Nuclear Information System (INIS)

Silverman, S.; Goodrich, L.D.

1977-01-01

One of the basic quantities of interest during a loss-of-coolant experiment (LOCE) is the primary system mass flow rate. Presently, there are no transducers commercially available which continuously measure this parameter. Therefore, a transducer was designed at EG and G Idaho, Inc. which combines a drag-disc and turbine into a single unit. The basis for the design was that the drag-disc would measure momentum flux (rhoV 2 ), the turbine would measure velocity and the mass flow rate could then be calculated from the two quantities by assuming a flow profile. For two-phase flow, the outputs are approximately proportional to the desired parameter, but rather large errors can be expected under those assumptions. Preliminary evaluation of the experimental two- and single-phase calibration data has resulted in uncertainty estimates of +-8% of range for the turbine and +-20% of range for the drag-disc. In an effort to reduce the errors, further investigations were made to determine what the drag-disc and turbine really measure. In the present paper, three turbine models for vertical, two-phase, steam/water flow are investigated; the Aya Model, the Rouhani Model, and a volumetric flow model. Theoretical predictions are compared with experimental data for vertical, two-phase steam/water flow. For the purposes of the mass flow calculation, velocity profiles were assumed to be flat for the free-field condition. It is appreciated that this may not be true for all cases investigated, but for an initial inspection, flat profiles were assumed

Modeling and measurement of interfacial area concentration in two-phase flow

International Nuclear Information System (INIS)

Paranjape, Sidharth; Ishii, Mamoru; Hibiki, Takashi

2010-01-01

This paper presents experimental and modeling approaches in characterizing interfacial structures in gas-liquid two-phase flow. For the modeling of the interfacial structure characterization, the interfacial area transport equation proposed earlier has been studied to provide a dynamic and mechanistic prediction tool for two-phase flow analysis. A state-of-the-art four-sensor conductivity probe technique has been developed to obtain detailed local interfacial structure information in a wide range of flow regimes spanning from bubbly to churn-turbulent flows. Newly obtained interfacial area data in 8 x 8 rod-bundle test section are also presented. This paper also reviews available models of the interfacial area sink and source terms and existing databases. The interfacial area transport equation has been benchmarked using condensation bubbly flow data.

Dynamic Modeling of Phase Crossings in Two-Phase Flow

DEFF Research Database (Denmark)

Madsen, Søren; Veje, Christian; Willatzen, Morten

2012-01-01

by a high resolution finite difference scheme due to Kurganov and Tadmore. The homogeneous formulation requires a set of thermodynamic relations to cover the entire range from liquid to gas state. This leads a number of numerical challenges since these relations introduce discontinuities in the derivative...... 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...

Development of two phase turbulent mixing model for subchannel analysis relevant to BWR

International Nuclear Information System (INIS)

Sharma, M.P.; Nayak, A.K.; Kannan, Umasankari

2014-01-01

A two phase flow model is presented, which predicts both liquid and gas phase turbulent mixing rate between adjacent subchannels of reactor rod bundles. The model presented here is for slug churn flow regime, which is dominant as compared to the other regimes like bubbly flow and annular flow regimes, since turbulent mixing rate is the highest in slug churn flow regime. In this paper, we have defined new dimensionless parameters i.e. liquid mixing number and gas mixing number for two phase turbulent mixing. The liquid mixing number is a function of mixture Reynolds number whereas the gas phase mixing number is a function of both mixture Reynolds number and volumetric fraction of gas. The effect of pressure, geometrical influence of subchannel is also included in this model. The present model has been tested against low pressure and temperature air-water and high pressure and temperature steam-water experimental data found that it shows good agreement with available experimental data. (author)

Investigation of Power Losses of Two-Stage Two-Phase Converter with Two-Phase Motor

Directory of Open Access Journals (Sweden)

Michal Prazenica

2011-01-01

Full Text Available The paper deals with determination of losses of two-stage power electronic system with two-phase variable orthogonal output. The simulation is focused on the investigation of losses in the converter during one period in steady-state operation. Modeling and simulation of two matrix converters with R-L load is shown in the paper. 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 in application with high frequency voltage sources.

Comparison of Two-Phase Pipe Flow in OpenFOAM with a Mechanistic Model

International Nuclear Information System (INIS)

Shuard, Adrian M; Mahmud, Hisham B; King, Andrew J

2016-01-01

Two-phase pipe flow is a common occurrence in many industrial applications such as power generation and oil and gas transportation. Accurate prediction of liquid holdup and pressure drop is of vast importance to ensure effective design and operation of fluid transport systems. In this paper, a Computational Fluid Dynamics (CFD) study of a two-phase flow of air and water is performed using OpenFOAM. The two-phase solver, interFoam is used to identify flow patterns and generate values of liquid holdup and pressure drop, which are compared to results obtained from a two-phase mechanistic model developed by Petalas and Aziz (2002). A total of 60 simulations have been performed at three separate pipe inclinations of 0°, +10° and -10° respectively. A three dimensional, 0.052m diameter pipe of 4m length is used with the Shear Stress Transport (SST) k - ω turbulence model to solve the turbulent mixtures of air and water. Results show that the flow pattern behaviour and numerical values of liquid holdup and pressure drop compare reasonably well to the mechanistic model. (paper)

Thermodynamic modelling of phase equilibrium for water + poly(Ethylene glycol + salt aqueous two-phase systems

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.

Steady states and outbreaks of two-phase nonlinear age-structured model of population dynamics with discrete time delay.

Science.gov (United States)

Akimenko, Vitalii; Anguelov, Roumen

2017-12-01

In this paper we study the nonlinear age-structured model of a polycyclic two-phase population dynamics including delayed effect of population density growth on the mortality. Both phases are modelled as a system of initial boundary values problem for semi-linear transport equation with delay and initial problem for nonlinear delay ODE. The obtained system is studied both theoretically and numerically. Three different regimes of population dynamics for asymptotically stable states of autonomous systems are obtained in numerical experiments for the different initial values of population density. The quasi-periodical travelling wave solutions are studied numerically for the autonomous system with the different values of time delays and for the system with oscillating death rate and birth modulus. In both cases it is observed three types of travelling wave solutions: harmonic oscillations, pulse sequence and single pulse.

Computational fluid dynamics modeling of two-phase flow in a BWR fuel assembly

International Nuclear Information System (INIS)

Andrey Ioilev; Maskhud Samigulin; Vasily Ustinenko; Simon Lo; Adrian Tentner

2005-01-01

Full text of publication follows: The goal of this project is to develop an advanced Computational Fluid Dynamics (CFD) computer code (CFD-BWR) that allows the detailed analysis of the two-phase flow and heat transfer phenomena in a Boiling Water Reactor (BWR) fuel bundle under various operating conditions. This code will include more fundamental physical models than the current generation of sub-channel codes and advanced numerical algorithms for improved computational accuracy, robustness, and speed. It is highly desirable to understand the detailed two-phase flow phenomena inside a BWR fuel bundle. These phenomena include coolant phase changes and multiple flow regimes which directly influence the coolant interaction with fuel assembly and, ultimately, the reactor performance. Traditionally, the best analysis tools for the analysis of two-phase flow phenomena inside the BWR fuel assembly have been the sub-channel codes. However, the resolution of these codes is still too coarse for analyzing the detailed intra-assembly flow patterns, such as flow around a spacer element. Recent progress in Computational Fluid Dynamics (CFD), coupled with the rapidly increasing computational power of massively parallel computers, shows promising potential for the fine-mesh, detailed simulation of fuel assembly two-phase flow phenomena. However, the phenomenological models available in the commercial CFD programs are not as advanced as those currently being used in the sub-channel codes used in the nuclear industry. In particular, there are no models currently available which are able to reliably predict the nature of the flow regimes, and use the appropriate sub-models for those flow regimes. The CFD-BWR code is being developed as a customized module built on the foundation of the commercial CFD Code STAR-CD which provides general two-phase flow modeling capabilities. The paper describes the model development strategy which has been adopted by the development team for the

Electroweak phase transition in two Higgs doublet models

International Nuclear Information System (INIS)

Cline, J.M.; Lemieux, P.

1997-01-01

We reexamine the strength of the first-order phase transition in the electroweak theory supplemented by an extra Higgs doublet. The finite-temperature effective potential V eff is computed to one-loop order, including the summation of ring diagrams, to study the ratio φ c /T c of the Higgs field VEV to the critical temperature. We make a number of improvements over previous treatments, including a consistent treatment of Goldstone bosons in V eff , an accurate analytic approximation to V eff valid for any mass-to-temperature ratios, and use of the experimentally measured top quark mass. For two-Higgs-doublet models, we identify a significant region of parameter space where φ c /T c is large enough for electroweak baryogenesis, and we argue that this identification should persist even at higher orders in perturbation theory. In the case of the minimal supersymmetric standard model, our results indicate that the extra Higgs bosons have little effect on the strength of the phase transition. copyright 1997 The American Physical Society

Well-posed Euler model of shock-induced two-phase flow in bubbly liquid

Science.gov (United States)

Tukhvatullina, R. R.; Frolov, S. M.

2018-03-01

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.

Constitutive modeling of stress-driven grain growth in nanocrystalline metals

KAUST Repository

Gürses, Ercan

2013-02-08

In this work, we present a variational multiscale model for grain growth in face-centered cubic nanocrystalline (nc) metals. In particular, grain-growth-induced stress softening and the resulting relaxation phenomena are addressed. The behavior of the polycrystal is described by a conventional Taylor-type averaging scheme in which the grains are treated as two-phase composites consisting of a grain interior phase and a grain boundary-affected zone. Furthermore, a grain-growth law that captures the experimentally observed characteristics of the grain coarsening phenomena is proposed. To this end, the grain size is not taken as constant and varies according to the proposed stress-driven growth law. Several parametric studies are conducted to emphasize the influence of the grain-growth rule on the overall macroscopic response. Finally, the model is shown to provide a good description of the experimentally observed grain-growth-induced relaxation in nc-copper. © 2013 IOP Publishing Ltd.

Berry phase in a two-atom Jaynes-Cummings model with Kerr medium

International Nuclear Information System (INIS)

Bu Shenping; Zhang Guofeng; Liu Jia; Chen Ziyu

2008-01-01

The Jaynes-Cummings model (JCM) is an very important model for describing interaction between quantized electromagnetic fields and atoms in cavity quantum electrodynamics (QED). This model is generalized in many different directions since it predicts many novel quantum effects that can be verified by modern physics experimental technologies. In this paper, the Berry phase and entropy of the ground state for arbitrary photon number n of a two-atom Jaynes-Cummings model with Kerr-like medium are investigated. It is found that there is some correspondence between their images, especially the existence of a curve in the Δ-ε plane along which the energy, Berry phase and entropy all reach their special values. So it is available for detecting entanglement by applying Berry phase.

Berry phase in a two-atom Jaynes-Cummings model with Kerr medium

Energy Technology Data Exchange (ETDEWEB)

Bu Shenping; Zhang Guofeng; Liu Jia; Chen Ziyu [Department of Physics, School of Science, BeiHang University, Xueyuan Road, Beijing 100083 (China)], E-mail: chenzy@buaa.edu.cn

2008-12-15

The Jaynes-Cummings model (JCM) is an very important model for describing interaction between quantized electromagnetic fields and atoms in cavity quantum electrodynamics (QED). This model is generalized in many different directions since it predicts many novel quantum effects that can be verified by modern physics experimental technologies. In this paper, the Berry phase and entropy of the ground state for arbitrary photon number n of a two-atom Jaynes-Cummings model with Kerr-like medium are investigated. It is found that there is some correspondence between their images, especially the existence of a curve in the {delta}-{epsilon} plane along which the energy, Berry phase and entropy all reach their special values. So it is available for detecting entanglement by applying Berry phase.

A gas kinetic scheme for the Baer–Nunziato two-phase flow model

International Nuclear Information System (INIS)

Pan, Liang; Zhao, Guiping; Tian, Baolin; Wang, Shuanghu

2012-01-01

Numerical methods for the Baer–Nunziato (BN) two-phase flow model have attracted much attention in recent years. In this paper, we present a new gas kinetic scheme for the BN two-phase flow model containing non-conservative terms in the framework of finite volume method. In the view of microscopic aspect, a generalized Bhatnagar–Gross–Krook (BGK) model which matches with the BN model is constructed. Based on the integral solution of the generalized BGK model, we construct the distribution functions at the cell interface. Then numerical fluxes can be obtained by taking moments of the distribution functions, and non-conservative terms are explicitly introduced into the construction of numerical fluxes. In this method, not only the complex iterative process of exact solutions is avoided, but also the non-conservative terms included in the equation can be handled well.

A simple non-equilibrium, statistical-physics toy model of thin-film growth

International Nuclear Information System (INIS)

Ochab, Jeremi K; Nagel, Hannes; Janke, Wolfhard; Waclaw, Bartlomiej

2015-01-01

We present a simple non-equilibrium model of mass condensation with Lennard–Jones interactions between particles and the substrate. We show that when some number of particles is deposited onto the surface and the system is left to equilibrate, particles condense into an island if the density of particles becomes higher than some critical density. We illustrate this with numerically obtained phase diagrams for three-dimensional systems. We also solve a two-dimensional counterpart of this model analytically and show that not only the phase diagram but also the shape of the cross-sections of three-dimensional condensates qualitatively matches the two-dimensional predictions. Lastly, we show that when particles are being deposited with a constant rate, the system has two phases: a single condensate for low deposition rates, and multiple condensates for fast deposition. The behaviour of our model is thus similar to that of thin film growth processes, and in particular to Stranski–Krastanov growth. (paper)

Differential-discrete mathematical model of two phase flow heat exchanger

International Nuclear Information System (INIS)

Debeljkovic, D.Lj.; Zitek, Pavel; Simeunovic, G.; Inard, Christian

2007-01-01

A dynamic thermal-hydraulic mathematical model of evaporator dynamics of a once - through sub critical steam generator is derived and presented. This model allows the investigation of evaporator dynamics including its transients responses. The evaporator was considered as a part of three-section (economizer, evaporator and super-heater) model with time varying phase boundaries and is described by a set of linearized discrete - difference equations which, with some other algebraic equations, constitutes a closed system of equations possible for exact computer solution. This model has been derived upon the fundamental equations of mass, energy and momentum balance. For the first time, a discrete differential approach has been applied in order to investigate such complex, two phase processes. Namely, this approach allows one to escape from the model of this process usually described by a set of partial differential equations and enables one, using this method, to simulate evaporators dynamics in an extraordinarily simple way. In current literature this approach is sometimes called physical discretization. (author)

Bayesian hierarchical models for smoothing in two-phase studies, with application to small area estimation.

Science.gov (United States)

Ross, Michelle; Wakefield, Jon

2015-10-01

Two-phase study designs are appealing since they allow for the oversampling of rare sub-populations which improves efficiency. In this paper we describe a Bayesian hierarchical model for the analysis of two-phase data. Such a model is particularly appealing in a spatial setting in which random effects are introduced to model between-area variability. In such a situation, one may be interested in estimating regression coefficients or, in the context of small area estimation, in reconstructing the population totals by strata. The efficiency gains of the two-phase sampling scheme are compared to standard approaches using 2011 birth data from the research triangle area of North Carolina. We show that the proposed method can overcome small sample difficulties and improve on existing techniques. We conclude that the two-phase design is an attractive approach for small area estimation.

A Variational Model for Two-Phase Immiscible Electroosmotic Flow at Solid Surfaces

KAUST Repository

Shao, Sihong; Qian, Tiezheng

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

Phase transitions in two-dimensional uniformly frustrated XY models. I. antiferromagnetic model on a triangular lattice

International Nuclear Information System (INIS)

Korshunov, S.E.; Uimin, G.V.

1986-01-01

A most popular model in the family of two-dimensional uniformly-frustrated XY models is the antiferromagnetic model on a triangular lattice (AF XY(t) model). Its ground state is both continuously and twofold discretely degenerated. Different phase transitions possible in such systems are investigated. Relevant topological excitations are analyzed and a new class of such (vortices with a fractional number of circulation quanta) is discovered. Their role in determining the properties of the system proves itself essential. The characteristics of phase transitions related to breaking of discrete and continuous symmetries change. The phase diagram of the ''generalized'' AF XY(t) model is constructed. The results obtained are rederived in the representation of the Coulomb gas with half-interger charges, equivalent to the AF XY(t) model with the Berezinskii-Villain interaction

Modeling of Two-Phase Flow in Rough-Walled Fracture Using Level Set Method

Directory of Open Access Journals (Sweden)

Yunfeng Dai

2017-01-01

Full Text Available To describe accurately the flow characteristic of fracture scale displacements of immiscible fluids, an incompressible two-phase (crude oil and water flow model incorporating interfacial forces and nonzero contact angles is developed. The roughness of the two-dimensional synthetic rough-walled fractures is controlled with different fractal dimension parameters. Described by the Navier–Stokes equations, the moving interface between crude oil and water is tracked using level set method. The method accounts for differences in densities and viscosities of crude oil and water and includes the effect of interfacial force. The wettability of the rough fracture wall is taken into account by defining the contact angle and slip length. The curve of the invasion pressure-water volume fraction is generated by modeling two-phase flow during a sudden drainage. The volume fraction of water restricted in the rough-walled fracture is calculated by integrating the water volume and dividing by the total cavity volume of the fracture while the two-phase flow is quasistatic. The effect of invasion pressure of crude oil, roughness of fracture wall, and wettability of the wall on two-phase flow in rough-walled fracture is evaluated.

Interfacial shear modeling in two-phase annular flow

International Nuclear Information System (INIS)

Kumar, R.; Edwards, D.P.

1996-11-01

A new interfacial shear stress model called the law of the interface model, based on the law of the wall approach in turbulent flows, has been developed and locally applied in a fully developed, adiabatic, two-phase annular flow in a duct. Numerical results have been obtained using this model in conjunction with other models available in the literature that are required for the closure of the continuity and momentum equations. These results have been compared with droplet velocity data (using laser Doppler velocimetry and hot film anemometry), void fraction data (using gamma densitometry) and pressure drop data obtained in a R-134A refrigerant test facility. Droplet velocity results match the experimental data well, however, the prediction of the void fraction is less accurate. The poor prediction of void fraction, especially for the low void fraction cases, appears to be due to the lack of a good mechanistic model for entrainment

Interfacial shear modeling in two-phase annular flow

International Nuclear Information System (INIS)

Kumar, R.; Edwards, D.P.

1996-07-01

A new interfacial shear stress model called the law of the interface model, based on the law of the wall approach in turbulent flows, has been developed and locally applied in a fully developed, adiabatic, two-phase annular flow in a duct. Numerical results have been obtained using this model in conjunction with other models available in the literature that are required for the closure of the continuity and momentum equations. These results have been compared with droplet velocity data (using laser Doppler velocimetry and hot film anemometry), void fraction data (using gamma densitometry) and pressure drop data obtained in a R-134A refrigerant test facility. Droplet velocity results match the experimental data well, however, the prediction of the void fraction is less accurate. The poor prediction of void fraction, especially for the low void fraction cases, appears to be due to the lack of a good mechanistic model for entrainment

Validation of NEPTUNE-CFD two-phase flow models using experimental data

International Nuclear Information System (INIS)

Perez-Manes, Jorge; Sanchez Espinoza, Victor Hugo; Bottcher, Michael; Stieglitz, Robert; Sergio Chiva Vicent

2014-01-01

This paper deals with the validation of the two-phase flow models of the CFD code NEPTUNE-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. (authors)

Two Phase Flow Split Model for Parallel Channels | Iloeje | Nigerian ...

African Journals Online (AJOL)

The model and code are capable of handling single and two phase flows, steady states and transients, up to ten parallel flow paths, simple and complicated geometries, including the boilers of fossil steam generators and nuclear power plants. A test calculation has been made with a simplified three-channel system ...

Molecular analysis of bacterial microbiota associated with oysters (Crassostrea gigas and Crassostrea corteziensis) in different growth phases at two cultivation sites.

Science.gov (United States)

Trabal, Natalia; Mazón-Suástegui, José M; Vázquez-Juárez, Ricardo; Asencio-Valle, Felipe; Morales-Bojórquez, Enrique; Romero, Jaime

2012-08-01

Microbiota presumably plays an essential role in inhibiting pathogen colonization and in the maintenance of health in oysters, but limited data exist concerning their different growth phases and conditions. We analyzed the bacterial microbiota composition of two commercial oysters: Crassostrea gigas and Crassostrea corteziensis. Differences in microbiota were assayed in three growth phases: post-larvae at the hatchery, juvenile, and adult at two grow-out cultivation sites. Variations in the microbiota were assessed by PCR analysis of the 16S rRNA gene in DNA extracted from depurated oysters. Restriction fragment length polymorphism (RFLP) profiles were studied using Dice's similarity coefficient (Cs) and statistical principal component analysis (PCA). The microbiota composition was determined by sequencing temperature gradient gel electrophoresis (TGGE) bands. The RFLP analysis of post-larvae revealed homology in the microbiota of both oyster species (Cs > 88 %). Dice and PCA analyses of C. corteziensis but not C. gigas showed differences in the microbiota according to the cultivation sites. The sequencing analysis revealed low bacterial diversity (primarily β-Proteobacteria, Firmicutes, and Spirochaetes), with Burkholderia cepacia being the most abundant bacteria in both oyster species. This study provides the first description of the microbiota in C. corteziensis, which was shown to be influenced by cultivation site conditions. During early growth, we observed that B. cepacia colonized and remained strongly associated with the two oysters, probably in a symbiotic host-bacteria relationship. This association was maintained in the three growth phases and was not altered by environmental conditions or the management of the oysters at the grow-out site.

Coupling two-phase fluid flow with two-phase darcy flow in anisotropic porous media

KAUST Repository

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.

Coupling Two-Phase Fluid Flow with Two-Phase Darcy Flow in Anisotropic Porous Media

Directory of Open Access Journals (Sweden)

Jie Chen

2014-06-01

Full Text Available 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.

Magnetic islands modelled by a phase-field-crystal approach

Science.gov (United States)

Faghihi, Niloufar; Mkhonta, Simiso; Elder, Ken R.; Grant, Martin

2018-03-01

Using a minimal model based on the phase-field-crystal formalism, we study the coupling between the density and magnetization in ferromagnetic solids. Analytical calculations for the square phase in two dimensions are presented and the small deformation properties of the system are examined. Furthermore, numerical simulations are conducted to study the influence of an external magnetic field on various phase transitions, the anisotropic properties of the free energy functional, and the scaling behaviour of the growth of the magnetic domains in a crystalline solid. It is shown that the energy of the system can depend on the direction of the magnetic moments, with respect to the crystalline direction. Furthermore, the growth of the magnetic domains in a crystalline solid is studied and is shown that the growth of domains is in agreement with expected behaviour.

Numerical simulation of transient, adiabatic, two-dimensional two-phase flow using the two-fluid model

International Nuclear Information System (INIS)

Neves Conti, T. das.

1983-01-01

A numerical method is developed to simulate adiabatic, transient, two-dimensional two-phase flow. The two-fluid model is used to obtain the mass and momentum conservation equations. These are solved by an iterative algorithm emphoying a time-marching scheme. Based on the corrective procedure of Hirt and Harlow a poisson equation is derived for the pressure field. This equation is finite-differenced and solved by a suitable matrix inversion technique. In the absence of experiment results several numerical tests were made in order to chec accuracy, convergence and stability of the proposed method. Several tests were also performed to check whether the behavior of void fraction and phasic velocities conforms with previous observations. (Author) [pt

Liquid phase electro epitaxy growth kinetics of GaAs-A three-dimensional numerical simulation study

International Nuclear Information System (INIS)

Mouleeswaran, D.; Dhanasekaran, R.

2006-01-01

A three-dimensional numerical simulation study for the liquid phase electro epitaxial growth kinetic of GaAs is presented. The kinetic model is constructed considering (i) the diffusive and convective mass transport, (ii) the heat transfer due to thermoelectric effects such as Peltier effect, Joule effect and Thomson effect, (iii) the electric current distribution with electromigration and (iv) the fluid flow coupled with concentration and temperature fields. The simulations are performed for two configurations namely (i) epitaxial growth from the arsenic saturated gallium rich growth solution, i.e., limited solution model and (ii) epitaxial growth from the arsenic saturated gallium rich growth solution with polycrystalline GaAs feed. The governing equations of liquid phase electro epitaxy are solved numerically with appropriate initial and boundary conditions using the central difference method. Simulations are performed to determine the following, a concentration profiles of solute atoms (As) in the Ga-rich growth solution, shape of the substrate evolution, the growth rate of the GaAs epitaxial film, the contributions of Peltier effect and electromigration of solute atoms to the growth with various experimental growth conditions. The growth rate is found to increase with increasing growth temperature and applied current density. The results are discussed in detail

Modelling nonstationary thermohydrodynamic processes in heat-exchange circuits with a two-phase coolant

International Nuclear Information System (INIS)

Blinkov, V.N.

1993-01-01

This paper presents a mathematical model and a open-quotes fastclose quotes computer program for analyzing nonstationary thermohydrodynamic processes in distributed multi-element circuits containing a two-phase coolant. The author's approach is based on representing the distributed multi-element circuits with the two-phase coolant (such as cooling circuits of the reactor of an atomic power station) in the form of equivalent thermohydrodynamic chains composed of idealized elements with the intrinsic properties of the structure elements of real systems. The author has developed the nomenclature of such conceptual elements for objects which can be modelled; the nomenclature encompasses the control volumes (with a single-phase or two-phase coolant or a moving boundary of boiling/condensation) and the branch lines (type of tube and connections in dependence on the inertia of the coolant being taken into account) for a hydrodynamic submodel and the thermal components and lines for a thermal submodel. The mathematical models which have been developed and the program using them are designated for various forms of calculating slow thermohydrodynamic processes in multi-element coolant circuits in reactors and modeling test stands. The program facilitates calculation of the range of stable operation, detailed studies of stationary and nonstationary modes of operation, and forecasts of effective engineering measures to obtain stability with the aid of microcomputers

Growth models fitted to Dipturus chilensis length-at-age-data support a two phase growth Modelos de crecimiento ajustados a datos de largo a la edad de Dipturus chilensis confirman un crecimiento en dos fases

Directory of Open Access Journals (Sweden)

MARINA I AVERSA

2011-03-01

Full Text Available Age and growth for the beaked skate was estimated from bands in the vertebral centra of 689 individuals obtained from incidental catches of the Argentine hake (Merluccius hubbsi fishery. Age bias plots and indices of precision indicated that ageing method was precise and unbiased (% CV = 3 % PA = 82.09 %. Edge and marginal increment analysis of the vertebrae support the hypothesis of annual band pair deposition. Three growth models were fitted to length-at-age and the two-phase growth model produced the best fit. This feature has never been described before for D. chilensis and can be related to changes in energy allocation and the shift from juvenile to adult phase. The unrealistic biological estimates of the von Bertalanffy growth model illustrates the importance of fitting alternative models to the data. Female beaked skates reached greater size in length (L∝ as well as in disc width (L∝ = 138.2 cm; DW∝ = 92.46 cm and have lower growth rate (k = 0.08 yr-1 than males (L∝ = 106.7 cm; DW∝ = 74.52 cm; k = 0.121 yr-1. This study provides basic information on age and growth for the beaked skate, D. chilensis, which were previously not available for its south Atlantic range of distribution.La edad y el crecimiento de la raya picuda fue estimado a partir de las bandas en los cuerpos vertebrales de 689 individuos obtenidos de las capturas incidentales de la pesquería de merluza argentina (Merluccius hubbsi. Gráficos de sesgos y el análisis de precisión indicaron que el método utilizado para la determinación de la edad es preciso y no sesgado (% CV = 3 % PA = 82.09 %. El análisis del tipo de borde e incremento marginal vertebral confirmó la hipótesis del depósito anual de un par de bandas. Se ajustaron tres modelos de crecimiento a los datos de largo a la edad y el modelo de dos fases produjo el mejor ajuste. Esta característica nunca antes fue descripta para Dipturus chilensis y podría relacionarse con un cambio en la cuota de

Phase-Field Modeling of Sigma-Phase Precipitation in 25Cr7Ni4Mo Duplex Stainless Steel

Science.gov (United States)

Malik, Amer; Odqvist, Joakim; Höglund, Lars; Hertzman, Staffan; Ågren, John

2017-10-01

Phase-field modeling is used to simulate the formation of sigma phase in a model alloy mimicking a commercial super duplex stainless steel (SDSS) alloy, in order to study precipitation and growth of sigma phase under linear continuous cooling. The so-called Warren-Boettinger-McFadden (WBM) model is used to build the basis of the multiphase and multicomponent phase-field model. The thermodynamic inconsistency at the multiple junctions associated with the multiphase formulation of the WBM model is resolved by means of a numerical Cut-off algorithm. To make realistic simulations, all the kinetic and the thermodynamic quantities are derived from the CALPHAD databases at each numerical time step, using Thermo-Calc and TQ-Interface. The credibility of the phase-field model is verified by comparing the results from the phase-field simulations with the corresponding DICTRA simulations and also with the empirical data. 2D phase-field simulations are performed for three different cooling rates in two different initial microstructures. A simple model for the nucleation of sigma phase is also implemented in the first case. Simulation results show that the precipitation of sigma phase is characterized by the accumulation of Cr and Mo at the austenite-ferrite and the ferrite-ferrite boundaries. Moreover, it is observed that a slow cooling rate promotes the growth of sigma phase, while a higher cooling rate restricts it, eventually preserving the duplex structure in the SDSS alloy. Results from the phase-field simulations are also compared quantitatively with the experiments, performed on a commercial 2507 SDSS alloy. It is found that overall, the predicted morphological features of the transformation and the composition profiles show good conformity with the empirical data.

Numerical predictions of particle dispersed two-phase flows, using the LSD and SSF models

International Nuclear Information System (INIS)

Avila, R.; Cervantes de Gortari, J.; Universidad Nacional Autonoma de Mexico, Mexico City. Facultad de Ingenieria)

1988-01-01

A modified version of a numerical scheme which is suitable to predict parabolic dispersed two-phase flow, is presented. The original version of this scheme was used to predict the test cases discussed during the 3rd workshop on TPF predictions in Belgrade, 1986. In this paper, two particle dispersion models are included which use the Lagrangian approach predicting test case 1 and 3 of the 4th workshop. For the prediction of test case 1 the Lagrangian Stochastic Deterministic model (LSD) is used providing acceptable good results of mean and turbulent quantities for both solid and gas phases; however, the computed void fraction distribution is not in agreement with the measurements at locations away from the inlet, especially near the walls. Test case 3 is predicted using both the LSD and the Stochastic Separated Flow (SSF) models. It was found that the effects of turbulence modulation are large when the LSD model is used, whereas the particles have a negligible influence on the continuous phase if the SSF model is utilized for the computations. Predictions of gas phase properties based on both models agree well with measurements; however, the agreement between calculated and measured solid phase properties is less satisfactory. (orig.)

Analysis of phase dynamics in two-phase flow using latticegas automata

International Nuclear Information System (INIS)

Ohashi, H.; Hashimoto, Y.; Tsumaya, A.; Chen, Y.; Akiyama, M.

1998-01-01

In this paper, we describe lattice gas automaton models appropriate for two-phase flow simulation and their applications to study various phase dynamics of two-fluid mixtures. Several algorithms are added to the original immiscible Lattice Gas model to adjust surface tension and to introduce density difference between two fluids. Surface tension is controlled by the collision rules an difference in density is due to nonlocal forces between automaton particles. We simulate the relative motion of the dispersed phase in another continuous fluid. Deformation and disintegration of rising drops are reproduced. The interaction between multiple drops is also observed in calculations. Furutre, we obtain the transition of the two-phase flow pattern from bubbly, slug to annular flow. Density difference of two phase is one of the key ingredients to generate the annular flow pattern

Turbulence-induced bubble collision force modeling and validation in adiabatic two-phase flow using CFD

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

Viscous Growth in Spinodal Decomposition of the Two-component Lennard-Jones Model in Two Dimensions

DEFF Research Database (Denmark)

Laradji, M.; Toxvaerd, S.; Mouritsen, Ole G.

1997-01-01

The dynamics of phase separation of a two-component Lennard-Jones model in three dimensions is investigated by means of large scale molecular dynamics simulation. A systematic study over a wide range of quench temperatures within the coexistence region shows that the binary system reaches...

Regularized lattice Boltzmann model for immiscible two-phase flows with power-law rheology

Science.gov (United States)

Ba, Yan; Wang, Ningning; Liu, Haihu; Li, Qiang; He, Guoqiang

2018-03-01

In this work, a regularized lattice Boltzmann color-gradient model is developed for the simulation of immiscible two-phase flows with power-law rheology. This model is as simple as the Bhatnagar-Gross-Krook (BGK) color-gradient model except that an additional regularization step is introduced prior to the collision step. In the regularization step, the pseudo-inverse method is adopted as an alternative solution for the nonequilibrium part of the total distribution function, and it can be easily extended to other discrete velocity models no matter whether a forcing term is considered or not. The obtained expressions for the nonequilibrium part are merely related to macroscopic variables and velocity gradients that can be evaluated locally. Several numerical examples, including the single-phase and two-phase layered power-law fluid flows between two parallel plates, and the droplet deformation and breakup in a simple shear flow, are conducted to test the capability and accuracy of the proposed color-gradient model. Results show that the present model is more stable and accurate than the BGK color-gradient model for power-law fluids with a wide range of power-law indices. Compared to its multiple-relaxation-time counterpart, the present model can increase the computing efficiency by around 15%, while keeping the same accuracy and stability. Also, the present model is found to be capable of reasonably predicting the critical capillary number of droplet breakup.

Phase-Field Modeling of Polycrystalline Solidification: From Needle Crystals to Spherulites—A Review

Science.gov (United States)

Gránásy, László; Rátkai, László; Szállás, Attila; Korbuly, Bálint; Tóth, Gyula I.; Környei, László; Pusztai, Tamás

2014-04-01

Advances in the orientation-field-based phase-field (PF) models made in the past are reviewed. The models applied incorporate homogeneous and heterogeneous nucleation of growth centers and several mechanisms to form new grains at the perimeter of growing crystals, a phenomenon termed growth front nucleation. Examples for PF modeling of such complex polycrystalline structures are shown as impinging symmetric dendrites, polycrystalline growth forms (ranging from disordered dendrites to spherulitic patterns), and various eutectic structures, including spiraling two-phase dendrites. Simulations exploring possible control of solidification patterns in thin films via external fields, confined geometry, particle additives, scratching/piercing the films, etc. are also displayed. Advantages, problems, and possible solutions associated with quantitative PF simulations are discussed briefly.

Review of mathematical and physical basis of two-phase flow modelling

International Nuclear Information System (INIS)

Bottoni, M.; Sengpiel, W.

1992-08-01

Starting from a continuum-mechanical approach, this report gives a detailed overview of the deduction of conservation equations for the analytical description of two-phase flows by means of an adequate averaging process resulting in a two-fluid model and a homogeneous mixture model. The mathematical process of averaging leads to macroscopic formulations of stress terms and interfacial interaction terms. These terms depend on microscopic variables and thus give some helpful insight into the physical processes which have to be described by constitutive relations. (orig.) [de

Guidelines for the formulation of Lagrangian stochastic models for particle simulations of single-phase and dispersed two-phase turbulent flows

Science.gov (United States)

Minier, Jean-Pierre; Chibbaro, Sergio; Pope, Stephen B.

2014-11-01

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

Guidelines for the formulation of Lagrangian stochastic models for particle simulations of single-phase and dispersed two-phase turbulent flows

International Nuclear Information System (INIS)

Minier, Jean-Pierre; Chibbaro, Sergio; Pope, Stephen B.

2014-01-01

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

Seabrook simulator model upgrade: Implementation and validation of two-phase, nonequilibrium RCS and steam generator models

International Nuclear Information System (INIS)

Kao, S.

1990-01-01

A number of deficiencies in the original RCS and steam generator models on the Seabrook simulator were found to give unrealistic results under some off-normal and accident conditions. These deficiencies are attributed to the simplistic assumptions used in the original models, such as the homogeneous, equilibrium equations used in the pressurizer and steam generator models, and the single-phase flow model used in the RCS thermal-hydraulic model. To improve the fidelity of the simulator, efforts have been made to upgrade the RCS and steam generator models to include two-phase, nonequilibrium features. In the new RCS model, the following major assumptions are used to derive the finite difference form of the conservation equations: a donor-cell differencing scheme is adopted to allow flow reversal; a single pressure is used to evaluate properties; a single mass flow rate is assumed in each loop; enthalpy is assumed to vary linearly within each control volume; a homogeneous flow is assumed under two-phase conditions. The pressurizer is divided into a vapor region and a liquid region, each of which is represented by a set of mass and energy conservation equations. Interfacial mass and energy exchange mechanisms (condensation and flashing), thermal interactions between the vessel and fluids, and thermal nonequilibrium between the phases are included in the pressurizer model. The steam generator is divided into the vapor dome, riser, and downcomer regions. The assumptions applied are similar to those of the RCS and pressurizer models. A momentum model is incorporated to calculate the recirculation flow and simulate the downcomer level shrink/swell phenomenon. The new RCS and steam generator models are validated by comparing the simulator calculations against sister plant data and FSAR vendor analysis. The results show the new models give realistic and reliable calculations under off-normal and accident conditions

Two-phase modeling of DDT: Structure of the velocity-relaxation zone

International Nuclear Information System (INIS)

Kapila, A.K.; Son, S.F.; Bdzil, J.B.; Menikoff, R.; Stewart, D.S.

1997-01-01

The structure of the velocity relaxation zone in a hyperbolic, nonconservative, two-phase model is examined in the limit of large drag, and in the context of the problem of deflagration-to-detonation transition in a granular explosive. The primary motivation for the study is the desire to relate the end states across the relaxation zone, which can then be treated as a discontinuity in a reduced, equivelocity model, that is computationally more efficient than its parent. In contrast to a conservative system, where end states across thin zones of rapid variation are determined principally by algebraic statements of conservation, the nonconservative character of the present system requires an explicit consideration of the structure. Starting with the minimum admissible wave speed, the structure is mapped out as the wave speed increases. Several critical wave speeds corresponding to changes in the structure are identified. The archetypal structure is partly dispersed, monotonic, and involves conventional hydrodynamic shocks in one or both phases. The picture is reminiscent of, but more complex than, what is observed in such (simpler) two-phase media as a dusty gas. copyright 1997 American Institute of Physics

Experimental Study about Two-phase Damping Ratio on a Tube Bundle Subjected to Homogeneous Two-phase Flow

Energy Technology Data Exchange (ETDEWEB)

Sim, Woo Gun; Dagdan, Banzragch [Hannam Univ., Daejeon (Korea, Republic of)

2017-03-15

Two-phase cross flow exists in many shell-and-tube heat exchangers such as condensers, evaporators, and nuclear steam generators. The drag force acting on a tube bundle subjected to air/water flow is evaluated experimentally. The cylinders subjected to two-phase flow are arranged in a normal square array. The ratio of pitch to diameter is 1.35, and the diameter of the cylinder is 18 mm. The drag force along the flow direction on the tube bundles is measured to calculate the drag coefficient and the two-phase damping ratio. The two-phase damping ratios, given by the analytical model for a homogeneous two-phase flow, are compared with experimental results. The correlation factor between the frictional pressure drop and the hydraulic drag coefficient is determined from the experimental results. The factor is used to calculate the drag force analytically. It is found that with an increase in the mass flux, the drag force, and the drag coefficients are close to the results given by the homogeneous model. The result shows that the damping ratio can be calculated using the homogeneous model for bubbly flow of sufficiently large mass flux.

Numerical modeling of two-phase binary fluid mixing using mixed finite elements

KAUST Repository

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.

Phase-field modeling of microstructural pattern formation during directional solidification of peritectic alloys without morphological instability

International Nuclear Information System (INIS)

Shing Lo, Tak; Karma, Alain; Plapp, Mathis

2001-01-01

During the directional solidification of peritectic alloys, two stable solid phases (parent and peritectic) grow competitively into a metastable liquid phase of larger impurity content than either solid phase. When the parent or both solid phases are morphologically unstable, i.e., for a small temperature gradient/growth rate ratio (G/v p ), one solid phase usually outgrows and covers the other phase, leading to a cellular-dendritic array structure closely analogous to the one formed during monophase solidification of a dilute binary alloy. In contrast, when G/v p is large enough for both phases to be morphologically stable, the formation of the microstructure becomes controlled by a subtle interplay between the nucleation and growth of the two solid phases. The structures that have been observed in this regime (in small samples where convection effects are suppressed) include alternate layers (bands) of the parent and peritectic phases perpendicular to the growth direction, which are formed by alternate nucleation and lateral spreading of one phase onto the other as proposed in a recent model [R. Trivedi, Metall. Mater. Trans. A 26, 1 (1995)], as well as partially filled bands (islands), where the peritectic phase does not fully cover the parent phase which grows continuously. We develop a phase-field model of peritectic solidification that incorporates nucleation processes in order to explore the formation of these structures. Simulations of this model shed light on the morphology transition from islands to bands, the dynamics of spreading of the peritectic phase on the parent phase following nucleation, which turns out to be characterized by a remarkably constant acceleration, and the types of growth morphology that one might expect to observe in large samples under purely diffusive growth conditions

A turbulent two-phase flow model for nebula flows

International Nuclear Information System (INIS)

Champney, J.M.; Cuzzi, J.N.

1990-01-01

A new and very efficient turbulent two-phase flow numericaly model is described to analyze the environment of a protoplanetary nebula at a stage prior to the formation of planets. Focus is on settling processes of dust particles in flattened gaseous nebulae. The model employs a perturbation technique to improve the accuracy of the numerical simulations of such flows where small variations of physical quantities occur over large distance ranges. The particles are allowed to be diffused by gas turbulence in addition to settling under gravity. Their diffusion coefficients is related to the gas turbulent viscosity by the non-dimensional Schmidt number. The gas turbulent viscosity is determined by the means of the eddy viscosity hypothesis that assumes the Reynolds stress tensor proportional to the mean strain rate tensor. Zero- and two-equation turbulence models are employed. Modeling assumptions are detailed and discussed. The numerical model is shown to reproduce an existing analytical solution for the settling process of particles in an inviscid nebula. Results of nebula flows are presented taking into account turbulence effects of nebula flows. Diffusion processes are found to control the settling of particles. 24 refs

Challenges in modeling unstable two-phase flow experiments in porous micromodels

Science.gov (United States)

Meheust, Y.; Ferrari, A.; Jimenez-Martinez, J.; Le Borgne, T.; Lunati, I.

2014-12-01

The simulation of unstable invasion patterns in porous media flow is challenging since small perturbations tend to grow in time, so that slight differences in geometry or initial conditions potentially give rise to significantly different solutions. Here we present a detailed comparison of pore scale simulations and experiments of unstable primary drainage in porous micromodels. The porous medium consists of a Hele-Shaw cell containing cylindrical obstacles. Two experimental flow cells have been constructed by soft lithography, with different degrees of heterogeneity in the grain size distribution. To model two-phase flow at the pore scale, we solve Navier-Stokes equations for mass and momentum conservation in the discretized pore space and employ the Volume of Fluid (VOF) method to track the evolution of the interface. During drainage, if the defending fluid is the most viscous, viscous forces destabilize the interface, giving rise to the formation of preferential flow paths, in the form of a branched fingering structure. We test different numerical models (a 2D vertical integrated model and a full 3D model) and different initial conditions, studying their impact on the simulated spatial distributions of the fluid phases. Although due to the unstable nature of the invasion, small discrepancies between the experimental setup and the numerical model can result in different fluids patterns (see figure), simulations show a satisfactory agreement with the structures observed experimentally. To estimate the ability of the numerical approach to reproduce unstable displacement, we compare several quantities in both the statistical and deterministic sense. We demonstrate the impact of three main sources of uncertainty : i) the uncertainty on the pore space geometry, ii) the interface initialization and ii) three dimensional effects [1]. Simulations in weakly heterogeneous geometries are found to be more challenging because uncertainties on pore neck widths are on the same

Numerical calculation of two-phase turbulent jets

Energy Technology Data Exchange (ETDEWEB)

Saif, A.A.

1995-05-01

Two-phase turbulent round jets were numerically simulated using a multidimensional two-phase CFD code based on the two-fluid model. The turbulence phenomena were treated with the standard k-{epsilon} model. It was modified to take into account the additional dissipation of turbulent kinetic energy by the dispersed phase. Within the context of the two-fluid model it is more appropriate and physically justified to treat the diffusion by an interfacial force in the momentum equation. In this work, the diffusion force and the additional dissipation effect by the dispersed phase were modeled starting from the classical turbulent energy spectrum analysis. A cut-off frequency was proposed to decrease the dissipation effect by the dispersed phase when large size particles are introduced in the flow. The cut-off frequency combined with the bubble-induced turbulence effect allows for an increase in turbulence for large particles. Additional care was taken in choosing the right kind of experimental data from the literature so that a good separate effect test was possible for their models. The models predicted the experimental data very closely and they were general enough to predict extreme limit cases: water-bubble and air-droplet jets.

Numerical simulation of the two-phase flows in a hydraulic coupling by solving VOF model

International Nuclear Information System (INIS)

Luo, Y; Zuo, Z G; Liu, S H; Fan, H G; Zhuge, W L

2013-01-01

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–ε 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

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.

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)

Generalization of two-phase model with topology microstructure of mixture to Lagrange-Euler methodology

International Nuclear Information System (INIS)

Vladimir V Chudanov; Alexei A Leonov

2005-01-01

Full text of publication follows: One of the mathematical models (hyperbolic type) for describing evolution of compressible two-phase mixtures was offered in [1] to deal with the following applications: interfaces between compressible materials; shock waves in multiphase mixtures; evolution of homogeneous two-phase flows; cavitation in liquids. The basic difficulties of this model was connected to discretization of the non-conservative equation terms. As result, the class of problems concerned with passage of shock waves through fields with a discontinuing profile of a volume fraction was not described by means of this model. A class of schemes that are able to converge to the correct solution of such problems was received in [2] due to a deeper analysis of two-phase model. The technique offered in [2] was implemented on a Eulerian grid via the Godunov scheme. In present paper the additional analysis of two-phase model in view of microstructure of an mixture topology is carried out in Lagrange mass coordinates. As result, the equations averaged over the set of all possible realizations for two-phase mixture are received. The numerical solution is carried out with use of PPM method [3] in two steps: at first - the equations averaged over mass variable are solved; on the second - the solution, found on the previous step, is re-mapped to a fixed Eulerian grid. Such approach allows to expand the proposed technique on two-dimensional (three-dimensional) case, as in the Lagrange variables the Euler equations system is split on two (three) identical subsystems, each of which describes evolution of considered medium in the given direction. The accuracy and robustness of the described procedure are demonstrated on a sequence of the numerical problems. References: (1). R. Saurel, R. Abgrall, A multiphase Godunov method for compressible multi-fluid and multiphase flows, J. Comput. Phys. 150 (1999) 425-467; (2). R. Saurel, R. Abgrall, Discrete equations for physical and

A theoretical model for measuring mass flowrate and quality of two phase flow by the noise of throttling set

International Nuclear Information System (INIS)

Tong Yunxian; Wang Wenran

1992-03-01

The mass flowrate and steam quality measuring of two phase flowrate is an essential issue in the tests of loss-of-coolant accident (LOCA). The spatial stochastic distribution of phase concentration would cause a differential pressure noise when two phase flow is crossing a throttling set. Under the assumption of that the variance of disperse phase concentration is proportional to its mean phase concentration and by using the separated flow model of two phase flow, it has demonstrated that the variance of noise of differential pressure square root is approximately proportional to the flowrate of disperse phase. Thus, a theoretical model for measuring mass flowrate and quality of two phase flow by noise measurement is developed. It indicates that there is a possibility to measure two phase flowrate and steam quality by using the simple theoretical model and a single throttling set

Two-phase flow modeling in the rod bundle subchannel analysis

International Nuclear Information System (INIS)

Hisashi, Ninokata

2006-01-01

In order to practice a design-by-analysis of thermohydraulics design of BWR fuel rod bundles, the subchannel analysis would play a major role. There, the immediate concern is improvement in its predictive capability of CHF due in particular to the film dryout (boiling transition phenomena: BT) on the fuel rod surface. Constitutive equations in the subchannel analysis formulation are responsible for the quality of calculated results. The constitutive equations are a result of integration of the local and instantaneous description of two-phase flows over the subchannel control volume. In general, they are expressed in terms of subchannel-control-volume- as well as area-averaged two-phase flow state variables. In principle the information on local and instantaneous physical phenomena taking place inside subchannels must be counted for in the algebraic form of the equations on the basis of a more mechanistic modeling approach. They should include also influences of the multi-dimensional subchannel geometry and fluid material properties. Thermohydraulics phenomena of interests in this deed are: 1) vapor-liquid re-distribution by inter-subchannel exchanges due to the diversion cross flow, turbulent mixing and void drift, 2) liquid film behaviors, 3) transition of two-phase flow regimes, 4) droplet entrainment and deposition and 5) spacer-droplet interactions. These are considered to be five key factors in understanding the BT in BWR fuel rod bundles. In Japan, a university-industry consortium has been formed under the sponsorship of the Ministry of Economics, Trade and Industry. This paper describes an outline of the on-going project and, first, an outline of the current efforts is presented in developing a new two-fluid three field subchannel code NASCA being aimed at predicting onset of BT, and post BT phenomena in advanced BWR fuel rod bundles including those of the tight lattice configuration for a higher conversion. Then the current methodology adopted to improve

Two-phase flow modeling in the rod bundle subchannel analysis

International Nuclear Information System (INIS)

Hisashi, Ninokata

2004-01-01

Full text of publication follows:In order to practice a design-by-analysis of thermohydraulics design of BWR fuel rod bundles, the subchannel analysis would play a major role. There, the immediate concern is improvement in its predictive capability of CHF due in particular to the film dryout (boiling transition phenomena: BT) on the fuel rod surface. Constitutive equations in the subchannel analysis formulation are responsible for the quality of calculated results. The constitutive equations are a result of integration of the local and instantaneous description of two-phase flows over the subchannel control volume. In general, they are expressed in terms of subchannel-control-volume- as well as area-averaged two-phase flow state variables. In principle the information on local and instantaneous physical phenomena taking place inside subchannels must be counted for in the algebraic form of the equations on the basis of a more mechanistic modeling approach. They should include also influences of the multi-dimensional subchannel geometry and fluid material properties. Thermohydraulics phenomena of interests in this deed are: 1) vapor-liquid re-distribution by inter-subchannel exchanges due to the diversion cross flow, turbulent mixing and void drift, 2) liquid film behaviors, 3) transition of two-phase flow regimes, 4) droplet entrainment and deposition and 5) spacer-droplet interactions. These are considered to be five key factors in understanding the BT in BWR fuel rod bundles. In Japan, a university-industry consortium has been formed under the sponsorship of the Ministry of Economics, Trade and Industry. This paper describes an outline of the on-going project and, first, an outline of the current efforts is presented in developing a new two-fluid three field subchannel code NASCA being aimed at predicting onset of BT, and post BT phenomena in advanced BWR fuel rod bundles including those of the tight lattice configuration for a higher conversion. Then the current

Monte Carlo study of the phase diagram for the two-dimensional Z(4) model

International Nuclear Information System (INIS)

Carneiro, G.M.; Pol, M.E.; Zagury, N.

1982-05-01

The phase diagram of the two-dimensional Z(4) model on a square lattice is determined using a Monte Carlo method. The results of this simulation confirm the general features of the phase diagram predicted theoretically for the ferromagnetic case, and show the existence of a new phase with perpendicular order. (Author) [pt

A Two-Phase Solid/Fluid Model for Dense Granular Flows Including Dilatancy Effects

Science.gov (United States)

Mangeney, Anne; Bouchut, Francois; Fernandez-Nieto, Enrique; Narbona-Reina, Gladys

2015-04-01

We propose a thin layer depth-averaged two-phase model to describe solid-fluid mixtures such as debris flows. It describes the velocity of the two phases, the compression/dilatation of the granular media and its interaction with the pore fluid pressure, that itself modifies the friction within the granular phase (Iverson et al., 2010). 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., 2014). In particular, Pitman and Le 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 equations. We close the mixture equations by a weak compressibility relation involving a critical density, or equivalently a critical pressure. Moreover, we relax one boundary condition, making it possible for the fluid to escape the granular media when compression of the granular mass occurs. Furthermore, we introduce second order terms in the equations making it possible to describe the evolution of the pore fluid pressure in response to the compression/dilatation of the granular mass without prescribing an extra ad-hoc equation for the pore pressure. We prove that the energy balance associated with this Jackson closure is dissipative, as well as its thin layer associated model. We present several numerical tests for the 1D case that are compared to the

Thermo-fluid dynamics of two-phase flow

CERN Document Server

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.

Cellular Automaton Modeling of Dendritic Growth Using a Multi-grid Method

International Nuclear Information System (INIS)

Natsume, Y; Ohsasa, K

2015-01-01

A two-dimensional cellular automaton model with a multi-grid method was developed to simulate dendritic growth. In the present model, we used a triple-grid system for temperature, solute concentration and solid fraction fields as a new approach of the multi-grid method. In order to evaluate the validity of the present model, we carried out simulations of single dendritic growth, secondary dendrite arm growth, multi-columnar dendritic growth and multi-equiaxed dendritic growth. From the results of the grid dependency from the simulation of single dendritic growth, we confirmed that the larger grid can be used in the simulation and that the computational time can be reduced dramatically. In the simulation of secondary dendrite arm growth, the results from the present model were in good agreement with the experimental data and the simulated results from a phase-field model. Thus, the present model can quantitatively simulate dendritic growth. From the simulated results of multi-columnar and multi-equiaxed dendrites, we confirmed that the present model can perform simulations under practical solidification conditions. (paper)

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)

The difficult challenge of a two-phase CFD modelling for all flow regimes

International Nuclear Information System (INIS)

Bestion, D.

2014-01-01

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

Scalable solution-phase epitaxial growth of symmetry-mismatched heterostructures on two-dimensional crystal soft template.

Science.gov (United States)

Lin, Zhaoyang; Yin, Anxiang; Mao, Jun; Xia, Yi; Kempf, Nicholas; He, Qiyuan; Wang, Yiliu; Chen, Chih-Yen; Zhang, Yanliang; Ozolins, Vidvuds; Ren, Zhifeng; Huang, Yu; Duan, Xiangfeng

2016-10-01

Epitaxial heterostructures with precisely controlled composition and electronic modulation are of central importance for electronics, optoelectronics, thermoelectrics, and catalysis. In general, epitaxial material growth requires identical or nearly identical crystal structures with small misfit in lattice symmetry and parameters and is typically achieved by vapor-phase depositions in vacuum. We report a scalable solution-phase growth of symmetry-mismatched PbSe/Bi 2 Se 3 epitaxial heterostructures by using two-dimensional (2D) Bi 2 Se 3 nanoplates as soft templates. The dangling bond-free surface of 2D Bi 2 Se 3 nanoplates guides the growth of PbSe crystal without requiring a one-to-one match in the atomic structure, which exerts minimal restriction on the epitaxial layer. With a layered structure and weak van der Waals interlayer interaction, the interface layer in the 2D Bi 2 Se 3 nanoplates can deform to accommodate incoming layer, thus functioning as a soft template for symmetry-mismatched epitaxial growth of cubic PbSe crystal on rhombohedral Bi 2 Se 3 nanoplates. We show that a solution chemistry approach can be readily used for the synthesis of gram-scale PbSe/Bi 2 Se 3 epitaxial heterostructures, in which the square PbSe (001) layer forms on the trigonal/hexagonal (0001) plane of Bi 2 Se 3 nanoplates. We further show that the resulted PbSe/Bi 2 Se 3 heterostructures can be readily processed into bulk pellet with considerably suppressed thermal conductivity (0.30 W/m·K at room temperature) while retaining respectable electrical conductivity, together delivering a thermoelectric figure of merit ZT three times higher than that of the pristine Bi 2 Se 3 nanoplates at 575 K. Our study demonstrates a unique epitaxy mode enabled by the 2D nanocrystal soft template via an affordable and scalable solution chemistry approach. It opens up new opportunities for the creation of diverse epitaxial heterostructures with highly disparate structures and functions.

Comparison of differential pressure model based on flow regime for gas/liquid two-phase flow

International Nuclear Information System (INIS)

Dong, F; Zhang, F S; Li, W; Tan, C

2009-01-01

Gas/liquid two-phase flow in horizontal pipe is very common in many industry processes, because of the complexity and variability, the real-time parameter measurement of two-phase flow, such as the measurement of flow regime and flow rate, becomes a difficult issue in the field of engineering and science. The flow regime recognition plays a fundamental role in gas/liquid two-phase flow measurement, other parameters of two-phase flow can be measured more easily and correctly based on the correct flow regime recognition result. A multi-sensor system is introduced to make the flow regime recognition and the mass flow rate measurement. The fusion system is consisted of temperature sensor, pressure sensor, cross-section information system and v-cone flow meter. After the flow regime recognition by cross-section information system, comparison of four typical differential pressure (DP) models is discussed based on the DP signal of v-cone flow meter. Eventually, an optimum DP model has been chosen for each flow regime. The experiment result of mass flow rate measurement shows it is efficient to classify the DP models by flow regime.

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

Constitutive modeling of two phase materials using the Mean Field method for homogenization

NARCIS (Netherlands)

Perdahcioglu, Emin Semih; Geijselaers, Hubertus J.M.

2010-01-01

A Mean-Field homogenization framework for constitutive modeling of materials involving two distinct elastic-plastic phases is presented. With this approach it is possible to compute the macroscopic mechanical behavior of this type of materials based on the constitutive models of the constituent

Multi-scale diffuse interface modeling of multi-component two-phase flow with partial miscibility

Science.gov (United States)

Kou, Jisheng; Sun, Shuyu

2016-08-01

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

Multi-scale diffuse interface modeling of multi-component two-phase flow with partial miscibility

KAUST Repository

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

Thermal behavior for a nanoscale two ferromagnetic phase system based on random anisotropy model

International Nuclear Information System (INIS)

Muraca, D.; Sanchez, F.H.; Pampillo, L.G.; Saccone, F.D.

2010-01-01

Advances in theory that explain the magnetic behavior as function of temperature for two phase nanocrystalline soft magnetic materials are presented. The theory developed is based on the well known random anisotropy model, which includes the crystalline exchange stiffness and anisotropy energies in both amorphous and crystalline phases. The phenomenological behavior of the coercivity was obtained in the temperature range between the amorphous phase Curie temperature and the crystalline phase one.

Application of discontinuous Galerkin method for solving a compressible five-equation two-phase flow model

Science.gov (United States)

Saleem, M. Rehan; Ali, Ishtiaq; Qamar, Shamsul

2018-03-01

In this article, a reduced five-equation two-phase flow model is numerically investigated. The formulation of the model is based on the conservation and energy exchange laws. The model is non-conservative and the governing equations contain two equations for the mass conservation, one for the over all momentum and one for the total energy. The fifth equation is the energy equation for one of the two phases that includes a source term on the right hand side for incorporating energy exchange between the two fluids in the form of mechanical and thermodynamical works. A Runge-Kutta discontinuous Galerkin finite element method is applied to solve the model equations. The main attractive features of the proposed method include its formal higher order accuracy, its nonlinear stability, its ability to handle complicated geometries, and its ability to capture sharp discontinuities or strong gradients in the solutions without producing spurious oscillations. The proposed method is robust and well suited for large-scale time-dependent computational problems. Several case studies of two-phase flows are presented. For validation and comparison of the results, the same model equations are also solved by using a staggered central scheme. It was found that discontinuous Galerkin scheme produces better results as compared to the staggered central scheme.

Dynamic simulation of dispersed gas-liquid two-phase flow using a discrete bubble model.

NARCIS (Netherlands)

Delnoij, E.; Lammers, F.A.; Kuipers, J.A.M.; van Swaaij, Willibrordus Petrus Maria

1997-01-01

In this paper a detailed hydrodynamic model for gas-liquid two-phase flow will be presented. The model is based on a mixed Eulerian-Lagrangian approach and describes the time-dependent two-dimensional motion of small, spherical gas bubbles in a bubble column operating in the homogeneous regime. The

Direct numerical simulation of reactor two-phase flows enabled by high-performance computing

Energy Technology Data Exchange (ETDEWEB)

Fang, Jun; Cambareri, Joseph J.; Brown, Cameron S.; Feng, Jinyong; Gouws, Andre; Li, Mengnan; Bolotnov, Igor A.

2018-04-01

Nuclear reactor two-phase flows remain a great engineering challenge, where the high-resolution two-phase flow database which can inform practical model development is still sparse due to the extreme reactor operation conditions and measurement difficulties. Owing to the rapid growth of computing power, the direct numerical simulation (DNS) is enjoying a renewed interest in investigating the related flow problems. A combination between DNS and an interface tracking method can provide a unique opportunity to study two-phase flows based on first principles calculations. More importantly, state-of-the-art high-performance computing (HPC) facilities are helping unlock this great potential. This paper reviews the recent research progress of two-phase flow DNS related to reactor applications. The progress in large-scale bubbly flow DNS has been focused not only on the sheer size of those simulations in terms of resolved Reynolds number, but also on the associated advanced modeling and analysis techniques. Specifically, the current areas of active research include modeling of sub-cooled boiling, bubble coalescence, as well as the advanced post-processing toolkit for bubbly flow simulations in reactor geometries. A novel bubble tracking method has been developed to track the evolution of bubbles in two-phase bubbly flow. Also, spectral analysis of DNS database in different geometries has been performed to investigate the modulation of the energy spectrum slope due to bubble-induced turbulence. In addition, the single-and two-phase analysis results are presented for turbulent flows within the pressurized water reactor (PWR) core geometries. The related simulations are possible to carry out only with the world leading HPC platforms. These simulations are allowing more complex turbulence model development and validation for use in 3D multiphase computational fluid dynamics (M-CFD) codes.

Probabilistic physical characteristics of phase transitions at highway bottlenecks: incommensurability of three-phase and two-phase traffic-flow theories.

Science.gov (United States)

Kerner, Boris S; Klenov, Sergey L; Schreckenberg, Michael

2014-05-01

Physical features of induced phase transitions in a metastable free flow at an on-ramp bottleneck in three-phase and two-phase cellular automaton (CA) traffic-flow models have been revealed. It turns out that at given flow rates at the bottleneck, to induce a moving jam (F → J transition) in the metastable free flow through the application of a time-limited on-ramp inflow impulse, in both two-phase and three-phase CA models the same critical amplitude of the impulse is required. If a smaller impulse than this critical one is applied, neither F → J transition nor other phase transitions can occur in the two-phase CA model. We have found that in contrast with the two-phase CA model, in the three-phase CA model, if the same smaller impulse is applied, then a phase transition from free flow to synchronized flow (F → S transition) can be induced at the bottleneck. This explains why rather than the F → J transition, in the three-phase theory traffic breakdown at a highway bottleneck is governed by an F → S transition, as observed in real measured traffic data. None of two-phase traffic-flow theories incorporates an F → S transition in a metastable free flow at the bottleneck that is the main feature of the three-phase theory. On the one hand, this shows the incommensurability of three-phase and two-phase traffic-flow theories. On the other hand, this clarifies why none of the two-phase traffic-flow theories can explain the set of fundamental empirical features of traffic breakdown at highway bottlenecks.

Research on one-dimensional two-phase flow

International Nuclear Information System (INIS)

Adachi, Hiromichi

1988-10-01

In Part I the fundamental form of the hydrodynamic basic equations for a one-dimensional two-phase flow (two-fluid model) is described. Discussions are concentrated on the treatment of phase change inertial force terms in the equations of motion and the author's equations of motion which have a remarkable uniqueness on the following three points. (1) To express force balance of unit mass two-phase fluid instead of that of unit volume two-phase fluid. (2) To pick up the unit existing mass and the unit flowing mass as the unit mass of two-phase fluid. (3) To apply the kinetic energy principle instead of the momentum low in the evaluation of steady inertial force term. In these three, the item (1) is for excluding a part of momentum change or kinetic energy change due to mass change of the examined part of fluid, which is independent of force. The item (2) is not to introduce a phenomenological physical model into the evaluation of phase change inertial force term. And the item (3) is for correctly applying the momentum law taking into account the difference of representative velocities between the main flow fluid (vapor phase or liquid phase) and the phase change part of fluid. In Part II, characteristics of various kinds of high speed two-phase flow are clarified theoretically by the basic equations derived. It is demonstrated that the steam-water two-phase critical flow with violent flashing and the airwater two-phase critical flow without phase change can be described with fundamentally the same basic equations. Furthermore, by comparing the experimental data from the two-phase critical discharge test and the theoretical prediction, the two-phase discharge coefficient, C D , for large sharp-edged orifice is determined as the value which is not affected by the experimental facility characteristics, etc. (author)

The phases of isospin-asymmetric matter in the two-flavor NJL model

Energy Technology Data Exchange (ETDEWEB)

Lawley, S. [Special Research Centre for the Subatomic Structure of Matter, University of Adelaide, Adelaide, SA 5005 (Australia) and Jefferson Lab, 12000 Jefferson Avenue, Newport News, VA 23606 (United States)]. E-mail: slawley@jlab.org; Bentz, W. [Department of Physics, School of Science, Tokai University, Hiratsuka-shi, Kanagawa 259-1292 (Japan); Thomas, A.W. [Jefferson Lab, 12000 Jefferson Avenue, Newport News, VA 23606 (United States)

2006-01-19

We investigate the phase diagram of isospin-asymmetric matter at T=0 in the two-flavor Nambu-Jona-Lasinio model. Our approach describes the single nucleon as a confined quark-diquark state, the saturation properties of nuclear matter at normal densities, and the phase transition to normal or color superconducting quark matter at higher densities. The resulting equation of state of charge-neutral matter and the structure of compact stars are discussed.

Two-phase pressurized thermal shock investigations using a 3D two-fluid modeling of stratified flow with condensation

International Nuclear Information System (INIS)

Yao, W.; Coste, P.; Bestion, D.; Boucker, M.

2003-01-01

In this paper, a local 3D two-fluid model for a turbulent stratified flow with/without condensation, which can be used to predict two-phase pressurized thermal shock, is presented. A modified turbulent K- model is proposed with turbulence production induced by interfacial friction. A model of interfacial friction based on a interfacial sublayer concept and three interfacial heat transfer models, namely, a model based on the small eddies controlled surface renewal concept (HDM, Hughes and Duffey, 1991), a model based on the asymptotic behavior of the Eddy Viscosity (EVM), and a model based on the Interfacial Sublayer concept (ISM) are implemented into a preliminary version of the NEPTUNE code based on the 3D module of the CATHARE code. As a first step to apply the above models to predict the two-phase thermal shock, the models are evaluated by comparison of calculated profiles with several experiments: a turbulent air-water stratified flow without interfacial heat transfer; a turbulent steam-water stratified flow with condensation; turbulence induced by the impact of a water jet in a water pool. The prediction results agree well with the experimental data. In addition, the comparison of three interfacial heat transfer models shows that EVM and ISM gave better prediction results while HDM highly overestimated the interfacial heat transfers compared to the experimental data of a steam water stratified flow

Thermodynamically consistent modeling and simulation of multi-component two-phase flow model with partial miscibility

KAUST Repository

Kou, Jisheng; Sun, Shuyu

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

SedFoam-2.0: a 3-D two-phase flow numerical model for sediment transport

Directory of Open Access Journals (Sweden)

J. Chauchat

2017-11-01

Full Text Available In this paper, a three-dimensional two-phase flow solver, SedFoam-2.0, is presented for sediment transport applications. The solver is extended from twoPhaseEulerFoam available in the 2.1.0 release of the open-source CFD (computational fluid dynamics toolbox OpenFOAM. In this approach the sediment phase is modeled as a continuum, and constitutive laws have to be prescribed for the sediment stresses. In the proposed solver, two different intergranular stress models are implemented: the kinetic theory of granular flows and the dense granular flow rheology μ(I. For the fluid stress, laminar or turbulent flow regimes can be simulated and three different turbulence models are available for sediment transport: a simple mixing length model (one-dimensional configuration only, a k − ε, and a k − ω model. The numerical implementation is demonstrated on four test cases: sedimentation of suspended particles, laminar bed load, sheet flow, and scour at an apron. These test cases illustrate the capabilities of SedFoam-2.0 to deal with complex turbulent sediment transport problems with different combinations of intergranular stress and turbulence models.

SedFoam-2.0: a 3-D two-phase flow numerical model for sediment transport

Science.gov (United States)

Chauchat, Julien; Cheng, Zhen; Nagel, Tim; Bonamy, Cyrille; Hsu, Tian-Jian

2017-11-01

In this paper, a three-dimensional two-phase flow solver, SedFoam-2.0, is presented for sediment transport applications. The solver is extended from twoPhaseEulerFoam available in the 2.1.0 release of the open-source CFD (computational fluid dynamics) toolbox OpenFOAM. In this approach the sediment phase is modeled as a continuum, and constitutive laws have to be prescribed for the sediment stresses. In the proposed solver, two different intergranular stress models are implemented: the kinetic theory of granular flows and the dense granular flow rheology μ(I). For the fluid stress, laminar or turbulent flow regimes can be simulated and three different turbulence models are available for sediment transport: a simple mixing length model (one-dimensional configuration only), a k - ɛ, and a k - ω model. The numerical implementation is demonstrated on four test cases: sedimentation of suspended particles, laminar bed load, sheet flow, and scour at an apron. These test cases illustrate the capabilities of SedFoam-2.0 to deal with complex turbulent sediment transport problems with different combinations of intergranular stress and turbulence models.

Validation of Friction Models in MARS-MultiD Module with Two-Phase Cross Flow Experiment

International Nuclear Information System (INIS)

Choi, Chi-Jin; Yang, Jin-Hwa; Cho, Hyoung-Kyu; Park, Goon-Cher; Euh, Dong-Jin

2015-01-01

In the downcomer of Advanced Power Reactor 1400 (APR1400) which has direct vessel injection (DVI) lines as an emergency core cooling system, multidimensional 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 multidimensional modules of system analysis codes. In this study, MARS-MultiD was used to simulate the Yang's experiment, and obtained the local variables. Then, the friction models used in MARS-MultiD were validated by comparing the two-phase flow experimental results with the calculated local variables. In this study, the two-phase cross flow experiment was modeled by the MARS-MultiD. Compared with the experimental results, the calculated results by the code properly presented mass conservation which could be known from the relation between the liquid film velocity and thickness at the same flow rate. The magnitude and direction of the liquid film, however, did not follow well with experimental results. According to the results of Case-2, wall friction should be increased, and interfacial friction should be decreased in MARS-MultiD. These results show that it is needed to modify the friction models in the MARS-MultiD to simulate the two-phase cross flow

Validation of model predictions of pore-scale fluid distributions during two-phase flow

Science.gov (United States)

Bultreys, Tom; Lin, Qingyang; Gao, Ying; Raeini, Ali Q.; AlRatrout, Ahmed; Bijeljic, Branko; Blunt, Martin J.

2018-05-01

Pore-scale two-phase flow modeling is an important technology to study a rock's relative permeability behavior. To investigate if these models are predictive, the calculated pore-scale fluid distributions which determine the relative permeability need to be validated. In this work, we introduce a methodology to quantitatively compare models to experimental fluid distributions in flow experiments visualized with microcomputed tomography. First, we analyzed five repeated drainage-imbibition experiments on a single sample. In these experiments, the exact fluid distributions were not fully repeatable on a pore-by-pore basis, while the global properties of the fluid distribution were. Then two fractional flow experiments were used to validate a quasistatic pore network model. The model correctly predicted the fluid present in more than 75% of pores and throats in drainage and imbibition. To quantify what this means for the relevant global properties of the fluid distribution, we compare the main flow paths and the connectivity across the different pore sizes in the modeled and experimental fluid distributions. These essential topology characteristics matched well for drainage simulations, but not for imbibition. This suggests that the pore-filling rules in the network model we used need to be improved to make reliable predictions of imbibition. The presented analysis illustrates the potential of our methodology to systematically and robustly test two-phase flow models to aid in model development and calibration.

Modeling of two-phase flow with thermal and mechanical non-equilibrium

International Nuclear Information System (INIS)

Houdayer, G.; Pinet, B.; Le Coq, G.; Reocreux, M.; Rousseau, J.C.

1977-01-01

To improve two-phase flow modeling by taking into account thermal and mechanical non-equilibrium a joint effort on analytical experiment and physical modeling has been undertaken. A model describing thermal non-equilibrium effects is first presented. A correlation of mass transfer has been developed using steam water critical flow tests. This model has been used to predict in a satisfactory manner blowdown tests. It has been incorporated in CLYSTERE system code. To take into account mechanical non-equilibrium, a six equations model is written. To get information on the momentum transfers special nitrogen-water tests have been undertaken. The first results of these studies are presented

Hybrid-dimensional modelling of two-phase flow through fractured porous media with enhanced matrix fracture transmission conditions

Science.gov (United States)

Brenner, Konstantin; Hennicker, Julian; Masson, Roland; Samier, Pierre

2018-03-01

In this work, we extend, to two-phase flow, the single-phase Darcy flow model proposed in [26], [12] in which the (d - 1)-dimensional flow in the fractures is coupled with the d-dimensional flow in the matrix. Three types of so called hybrid-dimensional two-phase Darcy flow models are proposed. They all account for fractures acting either as drains or as barriers, since they allow pressure jumps at the matrix-fracture interfaces. The models also permit to treat gravity dominated flow as well as discontinuous capillary pressure at the material interfaces. The three models differ by their transmission conditions at matrix fracture interfaces: while the first model accounts for the nonlinear two-phase Darcy flux conservations, the second and third ones are based on the linear single phase Darcy flux conservations combined with different approximations of the mobilities. We adapt the Vertex Approximate Gradient (VAG) scheme to this problem, in order to account for anisotropy and heterogeneity aspects as well as for applicability on general meshes. Several test cases are presented to compare our hybrid-dimensional models to the generic equi-dimensional model, in which fractures have the same dimension as the matrix, leading to deep insight about the quality of the proposed reduced models.

Modeling of Eutectic Formation in Al-Si Alloy Using A Phase-Field Method

Directory of Open Access Journals (Sweden)

Ebrahimi Z.

2017-12-01

Full Text Available We have utilized a phase-field model to investigate the evolution of eutectic silicon in Al-Si alloy. The interfacial fluctuations are included into a phase-field model of two-phase solidification, as stochastic noise terms and their dominant role in eutectic silicon formation is discussed. We have observed that silicon spherical particles nucleate on the foundation of primary aluminum phase and their nucleation continues on concentric rings, through the Al matrix. The nucleation of silicon particles is attributed to the inclusion of fluctuations into the phase-field equations. The simulation results have shown needle-like, fish-bone like and flakes of silicon phase by adjusting the noise coefficients to larger values. Moreover, the role of primary Al phase on nucleation of silicon particles in Al-Si alloy is elaborated. We have found that the addition of fluctuations plays the role of modifiers in our simulations and is essential for phase-field modeling of eutectic growth in Al-Si system. The simulated finger-like Al phases and spherical Si particles are very similar to those of experimental eutectic growth in modified Al-Si alloy.

Development of Sodium Two Phase Flow Model for Kalimer Core Analysis

International Nuclear Information System (INIS)

Chang, W.P.; Hahn, Dohee

2002-01-01

An algorithm for sodium boiling is developed in order to extend the applicability of SSC-K, which is a main system analysis code for the KALIMER (Korea Advanced LIquid Metal Reactor) conceptual design. As the capability of the current SSC-K version is limited to simulation of only a single-phase sodium flow, its applicable range should not be enough to assess the fuel integrity under some of HCDA (Hypothetical Core Disruptive Accident) initiating events where sodium boiling is anticipated. The two-phase flow model similar to that used for the light water system is known to be no more effective directly to liquid metal reactors, because the phenomena observed between two reactor coolant systems are definitely different. The developing algorithm is based on a multiple-bubble slug ejection model, which allows a finite number of bubbles in a channel at any time. The present work is a continuous effort following the former study to confirm a qualitative acceptance on the model. Since the model has been applied only to the active fuel region in the former study, a part of its qualification seems to have already been demonstrated. For its application to the whole KALIMER core channel, however, the model needs to be examined the applicability to the fuel regions other than the active fuel. The present study primarily focuses on that point. In a result, although the model may be improved in a sense through the present study over the previous modeling, a clear limitation is also confirmed with the validity of the model. The further development, therefore, is required for this model to achieve its goal by resolving such limitations. (authors)

Debris bed coolability using a 3-D two phase model in a porous medium

Energy Technology Data Exchange (ETDEWEB)

Bechaud, C.; Duval, F.; Fichot, F. [CEA Cadarache, Inst. de Protection et de Surete Nucleaire13 - Saint-Paul-lez-Durance (France); Quintard, M. [Institut de Mecanique des Fluides de Toulouse, 31 (France); Parent, M. [CEA Grenoble, Dept. de Thermohydraulique et de Physique, 38 (France)

2001-07-01

During a severe nuclear accident, a part of the molten corium resulting from the core degradation may relocate in the lower plenum of the reactor vessel. In order to predict the safety margin of the reactor under such conditions, the coolability of this porous heat-generating medium is evaluated in this study and compared with other investigations. In this work, conservation equations derived for debris beds are implemented in the three dimensional thermal-hydraulic module of the CATHARE code. The coolant flow is a two phase flow with phase change. The momentum balance equation for each fluid phase is an extension of Darcy's law. This extension takes into account the capillary effects between the two phases, the relative permeabilities and passabilities of each phase, the interfacial drag force between liquid and gas, and the porous bed configuration (porosity, particle diameter,... ). The model developed is three-dimensional which is important to better predict the flow in configuration such as counter-current flow or to emphasize preferential ways induced by porous geometry. The energy balance equations of the three phases (liquid, gas and solid phase) are obtained by a volume averaging process of the local conservation equations. In this method, the local thermal non-equilibrium between the three phases is considered and the heat exchanges, the phase change rate as well as the thermal dispersion coefficients are calculated as a function of the local geometry of the porous medium. Such a method allows the numerical estimation of these thermal properties which are very difficult to determine experimentally. This feature is a great advantage of this approach. After a brief description of the thermal-hydraulic model, one-dimensional predictions of critical dryout fluxes are presented and compared with results from the literature. Reasonable agreement is obtained. Then a two-dimensional calculation is presented and shows the influence of the porous medium

Two dimensional kicked quantum Ising model: dynamical phase transitions

International Nuclear Information System (INIS)

Pineda, C; Prosen, T; Villaseñor, E

2014-01-01

Using an efficient one and two qubit gate simulator operating on graphical processing units, we investigate ergodic properties of a quantum Ising spin 1/2 model on a two-dimensional lattice, which is periodically driven by a δ-pulsed transverse magnetic field. We consider three different dynamical properties: (i) level density, (ii) level spacing distribution of the Floquet quasienergy spectrum, and (iii) time-averaged autocorrelation function of magnetization components. Varying the parameters of the model, we found transitions between ordered (non-ergodic) and quantum chaotic (ergodic) phases, but the transitions between flat and non-flat spectral density do not correspond to transitions between ergodic and non-ergodic local observables. Even more surprisingly, we found good agreement of level spacing distribution with the Wigner surmise of random matrix theory for almost all values of parameters except where the model is essentially non-interacting, even in regions where local observables are not ergodic or where spectral density is non-flat. These findings question the versatility of the interpretation of level spacing distribution in many-body systems and stress the importance of the concept of locality. (paper)

Modelling of bubbly and annular two-phase flow in subchannel geometries with BACCHUS-3D/TP

International Nuclear Information System (INIS)

Bottoni, M.; Lyczkowski, R.W.

1992-01-01

The theoretical and computational bases of the BACCHUS-3D/TP computer program are reviewed. The computer program is used for thermal-hydraulic analyses of nuclear fuel bundles under normal and accident conditions. The present program combines two models and solution procedures previously used separately, namely, the Improved Slip Model (ISM) and the Separated-Phases Model (SPM). The former model uses mixture equations with accounting for slip between the phases, whereas the latter uses separate continuity and momentum equations. At the present stage of development, both assume thermodynamic equilibrium. Techniques used to affect smooth transition between the two models are described. including treatment of frictional pressure drop and solution of the Poisson and momentum equations. A detailed derivation of the computation of mass transfer between the phases is given because it is a central and novel feature of the model

A multiscale coupled finite-element and phase-field framework to modeling stressed grain growth in polycrystalline thin films

Energy Technology Data Exchange (ETDEWEB)

Jamshidian, M., E-mail: jamshidian@cc.iut.ac.ir [Department of Mechanical Engineering, Isfahan University of Technology, Isfahan 84156-83111 (Iran, Islamic Republic of); Institute of Structural Mechanics, Bauhaus-University Weimar, Marienstrasse 15, 99423 Weimar (Germany); Thamburaja, P., E-mail: prakash.thamburaja@gmail.com [Department of Mechanical & Materials Engineering, Universiti Kebangsaan Malaysia (UKM), Bangi 43600 (Malaysia); Rabczuk, T., E-mail: timon.rabczuk@tdt.edu.vn [Division of Computational Mechanics, Ton Duc Thang University, Ho Chi Minh City (Viet Nam); Faculty of Civil Engineering, Ton Duc Thang University, Ho Chi Minh City (Viet Nam)

2016-12-15

A previously-developed finite-deformation- and crystal-elasticity-based constitutive theory for stressed grain growth in cubic polycrystalline bodies has been augmented to include a description of excess surface energy and grain-growth stagnation mechanisms through the use of surface effect state variables in a thermodynamically-consistent manner. The constitutive theory was also implemented into a multiscale coupled finite-element and phase-field computational framework. With the material parameters in the constitutive theory suitably calibrated, our three-dimensional numerical simulations show that the constitutive model is able to accurately predict the experimentally-determined evolution of crystallographic texture and grain size statistics in polycrystalline copper thin films deposited on polyimide substrate and annealed at high-homologous temperatures. In particular, our numerical analyses show that the broad texture transition observed in the annealing experiments of polycrystalline thin films is caused by grain growth stagnation mechanisms. - Graphical abstract: - Highlights: • Developing a theory for stressed grain growth in polycrystalline thin films. • Implementation into a multiscale coupled finite-element and phase-field framework. • Quantitative reproduction of the experimental grain growth data by simulations. • Revealing the cause of texture transition to be due to the stagnation mechanisms.

Contribution to the verification and the validation of an unsteady two-phase flow model

International Nuclear Information System (INIS)

Liu, Yujie

2013-01-01

This thesis contributes to the verification and the validation of the Baer-Nunziato (BN) model, to model water hammer phenomena in industrial piping systems. It consists of two parts, the first is to model water hammer flows with the BN model in Eulerian representation and the second is to extend this model to the ALE (Arbitrary Lagrangian Eulerian) formalism so as to take into account fluid-structure interaction (FSI). To model water hammer flows, closure laws of the BN model concerning the interfacial/source terms and the equations of state (EOS) were first studied. Then the whole system was simulated with a fractional step method including two steps, one for the resolution of the convective part, the other for the source terms. For the convective part, the Rusanov scheme was first checked, and some stability problems have been observed. Thus a more stable fractional step scheme has been proposed and verified. Regarding the source terms, four non-instantaneous relaxation schemes which represent the return to equilibrium of pressure, the transfers of momentum, heat and mass were successively applied. These schemes have been extended to 'generalized Stiffened Gas' EOS in order to represent phase-change. After regaining some typical phenomena associated with water hammer flows, the BN model was validated with the Simpson experiment, a classical water hammer test case, and the Canon experience, a rapid decompression of fluid in a high pressure duct. Moreover, the model was compared with two homogeneous models on these two experiments. Finally, an ALE version of the BN model was implemented, and verified on a case of wave propagation in a 'single' phase flow and a two-phase flow in a flexible pipe. The variation of wave propagation speed due to the coupling between the fluid and the structure has been well retrieved. The validation was performed on an experiment which examines the response of a pipe filled with water, subjected to a violent pressure peak (140 bar

A generalized diffusion model for growth of nanoparticles synthesized by colloidal methods.

Science.gov (United States)

Wen, Tianlong; Brush, Lucien N; Krishnan, Kannan M

2014-04-01

A nanoparticle growth model is developed to predict and guide the syntheses of monodisperse colloidal nanoparticles in the liquid phase. The model, without any a priori assumptions, is based on the Fick's law of diffusion, conservation of mass and the Gibbs-Thomson equation for crystal growth. In the limiting case, this model reduces to the same expression as the currently accepted model that requires the assumption of a diffusion layer around each nanoparticle. The present growth model bridges the two limiting cases of the previous model i.e. complete diffusion controlled and adsorption controlled growth of nanoparticles. Specifically, the results show that a monodispersion of nanoparticles can be obtained both with fast monomer diffusion and with surface reaction under conditions of small diffusivity to surface reaction constant ratio that results is growth 'focusing'. This comprehensive description of nanoparticle growth provides new insights and establishes the required conditions for fabricating monodisperse nanoparticles critical for a wide range of applications. Copyright © 2013 Elsevier Inc. All rights reserved.

A two-phase inspection model for a single component system with three-stage degradation

International Nuclear Information System (INIS)

Wang, Huiying; Wang, Wenbin; Peng, Rui

2017-01-01

This paper presents a two-phase inspection schedule and an age-based replacement policy for a single plant item contingent on a three-stage degradation process. The two phase inspection schedule can be observed in practice. The three stages are defined as the normal working stage, low-grade defective stage and critical defective stage. When an inspection detects that an item is in the low-grade defective stage, we may delay the preventive replacement action if the time to the age-based replacement is less than or equal to a threshold level. However, if it is above this threshold level, the item will be replaced immediately. If the item is found in the critical defective stage, it is replaced immediately. A hybrid bee colony algorithm is developed to find the optimal solution for the proposed model which has multiple decision variables. A numerical example is conducted to show the efficiency of this algorithm, and simulations are conducted to verify the correctness of the model. - Highlights: • A two-phase inspection model is studied. • The failure process has three stages. • The delayed replacement is considered.

Two-sector disequilibrium growth

NARCIS (Netherlands)

J.G.M. van Marrewijk (Charles); J.B.L.M. Verbeek (Jos)

1994-01-01

textabstractWe investigate the effects of (i) profit distribution to either laborers or capital-owners, (ii) sector-specific or efficient rationing schemes, and (iii) government consumption in a two-sector disequilibrium growth model with sluggish real wage rate adjustment (which affects capital

An Experimental Study of Two-Phase Pulse Flushing Technology in Water Distribution Systems

Directory of Open Access Journals (Sweden)

Zhaozhao Tang

2017-12-01

Full Text Available The deterioration of drinking water during distribution process is caused by many factors. The microorganisms and substances peeling off from the “growth-ring” make the secondary pollution in drinking water distribution systems. To reduce the secondary pollution, two-phase pulse flushing technology is introduced to quickly remove the “growth-ring”. In this study, experiment is undertaken for investigating the efficiency of the two-phase pulse flushing and finding the best setting combination. A case study is undertaken to compare the efficiencies between the two-phase pulse and the single-phase flushing. The best setting combination of the two-phase pulse flushing is at the frequency 4 s–6 s (air inflow time is 4 s and air cut off time is 6 s and the round air inflow nozzle is set at the bottom of the pipe. Two-phase pulse flushing technology can save 95% of water and 6 h 40 min flushing time.

Inverse modeling for the determination of hydrogeological parameters of a two-phase system

International Nuclear Information System (INIS)

Finsterle, S.

1993-02-01

Investigations related to the disposal of radioactive wastes in Switzerland consider formations containing natural gas as potential rocks for a repository. Moreover, gas generation in the repository itself may lead to an unsaturated zone of significant extent and impact on the system's performance. The site characterization procedure requires the estimation of hydraulic properties being used as input parameters for a two-phase two-component numerical simulator. In this study, estimates of gas-related formation parameters are obtained by inverse modeling. Based on discrete observations of the system's state, model parameters can be estimated within the framework of a given conceptual model by means of optimization techniques. This study presents the theoretical background that related field data to the model parameters. A parameter estimation procedure is proposed and implemented in a computer code for automatic model calibration. This tool allows identification of key parameters affecting flow of water and gas in porous media. The inverse modeling approach is verified using data from a synthetic laboratory experiment. In addition, the Gas test performed at the Grimsel Test Site is analyzed in order to demonstrate the applicability of the proposed procedure when used with data from a real geologic environment. Estimation of hydrogeologic parameters by automatic model calibration improves the understanding of the two-phase flow processes and therefore increases the reliability of the subsequent simulation runs. (author) figs., tabs., refs

Inverse modeling for the determination of hydrogeological parameters of a two-phase system

International Nuclear Information System (INIS)

Finsterle, S.

1993-01-01

Investigations related to the disposal of radioactive wastes in Switzerland are dealing with formations containing natural gas as potential host rock for a repository. Moreover, gas generation in the repository itself may lead to an unsaturated zone of significant extent and impact on the system's performance. The site characterization procedure requires the estimation of hydraulic properties being used as input parameters for a two-phase two-component numerical simulator. In this study, estimates of gas related formation parameters are obtained by inverse modeling. Based on discrete observations of the system's state, model parameters can be estimated within the framework of a given conceptual model by means of optimization techniques. This study presents the theoretical background that relates field data to the model parameters. A parameter estimation procedure is proposed and implemented in a computer code for automatic model calibration. This tool allows to identify key parameters affecting flow of water and gas in porous media. The inverse modeling approach is verified using data from a synthetic laboratory experiment. In addition, the Gastest performed at the Grimsel Test Site is analyzed in order to demonstrate the applicability of the proposed procedure when used with data from a real geologic environment. Estimation of hydrogeologic parameters by automatic model calibration improves the understanding of the two-phase flow processes and therefore increases the reliability of the subsequent simulation runs. (author) figs., tabs., 100 refs

Benchmark problems for numerical implementations of phase field models

International Nuclear Information System (INIS)

Jokisaari, A. M.; Voorhees, P. W.; Guyer, J. E.; Warren, J.; Heinonen, O. G.

2016-01-01

Here, we present the first set of benchmark problems for phase field models that are being developed by the Center for Hierarchical Materials Design (CHiMaD) and the National Institute of Standards and Technology (NIST). While many scientific research areas use a limited set of well-established software, the growing phase field community continues to develop a wide variety of codes and lacks benchmark problems to consistently evaluate the numerical performance of new implementations. Phase field modeling has become significantly more popular as computational power has increased and is now becoming mainstream, driving the need for benchmark problems to validate and verify new implementations. We follow the example set by the micromagnetics community to develop an evolving set of benchmark problems that test the usability, computational resources, numerical capabilities and physical scope of phase field simulation codes. In this paper, we propose two benchmark problems that cover the physics of solute diffusion and growth and coarsening of a second phase via a simple spinodal decomposition model and a more complex Ostwald ripening model. We demonstrate the utility of benchmark problems by comparing the results of simulations performed with two different adaptive time stepping techniques, and we discuss the needs of future benchmark problems. The development of benchmark problems will enable the results of quantitative phase field models to be confidently incorporated into integrated computational materials science and engineering (ICME), an important goal of the Materials Genome Initiative.

Experimental validation of a numerical model of two-phase displacement in porous medium

International Nuclear Information System (INIS)

Genty, A.

1996-01-01

Burial in geological layers appears to be an interesting solution to dispose of radioactive wastes. This thesis analyzes and simulates the behaviour of gas produced by waste barrels corrosion. The released contaminated gas drains the water initially present in the host rock and yields a water-gas two phase flow. A literature survey of two phase flow shows that fluid interfaces may display instabilities for definite flow characteristics. When the displacement is stable a smooth interface proceeds through the porous medium. When the interface shows fingering, the displacement is said to be 'viscous-unstable', and when the front is jagged the displacement is called 'capillary' displacement. A dimensional analysis of classical equations governing two phase flow in porous media is combined with a classification of dominant forces to define an original map of flow regimes that includes gravitational forces. The map is based on three dimensionless numbers and predicts a priori the flow type. For typical data describing a radioactive waste repository a 'viscous-unstable' displacement is predicted by the map. We simulate water-gas displacement with a numerical model previously developed; this code, based on the Muskat model, uses the mixed-hybrid finite elements technique and is therefore well adapted for tracking moving interfaces. Fluxes are well conserved, however instabilities cannot be simulated. We assume that there is always a scale to be found where instabilities can be averaged and we try to validate the model with experimental two phase flows. We performed laboratory water-gas flow experiments for a variety of flow conditions. The observed displacement types are consistent with the map of flow regimes. Good agreement with numerical simulations is obtained when precise parameters of the displacements are available, in particular relative permeability curves. We conclude that our model allows a first approach of migration of gas near a radioactive waste repository

Phase separation and shape deformation of two-phase membranes

International Nuclear Information System (INIS)

Jiang, Y.; Lookman, T.; Saxena, A.

2000-01-01

Within a coupled-field Ginzburg-Landau model we study analytically phase separation and accompanying shape deformation on a two-phase elastic membrane in simple geometries such as cylinders, spheres, and tori. Using an exact periodic domain wall solution we solve for the shape and phase separating field, and estimate the degree of deformation of the membrane. The results are pertinent to preferential phase separation in regions of differing curvature on a variety of vesicles. (c) 2000 The American Physical Society

Constitutive equations for two-phase flows

International Nuclear Information System (INIS)

Boure, J.A.

1974-12-01

The mathematical model of a system of fluids consists of several kinds of equations complemented by boundary and initial conditions. The first kind equations result from the application to the system, of the fundamental conservation laws (mass, momentum, energy). The second kind equations characterize the fluid itself, i.e. its intrinsic properties and in particular its mechanical and thermodynamical behavior. They are the mathematical model of the particular fluid under consideration, the laws they expressed are so called the constitutive equations of the fluid. In practice the constitutive equations cannot be fully stated without reference to the conservation laws. Two classes of model have been distinguished: mixture model and two-fluid models. In mixture models, the mixture is considered as a single fluid. Besides the usual friction factor and heat transfer correlations, a single constitutive law is necessary. In diffusion models, the mixture equation of state is replaced by the phasic equations of state and by three consitutive laws, for phase change mass transfer, drift velocity and thermal non-equilibrium respectively. In the two-fluid models, the two phases are considered separately; two phasic equations of state, two friction factor correlations, two heat transfer correlations and four constitutive laws are included [fr

Trade-offs between microbial growth phases lead to frequency-dependent and non-transitive selection.

Science.gov (United States)

Manhart, Michael; Adkar, Bharat V; Shakhnovich, Eugene I

2018-02-14

Mutations in a microbial population can increase the frequency of a genotype not only by increasing its exponential growth rate, but also by decreasing its lag time or adjusting the yield (resource efficiency). The contribution of multiple life-history traits to selection is a critical question for evolutionary biology as we seek to predict the evolutionary fates of mutations. Here we use a model of microbial growth to show that there are two distinct components of selection corresponding to the growth and lag phases, while the yield modulates their relative importance. The model predicts rich population dynamics when there are trade-offs between phases: multiple strains can coexist or exhibit bistability due to frequency-dependent selection, and strains can engage in rock-paper-scissors interactions due to non-transitive selection. We characterize the environmental conditions and patterns of traits necessary to realize these phenomena, which we show to be readily accessible to experiments. Our results provide a theoretical framework for analysing high-throughput measurements of microbial growth traits, especially interpreting the pleiotropy and correlations between traits across mutants. This work also highlights the need for more comprehensive measurements of selection in simple microbial systems, where the concept of an ordinary fitness landscape breaks down. © 2018 The Author(s).

Multi-dimensional rheology-based two-phase model for sediment transport and applications to sheet flow and pipeline scour

International Nuclear Information System (INIS)

Lee, Cheng-Hsien; Low, Ying Min; Chiew, Yee-Meng

2016-01-01

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 − 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 well-posedness of a two-fluid equations for bubbly two-phase flows

International Nuclear Information System (INIS)

Okawa, Tomio; Kataoka, Isao

2000-01-01

It is widely known that two-fluid equations used in most engineering applications do not satisfy the necessary condition for being mathematical well-posed as initial-value problems. In the case of stratified two-phase flows, several researchers have revealed that differential models satisfying the necessary condition are to be derived if the pressure difference between the phases is related to the spatial gradient of the void fraction through the effects of gravity or surface tension. While, in the case of dispersed two-phase flows, no physically reasonable method to derive mathematically well-posed two-fluid model has been proposed. In the present study, particularly focusing on the effect of interfacial pressure terms, we derived the mathematically closed form of the volume-averaged two-fluid model for bubbly two-phase flows. As a result of characteristic analyses, it was shown that the proposed two-fluid equations satisfy the necessary condition of mathematical well-posedness if the void fraction is sufficiently small. (author)

System identification on two-phase flow stability

International Nuclear Information System (INIS)

Wu Shaorong; Zhang Youjie; Wang Dazhong; Bo Jinghai; Wang Fei

1996-01-01

The theoretical principle, experimental method and results of interrelation analysis identification for the instability of two-phase flow are described. A completely new concept of test technology and method on two-phase flow stability was developed by using he theory of information science on system stability and system identification for two-phase flow stability in thermo-physics field. Application of this method would make it possible to identify instability boundary of two-phase flow under stable operation conditions of two-phase flow system. The experiment was carried out on the thermohydraulic test system HRTL-5. Using reverse repeated pseudo-random sequences of heating power as input signal sources and flow rate as response function in the test, the two-phase flow stability and stability margin of the natural circulation system are investigated. The effectiveness and feasibility of identifying two-phase flow stability by using this system identification method were experimentally demonstrated. Basic data required for mathematics modeling of two-phase flow and analysis of two-phase flow stability were obtained, which are useful for analyzing, monitoring of the system operation condition, and forecasting of two-phase flow stability in engineering system

UO2 Grain Growth: Developing Phase Field Models for Pore Dragging, Solute Dragging and Anisotropic Grain Boundary Energies

International Nuclear Information System (INIS)

Ahmed, K.; Tonks, M.; Zhang, Y.; Biner, B.

2016-01-01

A detailed phase field model for the effect of pore drag on grain growth kinetics was implemented in MARMOT. The model takes into consideration both the curvature-driven grain boundary motion and pore migration by surface diffusion. As such, the model accounts for the interaction between pore and grain boundary kinetics, which tends to retard the grain growth process. Our 2D and 3D simulations demonstrate that the model capture all possible pore-grain boundary interactions proposed in theoretical models. For high enough surface mobility, the pores move along with the migrating boundary as a quasi-rigid-body, albeit hindering its migration rate compared to the pore-free case. For less mobile pores, the migrating boundary can separate from the pores. For the pore-controlled grain growth kinetics, the model predicts a strong dependence of the growth rate on the number of pores, pore size, and surface diffusivity in agreement with theroretical models. An evolution equation for the grain size that includes these parameters was derived and showed to agree well with numerical solution. It shows a smooth transition from boundary-controlled kinetics to pore-controlled kinetics as the surface diffusivity decreases or the number of pores or their size increases. This equation can be utilized in BISON to give accurate estimate for the grain size evolution. This will be accomplished in the near future. The effect of solute drag and anisotropy of grain boundary on grain growth will be investigated in future studies.

Modeling the effects of ozone on soybean growth and yield.

Science.gov (United States)

Kobayashi, K; Miller, J E; Flagler, R B; Heck, W W

1990-01-01

A simple mechanistic model was developed based on an existing growth model in order to address the mechanisms of the effects of ozone on growth and yield of soybean [Glycine max. (L.) Merr. 'Davis'] and interacting effects of other environmental stresses. The model simulates daily growth of soybean plants using environmental data including shortwave radiation, temperature, precipitation, irrigation and ozone concentration. Leaf growth, dry matter accumulation, water budget, nitrogen input and seed growth linked to senescence and abscission of leaves are described in the model. The effects of ozone are modeled as reduced photosynthate production and accelerated senescence. The model was applied to the open-top chamber experiments in which soybean plants were exposed to ozone under two levels of soil moisture regimes. After calibrating the model to the growth data and seed yield, goodness-of-fit of the model was tested. The model fitted well for top dry weight in the vegetative growth phase and also at maturity. The effect of ozone on seen yield was also described satisfactorily by the model. The simulation showed apparent interaction between the effect of ozone and soil moisture stress on the seed yield. The model revealed that further work is needed concerning the effect of ozone on the senescence process and the consequences of alteration of canopy microclimate by the open-top chambers.

Constitutive modeling of two-phase metallic composites with application to tungsten-based composite 93W–4.9Ni–2.1Fe

International Nuclear Information System (INIS)

Lu, W.R.; Gao, C.Y.; Ke, Y.L.

2014-01-01

The two-phase metallic composites, composed by the metallic particulate reinforcing phase and the metallic matrix phase, have attracted a lot of attention in recent years for their excellent material properties. However, the constitutive modeling of two-phase metallic composites is still lacking currently. Most used models for them are basically oriented for single-phase homogeneous metallic materials, and have not considered the microstructural evolution of the components in the composite. This paper develops a new constitutive model for two-phase metallic composites based on the thermally activated dislocation motion mechanism and the volume fraction evolution. By establishing the relation between microscopic volume fraction and macroscopic state variables (strain, strain rate and temperature), the evolution law of volume fraction during the plastic deformation in two-phase composites is proposed for the first time and introduced into the new model. Then the new model is applied to a typical two-phase tungsten-based composite – 93W–4.9Ni–2.1Fe tungsten heavy alloy. It has been found that our model can effectively describe the plastic deformation behaviors of the tungsten-based composite, because of the introduction of volume fraction evolution and the connecting of macroscopic state variables and micromechanical characteristics in the constitutive model. The model's validation by experimental data indicates that our new model can provide a satisfactory prediction of flow stress for two-phase metallic composites, which is better than conventional single-phase homogeneous constitutive models including the Johnson–Cook (JC), Khan–Huang–Liang (KHL), Nemat-Nasser–Li (NNL), Zerilli–Armstrong (ZA) and Voyiadjis–Abed (VA) models

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.

An interfacial shear term evaluation study for adiabatic dispersed air–water two-phase flow with the two-fluid model using CFD

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

Two-phase flow characteristics analysis code: MINCS

International Nuclear Information System (INIS)

Watanabe, Tadashi; Hirano, Masashi; Akimoto, Masayuki; Tanabe, Fumiya; Kohsaka, Atsuo.

1992-03-01

Two-phase flow characteristics analysis code: MINCS (Modularized and INtegrated Code System) has been developed to provide a computational tool for analyzing two-phase flow phenomena in one-dimensional ducts. In MINCS, nine types of two-phase flow models-from a basic two-fluid nonequilibrium (2V2T) model to a simple homogeneous equilibrium (1V1T) model-can be used under the same numerical solution method. The numerical technique is based on the implicit finite difference method to enhance the numerical stability. The code structure is highly modularized, so that new constitutive relations and correlations can be easily implemented into the code and hence evaluated. A flow pattern can be fixed regardless of flow conditions, and state equations or steam tables can be selected. It is, therefore, easy to calculate physical or numerical benchmark problems. (author)

Evaluating Non-Linear Regression Models in Analysis of Persian Walnut Fruit Growth

Directory of Open Access Journals (Sweden)

I. Karamatlou

2016-02-01

of fruit growth according to length and width(diameter of fruit. Then to determine the most efficient model, different parameters of evaluation of model fitting were used. The best model was selected based on the highest value of R2and the lowest values for RMSE, AIC and BIC. The data were analyzed using SAS software (version 9.2 and Solver in Microsoft Excel. Results and Discussion Growth model based on fruit weight: According to the actual and estimated growth model based on fruit weight, double sigmoid function and logistic–monomolecular model showed a good prediction of fruit weight changes versus time data (days after full bloom. However, in general according to evaluation criteria, double sigmoid model was the best model to predict walnut fruit weight. Based on total fruit weight, fruit growth occurs at two stages: in the beginning of the growth phase, there is a slow growth for 30 days and then it is continued with a rapid growth until 60 days after full bloom. Thereafter, growth was again slow. At the beginning of the second phase of growth (70 to 85 days after full bloom, fruit growth increased again and then, walnut fruits started to ripe on the tree in summer, bright green husk (outer pericarp layer changed to a yellowish color and the growth again decreased (130 days after full bloom. Growth model based on fruit length and width measurements: Based on the actual and estimated growth pattern the Richard model describes the growth of fruit better than other models. The first phase lasted for about 15 days and the second phase of growth was very rapid and it lasted for 35 daysin most of genotypes. Then, fruit length and width did not change significantly until harvesting time. However, due to subtle changes of fruit length and width following fruit rapid growth stage, fruit weight is preferred for describing fruit growth of the Persian walnut. During the first phase of development, increasing size and weight are associated with the formation of new and

A novel drag force coefficient model for gas–water two-phase flows under different flow patterns

Energy Technology Data Exchange (ETDEWEB)

Shang, Zhi, E-mail: shangzhi@tsinghua.org.cn

2015-07-15

Graphical abstract: - Highlights: • A novel drag force coefficient model was established. • This model realized to cover different flow patterns for CFD. • Numerical simulations were performed under wide range flow regimes. • Validations were carried out through comparisons to experiments. - Abstract: A novel drag force coefficient model has been developed to study gas–water two-phase flows. In this drag force coefficient model, the terminal velocities were calculated through the revised drift flux model. The revised drift flux is different from the traditional drift flux model because the natural curve movement of the bubble was revised through considering the centrifugal force. Owing to the revisions, the revised drift flux model was to extend to 3D. Therefore it is suitable for CFD applications. In the revised drift flux model, the different flow patterns of the gas–water two-phase flows were able to be considered. This model innovatively realizes the drag force being able to cover different flow patterns of gas–water two-phase flows on bubbly flow, slug flow, churn flow, annular flow and mist flow. Through the comparisons of the numerical simulations to the experiments in vertical upward and downward pipe flows, this model was validated.

Analysis of forced convective transient boiling by homogeneous model of two-phase flow

International Nuclear Information System (INIS)

Kataoka, Isao

1985-01-01

Transient forced convective boiling is of practical importance in relation to the accident analysis of nuclear reactor etc. For large length-to-diameter ratio, the transient boiling characteristics are predicted by transient two-phase flow calculations. Based on homogeneous model of two-phase flow, the transient forced convective boiling for power and flow transients are analysed. Analytical expressions of various parameters of transient two-phase flow have been obtained for several simple cases of power and flow transients. Based on these results, heat flux, velocity and time at transient CHF condition are predicted analytically for step and exponential power increases, and step, exponential and linear velocity decreases. The effects of various parameters on heat flux, velocity and time at transient CHF condition have been clarified. Numerical approach combined with analytical method is proposed for more complicated cases. Solution method for pressure transient are also described. (author)

Inverse analyses of effective diffusion parameters relevant for a two-phase moisture model of cementitious materials

DEFF Research Database (Denmark)

Addassi, Mouadh; Johannesson, Björn; Wadsö, Lars

2018-01-01

Here we present an inverse analyses approach to determining the two-phase moisture transport properties relevant to concrete durability modeling. The purposed moisture transport model was based on a continuum approach with two truly separate equations for the liquid and gas phase being connected...... test, and, (iv) capillary suction test. Mass change over time, as obtained from the drying test, the two different cup test intervals and the capillary suction test, was used to obtain the effective diffusion parameters using the proposed inverse analyses approach. The moisture properties obtained...

A two-dimensional continuum model of biofilm growth incorporating fluid flow and shear stress based detachment

KAUST Repository

Duddu, Ravindra

2009-05-01

We present a two-dimensional biofilm growth model in a continuum framework using an Eulerian description. A computational technique based on the eXtended Finite Element Method (XFEM) and the level set method is used to simulate the growth of the biofilm. The model considers fluid flow around the biofilm surface, the advection-diffusion and reaction of substrate, variable biomass volume fraction and erosion due to the interfacial shear stress at the biofilm-fluid interface. The key assumptions of the model and the governing equations of transport, biofilm kinetics and biofilm mechanics are presented. Our 2D biofilm growth results are in good agreement with those obtained by Picioreanu et al. (Biotechnol Bioeng 69(5):504-515, 2000). Detachment due to erosion is modeled using two continuous speed functions based on: (a) interfacial shear stress and (b) biofilm height. A relation between the two detachment models in the case of a 1D biofilm is established and simulated biofilm results with detachment in 2D are presented. The stress in the biofilm due to fluid flow is evaluated and higher stresses are observed close to the substratum where the biofilm is attached. © 2008 Wiley Periodicals, Inc.

Near-earth Thin Current Sheets and Birkeland Currents during Substorm Growth Phase

International Nuclear Information System (INIS)

Sorin Zaharia; Cheng, C.Z.

2003-01-01

Two important phenomena observed during the magnetospheric substorm growth phase are modeled: the formation of a near-Earth (|X| ∼ 9 R E ) thin cross-tail current sheet, as well as the equatorward shift of the ionospheric Birkeland currents. Our study is performed by solving the 3-D force-balance equation with realistic boundary conditions and pressure distributions. The results show a cross-tail current sheet with large current (J φ ∼ 10 nA/m 2 ) and very high plasma β (β ∼ 40) between 7 and 10 R E . The obtained region-1 and region-2 Birkeland currents, formed on closed field lines due to pressure gradients, move equatorward and become more intense (J parallel max ∼ 3 (micro)A/m 2 ) compared to quiet times. Both results are in agreement with substorm growth phase observations. Our results also predict that the cross-tail current sheet maps into the ionosphere in the transition region between the region-1 and region-2 currents

A Two-Phase Model for Trade Matching and Price Setting in Double Auction Water Markets

Science.gov (United States)

Xu, Tingting; Zheng, Hang; Zhao, Jianshi; Liu, Yicheng; Tang, Pingzhong; Yang, Y. C. Ethan; Wang, Zhongjing

2018-04-01

Delivery in water markets is generally operated by agencies through channel systems, which imposes physical and institutional market constraints. Many water markets allow water users to post selling and buying requests on a board. However, water users may not be able to choose efficiently when the information (including the constraints) becomes complex. This study proposes an innovative two-phase model to address this problem based on practical experience in China. The first phase seeks and determines the optimal assignment that maximizes the incremental improvement of the system's social welfare according to the bids and asks in the water market. The second phase sets appropriate prices under constraints. Applying this model to China's Xiying Irrigation District shows that it can improve social welfare more than the current "pool exchange" method can. Within the second phase, we evaluate three objective functions (minimum variance, threshold-based balance, and two-sided balance), which represent different managerial goals. The threshold-based balance function should be preferred by most users, while the two-sided balance should be preferred by players who post extreme prices.

Digital Image Analysis of Yeast Single Cells Growing in Two Different Oxygen Concentrations to Analyze the Population Growth and to Assist Individual-Based Modeling.

Science.gov (United States)

Ginovart, Marta; Carbó, Rosa; Blanco, Mónica; Portell, Xavier

2017-01-01

Nowadays control of the growth of Saccharomyces to obtain biomass or cellular wall components is crucial for specific industrial applications. The general aim of this contribution is to deal with experimental data obtained from yeast cells and from yeast cultures to attempt the integration of the two levels of information, individual and population, to progress in the control of yeast biotechnological processes by means of the overall analysis of this set of experimental data, and to assist in the improvement of an individual-based model, namely, INDISIM- Saccha . Populations of S. cerevisiae growing in liquid batch culture, in aerobic and microaerophilic conditions, were studied. A set of digital images was taken during the population growth, and a protocol for the treatment and analyses of the images obtained was established. The piecewise linear model of Buchanan was adjusted to the temporal evolutions of the yeast populations to determine the kinetic parameters and changes of growth phases. In parallel, for all the yeast cells analyzed, values of direct morphological parameters, such as area, perimeter, major diameter, minor diameter, and derived ones, such as circularity and elongation, were obtained. Graphical and numerical methods from descriptive statistics were applied to these data to characterize the growth phases and the budding state of the yeast cells in both experimental conditions, and inferential statistical methods were used to compare the diverse groups of data achieved. Oxidative metabolism of yeast in a medium with oxygen available and low initial sugar concentration can be taken into account in order to obtain a greater number of cells or larger cells. Morphological parameters were analyzed statistically to identify which were the most useful for the discrimination of the different states, according to budding and/or growth phase, in aerobic and microaerophilic conditions. The use of the experimental data for subsequent modeling work was then

Experimental evaluation of the use of homogeneous and slip-flow two-phase dynamic models in evaporator modelling

DEFF Research Database (Denmark)

Jakobsen, Arne; Antonius, Jesper; Knudsen, Hans Jørgen Høgaard

1999-01-01

of the homogeneous model is approximately a factor 3 less than the charge calculated using the slip-flow model.The overall conclusion is that when one wants to investigate the dynamic behaviour due to the movement and amount of the refrigerant in the evaporator, then it is needed to use a slip-flow two-phase model...... shows that the dynamic response of the homogeneous model is too fast whereas the simulation results based on the slip-flow model agrees very well with the experimental results. Another difference in the results from the two types of models is the estimation of charge. The charge calculated by the use...

Phase field simulations of ice crystal growth in sugar solutions

NARCIS (Netherlands)

Sman, Van Der R.G.M.

2016-01-01

We present the first model ever, that describes explicitly ice crystal growth in a sugar solution during freezing. This 2-D model uses the phase field method, supplemented with realistic, and predictive theories on the thermodynamics and (diffusion) kinetics of this food system. We have to make

Phase transitions in two-dimensional uniformly frustrated XY models. II. General scheme

International Nuclear Information System (INIS)

Korshunov, S.E.

1986-01-01

For two-dimensional uniformly frustrated XY models the group of symmetry spontaneously broken in the ground state is a cross product of the group of two-dimensional rotations by some discrete group of finite order. Different possibilities of phase transitions in such systems are investigated. The transition to the Coulomb gas with noninteger charges is widely used when analyzing the properties of relevant topological excitations. The number of these excitations includes not only domain walls and traditional (integer) vortices, but also vortices with a fractional number of circulation quanta which are to be localized at bends and intersections of domain walls. The types of possible phase transitions prove to be dependent on their relative sequence: in the case the vanishing of domain wall free energy occurs earlier (at increasing temperature) than the dissociation of pairs of ordinary vortices, the second phase transition is to be associated with dissociation of pairs of fractional vortices. The general statements are illustrated with a number of examples

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.

The effect of membrane-regulated actin polymerization on a two-phase flow model for cell motility

KAUST Repository

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.

A scheme for reducing deceleration-phase Rayleigh-Taylor growth in inertial confinement fusion implosions

Science.gov (United States)

Wang, L. F.; Ye, W. H.; Wu, J. F.; Liu, Jie; Zhang, W. Y.; He, X. T.

2016-05-01

It is demonstrated that the growth of acceleration-phase instabilities in inertial confinement fusion implosions can be controlled, especially in the high-foot implosions [O. A. Hurricane et al., Phys. Plasmas 21, 056314 (2014)] on the National Ignition Facility. However, the excessive growth of the deceleration-phase instabilities can still destroy the hot spot ignition. A scheme is proposed to retard the deceleration-phase Rayleigh-Taylor instability growth by shock collision near the waist of the inner shell surface. Two-dimensional radiation hydrodynamic simulations confirm the improved deceleration-phase hot spot stability properties without sacrificing the fuel compression.

A scheme for reducing deceleration-phase Rayleigh–Taylor growth in inertial confinement fusion implosions

Energy Technology Data Exchange (ETDEWEB)

Wang, L. F., E-mail: wang-lifeng@iapcm.ac.cn; Ye, W. H.; Liu, Jie [Institute of Applied Physics and Computational Mathematics, Beijing 100094 (China); HEDPS, Center for Applied Physics and Technology, Peking University, Beijing 100871 (China); Center for Fusion Energy Science and Technology, Chinese Academy of Engineering Physics, Beijing 100088 (China); Wu, J. F. [Institute of Applied Physics and Computational Mathematics, Beijing 100094 (China); Center for Fusion Energy Science and Technology, Chinese Academy of Engineering Physics, Beijing 100088 (China); Zhang, W. Y. [Institute of Applied Physics and Computational Mathematics, Beijing 100094 (China); He, X. T. [Institute of Applied Physics and Computational Mathematics, Beijing 100094 (China); HEDPS, Center for Applied Physics and Technology, Peking University, Beijing 100871 (China)

2016-05-15

It is demonstrated that the growth of acceleration-phase instabilities in inertial confinement fusion implosions can be controlled, especially in the high-foot implosions [O. A. Hurricane et al., Phys. Plasmas 21, 056314 (2014)] on the National Ignition Facility. However, the excessive growth of the deceleration-phase instabilities can still destroy the hot spot ignition. A scheme is proposed to retard the deceleration-phase Rayleigh–Taylor instability growth by shock collision near the waist of the inner shell surface. Two-dimensional radiation hydrodynamic simulations confirm the improved deceleration-phase hot spot stability properties without sacrificing the fuel compression.

An implicit numerical model for multicomponent compressible two-phase flow in porous media

Science.gov (United States)

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.

Derivation of simplified basic equations of gas-liquid two-phase dispersed flow based on two-fluid model

International Nuclear Information System (INIS)

Kataoka, Isao; Tomiyama, Akio

2004-01-01

The simplified and physically reasonable basic equations for the gas-liquid dispersed flow were developed based on some appropriate assumptions and the treatment of dispersed phase as isothermal rigid particles. Based on the local instant formulation of mass, momentum and energy conservation of the dispersed flow, time-averaged equations were obtained assuming that physical quantities in the dispersed phase are uniform. These assumptions are approximately valid when phase change rate and/or chemical reaction rate are not so large at gas-liquid interface and there is no heat generation in within the dispersed phase. Detailed discussions were made on the characteristics of obtained basic equations and physical meanings of terms consisting the basic equations. It is shown that, in the derived averaged momentum equation, the terms of pressure gradient and viscous momentum diffusion do not appear and, in the energy equation, the term of molecular thermal diffusion heat flux does not appear. These characteristics of the derived equations were shown to be very consistent concerning the physical interpretation of the gas-liquid dispersed flow. Furthermore, the obtained basic equations are consistent with experiments for the dispersed flow where most of averaged physical quantities are obtained assuming that the distributions of those are uniform within the dispersed phase. Investigation was made on the problem whether the obtained basic equations are well-posed or ill-posed for the initial value problem. The eigenvalues of the simplified mass and momentum equations are calculated for basic equations obtained here and previous two-fluid basic equations with one pressure model. Well-posedness and ill-posedness are judged whether the eigenvalues are real or imaginary. The result indicated the newly developed basic equations always constitute the well-posed initial value problem while the previous two-fluid basic equations based on one pressure model constitutes ill

1D + 3D two-phase flow numerical model of a proton exchange membrane fuel cell

International Nuclear Information System (INIS)

Ferreira, Rui B.; Falcão, D.S.; Oliveira, V.B.; Pinto, A.M.F.R.

2017-01-01

Highlights: •A 1D + 3D model of a PEM fuel cell is described and experimentally validated. •VOF method tracks the two-phase flow and electrochemical reactions are considered. •Water dynamics inside a serpentine channel is analyzed for different voltages. •Water content in different regions of channel is quantified. •Important issues on coupling of the VOF model with electrochemical reactions are addressed. -- Abstract: In this work, a numerical model of a proton exchange membrane (PEM) fuel cell is presented. The volume of fluid (VOF) method is employed to simulate the air-water two-phase flow in the cathode gas channel, at the same time that the cell electrochemical performance is predicted. The model is validated against an experimental polarization curve and through the visualization of water distribution inside a transparent fuel cell. The water dynamics inside a serpentine gas channel is numerically analyzed under different operating voltages. Moreover, water content in different regions of the channel is quantified. Current density and water generation rate spatial distributions are also displayed and it is shown how they affect the process of water emergence into the gas channel. Important issues on the simulation of the PEM fuel cells two-phase flow are addressed, especially concerning the coupling of the VOF technique with electrochemical reactions. Both the model and the numerical results aim to contribute to a better understanding of the two-phase flow phenomenon that occurs in these devices.

Growth/no growth models for Zygosaccharomyces rouxii associated with acidic, sweet intermediate moisture food products

DEFF Research Database (Denmark)

Nielsen, Cecilie Lykke Marvig; Kristiansen, Rikke M.; Nielsen, Dennis Sandris

2015-01-01

sugar and fat and a traditionally long self-life of sweet IMFs, the presence of Z. rouxii in the raw materials for IMFs has made assessment of the microbiological stability a significant hurdle in product development. Therefore, knowledge on growth/no growth boundaries of Z. rouxii in sweet IMFs...... is important to ensure microbiological stability and aid product development. Several models have been developed for fat based, sweet IMFs. However, fruit/sugar based IMFs, such as fruit based chocolate fillings and jams, have lower pH and aw than what is accounted for in previously developed models....... In the present study growth/no growth models for acidified sweet IMFs were developed with the variables aw (0.65-0.80), pH (2.5-4.0), ethanol (0-14.5% (w/w) in water phase) and time (0-90 days). Two different strains of Z. rouxii previously found to show pronounced resistance to the investigated variables were...

Thermo-Fluid Dynamics of Two-Phase Flow

CERN Document Server

Ishii, Mamrou

2011-01-01

"Thermo-fluid Dynamics of Two-Phase Flow, Second Edition" is focused on the fundamental physics of two-phase flow. The authors present the detailed theoretical foundation of multi-phase flow thermo-fluid dynamics as they apply to: Nuclear reactor transient and accident analysis; Energy systems; Power generation systems; Chemical reactors and process systems; Space propulsion; Transport processes. This edition features updates on two-phase flow formulation and constitutive equations and CFD simulation codes such as FLUENT and CFX, new coverage of the lift force model, which is of part

Experimental on two sensors combination used in horizontal pipe gas-water two-phase flow

International Nuclear Information System (INIS)

Wu, Hao; Dong, Feng

2014-01-01

Gas-water two phase flow phenomenon widely exists in production and living and the measurement of it is meaningful. A new type of long-waist cone flow sensor has been designed to measure two-phase mass flow rate. Six rings structure of conductance probe is used to measure volume fraction and axial velocity. The calibration of them have been made. Two sensors have been combined in horizontal pipeline experiment to measure two-phase flow mass flow rate. Several model of gas-water two-phase flow has been discussed. The calculation errors of total mass flow rate measurement is less than 5% based on the revised homogeneous flow model

Natural Disasters in a Two-Sector Model of Endogenous Growth

OpenAIRE

Masako Ikefuji; Ryo Horii

2006-01-01

Using an endogenous growth model with physical and human capital accumulation, this paper considers the sustainability of economic growth when the use of a polluting input (e.g., fossil fuels) intensifies the risk of capital destruction through natural disasters. We find that growth is sustainable only if the tax rate on the polluting input increases over time. The long-term rate of economic growth follows an inverted V-shaped curve relative to the growth rate of the environmental tax, and it...

Modeling and analysis of LiFePO4/Carbon battery considering two-phase transition during galvanostatic charging/discharging

International Nuclear Information System (INIS)

Li, Xueyan; Xiao, Meng; Choe, Song-Yul; Joe, Won Tae

2015-01-01

Highlights: • Reduced order model for LiFePO 4 particles considering two-phase transition • Model validation with experimental results of current and voltage • Analysis of two-phase transition and path dependence - Abstract: Batteries with lithium iron phosphate (LFP) cathode and carbon anode have shown various advantages over those with other chemistries, but the plateau and path dependence caused by the two-phase transition taking place during charging and discharging make it difficult to estimate the states of battery. Thus, based on electrochemical principles we propose a new reduced order model that has been validated against experimental data obtained during galvanostatic charging/discharging. The mechanism of the two-phase transition during lithiation and delithiation in LFP particles is approximated using a shrinking corewith a moving interface between the two phases and is described by modified diffusion equations that take into account multiple layers formed within LFP particles. The shrinking core model is integrated into a cell model developed previously, which is used to analyze the path dependence at different load profiles. The results show that the model is capable of representing the characteristics of the plateau and path dependence. Particularly, the available charge at a certain State of Charge (SOC) varies dependent upon paths to reach the SOC. When an initial SOC is reached by discharging, the cell can accept more charges during charging, while when an initial SOC is reached by charging, more charge will be available during discharging

A compressible two-phase model for dispersed particle flows with application from dense to dilute regimes

Energy Technology Data Exchange (ETDEWEB)

McGrath, Thomas P., E-mail: thomas.p.mcgrath@navy.mil [Naval Surface Warfare Center Indian Head Explosive Ordnance Disposal Technology Division, 4013 Fowler Rd., Indian Head, Maryland 20640 (United States); St Clair, Jeffrey G. [Naval Surface Warfare Center Indian Head Explosive Ordnance Disposal Technology Division, 4013 Fowler Rd., Indian Head, Maryland 20640 (United States); Department of Mechanical and Aerospace Engineering, University of Florida, 231 MAE-A, P.O. Box 116250, Gainesville, Florida 32611 (United States); Balachandar, S. [Department of Mechanical and Aerospace Engineering, University of Florida, 231 MAE-A, P.O. Box 116250, Gainesville, Florida 32611 (United States)

2016-05-07

Multiphase flows are present in many important fields ranging from multiphase explosions to chemical processing. An important subset of multiphase flow applications involves dispersed materials, such as particles, droplets, and bubbles. This work presents an Eulerian–Eulerian model for multiphase flows containing dispersed particles surrounded by a continuous media such as air or water. Following a large body of multiphase literature, the driving force for particle acceleration is modeled as a direct function of both the continuous-phase pressure gradient and the gradient of intergranular stress existing within the particle phase. While the application of these two components of driving force is well accepted in much of the literature, other models exist in which the particle-phase pressure gradient itself drives particle motion. The multiphase model treats all phases as compressible and is derived to ensure adherence to the 2nd Law of Thermodynamics. The governing equations are presented and discussed, and a characteristic analysis shows the model to be hyperbolic, with a degeneracy in the case that the intergranular stress, which is modeled as a configuration pressure, is zero. Finally, results from a two sample problems involving shock-induced particle dispersion are presented. The results agree well with experimental measurements, providing initial confidence in the proposed model.

Dynamic Predictive Model for Growth of Bacillus cereus from Spores in Cooked Beans.

Science.gov (United States)

Juneja, Vijay K; Mishra, Abhinav; Pradhan, Abani K

2018-02-01

Kinetic growth data for Bacillus cereus grown from spores were collected in cooked beans under several isothermal conditions (10 to 49°C). Samples were inoculated with approximately 2 log CFU/g heat-shocked (80°C for 10 min) spores and stored at isothermal temperatures. B. cereus populations were determined at appropriate intervals by plating on mannitol-egg yolk-polymyxin agar and incubating at 30°C for 24 h. Data were fitted into Baranyi, Huang, modified Gompertz, and three-phase linear primary growth models. All four models were fitted to the experimental growth data collected at 13 to 46°C. Performances of these models were evaluated based on accuracy and bias factors, the coefficient of determination ( R 2 ), and the root mean square error. Based on these criteria, the Baranyi model best described the growth data, followed by the Huang, modified Gompertz, and three-phase linear models. The maximum growth rates of each primary model were fitted as a function of temperature using the modified Ratkowsky model. The high R 2 values (0.95 to 0.98) indicate that the modified Ratkowsky model can be used to describe the effect of temperature on the growth rates for all four primary models. The acceptable prediction zone (APZ) approach also was used for validation of the model with observed data collected during single and two-step dynamic cooling temperature protocols. When the predictions using the Baranyi model were compared with the observed data using the APZ analysis, all 24 observations for the exponential single rate cooling were within the APZ, which was set between -0.5 and 1 log CFU/g; 26 of 28 predictions for the two-step cooling profiles also were within the APZ limits. The developed dynamic model can be used to predict potential B. cereus growth from spores in beans under various temperature conditions or during extended chilling of cooked beans.

Study of two-phase flow redistribution between two passes of a heat exchanger

International Nuclear Information System (INIS)

Mendes de Moura, L.F.

1989-04-01

The object of the present thesis deals with the study of two-phase flow redistribution between two passes of a heat exchanger. Mass flow rate measurements of each component performed at each channel outlet of the second pass allowed us to determine the influence of mass flow, gas quality, flow direction (upward or downward) and common header geometry upon flow redistribution. Local void fraction inside common header was measured with an optical probe. A two-dimensional two-phase flow computational code was developed from a two-fluid model. Modelling of interfacial momentum transfer was used in order to take into account twp-phase flow patterns in common headers. Numerical simulation results show qualitative agreement with experimental results. Present theoretical model limitations are analysed and future improvements are proposed [fr

Two-phase semilinear free boundary problem with a degenerate phase

KAUST Repository

Matevosyan, Norayr

2010-10-16

We study minimizers of the energy functional ∫D[{pipe}∇u{pipe}2 + λ(u+)p]dx for p ∈ (0, 1) without any sign restriction on the function u. The distinguished feature of the problem is the lack of nondegeneracy in the negative phase. The main result states that in dimension two the free boundaries Γ+ = ∂{u > 0} ∩ D andΓ- = ∂{u < 0} ∩ D are C1,α-regular, provided 1 - ∈0 < p < 1. The proof is obtained by a careful iteration of the Harnack inequality to obtain a nontrivial growth estimate in the negative phase, compensating for the apriori unknown nondegeneracy. © 2010 Springer-Verlag.

Two-phase modeling of deflagration-to-detonation transition in granular materials: A critical examination of modeling issues

International Nuclear Information System (INIS)

Bdzil, J.B.; Menikoff, R.; Son, S.F.; Kapila, A.K.; Stewart, D.S.

1999-01-01

The two-phase mixture model developed by Baer and Nunziato (BN) to study the deflagration-to-detonation transition (DDT) in granular explosives is critically reviewed. The continuum-mixture theory foundation of the model is examined, with particular attention paid to the manner in which its constitutive functions are formulated. Connections between the mechanical and energetic phenomena occurring at the scales of the grains, and their manifestations on the continuum averaged scale, are explored. The nature and extent of approximations inherent in formulating the constitutive terms, and their domain of applicability, are clarified. Deficiencies and inconsistencies in the derivation are cited, and improvements suggested. It is emphasized that the entropy inequality constrains but does not uniquely determine the phase interaction terms. The resulting flexibility is exploited to suggest improved forms for the phase interactions. These improved forms better treat the energy associated with the dynamic compaction of the bed and the single-phase limits of the model. Companion papers of this study [Kapila et al., Phys. Fluids 9, 3885 (1997); Kapila et al., in preparation; Son et al., in preparation] examine simpler, reduced models, in which the fine scales of velocity and pressure disequilibrium between the phases allow the corresponding relaxation zones to be treated as discontinuities that need not be resolved in a numerical computation. copyright 1999 American Institute of Physics

Dynamics of the two-dimensional directed Ising model in the paramagnetic phase

Science.gov (United States)

Godrèche, C.; Pleimling, M.

2014-05-01

We consider the nonconserved dynamics of the Ising model on the two-dimensional square lattice, where each spin is influenced preferentially by its east and north neighbours. The single-spin flip rates are such that the stationary state is Gibbsian with respect to the usual ferromagnetic Ising Hamiltonian. We show the existence, in the paramagnetic phase, of a dynamical transition between two regimes of violation of the fluctuation-dissipation theorem in the nonequilibrium stationary state: a regime of weak violation where the stationary fluctuation-dissipation ratio is finite, when the asymmetry parameter is less than a threshold value, and a regime of strong violation where this ratio vanishes asymptotically above the threshold. This study suggests that this novel kind of dynamical transition in nonequilibrium stationary states, already found for the directed Ising chain and the spherical model with asymmetric dynamics, might be quite general. In contrast with the latter models, the equal-time correlation function for the two-dimensional directed Ising model depends on the asymmetry.

A Schur complement method for compressible two-phase flow models

International Nuclear Information System (INIS)

Dao, Thu-Huyen; Ndjinga, Michael; Magoules, Frederic

2014-01-01

In this paper, we will report our recent efforts to apply a Schur complement method for nonlinear hyperbolic problems. We use the finite volume method and an implicit version of the Roe approximate Riemann solver. With the interface variable introduced in [4] in the context of single phase flows, we are able to simulate two-fluid models ([12]) with various schemes such as upwind, centered or Rusanov. Moreover, we introduce a scaling strategy to improve the condition number of both the interface system and the local systems. Numerical results for the isentropic two-fluid model and the compressible Navier-Stokes equations in various 2D and 3D configurations and various schemes show that our method is robust and efficient. The scaling strategy considerably reduces the number of GMRES iterations in both interface system and local system resolutions. Comparisons of performances with classical distributed computing with up to 218 processors are also reported. (authors)

A modified homogeneous relaxation model for CO2 two-phase flow in vapour ejector

International Nuclear Information System (INIS)

Haida, M.; Palacz, M.; Smolka, J.; Nowak, A. J.; Hafner, A.; Banasiak, K.

2016-01-01

In this study, the homogenous relaxation model (HRM) for CO 2 flow in a two-phase ejector was modified in order to increase the accuracy of the numerical simulations The two- phase flow model was implemented on the effective computational tool called ejectorPL for fully automated and systematic computations of various ejector shapes and operating conditions. The modification of the HRM was performed by a change of the relaxation time and the constants included in the relaxation time equation based on the experimental result under the operating conditions typical for the supermarket refrigeration system. The modified HRM was compared to the HEM results, which were performed based on the comparison of motive nozzle and suction nozzle mass flow rates. (paper)

A modified homogeneous relaxation model for CO2 two-phase flow in vapour ejector

Science.gov (United States)

Haida, M.; Palacz, M.; Smolka, J.; Nowak, A. J.; Hafner, A.; Banasiak, K.

2016-09-01

In this study, the homogenous relaxation model (HRM) for CO2 flow in a two-phase ejector was modified in order to increase the accuracy of the numerical simulations The two- phase flow model was implemented on the effective computational tool called ejectorPL for fully automated and systematic computations of various ejector shapes and operating conditions. The modification of the HRM was performed by a change of the relaxation time and the constants included in the relaxation time equation based on the experimental result under the operating conditions typical for the supermarket refrigeration system. The modified HRM was compared to the HEM results, which were performed based on the comparison of motive nozzle and suction nozzle mass flow rates.

Investigation of representing hysteresis in macroscopic models of two-phase flow in porous media using intermediate scale experimental data

Science.gov (United States)

Cihan, Abdullah; Birkholzer, Jens; Trevisan, Luca; Gonzalez-Nicolas, Ana; Illangasekare, Tissa

2017-01-01

Incorporating hysteresis into models is important to accurately capture the two phase flow behavior when porous media systems undergo cycles of drainage and imbibition such as in the cases of injection and post-injection redistribution of CO2 during geological CO2 storage (GCS). In the traditional model of two-phase flow, existing constitutive models that parameterize the hysteresis associated with these processes are generally based on the empirical relationships. This manuscript presents development and testing of mathematical hysteretic capillary pressure—saturation—relative permeability models with the objective of more accurately representing the redistribution of the fluids after injection. The constitutive models are developed by relating macroscopic variables to basic physics of two-phase capillary displacements at pore-scale and void space distribution properties. The modeling approach with the developed constitutive models with and without hysteresis as input is tested against some intermediate-scale flow cell experiments to test the ability of the models to represent movement and capillary trapping of immiscible fluids under macroscopically homogeneous and heterogeneous conditions. The hysteretic two-phase flow model predicted the overall plume migration and distribution during and post injection reasonably well and represented the postinjection behavior of the plume more accurately than the nonhysteretic models. Based on the results in this study, neglecting hysteresis in the constitutive models of the traditional two-phase flow theory can seriously overpredict or underpredict the injected fluid distribution during post-injection under both homogeneous and heterogeneous conditions, depending on the selected value of the residual saturation in the nonhysteretic models.

Zero-G two phase flow regime modeling in adiabatic flow

International Nuclear Information System (INIS)

Reinarts, T.R.; Best, F.R.; Wheeler, M.; Miller, K.M.

1993-01-01

Two-phase flow, thermal management systems are currently being considered as an alternative to conventional, single phase systems for future space missions because of their potential to reduce overall system mass, size, and pumping power requirements. Knowledge of flow regime transitions, heat transfer characteristics, and pressure drop correlations is necessary to design and develop two-phase systems. This work is concerned with microgravity, two-phase flow regime analysis. The data come from a recent sets of experiments. The experiments were funded by NASA Johnson Space Center (JSC) and conducted by NASA JSC with Texas A ampersand M University. The experiment was on loan to NASA JSC from Foster-Miller, Inc., who constructed it with funding from the Air Force Phillips Laboratory. The experiment used R12 as the working fluid. A Foster-Miller two phase pump was used to circulate the two phase mixture and allow separate measurements of the vapor and liquid flow streams. The experimental package was flown 19 times for 577 parabolas aboard the NASA KC-135 aircraft which simulates zero-G conditions by its parabolic flight trajectory. Test conditions included bubbly, slug and annular flow regimes in 0-G. The superficial velocities of liquid and vapor have been obtained from the measured flow rates and are presented along with the observed flow regimes and several flow regime transition predictions. None of the predictions completely describe the transitions as indicated by the data

Light-optimized growth of cyanobacterial cultures: Growth phases and productivity of biomass and secreted molecules in light-limited batch growth.

Science.gov (United States)

Clark, Ryan L; McGinley, Laura L; Purdy, Hugh M; Korosh, Travis C; Reed, Jennifer L; Root, Thatcher W; Pfleger, Brian F

2018-03-27

Cyanobacteria are photosynthetic microorganisms whose metabolism can be modified through genetic engineering for production of a wide variety of molecules directly from CO 2 , light, and nutrients. Diverse molecules have been produced in small quantities by engineered cyanobacteria to demonstrate the feasibility of photosynthetic biorefineries. Consequently, there is interest in engineering these microorganisms to increase titer and productivity to meet industrial metrics. Unfortunately, differing experimental conditions and cultivation techniques confound comparisons of strains and metabolic engineering strategies. In this work, we discuss the factors governing photoautotrophic growth and demonstrate nutritionally replete conditions in which a model cyanobacterium can be grown to stationary phase with light as the sole limiting substrate. We introduce a mathematical framework for understanding the dynamics of growth and product secretion in light-limited cyanobacterial cultures. Using this framework, we demonstrate how cyanobacterial growth in differing experimental systems can be easily scaled by the volumetric photon delivery rate using the model organisms Synechococcus sp. strain PCC7002 and Synechococcus elongatus strain UTEX2973. We use this framework to predict scaled up growth and product secretion in 1L photobioreactors of two strains of Synechococcus PCC7002 engineered for production of l-lactate or L-lysine. The analytical framework developed in this work serves as a guide for future metabolic engineering studies of cyanobacteria to allow better comparison of experiments performed in different experimental systems and to further investigate the dynamics of growth and product secretion. Copyright © 2018 International Metabolic Engineering Society. Published by Elsevier Inc. All rights reserved.

Switching moving boundary models for two-phase flow evaporators and condensers

Science.gov (United States)

Bonilla, Javier; Dormido, Sebastián; Cellier, François E.

2015-03-01

The moving boundary method is an appealing approach for the design, testing and validation of advanced control schemes for evaporators and condensers. When it comes to advanced control strategies, not only accurate but fast dynamic models are required. Moving boundary models are fast low-order dynamic models, and they can describe the dynamic behavior with high accuracy. This paper presents a mathematical formulation based on physical principles for two-phase flow moving boundary evaporator and condenser models which support dynamic switching between all possible flow configurations. The models were implemented in a library using the equation-based object-oriented Modelica language. Several integrity tests in steady-state and transient predictions together with stability tests verified the models. Experimental data from a direct steam generation parabolic-trough solar thermal power plant is used to validate and compare the developed moving boundary models against finite volume models.

CFD model of diabatic annular two-phase flow using the Eulerian–Lagrangian approach

International Nuclear Information System (INIS)

Li, Haipeng; Anglart, Henryk

2015-01-01

Highlights: • A CFD model of annular two-phase flow with evaporating liquid film has been developed. • A two-dimensional liquid film model is developed assuming that the liquid film is sufficiently thin. • The liquid film model is coupled to the gas core flow, which is represented using the Eulerian–Lagrangian approach. - Abstract: A computational fluid dynamics (CFD) model of annular two-phase flow with evaporating liquid film has been developed based on the Eulerian–Lagrangian approach, with the objective to predict the dryout occurrence. Due to the fact that the liquid film is sufficiently thin in the diabatic annular flow and at the pre-dryout conditions, it is assumed that the flow in the wall normal direction can be neglected, and the spatial gradients of the dependent variables tangential to the wall are negligible compared to those in the wall normal direction. Subsequently the transport equations of mass, momentum and energy for liquid film are integrated in the wall normal direction to obtain two-dimensional equations, with all the liquid film properties depth-averaged. The liquid film model is coupled to the gas core flow, which currently is represented using the Eulerian–Lagrangian technique. The mass, momentum and energy transfers between the liquid film, gas, and entrained droplets have been taken into account. The resultant unified model 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 favorable 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

The use of a diffuse interface model to estimate effective transport properties for two-phase flows in porous media

International Nuclear Information System (INIS)

Fichot, Floriana; Duval, Fabiena; Garcia, Aureliena; Belloni, Julien; Quintard, Michel

2005-01-01

Full text of publication follows: In the framework of its research programme on severe nuclear reactor accidents, IRSN investigates the water flooding of an overheated porous bed, where complex two-phase flows are likely to exist. The goal is to describe the flow with a general model, covering rods and debris beds regions in the vessel. A better understanding of the flow at the pore level appears to be necessary in order to justify and improve closure laws of macroscopic models. Although the Direct Numerical Simulation (DNS) of two-phase flows is possible with several methods, applications are now limited to small computational domains, typically of the order of a few centimeters. Therefore, numerical solutions at the reactor scale can only be obtained by using averaged models. Volume averaging is the most traditional way of deriving such models. For nuclear safety codes, a control volume must include a few rods or a few debris particles, with a characteristic dimension of a few centimeters. The difficulty usually met with averaged models is the closure of several transport or source terms which appear in the averaged conservation equations (for example the interfacial drag or the heat transfers between phases) [2]. In the past, the closure of these terms was obtained, when possible, from one-dimensional experiments that allowed measurements of heat flux or pressure drops. For more complex flows, the experimental measurement of local parameters is often impossible and the effective properties cannot be determined easily. An alternative way is to perform 'numerical experiments' with numerical simulations of the local flow. As mentioned above, the domain of application of DNS corresponds to the size of control volumes necessary to derive averaged models. Therefore DNS appears as a powerful tool to investigate the local features of a two-phase flow in complex geometries. Diffuse interface methods provide a way to model flows with interfacial phenomena through an

Lumped parameter modeling of a two-phase thermal-hydraulic channel with interface tracking

International Nuclear Information System (INIS)

Jo, J.H.; Kaufman, J.M.; Ruger, C.J.; Stein, S.

1978-01-01

A nonhomogenous, thermal nonequilibrium model for one-dimensional two-phase flow in a heated channel has been formulated in lumped parameter form. The channel is divided into a variable number of flow regimes separated by moving interfaces. The model can be used to predict the behavior of a LWR core and both primary and secondary sides of a steam generator under transient conditions. (author)

A numerical model of two-phase flow at the micro-scale using the volume-of-fluid method

Science.gov (United States)

Shams, Mosayeb; Raeini, Ali Q.; Blunt, Martin J.; Bijeljic, Branko

2018-03-01

This study presents a simple and robust numerical scheme to model two-phase flow in porous media where capillary forces dominate over viscous effects. The volume-of-fluid method is employed to capture the fluid-fluid interface whose dynamics is explicitly described based on a finite volume discretization of the Navier-Stokes equations. Interfacial forces are calculated directly on reconstructed interface elements such that the total curvature is preserved. The computed interfacial forces are explicitly added to the Navier-Stokes equations using a sharp formulation which effectively eliminates spurious currents. The stability and accuracy of the implemented scheme is validated on several two- and three-dimensional test cases, which indicate the capability of the method to model two-phase flow processes at the micro-scale. In particular we show how the co-current flow of two viscous fluids leads to greatly enhanced flow conductance for the wetting phase in corners of the pore space, compared to a case where the non-wetting phase is an inviscid gas.

A computer model for hydride blister growth in zirconium alloys

International Nuclear Information System (INIS)

White, A.J.; Sawatzky, A.; Woo, C.H.

1985-06-01

The failure of a Zircaloy-2 pressure tube in the Pickering unit 2 reactor started at a series of zirconium hydride blisters on the outside of the pressure tube. These blisters resulted from the thermal diffusion of hydrogen to the cooler regions of the pressure tube. In this report the physics of thermal diffusion of hydrogen in zirconium is reviewed and a computer model for blister growth in two-dimensional Cartesian geometry is described. The model is used to show that the blister-growth rate in a two-phase zirconium/zirconium-hydride region does not depend on the initial hydrogen concentration nor on the hydrogen pick-up rate, and that for a fixed far-field temperature there is an optimum pressure-type/calandria-tube contact temperature for growing blisters. The model described here can also be used to study large-scale effects, such as hydrogen-depletion zones around hydride blisters

Simultaneous thermal and optical imaging of two-phase flow in a micro-model.

Science.gov (United States)

Karadimitriou, N K; Nuske, P; Kleingeld, P J; Hassanizadeh, S M; Helmig, R

2014-07-21

In the study of non-equilibrium heat transfer in multiphase flow in porous media, parameters and constitutive relations, like heat transfer coefficients between phases, are unknown. In order to study the temperature development of a relatively hot invading immiscible non-wetting fluid and, ultimately, approximate heat transfer coefficients, a transparent micro-model is used as an artificial porous medium. In the last few decades, micro-models have become popular experimental tools for two-phase flow studies. In this work, the design of an innovative, elongated, PDMS (polydimethylsiloxane) micro-model with dimensions of 14.4 × 39 mm(2) and a constant depth of 100 microns is described. A novel setup for simultaneous thermal and optical imaging of flow through the micro-model is presented. This is the first time that a closed flow cell like a micro-model is used in simultaneous thermal and optical flow imaging. The micro-model is visualized by a novel setup that allowed us to monitor and record the distribution of fluids throughout the length of the micro-model continuously and also record the thermal signature of the fluids. Dynamic drainage and imbibition experiments were conducted in order to obtain information about the heat exchange between the phases. In this paper the setup as well as analysis and qualitative results are presented.

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.

Modeling of annular two-phase flow using a unified CFD approach

International Nuclear Information System (INIS)

Li, Haipeng; Anglart, Henryk

2016-01-01

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.

Bulk water phase and biofilm growth in drinking water at low nutrient conditions

DEFF Research Database (Denmark)

Boe-Hansen, Rasmus; Albrechtsen, Hans-Jørgen; Arvin, Erik

2002-01-01

, and cell-specific leucine incorporation rate. Bacteria in the bulk water phase incubated without the presence of biofilmexhibited a bacterial growth rate of 0.30 day1. The biofilmwas radioactively labelled by the addition of 14C-benzoic acid. Subsequently, a biofilmdetachm ent rate of 0.013 day1...... the formation of a mature quasi-stationary biofilm. At retention times of 12 h, total bacterial counts increased equivalent to a net bacterial growth rate of 0.048 day1. The bulk water phase bacteria exhibited a higher activity than the biofilmbacteria in terms of culturability, cell-specific ATP content......In this study, the bacterial growth dynamics of a drinking water distribution system at low nutrient conditions was studied in order to determine bacterial growth rates by a range of methods, and to compare growth rates in the bulk water phase and the biofilm. A model distribution system was used...

Testing mechanistic models of growth in insects.

Science.gov (United States)

Maino, James L; Kearney, Michael R

2015-11-22

Insects are typified by their small size, large numbers, impressive reproductive output and rapid growth. However, insect growth is not simply rapid; rather, insects follow a qualitatively distinct trajectory to many other animals. Here we present a mechanistic growth model for insects and show that increasing specific assimilation during the growth phase can explain the near-exponential growth trajectory of insects. The presented model is tested against growth data on 50 insects, and compared against other mechanistic growth models. Unlike the other mechanistic models, our growth model predicts energy reserves per biomass to increase with age, which implies a higher production efficiency and energy density of biomass in later instars. These predictions are tested against data compiled from the literature whereby it is confirmed that insects increase their production efficiency (by 24 percentage points) and energy density (by 4 J mg(-1)) between hatching and the attainment of full size. The model suggests that insects achieve greater production efficiencies and enhanced growth rates by increasing specific assimilation and increasing energy reserves per biomass, which are less costly to maintain than structural biomass. Our findings illustrate how the explanatory and predictive power of mechanistic growth models comes from their grounding in underlying biological processes. © 2015 The Author(s).

Two-phase plate-fin heat exchanger modeling for waste heat recovery systems in diesel engines

NARCIS (Netherlands)

Feru, E.; Jager, de A.G.; Willems, F.P.T.; 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

Two-fluid model of two-phase flow in a pin bundle of a nuclear reactor

International Nuclear Information System (INIS)

Chawla, T.C.; Ishii, M.

1980-01-01

By considering two-phase flow as a field which is subdivided into two turbulent single-phase regions with moving boundaries separating the two constituent phases, such that the differential balances for three-dimensional turbulent flow hold for each subregion and for the interface, we perform the Eulerian area averaging over the cross-sectional area of each phase in a given channel and segment averaging of transverse momentum equation along the phase intercepts at the interchannel boundaries. To simplify the governing equations obtained as a result of these operations, we invoke the assumption that the motion of the fluid in each phase is dominantly in axial direction, that is the transverse components of velocity are small compared to axial components. We further assume that the variation of axial component of velocity within a channel is much stronger than the variation along the axial direction. We also assume that similar arguments can also be applied to the variation of enthalpy in a channel. As a result of these considerations, we obtain two sets of continuity, momentum, and energy equations describing motion of each phase in the axial direction. The phasic interaction terms which appear in these equations are governed by interfacial transfer conditions obtained from interface balances. The segment-averaged transverse-momentum equation for each phase provides the governing equation for cross flow. (author)

Modelling and numerical simulation of two-phase flows using the two-fluid two-pressure approach; Modelisation et simulation numerique des ecoulements diphasiques par une approche bifluide a deux pressions

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

Extension of CFD Codes Application to Two-Phase Flow Safety Problems - Phase 3

International Nuclear Information System (INIS)

Bestion, D.; Anglart, H.; Mahaffy, J.; Lucas, D.; Song, C.H.; Scheuerer, M.; Zigh, G.; Andreani, M.; Kasahara, F.; Heitsch, M.; Komen, E.; Moretti, F.; Morii, T.; Muehlbauer, P.; Smith, B.L.; Watanabe, T.

2014-11-01

The Writing Group 3 on the extension of CFD to two-phase flow safety problems was formed following recommendations made at the 'Exploratory Meeting of Experts to Define an Action Plan on the Application of Computational Fluid Dynamics (CFD) Codes to Nuclear Reactor Safety Problems' held in Aix-en-Provence, in May 2002. Extension of CFD codes to two-phase flow is significant potentiality for the improvement of safety investigations, by giving some access to smaller scale flow processes which were not explicitly described by present tools. Using such tools as part of a safety demonstration may bring a better understanding of physical situations, more confidence in the results, and an estimation of safety margins. The increasing computer performance allows a more extensive use of 3D modelling of two-phase Thermal hydraulics with finer nodalization. However, models are not as mature as in single phase flow and a lot of work has still to be done on the physical modelling and numerical schemes in such two-phase CFD tools. The Writing Group listed and classified the NRS problems where extension of CFD to two-phase flow may bring real benefit, and classified different modelling approaches in a first report (Bestion et al., 2006). First ideas were reported about the specification and analysis of needs in terms of validation and verification. It was then suggested to focus further activity on a limited number of NRS issues with a high priority and a reasonable chance to be successful in a reasonable period of time. The WG3-step 2 was decided with the following objectives: - selection of a limited number of NRS issues having a high priority and for which two-phase CFD has a reasonable chance to be successful in a reasonable period of time; - identification of the remaining gaps in the existing approaches using two-phase CFD for each selected NRS issue; - review of the existing data base for validation of two-phase CFD application to the selected NRS problems

Phase competition in the growth of SrCoOx/LaAlO3 thin films

Science.gov (United States)

Zhang, Jie; Meng, Dechao; Huang, Haoliang; Cai, Honglei; Huang, Qiuping; Wang, Jianlin; Yang, Yuanjun; Zhai, Xiaofang; Fu, Zhengping; Lu, Yalin

2018-02-01

The reversible topotactic phase transformation between brownmillerite SrCoO2.5 to perovskite SrCoO3 has attracted more and more attention for potential applications as solid oxide fuels and electrolysis cells. However, the relatively easy transformation result from small thermal stable energy barriers between the two phases leads to unstable the structures. In the paper, amounts of SrCoO3-δ films have been prepared by pulsed laser deposition at optimized growth conditions with the temperature range of 590-720°C. The X-ray diffraction (XRD) results demonstrated that a phase competition emerged around 650°C. The Gibbs free energies of two phases at high temperature revealed the difference of stability of these two phases under different growth temperature. The optical spectroscopies and X-ray photoelectron spectroscopies were used to verify the electronic structure and chemical state differences between the two phases with distinct crystal structures.

Phase competition in the growth of SrCoOx/LaAlO3 thin films

Directory of Open Access Journals (Sweden)

Jie Zhang

2018-02-01

Full Text Available The reversible topotactic phase transformation between brownmillerite SrCoO2.5 to perovskite SrCoO3 has attracted more and more attention for potential applications as solid oxide fuels and electrolysis cells. However, the relatively easy transformation result from small thermal stable energy barriers between the two phases leads to unstable the structures. In the paper, amounts of SrCoO3-δ films have been prepared by pulsed laser deposition at optimized growth conditions with the temperature range of 590-720°C. The X-ray diffraction (XRD results demonstrated that a phase competition emerged around 650°C. The Gibbs free energies of two phases at high temperature revealed the difference of stability of these two phases under different growth temperature. The optical spectroscopies and X-ray photoelectron spectroscopies were used to verify the electronic structure and chemical state differences between the two phases with distinct crystal structures.

An introduction to two-phase flows

International Nuclear Information System (INIS)

Lemonnier, Herve

2006-01-01

This course aims at proposing the necessary background for a rational approach to two-phase flows which are notably present in numerous industrial devices and equipment designed to perform energy transfer or mass transfer. The first part proposes a phenomenological approach to main two-phase flow structures and presents their governing variables. The second part presents some proven measurement techniques. The third part focuses on modelling. It recalls the equation elaboration techniques which are based on basic principles of mechanics and thermodynamics and on the application of different averaging operators to these principles. Some useful models are then presented such as models of pressure loss in a duct. The last chapter addresses some fundamental elements of heat transfers in ebullition and condensation

Application of non-equilibrium thermodynamics to two-phase flows with a change of phase

International Nuclear Information System (INIS)

Delhaye, J.M.

1969-01-01

In this report we use the methods of non-equilibrium thermodynamics in two-phase flows. This paper follows a prior one in which we have studied the conservation laws and derived the general equations of two-phase flow. In the first part the basic ideas of thermodynamics of irreversible systems are given. We follow the classical point of view. The second part is concerned with the derivation of a closed set of equations for the two phase elementary volume model. In this model we assume that the elementary volume contains two phases and that it is possible to define a volumetric local concentration. To obtain the entropy balance we can choose either the reversibility of the barycentric motion or the reversibility of each phase. We adopt the last assumption and our derivation is the same as this of I.Prigogine and P. Mazur about the hydrodynamics of liquid helium. The scope of this work is not to find a general solution to the problems of two phase flows but to obtain a new set of equations which may be used to explain some characteristic phenomena of two-phase flow such as wave propagation or critical states. (author) [fr

Validity of two-phase polymer electrolyte membrane fuel cell models with respect to the gas diffusion layer

Science.gov (United States)

Ziegler, C.; Gerteisen, D.

A dynamic two-phase model of a proton exchange membrane fuel cell with respect to the gas diffusion layer (GDL) is presented and compared with chronoamperometric experiments. Very good agreement between experiment and simulation is achieved for potential step voltammetry (PSV) and sine wave testing (SWT). Homogenized two-phase models can be categorized in unsaturated flow theory (UFT) and multiphase mixture (M 2) models. Both model approaches use the continuum hypothesis as fundamental assumption. Cyclic voltammetry experiments show that there is a deterministic and a stochastic liquid transport mode depending on the fraction of hydrophilic pores of the GDL. ESEM imaging is used to investigate the morphology of the liquid water accumulation in the pores of two different media (unteflonated Toray-TGP-H-090 and hydrophobic Freudenberg H2315 I3). The morphology of the liquid water accumulation are related with the cell behavior. The results show that UFT and M 2 two-phase models are a valid approach for diffusion media with large fraction of hydrophilic pores such as unteflonated Toray-TGP-H paper. However, the use of the homgenized UFT and M 2 models appears to be invalid for GDLs with large fraction of hydrophobic pores that corresponds to a high average contact angle of the GDL.

An Eulerian two-phase flow model for sediment transport under realistic surface waves

Science.gov (United States)

Hsu, T. J.; Kim, Y.; Cheng, Z.; Chauchat, J.

2017-12-01

Wave-driven sediment transport is of major importance in driving beach morphology. However, the complex mechanisms associated with unsteadiness, free-surface effects, and wave-breaking turbulence have not been fully understood. Particularly, most existing models for sediment transport adopt bottom boundary layer approximation that mimics the flow condition in oscillating water tunnel (U-tube). However, it is well-known that there are key differences in sediment transport when comparing to large wave flume datasets, although the number of wave flume experiments are relatively limited regardless of its importance. Thus, a numerical model which can resolve the entire water column from the bottom boundary layer to the free surface can be a powerful tool. This study reports an on-going effort to better understand and quantify sediment transport under shoaling and breaking surface waves through the creation of open-source numerical models in the OpenFOAM framework. An Eulerian two-phase flow model, SedFoam (Cheng et al., 2017, Coastal Eng.) is fully coupled with a volume-of-fluid solver, interFoam/waves2Foam (Jacobsen et al., 2011, Int. J. Num. Fluid). The fully coupled model, named SedWaveFoam, regards the air and water phases as two immiscible fluids with the interfaces evolution resolved, and the sediment particles as dispersed phase. We carried out model-data comparisons with the large wave flume sheet flow data for nonbreaking waves reported by Dohmen-Janssen and Hanes (2002, J. Geophysical Res.) and good agreements were obtained for sediment concentration and net transport rate. By further simulating a case without free-surface (mimic U-tube condition), the effects of free-surface, most notably the boundary layer streaming effect on total transport, can be quantified.

Phase-field modelling of microstructural evolution and properties

Science.gov (United States)

Zhu, Jingzhi

externally applied strain. Specifically the effects of elastic inhomogeneity on the coarsening of a two-phase microstructure were investigated. It was generally found that the hard phase tends to form precipitates surrounded by the soft matrix phase to reduce the elastic energy, in agreement with prior studies using first-order approximations. Increasing the elastic inhomogeneity will reduce the growth exponent. A three-dimensional phase-field model was developed which can be linked with the CALPHAD method through the local free energy construction as a function of field variables. The model takes most important thermodynamic and kinetic parameters, such as lattice parameters, interfacial energy and elastic constants, from either a database or independent experimental measurements. The Ni 3Al precipitate shape evolution in a binary Ni-Al system was studied as an example. Depending on the balance between interfacial energy and elastic energy relaxation, the simulated microstructures developed different shapes at different sizes. The diffuse-interface model can also be employed for modelling temporal mass diffusion transport through an arbitrary microstructure as well as the corresponding effective properties. From the comparison results in a wide variety of examples including the three kinetic regimes of grain boundary diffusion, the effective property prediction obtained by the diffuse-interface model was in good agreement with that obtained by using a conventional sharp-interface model.

Income and Wealth Distribution in a Neoclassical Two-Sector Heterogeneous-Households Growth Model with Elastic Labor Supply and Consumer Durable Goods

Directory of Open Access Journals (Sweden)

Wei-Bin ZHANG

2017-06-01

Full Text Available This paper proposes a two-sector two-group growth model with elastic labor supply and consumer durable goods. We study dynamics of wealth and income distribution in a competitive economy with capital accumulation as the main engine of economic growth. The model is built on the Uzawa two-sector model. It is also influenced by the neoclassical growth theory and the post-Keynesian theory of growth and distribution. We plot the motion of the economic system and determine the economic equilibrium. We carry out comparative dynamic analysis with regard to the propensity to save and improvements in human capital and technology.

Pressure drop calculation using a one-dimensional mathematical model for two-phase flow through an orifice

DEFF Research Database (Denmark)

Petkov, K.P.; Puton, M; Madsen, Søren Peder

2014-01-01

are accounted for through both friction and acceleration as in a conventional formulation. However, in this analysis the acceleration term is both attributed geometrical effects through the area change and fluid dynamic effects through the expansion of the two-phase flow. The comparison of numerical...... 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...

Numerical simulations of counter-current two-phase flow experiments in a PWR hot leg model using an interfacial area density model

Energy Technology Data Exchange (ETDEWEB)

Hoehne, Thomas, E-mail: t.hoehne@hzdr.de [Helmholtz-Zentrum Dresden-Rossendorf (HZDR), Institute of Safety Research, P.O. Box 510 119, D-01314 Dresden (Germany); Deendarlianto,; Lucas, Dirk [Helmholtz-Zentrum Dresden-Rossendorf (HZDR), Institute of Safety Research, P.O. Box 510 119, D-01314 Dresden (Germany)

2011-10-15

In order to improve the understanding of counter-current two-phase flows and to validate new physical models, CFD simulations of 1/3rd scale model of the hot leg of a German Konvoi PWR with rectangular cross section was performed. Selected counter-current flow limitation (CCFL) experiments at the Helmholtz-Zentrum Dresden-Rossendorf (HZDR) were calculated with ANSYS CFX 12.1 using the multi-fluid Euler-Euler modeling approach. The transient calculations were carried out using a gas/liquid inhomogeneous multiphase flow model coupled with a k-{omega} turbulence model for each phase. In the simulation, the surface drag was approached by a new correlation inside the Algebraic Interfacial Area Density (AIAD) model. The AIAD model allows the detection of the morphological form of the two phase flow and the corresponding switching via a blending function of each correlation from one object pair to another. As a result this model can distinguish between 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 indicated that quantitative agreement of the CCFL characteristics between calculation and experimental data was obtained. The goal is to provide an easy usable AIAD framework for all Code users, with the possibility of the implementation of their own correlations.

Numerical simulations of counter-current two-phase flow experiments in a PWR hot leg model using an interfacial area density model

Energy Technology Data Exchange (ETDEWEB)

Hohne, T.; Deendarlianto; Vallee, C.; Lucas, D.; Beyer, M., E-mail: t.hoehne@hzdr.de [Helmholtz-Zentrum Dresden-Rossendorf (HZDR), Inst. of Safety Research, Dresden (Germany)

2011-07-01

In order to improve the understanding of counter-current two-phase flows and to validate new physical models, CFD simulations of 1/3rd scale model of the hot leg of a German Konvoi PWR with rectangular cross section was performed. Selected counter-current flow limitation (CCFL) experiments at the Helmholtz-Zentrum Dresden- Rossendorf (HZDR) were calculated with ANSYS CFX 12.1 using the multi-fluid Euler-Euler modeling approach. The transient calculations were carried out using a gas/liquid inhomogeneous multiphase flow model coupled with a SST turbulence model for each phase. In the simulation, the surface drag was approached by a new correlation inside the Algebraic Interfacial Area Density (AIAD) model. The AIAD model allows the detection of the morphological form of the two phase flow and the corresponding switching via a blending function of each correlation from one object pair to another. As a result this model can distinguish between 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 indicated that quantitative agreement of the CCFL characteristics between calculation and experimental data was obtained. The goal is to provide an easy usable AIAD framework for all ANSYS CFX users, with the possibility of the implementation of their own correlations. (author)

Multi-scale diffuse interface modeling of multi-component two-phase flow with partial miscibility

KAUST Repository

Kou, Jisheng; Sun, Shuyu

2016-01-01

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

Mechanical disequilibria in two-phase flow models: approaches by relaxation and by a reduced model; Modelisation des desequilibres mecaniques dans les ecoulements diphasiques: approches par relaxation et par modele reduit

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)

One-dimensional two-phase thermal hydraulics (ENSTA course)

International Nuclear Information System (INIS)

Olive, J.

1995-11-01

This course is part of the ENSTA 3rd year thermal hydraulics program (nuclear power option). Its purpose is to provide the theoretical basis and main physical notions pertaining to two-phase flow, mainly focussed on water-steam flows. The introduction describes the physical specificities of these flows, emphasizing their complexity. The mathematical bases are then presented (partial derivative equations), leading to a one-dimensional type, simplified description. Balances drawn up for a pipe length volume are used to introduce the mass conservation. motion and energy equations for each phase. Various postulates used to simplify two-phase models are presented, culminating in homogeneous model definitions and equations, several common examples of which are given. The model is then applied to the calculation of pressure drops in two-phase flows. This involves presenting the models most frequently used to represent pressure drops by friction or due to pipe irregularities, without giving details (numerical values of parameters). This chapter terminates with a brief description of static and dynamic instabilities in two-phase flows. Finally, heat transfer conditions frequently encountered in liquid-steam flows are described, still in the context of a 1D model. This chapter notably includes reference to under-saturated boiling conditions and the various forms of DNB. The empirical heat transfer laws are not discussed in detail. Additional material is appended, some of which is in the form of corrected exercises. (author). 6 appends

Stochastic Differential Equation-Based Flexible Software Reliability Growth Model

Directory of Open Access Journals (Sweden)

P. K. Kapur

2009-01-01

Full Text Available Several software reliability growth models (SRGMs have been developed by software developers in tracking and measuring the growth of reliability. As the size of software system is large and the number of faults detected during the testing phase becomes large, so the change of the number of faults that are detected and removed through each debugging becomes sufficiently small compared with the initial fault content at the beginning of the testing phase. In such a situation, we can model the software fault detection process as a stochastic process with continuous state space. In this paper, we propose a new software reliability growth model based on Itô type of stochastic differential equation. We consider an SDE-based generalized Erlang model with logistic error detection function. The model is estimated and validated on real-life data sets cited in literature to show its flexibility. The proposed model integrated with the concept of stochastic differential equation performs comparatively better than the existing NHPP-based models.

Entropic multiple-relaxation-time multirange pseudopotential lattice Boltzmann model for two-phase flow

Science.gov (United States)

Qin, Feifei; Mazloomi Moqaddam, Ali; Kang, Qinjun; Derome, Dominique; Carmeliet, Jan

2018-03-01

An entropic multiple-relaxation-time lattice Boltzmann approach is coupled to a multirange Shan-Chen pseudopotential model to study the two-phase flow. Compared with previous multiple-relaxation-time multiphase models, this model is stable and accurate for the simulation of a two-phase flow in a much wider range of viscosity and surface tension at a high liquid-vapor density ratio. A stationary droplet surrounded by equilibrium vapor is first simulated to validate this model using the coexistence curve and Laplace's law. Then, two series of droplet impact behavior, on a liquid film and a flat surface, are simulated in comparison with theoretical or experimental results. Droplet impact on a liquid film is simulated for different Reynolds numbers at high Weber numbers. With the increase of the Sommerfeld parameter, onset of splashing is observed and multiple secondary droplets occur. The droplet spreading ratio agrees well with the square root of time law and is found to be independent of Reynolds number. Moreover, shapes of simulated droplets impacting hydrophilic and superhydrophobic flat surfaces show good agreement with experimental observations through the entire dynamic process. The maximum spreading ratio of a droplet impacting the superhydrophobic flat surface is studied for a large range of Weber numbers. Results show that the rescaled maximum spreading ratios are in good agreement with a universal scaling law. This series of simulations demonstrates that the proposed model accurately captures the complex fluid-fluid and fluid-solid interfacial physical processes for a wide range of Reynolds and Weber numbers at high density ratios.

Comparison of Two Mechanistic Microbial Growth Models to Estimate Shelf Life of Perishable Food Package under Dynamic Temperature Conditions

Directory of Open Access Journals (Sweden)

Dong Sun Lee

2014-01-01

Full Text Available Two mechanistic microbial growth models (Huang’s model and model of Baranyi and Roberts given in differential and integrated equation forms were compared in predicting the microbial growth and shelf life under dynamic temperature storage and distribution conditions. Literatures consistently reporting the microbial growth data under constant and changing temperature conditions were selected to obtain the primary model parameters, set up the secondary models, and apply them to predict the microbial growth and shelf life under fluctuating temperatures. When evaluated by general estimation behavior, bias factor, accuracy factor, and root-mean-square error, Huang’s model was comparable to Baranyi and Roberts’ model in the capability to estimate microbial growth under dynamic temperature conditions. Its simple form of single differential equation incorporating directly the growth rate and lag time may work as an advantage to be used in online shelf life estimation by using the electronic device.

Present status of numerical analysis on transient two-phase flow

International Nuclear Information System (INIS)

Akimoto, Masayuki; Hirano, Masashi; Nariai, Hideki.

1987-01-01

The Special Committee for Numerical Analysis of Thermal Flow has recently been established under the Japan Atomic Energy Association. Here, some methods currently used for numerical analysis of transient two-phase flow are described citing some information given in the first report of the above-mentioned committee. Many analytical models for transient two-phase flow have been proposed, each of which is designed to describe a flow by using differential equations associated with conservation of mass, momentum and energy in a continuous two-phase flow system together with constructive equations that represent transportation of mass, momentum and energy though a gas-liquid interface or between a liquid flow and the channel wall. The author has developed an analysis code, called MINCS, that serves for systematic examination of conservation equation and constructive equations for two-phase flow models. A one-dimensional, non-equilibrium two-liquid flow model that is used as the basic model for the code is described. Actual procedures for numerical analysis is shown and some problems concerning transient two-phase analysis are described. (Nogami, K.)

Mechanistic multidimensional analysis of horizontal two-phase flows

International Nuclear Information System (INIS)

Tselishcheva, Elena A.; Antal, Steven P.; Podowski, Michael Z.

2010-01-01

The purpose of this paper is to discuss the results of analysis of two-phase flow in horizontal tubes. Two flow situations have been considered: gas/liquid flow in a long straight pipe, and similar flow conditions in a pipe with 90 deg. elbow. The theoretical approach utilizes a multifield modeling concept. A complete three-dimensional two-phase flow model has been implemented in a state-of-the-art computational multiphase fluid dynamics (CMFD) computer code, NPHASE. The overall model has been tested parametrically. Also, the results of NPHASE simulations have been compared against experimental data for a pipe with 90 deg. elbow.

Computational fluid dynamics modeling of two-phase flow in a BWR fuel assembly. Final CRADA Report

International Nuclear Information System (INIS)

Tentner, A.

2009-01-01

A direct numerical simulation capability for two-phase flows with heat transfer in complex geometries can considerably reduce the hardware development cycle, facilitate the optimization and reduce the costs of testing of various industrial facilities, such as nuclear power plants, steam generators, steam condensers, liquid cooling systems, heat exchangers, distillers, and boilers. Specifically, the phenomena occurring in a two-phase coolant flow in a BWR (Boiling Water Reactor) fuel assembly include coolant phase changes and multiple flow regimes which directly influence the coolant interaction with fuel assembly and, ultimately, the reactor performance. Traditionally, the best analysis tools for this purpose of two-phase flow phenomena inside the BWR fuel assembly have been the sub-channel codes. However, the resolution of these codes is too coarse for analyzing the detailed intra-assembly flow patterns, such as flow around a spacer element. Advanced CFD (Computational Fluid Dynamics) codes provide a potential for detailed 3D simulations of coolant flow inside a fuel assembly, including flow around a spacer element using more fundamental physical models of flow regimes and phase interactions than sub-channel codes. Such models can extend the code applicability to a wider range of situations, which is highly important for increasing the efficiency and to prevent accidents.

Numerical method for two-phase flow discontinuity propagation calculation

International Nuclear Information System (INIS)

Toumi, I.; Raymond, P.

1989-01-01

In this paper, we present a class of numerical shock-capturing schemes for hyperbolic systems of conservation laws modelling two-phase flow. First, we solve the Riemann problem for a two-phase flow with unequal velocities. Then, we construct two approximate Riemann solvers: an one intermediate-state Riemann solver and a generalized Roe's approximate Riemann solver. We give some numerical results for one-dimensional shock-tube problems and for a standard two-phase flow heat addition problem involving two-phase flow instabilities

Geometrical automata for two phase flow simulation

International Nuclear Information System (INIS)

Herrero, V.; Guido-Lavalle, G.; Clausse, A.

1996-01-01

An automaton is an entity defined by a mathematical state which changes following iterative rules representing the interaction with the neighborhood. A model of automata for two-phase flow simulation consisting in a field of disks which are allowed to change their radii and move in a plane is presented. The model is more general than the classical cellular automata in two respects: (1) the grid of cellular automata is dismissed in favor of a trajectory generator; and (2) the rules of interaction involve parameters intended to represent some of the most relevant variables governing the actual physical interactions between phases. Computational experiments show that the algorithm captures the essential physics underlying two-phase flow problems such as bubbly-slug pattern transition and void fraction development along tubes. A comparison with experimental data of void fraction profiles is presented, showing excellent agreement. (orig.)

Experimental determination and thermodynamic modeling of phase equilibrium and protein partitioning in aqueous two-phase systems containing biodegradable salts

International Nuclear Information System (INIS)

Perez, Brenda; Malpiedi, Luciana Pellegrini; Tubío, Gisela; Nerli, Bibiana; Alcântara Pessôa Filho, Pedro de

2013-01-01

Highlights: ► Binodal data of systems (water + polyethyleneglycol + sodium) succinate are reported. ► Pitzer model describes the phase equilibrium of systems formed by polyethyleneglycol and biodegradable salts satisfactorily. ► This simple thermodynamic framework was able to predict the partitioning behaviour of model proteins acceptably well. - Abstract: Phase diagrams of sustainable aqueous two-phase systems (ATPSs) formed by polyethyleneglycols (PEGs) of different average molar masses (4000, 6000, and 8000) and sodium succinate are reported in this work. Partition coefficients (Kps) of seven model proteins: bovine serum albumin, catalase, beta-lactoglobulin, alpha-amylase, lysozyme, pepsin, urease and trypsin were experimentally determined in these systems and in ATPSs formed by the former PEGs and other biodegradable sodium salts: citrate and tartrate. An extension of Pitzer model comprising long and short-range term contributions to the excess Gibbs free energy was used to describe the (liquid + liquid) equilibrium. Comparison between experimental and calculated tie line data showed mean deviations always lower than 3%, thus indicating a good correlation. The partition coefficients were modeled by using the same thermodynamic approach. Predicted and experimental partition coefficients correlated quite successfully. Mean deviations were found to be lower than the experimental uncertainty for most of the assayed proteins.

RELAP5 two-phase fluid model and numerical scheme for economic LWR system simulation

International Nuclear Information System (INIS)

Ransom, V.H.; Wagner, R.J.; Trapp, J.A.

1981-01-01

The RELAP5 two-phase fluid model and the associated numerical scheme are summarized. The experience accrued in development of a fast running light water reactor system transient analysis code is reviewed and example of the code application are given

Phase transitions and steady-state microstructures in a two-temperature lattice-gas model with mobile active impurities

DEFF Research Database (Denmark)

Henriksen, Jonas Rosager; Sabra, Mads Christian; Mouritsen, Ole G.

2000-01-01

The nonequilibrium, steady-state phase transitions and the structure of the different phases of a two-dimensional system with two thermodynamic temperatures are studied via a simple lattice-gas model with mobile active impurities ("hot/cold spots'') whose activity is controlled by an external drive...... on the temperatures, microstructured phases of both lamellar and droplet symmetry arise, described by a length scale that is determined by the characteristic temperature controlling the diffusive motion of the active impurities....

The phase field technique for modeling multiphase materials

Science.gov (United States)

Singer-Loginova, I.; Singer, H. M.

2008-10-01

This paper reviews methods and applications of the phase field technique, one of the fastest growing areas in computational materials science. The phase field method is used as a theory and computational tool for predictions of the evolution of arbitrarily shaped morphologies and complex microstructures in materials. In this method, the interface between two phases (e.g. solid and liquid) is treated as a region of finite width having a gradual variation of different physical quantities, i.e. it is a diffuse interface model. An auxiliary variable, the phase field or order parameter \\phi(\\vec{x}) , is introduced, which distinguishes one phase from the other. Interfaces are identified by the variation of the phase field. We begin with presenting the physical background of the phase field method and give a detailed thermodynamical derivation of the phase field equations. We demonstrate how equilibrium and non-equilibrium physical phenomena at the phase interface are incorporated into the phase field methods. Then we address in detail dendritic and directional solidification of pure and multicomponent alloys, effects of natural convection and forced flow, grain growth, nucleation, solid-solid phase transformation and highlight other applications of the phase field methods. In particular, we review the novel phase field crystal model, which combines atomistic length scales with diffusive time scales. We also discuss aspects of quantitative phase field modeling such as thin interface asymptotic analysis and coupling to thermodynamic databases. The phase field methods result in a set of partial differential equations, whose solutions require time-consuming large-scale computations and often limit the applicability of the method. Subsequently, we review numerical approaches to solve the phase field equations and present a finite difference discretization of the anisotropic Laplacian operator.

Two-phase flow

International Nuclear Information System (INIS)

Olive, J.

1990-01-01

The design, operation and safety of nuclear components requires increasingly accurate knowledge of two-phase flows. This knowledge is also necessary for some studies related to electricity applications. The author presents some concrete examples showing the range of problems and the complexity of the phenomena involved in these types of flows. Then, the basic principles of their numerical modelling are explained, as well as the new tendency to use increasingly local and refined models. The newest computer codes developed at EDF are briefly presented. Experimental studies dealing with twophase flow are also referred to, and their connections to numerical modelling are explained. Emphasis is placed on the major efforts devoted to the development of new test rigs and instrumentation [fr

Piecewise Linear-Linear Latent Growth Mixture Models with Unknown Knots

Science.gov (United States)

Kohli, Nidhi; Harring, Jeffrey R.; Hancock, Gregory R.

2013-01-01

Latent growth curve models with piecewise functions are flexible and useful analytic models for investigating individual behaviors that exhibit distinct phases of development in observed variables. As an extension of this framework, this study considers a piecewise linear-linear latent growth mixture model (LGMM) for describing segmented change of…

Modelling of toluene biodegradation and biofilm growth in a fixed biofilm reactor

DEFF Research Database (Denmark)

Arcangeli, Jean-Pierre; Arvin, Erik

1992-01-01

The modelling of aerobic biodegradation of toluene and the associated biofilm growth in a fixed biofilm system is presented. The model includes four biomass fractions, three dissolved components, and seven processes. It is assumed that part of the active biomass is composed of filamentous bacteria...... which grow relatively fast and detach easily, leading to a biomass growth delayed with respect to substrate degradation. The non-filamentous bacteria inside the biofilm also degrade toluene but with a slower rate compared to the filamentous bacteria. Because the nonfilamentous bacteria do not detach......, they are primarily responsible for the biofilm growth. The active biomass decays into biodegradable and ``inert'' dead biomass which is hydrolyzed into soluble products at two different rates. These products are partly degradable by the biomass and constitute the endogenous respiration. The dynamic growth phase...

Modelling of toluene biodegradation and biofilm growth in a fixed biofilm reactor

DEFF Research Database (Denmark)

Arcangeli, Jean-Pierre; Arvin, Erik

1992-01-01

The modelling of aerobic biodegradation of toluene and the associated biofilm growth in a fixed biofilm system is presented. The model includes four biomass fractions, three dissolved components, and seven processes. It is assumed that part of the active biomass is composed of filamentous bacteria......, they are primarily responsible for the biofilm growth. The active biomass decays into biodegradable and ``inert'' dead biomass which is hydrolyzed into soluble products at two different rates. These products are partly degradable by the biomass and constitute the endogenous respiration. The dynamic growth phase...... which grow relatively fast and detach easily, leading to a biomass growth delayed with respect to substrate degradation. The non-filamentous bacteria inside the biofilm also degrade toluene but with a slower rate compared to the filamentous bacteria. Because the nonfilamentous bacteria do not detach...

Effect of food microstructure on growth dynamics of Listeria monocytogenes in fish-based model systems.

Science.gov (United States)

Verheyen, Davy; Bolívar, Araceli; Pérez-Rodríguez, Fernando; Baka, Maria; Skåra, Torstein; Van Impe, Jan F

2018-06-01

Traditionally, predictive growth models for food pathogens are developed based on experiments in broth media, resulting in models which do not incorporate the influence of food microstructure. The use of model systems with various microstructures is a promising concept to get more insight into the influence of food microstructure on microbial dynamics. By means of minimal variation of compositional and physicochemical factors, these model systems can be used to study the isolated effect of certain microstructural aspects on microbial growth, survival and inactivation. In this study, the isolated effect on microbial growth dynamics of Listeria monocytogenes of two food microstructural aspects and one aspect influenced by food microstructure were investigated, i.e., the nature of the food matrix, the presence of fat droplets, and microorganism growth morphology, respectively. To this extent, fish-based model systems with various microstructures were used, i.e., a liquid, a second more viscous liquid system containing xanthan gum, an emulsion, an aqueous gel, and a gelled emulsion. Growth experiments were conducted at 4 and 10 °C, both using homogeneous and surface inoculation (only for the gelled systems). Results regarding the influence of the growth morphology indicated that the lag phase of planktonic cells in the liquid system was similar to the lag phase of submerged colonies in the xanthan system. The lag phase of submerged colonies in each gelled system was considerably longer than the lag phase of surface colonies on these respective systems. The maximum specific growth rate of planktonic cells in the liquid system was significantly lower than for submerged colonies in the xanthan system at 10 °C, while no significant differences were observed at 4 °C. The maximum cell density was higher for submerged colonies than for surface colonies. The nature of the food matrix only exerted an influence on the maximum specific growth rate, which was

Two-phase critical flow models: a technical addendum to the CSNI state of the art report on critical flow modelling

International Nuclear Information System (INIS)

D'Auria, F.; Vigni, P.

1980-05-01

The purpose of this work was to obtain a comprehensive survey on the two-phase flow dynamics during accidental situations in nuclear reactors. About sixty theories regarding the two-phase flow calculation have been reviewed in this report with particular reference to their physical basis and assumptions; the aim is to control their applicability to nuclear safety problems. The main conclusions may be drawn as follows: the examined theories (perfect fluid, theories assuming thermodynamical equilibrium between liquid and vapor phases, non equilibrium models, etc.) are very different both for formulation and results; general validity of most theories is troublesome to check for the use of empirical coefficients. Moreover, according to the author's opinion, it is necessary to set up an organic program to obtain reliable experimental results in this field and to develop a model considering the whole blowdown transient

Nitrogen controlled iron catalyst phase during carbon nanotube growth

Energy Technology Data Exchange (ETDEWEB)

Bayer, Bernhard C., E-mail: bernhard.bayer@univie.ac.at [Department of Engineering, University of Cambridge, Cambridge CB3 0FA (United Kingdom); Faculty of Physics, University of Vienna, A-1090 Vienna (Austria); Baehtz, Carsten [Institute of Ion Beam Physics and Materials Research, Helmholtz-Zentrum Dresden-Rossendorf, D-01314 Dresden (Germany); Kidambi, Piran R.; Weatherup, Robert S.; Caneva, Sabina; Cabrero-Vilatela, Andrea; Hofmann, Stephan [Department of Engineering, University of Cambridge, Cambridge CB3 0FA (United Kingdom); Mangler, Clemens; Kotakoski, Jani; Meyer, Jannik C. [Faculty of Physics, University of Vienna, A-1090 Vienna (Austria); Goddard, Caroline J. L. [Department of Materials Science and Metallurgy, University of Cambridge, Cambridge CB3 0FS (United Kingdom)

2014-10-06

Close control over the active catalyst phase and hence carbon nanotube structure remains challenging in catalytic chemical vapor deposition since multiple competing active catalyst phases typically co-exist under realistic synthesis conditions. Here, using in-situ X-ray diffractometry, we show that the phase of supported iron catalyst particles can be reliably controlled via the addition of NH{sub 3} during nanotube synthesis. Unlike polydisperse catalyst phase mixtures during H{sub 2} diluted nanotube growth, nitrogen addition controllably leads to phase-pure γ-Fe during pre-treatment and to phase-pure Fe{sub 3}C during growth. We rationalize these findings in the context of ternary Fe-C-N phase diagram calculations and, thus, highlight the use of pre-treatment- and add-gases as a key parameter towards controlled carbon nanotube growth.

Physical, experimental and numerical study of fundamental mechanisms involved in two-phase flows