An accurate two-phase approximate solution to the acute viral infection model
Perelson, Alan S [Los Alamos National Laboratory
2009-01-01
During an acute viral infection, virus levels rise, reach a peak and then decline. Data and numerical solutions suggest the growth and decay phases are linear on a log scale. While viral dynamic models are typically nonlinear with analytical solutions difficult to obtain, the exponential nature of the solutions suggests approximations can be found. We derive a two-phase approximate solution to the target cell limited influenza model and illustrate the accuracy using data and previously established parameter values of six patients infected with influenza A. For one patient, the subsequent fall in virus concentration was not consistent with our predictions during the decay phase and an alternate approximation is derived. We find expressions for the rate and length of initial viral growth in terms of the parameters, the extent each parameter is involved in viral peaks, and the single parameter responsible for virus decay. We discuss applications of this analysis in antiviral treatments and investigating host and virus heterogeneities.
On the Stable Numerical Approximation of Two-Phase Flow with Insoluble Surfactant
Barrett, John W; Nürnberg, Robert
2013-01-01
We present a parametric finite element approximation of two-phase flow with insoluble surfactant. This free boundary problem is given by the Navier--Stokes equations for the two-phase flow in the bulk, which are coupled to the transport equation for the insoluble surfactant on the interface that separates the two phases. We combine the evolving surface finite element method with an approach previously introduced by the authors for two-phase Navier--Stokes flow, which maintains good mesh properties. The derived finite element approximation of two-phase flow with insoluble surfactant can be shown to be stable. Several numerical simulations demonstrate the practicality of our numerical method.
Xiao-Ying Qin
2014-01-01
Full Text Available An Adomian decomposition method (ADM is applied to solve a two-phase Stefan problem that describes the pure metal solidification process. In contrast to traditional analytical methods, ADM avoids complex mathematical derivations and does not require coordinate transformation for elimination of the unknown moving boundary. Based on polynomial approximations for some known and unknown boundary functions, approximate analytic solutions for the model with undetermined coefficients are obtained using ADM. Substitution of these expressions into other equations and boundary conditions of the model generates some function identities with the undetermined coefficients. By determining these coefficients, approximate analytic solutions for the model are obtained. A concrete example of the solution shows that this method can easily be implemented in MATLAB and has a fast convergence rate. This is an efficient method for finding approximate analytic solutions for the Stefan and the inverse Stefan problems.
Approximate Riemann solvers and flux vector splitting schemes for two-phase flow
These course notes, presented at the 30. Von Karman Institute Lecture Series in Computational Fluid Dynamics, give a detailed and through review of upwind differencing methods for two-phase flow models. After recalling some fundamental aspects of two-phase flow modelling, from mixture model to two-fluid models, the mathematical properties of the general 6-equation model are analysed by examining the Eigen-structure of the system, and deriving conditions under which the model can be made hyperbolic. The following chapters are devoted to extensions of state-of-the-art upwind differencing schemes such as Roe's Approximate Riemann Solver or the Characteristic Flux Splitting method to two-phase flow. Non-trivial steps in the construction of such solvers include the linearization, the treatment of non-conservative terms and the construction of a Roe-type matrix on which the numerical dissipation of the schemes is based. Extension of the 1-D models to multi-dimensions in an unstructured finite volume formulation is also described; Finally, numerical results for a variety of test-cases are shown to illustrate the accuracy and robustness of the methods. (authors)
Diwakar, S. V.; Das, Sarit K.; Sundararajan, T.
2009-12-01
A new Quadratic Spline based Interface (QUASI) reconstruction algorithm is presented which provides an accurate and continuous representation of the interface in a multiphase domain and facilitates the direct estimation of local interfacial curvature. The fluid interface in each of the mixed cells is represented by piecewise parabolic curves and an initial discontinuous PLIC approximation of the interface is progressively converted into a smooth quadratic spline made of these parabolic curves. The conversion is achieved by a sequence of predictor-corrector operations enforcing function ( C0) and derivative ( C1) continuity at the cell boundaries using simple analytical expressions for the continuity requirements. The efficacy and accuracy of the current algorithm has been demonstrated using standard test cases involving reconstruction of known static interface shapes and dynamically evolving interfaces in prescribed flow situations. These benchmark studies illustrate that the present algorithm performs excellently as compared to the other interface reconstruction methods available in literature. Quadratic rate of error reduction with respect to grid size has been observed in all the cases with curved interface shapes; only in situations where the interface geometry is primarily flat, the rate of convergence becomes linear with the mesh size. The flow algorithm implemented in the current work is designed to accurately balance the pressure gradients with the surface tension force at any location. As a consequence, it is able to minimize spurious flow currents arising from imperfect normal stress balance at the interface. This has been demonstrated through the standard test problem of an inviscid droplet placed in a quiescent medium. Finally, the direct curvature estimation ability of the current algorithm is illustrated through the coupled multiphase flow problem of a deformable air bubble rising through a column of water.
Fast and accurate water and steam properties programs for two-phase flow calculations
The ATHLET code (M.J. Burwell et al., The thermalhydraulic code ATHLET for analysis of PWR and BWR systems, NURETH-4, Karlsruhe, 1989) is being developed at GRS for the thermohydraulic analysis of the behavior of PWRs and BWRs under postulated transient and accidental conditions. In order to cut down computing costs most thermohydraulic codes use specially designed water and steam property packages which run much faster than the very accurate reference package IFC85 by Haar, Gallagher and Kell (NBS/NRC Wasserdampftafeln, London, 1988). At GRS work has been carried out to improve the packages used in the ATHLET code, which are fast running specially designed subroutines based on cubic and bicubic interpolation. The main points of the new package are as follows.(i) For saturation values depending on pressure: extended range for pressure and temperature (0.01 bar, 6.9 C to 215 bar, 371.5 C); improved accuracy at the same computing effort by optimum selection of nodes; spline-based cubic interpolation leading to continuous second derivatives; common grid for all properties; consistent derivatives calculated by analytical differentiation of the interpolation functions(i) For property values depending on pressure and temperature (subcooled, superheated, coexisting phases): extended range for pressure and temperature (liquid 0.01 bar, 6.9 C to 215 bar, 371.5 C; vapor 0.01 bar, 6.9 C to 215 bar, 2000 C); fast computation of subcooled and superheated values by combining analytical functions and bicubic interpolation; bicubic interpolation-based and 2D spline interpolation on a transformed curvilinear grid; linear continuation into the domain of coexisting phases (thermodynamic nonequilibrium); 2D functions to match the saturation values at the saturation line exactly; common 2D grid for all property functions; consistent derivatives calculated by analytical differentiation of the interpolation functions. The new package calculates only the material properties and leaves
Equation systems describing one-dimensional, transient, two-phase flow with separate continuity, momentum, and energy equations for each phase are classified by use of the method of characteristics. Little attempt is made to justify the physics of these equations. Many of the equation systems possess complex-valued characteristics and hence, according to well-known mathematical theorems, are not well-posed as initial-value problems (IVPs). Real-valued characteristics are necessary but not sufficient to insure well-posedness. In the absence of lower order source or sink terms (potential type flows), which can affect the well-posedness of IVPs, the complex characteristics associated with these two-phase flow equations imply unbounded exponential growth for disturbances of all wavelengths. Analytical and numerical examples show that the ill-posedness of IVPs for the two-phase flow partial differential equations which possess complex characteristics produce unstable numerical schemes. These unstable numerical schemes can produce apparently stable and even accurate results if the growth rate resulting from the complex characteristics remains small throughout the time span of the numerical experiment or if sufficient numerical damping is present for the increment size used. Other examples show that clearly nonphysical numerical instabilities resulting from the complex characteristics can be produced. These latter types of numerical instabilities are shown to be removed by the addition of physically motivated differential terms which eliminate the complex characteristics. (auth)
Accurate Period Approximation for Any Simple Pendulum Amplitude
XUE De-Sheng; ZHOU Zhao; GAO Mei-Zhen
2012-01-01
Accurate approximate analytical formulae of the pendulum period composed of a few elementary functions for any amplitude are constructed.Based on an approximation of the elliptic integral,two new logarithmic formulae for large amplitude close to 180° are obtained.Considering the trigonometric function modulation results from the dependence of relative error on the amplitude,we realize accurate approximation period expressions for any amplitude between 0 and 180°.A relative error less than 0.02％ is achieved for any amplitude.This kind of modulation is also effective for other large-amplitude logarithmic approximation expressions.%Accurate approximate analytical formulae of the pendulum period composed of a few elementary functions for any amplitude are constructed. Based on an approximation of the elliptic integral, two new logarithmic formulae for large amplitude close to 180° are obtained. Considering the trigonometric function modulation results from the dependence of relative error on the amplitude, we realize accurate approximation period expressions for any amplitude between 0 and 180°. A relative error less than 0.02% is achieved for any amplitude. This kind of modulation is also effective for other large-amplitude logarithmic approximation expressions.
Xu, Xuemiao; Zhang, Huaidong; Han, Guoqiang; Kwan, Kin Chung; Pang, Wai-Man; Fang, Jiaming; Zhao, Gansen
2016-01-01
Exterior orientation parameters' (EOP) estimation using space resection plays an important role in topographic reconstruction for push broom scanners. However, existing models of space resection are highly sensitive to errors in data. Unfortunately, for lunar imagery, the altitude data at the ground control points (GCPs) for space resection are error-prone. Thus, existing models fail to produce reliable EOPs. Motivated by a finding that for push broom scanners, angular rotations of EOPs can be estimated independent of the altitude data and only involving the geographic data at the GCPs, which are already provided, hence, we divide the modeling of space resection into two phases. Firstly, we estimate the angular rotations based on the reliable geographic data using our proposed mathematical model. Then, with the accurate angular rotations, the collinear equations for space resection are simplified into a linear problem, and the global optimal solution for the spatial position of EOPs can always be achieved. Moreover, a certainty term is integrated to penalize the unreliable altitude data for increasing the error tolerance. Experimental results evidence that our model can obtain more accurate EOPs and topographic maps not only for the simulated data, but also for the real data from Chang'E-1, compared to the existing space resection model. PMID:27077855
Xuemiao Xu
2016-04-01
Full Text Available Exterior orientation parameters’ (EOP estimation using space resection plays an important role in topographic reconstruction for push broom scanners. However, existing models of space resection are highly sensitive to errors in data. Unfortunately, for lunar imagery, the altitude data at the ground control points (GCPs for space resection are error-prone. Thus, existing models fail to produce reliable EOPs. Motivated by a finding that for push broom scanners, angular rotations of EOPs can be estimated independent of the altitude data and only involving the geographic data at the GCPs, which are already provided, hence, we divide the modeling of space resection into two phases. Firstly, we estimate the angular rotations based on the reliable geographic data using our proposed mathematical model. Then, with the accurate angular rotations, the collinear equations for space resection are simplified into a linear problem, and the global optimal solution for the spatial position of EOPs can always be achieved. Moreover, a certainty term is integrated to penalize the unreliable altitude data for increasing the error tolerance. Experimental results evidence that our model can obtain more accurate EOPs and topographic maps not only for the simulated data, but also for the real data from Chang’E-1, compared to the existing space resection model.
Drift flux model as approximation of two fluid model for two phase dispersed and slug flow in tube
The analysis of one-dimensional schematizing for non-steady two-phase dispersed and slug flow in tube is presented. Quasi-static approximation, when inertia forces because of the accelerations of the phases may be neglected, is considered. Gas-liquid bubbly and slug vertical upward flows are analyzed. Non-trivial theoretical equations for slip velocity for these flows are derived. Juxtaposition of the derived equations for slip velocity with the famous Zuber-Findlay correlation as cross correlation coefficients is criticized. The generalization of non-steady drift flux Wallis theory taking into account influence of wall friction on the bubbly or slug flows for kinematical waves is considered
Drift flux model as approximation of two fluid model for two phase dispersed and slug flow in tube
Nigmatulin, R.I.
1995-09-01
The analysis of one-dimensional schematizing for non-steady two-phase dispersed and slug flow in tube is presented. Quasi-static approximation, when inertia forces because of the accelerations of the phases may be neglected, is considered. Gas-liquid bubbly and slug vertical upward flows are analyzed. Non-trivial theoretical equations for slip velocity for these flows are derived. Juxtaposition of the derived equations for slip velocity with the famous Zuber-Findlay correlation as cross correlation coefficients is criticized. The generalization of non-steady drift flux Wallis theory taking into account influence of wall friction on the bubbly or slug flows for kinematical waves is considered.
Büsing, Henrik
2013-04-01
Two-phase flow in porous media occurs in various settings, such as the sequestration of CO2 in the subsurface, radioactive waste management, the flow of oil or gas in hydrocarbon reservoirs, or groundwater remediation. To model the sequestration of CO2, we consider a fully coupled formulation of the system of nonlinear, partial differential equations. For the solution of this system, we employ the Box method after Huber & Helmig (2000) for the space discretization and the fully implicit Euler method for the time discretization. After linearization with Newton's method, it remains to solve a linear system in every Newton step. We compare different iterative methods (BiCGStab, GMRES, AGMG, c.f., [Notay (2012)]) combined with different preconditioners (ILU0, ASM, Jacobi, and AMG as preconditioner) for the solution of these systems. The required Jacobians can be obtained elegantly with automatic differentiation (AD) [Griewank & Walther (2008)], a source code transformation providing exact derivatives. We compare the performance of the different iterative methods with their respective preconditioners for these linear systems. Furthermore, we analyze linear systems obtained by approximating the Jacobian with finite differences in terms of Newton steps per time step, steps of the iterative solvers and the overall solution time. Finally, we study the influence of heterogeneities in permeability and porosity on the performance of the iterative solvers and their robustness in this respect. References [Griewank & Walther(2008)] Griewank, A. & Walther, A., 2008. Evaluating Derivatives: Principles and Techniques of Algorithmic Differentiation, SIAM, Philadelphia, PA, 2nd edn. [Huber & Helmig(2000)] Huber, R. & Helmig, R., 2000. Node-centered finite volume discretizations for the numerical simulation of multiphase flow in heterogeneous porous media, Computational Geosciences, 4, 141-164. [Notay(2012)] Notay, Y., 2012. Aggregation-based algebraic multigrid for convection
Evje, Steinar; Friis, Helmer André
2012-01-01
This paper examines two-phase flow in porous media with heterogeneous capillary pressure functions. This problem has received very little attention in the literature, and constitutes a challenge for numerical discretization, since saturation discontinuities arise at the interface between the different homogeneous regions in the domain. As a motivation we first consider a one-dimensional model problem, for which a semi-analytical solution is known, and examine some different fin...
Xin Chen
2015-01-01
Full Text Available Adaptive Dynamic Programming (ADP with critic-actor architecture is an effective way to perform online learning control. To avoid the subjectivity in the design of a neural network that serves as a critic network, kernel-based adaptive critic design (ACD was developed recently. There are two essential issues for a static kernel-based model: how to determine proper hyperparameters in advance and how to select right samples to describe the value function. They all rely on the assessment of sample values. Based on the theoretical analysis, this paper presents a two-phase simultaneous learning method for a Gaussian-kernel-based critic network. It is able to estimate the values of samples without infinitively revisiting them. And the hyperparameters of the kernel model are optimized simultaneously. Based on the estimated sample values, the sample set can be refined by adding alternatives or deleting redundances. Combining this critic design with actor network, we present a Gaussian-kernel-based Adaptive Dynamic Programming (GK-ADP approach. Simulations are used to verify its feasibility, particularly the necessity of two-phase learning, the convergence characteristics, and the improvement of the system performance by using a varying sample set.
Shock Emergence in Supernovae: Limiting Cases and Accurate Approximations
Ro, Stephen
2013-01-01
We examine the dynamics of accelerating normal shocks in stratified planar atmospheres, providing accurate fitting formulae for the scaling index relating shock velocity to the initial density and for the post-shock acceleration factor as functions of the polytropic and adiabatic indices which parameterize the problem. In the limit of a uniform initial atmosphere there are analytical formulae for these quantities. In the opposite limit of a very steep density gradient the solutions match the outcome of shock acceleration in exponential atmospheres.
Shock Emergence in Supernovae: Limiting Cases and Accurate Approximations
Ro, Stephen; Matzner, Christopher D.
2013-08-01
We examine the dynamics of accelerating normal shocks in stratified planar atmospheres, providing accurate fitting formulae for the scaling index relating shock velocity to the initial density and for the post-shock acceleration factor as functions of the polytropic and adiabatic indices which parameterize the problem. In the limit of a uniform initial atmosphere, there are analytical formulae for these quantities. In the opposite limit of a very steep density gradient, the solutions match the outcome of shock acceleration in exponential atmospheres.
SHOCK EMERGENCE IN SUPERNOVAE: LIMITING CASES AND ACCURATE APPROXIMATIONS
Ro, Stephen; Matzner, Christopher D. [Department of Astronomy and Astrophysics, University of Toronto, 50 St. George St., Toronto, ON M5S 3H4 (Canada)
2013-08-10
We examine the dynamics of accelerating normal shocks in stratified planar atmospheres, providing accurate fitting formulae for the scaling index relating shock velocity to the initial density and for the post-shock acceleration factor as functions of the polytropic and adiabatic indices which parameterize the problem. In the limit of a uniform initial atmosphere, there are analytical formulae for these quantities. In the opposite limit of a very steep density gradient, the solutions match the outcome of shock acceleration in exponential atmospheres.
In this paper a theoretical approach to heat bundle parameter calculation in boiling reactors which resulted in the use of the subchannel approximation procedure with the verified system of equations for the subchannels is described. The system of equations is written for the drift flux model of the two-phase non-equilibrium flow in the quasi-two-dimensional approximation. Recommendations for calculating the distribution parameters included in the quasi-two-dimensional problem formulation are given. Combining the subchannel approximation with the quasi-two-dimensional approach helps to keep up acceptable calculation precision for the bundles with relatively large subchannels when the cross-sectional phase parameter distribution for each subchannel must be taken into consideration. Some calculation results are presented
Toumi, I.; Kumbaro, A.; Paillere, H
1999-07-01
These course notes, presented at the 30. Von Karman Institute Lecture Series in Computational Fluid Dynamics, give a detailed and through review of upwind differencing methods for two-phase flow models. After recalling some fundamental aspects of two-phase flow modelling, from mixture model to two-fluid models, the mathematical properties of the general 6-equation model are analysed by examining the Eigen-structure of the system, and deriving conditions under which the model can be made hyperbolic. The following chapters are devoted to extensions of state-of-the-art upwind differencing schemes such as Roe's Approximate Riemann Solver or the Characteristic Flux Splitting method to two-phase flow. Non-trivial steps in the construction of such solvers include the linearization, the treatment of non-conservative terms and the construction of a Roe-type matrix on which the numerical dissipation of the schemes is based. Extension of the 1-D models to multi-dimensions in an unstructured finite volume formulation is also described; Finally, numerical results for a variety of test-cases are shown to illustrate the accuracy and robustness of the methods. (authors)
An analytical model was developed to estimate the viscous and squeeze-film damping ratios of heat exchanger tubes subjected to a two-phase cross-flow. Damping information is required to analyze the flow-induced vibration problem for heat exchange tubes. In heat exchange tubes, the most important energy dissipation mechanisms are related to the dynamic interaction between structures such as the tube and support and the liquid. The present model was formulated considering the added mass coefficient, based on an approximate model by Sim (1997). An approximate analytical method was developed to estimate the hydrodynamic forces acting on an oscillating inner cylinder with a concentric annulus. The forces, including the damping force, were calculated using two models developed for relatively high and low oscillatory Reynolds numbers, respectively. The equivalent diameters for the tube bundles and tube support, and the penetration depth, are important parameters to calculate the viscous damping force acting on tube bundles and the squeeze-film damping forces on the tube support, respectively. To calculate the void fraction of a two-phase flow, a homogeneous model was used. To verify the present model, the analytical results were compared to the results given by existing theories. It was found that the present model was applicable to estimate the viscous damping ratio and squeeze-film damping ratio
Coquerelle, Mathieu; Glockner, Stéphane
2016-01-01
We propose an accurate and robust fourth-order curvature extension algorithm in a level set framework for the transport of the interface. The method is based on the Continuum Surface Force approach, and is shown to efficiently calculate surface tension forces for two-phase flows. In this framework, the accuracy of the algorithms mostly relies on the precise computation of the surface curvature which we propose to accomplish using a two-step algorithm: first by computing a reliable fourth-order curvature estimation from the level set function, and second by extending this curvature rigorously in the vicinity of the surface, following the Closest Point principle. The algorithm is easy to implement and to integrate into existing solvers, and can easily be extended to 3D. We propose a detailed analysis of the geometrical and numerical criteria responsible for the appearance of spurious currents, a well known phenomenon observed in various numerical frameworks. We study the effectiveness of this novel numerical method on state-of-the-art test cases showing that the resulting curvature estimate significantly reduces parasitic currents. In addition, the proposed approach converges to fourth-order regarding spatial discretization, which is two orders of magnitude better than algorithms currently available. We also show the necessity for high-order transport methods for the surface by studying the case of the 2D advection of a column at equilibrium thereby proving the robustness of the proposed approach. The algorithm is further validated on more complex test cases such as a rising bubble.
Efficient and Accurate Log-Levy Approximations of Levy-Driven LIBOR Models
Papapantoleon, Antonis; Schoenmakers, John; Skovmand, David
2012-01-01
-driven LIBOR model and aim to develop accurate and efficient log-Lévy approximations for the dynamics of the rates. The approximations are based on the truncation of the drift term and on Picard approximation of suitable processes. Numerical experiments for forward-rate agreements, caps, swaptions and sticky...
Weber, J. W.; Bol, A. A.; M. C. M. van de Sanden,
2014-01-01
This work presents an improved thin film approximation to extract the optical conductivity from infrared transmittance in a simple yet accurate way. This approximation takes into account the incoherent reflections from the backside of the substrate. These reflections are shown to have a significant
Accurate atomic quantum defects from particle-particle random phase approximation
Yang, Yang; Yang, Weitao
2015-01-01
The accuracy of calculations of atomic Rydberg excitations cannot be judged by the usual measures, such as mean unsigned errors of many transitions. We show how to use quantum defect theory to (a) separate errors due to approximate ionization potentials, (b) extract smooth quantum defects to compare with experiment, and (c) quantify those defects with a few characteristic parameters. The particle-particle random phase approximation (pp-RPA) produces excellent Rydberg transitions that are an order of magnitude more accurate than those of time-dependent density functional theory with standard approximations. We even extract reasonably accurate defects from the lithium Rydberg series, despite the reference being open-shell. Our methodology can be applied to any Rydberg series of excitations with 4 transitions or more to extract the underlying threshold energy and characteristic quantum defect parameters. Our pp-RPA results set a demanding challenge for other excitation methods to match.
Symplectic Approximation Of Hamiltonian Flows And Accurate Simulation Of Fringe Field Effects
Erdélyi, B
2001-01-01
In the field of accelerator physics, the motion of particles in the electromagnetic fields of periodic accelerators is usually approximated by the iteration of a symplectic map, which represents the system over short time, such as one turn around the accelerator. Unfortunately, due to the complexity of the systems, in practice only some approximation of the one-turn map can be computed, as, for example, the truncated Taylor series. To this end, simulation of the nonlinear dynamics consists, in general, of the following three steps: (1) Computation of the truncated Taylor approximation of the one-turn map, (2) Symplectification of the Taylor map, and (3) Iteration of the resulting exactly symplectic map. This dissertation addresses all three components of the process, with the emphasis being on developing new methods that allow long-term tracking as accurately and efficiently as possible. Specifically, the contributions to the first step concern the fringe field effects. The truncate...
A modified generalized, rational harmonic balance method is used to construct approximate frequency-amplitude relations for a conservative nonlinear singular oscillator in which the restoring force is inversely proportional to the dependent variable. The procedure is used to solve the nonlinear differential equation approximately. The approximate frequency obtained using this procedure is more accurate than those obtained using other approximate methods and the discrepancy between the approximate frequency and the exact one is lower than 0.40%
Most elliptic interface solvers become complicated for complex interface problems at those “exceptional points” where there are not enough neighboring interior points for high order interpolation. Such complication increases especially in three dimensions. Usually, the solvers are thus reduced to low order accuracy. In this paper, we classify these exceptional points and propose two recipes to maintain order of accuracy there, aiming at improving the previous coupling interface method [26]. Yet the idea is also applicable to other interface solvers. The main idea is to have at least first order approximations for second order derivatives at those exceptional points. Recipe 1 is to use the finite difference approximation for the second order derivatives at a nearby interior grid point, whenever this is possible. Recipe 2 is to flip domain signatures and introduce a ghost state so that a second-order method can be applied. This ghost state is a smooth extension of the solution at the exceptional point from the other side of the interface. The original state is recovered by a post-processing using nearby states and jump conditions. The choice of recipes is determined by a classification scheme of the exceptional points. The method renders the solution and its gradient uniformly second-order accurate in the entire computed domain. Numerical examples are provided to illustrate the second order accuracy of the presently proposed method in approximating the gradients of the original states for some complex interfaces which we had tested previous in two and three dimensions, and a real molecule ( (1D63)) which is double-helix shape and composed of hundreds of atoms
Accurate and Approximate Calculations of Raman Scattering in the Atmosphere of Neptune
Sromovsky, Lawrence
2015-01-01
Raman scattering by H$_2$ in Neptune's atmosphere has significant effects on its reflectivity for $\\lambda <$ 0.5 $\\mu$m, producing baseline decreases of $\\sim$ 20% in a clear atmosphere and $\\sim$ 10% in a hazy atmosphere. Here we present the first radiation transfer algorithm that includes both polarization and Raman scattering and facilitates computation of spatially resolved spectra. New calculations show that Cochran and Trafton's (1978, Astrophys. J. 219, 756-762) suggestion that light reflected in the deep CH$_4$ bands is mainly Raman scattered is not valid for current estimates of the CH$_4$vertical distribution, which implies only a 4% Raman contribution. Comparisons with IUE, HST, and groundbased observations confirm that high altitude haze absorption is reducing Neptune's geometric albedo by $\\sim$6% in the 0.22-0.26 $\\mu$m range and by $\\sim$13% in the 0.35-0.45 $\\mu$m range. We used accurate calculations to evaluate several approximations of Raman scattering. The Karkoschka (1994, Icarus 111, ...
Development of highly accurate approximate scheme for computing the charge transfer integral.
Pershin, Anton; Szalay, Péter G
2015-08-21
The charge transfer integral is a key parameter required by various theoretical models to describe charge transport properties, e.g., in organic semiconductors. The accuracy of this important property depends on several factors, which include the level of electronic structure theory and internal simplifications of the applied formalism. The goal of this paper is to identify the performance of various approximate approaches of the latter category, while using the high level equation-of-motion coupled cluster theory for the electronic structure. The calculations have been performed on the ethylene dimer as one of the simplest model systems. By studying different spatial perturbations, it was shown that while both energy split in dimer and fragment charge difference methods are equivalent with the exact formulation for symmetrical displacements, they are less efficient when describing transfer integral along the asymmetric alteration coordinate. Since the "exact" scheme was found computationally expensive, we examine the possibility to obtain the asymmetric fluctuation of the transfer integral by a Taylor expansion along the coordinate space. By exploring the efficiency of this novel approach, we show that the Taylor expansion scheme represents an attractive alternative to the "exact" calculations due to a substantial reduction of computational costs, when a considerably large region of the potential energy surface is of interest. Moreover, we show that the Taylor expansion scheme, irrespective of the dimer symmetry, is very accurate for the entire range of geometry fluctuations that cover the space the molecule accesses at room temperature. PMID:26298117
Development of highly accurate approximate scheme for computing the charge transfer integral
The charge transfer integral is a key parameter required by various theoretical models to describe charge transport properties, e.g., in organic semiconductors. The accuracy of this important property depends on several factors, which include the level of electronic structure theory and internal simplifications of the applied formalism. The goal of this paper is to identify the performance of various approximate approaches of the latter category, while using the high level equation-of-motion coupled cluster theory for the electronic structure. The calculations have been performed on the ethylene dimer as one of the simplest model systems. By studying different spatial perturbations, it was shown that while both energy split in dimer and fragment charge difference methods are equivalent with the exact formulation for symmetrical displacements, they are less efficient when describing transfer integral along the asymmetric alteration coordinate. Since the “exact” scheme was found computationally expensive, we examine the possibility to obtain the asymmetric fluctuation of the transfer integral by a Taylor expansion along the coordinate space. By exploring the efficiency of this novel approach, we show that the Taylor expansion scheme represents an attractive alternative to the “exact” calculations due to a substantial reduction of computational costs, when a considerably large region of the potential energy surface is of interest. Moreover, we show that the Taylor expansion scheme, irrespective of the dimer symmetry, is very accurate for the entire range of geometry fluctuations that cover the space the molecule accesses at room temperature
Ahmad, Zahoor; Hanif, Muhammad
2013-01-01
The development of estimators of population parameters based on two-phase sampling schemes has seen a dramatic increase in the past decade. Various authors have developed estimators of population using either one or two auxiliary variables. The present volume is a comprehensive collection of estimators available in single and two phase sampling. The book covers estimators which utilize information on single, two and multiple auxiliary variables of both quantitative and qualitative nature. Th...
We describe a method for computing linear observer statistics for maximum a posteriori (MAP) reconstructions of PET images. The method is based on a theoretical approximation for the mean and covariance of MAP reconstructions. In particular, we derive here a closed form for the channelized Hotelling observer (CHO) statistic applied to 2D MAP images. We show reasonably good correspondence between these theoretical results and Monte Carlo studies. The accuracy and low computational cost of the approximation allow us to analyze the observer performance over a wide range of operating conditions and parameter settings for the MAP reconstruction algorithm
A method for the accurate and smooth approximation of standard thermodynamic functions
Coufal, O.
2013-01-01
A method is proposed for the calculation of approximations of standard thermodynamic functions. The method is consistent with the physical properties of standard thermodynamic functions. This means that the approximation functions are, in contrast to the hitherto used approximations, continuous and smooth in every temperature interval in which no phase transformations take place. The calculation algorithm was implemented by the SmoothSTF program in the C++ language which is part of this paper. Program summaryProgram title:SmoothSTF Catalogue identifier: AENH_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AENH_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 3807 No. of bytes in distributed program, including test data, etc.: 131965 Distribution format: tar.gz Programming language: C++. Computer: Any computer with gcc version 4.3.2 compiler. Operating system: Debian GNU Linux 6.0. The program can be run in operating systems in which the gcc compiler can be installed, see http://gcc.gnu.org/install/specific.html. RAM: 256 MB are sufficient for the table of standard thermodynamic functions with 500 lines Classification: 4.9. Nature of problem: Standard thermodynamic functions (STF) of individual substances are given by thermal capacity at constant pressure, entropy and enthalpy. STF are continuous and smooth in every temperature interval in which no phase transformations take place. The temperature dependence of STF as expressed by the table of its values is for further application approximated by temperature functions. In the paper, a method is proposed for calculating approximation functions which, in contrast to the hitherto used approximations, are continuous and smooth in every temperature interval. Solution method: The approximation functions are
Precise and accurate train run data: Approximation of actual arrival and departure times
Richter, Troels; Landex, Alex; Andersen, Jonas Lohmann Elkjær
On the most intensively used parts of the Danish railway network, registration of arrivals and departure times are based on occupation of main track circuits and block sections. These measurements are precise. However, due to the nature of track circuits, they do not register the actual time when...... trains have come to a halt nor when trains have set in motion again. Thus the measurements are inaccurate and do not express the experience of the passengers. A commonly accepted method to make this measurement possible is to construct a correction function to the track circuit based measurement....... This function estimates the inaccuracy or bias of the measurement and thus which offset is needed to approximate the actual arrival and departure times. The development of such a function is described in this paper. The development is based on international best practices combined with what is technically...
Kottmann, Jakob S; Höfener, Sebastian; Bischoff, Florian A
2015-12-21
In the present work, we report an efficient implementation of configuration interaction singles (CIS) excitation energies and oscillator strengths using the multi-resolution analysis (MRA) framework to address the basis-set convergence of excited state computations. In MRA (ground-state) orbitals, excited states are constructed adaptively guaranteeing an overall precision. Thus not only valence but also, in particular, low-lying Rydberg states can be computed with consistent quality at the basis set limit a priori, or without special treatments, which is demonstrated using a small test set of organic molecules, basis sets, and states. We find that the new implementation of MRA-CIS excitation energy calculations is competitive with conventional LCAO calculations when the basis-set limit of medium-sized molecules is sought, which requires large, diffuse basis sets. This becomes particularly important if accurate calculations of molecular electronic absorption spectra with respect to basis-set incompleteness are required, in which both valence as well as Rydberg excitations can contribute to the molecule's UV/VIS fingerprint. PMID:25913482
In a previous work, O'Connell (Phys. Teach. 40, 24 (2002)) investigated the time dependence of the tension in the string of a simple pendulum oscillating within the small-angle regime. In spite of the approximation sin θ ∼ θ being accurate only for amplitudes below 7 deg., his experimental results are for a pendulum oscillating with an amplitude of about 18 deg., therefore beyond the small-angle regime. This lapse may also be found in some textbooks, laboratory manuals and internet. By noting that the exact analytical solution for this problem involves the so-called Jacobi elliptic functions, which are unknown to most students (even instructors), I take into account a sinusoidal approximate solution for the pendulum equation I introduced in a recent work (Eur. J. Phys. 29 1091 (2008)) for deriving a simple trigonometric approximation for the tension valid for all possible amplitudes. This approximation is compared to both the O'Connell and the exact results, revealing that it is accurate enough for analysing large-angle pendulum experiments. (letters and comments)
Two-phase viscoelastic jetting
Yu, J-D; Sakai, S.; Sethian, J.A.
2008-12-10
A coupled finite difference algorithm on rectangular grids is developed for viscoelastic ink ejection simulations. The ink is modeled by the Oldroyd-B viscoelastic fluid model. The coupled algorithm seamlessly incorporates several things: (1) a coupled level set-projection method for incompressible immiscible two-phase fluid flows; (2) a higher-order Godunov type algorithm for the convection terms in the momentum and level set equations; (3) a simple first-order upwind algorithm for the convection term in the viscoelastic stress equations; (4) central difference approximations for viscosity, surface tension, and upper-convected derivative terms; and (5) an equivalent circuit model to calculate the inflow pressure (or flow rate) from dynamic voltage.
Numerical method for two-phase flow discontinuity propagation calculation
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
Hierarchy of two-phase flow models for autonomous control of cryogenic loading operation
Luchinskiy, Dmitry G.; Ponizovskaya-Devine, Ekaterina; Hafiychuk, Vasyl; Kashani, Ali; Khasin, Michael; Timucin, Dogan; Sass, Jared; Perotti, Jose; Brown, Barbara
2015-12-01
We report on the development of a hierarchy of models of cryogenic two-phase flow motivated by NASA plans to develop and maturate technology of cryogenic propellant loading on the ground and in space. The solution of this problem requires models that are fast and accurate enough to identify flow conditions, detect faults, and to propose optimal recovery strategy. The hierarchy of models described in this presentation is ranging from homogeneous moving- front approximation to separated non-equilibrium two-phase cryogenic flow. We compare model predictions with experimental data and discuss possible application of these models to on-line integrated health management and control of cryogenic loading operation.
Hadzi-Velkov, Zoran; Karagiannidis, George K; 10.1109/ICC.2009.5198714
2009-01-01
We present a novel and accurate approximation for the distribution of the sum of equally correlated Nakagami-m variates. Ascertaining on this result we study the performance of Equal Gain Combining (EGC) receivers, operating over equally correlating fading channels. Numerical results and simulations show the accuracy of the proposed approximation and the validity of the mathematical analysis.
Thomas Philipp
2012-05-01
Full Text Available Abstract Background It is well known that the deterministic dynamics of biochemical reaction networks can be more easily studied if timescale separation conditions are invoked (the quasi-steady-state assumption. In this case the deterministic dynamics of a large network of elementary reactions are well described by the dynamics of a smaller network of effective reactions. Each of the latter represents a group of elementary reactions in the large network and has associated with it an effective macroscopic rate law. A popular method to achieve model reduction in the presence of intrinsic noise consists of using the effective macroscopic rate laws to heuristically deduce effective probabilities for the effective reactions which then enables simulation via the stochastic simulation algorithm (SSA. The validity of this heuristic SSA method is a priori doubtful because the reaction probabilities for the SSA have only been rigorously derived from microscopic physics arguments for elementary reactions. Results We here obtain, by rigorous means and in closed-form, a reduced linear Langevin equation description of the stochastic dynamics of monostable biochemical networks in conditions characterized by small intrinsic noise and timescale separation. The slow-scale linear noise approximation (ssLNA, as the new method is called, is used to calculate the intrinsic noise statistics of enzyme and gene networks. The results agree very well with SSA simulations of the non-reduced network of elementary reactions. In contrast the conventional heuristic SSA is shown to overestimate the size of noise for Michaelis-Menten kinetics, considerably under-estimate the size of noise for Hill-type kinetics and in some cases even miss the prediction of noise-induced oscillations. Conclusions A new general method, the ssLNA, is derived and shown to correctly describe the statistics of intrinsic noise about the macroscopic concentrations under timescale separation conditions
A Godunov-type method for the seven-equation model of compressible two-phase flow
Ambroso, Annalisa; Chalons, Christophe; Raviart, Pierre-Arnaud
2010-01-01
We are interested in the numerical approximation of the solutions of the compressible seven-equation two-phase flow model. We propose a numerical srategy based on the derivation of a simple, accurate and explicit approximate Riemann solver. The source terms associated with the external forces and the drag force are included in the definition of the Riemann problem, and thus receive an upwind treatment. The objective is to try to preserve, at the numerical level, the asymptotic property of the...
Cook, M; Granato, G L
2009-01-01
We propose and test a scenario for the assembly and evolution of luminous matter in galaxies which substantially differs from that adopted by other semianalytic models. As for the dark matter (DM), we follow the detailed evolution of halos within the canonical LCDM cosmology using standard Montecarlo methods. However, when overlaying prescriptions for baryon evolution, we take into account an effect pointed out in the past few years by a number of studies mostly based on intensive N-body simulations, namely that typical halo growth occurs in two phases: an early, fast collapse phase featuring several major merger events, followed by a late, quiescent accretion onto the halo outskirts. We propose that the two modes of halo growth drive two distinct modes for the evolution of baryonic matter, favoring the development of the spheroidal and disc components of galaxies, respectively. We test this idea using the semianalytic technique. Our galaxy formation model envisages an early coevolution of spheroids and the c...
Wallis, Graham B.
1989-01-01
Some features of two recent approaches of two-phase potential flow are presented. The first approach is based on a set of progressive examples that can be analyzed using common techniques, such as conservation laws, and taken together appear to lead in the direction of a general theory. The second approach is based on variational methods, a classical approach to conservative mechanical systems that has a respectable history of application to single phase flows. This latter approach, exemplified by several recent papers by Geurst, appears generally to be consistent with the former approach, at least in those cases for which it is possible to obtain comparable results. Each approach has a justifiable theoretical base and is self-consistent. Moreover, both approaches appear to give the right prediction for several well-defined situations.
Adaptive moving grid methods for two-phase flow in porous media
Dong, Hao
2014-08-01
In this paper, we present an application of the moving mesh method for approximating numerical solutions of the two-phase flow model in porous media. The numerical schemes combine a mixed finite element method and a finite volume method, which can handle the nonlinearities of the governing equations in an efficient way. The adaptive moving grid method is then used to distribute more grid points near the sharp interfaces, which enables us to obtain accurate numerical solutions with fewer computational resources. The numerical experiments indicate that the proposed moving mesh strategy could be an effective way to approximate two-phase flows in porous media. © 2013 Elsevier B.V. All rights reserved.
Two-phase-flow models and their limitations
An accurate prediction of transient two-phase flow is essential to safety analyses of nuclear reactors under accident conditions. The fluid flow and heat transfer encountered are often extremely complex due to the reactor geometry and occurrence of transient two-phase flow. Recently considerable progresses in understanding and predicting these phenomena have been made by a combination of rigorous model development, advanced computational techniques, and a number of small and large scale supporting experiments. In view of their essential importance, the foundation of various two-phase-flow models and their limitations are discussed in this paper
Cabrera-Trujillo, R., E-mail: trujillo@fis.unam.mx [Instituto de Ciencias Físicas, Universidad Nacional Autónoma de México, Ap. Postal 48-3, Cuernavaca, Morelos 62251 (Mexico); Departamento de Física, Universidad Autónoma Metropolitana-Iztapalapa, Ap. Postal 55-534, 09340 México, D.F. (Mexico); Cruz, S.A., E-mail: cruz@xanum.uam.mx [Departamento de Física, Universidad Autónoma Metropolitana-Iztapalapa, Ap. Postal 55-534, 09340 México, D.F. (Mexico)
2014-02-01
Atomic hydrogen is used as a fundamental reference target system to explore pressure effects on the electronic stopping cross section, S{sub e}, of swift bare ions such as protons and α-particles. This is achieved by considering the hydrogen atom under pressure as a padded spherically-confined quantum system. Within this scheme, S{sub e} is calculated rigorously in the first Born approximation taking into account the full target excitation spectrum and momentum transfer distribution for different confinement conditions (pressures) and fixed projectile charge states. Pressure effects on the target mean excitation energy, I, are also formally calculated and compared with corresponding accurate calculations based on the Local Plasma Approximation (LPA). Even though atomic hydrogen is the simplest target system, its accurate treatment to account for the role of pressure in the stopping dynamics is found to provide useful means to understand the behavior of more complex systems under similar conditions. It is found that: (i) the region of projectile velocities for which the Bethe approximation remains valid is shifted towards higher values as pressure increases; (ii) shell corrections are enhanced relative to the free-atom case as pressure increases, and (iii) the LPA seems to underestimate I as pressure is increased. The results of this work for atomic hydrogen may serve as accurate benchmark reference values for studies of pressure effects on S{sub e} and I using different methodologies.
Neese, Frank; Wennmohs, Frank; Hansen, Andreas
2009-03-01
Coupled-electron pair approximations (CEPAs) and coupled-pair functionals (CPFs) have been popular in the 1970s and 1980s and have yielded excellent results for small molecules. Recently, interest in CEPA and CPF methods has been renewed. It has been shown that these methods lead to competitive thermochemical, kinetic, and structural predictions. They greatly surpass second order Møller-Plesset and popular density functional theory based approaches in accuracy and are intermediate in quality between CCSD and CCSD(T) in extended benchmark studies. In this work an efficient production level implementation of the closed shell CEPA and CPF methods is reported that can be applied to medium sized molecules in the range of 50-100 atoms and up to about 2000 basis functions. The internal space is spanned by localized internal orbitals. The external space is greatly compressed through the method of pair natural orbitals (PNOs) that was also introduced by the pioneers of the CEPA approaches. Our implementation also makes extended use of density fitting (or resolution of the identity) techniques in order to speed up the laborious integral transformations. The method is called local pair natural orbital CEPA (LPNO-CEPA) (LPNO-CPF). The implementation is centered around the concepts of electron pairs and matrix operations. Altogether three cutoff parameters are introduced that control the size of the significant pair list, the average number of PNOs per electron pair, and the number of contributing basis functions per PNO. With the conservatively chosen default values of these thresholds, the method recovers about 99.8% of the canonical correlation energy. This translates to absolute deviations from the canonical result of only a few kcal mol-1. Extended numerical test calculations demonstrate that LPNO-CEPA (LPNO-CPF) has essentially the same accuracy as parent CEPA (CPF) methods for thermochemistry, kinetics, weak interactions, and potential energy surfaces but is up to 500
Nodal analysis of two-phase instabilities
Nodal models having moving nodal boundaries have been developed for the analysis of two-phase flow instabilities in a boiling channel. The first model, which was based on a Galerkin method for the discretization, has been found to be accurate in the prediction of the onset of instabilities as well as the frequency of oscillations. This model however, had some problems with the prediction of chaotic phenomena and did not allow for flow reversal in the channel. A second nodal model, based on a finite difference approach, has been found to perform better for the prediction of non-linear response and it also allows for flow reversal. Both models are numerically more efficient than the existing fixed grid models for instabilities analysis
Adiabatic boiling of two-phase coolant in upward flow
A mathematical model of the process of adiabatic boiling (self-condensation) of a two-phase coolant in upward (downward) flow is developed. The model takes account of changes in phase properties with static pressure decrease. The process is investigated numerically. Approximate analytical formulas for design calculations are obtained. It is shown that effects of adiabatic boiling (self-condensation) should be taken into account when calculating two-phase coolant flow in stretched vertical channels
Transient two-phase performance of LOFT reactor coolant pumps
Performance characteristics of Loss-of-Fluid Test (LOFT) reactor coolant pumps under transient two-phase flow conditions were obtained based on the analysis of two large and small break loss-of-coolant experiments conducted at the LOFT facility. Emphasis is placed on the evaluation of the transient two-phase flow effects on the LOFT reactor coolant pump performance during the first quadrant operation. The measured pump characteristics are presented as functions of pump void fraction which was determined based on the measured density. The calculated pump characteristics such as pump head, torque (or hydraulic torque), and efficiency are also determined as functions of pump void fractions. The importance of accurate modeling of the reactor coolant pump performance under two-phase conditions is addressed. The analytical pump model, currently used in most reactor analysis codes to predict transient two-phase pump behavior, is assessed
Simulation of Two-Phase Flow in Sloshing Tanks
Luppes, Roel; Veldman, Arthur; Wemmenhove, Rik; Kuzmin, A
2011-01-01
The CFD simulation tool ComFLOW is applied to study the effect of tank motions on two-phase flow phenomena inside a sloshing tank. An improved VOF method is used to assure an accurate description of the fluid displacement. With a novel “gravity-consistent” density averaging method, spurious velociti
Palmer, T S
2003-01-01
In this NEER project, researchers from Oregon State University have investigated the limitations of the treatment of two-phase coolants as a homogeneous mixture in neutron transport calculations. Improved methods of calculating the neutron distribution in binary stochastic mixtures have been developed over the past 10-15 years and are readily available in the transport literature. These methods are computationally more expensive than the homogeneous (or atomic mix) models, but can give much more accurate estimates of ensemble average fluxes and reaction rates provided statistical descriptions of the distributions of the two materials are know. A thorough review of the two-phase flow literature has been completed and the relevant mixture distributions have been identified. Using these distributions, we have performed Monte Carlo criticality calculations of fuel assemblies to assess the accuracy of the atomic mix approximation when compared to a resolved treatment of the two-phase coolant. To understand the ben...
Fluctuation model of a nonequilibrium two-phase channel flow
An ill-posed Cauchy problem for a model of a nonequilibrium two-phase flow in the barotropic approximation is transformed into a well-posed problem by changing the type of the initial hyperbolic equations. Approximation of fluctuations of the phase velocities by a random delta-correlated process and averaging of the equations over its realizations generate a system of parabolic equations. Results of numerical integration of this system are compared with experiment and calculations by well-known models
Fluctuation model of a nonequilibrium two-phase channel flow
Krivoshei, F.A. [Inst. of Engineering Thermophysics, Kiev (Ukraine)
1994-12-01
An ill-posed Cauchy problem for a model of a nonequilibrium two-phase flow in the barotropic approximation is transformed into a well-posed problem by changing the type of the initial hyperbolic equations. Approximation of fluctuations of the phase velocities by a random delta-correlated process and averaging of the equations over its realizations generate a system of parabolic equations. Results of numerical integration of this system are compared with experiment and calculations by well-known models.
Two-Phase flow instrumentation for nuclear accidents simulation
Monni, G.; De Salve, M.; Panella, B.
2014-11-01
The paper presents the research work performed at the Energy Department of the Politecnico di Torino, concerning the development of two-phase flow instrumentation and of models, based on the analysis of experimental data, that are able to interpret the measurement signals. The study has been performed with particular reference to the design of power plants, such as nuclear water reactors, where the two-phase flow thermal fluid dynamics must be accurately modeled and predicted. In two-phase flow typically a set of different measurement instruments (Spool Piece - SP) must be installed in order to evaluate the mass flow rate of the phases in a large range of flow conditions (flow patterns, pressures and temperatures); moreover, an interpretative model of the SP need to be developed and experimentally verified. The investigated meters are: Turbine, Venturi, Impedance Probes, Concave sensors, Wire mesh sensor, Electrical Capacitance Probe. Different instrument combinations have been tested, and the performance of each one has been analyzed.
Contribution to the theory of the two phase blowdown phenomenon
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
Two-phase flow in refrigeration systems
Gu, Junjie; Gan, Zhongxue
2013-01-01
Two-Phase Flow in Refrigeration Systems presents recent developments from the authors' extensive research programs on two-phase flow in refrigeration systems. This book covers advanced mass and heat transfer and vapor compression refrigeration systems and shows how the performance of an automotive air-conditioning system is affected through results obtained experimentally and theoretically, specifically with consideration of two-phase flow and oil concentration. The book is ideal for university postgraduate students as a textbook, researchers and professors as an academic reference book, and b
Highlights: • Highly accurate all-electron FP-LAPW+lo method is used. • New physical parameters are reported, important for the fabrication of optoelectronic devices. • A comparative study that involves FP-LAPW+lo method and modified approximations. • Computed band gap values have good agreement with the experimental values. • Optoelectronic results of fundamental importance can be utilized for the fabrication of devices. - Abstract: We report the structural, electronic and optical properties of the thiospinels XIn2S4 (X = Cd, Mg), using highly accurate all-electron full potential linearized augmented plane wave plus local orbital method. In order to calculate the exchange and correlation energies, the method is coupled with modified techniques such as GGA+U and mBJ-GGA, which yield improved results as compared to the previous studies. GGA+SOC approximation is also used for the first time on these compounds to examine the spin orbit coupling effect on the band structure. From the analysis of the structural parameters, robust character is predicted for both materials. Energy band structures profiles are fairly the same for GGA, GGA+SOC, GGA+U and mBJ-GGA, confirming the indirect and direct band gap nature of CdIn2S4 and MgIn2S4 materials, respectively. We report the trend of band gap results as: (mBJ-GGA) > (GGA+U) > (GGA) > (GGA+SOC). Localized regions appearing in the valence bands for CdIn2S4 tend to split up nearly by ≈1 eV in the case of GGA+SOC. Many new physical parameters are reported that can be important for the fabrication of optoelectronic devices. Optical spectra namely, dielectric function (DF), refractive index n(ω), extinction coefficient k(ω), reflectivity R(ω), optical conductivity σ(ω), absorption coefficient α(ω) and electron loss function are discussed. Optical’s absorption edge is noted to be 1.401 and 1.782 for CdIn2S4 and MgIn2S4, respectively. The prominent peaks in the electron energy spectrum situated between 15 eV and
B Zeinali-Rafsanjani
2015-01-01
Full Text Available To accurately recompute dose distributions in chest-wall radiotherapy with 120 kVp kilovoltage X-rays, an MCNP4C Monte Carlo model is presented using a fast method that obviates the need to fully model the tube components. To validate the model, half-value layer (HVL, percentage depth doses (PDDs and beam profiles were measured. Dose measurements were performed for a more complex situation using thermoluminescence dosimeters (TLDs placed within a Rando phantom. The measured and computed first and second HVLs were 3.8, 10.3 mm Al and 3.8, 10.6 mm Al, respectively. The differences between measured and calculated PDDs and beam profiles in water were within 2 mm/2% for all data points. In the Rando phantom, differences for majority of data points were within 2%. The proposed model offered an approximately 9500-fold reduced run time compared to the conventional full simulation. The acceptable agreement, based on international criteria, between the simulations and the measurements validates the accuracy of the model for its use in treatment planning and radiobiological modeling studies of superficial therapies including chest-wall irradiation using kilovoltage beam.
Advanced numerical methods for three dimensional two-phase flow calculations
Toumi, I. [Laboratoire d`Etudes Thermiques des Reacteurs, Gif sur Yvette (France); Caruge, D. [Institut de Protection et de Surete Nucleaire, Fontenay aux Roses (France)
1997-07-01
This paper is devoted to new numerical methods developed for both one and three dimensional two-phase flow calculations. These methods are finite volume numerical methods and are based on the use of Approximate Riemann Solvers concepts to define convective fluxes versus mean cell quantities. The first part of the paper presents the numerical method for a one dimensional hyperbolic two-fluid model including differential terms as added mass and interface pressure. This numerical solution scheme makes use of the Riemann problem solution to define backward and forward differencing to approximate spatial derivatives. The construction of this approximate Riemann solver uses an extension of Roe`s method that has been successfully used to solve gas dynamic equations. As far as the two-fluid model is hyperbolic, this numerical method seems very efficient for the numerical solution of two-phase flow problems. The scheme was applied both to shock tube problems and to standard tests for two-fluid computer codes. The second part describes the numerical method in the three dimensional case. The authors discuss also some improvements performed to obtain a fully implicit solution method that provides fast running steady state calculations. Such a scheme is not implemented in a thermal-hydraulic computer code devoted to 3-D steady-state and transient computations. Some results obtained for Pressurised Water Reactors concerning upper plenum calculations and a steady state flow in the core with rod bow effect evaluation are presented. In practice these new numerical methods have proved to be stable on non staggered grids and capable of generating accurate non oscillating solutions for two-phase flow calculations.
Wei-Yang Xie; Xiao-Ping Li; Lie-Hui Zhang; Xiao-Hua Tan; Jun-Chao Wang; Hai-Tao Wang
2015-01-01
After multistage fracturing, the flowback of fracturing fluid will cause two-phase flow through hydraulic fractures in shale gas reservoirs. With the consideration of two-phase flow and desorbed gas transient diffusion in shale gas reservoirs, a two-phase transient flow model of multistage fractured horizontal well in shale gas reservoirs was created. Accurate solution to this flow model is obtained by the use of source function theory, Laplace transform, three-dimensional eigenvalue method, ...
Laser diagnostics in two phase flows
Krueger, S.
2001-06-01
The existence of a huge lack of experimental data from both technical and fundamental two phase flows was mentioned. The development of laser based non-intrusive measurement techniques to overcome this problem were the task of this work. An optical flow algorithm was adapted for the determination of the velocity fields of continuous and dispersed phase in flow systems. It was used as data reduction method for the newly developed gaseous imaging velocimetry (GIV) technique. The measurement technique including the data reduction has been validated by comparing it to the well-established particle image velocimetry (PIV). Its applicability on scalar data from 2D two-phase flows and reacting gaseous flows was demonstrated. Laser based measurement techniques concerning 3D two-phase flows have also been developed. Solutions for the measurement of the velocity field of the gaseous phase in between the droplets as well as of the liquid phase in an automotive DI spray have been given. (orig.)
Numerical modeling of two-phase binary fluid mixing using mixed finite elements
Sun, Shuyu
2012-07-27
Diffusion coefficients of dense gases in liquids can be measured by considering two-phase binary nonequilibrium fluid mixing in a closed cell with a fixed volume. This process is based on convection and diffusion in each phase. Numerical simulation of the mixing often requires accurate algorithms. In this paper, we design two efficient numerical methods for simulating the mixing of two-phase binary fluids in one-dimensional, highly permeable media. Mathematical model for isothermal compositional two-phase flow in porous media is established based on Darcy\\'s law, material balance, local thermodynamic equilibrium for the phases, and diffusion across the phases. The time-lag and operator-splitting techniques are used to decompose each convection-diffusion equation into two steps: diffusion step and convection step. The Mixed finite element (MFE) method is used for diffusion equation because it can achieve a high-order and stable approximation of both the scalar variable and the diffusive fluxes across grid-cell interfaces. We employ the characteristic finite element method with moving mesh to track the liquid-gas interface. Based on the above schemes, we propose two methods: single-domain and two-domain methods. The main difference between two methods is that the two-domain method utilizes the assumption of sharp interface between two fluid phases, while the single-domain method allows fractional saturation level. Two-domain method treats the gas domain and the liquid domain separately. Because liquid-gas interface moves with time, the two-domain method needs work with a moving mesh. On the other hand, the single-domain method allows the use of a fixed mesh. We derive the formulas to compute the diffusive flux for MFE in both methods. The single-domain method is extended to multiple dimensions. Numerical results indicate that both methods can accurately describe the evolution of the pressure and liquid level. © 2012 Springer Science+Business Media B.V.
Two-phase flow in fractured rock
This report gives the results of a three-day workshop on two-phase flow in fractured rock. The workshop focused on two-phase flow processes that are important in geologic disposal of nuclear waste as experienced in a variety of repository settings. The goals and objectives of the workshop were threefold: exchange information; describe the current state of understanding; and identify research needs. The participants were divided into four subgroups. Each group was asked to address a series of two-phase flow processes. The following groups were defined to address these processes: basic flow processes; fracture/matrix interactions; complex flow processes; and coupled processes. For each process, the groups were asked to address these four issues: (1) describe the two-phase flow processes that are important with respect to repository performance; (2) describe how this process relates to the specific driving programmatic issues given above for nuclear waste storage; (3) evaluate the state of understanding for these processes; and (4) suggest additional research to address poorly understood processes relevant to repository performance. The reports from each of the four working groups are given here
Two-fluid model for two-phase flow
Ishii, M.
1987-06-01
The two-fluid model formulation is discussed in detail. The emphasis of the paper is on the three-dimensional formulation and the closure issues. The origin of the interfacial and turbulent transfer terms in the averaged formulation is explained and their original mathematical forms are examined. The interfacial transfer of mass, momentum, and energy is proportional to the interfacial area and driving force. This is not a postulate but a result of the careful examination of the mathematical form of the exact interfacial terms. These two effects are considered separately. Since all the interfacial transfer terms involve the interfacial area concentration, the accurate modeling of the local interfacial area concentration is the first step to be taken for a development of a reliable two-fluid model closure relations. The interfacial momentum interaction has been studied in terms of the standard-drag, lift, virtual mass, and Basset forces. Available analytical and semi-empirical correlations and closure relations are reviewed and existing shortcomings are pointed out. The other major area of importance is the modeling of turbulent transfer in two-phase flow. The two-phase flow turbulence problem is coupled with the phase separation problem even in a steady-state fully developed flow. Thus the two-phase turbulence cannot be understood without understanding the interfacial drag and lift forces accurately. There are some indications that the mixing length type model may not be sufficient to describe the three-dimensional turbulent and flow structures. Although it is a very difficult challenge, the two-phase flow turbulence should be investigated both experimentally and analytically with long time-scale research.
Hybrid flux splitting schemes for numerical resolution of two-phase flows
Flaatten, Tore
2003-07-01
This thesis deals with the construction of numerical schemes for approximating. solutions to a hyperbolic two-phase flow model. Numerical schemes for hyperbolic models are commonly divided in two main classes: Flux Vector Splitting (FVS) schemes which are based on scalar computations and Flux Difference Splitting (FDS) schemes which are based on matrix computations. FVS schemes are more efficient than FDS schemes, but FDS schemes are more accurate. The canonical FDS schemes are the approximate Riemann solvers which are based on a local decomposition of the system into its full wave structure. In this thesis the mathematical structure of the model is exploited to construct a class of hybrid FVS/FDS schemes, denoted as Mixture Flux (MF) schemes. This approach is based on a splitting of the system in two components associated with the pressure and volume fraction variables respectively, and builds upon hybrid FVS/FDS schemes previously developed for one-phase flow models. Through analysis and numerical experiments it is demonstrated that the MF approach provides several desirable features, including (1) Improved efficiency compared to standard approximate Riemann solvers, (2) Robustness under stiff conditions, (3) Accuracy on linear and nonlinear phenomena. In particular it is demonstrated that the framework allows for an efficient weakly implicit implementation, focusing on an accurate resolution of slow transients relevant for the petroleum industry. (author)
A pumped two-phase cooling system for spacecraft
Ollendorf, S.; Costello, F. A.
1983-01-01
A pumped, two-phase heat-transport system is being developed for possible use for temperature control of scientific instruments on future NASA missions. As compared to a single-phase system, this two-phase system can maintain tighter temperature control with less pumping power. A laboratory model of the system has been built and tested. The measured heat transfer coefficients were approximately the same as in heat pipes, 220 Btu/hr-sq ft-F, as compared to 25 Btu/hr-sq ft-F for single-phase liquid flow. Heat shearing between experiments has been demonstrated wherein vapor generated in the cold plate of an active experiment was condensed in a cold, unheated experiment. System stability has been observed. However, additional development is needed. The use of non-azeotropic mixtures of coolants appears especially promising as a simple way to determine exit quality and thus control the flow rates to prevent dryout.
Review of two-phase water hammer
In a thermalhydraulic system like a nuclear power plant, where steam and water mix and are used to transport large amounts of energy, there is a potential to create two-phase water hammer. Large water hammer pressure transients are a threat to piping integrity and represent an important safety concern. Such events may cause unscheduled plant down time. The objective of this review is to provide a summary of the information on two-phase water hammer available in the open literature with particular emphasis on water hammer occurrences in nuclear power plants. Past reviews concentrated on studies concerned with preventing water hammer. The present review focuses on the fundamental experimental, analytical, and modelling studies. The papers discussed here were chosen from searches covering up to July 1993. (author)
An introduction to two-phase flows
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
Interfacial area measurements in two-phase flow
A thorough understanding of two-phase flow requires the accurate measurement of the time-averaged interfacial area per unit volume (also called the time-averaged integral specific area). The so-called 'specific area' can be estimated by several techniques described in the literature. These different methods are reviewed and the flow conditions which lead to a rigourous determination of the time-averaged integral specific area are clearly established. The probe technique, involving local measurements seems very attractive because of its large range of application
Gauging a two phase hadron model
We generate a two phase model for hadrons starting from a lagrangian density in terms of quarks and meson fields which extend over all space-time. Our procedure is based on the non-topological soliton approach of Friedberg and Lee. We then apply this scheme to study the coupling of gauge weak bosons, for which the surface is transparent, in a consistent manner. (orig.)
Chi, Changqing
2016-01-01
Ferrofluids currently are the only type of magnetic liquid materials with wide practical use. The theory on ferrofluids is an example of success to apply statistics to science. Ferrofluids are two-phase liquids consisting of dispersed nanoscale ferromagnetic particles suspended in a carrier fluid. Due to their tiny size, individual ferromagnetic particles clearly exhibit Brownian motions. Only when a large number of randomly-moving particles are subject to an external magnetic field, can they...
Two phase picture in driven polymer translocation
Saito, Takuya; Sakaue, Takahiro
2012-01-01
Two phase picture is a simple and effective methodology to capture the nonequilibrium dynamics of polymer associated with tension propagation. When applying it to the driven translocation process, there is a point to be noted, as briefly discussed in our recent article [Phys. Rev. E 85, 061803 (2012)]. In this article, we address this issue in detail and modify our previous prediction [Euro. Phys. J. E 34, 135 (2011)] by adopting an alternative steady-state ansatz. The modified scaling predic...
A two-phase level tracking method
Interfacial closure models in most two-fluid system codes for reactor safety are usually tied to the flow regime map through the mean void fraction in a computational cell. When a void fraction discontinuity exists in a computational volume, neither heat nor momentum exchange at the phase interface for this particular cell can be properly represented in finite-difference equations governing the fluid flow. Moreover, finite-difference methods with a fixed, Eulerian grid will inaccurately predict the cell-to-cell convection of mass, momentum and energy when the mean cell macroscopic variables are convected from the cell containing the void fraction front. The adequate modeling of two-phase mixture levels requires the knowledge of front position and void fractions above and below the front. In order to obtain such information, an efficient and simple tracking method was implemented in the TRAC-BWR code (released April 1984). We have tested this method with a simple problem involving a moving two-phase air/water mixture level. The results revealed inconsistencies in the behavior of velocities, pressures and interfacial friction, and some bounded numerical oscillations. Following our numerical experiment, we developed a systematic approach to improve the two-phase level tracking method. We present this approach and the results of implementation in the TRAC-BWR code. (orig.)
Two-phase charge-coupled device
Kosonocky, W. F.; Carnes, J. E.
1973-01-01
A charge-transfer efficiency of 99.99% per stage was achieved in the fat-zero mode of operation of 64- and 128-stage two-phase charge-coupled shift registers at 1.0-MHz clock frequency. The experimental two-phase charge-coupled shift registers were constructed in the form of polysilicon gates overlapped by aluminum gates. The unidirectional signal flow was accomplished by using n-type substrates with 0.5 to 1.0 ohm-cm resistivity in conjunction with a channel oxide thickness of 1000 A for the polysilicon gates and 3000 A for the aluminum gates. The operation of the tested shift registers with fat zero is in good agreement with the free-charge transfer characteristics expected for the tested structures. The charge-transfer losses observed when operating the experimental shift registers without the fat zero are attributed to fast interface state trapping. The analytical part of the report contains a review backed up by an extensive appendix of the free-charge transfer characteristics of CCD's in terms of thermal diffusion, self-induced drift, and fringing field drift. Also, a model was developed for the charge-transfer losses resulting from charge trapping by fast interface states. The proposed model was verified by the operation of the experimental two-phase charge-coupled shift registers.
Two-Phase flow instrumentation for nuclear accidents simulation
The paper presents the research work performed at the Energy Department of the Politecnico di Torino, concerning the development of two-phase flow instrumentation and of models, based on the analysis of experimental data, that are able to interpret the measurement signals. The study has been performed with particular reference to the design of power plants, such as nuclear water reactors, where the two-phase flow thermal fluid dynamics must be accurately modeled and predicted. In two-phase flow typically a set of different measurement instruments (Spool Piece – SP) must be installed in order to evaluate the mass flow rate of the phases in a large range of flow conditions (flow patterns, pressures and temperatures); moreover, an interpretative model of the SP need to be developed and experimentally verified. The investigated meters are: Turbine, Venturi, Impedance Probes, Concave sensors, Wire mesh sensor, Electrical Capacitance Probe. Different instrument combinations have been tested, and the performance of each one has been analyzed
Coupling two-phase fluid flow with two-phase darcy flow in anisotropic porous media
Chen, J.
2014-06-03
This paper reports a numerical study of coupling two-phase fluid flow in a free fluid region with two-phase Darcy flow in a homogeneous and anisotropic porous medium region. The model consists of coupled Cahn-Hilliard and Navier-Stokes equations in the free fluid region and the two-phase Darcy law in the anisotropic porous medium region. A Robin-Robin domain decomposition method is used for the coupled Navier-Stokes and Darcy system with the generalized Beavers-Joseph-Saffman condition on the interface between the free flow and the porous media regions. Obtained results have shown the anisotropic properties effect on the velocity and pressure of the two-phase flow. 2014 Jie Chen et al.
Two-phase flow dynamics in ECC
The present report summarizes the achievements within the project ''Two-phase Systems and ECC''. The results during 1978 - 1980 are accounted for in brief as they have been documented in earlier reports. The results during the first half of 1981 are accounted for in greater detail. They contain a new model for the Basset force and test runs with this model using the test code RISQUE. Furthermore, test runs have been performed with TRAC-PD2 MOD 1. This code was implemented on Edwards Pipe Blowdown experiment (a standard test case) and UC-Berkeley Reflooding experiment (a non-standard test case.) (Auth.)
Two-Phase Flow in Heterogeneous Media
Ghaffari, Hamed O
2009-01-01
In this study, we investigate the appeared complexity of two-phase flow (air-water) in a heterogeneous soil where the supposed porous media is non-deformable media which is under the time-dependent gas pressure. After obtaining of governing equations and considering the capillary pressure-saturation and permeability functions, the evolution of the models unknown parameters were obtained. In this way, using COMSOL (FEMLAB) and fluid flow-script Module, the role of heterogeneity in intrinsic permeability was analysed. Also, the evolution of relative permeability of wetting and non-wetting fluid, capillary pressure and other parameters were elicited.
Dynamic failure in two-phase materials
Fensin, S. J.; Walker, E. K.; Cerreta, E. K.; Trujillo, C. P.; Martinez, D. T.; Gray, G. T.
2015-12-01
Previous experimental research has shown that microstructural features such as interfaces, inclusions, vacancies, and heterogeneities can all act as void nucleation sites. However, it is not well understood how important these interfaces are to damage evolution and failure as a function of the surrounding parent materials. In this work, we present results on three different polycrystalline materials: (1) Cu, (2) Cu-24 wt. %Ag, and (3) Cu-15 wt. %Nb which were studied to probe the influence of bi-metal interfaces on void nucleation and growth. These materials were chosen due to the range of difference in structure and bulk properties between the two phases. The initial results suggest that when there are significant differences between the bulk properties (for example: stacking fault energy, melting temperature, etc.) the type of interface between the two parent materials does not principally control the damage nucleation and growth process. Rather, it is the "weaker" material that dictates the dynamic spall strength of the overall two-phase material.
Two Phase Flow Simulation Using Cellular Automata
The classical mathematical treatment of two-phase flows is based on the average of the conservation equations for each phase.In this work, a complementary approach to the modeling of these systems based on statistical population balances of aut omata sets is presented.Automata are entities defined by mathematical states that change following iterative rules representing interactions with the neighborhood.A model of automata for two-phase flow simulation is presented.This model consists of fie lds of virtual spheres that change their volumes and move around a certain environment.The model is more general than the classical cellular automata in two respects: the grid of cellular automata is dismissed in favor of a trajectory generator, and the rules of interaction involve parameters representing the actual physical interactions between phases.Automata simulation was used to study unsolved two-phase flow problems involving high heat flux rates. One system described in this work consists of a vertical channel with saturated water at normal pressure heated from the lower surface.The heater causes water to boil and starts the bubble production.We used cellular automata to describe two-phase flows and the interaction with the heater.General rule s for such cellular automata representing bubbles moving in stagnant liquid were used, with special attention to correct modeling of different mechanisms of heat transfer.The results of the model were compared to previous experiments and correlations finding good agreement.One of the most important findings is the confirmation of Kutateladze's idea about a close relation between the start of critical heat flux and a change in the flow's topology.This was analyzed using a control volume located in the upper surface of the heater.A strong decrease in the interfacial surface just before the CHF start was encountered.The automata describe quite well some characteristic parameters such as the shape of the local void fraction in the
Graphical abstract: This review summarizes the studies of the exact solutions of the Schrödinger and Dirac equations of H2+ in non-relativistic, relativistic, non-Born-Oppenheimer, and under magnetic field conditions, by the free-complement (FC) method. Highlights: ► The studies of the exact solutions of the Schrödinger and Dirac equations of H2+ are reviewed. ► The Schrödinger and Dirac equations are solved by the free-complement (FC) method. ► Non-Born–Oppenheimer and magnetic field cases are also solved. - Abstract: We here give a review of our studies of hydrogen molecular ion (H2+) based on the accurate solutions of the Schrödinger equation (SE) and Dirac equations (DE) obtained by the free-complement (FC) methodology developed in our laboratory. We summarize the results of non-relativistic and relativistic studies of H2+ and its isotopomers HD+, and HT+, under the Born–Oppenheimer (BO) and non-BO treatments and with and without external magnetic field. H2+ is a simple one-electron molecule, and so has basic importance in quantum chemistry. Further, it is stable and of rich history of studies, particularly in interstellar science. For the non-relativistic SE, the convergence speed to the exact solution of the FC method is faster than that of the “exact” expansion, exhibiting high efficiency of the FC method. For the relativistic DE, not only accurate energy upper bounds but also lower bounds are calculated. The potential energy curves are also calculated at the non-relativistic and relativistic levels for all isotopomers, and chemically interesting information such as spectroscopic constants and transition frequencies are provided. The non-BO problem is also successfully solved for all isotopomers, and extremely accurate 11S and 13P energies, expectation values of interparticle distances are calculated for the ground and excited vibrational states. In the magnetic field calculation, our method is accurate in any strengths and any directions
Sun, Zhigang
2016-01-01
We proposed a distributed approximating functional method for efficiently describing the electronic dynamics in atoms and molecules in the presence of the Coulomb singularities, using the kernel of a grid representation derived by using the solutions of the Coulomb differential equation based upon the Schwartz's interpolation formula, and a grid representation using the Lobatto/Radau shape functions. The elements of the resulted Hamiltonian matrix are confined in a narrow diagonal band, which is similar to that using the (higher order) finite difference methods. However, the spectral convergence properties of the original grid representations are retained in the proposed distributed approximating functional method for solving the Schr\\"odinger equation involving the Coulomb singularity. Thus the method is effective for solving the electronic Schr\\"odinger equation using iterative methods where the action of the Hamiltonian matrix on the wave function need to evaluate many times. The method is investigated by ...
Boyd, John P.
2011-02-01
Radial basis function (RBF) interpolants have become popular in computer graphics, neural networks and for solving partial differential equations in many fields of science and engineering. In this article, we compare five different species of RBFs: Gaussians, hyperbolic secant (sech's), inverse quadratics, multiquadrics and inverse multiquadrics. We show that the corresponding cardinal functions for a uniform, unbounded grid are all approximated by the same function: C(X) ∼ (1/(ρ)) sin (πX)/sinh (πX/ρ) for some constant ρ(α) which depends on the inverse width parameter (“shape parameter”) α of the RBF and also on the RBF species. The error in this approximation is exponentially small in 1/α for sech's and inverse quadratics and exponentially small in 1/α2 for Gaussians; the error is proportional to α4 for multiquadrics and inverse multiquadrics. The error in all cases is small even for α ∼ O(1). These results generalize to higher dimensions. The Gaussian RBF cardinal functions in any number of dimensions d are, without approximation, the tensor product of one dimensional Gaussian cardinal functions: Cd(x1,x2…,xd)=∏j=1dC(xj). For other RBF species, we show that the two-dimensional cardinal functions are well approximated by the products of one-dimensional cardinal functions; again the error goes to zero as α → 0. The near-identity of the cardinal functions implies that all five species of RBF interpolants are (almost) the same, despite the great differences in the RBF ϕ's themselves.
Wei-Yang Xie
2015-01-01
Full Text Available After multistage fracturing, the flowback of fracturing fluid will cause two-phase flow through hydraulic fractures in shale gas reservoirs. With the consideration of two-phase flow and desorbed gas transient diffusion in shale gas reservoirs, a two-phase transient flow model of multistage fractured horizontal well in shale gas reservoirs was created. Accurate solution to this flow model is obtained by the use of source function theory, Laplace transform, three-dimensional eigenvalue method, and orthogonal transformation. According to the model’s solution, the bilogarithmic type curves of the two-phase model are illustrated, and the production decline performance under the effects of hydraulic fractures and shale gas reservoir properties are discussed. The result obtained in this paper has important significance to understand pressure response characteristics and production decline law of two-phase flow in shale gas reservoirs. Moreover, it provides the theoretical basis for exploiting this reservoir efficiently.
Two-phase fluids in centrifugal separators
In nuclear power plants centrifugal separators are often used for the separation of mixtures of gas and liquid. The investigations described in this paper are concerned with flow distributions in such separators or in other apparatus with a two-phase fluid as the working medium. The measuring methods used for the determination of the local parameters of flow are described. Tests of cascades were performed. The profiles had a mean line of an arc of circle and constant thickness. Blades like these are commonly used in separators. Furthermore the results of measurements in the separation zones of separators of the tangential and the axial type are presented. Finally it will be discussed, in as far the data obtained with a mixture of air and water can also be applied to other mixtures. (orig.)
Stability of oscillatory two phase Couette flow
Coward, Adrian V.; Papageorgiou, Demetrios T.
1993-01-01
We investigate the stability of two phase Couette flow of different liquids bounded between plane parallel plates. One of the plates has a time dependent velocity in its own plane, which is composed of a constant steady part and a time harmonic component. In the absence of time harmonic modulations, the flow can be unstable to an interfacial instability if the viscosities are different and the more viscous fluid occupies the thinner of the two layers. Using Floquet theory, we show analytically in the limit of long waves, that time periodic modulations in the basic flow can have a significant influence on flow stability. In particular, flows which are otherwise unstable for extensive ranges of viscosity ratios, can be stabilized completely by the inclusion of background modulations, a finding that can have useful consequences in many practical applications.
Modeling of two-phase slug flow
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
Two-phase ozonation of chlorinated organics
In the last few years the amount of research being conducted in the field of single-phase ozonation has grown extensively. However, traditional aqueous-phase ozonation systems are limited by a lack of selective oxidation potential, low ozone solubility in water, and slow intermediate decomposition rates. Furthermore, ozone may decompose before it can be utilized for pollutant destruction since ozone can be highly unstable in aqueous solutions. Naturally occurring compounds such as NaHCO3 also affect ozone reactions by inhibiting the formation of OH-free radicals. To compensate for these factors, excess ozone is typically supplied to a reactor. Since ozone generation requires considerable electric power consumption (16 - 24 kWh/kg of O3), attempts to enhance the ozone utilization rate and stability should lead to more efficient application of this process to hazardous waste treatment. To improve the process, ozonation may be more efficiently carried out in a two-phase system consisting of an inert solvent (saturated with O3) contacted with an aqueous phase containing pollutants. The non-aqueous phase must meet the following criteria: (1) non-toxic, (2) very low vapor pressure, (3) high density (for ease of separation), (4) complete insolubility in water, (5) reusability, (6) selective pollutant extractability, (7) high oxidant solubility, and (8) extended O3 stability. Previously published studies (1) have indicated that a number of fluorinated hydrocarbon compounds fit these criteria. For this project, FC40 (a product of 3M Co.) was chosen due to its low vapor pressure (3 mm Hg) and high specific gravity (1.9). The primary advantages of the FC40 solvent are that it is non-toxic, reusable, has an ozone solubility 10 times that of water, and that 85 % of the ozone remains in the solvent even after 2 hours. This novel two-phase process has been utilized to study the rapid destruction of organic chlorine compounds and organic mixtures
A Godunov-type method for the seven-equation model of compressible two-phase flow
We are interested in the numerical approximation of the solutions of the compressible seven-equation two-phase flow model. We propose a numerical strategy based on the derivation of a simple, accurate and explicit approximate Riemann solver. The source terms associated with the external forces and the drag force are included in the definition of the Riemann problem, and thus receive an upwind treatment. The objective is to try to preserve, at the numerical level, the asymptotic property of the solutions of the model to behave like the solutions of a drift-flux model with an algebraic closure law when the source terms are stiff. Numerical simulations and comparisons with other strategies are proposed. (authors)
Tracer Partitioning in Two-Phase Flow
Sathaye, K.; Hesse, M. A.
2012-12-01
The concentration distributions of geochemical tracers in a subsurface reservoir can be used as an indication of the reservoir flow paths and constituent fluid origin. In this case, we are motivated by the origin of marked geochemical gradients in the Bravo Dome natural CO2 reservoir in northeastern New Mexico. This reservoir contains 99% CO2 with various trace noble gas components and overlies the formation brine in a sloping aquifer. It is thought that magmatic CO2 entered the reservoir, and displaced the brine. This displacement created gradients in the concentrations of the noble gases. Two models to explain noble gas partitioning in two-phase flow are presented here. The first model assumes that the noble gases act as tracers and uses a first order non-linear partial differential equation to compute the volume fraction of each phase along the displament path. A one-way coupled partial differential equation determines the tracer concentration, which has no effect on the overall flow or phase saturations. The second model treats each noble gas as a regular component resulting in a three-component, two-phase system. As the noble gas injection concentration goes to zero, we see the three-component system behave like the one-way coupled system of the first model. Both the analytical and numerical solutions are presented for these models. For the process of a gas displacing a liquid, we see that a noble gas tracer with greater preference for the gas phase, such as Helium, will move more quickly along the flowpath than a heavier tracer that will more easily enter the liquid phase, such as Argon. When we include partial miscibility of both the major and trace components, these differences in speed are shown in a bank of the tracer at the saturation front. In the three component model, the noble gas bank has finite width and concentration. In the limit where the noble gas is treated as a tracer, the width of the bank is zero and the concentration increases linearly
Phase appearance or disappearance in two-phase flows
Cordier, Floraine; Kumbaro, Anela
2011-01-01
This paper is devoted to the treatment of specific numerical problems which appear when phase appearance or disappearance occurs in models of two-phase flows. Such models have crucial importance in many industrial areas such as nuclear power plant safety studies. In this paper, two outstanding problems are identified: first, the loss of hyperbolicity of the system when a phase appears or disappears and second, the lack of positivity of standard shock capturing schemes such as the Roe scheme. After an asymptotic study of the model, this paper proposes accurate and robust numerical methods adapted to the simulation of phase appearance or disappearance. Polynomial solvers are developed to avoid the use of eigenvectors which are needed in usual shock capturing schemes, and a method based on an adaptive numerical diffusion is designed to treat the positivity problems. An alternate method, based on the use of the hyperbolic tangent function instead of a polynomial, is also considered. Numerical results are presente...
Condensation in a two-phase pool
We consider the case of vapor condensation in a liquid pool, when the heat transfer is controlled by heat losses through the walls. The analysis is based on drift flux theory for phase separation in the pool, and determines the two-phase mixture height for the pool. To our knowledge this is the first analytical treatment of this classic problem that gives an explicit result, previous work having established the result for the evaporative case. From conservation of mass and energy in a one-dimensional steady flow, together with a void relation between the liquid and vapor fluxes, we determine the increase in the mixture level from the base level of the pool. It can be seen that the thermal and hydrodynamic influences are separable. Thus, the thermal influence of the wall heat transfer appears through its effect on the condensing length L*, so that at high condensation rates the pool is all liquid, and at low rates overflows (the level swell or foaming effect). Similarly, the phase separation effect hydrodynamically determines the height via the relative velocity of the mixture to the entering flux. We examine some practical applications of this result to level swell in condensing flows, and also examine some limits in ideal cases
Numerical calculation of two-phase flows
The theoretical study of time-varying two-phase flow problems in several space dimensions introduces such a complicated set of coupled nonlinear partial differential equations that numerical solution procedures for high-speed computers are required in almost all but the simplest examples. Efficient attainment of realistic solutions for practical problems requires a finite- difference formulation that is simultaneously implicit in the treatment of mass convection, equations of state, and the momentum coupling between phases. Such a method is described, the equations on which it is based are discussed, and its properties are illustrated by means of examples. In particular, the capability for calculating physical instabilities and other time-varying dynamics, at the same time avoiding numerical instability is emphasized. The computer code is applicable to problems in reactor safety analysis, the dynamics of fluidized dust beds, raindrops or aerosol transport, and a variety of similar circumstances, including the effects of phase transitions and the release of latent heat or chemical energy. (U.S.)
Two phase simulation of ultrarelativistic nuclear collisions
A two phase cascade is presented for ultrahigh energy ion-ion collisions from √(s)=17 - 200GeV. First a high-energy cascade is performed, in which original baryons and any freed hard partons collide. This stage ignores energy loss from soft processes. In this first version no hard processes, aside from Drell-Yan production, are included. The space-time history of the hard cascade is used to reconstruct the soft energy loss. Soft meson production is treated as coherent over groups of interacting nucleons. Two body data, though, are used to guide this reconstruction. A second, low-energy cascade is then carried out. The model selected to describe elementary hadron-hadron collisions in the soft cascade incorporates generic mesons and baryons as the agents for rescattering. We imagine a constituent quark model applies, with generic mesons consisting of an excited q bar q pair, and generic baryons constructed from three quarks. The chief result is a reconciliation of the important Drell-Yan measurements, indicating high-mass lepton pairs are produced as if no energy is lost from the nucleons, with the apparent success of a purely hadronic, soft cascade in describing nucleon stopping and meson production in heavy ion experiments at the CERN SPS. The LUCIFER II code may be downloaded under the GNU General Public License from http://bnlnth.phy.bnl.gov/. copyright 1998 The American Physical Society
Two phase simulation of ultrarelativistic nuclear collisions
Kahana, S.H. [Physics Department, Brookhaven National Laboratory, Upton, New York 11973 (United States)] Kahana, D.E. [Physics Department, State University of New York at Stony Brook, Stony Brook, New York 11791 (United States)
1998-12-01
A two phase cascade is presented for ultrahigh energy ion-ion collisions from {radical}(s)=17{endash}200thinspGeV. First a high-energy cascade is performed, in which original baryons and any freed hard partons collide. This stage ignores energy loss from soft processes. In this first version no hard processes, aside from Drell-Yan production, are included. The space-time history of the hard cascade is used to reconstruct the soft energy loss. Soft meson production is treated as coherent over groups of interacting nucleons. Two body data, though, are used to guide this reconstruction. A second, low-energy cascade is then carried out. The model selected to describe elementary hadron-hadron collisions in the soft cascade incorporates generic mesons and baryons as the agents for rescattering. We imagine a constituent quark model applies, with generic mesons consisting of an excited q{bar q} pair, and generic baryons constructed from three quarks. The chief result is a reconciliation of the important Drell-Yan measurements, indicating high-mass lepton pairs are produced {ital as if no energy is lost from the nucleons}, with the apparent success of a purely hadronic, soft cascade in describing nucleon stopping and meson production in heavy ion experiments at the CERN SPS. The LUCIFER II code may be downloaded under the GNU General Public License from http://bnlnth.phy.bnl.gov/. {copyright} {ital 1998} {ital The American Physical Society}
Advances in two-phase flow instrumentation
Multiphase flow measurements have become increasingly in a number of process and power systems. However, the need to predict system behavior under transient and accident conditions in nuclear reactors has given impetus to research in this area. Since moving internal interfaces make theoretical predictions difficult, much information for design and supporting analyses is based on experimental observation. The simplest models involving parameters representing mixture density and mixture mass flux, assume thermal equillibrium of the two phases, and are applicable only to a limited number of situations. Most of the parameters, such as interface area and local mixture density, needed for more sophisticated models, are particularly difficult to measure. At present, there are no truly direct methods for measuring local void fraction or mass flux. Local measurements can be taken for a cross-section using, for example, a system of simultaneously quick-closing valves. These valves obtained for the cross section can be integrated, and the result compared with direct measurements for an entire pipeline. Consistent results tend to support the response-model used
Estimation of the sugar cane cultivated area from LANDSAT images using the two phase sampling method
Parada, N. D. J. (Principal Investigator); Cappelletti, C. A.; Mendonca, F. J.; Lee, D. C. L.; Shimabukuro, Y. E.
1982-01-01
A two phase sampling method and the optimal sampling segment dimensions for the estimation of sugar cane cultivated area were developed. This technique employs visual interpretations of LANDSAT images and panchromatic aerial photographs considered as the ground truth. The estimates, as a mean value of 100 simulated samples, represent 99.3% of the true value with a CV of approximately 1%; the relative efficiency of the two phase design was 157% when compared with a one phase aerial photographs sample.
Ostwald ripening in two-phase mixtures
Experimental measurements of the temperature of a rapidly solidified solid-liquid mixture have been made over a range of volume fractions solid 0.23 to 0.95. These experiments demonstrate the viability of measuring the change in interfacial curvature with time via precision thermometry. The experimental measurements also indicate that there is no radical change in interface morphology over a wide range of volume fractions solid. A solution to the multi-particle diffusion problem (MDP) has been constructed through the use of potential theory. The solution to the MDP was used to describe the diffusion field within a coarsening two-phase mixture consisting of dispersed spherical second-phase particles. Since this theory is based upon the MDP, interparticle diffusional interactions are specifically included in the treatment. As a result, the theory yields, for the first time, insights into the influence of the local distribution of curvature on a particle's coarsening rate. The effect of interparticle interactions on the collective behavior of an ensemble of coarsening particles was also investigated. It was found that any arbitrary distribution of particle radii will tend to a specific time independent distribution when the particle radii are scaled by the average particle radius. Furthermore, it was determined that with increasing volume fraction of coarsening phase, these time independent distributions become broader and more symmetric. It was also found that the ripening kinetics, as measured by the growth rate of the average particle size, increases by a factor of five upon increasing the volume fraction of coarsening phase from zero to 0.5
Numerical modelling of two phase flow with hysteresis in heterogeneous porous media
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)
A TWO-PHASE APPROACH TO FUZZY SYSTEM IDENTIFICATION
Ta-Wei HUNG; Shu-Cherng FANG; Henry L.W.NUTTLE
2003-01-01
A two-phase approach to fuzzy system identification is proposed. The first phase produces a baseline design to identify a prototype fuzzy system for a target system from a coIlection of input-output data pairs. It uses two easily implemented clustering techniques: the subtractive clustering method and the fuzzy c-means (FCM) clustering algorithm. The second phase (fine tuning)is executed to adjust the parameters identified in the baseline design. This phase uses the steepest descent and recursive least-squares estimation methods. The proposed approach is validated by applying it to both a function approximation type of problem and a classification type of problem. An analysis of the learning behavior of the proposed approach for the two test problems is conducted for further confirmation.
Unsteady interfacial coupling of two-phase flow models
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)
Two phase flow models in DxUNSp code platform
Catalin NAE
2011-09-01
Full Text Available The aim of this work is to find an efficient implementation for a two phase flow model in an existing URANS CFD code platform (DxUNSp, initially based on unsteady URANS equations with a k- turbulence model and various other extensions, ranging from a broad selection of wall laws up to a very efficient LES model. This code has the capability for development for nonreacting/reacting multifluid flows for research applications and is under continuous progress. It is intend to present mainly three aspects of this implementation for unstructured mesh based solvers, for high Reynolds compressible flows: the importance of the 5/7 equation model, performance with respect to a basic test cases and implementation details of the proposed schemes. From a numerical point of view, we propose a new approximation schemes of this system based on the VFRoe-ncv.
Vapor Compressor Driven Hybrid Two-Phase Loop Project
National Aeronautics and Space Administration — This Small Business Innovation Research Phase I project will demonstrate a vapor compressor driven hybrid two-phase loop technology. The hybrid two-phase loop...
Two-Phase Flow Pressure Drop in Superhydrophobic Channels
Stevens, Kimberly; Crockett, Julie; Maynes, Daniel R.; Iverson, Brian C.
2015-01-01
Superhydrophobic surfaces promote dropwise condensation, which increases the rate of thermal transport, making them desirable for use in condensers. Adiabatic two-phase flow loops have been constructed to gain insight into the hydrodynamics of two-phase systems, laying the groundwork for further study of condensing flow on superhydrophobic surfaces. A two-phase flow loop to measure pressure drop and visualize the flow patterns of two-phase flow in superhydrophobic channels relative to classic...
Objective characterization of interfacial structures in two-phase flow
In view of establishing a detailed and reliable measurement technique for characterizing the interfacial structures and identifying flow regimes in two-phase flow, two objective approaches are presented. First, the state-of-the-art four-sensor conductivity probe technique is presented to obtain the detailed local information. The newly designed four-sensor conductivity probe accommodates the double-sensor probe capability. Hence, it can be applied in a wide range of two-phase flow regimes spanning from bubbly to churn-turbulent flows with a measurement error of approximately ± 10%. The signal processing scheme is developed such that it accounts for the missing bubbles and defective signals. Furthermore, it categorizes the acquired parameters into two groups based on bubble cord length information. Local information on the void fraction, interfacial area concentration, Sauter mean diameter, interface velocity for each group of bubbles was obtained successfully. Second, a global measurement technique using the non-intrusive impedance voidmeter and neural networks is presented. In this method, an advanced non-intrusive impedance voidmeter provides global interfacial structure information to neural networks which are used to identify the flow regimes. Both supervised and self-organizing neural network learning paradigms performed flow regime identification successfully. In the application of this global method, two approaches are presented, namely: One based on the Probability Density Function (PDF input method), and another based on the ordered set of void fraction measurements which were acquired in a very short time period (instantaneous direct signal input method). The direct signal input method minimizes the time required for identifying the flow regime
Prediction of a subcooled boiling flow with advanced two-phase flow models
Highlights: ► In this study, advanced two-phase flow models were examined to enhance the prediction capability of subcooled boiling flows for the CFD code. ► They consist of Sγ bubbles size, new wall boiling and two-phase logarithmic wall function models. ► The benchmark calculation confirms that advanced two-phase flow models show good prediction results. - Abstract: Prediction of bubble size which governs interfacial transfer terms between the two phases is of importance for an accurate prediction of the subcooled boiling flow. In the present work, a mechanistic bubbles size model, Sγ was examined to enhance the prediction capability of subcooled boiling flows for the CFD (computational fluid dynamics) code. In addition to this, advanced subcooled boiling models such as new wall boiling and two-phase logarithmic wall function models were also applied for an improvement of energy partitioning and two-phase turbulence models, respectively. The benchmark calculation against the DEBORA subcooled boiling data confirms that the Sγ bubble size model with the two advanced subcooled boiling models shows good prediction results and is applicable to the wide range of flow conditions that are expected in the nominal and postulated accidental conditions of a nuclear power plant.
New concept of analytical method for two-phase flow
The authors are developing a new analytical method for vertical upward two-phase flow based on a concept that two-phase flow with minimum pressure energy consumption rate is the most stable and easily flowable two-phase flow for the given boundary conditions and, thus, such two-phase flow should be realized actually. Although this concept is applied basically one-dimensionally in the analytical method, gravity convection effect due to density difference between liquid film on the channel wall and two-phase flow core in the central region of the channel is taken into account through a two-dimensional turbulent flow analysis. An air-water two-phase flow experiment was performed to verify the proposed analytical method. In the present paper, results of the experimental analysis with the proposed method are reported. (author)
A bi-directional two-phase/two-phase heat exchanger
Ku, Jentung; Ottenstein, Laura
1993-01-01
This paper describes the design and test of a heat exchanger that transfers heat from one two-phase thermal loop to another with very small drops in temperature and pressure. The heat exchanger condenses the vapor in one loop while evaporating the liquid in the other without mixing of the condensing and evaporating fluids. The heat exchanger is bidirectional in that it can transfer heat in reverse, condensing on the normally evaporating side and vice versa. It is fully compatible with capillary pumped loops and mechanically pumped loops. Test results verified that performance of the heat exchanger met the design requirements. It demonstrated a heat transfer rate of 6800 watts in the normal mode of operation and 1000 watts in the reverse mode with temperature drops of less than 5 C between two thermal loops.
DNS and LES of two-phase flows with cavitation
Hickel, Stefan
2014-01-01
We report on recent progress in the physical and numerical modeling of compressible two-phase flows that involve phase transition between the liquid and gaseous state of the fluid. The high-speed dynamics of cavitation bubbles is studied in well-resolved simulations (DNS) with a sharp-interface numerical model on a micro scale. The underlying assumption of the employed evaporation/condensation model is that phase change occurs in thermal non-equilibrium and that the associated timescale is larger than that of the wave dynamics. Results for the collapse of a spherical vapor bubble close to a solid wall are discussed for three different bubble-wall configurations. The major challenge for such numerical investigations is to accurately reproduce the dynamics of the interface between liquid and vapor during the entire collapse process, including the high-speed dynamics of the late stages, where compressibility of both phases plays a decisive role. Direct interface resolving simulations are intractable for real wor...
Hybrid dynamic modeling for two phase flow condensers
In this paper, a hybrid modeling approach is proposed to describe the dynamic behavior of the two phase flow condensers used in air-conditioning and refrigeration systems. The model is formulated based on fundamental energy and mass balance governing equations, and thermodynamic principles, while some constants and less important variables that change very little during normal operation, such as cross-sectional areas, mean void fraction, the derivative of the saturation enthalpy with respect to pressure, etc., are lumped into several unknown parameters. These parameters are then obtained by experimental data using least squares identification method. The proposed modeling method takes advantages of both physical and empirical modeling approaches, can accurately predict the transient behaviors in real-time and significantly reduce the computational burden. Other merits of the proposed approach are that the order of the model is very low and all the state variables can be easily measured. These advantages make it easy to be applied to model based control system design. The model validation studies on an experimental system show that the model predicts the system dynamic well. -- Highlights: • A hybrid modeling approach is proposed to describe the dynamic behavior of condensers. • This modeling approach balances the trade-offs between complexity and accuracy. • The model order is very low and all the state variables are available for measurement. • The model validation studies show that the model predicts the system dynamic well. • The model is suitable for dynamic analysis and model-based controller design
Next steps in two-phase flow: executive summary
DiPippo, R.
1980-09-01
The executive summary includes the following topics of discussion: the state of affairs; the fundamental governing equations; the one-dimensional mixture model; the drift-flux model; the Denver Research Institute two-phase geothermal flow program; two-phase flow pattern transition criteria; a two-fluid model under development; the mixture model as applied to geothermal well flow; DRI downwell instrumentation; two-phase flow instrumentation; the Sperry Research Corporation downhole pump and gravity-head heat exchanger systems; and the Brown University two-phase flow experimental program. (MHR)
Calculating the hydraulic characteristics of two-phase-helium circulation systems
Gorbachev, S. P.
1981-09-01
An approximate analytical solution is obtained for calculating the pressure drop in the flows of a boiling two-phase liquid in a heated channel. The dependence of the maximum temperature in the channel on the rate of flow of the cryogenic fluid is determined.
Two-phase flow heat transfer in nuclear reactor systems
occurring in at least two different spatial scales. Uncertainty in modelling of bubble departure diameter at boiling was studied by M. Matkovic and B. Koncar. In this article the propagation of input uncertainties for the simplified model of bubble departure size is evaluated. A methodology for estimating the prediction capability of a given correlation is provided taking into account its range of applicability. Aqueous nanofluids have a great potential for cooling applications, hence they have been studied in the article of P.N. Alekseev et al. as a possible coolant in pressurized water reactor (PWR). The theoretical study presents how a stable formation of nanoparticles in water solution can be established. Formation of fractal nanoparticles with a higher thermal conductivity than water can enhance the heat transfer of water used as a coolant in PWR. Apart from solid particles, also alternative formation of gaseous nanoparticles in density fluctuations of water is discussed. The article of R. Rzehak and E. Krepper provides a comprehensive overview of the state-of-the-art in the field of CFD modelling of subcooled flow boiling. The efficient predictive capability of current models requires calibration of model parameters over a wide range of measured data and operating conditions.The results presented in the article confirmed the great potential of the existing modelling approach for the 3D simulation of subcooled flow boiling in industrial applications but also highlight the need for specific model improvements to achieve highly accurate predictions. Two articles deal with one-dimensional analyses of two phase flows. In the article of O.Costa et al., a rapid depressurization in vertical heated pipe is simulated with the in-house 1D computer code WAHA, which was developed specifically for simulations of two-phase water hammer phenomena. The WAHA results were confronted with the simulations of the well-known system code RELAP5 on the same experimental data. The thermal
Two Phases of Coherent Structure Motions in Turbulent Boundary Layer
LIU Jian-Hua; JIANG Nan
2007-01-01
Two phases of coherent structure motion are acquired after obtaining conditional phase-averaged waveforms for longitudinal velocity of coherent structures in turbulent boundary layer based on Harr wavelet transfer. The correspondences of the two phases to the two processes (i.e. ejection and sweep) during a burst are determined.
Two-phase flow characterisation by nuclear magnetic resonance
The results presented in this paper demonstrate the performance of the PFGSE-NMR to obtain a complete characterisation of two-phase flows. Different methods are proposed to characterise air-water flows in different regimes: stationary two-phase flows and flows in transient condition. Finally a modified PFGSE is proposed to analyse the turbulence of air-water bubbly flow. (author)
Stochastic Discrete Equation Method (sDEM) for two-phase flows
A new scheme for the numerical approximation of a five-equation model taking into account Uncertainty Quantification (UQ) is presented. In particular, the Discrete Equation Method (DEM) for the discretization of the five-equation model is modified for including a formulation based on the adaptive Semi-Intrusive (aSI) scheme, thus yielding a new intrusive scheme (sDEM) for simulating stochastic two-phase flows. Some reference test-cases are performed in order to demonstrate the convergence properties and the efficiency of the overall scheme. The propagation of initial conditions uncertainties is evaluated in terms of mean and variance of several thermodynamic properties of the two phases
Stochastic Discrete Equation Method (sDEM) for two-phase flows
Abgrall, R., E-mail: remi.abgrall@inria.fr [Institut für Mathematik, Universität Zürich, Winterthurerstrasse 190, CH-8057 Zürich (Switzerland); Congedo, P.M., E-mail: pietro.congedo@inria.fr [INRIA Bordeaux-Sud-Ouest, Equipe Cardamom, 200 Avenue de la Vieille Tour, 33405 Talence (France); Geraci, G., E-mail: ggeraci@stanford.edu [Flow Physics and Computational Engineering, Stanford University, 488 Escondido Mall, Building 500, Stanford, CA 94305-3035 (United States); Rodio, M.G., E-mail: maria-giovanna.rodio@inria.fr [INRIA Bordeaux-Sud-Ouest, Equipe Cardamom, 200 Avenue de la Vieille Tour, 33405 Talence (France)
2015-10-15
A new scheme for the numerical approximation of a five-equation model taking into account Uncertainty Quantification (UQ) is presented. In particular, the Discrete Equation Method (DEM) for the discretization of the five-equation model is modified for including a formulation based on the adaptive Semi-Intrusive (aSI) scheme, thus yielding a new intrusive scheme (sDEM) for simulating stochastic two-phase flows. Some reference test-cases are performed in order to demonstrate the convergence properties and the efficiency of the overall scheme. The propagation of initial conditions uncertainties is evaluated in terms of mean and variance of several thermodynamic properties of the two phases.
The pressure effects on two-phase anaerobic digestion
Highlights: • The pressure effect on anaerobic digestion up to 9 bar was examined. • Increasing pressure decreased pH value in the anaerobic filter. • Increasing pressure increased methane content. • Increasing pressure decreased specific methane yield slightly. • The pressurized methane reactor was very stable and performed well. - Abstract: Two-phase pressurized anaerobic digestion is a novel process aimed at facilitating injection of the produced biogas into the natural gas grid by integrating the fermentative biogas production and upgrading it to substitute natural gas. In order to understand the mechanisms, knowledge of pressure effects on anaerobic digestion is required. To examine the effects of pressure on the anaerobic digestion process, a two-phase anaerobic digestion system was built up in laboratory scale, including three acidogenesis-leach-bed-reactors and one pressure-resistant anaerobic filter. Four different pressure levels (the absolute pressure of 1 bar, 3 bar, 6 bar and 9 bar) were applied to the methane reactor in sequence, with the organic loading rate maintained at approximately 5.1 kgCOD m−3 d−1. Gas production, gas quality, pH value, volatile fatty acids, alcohol, ammonium-nitrogen, chemical oxygen demand (COD) and alkaline buffer capacity were analyzed. No additional caustic chemicals were added for pH adjustment throughout the experiment. With the pressure increasing from 1.07 bar to 8.91 bar, the pH value decreased from 7.2 to 6.5, the methane content increased from 66% to 75%, and the specific methane yield was slightly reduced from 0.33 lN g−1COD to 0.31 lN g−1COD. There was almost no acid-accumulation during the entire experiment. The average COD-degradation grade was always more than 93%, and the average alkaline buffering capacity (VFA/TIC ratio) did not exceed 0.2 at any pressure level. The anaerobic filter showed a very stable performance, regardless of the pressure variation
Experimental Studies on the Measurement of Oil-water Two-phase Flow
Ma, Longbo; Zhang, Hongjian; Hua, Yuefang; Zhou, Hongliang
2007-06-01
Oil-water two-phase flow measurement was investigated with a Venturi meter and double-U Coriolis meter in this work. Based on the Venturi differential pressure and the quality of two-phase flow, a model for measuring oil-water mass flow rate was developed, in which fluid asymmetry of oil-water two-phase flow was considered. However, measuring the quality of two-phase flow on-line is rather difficult at present. Though double-U Coriolis meter can provide accurate measurement of two-phase flow, it can not provide desired respective mass flow rate. Therefore, a double-parameter measurement method with Venturi meter and double-U Coriolis meter is proposed. According to the flow rate requirement of Venturi, a new flow regime identification method based on Support Vector Machine (SVM) has been developed for the separated flow and the dispersed flow. With the Venturi model developed in this paper and mass flow rate of oil-water mixture measured with double-U Coriolis meter, mixture mass flow rate, oil mass flow rate and water mass flow rate could be obtained by the correlation. Experiments of flow rate measurement of oil-water two-phase flow were carried out in the horizontal tube with 25mm inner diameter. The water fraction range is from 5% to 95%. Experimental results showed that the flow regime could be identified well with SVM, and the relative error of the total mass flow rate and respective mass flow rate of oil-water two-phase flow was less than ±1.5% and ±10%, respectively.
Pressure drop modeling and comparisons with experiments for single- and two-phase sodium flow
Highlights: → We present further validation of the TRACE code to sodium two-phase flow modeling. → We qualify correlations for pressure-loss modeling in tube and bundle geometries. → The validation is done on the basis of experiments from the Ispra Research Center. → We give recommendations for the modeling of pressure drop in sodium two-phase flow. - Abstract: The thermal-hydraulic code TRACE is currently being extended at the Paul Scherrer Institute (PSI) for enabling the study of sodium-cooled fast reactor (SFR) core behavior during transients in which boiling is anticipated. An accurate prediction of pressure losses across fuel bundles - under both single- and two-phase sodium flow conditions - is necessary in this context. The present paper addresses the assessment, and implementation in TRACE, of appropriate friction factor models for round tubes and wire-wrapped fuel bundles, as well as local pressure drop models for grid spacers. Validity of the implemented correlations has been confirmed via the analysis of a range of experiments conducted earlier at the Joint Research Centre, Ispra. The measurements utilized are those of single- and two-phase pressure loss for sodium flow in tubes and 12-pin bundles, as a function of the inlet velocity under quasi steady-state conditions. The reported study thus represents an important further development step for the reliable simulation of two-phase sodium flow in TRACE.
Multi-needle capacitance probe for non-conductive two-phase flows
Monrós-Andreu, G.; Martinez-Cuenca, R.; Torró, S.; Escrig, J.; Hewakandamby, B.; Chiva, S.
2016-07-01
Despite its variable degree of application, intrusive instrumentation is the most accurate way to obtain local information in a two-phase flow system, especially local interfacial velocity and local interfacial area parameters. In this way, multi-needle probes, based on conductivity or optical principles, have been extensively used in the past few decades by many researchers in two-phase flow investigations. Moreover, the signal processing methods used to obtain the time-averaged two-phase flow parameters in this type of sensor have been thoroughly discussed and validated by many experiments. The objective of the present study is to develop a miniaturized multi-needle probe, based on capacitance measurements applicable to a wide range of non-conductive two-phase flows and, thus, to extend the applicability of multi-needle sensor whilst also maintaining a signal processing methodology provided in the literature for conductivity probes. Results from the experiments performed assess the applicability of the proposed sensor measurement principle and signal processing method for the bubbly flow regime. These results also provide an insight into the sensor application for more complex two-phase flow regimes.
Effects of two-phase flow in a model for nitramine deflagration
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
Research on one-dimensional two-phase flow
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, CD, for large sharp-edged orifice is determined as the value which is not affected by the experimental facility characteristics, etc. (author)
Thermo-Fluid Dynamics of Two-Phase Flow
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
What types of investors generate the two-phase phenomenon?
Ryu, Doojin
2013-12-01
We examine the two-phase phenomenon described by Plerou, Gopikrishnan, and Stanley (2003) [1] in the KOSPI 200 options market, one of the most liquid options markets in the world. By analysing a unique intraday dataset that contains information about investor type for each trade and quote, we find that the two-phase phenomenon is generated primarily by domestic individual investors, who are generally considered to be uninformed and noisy traders. In contrast, our empirical results indicate that trades by foreign institutions, who are generally considered informed and sophisticated investors, do not exhibit two-phase behaviour.
Tunable two-phase coexistence in half-doped manganites
P Chaddah; A Banerjee
2008-02-01
We discuss our very interesting experimental observation that the low-temperature two-phase coexistence in half-doped manganites is multi-valued (at any field) in that we can tune the coexisting antiferromagnetic-insulating (AF-I) and the ferromagnetic-metallic (FM-M) phase fractions by following different paths in (; ) space. We have shown experimentally that the phase fraction, in this two-phase coexistence, can take continuous infinity of values. All but one of these are metastable, and two-phase coexistence is not an equilibrium state.
Two-Phase Ammonia-Water Absorption in Mini-Channel Annulus
van de Bor, Dennis Marijn; Vasilescu, Catalina; Infante Ferreira, Carlos
2012-01-01
In order to reduce investment costs and refrigerant charge for heat pump equipment, the design of the required heat exchangers should be optimized. Mini-channels heat exchangers are proposed since they can dissipate a higher heat flux and they can be more compact. An accurate prediction of the two-phase heat transfer coefficient in mini-channels is necessary for the heat exchangers design. Several correlations have been proposed in the literature but they cannot cover the wide ranges of worki...
Numerical experiments of two-phase flow in pipelines with a two-fluid compressible model
Loilier, P.; Omgba-Essama, C.; Thompson, Chris
2005-01-01
Getting an accurate understanding of the dynamics of multiphase transport for the design of efficient pipelines is an important issue in the oil and gas industry. This paper presents simulations of one-dimensional two-phase flow in pipelines. The compressible model used is derived from the two-fluid model where pressure relaxation terms are added. The governing system consists of five time- dependent partial differential equations solved explicitly by a finite volume approac...
Two-phase repository construction concept: Engineering feasibility study
As part of the Conceptual Design of a High Level Nuclear Waste Repository in Salt, and Engineering Feasibility Study was performed to evaluate the validity of the proposed two-phase repository construction concept as described in the Mission Plan. As a result of this study, the two-phase repository construction concept can be considered valid. The uncertainty associated with the site-related permitting and licensing process remains the major element of risk to the program schedule. With the application of the two-phase approach, surface and subsurface construction activities can be removed from the critical path. For this study, the Davis Canyon, Utah site was used. The study includes preliminary designs of the two-phase repository, surface and subsurface layouts, an overall integrated schedule, and cost estimates and evaluations regarding schedule and technical issues. 4 refs., 19 figs., 21 tabs
Vapor Compressor Driven Hybrid Two-Phase Loop Project
National Aeronautics and Space Administration — The Phase I project successfully demonstrated the feasibility of the vapor compression hybrid two-phase loop (VCHTPL). The test results showed the high...
Refrigeration. Two-Phase Flow. Flow Regimes and Pressure Drop
Knudsen, Hans-Jørgen Høgaard
2002-01-01
The note gives the basic definitions used in two-phase flow. Flow regimes and flow regimes map are introduced. The different contributions to the pressure drop are stated together with an imperical correlation from the litterature....
Scaling of Two-Phase Systems Across Gravity Levels Project
National Aeronautics and Space Administration — There is a defined need for long term earth based testing for the development and deployment of two-phase flow systems in reduced-gravity, including lunar gravity,...
Gravity Independence of Microchannel Two-Phase Flow Project
National Aeronautics and Space Administration — Most of the amassed two-phase flow and heat transfer knowledge comes from experiments conducted in Earth’s gravity. Space missions span varying gravity...
Yousaf, Masood [Department of Physics, Ulsan National Institute of Science and Technology, Ulsan 689-798 (Korea, Republic of); Physics Department, Faculty of Science, Universiti Teknologi Malaysia, Skudai 81310, Johor (Malaysia); Dalhatu, S.A. [Physics Department, Faculty of Science, Universiti Teknologi Malaysia, Skudai 81310, Johor (Malaysia); Murtaza, G. [Department of Physics, Islamia College, Peshawar, KPK (Pakistan); Khenata, R. [Laboratoire de Physique Quantique et de Modélisation Mathématique (LPQ3M), Département de Technologie, Université de Mascara, 29000 Mascara (Algeria); Sajjad, M. [School of Electronic Engineering, Beijing University of Posts and Telecommunications, Beijing 100876 (China); Musa, A. [Physics Department, Faculty of Science, Universiti Teknologi Malaysia, Skudai 81310, Johor (Malaysia); Rahnamaye Aliabad, H.A. [Department of Physics, Hakim Sabzevari University (Iran, Islamic Republic of); Saeed, M.A., E-mail: saeed@utm.my [Physics Department, Faculty of Science, Universiti Teknologi Malaysia, Skudai 81310, Johor (Malaysia)
2015-03-15
Highlights: • Highly accurate all-electron FP-LAPW+lo method is used. • New physical parameters are reported, important for the fabrication of optoelectronic devices. • A comparative study that involves FP-LAPW+lo method and modified approximations. • Computed band gap values have good agreement with the experimental values. • Optoelectronic results of fundamental importance can be utilized for the fabrication of devices. - Abstract: We report the structural, electronic and optical properties of the thiospinels XIn{sub 2}S{sub 4} (X = Cd, Mg), using highly accurate all-electron full potential linearized augmented plane wave plus local orbital method. In order to calculate the exchange and correlation energies, the method is coupled with modified techniques such as GGA+U and mBJ-GGA, which yield improved results as compared to the previous studies. GGA+SOC approximation is also used for the first time on these compounds to examine the spin orbit coupling effect on the band structure. From the analysis of the structural parameters, robust character is predicted for both materials. Energy band structures profiles are fairly the same for GGA, GGA+SOC, GGA+U and mBJ-GGA, confirming the indirect and direct band gap nature of CdIn{sub 2}S{sub 4} and MgIn{sub 2}S{sub 4} materials, respectively. We report the trend of band gap results as: (mBJ-GGA) > (GGA+U) > (GGA) > (GGA+SOC). Localized regions appearing in the valence bands for CdIn{sub 2}S{sub 4} tend to split up nearly by ≈1 eV in the case of GGA+SOC. Many new physical parameters are reported that can be important for the fabrication of optoelectronic devices. Optical spectra namely, dielectric function (DF), refractive index n(ω), extinction coefficient k(ω), reflectivity R(ω), optical conductivity σ(ω), absorption coefficient α(ω) and electron loss function are discussed. Optical’s absorption edge is noted to be 1.401 and 1.782 for CdIn{sub 2}S{sub 4} and MgIn{sub 2}S{sub 4}, respectively. The
Numerical approach of multi-field two-phase flow models in the OVAP code
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
Two-phase model with vector-meson stabilization
We present a topological chiral two-phase model for baryons with isoscalar vector meson stabilizing term in the soliton sector instead of the usual Skyrme stabilizing term and compare with a closely related model where the omega meson has been eliminated in the limit of infinite mass and coupling constant. In both cases the static properties come out well and the energy is insensitive to changes in the bag radius, as in other nonperturbative two-phase models. (orig.)
Two-phase cooling fluids; Les fluides frigoporteurs diphasiques
Lallemand, A. [Institut National des Sciences Appliquees (INSA), 69 - Lyon (France)
1997-12-31
In the framework of the diminution of heat transfer fluid consumption, the concept of indirect refrigerating circuits, using cooling intermediate fluids, is reviewed and the fluids that are currently used in these systems are described. Two-phase cooling fluids advantages over single-phase fluids are presented with their thermophysical characteristics: solid fraction, two-phase mixture enthalpy, thermal and rheological properties, determination of heat and mass transfer characteristics, and cold storage through ice slurry
Stochastic modelling of two-phase flows including phase change
Stochastic modelling has already been developed and applied for single-phase flows and incompressible two-phase flows. In this article, we propose an extension of this modelling approach to two-phase flows including phase change (e.g. for steam-water flows). Two aspects are emphasised: a stochastic model accounting for phase transition and a modelling constraint which arises from volume conservation. To illustrate the whole approach, some remarks are eventually proposed for two-fluid models. (authors)
Aspects of two-phase gas--liquid flow
A wide range of topics related to current research on liquid-gas flow is reviewed, and the relevance of these topics to the design of heat exchangers is discussed. Information is included on flow patterns; system variables; mathematical models for parallel flow and non-parallel flow; critical two-phase flow; unsteady flow; and types of two-phase flow equipment used in industry. (U.S.)
Review on two-phase flow instabilities in narrow spaces
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
Dynamic modeling strategy for flow regime transition in gas-liquid two-phase flows
In modeling gas-liquid two-phase flows, the concept of flow regime 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 often flow regime dependent. Currently, the determination of the flow regimes is primarily based on flow regime maps or transition criteria, which were developed for steady-state, fully-developed flows and have been widely applied in nuclear reactor system safety analysis codes. As two-phase flows are dynamic in nature (fully-developed two-phase flows generally do not exist in real applications), it is of importance to model the flow regime transition dynamically to be able to predict two-phase flows more accurately. 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 and destruction of the interfacial area, such as the fluid particle (bubble or liquid droplet) disintegration, boiling and evaporation; and fluid particle coalescence and condensation, respectively. For the flow regimes beyond bubbly flows, a two-group IATE has been proposed, in which bubbles are divided into two groups based on their size and 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. (author)
Some applications of mixed finite elements to an ultra compressible or a two phase flow computations
An homogeneous model solving two phase flow equations leads to study Euler equations as for compressible flow. An application of mixed element method built for Navier-Stokes equations is presented with a semi-implicit scheme (2D and 3D case). Some theoretical results about stability and approximation have been obtained and numerical tests have been performed and have given satisfactory results: the first one is a computation in a steam generator and the second one about a nozzle study
袁益让
1999-01-01
For compressible two-phase displacement problem, a kind of characteristic finite difference fractional steps schemes is put forward and thick and thin grids are used to form a complete set. Some techniques, such as piecewise biquadratic interpolation, of calculus of variations, multiplicative commutation rule of difference operators, decomposition of high order difference operators and prior estimates are adopted. Optimal order estimates in L~2 norm are derived to determine the error in the approximate solution.
Numerical method for nonlinear two-phase displacement problem and its application
YUAN Yi-rang; LIANG Dong; RUI Hong-xing; DU Ning; WANG Wen-qia
2008-01-01
For the three-dimensional nonlinear two-phase displacement problem, the modified upwind finite difference fractional steps schemes were put forward. Some techniques, such as calculus of variations, induction hypothesis, decomposition of high order difference operators, the theory of prior estimates and techniques were used. Optimal order estimates were derived for the error in the approximation solution. These methods have been successfully used to predict the consequences of seawater intrusion and protection projects.
SOLUTION OF THE TWO-PHASE STEFAN PROBLEM BY USING THE PICARD'S ITERATIVE METHOD
Roman Witula; Edyta Hetmaniok; Damian Slota; Adam Zielonka
2011-01-01
In this paper, an application of the Picard's iterative method for finding the solution of two phase Stefan problem is presented. In the proposed method an iterative connection is formulated, which allows to determine the temperature distribution in considered domain. Another unknown function, describing position of the moving interface, is approximated with the aid of linear combination of some base functions. Coefficients of this combination are determined by minimizing a properly construct...
New four-sensor probe theory for multi-dimensional two-phase flow measurement
This paper has newly developed a complete four-sensor probe measurement theory of local instantaneous 3D bubble velocity vector, local instantaneous bubble diameter and local instantaneous interfacial normal unit vector and local time-averaged interfacial area concentration (IAC) in a multi-dimensional two-phase flow by assuming the bubbles to be spherical. The newly-developed theory has opened a way for the measurement of bubble diameter with a four-sensor probe. The conventional IAC, 3D bubble velocity vector and interfacial normal unit vector measurement theories of a four-sensor probe have become an example of the newly-developed theory when the bubbles have much larger sizes than a four-sensor probe. Spherical bubbles in a practical two-phase flow are distinguished from non-spherical bubbles by introducing a bubble deviation coefficient from spherical shape. Based on the spherical bubbles, the newly-developed theory was employed to measure local parameters in a two-phase flow. Its measurement results were checked against void fraction measurement using differential pressure (DP) gauges, superficial gas velocity measurement using gas flow meters, bubble diameter measurement using photographic image and IAC measurement using the conventional four-sensor probe theory. The satisfactory comparing results show that the newly-developed theory can perform the accurate and reliable measurements for practical multi-dimensional two-phase flow. (author)
A new correlation of two-phase frictional pressure drop for condensing flow in pipes
Highlights: • Survey of two-phase frictional pressure drop (THFPD) experimental data of condensing flow is conducted. • Applicability of the existing THFPD correlations to condensing flow is assessed. • A new THFPD correlation for condensing flow in pipes is proposed. -- Abstract: The calculation of two-phase frictional pressure drop for condensing flow in pipes is essential in many areas. Although numerous studies concerning this issue have been conducted, an accurate correlation is still required. In this paper, an overall survey of correlations and experimental investigations of two-phase frictional pressure drop is carried out. There 525 experimental data points of 9 refrigerants are gathered from literature, with hydraulic diameter from 0.1 to 10.07 mm, mass flux from 20 to 800 kg/m2 s, and heat flux from 2 to 55.3 kW/m2. The 29 existing correlations are evaluated against the experimental database, among which the best one has a mean absolute relative deviation (MARD) of 25.2%. Based on all the experimental data, a new correlation which has an MARD of 19.4% is proposed, improving significantly the prediction of two-phase frictional pressure drop for pipe condensing flow
Comparison of Two-Phase Pipe Flow in OpenFOAM with a Mechanistic Model
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.
Research on one-dimensional two-phase flow
In the Part I, the author describes about the fundamental form of the hydraulic basic equations for a one-dimensional two-phase flow (two fluid model). Most of the discussions are concentrated on the treatment of phase change inertial force terms in the equations of motion and the author's equations of motion have a strong uniqueness on the following three points in comparison with conventional equations of motion. (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 stational inertia 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 elementary 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 the Part II, characteristics of various kinds of high speed two-phase flow are clarified theoretically by using the basic equations derived in the Part I. It is demonstrated that the steam-water two-phase critical flow with violent flashing and the air-water 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 author's theoretical prediction, the two-phase discharge coefficient, CD, for large sharp-edged orifice is determined as the value which is not affected by the experimental facility characteristics, etc.. (J.P.N.)
Two phase discharge flow prediction in safety valves
Safety relief valves (SRV) are necessary elements in the protection of any pressurised system and the prediction of the expected discharge flows is an important consideration for the valve sizing to ensure that rupture pressures do not occur. The high speed flows that occur inside the SRV are complex particularly when a two-phase flow is involved and lead to a less capable protection device which result in larger valves compared to single phase flows. In this paper the ability of a CFD based two phase mixture model to predict the critical flows of air and water through a safety valve is examined. An industrial refrigeration safety relief valve of ¼″ inlet bore size has been tested experimentally over a pressure range of 6–15 barg and air mass qualities from 0.1 to 1 when discharging to near atmospheric conditions for a fully open condition. A two-dimensional mixture model consisting of mixture mass, momentum, and energy equations, combined with a liquid mass equation and the standard k–ε turbulence model for mixture turbulent transport has been used to predict the two phase flows through the valve. The mixture model results have been compared with the Homogenous Equilibrium Model (HEM) commonly used for in valve sizing in non flashing two phase flow conditions. The accuracy of the models over the two phase flow range are quantified and discussed
Experimental investigation two phase flow in direct methanol fuel cells
Direct methanol fuel cells (DMFC) have received many attentions specifically for portable electronic applications since it utilize methanol which is in liquid form in atmospheric condition and high energy density of the methanol. Thus it eliminates the storage problem of hydrogen. It also eliminates humidification requirement of polymeric membrane which is a problem in PEM fuel cells. Some electronic companies introduced DMFC prototypes for portable electronic applications. Presence of carbon dioxide gases due to electrochemical reactions in anode makes the problem a two phase problem. A two phase flow may occur at cathode specifically at high current densities due to the excess water. Presence of gas phase in anode region and liquid phase in cathode region prevents diffusion of fuel and oxygen to the reaction sites thus reduces the performance of the system. Uncontrolled pressure buildup in anode region increases methanol crossover through membrane and adversely effect the performance. Two phase flow in both anode and cathode region is very effective in the performance of DMYC system and a detailed understanding of two phase flow for high performance DMFC systems. Although there are many theoretical and experimental studies available on the DMFC systems in the literature, only few studies consider problem as a two-phase flow problem. In this study, an experimental set up is developed and species distributions on system are measured with a gas chromatograph. System performance characteristics (V-I curves) is measured depending on the process parameters (temperature, fuel ad oxidant flow rates, methanol concentration etc)
Definition of two-phase flow behaviors for spacecraft design
Reinarts, Thomas R.; Best, Frederick R.; Miller, Katherine M.; Hill, Wayne S.
1991-01-01
Data for complete models of two-phase flow in microgravity are taken from in-flight experiments and applied to an adiabatic flow-regime analysis to study the feasibility of two-phase systems for spacecraft. The data are taken from five in-flight experiments by Hill et al. (1990) in which a two-phase pump circulates a freon mixture and vapor and liquid flow streams are measured. Adiabatic flow regimes are analyzed based on the experimental superficial velocities of liquid and vapor, and comparisons are made with the results of two-phase flow regimes at 1 g. A motion analyzer records the flow characteristics at a rate of 1000 frames/sec, and stratified flow regimes are reported at 1 g. The flow regimes observed under microgravitational conditions are primarily annular and include slug and bubbly-slug regimes. The present data are of interest to the design and analysis of two-phase thermal-management systems for use in space missions.
Microgravity fluid management in two-phase thermal systems
Parish, Richard C.
1987-01-01
Initial studies have indicated that in comparison to an all liquid single phase system, a two-phase liquid/vapor thermal control system requires significantly lower pumping power, demonstrates more isothermal control characteristics, and allows greater operational flexibility in heat load placement. As a function of JSC's Work Package responsibility for thermal management of space station equipment external to the pressurized modules, prototype development programs were initiated on the Two-Phase Thermal Bus System (TBS) and the Space Erectable Radiator System (SERS). JSC currently has several programs underway to enhance the understanding of two-phase fluid flow characteristics. The objective of one of these programs (sponsored by the Microgravity Science and Applications Division at NASA-Headquarters) is to design, fabricate, and fly a two-phase flow regime mapping experiment in the Shuttle vehicle mid-deck. Another program, sponsored by OAST, involves the testing of a two-phase thermal transport loop aboard the KC-135 reduced gravity aircraft to identify system implications of pressure drop variation as a function of the flow quality and flow regime present in a representative thermal system.
Two-phase flow characteristics analysis code: MINCS
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)
Mathematical modeling of disperse two-phase flows
Morel, Christophe
2015-01-01
This book develops the theoretical foundations of disperse two-phase flows, which are characterized by the existence of bubbles, droplets or solid particles finely dispersed in a carrier fluid, which can be a liquid or a gas. Chapters clarify many difficult subjects, including modeling of the interfacial area concentration. Basic knowledge of the subjects treated in this book is essential to practitioners of Computational Fluid Dynamics for two-phase flows in a variety of industrial and environmental settings. The author provides a complete derivation of the basic equations, followed by more advanced subjects like turbulence equations for the two phases (continuous and disperse) and multi-size particulate flow modeling. As well as theoretical material, readers will discover chapters concerned with closure relations and numerical issues. Many physical models are presented, covering key subjects including heat and mass transfers between phases, interfacial forces and fluid particles coalescence and breakup, a...
Velocity and energy relaxation in two-phase flows
Meyapin, Yannick; Gisclon, Marguerite
2009-01-01
In the present study we investigate analytically the process of velocity and energy relaxation in two-phase flows. We begin our exposition by considering the so-called six equations two-phase model [Ishii1975, Rovarch2006]. This model assumes each phase to possess its own velocity and energy variables. Despite recent advances, the six equations model remains computationally expensive for many practical applications. Moreover, its advection operator may be non-hyperbolic which poses additional theoretical difficulties to construct robust numerical schemes |Ghidaglia et al, 2001]. In order to simplify this system, we complete momentum and energy conservation equations by relaxation terms. When relaxation characteristic time tends to zero, velocities and energies are constrained to tend to common values for both phases. As a result, we obtain a simple two-phase model which was recently proposed for simulation of violent aerated flows [Dias et al, 2010]. The preservation of invariant regions and incompressible li...
Two-Phase Phenomena In Wet Flue Gas Desulfurization Process
In order to reduce sulfur oxides discharge, Israel Electric Corporation (IEC) is building a wet Flue Gas Desulfurization (FGD) facility at Rutenberg B power station. The primary objective of IEC is to minimize the occurrence of stack liquid discharge and avoid the discharge of large droplets, in order to prevent acid rain around the stack. Liquid discharge from the stack is the integrated outcome of two-phase processes, which are discussed in this work. In order to estimate droplets discharge the present investigation employs analytical models, empirical tests, and numerical calculations of two-phase phenomena. The two-phase phenomena are coupled and therefore cannot be investigated separately. The present work concerns the application of Computational Fluid Dynamic (CFD) as an engineering complementary tool in the IEC investigation
The secondary side of the nuclear power plant steam generator is working in a two-phase convective boiling process in which two-phase flow instability must be avoided in design. The time domain method was used to study the two-phase flow instability in a vertical up-flow tube. One-dimensional model was established and a numerical program was compiled. Two-phase flow density-wave instability was simulated, and transient parameter distribution in the tube during the dynamic process was presented. The program was also used to analyze the effects of mass velocity, system pressure, and inlet sub-cooling on flow instability. The result shows that the transient parameter distribution from the program agree well with the experimental results, and it can predict the instability boundary, which is more accurate than that of the usually used Khabenski nomographic method. (authors)
Structure of two-phase slug flow in vertical channels
Based on a suggested model of two-phase slug flow in a wide range of varying regime parameters the available literary data and experimental data obtained by the authors on the intensity of void fraction fluctuations, lengths of slugs and liquid plugs are generalized. It is shown that the magnitude of the void fraction is the determining parameter in the formation of the flow regime and structure. The technique for calculating the characteristic frequency of fluctuations of a two-phase flow is suggested
Mechanistic multidimensional analysis of horizontal two-phase flows
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.
Forced Two-Phase Helium Cooling Scheme for the Mu2e Transport Solenoid
Tatkowski, G. [Fermilab; Cheban, S. [Fermilab; Dhanaraj, N. [Fermilab; Evbota, D. [Fermilab; Lopes, M. [Fermilab; Nicol, T. [Fermilab; Sanders, R. [Fermilab; Schmitt, R. [Fermilab; Voirin, E. [Fermilab
2015-01-01
The Mu2e Transport Solenoid (TS) is an S-shaped magnet formed by two separate but similar magnets, TS-u and TS-d. Each magnet is quarter-toroid shaped with a centerline radius of approximately 3 m utilizing a helium cooling loop consisting of 25 to 27 horizontal-axis rings connected in series. This cooling loop configuration has been deemed adequate for cooling via forced single phase liquid helium; however it presents major challenges to forced two-phase flow such as “garden hose” pressure drop, concerns of flow separation from tube walls, difficulty of calculation, etc. Even with these disadvantages, forced two-phase flow has certain inherent advantages which make it a more attractive option than forced single phase flow. It is for this reason that the use of forced two-phase flow was studied for the TS magnets. This paper will describe the analysis using helium-specific pressure drop correlations, conservative engineering approach, helium properties calculated and updated at over fifty points, and how the results compared with those in literature. Based on the findings, the use of forced-two phase helium is determined to be feasible for steady-state cooling of the TS solenoids
Numerical simulation on vapor-liquid two-phase flow of the secondary circuit steam generator
Taken the steam generator of Daya Bay Nuclear Power Station as the proto- type, the 'unit pipe' three-dimensional physical model of steam generator was established under the guidance of the similarity principle. Adopting Particle model and thermal phase change model, numerical simulation was implemented on two-phase flow and boiling heat transfer characteristics of the secondary circuit in steam generator based on CFX software. The results show that heat transfer coefficient and cross-section void fraction increase along the height of tubes at full load. The error of average heat transfer coefficient is 8.4% between numerical simulation and Rohsenow empirical correlation. The export mass fraction is consistent with the actual operating parameters of Daya Bay Nuclear Power Station The successful application of thermal phase change model to two-phase flow numerical simulation of the steam generator can supply reference for thermal-hydraulic accurate analysis of the steam generator. (authors)
Heat treatment method for two-phase stainless steel
A two-phase stainless steel the toughness of which is reduced by exposure to a high temperature is kept at from 900degC to 1040degC to be solidified and then quenched. With such procedures, a δ-phase deposited in a ferrite phase can be eliminated to restore the toughness. In the solidification step, the two-phase stainless steel having a plate thickness of 1cm or less is kept for 15mins or more, and is kept for additional 5min on every increase of the thickness of 1cm, and then it is compulsorily cooled with water or air. In the heat treatment comprising such steps, a Cr-depleted layer of the welded portion of the two-phase stainless steel of reduced toughness is eliminated to restore an initial state thereby enabling to maintain the integrity of the welded portion. Since the δ-phase deposited in the ferrite phase can be eliminated by solid-solubilizing the two phase stainless steel of reduced toughness by induction heating, reduced toughness can be restored thereby enabling to keep the integrity. (T.M.)
Controlling two-phase flow in microfluidic systems using electrowetting
Gu, Hao
2011-01-01
Electrowetting (EW)-based digital microfluidic systems (DMF) and droplet-based two-phase flow microfluidic systems (TPF) with closed channels are the most widely used microfluidic platforms. In general, these two approaches have been considered independently. However, integrating the two technologie
Numerical simulation of two phase flows in heat exchangers
The report presents globally the works done by the author in the thermohydraulic applied to nuclear reactors flows. It presents the studies done to the numerical simulation of the two phase flows in the steam generators and a finite element method to compute these flows. (author)
Thermalhydraulic instability analysis of a two phase natural circulation loop
This work presents an analysis of a loop operating in natural circulation regime. Experiments were done in a rectangular closed circuit in one and two-phase flows. Numerical analysis were performed initially with the CIRNAT code and afterwards with RELAP5/MOD2. The limitations of CIRNAT were studied and new developments for this code are proposed. (author)
Safety relief valve performance for two-phase flow
The performance of main steam safety relief valve has been evaluated with respect only to the steam. In the present study, two-phase flow and subcooled water blow-out tests with model valves were performed in order to evaluate the valve's characteristics and performance. From the test results, it was made clear that not only for the steam but also for the two-phase flow the measurement data were hardly affected by scaling and also that the reaction force of the fluid to the valve stem was hardly dependent upon the void fraction. Analytical study was performed using the two-phase flow model in the valve. The results of the analysis showed good agreement with the test data. It was shown from the test and analysis results that the reaction force of the two-phase flow and subcooled water to the valve stem was almost as much as that of the steam flow, and the integrity of the safety relief valve could be maintained. (author)
Two-Phase Equilibrium in Small Alloy Particles
Weissmüller, J.; Bunzel, P.; Wilde, G.
2004-01-01
The coexistence of two phases within a particle requires an interface with a significant capillary energy. We show that this entails changes in the nature of alloy phase equilibria at small size. Most notably, the eutectic points in alloy phase diagrams degenerate into intervals of composition where the alloy melts discontinuously.
Coal-Face Fracture With A Two-Phase Liquid
Collins, E. R., Jr.
1985-01-01
In new method for mining coal without explosive, two-phase liquid such as CO2 and water, injected at high pressure into deeper ends of holes drilled in coal face. Liquid permeates coal seam through existing microfractures; as liquid seeps back toward face, pressure eventually drops below critical value at which dissolved gas flashvaporizes, breaking up coal.
One-dimensional two-phase thermal hydraulics (ENSTA course)
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
Dynamic Modeling of Phase Crossings in Two-Phase Flow
Madsen, Søren; Veje, Christian; Willatzen, Morten
2012-01-01
here a numerical implementation and novel study of a fully distributed dynamic one-dimensional model of two-phase flow in a tube, including pressure drop, heat transfer, and variations in tube cross-section. The model is based on a homogeneous formulation of the governing equations, discretized by a...
Determination of bubble parameters in two-phase flow
A development of a probe-detector system for measurement of bubble parameters like size, rise velocity and void fraction in two-phase flow is presented. The method uses an electro resistivity probe and a compact electronic circuit has been developed for obtain this purpose. (author)
Two-phase boundary layer prediction in upward boiling flow
In the present work, the numerical modelling of the two-phase turbulent boundary layer in upward boiling flow was investigated. First, non-dimensional liquid velocity and temperature profiles in the two-phase boundary layer were validated on the one-dimensional section of a pipe with prescribed radial void fraction profiles. Simulations were performed on a fine grid with a commercial code CFX-5 using the k-ω turbulence model. A significant deviation of results from the analytical single-phase and two-phase wall functions from the literature was observed. Second, a wall boiling model in a vertical heated pipe was simulated (CFX-5) on the coarse grid. Here the prediction of the two-phase thermal boudary layer was compared to the experimental data, k-ω calculation on the fine grid and against the singlephase analytical wall function. Again a major deviation against single-phase temperature wall function was obtained. Presented analyses suggest that the existing analytical velocity and temperature wall functions cannot be valid for the boiling boundary layer with the high void fraction on the wall. (author)
Anomales in two-phase convection in cryogenic helium
Schmoranzer, D.; Urban, Pavel; Hanzelka, Pavel; Skrbek, L.
Buenos Aires: Institute of Physics of Buenos Aires, 2014. s. 100. [LT27. International Conference on Low Temperature Physics /27./. 06.08.2014-13.08.2014, Buenos Aires] R&D Projects: GA ČR GA14-02005S Institutional support: RVO:68081731 Keywords : cryogenic helium * two-phase convection * temperature inversion * rain formation * cryogenics Subject RIV: BK - Fluid Dynamics
Orientation relationship representation in two-phase material
A. Góral; Jura, J.
2008-01-01
Purpose: Orientation characteristics determination, especially orientation relationship, in two-phase materialsis important in predicting the material properties. The possible orientation relationship representations werepresented and discussed in the paper.Design/methodology/approach: Mathematical formalisms of the quantitative texture and microtextureanalysis were applied.Findings: Various orientation characteristics, especially orientation relationship representation may be used inthe quan...
TWO-PHASE EJECTOR of CARBON DIOXIDE HEAT PUMP CALCULUS
Sit B.M.
2010-12-01
Full Text Available It is presented the calculus of the two-phase ejector for carbon dioxide heat pump. The method of calculus is based on the method elaborated by S.M. Kandil, W.E. Lear, S.A. Sherif, and is modified taking into account entrainment ratio as the input for the calculus.
Modelling of two-phase flow based on separation of the flow according to velocity
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
Modelling of two-phase flow based on separation of the flow according to velocity
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.
Approximation Behooves Calibration
da Silva Ribeiro, André Manuel; Poulsen, Rolf
2013-01-01
Calibration based on an expansion approximation for option prices in the Heston stochastic volatility model gives stable, accurate, and fast results for S&P500-index option data over the period 2005–2009.......Calibration based on an expansion approximation for option prices in the Heston stochastic volatility model gives stable, accurate, and fast results for S&P500-index option data over the period 2005–2009....
Study on flooding in two-phase flow
In a countercurrent two-phase flow, where gas phase flows in the upward direction against a gravity-driven liquid downflow, the liquid downflow rate begins to be limited when the gas flow rate exceeds a certain threshold value. This phenomenon, termed 'flooding', may occur during a loss-of-coolant accident (LOCA) at such locations in reactor coolant system as steam generator (SG) U-tubes in a pressurized water reactor (PWR). Flooding generally tends to reduce the amount of water available for core cooling in emergency situations. Flooding has been studied for various flow conditions and geometries, in particular for vertical channels. Most of these studies were concerned with those situations where the lower entry of the channel is exposed to the gas phase or a gas-continuous two-phase flow, and scarcely dealt with such situations where the liquid is the continuous phase at the channel lower entry. However, in a PWR small-break LOCA, where the reactor coolant inventory is depleted only slowly, the latter situations would be encountered more frequently than the former. The present study is concerned with flooding in a vertical channel whose lower entry is facing to a liquid-continuous two-phase flow. Experiments were conducted using Freon R-113 as a simulant of high-pressure steam-water two-phase flow. Experimental results indicate that flooding for this situation initiates when the two-phase mixture swell level in the channel, which indicates large fluctuations with time, reaches the channel top entry at the peaks of level fluctuations. It was also found that the flooding correlation developed formerly by the authors for air-water flows can be applied to the present R-113 case if the difference in fluid properties are considered appropriately. (author)
High speed motion neutron radiography of two-phase flow
Current research in the area of two-phase flow utilizes a wide variety of sensing devices, but some limitations exist on the information which can be obtained. Neutron radiography is a feasible alternative to ''see'' the two-phase flow. A system to perform neutron radiographic analysis of dynamic events which occur on the order of several milliseconds has been developed at Oregon State University. Two different methods have been used to radiograph the simulated two-phase flow. These are pulsed, or ''flash'' radiography, and high speed movie neutron radiography. The pulsed method serves as a ''snap-shot'' with an exposure time ranging from 10 to 20 milliseconds. In high speed movie radiography, a scintillator is used to convert neutrons into light which is enhanced by an optical intensifier and then photographed by a high speed camera. Both types of radiography utilize the pulsing capability of the OSU TRIGA reactor. The principle difficulty with this type of neutron radiography is the fogging of the image due to the large amount of scattering in the water. This difficulty can be overcome by using thin regions for the two-phase flow or using heavy water instead of light water. The results obtained in this paper demonstrate the feasibility of using neutron radiography to obtain data in two-phase flow situations. Both movies and flash radiographs have been obtained of air bubbles in water and boiling from a heater element. The neutron radiographs of the boiling element show both nucleate boiling and film boiling. (Auth.)
Modeling and numerical study of two phase flow
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)
Two-phase convective CO2 dissolution in saline aquifers
Martinez, M. J.; Hesse, M. A.
2016-01-01
Geologic carbon storage in deep saline aquifers is a promising technology for reducing anthropogenic emissions into the atmosphere. Dissolution of injected CO2 into resident brines is one of the primary trapping mechanisms generally considered necessary to provide long-term storage security. Given that diffusion of CO2 in brine is woefully slow, convective dissolution, driven by a small increase in brine density with CO2 saturation, is considered to be the primary mechanism of dissolution trapping. Previous studies of convective dissolution have typically only considered the convective process in the single-phase region below the capillary transition zone and have either ignored the overlying two-phase region where dissolution actually takes place or replaced it with a virtual region with reduced or enhanced constant permeability. Our objective is to improve estimates of the long-term dissolution flux of CO2 into brine by including the capillary transition zone in two-phase model simulations. In the fully two-phase model, there is a capillary transition zone above the brine-saturated region over which the brine saturation decreases with increasing elevation. Our two-phase simulations show that the dissolution flux obtained by assuming a brine-saturated, single-phase porous region with a closed upper boundary is recovered in the limit of vanishing entry pressure and capillary transition zone. For typical finite entry pressures and capillary transition zone, however, convection currents penetrate into the two-phase region. This removes the mass transfer limitation of the diffusive boundary layer and enhances the convective dissolution flux of CO2 more than 3 times above the rate assuming single-phase conditions.
Thermally induced flow oscillation in vertical two-phase natural circulation loop
In order to study the two-phase natural circulation during a small break loss of coolant accident in LWR, simulation experiments have been performed using Freon-113 boiling and condensation loop. In quasi-steady state, the flow became relatively stabilized and certain regular patterns of flow oscillations were detected with ranges of periods in 8-/approximately/35 seconds and 2.5-/approximately/4 minutes. In order to find out the nature of these oscillations, one-dimensional field equations for the single-phase (liquid) and two-phase region were set up, and these field equations were integrated along the loop. The homogeneous flow model was used for the two-phase region. Then the characteristic equation was derived using perturbation method. Thermal non-equilibrium and compressibility of each phase were not considered in the present analysis. The characteristic equation derived can be used to obtain the stability criteria. A simplified approach showed that the short-period oscillation were the manometer oscillation. The longer period oscillations were the density wave oscillation which had the period of oscillations close to the residence time of a fluid around the loop
GEOTHER: a two-phase fluid-flow and heat-transport code
GEOTHER is a three-dimensional geothermal reservoir simulation code. The model describes heat transport and flow of a single component, two-phase fluid in porous media. It is based on the continuity equations for steam and water, which are reduced to two nonlinear partial differential equations in which the dependent variables are fluid pressure and enthalpy. These equations, describing three-dimensional effects, are approximated using finite-difference techniques and are solved using an iterative technique. The nonlinear coefficients are calculated using Newton-Raphson iteration, and an option is provided for using either upstream or midpoint weighting on the mobility terms. GEOTHER can be used to simulate the fluid-thermal interaction in rock that can be approximated by a porous media representation. It can simulate heat transport and the flow of compressed water, two-phase mixtures, and super-heated steam in porous media over a temperature range of 10 to 3000C. In addition, it can treat the conversion from single- to two-phase flow, and vice versa. It can be used for evaluation of a near repository spatial scale and a time scale of a few years to thousands of years. The model can be used to investigate temperature and fluid pressure changes in response to thermal loading by waste materials. In Section 1.5 of this document the code custodianship and control is described along with the status of verification, validation and peer review of this report
MHD Generators Operating with Two-Phase Liquid Metal Flows
A simplified one- component liquid metal MHD cycle which utilizes two-phase mixtures passing directly through the generator has been proposed and is being studied. Analysis indicates that a nuclear dual-cycle power system utilizing the proposed liquid metal conversion scheme as a topping cycle has overall efficiencies that are comparable to a plasma dual-cycle system at much lower,temperatures. The key to the potential of this cycle is the performance of the MHD generator operating with two-phase mixtures. A large NaK-N2 loop capable of accommodating both d.c. conduction or a.c. induction generators operating with either single-phase or two-phase flows has been built and recently put into operation. Recirculating NaK flow rates up to 200 gal/min and gas flows of 750 ft3/min can be obtained. The efficiency of a generator operating with two-phase flow will depend upon the nature of the flow and the degree to which the total entering liquid flow.interacts with the magnetic field. Because the flow pattern of a two-phase mixture changes from a dispersion of gas in liquid to a dispersion of liquid in gas as the mixture quality is increased, two different types of generators are proposed and are being studied. In the first generator, referred to as a film generator, the two-phase mixture enters at a slight angle to the lower surface of the generator. The liquid is separated by impingement. The high-velocity free surface liquid film that is formed interacts with a transverse magnetic film. The efficiency of this type of generator is a function of the separation ratio, skin friction and momentum losses. A 2 kW version of the generator has been built and is currently being run. Initial tests up to 250 W have been made, which have shown that the generator concept is feasible and that the flow is stable. This generator has run with inlet qualities to 0.05 and magnetic fields up to 12 kG. Measured voltages and amperages have ranged to 0.60 V and 60 A. It is planned to continue
Radiogauging to investigate two phase flow. Graduation report
New measuring methods are developed and are tested with the small reactor simulator MIDAS (Mini Dodewaard ASsembly). The purpose of this work is to be able to measure accurately as many different properties of the flow as possible in the coming bigger simulator SIDAS (Simulated Dodewaard ASsembly). In SIDAS the flow around a fuel assembly of the Dutch Dodewaard reactor will be simulated. An extensive evaluation of the gamma detection system showed that the detection system could be simplified strongly. The simplified system is used to measure the radial and axial distribution of the void fraction in the core of MIDAS for three different operating conditions. Two new measuring methods have been developed and tested. A method to estimate the probability density of the void fraction in time. Due to the nonlinear relation between transmission and void fraction the determined average value of the void fraction in general will contain a systematic error. In this investigation it is shown that this error can be maximally 7.5% in MIDAS and maximally 25% in SIDAS. Therefore a new measuring method has been developed in which the true probability density of the void fraction in time is approximated by two different values of the void fraction, each with a certain probability. With this new method firstly the average void fraction can be determined much more precisely and secondly it often can be used to determine the flow pattern. (orig./WL)
Two-phase wall function for modeling of turbulent boundary layer in subcooled boiling flow
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
Two-phase velocity measurements around cylinders using particle image velocimetry
Hassan, Y.A.; Philip, O.G.; Schmidl, W.D. [Texas A& M Univ., College Station, TX (United States)] [and others
1995-09-01
The particle Image Velocimetry flow measurement technique was used to study both single-phase flow and two-phase flow across a cylindrical rod inserted in a channel. First, a flow consisting of only a single-phase fluid was studied. The experiment consisted of running a laminar flow over four rods inserted in a channel. The water flow rate was 126 cm{sup 3}/s. Then a two-phase flow was studied. A mixture of water and small air bubbles was used. The water flow rate was 378 cm{sup 3}/s and the air flow rate was approximately 30 cm{sup 3}/s. The data are analyzed to obtain the velocity fields for both experiments. After interpretation of the velocity data, forces acting on a bubble entrained by the vortex were calculated successfully. The lift and drag coefficients were calculated using the velocity measurements and the force data.
Kou, Jisheng
2013-01-01
A class of discontinuous Galerkin methods with interior penalties is presented for incompressible two-phase flow in heterogeneous porous media with capillary pressures. The semidiscrete approximate schemes for fully coupled system of two-phase flow are formulated. In highly heterogeneous permeable media, the saturation is discontinuous due to different capillary pressures, and therefore, the proposed methods incorporate the capillary pressures in the pressure equation instead of saturation equation. By introducing a coupling approach for stability and error estimates instead of the conventional separate analysis for pressure and saturation, the stability of the schemes in space and time and a priori hp error estimates are presented in the L2(H 1) for pressure and in the L∞(L2) and L2(H1) for saturation. Two time discretization schemes are introduced for effectively computing the discrete solutions. © 2013 Societ y for Industrial and Applied Mathematics.
Two-phase velocity measurements around cylinders using particle image velocimetry
The particle Image Velocimetry flow measurement technique was used to study both single-phase flow and two-phase flow across a cylindrical rod inserted in a channel. First, a flow consisting of only a single-phase fluid was studied. The experiment consisted of running a laminar flow over four rods inserted in a channel. The water flow rate was 126 cm3/s. Then a two-phase flow was studied. A mixture of water and small air bubbles was used. The water flow rate was 378 cm3/s and the air flow rate was approximately 30 cm3/s. The data are analyzed to obtain the velocity fields for both experiments. After interpretation of the velocity data, forces acting on a bubble entrained by the vortex were calculated successfully. The lift and drag coefficients were calculated using the velocity measurements and the force data
Critical equilibrium two-phase flow with quasi-constant slip
On the basis of the mass-, momentum- and energy-conservation equations, assuming a quasi-constant slip, a mathematical model of the critical non-homogeneous equilibrium two-phase flow is developed. The slip is varied to find the maximum of the critical mass flow rate for low qualities. For qualities greater than 0.1 it is found that the critical mass flow rate has no extreme values and approaches a constant value when the slip increases. Following the concept of Henry and Fauske the model is extended to describe non-homogeneous non-equilibrium two-phase flows, too. The comparison with published experimental data demonstrates that the theory can approximate well different experimental results on determination of the local critical mass flow rate. (orig.)
Some issues in the simulation of two-phase flows: The relative velocity
Gräbel, J.; Hensel, S.; Ueberholz, P.; Zeidan, D.; Farber, P.
2016-06-01
In this paper we compare numerical approximations for solving the Riemann problem for a hyperbolic two-phase flow model in two-dimensional space. The model is based on mixture parameters of state where the relative velocity between the two-phase systems is taken into account. This relative velocity appears as a main discontinuous flow variable through the complete wave structure and cannot be recovered correctly by some numerical techniques when simulating the associated Riemann problem. Simulations are validated by comparing the results of the numerical calculation qualitatively with OpenFOAM software. Simulations also indicate that OpenFOAM is unable to resolve the relative velocity associated with the Riemann problem.
Investigations of two-phase flame propagation under microgravity conditions
Gokalp, Iskender
2016-07-01
Investigations of two-phase flame propagation under microgravity conditions R. Thimothée, C. Chauveau, F. Halter, I Gökalp Institut de Combustion, Aérothermique, Réactivité et Environnement (ICARE), CNRS, 1C Avenue de la Recherche Scientifique, 45071 Orléans Cedex 2, France This paper presents and discusses recent results on two-phase flame propagation experiments we carried out with mono-sized ethanol droplet aerosols under microgravity conditions. Fundamental studies on the flame propagation in fuel droplet clouds or sprays are essential for a better understanding of the combustion processes in many practical applications including internal combustion engines for cars, modern aircraft and liquid rocket engines. Compared to homogeneous gas phase combustion, the presence of a liquid phase considerably complicates the physico-chemical processes that make up combustion phenomena by coupling liquid atomization, droplet vaporization, mixing and heterogeneous combustion processes giving rise to various combustion regimes where ignition problems and flame instabilities become crucial to understand and control. Almost all applications of spray combustion occur under high pressure conditions. When a high pressure two-phase flame propagation is investigated under normal gravity conditions, sedimentation effects and strong buoyancy flows complicate the picture by inducing additional phenomena and obscuring the proper effect of the presence of the liquid droplets on flame propagation compared to gas phase flame propagation. Conducting such experiments under reduced gravity conditions is therefore helpful for the fundamental understanding of two-phase combustion. We are considering spherically propagating two-phase flames where the fuel aerosol is generated from a gaseous air-fuel mixture using the condensation technique of expansion cooling, based on the Wilson cloud chamber principle. This technique is widely recognized to create well-defined mono-size droplets
Multiparticle imaging velocimetry measurements in two-phase flow
The experimental flow visualization tool, Particle Image Velocimetry (PIV), is being extended to determine the velocity fields in two and three-dimensional, two-phase fluid flows. In the past few years, the technique has attracted quite a lot of interest. PIV enables fluid velocities across a region of a flow to be measured at a single instant in time in global domain. This instantaneous velocity profile of a given flow field is determined by digitally recording particle (microspheres or bubbles) images within the flow over multiple successive video frames and then conducting flow pattern identification and analysis of the data. This paper presents instantaneous velocity measurements in various two and three- dimensional, two-phase flow situations. (author)
Weighted likelihood estimation under two-phase sampling
Saegusa, Takumi
2011-01-01
We develop asymptotic theory for weighted likelihood estimators (WLE) under two-phase stratified sampling without replacement. Although this sampling scheme induces dependence among observations, independent Bernoulli sampling is often assumed for convenience. Because our result shows that the asymptotic variance is smaller than under Bernoulli sampling, correctly accounting for a sampling scheme is particularly important. In this paper, we establish a Glivenko-Cantelli theorem, a theorem for rates of convergence of Z-estimators, and a Donsker theorem for the inverse probability weighted empirical processes under two-phase sampling. With these general results, we derive asymptotic distributions of the WLE of a finite dimensional parameter in a general semiparametric model where an estimator of a nuisance parameter is estimable either at regular or non-regular rates. We illustrate these results and methods in the Cox model with right censoring and interval censoring. Along the way we incorporate results for im...
Mechanisms and kinetic of recrystallisation in two phase alloys
Following a brief summary of the classical nucleation models, the various deformations modes of two phase alloys are reviewed in relation with the strain amplitude, strain rate and particle size. Most cases are illustrated by observations made on nickel base superalloys deformed at high temperature. Nucleation and growth processes in two phase alloys have been studied in detail in general systems and their understanding sheds some light on the early stages of the recrystallisation process. The inhibiting effect of small finely dispersed particles is compared to the enhanced nucleation rate observed in the vicinity of large particles in connection with their associated deformation zone. An example of a bimodal distribution of γ' precipitates in a PM nickel base superalloy is presented and its improvement of the mechanical properties is discussed
Two-phase treatment of inflamatory candidiasis of vulva
K. Drljević
2006-02-01
Full Text Available The purpose of this prospective study was to examine successfulnes of applaying two-phase treatment of vulvar inflamatory candidiasis. At the initial phase antimycotic izokonazol 1% nitrate in combination with corticosteriod diflucorton valerate (Travocort, Schering AG, Germany was localy applied, and then pure antimycotic izoconasol nitrate (Travogen, Schering AG, Germany. Parametars that have been analyzed in the first phase of treatment were regression of inflamatory changes of vulva, and in the second phase healing of fungal disease. Two-phase treatment of vulvar inflamatory candidiasis showed full therapy benefit at cured patients. The initial short-term local application of combination corticosteroid and antimycotic showed almost a hundred percent regression of inflamatory changes and simptoms of vulvar inflamatory candidiasis, without any side-effects noted.
Reactor vessel and core two-phase flow ultrasonic densitometer
A local ultrasonic density (LUD) detector has been developed by EG and G Idaho, Inc., at the Idaho National Engineering Laboratory (INEL) for the Loss-of-Fluid Test (LOFT) reactor vessel and core two-phase flow density measurements. The principle of operating the sensor is the change in propagation time of a torsional ultrasonic wave in a metal transmission line as a function of the density of the surrounding media. A theoretical physics model is presented which represents the total propagation time as a function of the sensor modulus of elasticity and polar moment of inertia. Separate effects tests and two-phase flow tests have been conducted to characterize the detector. Tests show the detector can perform in a 3430C pressurized water reactor environment and measure the average density of the media surrounding the sensor
Stability of interfacial waves in two-phase flows
The influence of the interfacial pressure and the flow distribution in the one-dimensional two-fluid model on the stability problems of interfacial waves is discussed. With a proper formulation of the interfacial pressure, the following two-phase phenomena can be predicted from the stability and stationary criteria of the interfacial waves: onset of slug flow, stationary hydraulic jump in a stratified flow, flooding in a vertical pipe, and the critical void fraction of a bubbly flow. It can be concluded that the interfacial pressure plays an important role in the interfacial wave propagation of the two-fluid model. The flow distribution parameter may enhance the flow stability range, but only plays a minor role in the two-phase characteristics. (author). 20 refs., 3 tabs., 4 figs
Mathematical modeling and the two-phase constitutive equations
The problems raised by the mathematical modeling of two-phase flows are summarized. The models include several kinds of equations, which cannot be discussed independently, such as the balance equations and the constitutive equations. A review of the various two-phase one-dimensional models proposed to date, and of the constitutive equations they imply, is made. These models are either mixture models or two-fluid models. Due to their potentialities, the two-fluid models are discussed in more detail. To avoid contradictions, the form of the constitutive equations involved in two-fluid models must be sufficiently general. A special form of the two-fluid models, which has particular advantages, is proposed. It involves three mixture balance equations, three balance equations for slip and thermal non-equilibriums, and the necessary constitutive equations
Two-phase relative permeability models in reservoir engineering calculations
Siddiqui, S.; Hicks, P.J.; Ertekin, T.
1999-01-15
A comparison of ten two-phase relative permeability models is conducted using experimental, semianalytical and numerical approaches. Model predicted relative permeabilities are compared with data from 12 steady-state experiments on Berea and Brown sandstones using combinations of three white mineral oils and 2% CaCl1 brine. The model results are compared against the experimental data using three different criteria. The models are found to predict the relative permeability to oil, relative permeability to water and fractional flow of water with varying degrees of success. Relative permeability data from four of the experimental runs are used to predict the displacement performance under Buckley-Leverett conditions and the results are compared against those predicted by the models. Finally, waterflooding performances predicted by the models are analyzed at three different viscosity ratios using a two-dimensional, two-phase numerical reservoir simulator. (author)
Transition from boiling to two-phase forced convection
The paper presents a method for the prediction of the boundary points of the transition region between fully developed boiling and two-phase forced convection. It is shown that the concept for the determination of the onset of fully developed boiling can also be applied for the calculation of the point where the heat transfer is effected again by the forced convection. Similarly, the criterion for the onset of nucleate boiling can be used for the definition of the point where boiling is completely suppressed and pure two-phase forced convection starts. To calculate the heat transfer coefficient for the transition region, an equation is proposed that applies the boundary points and a relaxation function ensuring the smooth transition of the heat transfer coefficient at the boundaries
Preparation of cationic polyacrylamide by aqueous two-phase polymerization
2010-05-01
Full Text Available Cationic polyacrylamide (CPAM was synthesized by aqueous two-phase polymerization technique using acrylamide (AM and dimethylaminoethyl methacrylate methyl chloride (DMC as raw materials, aqueous polyethylene glycol 20000 (PEG 20000 solution as dispersant, 2,2′-azobis(2-amidinopropane dihydrochloride (V-50 as initiator and poly(dimethylaminoethyl methacrylate methyl chloride (PDMC as stabilizer. The polymer was characterized by infrared (IR spectroscopy, 1H-NMR spectrum and transmission electron microscopy (TEM. The copolymer composition was analyzed. The effect of monomers concentration, PEG 20000 concentration and stabilizer concentration on copolymer were investigated, respectively. The optimum reaction conditions for obtaining a stable CPAM aqueous two-phase system were monomers concentration 8~15%, PEG 20000 concentration 15~25%, and PDMC concentration 0.5~1.5%. Finally, the formation process of copolymer particles was investigated by optical microscope.
Numerical analyses of boiling two-phase bubbly flows in pipes with particle tracking method
The present study deals with the numerical modeling of two-phase bubbly flows with subcooled boiling in a flow channel using Particle Tracking Method. It is an on-going project whose final aim is to develop a computer code to more accurately predict, and better understand, the Departure from Nuclear Boiling (DNB) under PWR accidental conditions. At the first stage of the present study, this presentation reports the development of bubble dynamics models such as the bubble coalesces/break models and bubble heat transfer models. The validation of the models by comparing simulation results with experimental data in literature is also reported. (author)
Two phase flow instabilities in horizontal straight tube evaporator
Liang, Nan; Shuangquan, Shao; Tian, Changqing; Yan, Y. Y.
2010-01-01
Abstract It is essential to ensure the stability of a refrigeration system if the oscillation in evaporation process is the primary cause for the whole system instability. This paper is concerned with an experimental investigation of two phase flow instabilities in a horizontal straight tube evaporator of a refrigeration system. The relationship between pressure drop and mass flow with constant heat flux and evaporation pressure is measured and determined. It is found that there is...
Controlling two-phase flow in microfluidic systems using electrowetting
Gu, Hao
2011-01-01
Electrowetting (EW)-based digital microfluidic systems (DMF) and droplet-based two-phase flow microfluidic systems (TPF) with closed channels are the most widely used microfluidic platforms. In general, these two approaches have been considered independently. However, integrating the two technologies into one allows to combine the advantages of both worlds: (i) high throughput (from TPF) and (ii) precise control over each individual drop (from EW). Thus the aim of this thesis was to investiga...
Phase appearance or disappearance in two-phase flows
Cordier, Floraine; Degond, Pierre; Kumbaro, Anela
2011-01-01
This paper is devoted to the treatment of specific numerical problems which appear when phase appearance or disappearance occurs in models of two-phase flows. Such models have crucial importance in many industrial areas such as nuclear power plant safety studies. In this paper, two outstanding problems are identified: first, the loss of hyperbolicity of the system when a phase appears or disappears and second, the lack of positivity of standard shock capturing schemes such as the Roe scheme. ...
Two-Phase Slug Flow Experiments with Viscous Liquids
Diaz, Mariana J.C.
2016-01-01
The challenges behind the multiphase transport of oil and gas mixtures are increasing as the oil and gas industry is moving towards production from non-conventional reservoirs and in remote locations. Transport of high viscosity fluids in long multiphase pipelines is a particular challenge. Previous experiments have shown that gas-liquid slug flow is a frequent two-phase flow pattern at high liquid viscosities. The slug flow regime is an unstable flow, which may lead to operati...
Design Of A Turgo Two-Phase Turbine Runner
Aaraj, Youssef; Mortada, Sorina; Clodic, Denis; Nemer, Maroun
2014-01-01
A two-phase impulse turbine used to replace the classic expansion valve in a refrigeration system needs a nozzle/expander to transform the flow stored enthalpy into kinetic energy, and a runner that comes afterwards to transform the flow kinetic energy into torque. That process transforms the isenthalpic expansion of the refrigerant into, ideally, an isentropic one. Replacing a classic isenthalpic expansion with a nearly isentropic one increases the cycle cooling capacity by 8% up to 20 % for...
Flow visualization on flooding phenomena in two phase flow
Flow pattern on flooding phenomena in counter-current two phase flow in vertical tube is experimentally studied by means of dye tracer technique for the following condition: the length -to-diameter ratio L/D=30. Just before flooding, oscillatory motion of the liquid upwards and downwards in the tube is observed. Under flooding conditions, churn flow in the tube is observed. (author)
Empirical Study in Finite Correlation Coefficient in Two Phase Estimation
2003-01-01
This paper proposes a class of estimators for population correlation coefficient when information about the population mean and population variance of one of the variables is not available but information about these parameters of another variable (auxiliary) is available, in two phase sampling and analyzes its properties. Optimum estimator in the class is identified with its variance formula. The estimators of the class involve unknown constants whose optimum values depend on unknown populat...
Simulation of two-phase flow with varying surface tension.
Lervåg, Karl Yngve
2008-01-01
This thesis is a study on the effects of varying surface tension along an interface separating two fluids. Varying surface tension leads to tangential forces along the interface. This is often called the Marangoni effect. These forces are discussed in detail, and two test cases are considered to analyse the Marangoni effect, and to verify the present implementation. The first test studies steady-state two-phase flow where the fluids are separated with plane interfaces and the flow is driv...
Controllability and observability in two-phase porous media flow
Van Doren, J.F.M.; Van den Hof, P.M.J.; Bosgra, O.H.; Jansen, J. D.
2013-01-01
Reservoir simulation models are frequently used to make decisions on well locations, recovery optimization strategies etc. The success of these applications is, among other aspects, determined by the controllability and observability properties of the reservoir model. In this paper it is shown how the controllability and observability of two-phase flow reservoir models can be analyzed and quantified with aid of generalized empirical Gramians. The empirical controllability Gramian can be inter...
Two-phase algorithms for the parametric shortest path problem
Fischer, Eldar; Lachish, Oded; Yuster, Raphael
2010-01-01
A {\\em parametric weighted graph} is a graph whose edges are labeled with continuous real functions of a single common variable. For any instantiation of the variable, one obtains a standard edge-weighted graph. Parametric weighted graph problems are generalizations of weighted graph problems, and arise in various natural scenarios. Parametric weighted graph algorithms consist of two phases. A {\\em preprocessing phase} whose input is a parametric weighted graph, and whose output is a data str...
A posteriori error estimates for two-phase obstacle problem
Repin, S.; Valdman, Jan
2015-01-01
Roč. 107, č. 2 (2015), s. 324-335. ISSN 1072-3374 R&D Projects: GA ČR GA13-18652S Institutional support: RVO:67985556 Keywords : two-phase obstacle problem * a posteriori error estimate * finite element method * variational inequalities Subject RIV: BA - General Mathematics http://library.utia.cas.cz/separaty/2015/MTR/valdman-0444082.pdf
A diffuse interface model for two-phase ferrofluid flows
Nochetto, Ricardo H.; Salgado, Abner J.; Tomas, Ignacio
2016-01-01
We develop a model describing the behavior of two-phase ferrofluid flows using phase field-techniques and present an energy-stable numerical scheme for it. For a simplified, yet physically realistic, version of this model and the corresponding numerical scheme we prove, in addition to stability, convergence and as by-product existence of solutions. With a series of numerical experiments we illustrate the potential of these simple models and their ability to capture basic phenomenological feat...
Two-phase Flow Distribution in Heat Exchanger Manifolds
Vist, Sivert
2004-01-01
The current study has investigated two-phase refrigerant flow distribution in heat exchange manifolds. Experimental data have been acquired in a heat exchanger test rig specially made for measurement of mass flow rate and gas and liquid distribution in the manifolds of compact heat exchangers. Twelve different manifold designs were used in the experiments, and CO2 and HFC-134a were used as refrigerants.
Two-phase computer codes for zero-gravity applications
Krotiuk, W.J.
1986-10-01
This paper discusses the problems existing in the development of computer codes which can analyze the thermal-hydraulic behavior of two-phase fluids especially in low gravity nuclear reactors. The important phenomenon affecting fluid flow and heat transfer in reduced gravity is discussed. The applicability of using existing computer codes for space applications is assessed. Recommendations regarding the use of existing earth based fluid flow and heat transfer correlations are made and deficiencies in these correlations are identified.
Recent advances in two-phase flow numerics
The authors review three topics in the broad field of numerical methods that may be of interest to individuals modeling two-phase flow in nuclear power plants. The first topic is iterative solution of linear equations created during the solution of finite volume equations. The second is numerical tracking of macroscopic liquid interfaces. The final area surveyed is the use of higher spatial difference techniques
Recent advances in two-phase flow numerics
Mahaffy, J.H.; Macian, R. [Pennsylvania State Univ., University Park, PA (United States)
1997-07-01
The authors review three topics in the broad field of numerical methods that may be of interest to individuals modeling two-phase flow in nuclear power plants. The first topic is iterative solution of linear equations created during the solution of finite volume equations. The second is numerical tracking of macroscopic liquid interfaces. The final area surveyed is the use of higher spatial difference techniques.
Eutectic Growth in Two-Phase Multicomponent Alloys
Senninger, Oriane; Voorhees, Peter W.
2016-01-01
A theory of two-phase eutectic growth for a multicomponent alloy is presented. This theory employs the thermodynamic equilibrium at the solid/liquid interface and thus makes it possible to use standard CALPHAD databases to determine the effects of multicomponent phase equilibrium on eutectic growth. Using the same hypotheses as the Jackson Hunt theory, we find that the growth law determined for binary alloys in the Jackson Hunt theory can be generalized to systems with N elements. In particul...
Two-phase mixtures explosion study: hydrogen and dusts
The context of the study is the safety of the ITER installation. Indeed, studies have shown that it exists a risk for two-phase mixtures of hydrogen and dust can explode and create a safety risk for the ITER installation. This aims to obtain the fundamental data which characterize the explosion of these mixtures and to evaluate the pressure loads they can generate. To do so, experiments in spherical bomb have been carried out for hydrogen - oxygen - nitrogen mixtures at two initial temperatures (303 and 343 K) and pressures (50 and 100 kPa) for different hydrogen concentrations and different N2/O2 ratios. Explosion parameters like maximum combustion pressures (PMAX), deflagration indexes (KG or KST), combustion times (tC), fundamental flame speeds (SL0) and Markstein lengths have been determined. A kinetic modelling of the flame speed, using the COSILAB software was performed based on three detailed kinetic models available in the literature and allowed the calculation of the global activation energy on the basis of the kinetic model which showed the best agreement with the experimental data. Moreover equilibrium calculations were achieved to compare PMAX to the theoretical values. For two-phase mixtures, a new introduction device was tested and set up and experiments characterizing the explosions parameters of the two-phase mixtures have been performed in the spherical bomb. They were able to stress out the fact that, under some circumstances, dust explosion can be concomitant to a hydrogen explosion. (author)
Fluid dynamics of cryogenic two-phase flows
The objective of this study was to examine the flow behavior of a methane hydrate/methane-liquid hydrogen dispersed two-phase fluid through a given design of a moderator chamber for the ESS target system. The calculations under simplified conditions, e.g., taking no account of heat input from outside, have shown that the computer code used, CFX, was able to simulate the behavior of the two-phase flow through the moderator chamber, producing reasonable results up to a certain level of the solid phase fraction, that allowed a continuous flow process through the chamber. Inlet flows with larger solid phase fractions than 40 vol% were found to be a ''problem'' for the computer code. From the computer runs based on fractions between 20 and 40 vol%, it was observed that with increasing solid phase fraction at the inlet, the resulting flow pattern revealed a strong tendency for blockage within the chamber, supported by the ''heavy weight'' of the pellets compared to the carrying liquid. Locations which are prone to the development of such uneven flow behavior are the areas around the turning points in the semispheres and near the exit of the moderator. The considered moderator chamber with horizontal inlet and outlet flow for a solid-liquid two-phase fluid does not seem to be an appropriate design. (orig.)
Cold water injection into two-phase mixtures
This report presents the results of a review of the international literature regarding the dynamic loadings associated with the injection of cold water into two-phase mixtures. The review placed emphasis on waterhammer in nuclear power plants. Waterhammmer incidence data were reviewed for information related to thermalhydraulic conditions, underlying causes and consequential damage. Condensation induced waterhammer was found to be the most significant consequence of injecting cold water into a two-phase system. Several severe waterhammer incidents have been attributed to slug formation and steam bubble collapse under conditions of stratified steam and cold water flows. These phenomena are complex and not well understood. The current body of experimental and analytical knowledge is not large enough to establish maps of expected regimes of condensation induced waterhammer. The Electric Power Research Institute, in the United States, has undertaken a major research and development programme to develop the knowledge base for this area. The limited models and data currently available show that mechanical parameters are as important as thermodynamic conditions for the initiation of condensation induced waterhammer. Examples of bounds for avoiding two-phase waterhammer are given. These bounds are system specific and depend upon parameters such as pump capacity, pipe length and pipe orientation
Designing piping systems for two-phase flow
A wide range of industrial systems, such as thermosiphon reboilers and chemical reactors, involve two-phase gas-liquid flow in conduits. Design of these systems requires information about the flow regime, pressure drop, slug velocity and length, and heat transfer coefficient. An understanding of two-phase flow is critical for the reliable and cost-effective design of such systems. The successful design of a pipeline in two-phase flow, for example, is a two-step process. The first step is the determination of the flow regime. If an undesirable flow regime, such as slug flow, is not anticipated and adequately designed for, the resulting flow pattern can upset a tower control system or cause mechanical failures of piping components. The second step is the calculation of flow parameters such as pressure drop and density to size lines and equipment. Since the mechanism of fluid flow (and heat transfer) depends on the flow pattern, separate flow models are required for different flow patterns
Flow pattern maps in two phase flow: present panorama
In this work is presented a general panorama on the condition that watch over the related understanding to the pattern maps of flux regimes in the two-phase flow. The revision that has been done no exhaustive treat of flux patterns observed in vertical and horizontal ducts. As resulting of this investigation, it has been to make evident the necessity of lighting up with precision the use of flux pattern maps that they are not framed respect to really two-phase flow, but that they correspond really to the simultaneous flux of a gas and a liquid un miscible flowing in adiabatic conditions. The case more common of late these is the relative to the air-water mixture. The observed necessity has generated in the Thermo fluids Department of National Institute of Nuclear Research the restlessness of realizing experimental studies in this area. This in spite of being motive of research over 40 years and also of counting with a vast reported bibliography, on one the hand it has not conveyed to obtain representations of general character. And on the other hand it has origined a great confusion about the applicability of available information. In the same way it is described the advances developed in the experimental studies in the field of forced convection, as to only phase as one in two phases. (Author)
Two-phase flow measurement by pulsed neutron activation techniques
The Pulsed Neutron Activation (PNA) technique for measuring the mass flow velocity and the average density of two-phase mixtures is described. PNA equipment can be easily installed at different loops, and PNA techniques are non-intrusive and independent of flow regimes. These features of the PNA technique make it suitable for in-situ measurement of two-phase flows, and for calibration of more conventional two-phase flow measurement devices. Analytic relations governing the various PNA methods are derived. The equipment and procedures used in the first air-water flow measurement by PNA techniques are discussed, and recommendations are made for improvement of future tests. In the present test, the mass flow velocity was determined with an accuracy of 2%, and average densities were measured down to 0.08 g/cm3 with an accuracy of 0.04 g/cm3. Both the accuracy of the mass flow velocity measurement and the lower limit of the density measurement are functions of the injected activity and of the total number of counts. By using a stronger neutron source and a larger number of detectors, the measurable density can be decreased by a factor of 12 to .007 g/cm3 for 12.5 cm pipes, and to even lower ranges for larger pipes
An accurate subchannel database is crucial for modeling the multidimensional two-phase flow in a rod bundle and for validating subchannel analysis codes. Based on available reference, it can be said that a point-measurement sensor for acquiring void fractions and bubble velocity distributions do not infer interactions of the subchannel flow dynamics, such as a cross flow and flow distribution, etc. In order to acquire multidimensional two-phase flow in a 10×10 rod bundle with an o.d. of 10 mm and 3110 mm length, a new sensor consisting of 11-wire by 11-wire and 10-rod by 10-rod electrodes was developed. Electric potential in the proximity region between two wires creates a void fraction in the center subchannel region, like a so-called wire mesh sensor. A unique aspect of the devised sensor is that the void fraction near the rod surface can be estimated from the electric potential in the proximity region between one wire and one rod. The additional 400 points of void fraction and phasic velocity in 10×10 bundle can therefore be acquired. The devised sensor exhibits the quasi three-dimensional flow structures, i.e. void fraction, phasic velocity and bubble chord length distributions. These quasi three-dimensional structures exhibit the complexity of two-phase flow dynamics, such as coalescence and the breakup of bubbles in transient phasic velocity distributions. (author)
Simulation of the catalyst layer in PEMFC based on a novel two-phase lattice model
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.
A Simple and Efficient Diffuse Interface Method for Compressible Two-Phase Flows
In nuclear reactor safety and optimization there are key issues that rely on in-depth understanding of basic two-phase flow phenomena with heat and mass transfer. For many reasons, to be discussed, there is growing interest in the application of two-phase flow models to provide diffuse, but nevertheless resolved, simulation of interfaces between two immiscible compressible fluids - diffuse interface method (DIM). Because of its ability to dynamically create interfaces and to solve interfaces separating pure media and mixtures for DNS-like (Direct Numerical Simulation) simulations of interfacial flows, we examine the construction of a simple, robust, fast, and accurate numerical formulation for the 5-equation Kapila et al. (1) reduced two-phase model. Though apparently simple, the Kapila et al. model contains a volume fraction differential transport equation containing a nonlinear, non-conservative term which poses serious computational challenges. To circumvent the difficulties encountered with the single velocity and single pressure Kapila et al. (1) multiphase flow model, a 6-equation relaxation hyperbolic model is built to solve interface problems with compressible fluids. In this approach, pressure non-equilibrium is first restored, followed by a relaxation to an asymptotic solution which is convergent to the solutions of the Kapila et al. reduced model. The apparent complexity introduced with this extended hyperbolic model actually leads to considerable simplifications regarding numerical resolution, and the various ingredients used by this method are general enough to consider future extensions to problems involving complex physics
Numerical methods for limit problems in two-phase flow models
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)
A Novel Hyperbolization Procedure for The Two-Phase Six-Equation Flow Model
Samet Y. Kadioglu; Robert Nourgaliev; Nam Dinh
2011-10-01
We introduce a novel approach for the hyperbolization of the well-known two-phase six equation flow model. The six-equation model has been frequently used in many two-phase flow applications such as bubbly fluid flows in nuclear reactors. One major drawback of this model is that it can be arbitrarily non-hyperbolic resulting in difficulties such as numerical instability issues. Non-hyperbolic behavior can be associated with complex eigenvalues that correspond to characteristic matrix of the system. Complex eigenvalues are often due to certain flow parameter choices such as the definition of inter-facial pressure terms. In our method, we prevent the characteristic matrix receiving complex eigenvalues by fine tuning the inter-facial pressure terms with an iterative procedure. In this way, the characteristic matrix possesses all real eigenvalues meaning that the characteristic wave speeds are all real therefore the overall two-phase flowmodel becomes hyperbolic. The main advantage of this is that one can apply less diffusive highly accurate high resolution numerical schemes that often rely on explicit calculations of real eigenvalues. We note that existing non-hyperbolic models are discretized mainly based on low order highly dissipative numerical techniques in order to avoid stability issues.
The Condensation effect on the two-phase flow stability
A one-dimensional analytical model has been developed to be used for the linear analysis of density-wave oscillations in a parallel heated channel and a natural circulation loop.The heater and the riser sections are divided into a single-phase and a two-phase region.The two-phase region is represented by the drift-flux model. The model accounts for aphasic slip and subcooled boiling.The localized friction at the heater and the riser exit is treated considering the two-phase mixture.Also the effects of the condensation in the riser and the change in the system pressure have been studied.The exact equation for the heated channel and the total loop pressure drop is perturbed around the steady state.he stability characteristics of the heated channel and the loop are investigated using the Root finding method criterion.The results are summarized on instability maps in the plane of subcooled boiling number vs. phase change number (i.e., inlet subcooling vs. heater heat flux).The predictions of the model are compared with experimental results published in open literature. The results show that, the treatment effect of localized friction in two-phase mixtures stabilizes the system and improves the agreement of the calculations with the experimental results.For a parallel heated channel, the results indicate a more stable system with high inlet restriction, low outlet restriction, and high inlet velocity. And for a natural circulation loop, an increase in the inlet restriction broadened the range of the continuous circulation mode and stabilized the system, a decrease in the exit restriction or the liquid charging level shifted to the right the range of the continuous circulation mode and stabilized the system and an increase in the riser condensation shifted to the right the range of the continuous circulation mode and stabilized the system.The results show that the model agrees well with the available experimental data. In particular, the results show the significance of
Central upwind scheme for a compressible two-phase flow model.
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.
Influence of lactic acid on the two-phase anaerobic digestion of kitchen wastes
ZHANG Bo; CAI Wei-min; HE Pin-jing
2007-01-01
To evaluate the influence of lactic acid on the methanogenesis, anaerobic digestion of kitchen wastes was firstly conducted in a two-phase anaerobic digestion process, and performance of two digesters fed with lactic acid and glucose was subsequently compared.The results showed that the lactic acid was the main fermentation products of hydrolysis-acidification stage in the two-phase anaerobic digestion process for kitchen wastes. The lactic acid concentration constituted approximately 50% of the chemical oxygen demand (COD) concentration in the hydrolysis-acidification liquid. The maximum organic loading rate was lower in the digester fed with lactic acid than that fed with glucose. Volatile fatty acids (VFAs) and COD removal were deteriorated in the methanogenic reactor fed with to the high concentration of lactic acid fed. It could be concluded that avoiding the presence of the lactic acid is necessary in the hydrolysis-acidification process for the improvement of the two-phase anaerobic digestion process of kitchen wastes.
Discrete vs. continuum-scale simulation of radiative transfer in semitransparent two-phase media
The mathematical formulation of the continuum approach to radiative transfer modeling in two-phase semi-transparent media is numerically validated by comparing radiative fluxes computed by (i) direct, discrete-scale and (ii) continuum-scale approaches. The analysis is based on geometrical optics. The discrete-scale approach uses the Monte Carlo ray-tracing applied directly to real 3D geometry measured by computed tomography. The continuum-scale approach is based on a set of continuum-scale radiative transfer equations and associated radiative properties, and employs the Monte Carlo ray-tracing for computations of radiative fluxes and for computations of the radiative properties. The model two-phase media are reticulate porous ceramics and a particle packed bed, each composed of semitransparent solid and fluid phases. The results obtained by the two approaches are in good agreement within the limits of statistical uncertainty. The continuum-scale approach leads to a reduction in computational time by approximately one order of magnitude, and is therefore suited to treat radiative transfer problems in two-phase media in a wide range of engineering applications.
Scaling and design of a transparent two-phase natural circulation loop
This paper presents the scaling analysis performed for the design of a 1/4 length scale, transparent model of a typical Westinghouse pressurized water reactor steam supply system. The experimental investigations to be performed in this facility include measurements of two-phase natural circulation heat transfer in rod bundle arrays and two-phase natural circulation loop flow stagnation. Applications to advanced, passively safe, reactor designs will also be examined. These tests will be performed at low pressure; approximately 0.2 MPa (30 psia). Because of the low pressure requirement, the scaling analysis is particularly important. The scaling criteria developed by Ishii, coupled with fluid property correlations for water and freon have been used to develop a scaling analysis package. This package has been used to determine the piping and heater rod lengths, the diameters and the wall thicknesses required to scale the thermal hydraulic phenomena of interest. The scaling analysis indicates that by satisfying the two-phase power density scaling criteria, with either freon or water as the working fluid, a transparent model can be designed to simulate important thermal hydraulic phenomena. This includes pressure transients in the hot leg and steam generator tubes
Modeling, mathematical and numerical analysis of two-phase flow two-fluid models
This thesis work is devoted to the study of two-fluid isentropic model describing a two-phase flow. We prove that the model is strictly hyperbolic under some conditions. We solve the Riemann problem. Two cases are distinguished: a two-fluid model written under a conservative form or under a non-conservative form. We choose to present a numerical approximation of conservation laws governing the evolution of compressible two-phase flow by the Roe approach. The approximate Riemann solver based in the Roe approach is applied to a hyperbolic model of conservation laws. We extend the Riemann solver approach to a non-conservative hyperbolic two-fluid model. We use a generalised Roe's approximate Riemann solver, based on a regular continuous path defined in the states space. The numerical results obtained with different test problems show that the Roe approach gives a robust and precise discretization of the nonlinear effects in the model such as the propagation of different shocks and rarefaction waves. (author)
A two-phase linear programming approach for redundancy allocation problems
Hsieh Yi-Chih
2002-01-01
Full Text Available Provision of redundant components in parallel is an efficient way to increase the system reliability, however, the weight, volume and cost of the system will increase simultaneously. This paper proposes a new two-phase linear programming approach for solving the nonlinear redundancy allocation problems subject to multiple linear constraints. The first phase is used to approximately allocate the resource by using a general linear programming, while the second phase is used to re-allocate the slacks of resource by using a 0-1 integer linear programming. Numerical results demonstrate the effectiveness and efficiency of the proposed approach.
Critical temperatures of two phase transitions in mixtures of spherical and ellipsoidal molecules
In this paper we have derived, in the usual molecular field approximation, an equation for the thermodynamic potential for determining the critical temperatures of two phase transitions in a mixture of ellipsoidal and spherical molecules. These molecules are dispersed on b.c.c.-lattice and their ratio of concentrations is different form 1:1. We have also obtained the bound lines of the orientational and positional transitions in the temperature-concentration diagram for different values of molecular parameter (of ellipsoidal molecules) and interaction parameters. (author). 15 refs, 2 figs, 1 tab
Yi-rang Yuan
2004-01-01
For compressible two-phase displacement problem,the modified upwind finite difference fractional steps schemes are put forward.Some techniques,such as calculus of variations,commutative law of multiplication of difference operators,decomposition of high order difference operators,the theory of prior estimates and techniques are used.Optimal order estimates in L 2 norm are derived for the error in the approximate solution.This method has already been applied to the numerical simulation of seawater intrusion and migration-accumulation of oil resources.
WENO wavelet method for a hyperbolic model of two-phase flow in conservative form
Zeidan, Dia; Kozakevicius, Alice J.; Schmidt, Alex A.; Jakobsson, Stefan
2016-06-01
The current work presents a WENO wavelet adaptive method for solving multiphase flow problems. The grid adaptivity in each time step is obtained by the application of a thresholded interpolating wavelet transform, which allows the construction of a small yet effective sparse point representation of the solution. The spatial operator is solved by the Lax-Friedrich flux splitting approach in which the flux derivatives are approximated by the WENO scheme. Hyperbolic models of two-phase flow in conservative form are efficiently solved since shocks and rarefaction waves are precisely captured by the chosen methodology. Substantial computational gains are obtained through the grid reduction feature while maintaining the quality of the solutions.
A two-phase solid/fluid model for dense granular flows including dilatancy effects
Mangeney, Anne; Bouchut, Francois; Fernandez-Nieto, Enrique; Koné, El-Hadj; Narbona-Reina, Gladys
2016-04-01
account for this transfer of fluid into and out of the mixture, a two-layer model is proposed with a fluid layer on top of the two-phase mixture layer. Mass and momentum conservation are satisfied for the two phases, and mass and momentum are transferred between the two layers. A thin-layer approximation is used to derive average equations. Special attention is paid to the drag friction terms that are responsible for the transfer of momentum between the two phases and for the appearance of an excess pore pressure with respect to the hydrostatic pressure. We present several numerical tests of two-phase granular flows over sloping topography that are compared to the results of the model proposed by {Pitman and Le} [2005]. In particular, we quantify the role of the fluid and compression/dilatation processes on granular flow velocity field and runout distance. F. Bouchut, E.D. Fernandez-Nieto, A. Mangeney, G. Narbona-Reina, A two-phase shallow debris flow model with energy balance, {ESAIM: Math. Modelling Num. Anal.}, 49, 101-140 (2015). F. Bouchut, E. D. Fernandez-Nieto, A. Mangeney, G. Narbona-Reina, A two-phase two-layer model for fluidized granular flows with dilatancy effects, {J. Fluid Mech.}, submitted (2016). R.M. Iverson, M. Logan, R.G. LaHusen, M. Berti, The perfect debris flow? Aggregated results from 28 large-scale experiments, {J. Geophys. Res.}, 115, F03005 (2010). R. Jackson, The Dynamics of Fluidized Particles, {Cambridges Monographs on Mechanics} (2000). E.B. Pitman, L. Le, A two-fluid model for avalanche and debris flows, {Phil.Trans. R. Soc. A}, 363, 1573-1601 (2005). S. Roux, F. Radjai, Texture-dependent rigid plastic behaviour, {Proceedings: Physics of Dry Granular Media}, September 1997. (eds. H. J. Herrmann et al.). Kluwer. Cargèse, France, 305-311 (1998).
Implicitly balanced solution of the two-phase flow equations coupled to nonlinear heat conduction
This paper presents the solution of the two-phase flow equations coupled to nonlinear heat conduction using the Jacobian-free Newton-Krylov (JFNK) method which employs a physics-based preconditioner. Computer simulations will demonstrate that the implicitly balanced solution obtained from the JFNK method is more accurate than traditional approaches that employ operator splitting and linearizing. Results will also indicate that by employing a physics-based preconditioner the implicitly balanced solution can provide a more accurate solution for the same amount of computer time compared to the traditional approach for solving these equations. Finally, convergence plots will show that as the transient time lengthens, the implicitly balanced solution can maintain this higher level of accuracy at much larger time steps
Experimental study of a two-phase surface jet
Perret, Matias; Esmaeilpour, Mehdi; Politano, Marcela S.; Carrica, Pablo M.
2013-04-01
Results of an experimental study of a two-phase jet are presented, with the jet issued near and below a free surface, parallel to it. The jet under study is isothermal and in fresh water, with air injectors that allow variation of the inlet air volume fraction between 0 and 13 %. Measurements of water velocity have been performed using LDV, and the jet exit conditions measured with PIV. Air volume fraction, bubble velocity and chord length distributions were measured with sapphire optical local phase detection probes. The mean free surface elevation and RMS fluctuations were obtained using local phase detection probes as well. Visualization was performed with laser-induced fluorescence. Measurements reveal that the mean free surface elevation and turbulent fluctuations significantly increase with the injection of air. The water normal Reynolds stresses are damped by the presence of bubbles in the bulk of the liquid, but very close to the free surface the effect is reversed and the normal Reynolds stresses increase slightly for the bubbly flow. The Reynolds shear stresses < {u^' } w^' } } rangle decrease when bubbles are injected, indicating turbulence attenuation, and are negative at deeper locations, as turbulent eddies shed downward carry high axial momentum deeper into the flow. Flow visualization reveals that the two-phase jet is lifted with the presence of bubbles and reaches the free surface sooner. Significant bubble coalescence is observed, leading to an increase in mean bubble size as the jet develops. The coalescence near the free surface is particularly strong, due to the time it takes the bubbles to pierce the free surface, resulting in a considerable increase in the local air volume fraction. In addition to first explore a bubbly surface jet, the comprehensive dataset reported herein can be used to validate two-phase flow models and computational tools.
Fraser, D.W.H. [Univ. of British Columbia (Canada); Abdelmessih, A.H. [Univ. of Toronto, Ontario (Canada)
1995-09-01
A general unified model is developed to predict one-component critical two-phase pipe flow. Modelling of the two-phase flow is accomplished by describing the evolution of the flow between the location of flashing inception and the exit (critical) plane. The model approximates the nonequilibrium phase change process via thermodynamic equilibrium paths. Included are the relative effects of varying the location of flashing inception, pipe geometry, fluid properties and length to diameter ratio. The model predicts that a range of critical mass fluxes exist and is bound by a maximum and minimum value for a given thermodynamic state. This range is more pronounced at lower subcooled stagnation states and can be attributed to the variation in the location of flashing inception. The model is based on the results of an experimental study of the critical two-phase flow of saturated and subcooled water through long tubes. In that study, the location of flashing inception was accurately controlled and adjusted through the use of a new device. The data obtained revealed that for fixed stagnation conditions, the maximum critical mass flux occurred with flashing inception located near the pipe exit; while minimum critical mass fluxes occurred with the flashing front located further upstream. Available data since 1970 for both short and long tubes over a wide range of conditions are compared with the model predictions. This includes test section L/D ratios from 25 to 300 and covers a temperature and pressure range of 110 to 280{degrees}C and 0.16 to 6.9 MPa. respectively. The predicted maximum and minimum critical mass fluxes show an excellent agreement with the range observed in the experimental data.
The topic of the present thesis is the direct numerical simulation of gas-liquid two-phase flow in rectangular channels with hydraulic diameter of the order of 1 mm with heat transfer. A new volume-averaged equation for enthalpy is derived and implemented in the finite volume code TURBIT-VoF for the case when both fluids are considered as incompressible. The numerical approximation of this equation reduces the oscillations associated with the discontinuities at the interface using an accurate reconstruction of the convective and conductive heat fluxes. To model convective heat transfer for a spatially periodic two-phase flow in a channel with large length-to-hydraulic diameter ratio, a new concept, called periodic fully developed flow and heat transfer, is proposed. After a few hydraulic diameters away from the channel inlet the flow characteristics are free from entrance effects. For this region, the identification of the periodicity characteristics of the flow enables to restrict the analysis of the flow field and temperature distribution to a single isolated module. As typical example of periodic gas-liquid two-phase flow, the slug flow in small channels is considered. The flow of a train of large bubbles uniformly distributed along a channel with square cross-section is simulated. The bubble shape, the flow structure inside the bubble and in the liquid slug are analyzed. The bubble diameter, bubble velocity and relative bubble velocity for two different capillary numbers are computed and compared with the experimental data from the literature showing good agreement. The convection and conduction of heat inside the channel due to a uniform, both axially and perimetrically, heat flux is also considered. The modification of the temperature field due to the presence of the bubble is analyzed. (orig.)
Modeling and numerical analysis of non-equilibrium two-phase flows
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)
Is 2D impedance tomography a reliable technique for two-phase flow?
Impedance tomography consists in reconstructing the conductivity distribution from electrical data which characterize the electrical response of a medium to arbitrary excitations. Impedance tomography is an ill-conditioned problem and designing a tomograph therefore requires the quantitative knowledge of the sensitivity of the reconstruction to the measurements noise. The numerical conditioning of an original and accurate algorithm has been studied. This algorithm does not suffer from the shortcomings already identified in the literature. It is shown that for media encompassing inclusions which is a typical situation in two-phase flows, the necessary accuracy for the measurements if far beyond any technological reach. Moreover, within these high requirements for accuracy, some side effects must be carefully controlled or compensated and relevant procedures arc provided. Furthermore. reconstruction artifacts are shown and they are found to derive from the unavoidable tridimensional nature of the electric field. For all these reasons, it is concluded that impedance tomography has very low potentialities as an accurate phase fraction distribution measuring technique in any arbitrary two-phase flows. (author)
A real two-phase submarine debris flow and tsunami
Pudasaini, Shiva P.; Miller, Stephen A. [Department of Geodynamics and Geophysics, Steinmann Institute, University of Bonn Nussallee 8, D-53115, Bonn (Germany)
2012-09-26
The general two-phase debris flow model proposed by Pudasaini is employed to study subaerial and submarine debris flows, and the tsunami generated by the debris impact at lakes and oceans. The model, which includes three fundamentally new and dominant physical aspects such as enhanced viscous stress, virtual mass, and generalized drag (in addition to buoyancy), constitutes the most generalized two-phase flow model to date. The advantage of this two-phase debris flow model over classical single-phase, or quasi-two-phase models, is that the initial mass can be divided into several parts by appropriately considering the solid volume fraction. These parts include a dry (landslide or rock slide), a fluid (water or muddy water; e.g., dams, rivers), and a general debris mixture material as needed in real flow simulations. This innovative formulation provides an opportunity, within a single framework, to simultaneously simulate the sliding debris (or landslide), the water lake or ocean, the debris impact at the lake or ocean, the tsunami generation and propagation, the mixing and separation between the solid and fluid phases, and the sediment transport and deposition process in the bathymetric surface. Applications of this model include (a) sediment transport on hill slopes, river streams, hydraulic channels (e.g., hydropower dams and plants); lakes, fjords, coastal lines, and aquatic ecology; and (b) submarine debris impact and the rupture of fiber optic, submarine cables and pipelines along the ocean floor, and damage to offshore drilling platforms. Numerical simulations reveal that the dynamics of debris impact induced tsunamis in mountain lakes or oceans are fundamentally different than the tsunami generated by pure rock avalanches and landslides. The analysis includes the generation, amplification and propagation of super tsunami waves and run-ups along coastlines, debris slide and deposition at the bottom floor, and debris shock waves. It is observed that the
Numerical simulation of two phase flows in heat exchangers
The author gives an overview of his research activity since 1981. He first gives a detailed presentation of properties and equations of two-phase flows in heat exchangers, and of their mathematical and numerical investigation: semi-local equations (mass conservation, momentum conservation and energy conservation), homogenized conservation equations (mass, momentum and enthalpy conservation, boundary conditions), equation closures, discretization, resolution algorithm, computational aspects and applications. Then, he reports the works performed in the field of turbulent flows, hyperbolic methods, low Mach methods, the Neptune project, and parallel computing
Spectral Optical Coherence Tomography Using Two-Phase Shifting Method
MA Zhen-He; Ruikang K. Wang; ZHANG Fan; YAO Jian-Quan
2005-01-01
@@ A two-phase shifting method is introduced to eliminate the strong autocorrelation noise inherent in spectral optical coherence tomography and to mitigate the unwanted auto- and cross-coherent terms introduced by the reflections from various optical interfaces present in the system. Furthermore, this method is also able to amplify the desired signal by a factor of 2. The feasibility of such a method is demonstrated using a mirror-like object. An intact porcine cornea tissue in vitro is also used to show the potential of this method for biological imaging.
Experimental and numerical investigation on two-phase flow instabilities
Ruspini, Leonardo Carlos
2013-03-01
Two-phase flow instabilities are experimentally and numerically studied within this thesis. In particular, the phenomena called Ledinegg instability, density wave oscillations and pressure drop oscillations are investigated. The most important investigations regarding the occurrence of two-phase flow instabilities are reviewed. An extensive description of the main contributions in the experimental and analytical research is presented. In addition, a critical discussion and recommendations for future investigations are presented. A numerical framework using a hp-adaptive method is developed in order to solve the conservation equations modelling general thermo-hydraulic systems. A natural convection problem is analysed numerically in order to test the numerical solver. Moreover, the description of an adaptive strategy to solve thermo-hydraulic problems is presented. In the second part of this dissertation, a homogeneous model is used to study Ledinegg, density wave and pressure drop oscillations phenomena numerically. The dynamic characteristics of the Ledinegg (flow excursion) phenomenon are analysed through the simulation of several transient examples. In addition, density wave instabilities in boiling and condensing systems are investigated. The effects of several parameters, such as the fluid inertia and compressibility volumes, on the stability limits of Ledinegg and density wave instabilities are studied, showing a strong influence of these parameters. Moreover, the phenomenon called pressure drop oscillations is numerically investigated. A discussion of the physical representation of several models is presented with reference to the obtained numerical results. Finally, the influence of different parameters on these phenomena is analysed. In the last part, an experimental investigation of these phenomena is presented. The designing methodology used for the construction of the experimental facility is described. Several simulations and a non
A real two-phase submarine debris flow and tsunami
The general two-phase debris flow model proposed by Pudasaini is employed to study subaerial and submarine debris flows, and the tsunami generated by the debris impact at lakes and oceans. The model, which includes three fundamentally new and dominant physical aspects such as enhanced viscous stress, virtual mass, and generalized drag (in addition to buoyancy), constitutes the most generalized two-phase flow model to date. The advantage of this two-phase debris flow model over classical single-phase, or quasi-two-phase models, is that the initial mass can be divided into several parts by appropriately considering the solid volume fraction. These parts include a dry (landslide or rock slide), a fluid (water or muddy water; e.g., dams, rivers), and a general debris mixture material as needed in real flow simulations. This innovative formulation provides an opportunity, within a single framework, to simultaneously simulate the sliding debris (or landslide), the water lake or ocean, the debris impact at the lake or ocean, the tsunami generation and propagation, the mixing and separation between the solid and fluid phases, and the sediment transport and deposition process in the bathymetric surface. Applications of this model include (a) sediment transport on hill slopes, river streams, hydraulic channels (e.g., hydropower dams and plants); lakes, fjords, coastal lines, and aquatic ecology; and (b) submarine debris impact and the rupture of fiber optic, submarine cables and pipelines along the ocean floor, and damage to offshore drilling platforms. Numerical simulations reveal that the dynamics of debris impact induced tsunamis in mountain lakes or oceans are fundamentally different than the tsunami generated by pure rock avalanches and landslides. The analysis includes the generation, amplification and propagation of super tsunami waves and run-ups along coastlines, debris slide and deposition at the bottom floor, and debris shock waves. It is observed that the
A real two-phase submarine debris flow and tsunami
Pudasaini, Shiva P.; Miller, Stephen A.
2012-09-01
The general two-phase debris flow model proposed by Pudasaini [1] is employed to study subaerial and submarine debris flows, and the tsunami generated by the debris impact at lakes and oceans. The model, which includes three fundamentally new and dominant physical aspects such as enhanced viscous stress, virtual mass, and generalized drag (in addition to buoyancy), constitutes the most generalized two-phase flow model to date. The advantage of this two-phase debris flow model over classical single-phase, or quasi-two-phase models, is that the initial mass can be divided into several parts by appropriately considering the solid volume fraction. These parts include a dry (landslide or rock slide), a fluid (water or muddy water; e.g., dams, rivers), and a general debris mixture material as needed in real flow simulations. This innovative formulation provides an opportunity, within a single framework, to simultaneously simulate the sliding debris (or landslide), the water lake or ocean, the debris impact at the lake or ocean, the tsunami generation and propagation, the mixing and separation between the solid and fluid phases, and the sediment transport and deposition process in the bathymetric surface. Applications of this model include (a) sediment transport on hill slopes, river streams, hydraulic channels (e.g., hydropower dams and plants); lakes, fjords, coastal lines, and aquatic ecology; and (b) submarine debris impact and the rupture of fiber optic, submarine cables and pipelines along the ocean floor, and damage to offshore drilling platforms. Numerical simulations reveal that the dynamics of debris impact induced tsunamis in mountain lakes or oceans are fundamentally different than the tsunami generated by pure rock avalanches and landslides. The analysis includes the generation, amplification and propagation of super tsunami waves and run-ups along coastlines, debris slide and deposition at the bottom floor, and debris shock waves. It is observed that the
Modeling transient two-phase stratified flow in pipelines
An isothermal, two-fluid model, comprised of separate mass and linear momentum conservation equations for the gas and liquid phases was formulated. Interfacial mass transfer effects were modeled via the black oil method. Both equal and unequal phase pressure formulations were evaluated. The model was used to investigate transient two-phase stratified flow in pipelines. An explicit numerical scheme was used to solve the system of equations. Experimental data were collected in an existing 425 m long, 76.2 mm diameter horizontal pipeline. Good agreement was observed between experimental and predicted results
Design and construction of two phases flow meter
This paper deals with design of the gamma ray correlometer and flow loop system for measuring the velocity between two parallel cross-sections of a pipeline. In the laboratory, the radioisotope source and detector were collimated by brass with small beam slit respectively. The flow loop system consists of transparent pipeline, adjustable frequency pump and water container. As a result, when the construction of the flow loop and correlometer is completed, the velocity of two phases flow can be measured by the cross-correlation techniques. (Author)
Separation of aqueous two-phase polymer systems in microgravity
Vanalstine, J. M.; Harris, J. M.; Synder, S.; Curreri, P. A.; Bamberger, S. B.; Brooks, D. E.
1984-01-01
Phase separation of polymer systems in microgravity is studied in aircraft flights to prepare shuttle experiments. Short duration (20 sec) experiments demonstrate that phase separation proceeds rapidly in low gravity despite appreciable phase viscosities and low liquid interfacial tensions (i.e., 50 cP, 10 micro N/m). Ostwald ripening does not appear to be a satisfactory model for the phase separation mechanism. Polymer coated surfaces are evaluated as a means to localize phases separated in low gravity. Contact angle measurements demonstrate that covalently coupling dextran or PEG to glass drastically alters the 1-g wall wetting behavior of the phases in dextran-PEG two phase systems.
Partitioning of glycomacropeptide in aqueous two-phase systems
Silva, C. A. S.; Coimbra, Jane Sélia dos Reis; Rojas, Edwin Elard Garcia; Teixeira, J. A.
2009-01-01
The partition behavior of glycomacropeptide (GMP) was determined in polyethylene glycol (PEG) and sodium citrate aqueous two-phase systems (ATPS). It was found that the partitioning of GMP depends on PEG molar mass, tie line length, pH, NaCl concentration and temperature. The obtained data indicates that GMP is preferentially partitioned into the PEG phase without addition of NaCl at pH 8.0. Larger tie line lengths and higher temperatures favor GMP partition to the PEG phase. Furt...
Two-Phase pipeflow simulations with OpenFoam
Izarra Labeaga, Jon; Herreras Omagogeascoa, Nerea
2013-01-01
The main purpose of this thesis is to develop two-phase simulations using OpenFOAM. Two different situations are studied: open and closed channel flow. Different parameters are changed in each case to obtain different results, such as the inclination of the channel and the values of the velocity inlets for each phase. When dealing with the open-channel flow different inclinations are simulated and the influence of the Froude number is analyzed. The results obtained are compared with the analy...
Dynamic modelling for two-phase flow systems
Several models for two-phase flow have been studied, developing a thermal-hydraulic analysis code with one of these models. The program calculates, for one-dimensional cases with variable flow area, the transient behaviour of system process variables, when the boundary conditions (heat flux, flow rate, enthalpy and pressure) are functions of time. The modular structure of the code, eases the program growth. In fact, the present work is the basis for a general purpose accident and transient analysis code in nuclear reactors. Code verification has been made against RETRAN-02 results. Satisfactory results have been achieved with the present version of the code. (Author)
Ratkovich, Nicolas Rios; Bentzen, Thomas Ruby; Majumder, S.;
Gas-liquid two-phase flows are presented everywhere in industrial processes (i.e. gas-oil pipelines). In spite of the common occurrence of these two-phase flows, their understanding is limited compared to single-phase flows. Different studies on two-phase flow have focus on developing empirical...... correlations based on large sets of experiment data for void fraction [1,2] and pressure drop [3,4] which have proven to be accurate for the specific condition that their where developed for. Currently, dozens of void fraction and pressure drop correlations for different flow patterns are available in the...... literature but none of them is enough robust and suitable for different conditions (i.e. flow patterns, gas-liquid combinations, pipe inclination angles, etc.). This clearly represents a drawback and more research in required on this field....
In the present study a new measurement technique has been developed, which uses an ultrasonic transmission signal in order to determine the vertical two phase flow pattern. The ultrasonic measurement system developed in the present study not only provides the measurement functions required for the identification of vertical two phase flow pattern but also makes the real time identification possible. Various vertical two phase flow patterns such as bubbly, slug, churn, annular flow etc have been accurately identified with the present ultrasonic measurement system. In addition to the identification of flow patterns, the qualitative information for each flow pattern can be obtained, which includes void fraction in bubbly flow, length of slug bubble and liquid tail characteristics in slug flow, and stable or transient condition of the flow patterns, etc
Hou, Jiangyong
2016-02-05
In this paper, we present a hybrid method, which consists of a mixed-hybrid finite element method and a penalty discontinuous Galerkin method, for the approximation of a fractional flow formulation of a two-phase flow problem in heterogeneous media with discontinuous capillary pressure. The fractional flow formulation is comprised of a wetting phase pressure equation and a wetting phase saturation equation which are coupled through a total velocity and the saturation affected coefficients. For the wetting phase pressure equation, the continuous mixed-hybrid finite element method space can be utilized due to a fundamental property that the wetting phase pressure is continuous. While it can reduce the computational cost by using less degrees of freedom and avoiding the post-processing of velocity reconstruction, this method can also keep several good properties of the discontinuous Galerkin method, which are important to the fractional flow formulation, such as the local mass balance, continuous normal flux and capability of handling the discontinuous capillary pressure. For the wetting phase saturation equation, the penalty discontinuous Galerkin method is utilized due to its capability of handling the discontinuous jump of the wetting phase saturation. Furthermore, an adaptive algorithm for the hybrid method together with the centroidal Voronoi Delaunay triangulation technique is proposed. Five numerical examples are presented to illustrate the features of proposed numerical method, such as the optimal convergence order, the accurate and efficient velocity approximation, and the applicability to the simulation of water flooding in oil field and the oil-trapping or barrier effect phenomena.
Acute cholecystitis: two-phase spiral CT finding
Oh, Eung Young; Yoon, Myung Hwan; Yang, Dal Mo; Chun Seok; Bae, Jun Gi; Kim, Hak Soo; Kim, Hyung Sik [Chungang Ghil Hospital, Incheon (Korea, Republic of)
1998-07-01
To describe the two-phase spiral CT findings of acute cholecystitis. Materials and Methods : CT scans of nine patients with surgically-proven acute cholecystitis were retrospectively reviewed for wall thickening, enhancement pattern of the wall, attenuation of the liver adjacent to the gallbladder, gallstones,gallbladder distension, gas collection within the gallbladder, pericholecystic fluid and infiltration of pericholecystic fat. Results : In all cases, wall thickening of the gallbladder was seen, though this was more distinct on delayed images, Using high-low-high attenuation, one layer was seen in five cases, nd three layers in four. On arterial images, eight cases showed transient focal increased attenuation of the liver adjacent to the gall bladder;four of these showed curvilinear attenuation and four showed subsegmental attenuation. One case showed curvilinear decreased attenuation between increased attenuation of the liver and the gallbladder, and during surgery, severe adhesion between the liver and gallbladder was confirmed. Additional CT findings were infiltration of pericholecystic fat (n=9), gallstones (n=7), gallbladder distension (n=6), pericholecystic fluid(n=3), and gas collection within the gallbladder (n=2). Conclusion : In patients with acute cholecystitis,two-phase spiral CT revealed wall thickening in one or three layers ; on delayed images this was more distinct. In many cases, arterial images showed transient focal increased attenuation of the liver adjacent to the gallbladder.
Two phase instabilities system analysis with application on Clotaire experiments
Pascal Monier; Jacques Belleudy; Georges Brochier [PRINCIPIA R.D., Z.I. Athelia I, 13705 La Ciotat Cedex (France); Valerie Saldo; Jean-Marie Gouirand; Pierre Gubernatis [CEA Cadarache, 13108 St Paul Lez Durance, Cedex (France)
2005-07-01
Full text of publication follows: Natural-circulation cooled Boiling Water Reactors are susceptible to undergo thermal hydraulics instabilities. The so-called Type-II instabilities due to frictional pressure losses in the core may be observed typically at nominal pressure and relatively high power in BWRs. In the framework of the NACUSP (Natural Circulation and Stability Performance) Project, a test section simulating the riser at the exit of an ESBWR core (European Simplified Boiling Water Reactor) has been set up in the CLOTAIRE facility in CEA, Center of Cadarache. Test campaigns have been conducted with stationary tests demonstrating the correct scaling of the loop with R124a as coolant fluid and with unstable tests identifying the instability thresholds. The CEDRIC thermal hydraulics code was developed with TECHNICATOME in order to simulate one or two phase flow in compact on-board PWR used for marine propulsion. A generic version of this tool, CEDRIC MultiFluides has been used for modeling transient two phase flow until stability limit with large amplitude flow oscillations such as observed during the CLOTAIRE tests. This 1D unsteady model is based on a 3-equations model together with a phase velocities difference closure law in the frame of a Drift Flux Model. The main purpose of this paper is to present the experimental results of the CLOTAIRE tests together with the validation calculations. (authors)
Aqueous Two Phase System Assisted Self-Assembled PLGA Microparticles
Yeredla, Nitish; Kojima, Taisuke; Yang, Yi; Takayama, Shuichi; Kanapathipillai, Mathumai
2016-06-01
Here, we produce poly(lactide-co-glycolide) (PLGA) based microparticles with varying morphologies, and temperature responsive properties utilizing a Pluronic F127/dextran aqueous two-phase system (ATPS) assisted self-assembly. The PLGA polymer, when emulsified in Pluronic F127/dextran ATPS, forms unique microparticle structures due to ATPS guided-self assembly. Depending on the PLGA concentration, the particles either formed a core-shell or a composite microparticle structure. The microparticles facilitate the simultaneous incorporation of both hydrophobic and hydrophilic molecules, due to their amphiphilic macromolecule composition. Further, due to the lower critical solution temperature (LCST) properties of Pluronic F127, the particles exhibit temperature responsiveness. The ATPS based microparticle formation demonstrated in this study, serves as a novel platform for PLGA/polymer based tunable micro/nano particle and polymersome development. The unique properties may be useful in applications such as theranostics, synthesis of complex structure particles, bioreaction/mineralization at the two-phase interface, and bioseparations.
The PDF method for Lagrangian two-phase flow simulations
A recent turbulence model put forward by Pope (1991) in the context of PDF modelling has been used. In this approach, the one-point joint velocity-dissipation pdf equation is solved by simulating the instantaneous behaviour of a large number of Lagrangian fluid particles. Closure of the evolution equations of these Lagrangian particles is based on stochastic models and more specifically on diffusion processes. Such models are of direct use for two-phase flow modelling where the so-called fluid seen by discrete inclusions has to be modelled. Full Lagrangian simulations have been performed for shear-flows. It is emphasized that this approach gives far more information than traditional turbulence closures (such as the K-ε model) and therefore can be very useful for situations involving complex physics. It is also believed that the present model represents the first step towards a complete Lagrangian-Lagrangian model for dispersed two-phase flow problems. (authors). 21 refs., 6 figs
Droplets Formation and Merging in Two-Phase Flow Microfluidics
Hao Gu
2011-04-01
Full Text Available Two-phase flow microfluidics is emerging as a popular technology for a wide range of applications involving high throughput such as encapsulation, chemical synthesis and biochemical assays. Within this platform, the formation and merging of droplets inside an immiscible carrier fluid are two key procedures: (i the emulsification step should lead to a very well controlled drop size (distribution; and (ii the use of droplet as micro-reactors requires a reliable merging. A novel trend within this field is the use of additional active means of control besides the commonly used hydrodynamic manipulation. Electric fields are especially suitable for this, due to quantitative control over the amplitude and time dependence of the signals, and the flexibility in designing micro-electrode geometries. With this, the formation and merging of droplets can be achieved on-demand and with high precision. In this review on two-phase flow microfluidics, particular emphasis is given on these aspects. Also recent innovations in microfabrication technologies used for this purpose will be discussed.
Theory and tests of two-phase turbines
Elliot, D.G.
1982-03-15
Two-phase turbines open the possibility of new types of power cycles operating with extremely wet mixtures of steam and water, organic fluids, or immiscible liquids and gases. Possible applications are geothermal power, waste-heat recovery, refrigerant expansion, solar conversion, transportation turbine engines, and engine bottoming cycles. A theoretical model for two-phase impulse turbines was developed. Apparatus was constructed for testing one- and two-stage turbines (using speed decrease from stage to stage). Turbines were tested with water-and-nitrogen mixtures and Refrigerant 22. Nozzle efficiencies were 0.78 (measured) and 0.72 (theoretical) for water-and-nitrogen mixtures at a water/nitrogen mixture ratio of 68, by mass; and 0.89 (measured) and 0.84 (theoretical) for Refrigerant 22 expanding from 0.02 quality to 0.28 quality. Blade efficiencies (shaft power before windage and bearing loss divided by nozzle jet power) were 0.63 (measured) and 0.71 (theoretical) for water-and-nitrogen mixtures and 0.62 (measured) and 0.63 (theoretical) for Refrigerant 22 with a single-stage turbine, and 0.70 (measured) and 0.85 (theoretical) for water-and-nitrogen mixtures with a two-stage turbine.
Droplets formation and merging in two-phase flow microfluidics.
Gu, Hao; Duits, Michel H G; Mugele, Frieder
2011-01-01
Two-phase flow microfluidics is emerging as a popular technology for a wide range of applications involving high throughput such as encapsulation, chemical synthesis and biochemical assays. Within this platform, the formation and merging of droplets inside an immiscible carrier fluid are two key procedures: (i) the emulsification step should lead to a very well controlled drop size (distribution); and (ii) the use of droplet as micro-reactors requires a reliable merging. A novel trend within this field is the use of additional active means of control besides the commonly used hydrodynamic manipulation. Electric fields are especially suitable for this, due to quantitative control over the amplitude and time dependence of the signals, and the flexibility in designing micro-electrode geometries. With this, the formation and merging of droplets can be achieved on-demand and with high precision. In this review on two-phase flow microfluidics, particular emphasis is given on these aspects. Also recent innovations in microfabrication technologies used for this purpose will be discussed. PMID:21731459
Experimental study of two-phase natural circulation circuit
This paper reports an experimental study on the behavior of fluid flow in natural circulation under single-and two-phase flow conditions. The natural circulation circuit was designed based on concepts of similarity and scale in proportion to the actual operating conditions of a nuclear reactor. This test equipment has similar performance to the passive system for removal of residual heat presents in Advanced Pressurized Water Reactors (A PWR). The experiment was carried out by supplying water to primary and secondary circuits, as well as electrical power resistors installed inside the heater. Power controller has available to adjust the values for supply of electrical power resistors, in order to simulate conditions of decay of power from the nuclear reactor in steady state. Data acquisition system allows the measurement and control of the temperature at different points by means of thermocouples installed at several points along the circuit. The behavior of the phenomenon of natural circulation was monitored by a software with graphical interface, showing the evolution of temperature measurement points and the results stored in digital format spreadsheets. Besides, the natural circulation flow rate was measured by a flowmeter installed on the hot leg. A flow visualization technique was used the for identifying vertical flow regimes of two-phase natural circulation. Finally, the Reynolds Number was calculated for the establishment of a friction factor correlation dependent on the scale geometrical length, height and diameter of the pipe. (author)
Computer simulation of two-phase flow in nuclear reactors
Two-phase flow models dominate the requirements of economic resources for the development and use of computer codes which serve to analyze thermohydraulic transients in nuclear power plants. An attempt is made to reduce the effort of analyzing reactor transients by combining purpose-oriented modelling with advanced computing techniques. Six principles are presented on mathematical modeling and the selection of numerical methods, along with suggestions on programming and machine selection, all aimed at reducing the cost of analysis. Computer simulation is contrasted with traditional computer calculation. The advantages of run-time interactive access operation in a simulation environment are demonstrated. It is explained that the drift-flux model is better suited than the two-fluid model for the analysis of two-phase flow in nuclear reactors, because of the latter's closure problems. The advantage of analytical over numerical integration is demonstrated. Modeling and programming techniques are presented which minimize the number of needed arithmetical and logical operations and thereby increase the simulation speed, while decreasing the cost. (orig.)
Characteristics of spatiotemporal intermittency in two phase flows
The characteristics of temporal and spatiotemporal intermittent, or slug flow, in two phase flashing flows are analyzed in the context of intermittency transition to chaos. Particularly, the possibility of occurence of generic intermittency routes (Types I, II and III) is investigated in the presence of density wave instability in the system and conclusive evidence for the occurrence of Types I and III is presented. Particularly important is the prediction of the mean slug length and the slug length distribution since the slug flow represents an unfavorable flow regime for gas-liquid transportation in pipes. Identification of two generic intermittency routes automatically gives a quantitative prediction concerning the length distribution of laminar and turbulent (slug) phases. Spatiotemporal analysis, based on the bi-othogonal decoposition and concepts from information theory, provides quantitative characterization and prediction of slug flows and possible mechanism of transition from spatiotemporal intermittency to spatiotemporal chaos (turbulence) is outlined. The analysis of the intermittency in two-phase flows was performed on the experimental data obtained in the study of natural circulation instabilities during small break loss-of-coolant accident. 7 refs., 14 figs
Intermittent phenomena in the boiling two-phase boundary layer
In order to investigate statistical properties of temperature fluctuation in a boiling two-phase boundary layer the corresponding intermittency functions, which describe liquid, vapour and interface region at an individual fixed point, have been defined. In water boiling on a horizontal surface the temperature fluctuation was measured with a microthermocouple and the signal was processed through the digital computer with the detector function specified for liquid, vapor and interface region. The results obtained confirm that the temperature fluctuation in the boiling two-phase layer can be divided into three parts corresponding to individual regions and that its statistical distribution depends on the properties of respective systems. It has also been shown that the temperature fluctuation in the interface region is determinative and corresponds to the temperature changes in the liquid layer surrounding vapor bubble growth. Amplitude distribution in the liquid region changes its form with the distance from the wall as a result of the change in intensity of turbulence at different distances. The probability density distribution in the vapor region shows very small amplitude fluctuation and is almost constant for all distances. (author)
无
2000-01-01
In the investigation of effect of KSCN on the partitioning of lysozyme in PEG2000/ammonium sulfate aqueous two-phase system, it was found that the KSCN could alter the pH difference between the two phases, and thus affect the partition of lysozyme. The relationship between partition coefficients of lysozyme and pH differences between two phases was discussed.
Investigation of Power Losses of Two-Stage Two-Phase Converter with Two-Phase Motor
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.
Two-phase flow induced vibrations in CANDU steam generators
The U-Bend region of nuclear steam generators tube bundles have suffered from two-phase cross flow induced vibrations. Tubes in this region have experienced high amplitude vibrations leading to catastrophic failures. Turbulent buffeting and fluid-elastic instability has been identified as the main causes. Previous investigations have focused on flow regime and two-phase flow damping ratio. However, tube bundles in steam generators have vapour generated on the surface of the tubes, which might affect the flow regime, void fraction distribution, turbulent intensity levels and tube-flow interaction, all of which have the potential to change the tube vibration response. A cantilevered tube bundle made of electric cartridges heaters was built and tested in a Freon-11 flow loop at McMaster University. Tubes were arranged in a parallel triangular configuration. The bundle was exposed to two-phase cross flows consisting of different combinations of void from two sources, void generated upstream of the bundle and void generated at the surface of the tubes. Tube tip vibration response was measured optically and void fraction was measured by gamma densitometry technique. It was found that tube vibration amplitude in the transverse direction was reduced by a factor of eight for void fraction generated at the tube surfaces only, when compared to the upstream only void generation case. The main explanation for this effect is a reduction in the correlation length of the turbulent buffeting forcing function. Theoretical calculations of the tube vibration response due to turbulent buffeting under the same experimental conditions predicted a similar reduction in tube amplitude. The void fraction for the fluid-elastic instability threshold in the presence of tube bundle void fraction generation was higher than that for the upstream void fraction generation case. The first explanation of this difference is the level of turbulent buffeting forces the tube bundle was exposed to
Gautschi, Walter; Rassias, Themistocles M
2011-01-01
Approximation theory and numerical analysis are central to the creation of accurate computer simulations and mathematical models. Research in these areas can influence the computational techniques used in a variety of mathematical and computational sciences. This collection of contributed chapters, dedicated to renowned mathematician Gradimir V. Milovanovia, represent the recent work of experts in the fields of approximation theory and numerical analysis. These invited contributions describe new trends in these important areas of research including theoretic developments, new computational alg
Thirty-two phase sequences design with good autocorrelation properties
S P Singh; K Subba Rao
2010-02-01
Polyphase Barker Sequences are ﬁnite length, uniform complex sequences; the magnitude of their aperiodic autocorrelation sidelobes are bounded by 1. Such sequences have been used in numerous real-world applications such as channel estimation, radar and spread spectrum communication. In this paper, thirty-two phase Barker sequences up to length 24 with an alphabet size of only 32 are presented. The sequences from length 25 to 289 have autocorrelation properties better than well-known Frank codes. Because of the complex structure the sequences are very difﬁcult to detect and analyse by an enemy’s electronic support measures (ESMs). The synthesized sequences are promising for practical application to radar and spread spectrum communication systems. These sequences are found using the Modiﬁed Simulated Annealing Algorithm (MSAA). The convergence rate of the algorithm is good.
On drag reduction in a two-phase flow
Gatapova, E. Ya.; Ajaev, V. S.; Kabov, O. A.
2015-02-01
Bubbles collected on a local hydrophobic surface with nanocoating in a two-phase flow in a minichannel have been detected experimentally. It has been proposed to use the effect of concentration of gas bubbles on hydrophobic segments of the surface of the channel with contrast wettability for ensuring drag reduction. A two-dimensional flow model with the Navier slip condition in the region of the bubble layer gives criteria of drag reduction, depending on the slip length, dimension of bubbles, and dimension of the segment with nanocoating. The presence of the bubble layer on half of the surface of the channel can increase the flow rate of a liquid flowing through the channel by 40% at a fixed pressure gradient.
Two-phase flow instability in a parallel multichannel system
HOU Suxia
2009-01-01
The two-phase flow instabilities observed in through parallel multichannel can be classified into three types, of which only one is intrinsic to parallel multichannel systems. The intrinsic instabilities observed in parallel multichannel system have been studied experimentally. The stable boundary of the flow in such a parallel-channel system are sought, and the nature of inlet flow oscillation in the unstable region has been examined experimentally under various conditions of inlet velocity, heat flux, liquid temperature, cross section of channel and entrance throttling. The results show that parallel multichannel system possess a characteristic oscillation that is quite independent of the magnitude and duration of the initial disturbance, and the stable boundary is influenced by the characteristic frequency of the system as well as by the exit quality when this is low, and upon raising the exit quality and reducing the characteristic frequency, the system increases its instability, and entrance throttling effectively contributes to stabilization of the system.
Solutal Marangoni instability in layered two-phase flows
Picardo, Jason R; Pushpavanam, S
2015-01-01
In this paper, the instability of layered two-phase flows caused by the presence of a soluble surfactant (or a surface active solute) is studied. The fluids have different viscosities, but are density matched to focus on Marangoni effects. The fluids flow between two flat plates, which are maintained at different solute concentrations. This establishes a constant flux of solute from one fluid to the other in the base state. A linear stability analysis is performed, using a combination of asymptotic and numerical methods. In the creeping flow regime, Marangoni stresses destabilize the flow, provided a concentration gradient is maintained across the fluids. One long wave and two short wave Marangoni instability modes arise, in different regions of parameter space. A well-defined condition for the long wave instability is determined in terms of the viscosity and thickness ratios of the fluids, and the direction of mass transfer. Energy budget calculations show that the Marangoni stresses that drive long and shor...
Equations of two-phase flow in spray chamber
李新禹; 张志红; 金星; 徐杰
2009-01-01
The downstream water-air heat and moisture transfer system in a moving coordinate was studied. The relationship between the diameter of the misted droplets and the spray pressure was determined. Based on the theory of the relative velocity,the two-phase flow mode of the spray chamber and the efficiency equation for heat and moisture exchange were established. Corrections were carried out for the efficiency equation with spray pressure of 157 kPa. The results show that the pressure plays an important part in determining the efficiency of heat and moisture exchange. When the spray pressure is less than 157 kPa,better coincidence is noticed between the theoretical analysis and the test results with the error less than 6%. Greater error will be resulted in the case when the spray pressure is beyond 157 kPa. After the correction treatment,the coincidence between the theoretical and the experimental results is greatly improved.
A simplified model for two phase face seal design
Lau, S. Y.; Hughes, W. F.; Basu, P.; Beatty, P. A.
1990-01-01
A simplified quasi-isothermal low-leakage laminar model for analyzing the stiffness and the stability characteristics of two-phase face seals with real fluids is developed. Sample calculations with this model for low-leakage operations are compared with calculations for high-leakage operations, performed using the adiabatic turbulent model of Beatty and Hughes (1987). It was found that the seal characteristics predicted using the two extreme models tend to overlap with each other, indicating that the simplified laminar model may be a useful tool for seal design. The effect of coning was investigated using the simplified model. The results show that, for the same balance, a coned seal has a higher leakage rate than a parallel face seal.
A simplified model for two phase face seal design
Lau, S.Y.; Hughes, W.F.; Basu, P.; Beatty, P.A. (Carnegie-Mellon Univ., Pittsburgh, PA (USA) EG G Sealol, Cranston, RI (USA) Vermont Univ., Burlington (USA))
1990-07-01
A simplified quasi-isothermal low-leakage laminar model for analyzing the stiffness and the stability characteristics of two-phase face seals with real fluids is developed. Sample calculations with this model for low-leakage operations are compared with calculations for high-leakage operations, performed using the adiabatic turbulent model of Beatty and Hughes (1987). It was found that the seal characteristics predicted using the two extreme models tend to overlap with each other, indicating that the simplified laminar model may be a useful tool for seal design. The effect of coning was investigated using the simplified model. The results show that, for the same balance, a coned seal has a higher leakage rate than a parallel face seal. 13 refs.
Two-Phase Dechlorination/Detoxification of Lindane (Hexachlorocyclohexane
Abdul Ghaffar
2014-01-01
Full Text Available Dechlorination of lindane was carried out in a two-phase reaction. In first phase Devarda’s alloy and sodium borohydride were used in aqueous/ethanol reaction media. The reaction duration and temperature were optimized. In first phase higher dechlorination (78% was achieved at 80°C with 40-minute reaction time and the products were chlorobenzene, dichlorobenzene, and chlorocyclohexane. In second phase, Ca(OH2 and sulfur were added in reaction media. The reactions conditions like temperature and reaction time were optimized. After 30 minutes, dechlorination was enhanced from 78% to 94% and the final products were benzene, phenol, catechol, benzenethiol, cyclohexane, cyclohexanol, and cyclohexanethiol. The results suggested that dechlorination of lindane in first and second phase was carried out through hydrodechlorination and substitution reactions, respectively. The developed method was applied for lindane containing real wastewater and higher dechlorination (91% was achieved under optimized reaction conditions.
On the performance limit of closed two-phase thermosiphons
This paper discusses an experiment conducted to investigate the performance limit of closed two-phase thermosiphons, together with visual observations of the flow state in the adiabatic section. The working fluids were R-113, methanol, and water. The flow state at the performance limit conditions was a violently disturbed slug type, in which the vapor plugs held up the liquid slugs periodically to a high level, causing a local circulation of liquid in the adiabatic section. This phenomenon is somewhat different from the flooding observed in open systems. An equation correlating the vapor velocity at the performance limit to the rising velocity of vapor plugs in stagnant liquid columns is proposed. This correlation compares satisfactorily with the performance limit data covering a wide range of parameters
Thermo-fluid dynamic theory of two-phase flow
A detailed discussion on the formulation of various mathematical models of two-phase flows based on the conservation laws of mass, momentum and energy is presented. Special emphasises have been put on the local instant formulation and on the time-averaged macroscopic models. Two important models have been presented: 1) the two-fluid model which is formulated by considering each phase separately, and 2) the diffusion model which is formulated by considering the mixture as a whole, thus it is expressed in terms of three mixture conservation equations of mass, momentum and energy with one additional diffusion equation. The present formulation can be used to obtain the wall laws by analyses, i.e., the friction factors and heat transfer coefficients. The high-light of the report is the proposed constitutive laws with special emphasis on the interfacial exchange terms as well as on the turbulent transfer terms
Dynamics Coefficient for Two-Phase Soil Model
Wrana Bogumił
2015-02-01
Full Text Available The paper investigates a description of energy dissipation within saturated soils-diffusion of pore-water. Soils are assumed to be two-phase poro-elastic materials, the grain skeleton of which exhibits no irreversible behavior or structural hysteretic damping. Description of motion and deformation of soil is introduced as a system of equations consisting of governing dynamic consolidation equations based on Biot theory. Selected constitutive and kinematic relations for small strains and rotation are used. This paper derives a closed form of analytical solution that characterizes the energy dissipation during steady-state vibrations of nearly and fully saturated poro-elastic columns. Moreover, the paper examines the influence of various physical factors on the fundamental period, maximum amplitude and the fraction of critical damping of the Biot column. Also the so-called dynamic coefficient which shows amplification or attenuation of dynamic response is considered.
Measurement of two-phase flow momentum with force transducers
This paper reports on two strain-gage-based drag transducers developed to measure two-phase flow in simulated pressurized water reactor (PWR) test facilities. One transducer, a drag body (DB), was designed to measure the bidirectional average momentum flux passing through an end box. The second drag sensor, a break through detector (BTD), was designed to sense liquid downflow from the upper plenum to the core region. After prototype sensors passed numerous acceptance tests, transducers were fabricated and installed in two experimental test facilities, one in Japan and one in West Germany. High-quality data were extracted from both the DBs and BTDs for a variety of loss-of-coolant (LOCA) scenarios. The information collected from these sensors has added to the understanding of the thermohydraulic phenomena that occur during the refill/reflood stage of a LOCA in PWR
Mathematical model of two-phase flow in accelerator channel
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.
Two-phase flow simulation of aeration on stepped spillway
CHENG Xiangju; LUO Lin; ZHAO Wenqian; LI Ran
2004-01-01
Stepped spillways have existed as escape works for a very long time. It is found that water can trap a lot of air when passing through steps and then increasing oxygen content in water body, so stepped spillways can be used as a measure of re-aeration and to improve water quality of water body. However, there is no reliable theoretical method on quantitative calculation of re-aeration ability for the stepped spillways. By introducing an air-water two-phase flow model, this paper used k-ε turbulence model to calculate the characteristic variables of free-surface aeration on stepped spillway. The calculated results fit with the experimental results well. It supports that the numerical modeling method is reasonable and offers firm foundation on calculating re-aeration ability of stepped spillways. The simulation approach can provide a possible optimization tool for designing stepped spillways of more efficient aeration capability.
Numerical modeling of two-phase transonic flow
Halama, Jan; Benkhaldoun, F.; Fořt, Jaroslav
2010-01-01
Roč. 80, č. 88 (2010), s. 1624-1635. ISSN 0378-4754 Grant ostatní: GA ČR(CZ) GA201/08/0012 Institutional research plan: CEZ:AV0Z20760514 Keywords : two-phase flow * condensation * fractional step method Subject RIV: BK - Fluid Dynamics Impact factor: 0.812, year: 2010 http://www.sciencedirect.com/science?_ob=MImg&_imagekey=B6V0T-4VNK68X-2-R&_cdi=5655&_user=640952&_pii=S0378475409000421&_origin=search&_coverDate=04%2F30%2F2010&_sk=999199991&view=c&wchp=dGLzVlb-zSkWb&md5=5ba607428fac339a3e5f67035d3996d0&ie=/sdarticle.pdf
Two-phase flow instabilities in a vertical annular channel
Babelli, I.; Nair, S.; Ishii, M. [Purdue Univ., West Lafayette, IN (United States)
1995-09-01
An experimental test facility was built to study two-phase flow instabilities in vertical annular channel with emphasis on downward flow under low pressure and low flow conditions. The specific geometry of the test section is similar to the fuel-target sub-channel of the Savannah River Site (SRS) Mark 22 fuel assembly. Critical Heat Flux (CHF) was observed following flow excursion and flow reversal in the test section. Density wave instability was not recorded in this series of experimental runs. The results of this experimental study show that flow excursion is the dominant instability mode under low flow, low pressure, and down flow conditions. The onset of instability data are plotted on the subcooling-Zuber (phase change) numbers stability plane.
Shrinkage rate in two-phase carbon materials under irradiation
A method is suggested for calculating the radiation stability of carbon materials consisting of two phases which differ in the degree of perfection of the crystalline lattice. It was found that the rate of shrinkage of a double phase carbon material induced by the radiation is the sum of rates of shrinkage of its phases multiplied by a proportionality factor equal to the weight proportions of the phases. The calculated rates agree satisfactorily with data from experiments conducted on specimens of GMZ graphite impregnated with pyrocarbon or phiA resin and irradiated with a fluence of 8x1021 neutr/cm2 in the range of temperatures of 300-900 deg C
Non-equilibrium effects in transient two-phase flow
Depressurisation tests were carried out on Refrigerant 113 liquid flowing in a horizontal pipeline, under conditions where vapour was formed by flash evaporation. The tests covered a range of initial velocities up to 2.1 m/s in a 51 mm diameter glass pipeline at starting pressure around 1.5 bar and with varying rates of depressurisation. Measurements were made of local pressure and temperature, circulation rate, pressure difference and void fraction variation over a test section length of 2m. The local pressure and temperature measurements give a direct indication of non-equilibrium effects. The vapour formed during the flash evaporation process quickly formed a stratified type flow and a theoretical model was developed on this basis. The model includes the transient two phase low conservation equations allied to a heat transfer equation. Satisfactory agreement between theoretical predictions and experimental results was obtained. (author)
Tsunami Generated by a Two-Phase Submarine Debris Flow
Pudasaini, S. P.
2012-04-01
The general two-phase debris flow model proposed by Pudasaini (2011) is employed to study subaerial and submarine debris flows, and the tsunami generated by the debris impact at lakes and oceans. The model includes several essential physical aspects, including Mohr-Coulomb plasticity for the solid stress, while the fluid stress is modelled as a solid volume fraction gradient enhanced non-Newtonian viscous stress. The generalized interfacial momentum transfer includes the viscous drag, buoyancy, and the virtual mass. The generalized drag covers both the solid-like and fluid-like contributions, and can be applied to linear to quadratic drags. Strong couplings exist between the solid and the fluid momentum transfer. The advantage of the real two-phase debris flow model over classical single-phase or quasi-two-phase models is that by considering the solid (and/or the fluid) volume fraction appropriately, the initial mass can be divided into several (even mutually disjoint) parts; a dry (landslide or rock slide), a fluid (water or muddy water; e.g., dams, rivers), and a general debris mixture material as needed in real flow simulations. This offers a unique and innovative opportunity within a single framework to simultaneously simulate (a) the sliding debris (or landslide), (b) the water lake or ocean, (c) the debris impact at the lake or ocean, (d) tsunami generation and propagation, (e) mixing and separation between the solid and the fluid phases, and (f) sediment transport and deposition process in the bathymetric surface. The new model is applied to two-phase subaerial and submarine debris flows. Benchmark numerical simulations reveal that the dynamics of the debris impact induced tsunamis are fundamentally different than the tsunami generated by pure rock avalanche and landslides. Special attention is paid to study the basic features of the debris impact to the mountain lakes or oceans. This includes the generation, amplification and propagation of the multiple
Rationale for two phase polymer system microgravity separation experiments
Brooks, D. E.; Bamberger, S. B.; Harris, J. M.; Vanalstine, J.
1984-01-01
The two-phase systems that result when aqueous solutions of dextran and poly(ethylene glycol) are mixed at concentrations above a few percent are discussed. They provide useful media for the partition and isolation of macromolecules and cell subpopulations. By manipulating their composition, separations based on a variety of molecular and surface properties are achieved, including membrane hydrophobic properties, cell surface charge, and membrane antigenicity. Work on the mechanism of cell partition shows there is a randomizing, nonthermal energy present which reduces separation resolution. This stochastic energy is probably associated with hydrodynamic interactions present during separation. Because such factors should be markedly reduced in microgravity, a series of shuttle experiments to indicate approaches to increasing the resolution of the procedure are planned.
Particle-fluid two-phase flow modeling
Mortensen, G. A.; Trapp, J. A.
This paper describes a numerical scheme and computer program, DISCON, for the calculation of two-phase flows that does not require the use of flow regime maps. This model is intermediate between-thermal instantaneous and the averaged two-fluid model. It solves the Eulerian continuity, momentum, and energy equations for each liquid control volume, and the Lagrangian mass, momentum, energy, and position equations for each bubble. The bubbles are modeled individually using a large representative number of bubbles, thus, avoiding the numerical diffusion associated with Eulerian models. DISCON has been used to calculate the bubbling of air through a column of water and the subcooled boiling of water in a flow channel. The results of these calculations are presented.
Two-phase flow and heat transfer under low gravity
Frost, W.
1981-11-01
Spacelab experiment to investigate two-phase flow patterns under gravity uses a water-air mixture experiment. Air and water are circulated through the system. The quality or the mixture or air-water is controlled. Photographs of the test section are made and at the same time pressure drop across the test section is measured. The data establishes a flow regime map under reduced gravity conditions with corresponding pressure drop correlations. The test section is also equipped with an electrical resistance heater in order to allow a flow boiling experiment to be carried out using Freon II. High-speed photographs of the test section are used to determine flow patterns. The temperature gradient and pressure drop along the duct can be measured. Thus, quality change can be measured, and heat transfer calculated.
Transient thermohydraulic modeling of two-phase fluid systems
This paper presents a transient thermohydraulic modeling, initially developed for a capillary pumped loop in gravitational applications, but also possibly suitable for all kinds of two-phase fluid systems. Using finite volumes method, it is based on Navier-Stokes equations for transcribing fluid mechanical aspects. The main feature of this 1D-model is based on a network representation by analogy with electrical. This paper also proposes a parametric study of a counterflow condenser following the sensitivity to inlet mass flow rate and cold source temperature. The comparison between modeling results and experimental data highlights a good numerical evaluation of temperatures. Furthermore, the model is able to represent a pretty good dynamic evolution of hydraulic variables.
Two-phase flow experiments through intergranular stress corrosion cracks
Experimental studies of critical two-phase water flow, through simulated and actual intergranular stress corrosion cracks, were performed to obtain data to evaluate a leak flow rate model and investigate acoustic transducer effectiveness in detecting and sizing leaks. The experimental program included a parametric study of the effects of crack geometry, fluid stagnation pressure and temperature, and crack surface roughness on leak flow rate. In addition, leak detection, location, and leak size estimation capabilities of several different acoustic transducers were evaluated as functions of leak rate and transducer position. This paper presents flow rate data for several different cracks and fluid conditions. It also presents the minimum flows rate detected with the acoustic sensors and a relationship between acoustic signal strength and leak flow rate
Stability of stratified two-phase flows in horizontal channels
Barmak, Ilya; Ullmann, Amos; Brauner, Neima; Vitoshkin, Helen
2016-01-01
Linear stability of stratified two-phase flows in horizontal channels to arbitrary wavenumber disturbances is studied. The problem is reduced to Orr-Sommerfeld equations for the stream function disturbances, defined in each sublayer and coupled via boundary conditions that account also for possible interface deformation and capillary forces. Applying the Chebyshev collocation method, the equations and interface boundary conditions are reduced to the generalized eigenvalue problems solved by standard means of numerical linear algebra for the entire spectrum of eigenvalues and the associated eigenvectors. Some additional conclusions concerning the instability nature are derived from the most unstable perturbation patterns. The results are summarized in the form of stability maps showing the operational conditions at which a stratified-smooth flow pattern is stable. It is found that for gas-liquid and liquid-liquid systems the stratified flow with smooth interface is stable only in confined zone of relatively lo...
Two-Phase Flow Complexity in Heterogeneous Media
Ghaffari, Hamed O
2009-01-01
In this study, we investigate the appeared complexity of two-phase flow (air/water) in a heterogeneous soil where the supposed porous media is non-deformable media which is under the timedependent gas pressure. After obtaining of governing equations and considering the capillary pressuresaturation and permeability functions, the evolution of the model unknown parameters were obtained. In this way, using COMSOL (FEMLAB) and fluid flow/script Module, the role of heterogeneity in intrinsic permeability was analysed. Also, the evolution of relative permeability of wetting and non-wetting fluid, capillary pressure and other parameters were elicited. In the last part, a complex network approach to analysis of emerged patterns will be employed.
Flooding in counter-current two-phase flow
Flooding is a phenomenon which is best described as the transition from counter-current to co-current flow. Early notice was taken of this phenomenon in the chemical engineering industry. Flooding also plays an important role in the field of two-phase heat transfer since it is a limit for many systems involving counter-current flow. Practical applications of flooding limited processes include wickless thermosyphons and the emergency core cooling system (ECCS) of pressurized water nuclear reactors. The phenomenon of flooding also is involved in the behavior of nuclear reactor core materials during severe accident conditions where flooding is one of the mechanisms governing the motion of the molten fuel pin cladding
A Large Interface Model for two-phase CFD
Highlights: ► CFD of PTS involves interfaces generally much larger than the computational cells. ► A two-phase model is developed to better take them into account. ► It includes interface recognition, friction, heat and mass transfer. ► The models are written in a three-cell stencil in a wall law-like format. -- Abstract: In the context of the Pressurized Thermal Shock (PTS) studies related to PWR life extension, a two-phase CFD (Eulerian two-field 3D transient) approach has been developed and validated during the last decade. The PTS CFD involves interfaces between liquid and vapour which are generally much larger than the computational cells size: the large interfaces. Special models to deal with them were developed and implemented in the NEPTUNECFD code: it is the Large Interface Model (LIM). It includes large interface recognition, interfacial transfer of momentum (friction), heat and mass transfer with direct contact condensation. The LIM takes into account large interfaces which can be smooth, wavy or rough. The models are written within a three-cell stencil around the large interface position. This stencil is used to calculate, on both the liquid and gas sides, the distance from the first computational cell to the large interface. Both distances are used in the models written in a wall law-like format. Some assumptions made to write the LIM were deduced from the picture given by the experimental data base which was defined for the CFD validation in the context of the PTS issue
Correct numerical simulation of a two-phase coolant
Kroshilin, A. E.; Kroshilin, V. E.
2016-02-01
Different models used in calculating flows of a two-phase coolant are analyzed. A system of differential equations describing the flow is presented; the hyperbolicity and stability of stationary solutions of the system is studied. The correctness of the Cauchy problem is considered. The models' ability to describe the following flows is analyzed: stable bubble and gas-droplet flows; stable flow with a level such that the bubble and gas-droplet flows are observed under and above it, respectively; and propagation of a perturbation of the phase concentration for the bubble and gas-droplet media. The solution of the problem about the breakdown of an arbitrary discontinuity has been constructed. Characteristic times of the development of an instability at different parameters of the flow are presented. Conditions at which the instability does not make it possible to perform the calculation are determined. The Riemann invariants for the nonlinear problem under consideration have been constructed. Numerical calculations have been performed for different conditions. The influence of viscosity on the structure of the discontinuity front is studied. Advantages of divergent equations are demonstrated. It is proven that a model used in almost all known investigating thermohydraulic programs, both in Russia and abroad, has significant disadvantages; in particular, it can lead to unstable solutions, which makes it necessary to introduce smoothing mechanisms and a very small step for describing regimes with a level. This does not allow one to use efficient numerical schemes for calculating the flow of two-phase currents. A possible model free from the abovementioned disadvantages is proposed.
Construction of the two-phase critical flow test facility
The two-phase critical test loop facility has been constructed in the KAERI engineering laboratory for the simulation of small break loss of coolant accident entrained with non-condensible gas of SMART. The test facility can operate at 12 MPa of pressure and 0 to 60 C of sub-cooling with 0.5 kg/s of non- condensible gas injection into break flow, and simulate up to 20 mm of pipe break. Main components of the test facility were arranged such that the pressure vessel containing coolant, a test section simulating break and a suppression tank inter-connected with pipings were installed vertically. As quick opening valve opens, high pressure/temperature coolant flows through the test section forming critical two-phase flow into the suppression tank. The pressure vessel was connected to two high pressure N2 gas tanks through a control valve to control pressure in the pressure vessel. Another N2 gas tank was also connected to the test section for the non-condensible gas injection. The test facility operation was performed on computers supported with PLC systems installed in the control room, and test data such as temperature, break flow rate, pressure drop across test section, gas injection flow rate were all together gathered in the data acquisition system for further data analysis. This test facility was classified as a safety related high pressure gas facility in law. Thus the loop design documentation was reviewed, and inspected during construction of the test loop by the regulatory body. And the regulatory body issued permission for the operation of the test facility
Two-phase flows in Pressurized Water Reactors belong to a wide range of Mach number flows. Computing accurate approximate solutions of those flows may be challenging from a numerical point of view as classical finite volume methods are too diffusive in the low Mach regime. In this thesis, we are interested in designing and studying some robust numerical schemes that are stable for large time steps and accurate even on coarse meshes for a wide range of flow regimes. An important feature is the strategy to construct those schemes. We use a mixed implicit-explicit strategy based on an operator splitting to solve fast and slow phenomena separately. Then, we introduce a modification of a Suliciu type relaxation scheme to improve the accuracy of the numerical scheme in some regime of interest. Two approaches have been used to assess the ability of our numerical schemes to deal with a wide range of flow regimes. The first approach, based on the asymptotic preserving property, has been used for the gas dynamics equations with stiff source terms. The second approach, based on the all-regime property, has been used for the gas dynamics equations and the homogeneous two-phase flows models HRM and HEM in the low Mach regime. We obtained some robustness and stability properties for our numerical schemes. In particular, some discrete entropy inequalities are shown. Numerical evidences, in 1D and in 2D on unstructured meshes, assess the gain in term of accuracy and CPU time of those asymptotic preserving and all-regime numerical schemes in comparison with classical finite volume methods. (author)
Modeling of fluidelastic instability in tube bundle subjected to two-phase cross-flow
Tube arrays in steam generators and heat exchangers operating in two-phase cross-flow are subjected sometimes to strong vibration due mainly to turbulence buffeting and fluidelastic forces. This can lead to tube damage by fatigue or fretting wear. A computer implementation of a fluidelastic instability model is proposed to determine with improved accuracy the fluidelastic forces and hence the critical instability flow velocity. Usually the fluidelastic instability is 'predicted', using the Connors relation with K=3. While the value of K can be determined experimentally to get an accurate prediction of the instability, the Connors relation does not allow good estimation of the fluid forces. Consequently the RMS value of the magnitude of vibration of the tube bundle, necessary to evaluate the work rate and the tube wear is only poorly estimated. The fluidelastic instability analysis presented here is based on the quasi-steady model, originally developed for single phase flow. The fluid forces are expressed in terms of the quasi-static drag and lift force coefficients and their derivatives which are determined experimentally. The forces also depend on the tube displacement and velocity. In the computer code ABAQUS, the fluid forces are provided in the user subroutines VDLOAD or VUEL. A typical simulation of the vibration of a single flexible tube within an array in two phase cross-flow is done in ABAQUS and the results are compared with the experimental measurements for a tube with similar physical properties. For a cantilever tube, in two phase cross-flow of void fraction 60%, the numerical critical flow velocity was 2.0 m/s compared to 1.8 m/s obtained experimentally. The relative error was 5% compared to 26.6% for the Connors relation with K=3. The simulation of the vibration of a typical tube in a steam generator is also presented. The numerical results show good agreement with experimental measurements. (author)
Flow pattern based correlations of two-phase pressure drop in rectangular microchannels
Choi, Chiwoong, E-mail: chiwoongchoi@gmail.com [Department of Mechanical Engineering, Pohang University of Science and Technology, Pohang, San 31, Hyoja Dong 790-784 (Korea, Republic of); Kim, Moohwan [Department of Mechanical Engineering, Pohang University of Science and Technology, Pohang, San 31, Hyoja Dong 790-784 (Korea, Republic of)
2011-12-15
Highlights: Black-Right-Pointing-Pointer Glass microchannels with embedded pressure ports were fabricated to obtain accurate measurements. Black-Right-Pointing-Pointer The assessments of seven HFM (Homogeneous Flow Model) and ten SFM (Separated Flow Model) were conducted. Black-Right-Pointing-Pointer The results indicate models shows best estimations. Black-Right-Pointing-Pointer In addition, the pressure drop is well agreed with flow pattern tendency. Black-Right-Pointing-Pointer Based on two-phase flow patterns, new correlations were proposed for both homogeneous and separated flow types. - Abstract: Numerous pressure drop correlations for microchannels have been proposed; most of them can be classified as either a homogeneous flow model (HFM) or a separated flow model (SFM). However, the predictions of these correlations have not been compared directly because they were developed in experiments conducted under a range of conditions, including channel shape, the number of channels, channel material and the working fluid. In this study, single rectangular microchannels with different aspect ratios and hydraulic diameters were fabricated in a photosensitive glass. Adiabatic water-liquid and Nitrogen-gas two-phase flow experiments were conducted using liquid superficial velocities of 0.06-1.0 m/s, gas superficial velocities of 0.06-72 m/s and hydraulic diameters of 141, 143, 304, 322 and 490 {mu}m. A pressure drop in microchannels was directly measured through embedded ports. The flow pattern was visualized using a high-speed camera and a long-distance microscope. A two-phase pressure drop in the microchannel was highly related to the flow pattern. Data were used to assess seven different HFM viscosity models and ten SFM correlations, and new correlations based on flow patterns were proposed for both HFMs and SFMs.
Flow pattern based correlations of two-phase pressure drop in rectangular microchannels
Highlights: ► Glass microchannels with embedded pressure ports were fabricated to obtain accurate measurements. ► The assessments of seven HFM (Homogeneous Flow Model) and ten SFM (Separated Flow Model) were conducted. ► The results indicate models shows best estimations. ► In addition, the pressure drop is well agreed with flow pattern tendency. ► Based on two-phase flow patterns, new correlations were proposed for both homogeneous and separated flow types. - Abstract: Numerous pressure drop correlations for microchannels have been proposed; most of them can be classified as either a homogeneous flow model (HFM) or a separated flow model (SFM). However, the predictions of these correlations have not been compared directly because they were developed in experiments conducted under a range of conditions, including channel shape, the number of channels, channel material and the working fluid. In this study, single rectangular microchannels with different aspect ratios and hydraulic diameters were fabricated in a photosensitive glass. Adiabatic water-liquid and Nitrogen-gas two-phase flow experiments were conducted using liquid superficial velocities of 0.06–1.0 m/s, gas superficial velocities of 0.06–72 m/s and hydraulic diameters of 141, 143, 304, 322 and 490 μm. A pressure drop in microchannels was directly measured through embedded ports. The flow pattern was visualized using a high-speed camera and a long-distance microscope. A two-phase pressure drop in the microchannel was highly related to the flow pattern. Data were used to assess seven different HFM viscosity models and ten SFM correlations, and new correlations based on flow patterns were proposed for both HFMs and SFMs.
Prediction of two-phase mixture density using artificial neural networks
In nuclear power plants, the density of boiling mixtures has a significant relevance due to its influence on the neutronic balance, the power distribution and the reactor dynamics. Since the determination of the two-phase mixture density on a purely analytical basis is in fact impractical in many situations of interest, heuristic relationships have been developed based on the parameters describing the two-phase system. However, the best or even a good structure for the correlation cannot be determined in advance, also considering that it is usually desired to represent the experimental data with the most compact equation. A possible alternative to empirical correlations is the use of artificial neural networks, which allow one to model complex systems without requiring the explicit formulation of the relationships existing among the variables. In this work, the neural network methodology was applied to predict the density data of two-phase mixtures up-flowing in adiabatic channels under different experimental conditions. The trained network predicts the density data with a root-mean-square error of 5.33%, being ∼ 93% of the data points predicted within 10%. When compared with those of two conventional well-proven correlations, i.e. the Zuber-Findlay and the CISE correlations, the neural network performances are significantly better. In spite of the good accuracy of the neural network predictions, the 'black-box' characteristic of the neural model does not allow an easy physical interpretation of the knowledge integrated in the network weights. Therefore, the neural network methodology has the advantage of not requiring a formal correlation structure and of giving very accurate results, but at the expense of a loss of model transparency. (author)
Approximations to toroidal harmonics
Toroidal harmonics P/sub n-1/2/1(cosh μ) and Q/sub n-1/2/1(cosh μ) are useful in solutions to Maxwell's equations in toroidal coordinates. In order to speed their computation, a set of approximations has been developed that is valid over the range 0 -10. The simple method used to determine the approximations is described. Relative error curves are also presented, obtained by comparing approximations to the more accurate values computed by direct summation of the hypergeometric series
Two-Phase Flow in Pipes: Numerical Improvements and Qualitative Analysis for a Refining Process
Teixeira R.G.D.
2015-03-01
Full Text Available Two-phase flow in pipes occurs frequently in refineries, oil and gas production facilities and petrochemical units. The accurate design of such processing plants requires that numerical algorithms be combined with suitable models for predicting expected pressure drops. In performing such calculations, pressure gradients may be obtained from empirical correlations such as Beggs and Brill, and they must be integrated over the total length of the pipe segment, simultaneously with the enthalpy-gradient equation when the temperature profile is unknown. This paper proposes that the set of differential and algebraic equations involved should be solved as a Differential Algebraic Equations (DAE System, which poses a more CPU-efficient alternative to the “marching algorithm” employed by most related work. Demonstrating the use of specific regularization functions in preventing convergence failure in calculations due to discontinuities inherent to such empirical correlations is also a key feature of this study. The developed numerical techniques are then employed to examine the sensitivity to heat-transfer parameters of the results obtained for a typical refinery two-phase flow design problem.
Two-phase micro- and macro-time scales in particle-laden turbulent channel flows
Bing Wang; Michael Manhart
2012-01-01
The micro- and macro-time scales in two-phase turbulent channel flows are investigated using the direct numerical simulation and the Lagrangian particle trajectory methods for the fluid- and the particle-phases,respectively.Lagrangian and Eulerian time scales of both phases are calculated using velocity correlation functions.Due to flow anisotropy,micro-time scales are not the same with the theoretical estimations in large Reynolds number (isotropic) turbulence.Lagrangian macro-time scales of particle-phase and of fluid-phase seen by particles are both dependent on particle Stokes number.The fluid-phase Lagrangian integral time scales increase with distance from the wall,longer than those time scales seen by particles.The Eulerian integral macro-time scales increase in near-wall regions but decrease in out-layer regions.The moving Eulerian time scales are also investigated and compared with Lagrangian integral time scales,and in good agreement with previous measurements and numerical predictions.For the fluid particles the micro Eulerian time scales are longer than the Lagrangian ones in the near wall regions,while away from the walls the micro Lagrangian time scales are longer.The Lagrangian integral time scales are longer than the Eulerian ones.The results are useful for further understanding two-phase flow physics and especially for constructing accurate prediction models of inertial particle dispersion.
Thermal effects in two-phase flow through face seals. Ph.D. Thesis
Basu, Prithwish
1988-01-01
When liquid is sealed at high temperature, it flashes inside the seal due to pressure drop and/or viscous heat dissipation. Two-phase seals generally exhibit more erratic behavior than their single phase counterparts. Thermal effects, which are often neglected in single phase seal analyses, play an important role in determining seal behavior under two-phase operation. It is necessary to consider the heat generation due to viscous shear, conduction into the seal rings and convection with the leakage flow. Analytical models developed work reasonably well at the two extremes - for low leakage rates when convection is neglected and for higher leakage rates when conduction is neglected. A preliminary model, known as the Film Coefficient Model, is presented which considers conduction and convection both, and allows continuous boiling over an extended region unlike the previous low-leakage rate model which neglects convection and always forces a discrete boiling interface. Another simplified, semi-analytical model, based on the assumption of isothermal conditions along the seal interafce, has been developed for low leakage rates. The Film Coefficient Model may be used for more accurate and realistic description.
Niven, Ivan
2008-01-01
This self-contained treatment originated as a series of lectures delivered to the Mathematical Association of America. It covers basic results on homogeneous approximation of real numbers; the analogue for complex numbers; basic results for nonhomogeneous approximation in the real case; the analogue for complex numbers; and fundamental properties of the multiples of an irrational number, for both the fractional and integral parts.The author refrains from the use of continuous fractions and includes basic results in the complex case, a feature often neglected in favor of the real number discuss
Analytical Evaluation of Two-Phase Natural Circulation Flow Under ERVC condition
The process of two-phase natural circulation flow induced in the annular gap between the reactor vessel and the insulation under external reactor vessel cooling conditions was investigated analytically. HERMES-HALF experiments were performed to observe and quantify the induced two-phase natural circulation flow in the annular gap. A half-scaled non-heating experimental facility was designed by utilizing the results of a scaling analysis to simulate the APR1400 reactor and its insulation system. The behavior of the boiling-induced two-phase natural circulation flow in the annular gap was observed, and the liquid mass flow rates driven by the natural circulation loop and the void fraction distribution were measured. To complement the HERMES-HALF experimental effort, an analytical study of the dependence of the induced natural circulation mass flow rate on the inlet area and the volumetric air injection rate was performed using a loop integration of the momentum equation. The loop-integrated momentum equation was formulated in terms of the dimensionless mass flow rate and the area ratio. Asymptotic solutions were obtained for two limiting cases for which the dimensionless mass flow rate was either very large or very small. First-order approximate solution was also obtained and was found to agree with the experimental data within 20% in most situations. The natural circulation mass flow rate was found to increase as the water inlet area and the volumetric air injection rate were increased. For large inlet areas, the mass flow rate was found to depend almost linearly on the inlet area
Numerical modeling of immiscible two-phase flow in micro-models using a commercial CFD code
Crandall, Dustin; Ahmadia, Goodarz; Smith, Duane H.
2009-01-01
Off-the-shelf CFD software is being used to analyze everything from flow over airplanes to lab-on-a-chip designs. So, how accurately can two-phase immiscible flow be modeled flowing through some small-scale models of porous media? We evaluate the capability of the CFD code FLUENT{trademark} to model immiscible flow in micro-scale, bench-top stereolithography models. By comparing the flow results to experimental models we show that accurate 3D modeling is possible.
This paper presents a novel approach for solving the conservative form of the incompressible two-phase Navier–Stokes equations. In order to overcome the numerical instability induced by the potentially large density ratio encountered across the interface, the proposed method includes a Volume-of-Fluid type integration of the convective momentum transport, a monotonicity preserving momentum rescaling, and a consistent and conservative Ghost Fluid projection that includes surface tension effects. The numerical dissipation inherent in the Volume-of-Fluid treatment of the convective transport is localized in the interface vicinity, enabling the use of a kinetic energy conserving discretization away from the singularity. Two- and three-dimensional tests are presented, and the solutions shown to remain accurate at arbitrary density ratios. The proposed method is then successfully used to perform the detailed simulation of a round water jet emerging in quiescent air, therefore suggesting the applicability of the proposed algorithm to the computation of realistic turbulent atomization
Le Chenadec, Vincent; Pitsch, Heinz
2013-09-01
This paper presents a novel approach for solving the conservative form of the incompressible two-phase Navier-Stokes equations. In order to overcome the numerical instability induced by the potentially large density ratio encountered across the interface, the proposed method includes a Volume-of-Fluid type integration of the convective momentum transport, a monotonicity preserving momentum rescaling, and a consistent and conservative Ghost Fluid projection that includes surface tension effects. The numerical dissipation inherent in the Volume-of-Fluid treatment of the convective transport is localized in the interface vicinity, enabling the use of a kinetic energy conserving discretization away from the singularity. Two- and three-dimensional tests are presented, and the solutions shown to remain accurate at arbitrary density ratios. The proposed method is then successfully used to perform the detailed simulation of a round water jet emerging in quiescent air, therefore suggesting the applicability of the proposed algorithm to the computation of realistic turbulent atomization.
A modified Rusanov scheme for shallow water equations with topography and two phase flows
Mohamed, Kamel; Benkhaldoun, F.
2016-06-01
In this work, we introduce a finite volume method for numerical simulation of shallow water equations with source terms in one and two space dimensions, and one-pressure model of two-phase flows in one space dimension. The proposed method is composed of two steps. The first, called predictor step, depends on a local parameter allowing to control the numerical diffusion. A strategy based on limiters theory enables to control this parameter. The second step recovers the conservation equation. The scheme can thus be turned to order 1 in the regions where the flow has a strong variation, and order 2 in the regions where the flow is regular. The numerical scheme is applied to several test cases in one and two space dimensions. This scheme demonstrates its well-balanced property, and that it is an efficient and accurate approach for solving shallow water equations with and without source terms, and water faucet problem.
Simulation of heterogeneous two-phase media using random fields and level sets
George STEFANOU[1,2
2015-01-01
The accurate and efficient simulation of random heterogeneous media is important in the framework of modeling and design of complex materials across multiple length scales. It is usually assumed that the morphology of a random microstructure can be described as a non-Gaussian random field that is completely defined by its multivariate distribution. A particular kind of non-Gaussian random fields with great practical importance is that of translation fields resulting from a simple memory-less transformation of an underlying Gaussian field with known second-order statistics. This paper provides a critical examination of existing random field models of heterogeneous two-phase media with emphasis on level-cut random fields which are a special case of translation fields. The case of random level sets, often used to represent the geometry of physical systems, is also examined. Two numerical examples are provided to illustrate the basic features of the different approaches.
Le Chenadec, Vincent, E-mail: vlechena@stanford.edu [Department of Mechanical Engineering, Stanford University, CA 94305 (United States); Pitsch, Heinz [Department of Mechanical Engineering, Stanford University, CA 94305 (United States); Institute for Combustion Technology, RWTH Aachen, Templergraben 64, 52056 Aachen (Germany)
2013-09-15
This paper presents a novel approach for solving the conservative form of the incompressible two-phase Navier–Stokes equations. In order to overcome the numerical instability induced by the potentially large density ratio encountered across the interface, the proposed method includes a Volume-of-Fluid type integration of the convective momentum transport, a monotonicity preserving momentum rescaling, and a consistent and conservative Ghost Fluid projection that includes surface tension effects. The numerical dissipation inherent in the Volume-of-Fluid treatment of the convective transport is localized in the interface vicinity, enabling the use of a kinetic energy conserving discretization away from the singularity. Two- and three-dimensional tests are presented, and the solutions shown to remain accurate at arbitrary density ratios. The proposed method is then successfully used to perform the detailed simulation of a round water jet emerging in quiescent air, therefore suggesting the applicability of the proposed algorithm to the computation of realistic turbulent atomization.
Study on two-phase flow dynamics in steam injectors
Analytical and experimental studies have been conducted on large-scale steam injectors for a next-generation reactor. The steam injectors are simple, compact, passive steam jet pumps for a steam-injector-driven passive core injection system (SI-PCIS) or steam-injector-driven primary loop recirculation system (SI-PLR). In order to check the feasibility of such large-scale steam injectors, we developed the separate-two-phase flow models installed in the PHOENICS Code, and scale-model tests were conducted for both SI-PCIS and SI-PLR. A 1/2 scale SI-PCIS model achieved a discharge pressure of almost 8 MPa with 7 MPa steam and 0.4 MPa water, and a 1/5 scale SI-PLR model attained a discharge pressure of 12.5 MPa with 3 MPa steam and 7 MPa water. Both results are in good agreement with the analysis, confirming the feasibility of both systems. The systems will help to simplify the next generation of BWRs. (author)
Abnormal breakdown characteristic in a two-phase mixture
A two-phase mixture (TPM) is a mixture of gas and macroparticles of high concentration. Based on Townsend's theory, a new cell-iterative model in analytical form for the breakdown mechanism in TPM is presented. Compared with the original cell-iterative model in our previous paper, the obstructive factor of the macroparticles that influences the electron avalanche propagation is considered, except for the macroparticles distorting the electrical field and capture of the electrons. The cell attractive parameter k is presented according to the classical continuum theory for field charging. The modified Paschen law for a TPM is presented to calculate the breakdown voltage. The breakdown voltage of the TPM, UTPM, increases gradually with an increase in the macroparticle number density (m). The voltage UTPM is lower than that of the pure gas at low m values and larger at high m values. With a decrease of the macroparticle volume fraction and the dielectric mismatch, the voltage UTPM increases gradually at low m values and decreases gradually at high m values. The voltage UTPM at pd 200 cm Torr is lower than that at pd = 760 cm Torr for low m values and larger for high m values. This kind of abnormal breakdown characteristic in the TPM occurs in the case of high macroparticle volume fraction. On the other hand, the minimum of the TPM's Paschen curve increases with increase in m. It provides the possibility and the conditions of greatly increasing the breakdown voltage in a nearly uniform field
Dielectric barrier discharge in a two-phase mixture
This paper reports the experimental investigation of the dielectric barrier discharge in which the gap area is filled with a two-phase mixture (TPM), air and solid particles. We found that there are two kinds of discharges in the TPM. One is the surface discharge generated on the surface of the solid particles and the other is the filament discharge generated in the air void. For the case of low volume fraction of solid particles, the surface discharge starts to occur when the applied voltage is higher than the onset voltage. At a further voltage increase, the filament discharge takes place at the same time. For the case of high volume fraction, such as the packed-bed reactor, only the surface discharge exists. Under the condition of the same volume fraction, the larger the diameter of the solid particles, the lower the surface discharge onset voltage. As a conclusion, we think that the plasma reactor using the form of low volume fraction of solid particles may be a better choice for waste-gas treatment enhanced by catalysts
A viscous two-phase model for contractile actomyosin bundles.
Oelz, Dietmar
2014-06-01
A mathematical model in one dimension for a non-sarcomeric actomyosin bundle featuring anti-parallel flows of anti-parallel F-actin is introduced. The model is able to relate these flows to the effect of cross-linking and bundling proteins, to the forces due to myosin-II filaments and to external forces at the extreme tips of the bundle. The modeling is based on a coarse graining approach starting with a microscopic model which includes the description of chemical bonds as elastic springs and the force contribution of myosin filaments. In a second step we consider the asymptotic regime where the filament lengths are small compared to the overall bundle length and restrict to the lowest order contributions. There it becomes apparent that myosin filaments generate forces which are partly compensated by drag forces due to cross-linking proteins. The remaining local contractile forces are then propagated to the tips of the bundle by the viscosity effect of bundling proteins in the filament gel. The model is able to explain how a disordered bundle of comparatively short actin filaments interspersed with myosin filaments can effectively contract the two tips of the actomyosin bundle. It gives a quantitative description of these forces and of the anti-parallel flows of the two phases of anti-parallel F-actin. An asymptotic version of the model with infinite viscosity can be solved explicitly and yields an upper bound to the contractile force of the bundle. PMID:23670678
Solutal Marangoni instability in layered two-phase flow
Picardo, Jason; Radhakrishna, T. G.; Pushpavanam, S.
2015-11-01
In this work, the instability of layered two-phase flow caused by the presence of a surface-active solute is studied. The fluids are density matched to focus on surfactant effects. The fluids flow between two flat plates, which are maintained at different solute concentrations. This establishes a constant flux of soluble surfactant from one fluid to the other, in the base state. A linear stability analysis is carried out, supported by energy budget calculations. The flow is first analyzed in the creeping flow regime. Long wave as well as short wave Marangoni instabilities are identified, each with a distinct energy signature. The short wave instability manifests as two distinct modes, characterized by the importance of interfacial deformations or lack thereof. The primary instability switches between these different modes as parameters are varied. The effect of small but finite inertia on these solutal Marangoni modes is then examined. The effect of soluble surfactant on a finte inertia flow is also studied, with focus on the transition from the viscosity-induced instability to solutal Marangoni instability. This analysis is relevant to microfluidic applications, such as solvent extraction, in which mass transfer is carried out between stratified immiscible fluids.
Unsteady flow analysis of a two-phase hydraulic coupling
Hur, N.; Kwak, M.; Lee, W. J.; Moshfeghi, M.; Chang, C.-S.; Kang, N.-W.
2016-06-01
Hydraulic couplings are being widely used for torque transmitting between separate shafts. A mechanism for controlling the transmitted torque of a hydraulic system is to change the amount of working fluid inside the system. This paper numerically investigates three-dimensional turbulent flow in a real hydraulic coupling with different ratios of charged working fluid. Working fluid is assumed to be water and the Realizable k-ɛ turbulence model together with the VOF method are used to investigate two-phase flow inside the wheels. Unsteady simulations are conducted using the sliding mesh technique. The primary wheel is rotating at a fixed speed of 1780 rpm and the secondary wheel rotates at different speeds for simulating different speed ratios. Results are investigated for different blade angles, speed ratios and also different water volume fractions, and are presented in the form of flow patterns, fluid average velocity and also torques values. According to the results, blade angle severely affects the velocity vector and the transmitted torque. Also in the partially-filled cases, air is accumulated in the center of the wheel forming a toroidal shape wrapped by water and the transmitted torque sensitively depends on the water volume fraction. In addition, in the fully-filled case the transmitted torque decreases as the speed ration increases and the average velocity associated with lower speed ratios are higher.
Analysis of two-phase liquid metal MHD induction converter
An analysis is made on the performance characteristics of a liquid-metal MHD induction converter with liquid-gas two-phase mixture as working fluid. The equivalent electrical conductivity and the velocity vary along the generator channel in this kind of induction converter. Two important parameters which represent the variations of the equivalent electrical conductivity and the velocity respectively are defined. With these parameters the induction equation is analytically solved with the perturbation technique. Quantities representing generator performance, such as power densities and generator efficiency, are obtained from the perturbed magnetic field and the parameters mentioned above. Suitable combination of values for these parameters will tend to let the effects brought by the variations of electrical conductivity and of velocity cancel each other, and the relation between these parameters is analytically derived that assures the non-perturbation of the magnetic field and of the gross output power density. In this condition of non-perturbation, the generator efficiency approaches that for the unperturbed case when the velocity variation and the inlet slip ratio are small. (auth.)
Passive Two-Phase Cooling of Automotive Power Electronics: Preprint
Moreno, G.; Jeffers, J. R.; Narumanchi, S.; Bennion, K.
2014-08-01
Experiments were conducted to evaluate the use of a passive two-phase cooling strategy as a means of cooling automotive power electronics. The proposed cooling approach utilizes an indirect cooling configuration to alleviate some reliability concerns and to allow the use of conventional power modules. An inverter-scale proof-of-concept cooling system was fabricated, and tests were conducted using the refrigerants hydrofluoroolefin HFO-1234yf and hydrofluorocarbon HFC-245fa. Results demonstrated that the system can dissipate at least 3.5 kW of heat with 250 cm3 of HFC-245fa. An advanced evaporator design that incorporates features to improve performance and reduce size was conceived. Simulation results indicate its thermal resistance can be 37% to 48% lower than automotive dual side cooled power modules. Tests were also conducted to measure the thermal performance of two air-cooled condensers--plain and rifled finned tube designs. The results combined with some analysis were then used to estimate the required condenser size per operating conditions and maximum allowable system (i.e., vapor and liquid) temperatures.
Mechanisms for two phase flow in porous media
For a better understanding of transport mechanisms in soil for a system with two phases of immiscible liquids the physics of porous media gives again important contributions. In this report, the considerations mainly concentrate on horizontal transport. Our approach is based on the similarity solution of the transport equation which reduces a given nonlinear partial differential equation (PDE) to an ordinary differential equation (ODE). It can be seen, how dimensionless similarity solutions of the ODE depend, in addition to the similarity variable, on two parameters: - the capillary number Nc, giving the ratio of capillary forces and viscous forces, and - the ratio of the viscosities of the two liquid phases. It is shown, under which conditions different mechanisms of transport are to be expected, such as - a completely stable displacement or - an unstable displacement, related to viscous fingering (DLA, Diffusion Limited Aggregation) or to capillary fingering (IP, Invasion Percolation). These mechanisms are also strongly dependent on certain critical exponents (characteristic for DLA or IP). These relations are discussed in our report. Again, for some regions of saturation, mechanisms of displacement are either clearly dominated - by imbibition (e.g. water pushing oil) or - by drain (e.g. oil pushing water). Some of the results are also transformed again from the similarity solution of the ODE to a solution of the PDE (with space- and time coordinates). It is seen, that even with this somewhat simplified approach, we obtain a considerable spectrum of mechanisms. (orig.)
Particle migration in two-phase, viscoelastic flows
Jaensson, Nick; Hulsen, Martien; Anderson, Patrick
2014-11-01
Particles suspended in creeping, viscoelastic flows can migrate across stream lines due to gradients in normal stresses. This phenomenon has been investigated both numerically and experimentally. However, particle migration in the presence of fluid-fluid interfaces is hardly studied. We present results of simulations in 2D and 3D of rigid spherical particles in two-phase flows, where either one or both of the fluids are viscoelastic. The fluid-fluid interface is assumed to be diffuse and is described using Cahn-Hilliard theory. The particle boundary is assumed to be sharp and is described by a boundary-fitted, moving mesh. The governing equations are solved using the finite element method. We show that differences in normal stresses between the two fluids can induce a migration of the particle towards the interface in a shear flow. Depending on the magnitude of the surface tension and the properties of the fluids, particle migration can be halted due to the induced Laplace pressure, the particle can be adsorbed at the interface, or the particle can cross the interface into the other fluid. Dutch Polymer Institute (DPI), P.O. Box 902, 5600 AX Eindhoven, The Netherlands.
Entrainment in vertical annular two-phase flow
Prediction of amount of entrained droplets or entrainment fraction in annular two-phase flow is essential for the estimation of dryout condition and analysis of post dryout heat transfer in light water nuclear reactors and steam boilers. In this study, air-water and organic fluid (Freon-113) annular flow entrainment experiments have been carried out in 9.4 and 10.2 mm diameter test sections, respectively. Both the experiments covered three distinct pressure conditions and wide range of liquid and gas flow conditions. The organic fluid experiments simulated high pressure steam-water annular flow conditions. In each of the experiments, measurements of entrainment fraction, droplet entrainment rate and droplet deposition rate have been performed by using a liquid film extraction method. A simple, explicit and non-dimensional correlation developed by Sawant et al. (2008a) for the prediction of entrainment fraction is further improved in this study in order to account for the existence of critical gas and liquid flow rates below which no entrainment is possible. Additionally, a new correlation is proposed for the estimation of minimum liquid film flow rate at the maximum entrainment fraction condition. The improved correlation successfully predicted the newly collected air-water and Freon-113 entrainment fraction data. Furthermore, the correlations satisfactorily compared with the air-water, helium-water and air-genklene experimental data measured by Willetts (1987). (author)
Two-phase pressure drop reduction BWR assembly design
Dix, G.E.; Crowther, R.L.; Colby, M.J.; Matzner, B.; Elkins, R.B.
1992-05-12
This patent describes a boiling water reactor having discrete bundles of fuel rods confined within channel enclosed fuel assemblies, an improvement to a fuel bundle assembly for placement in the reactor. It comprises a fuel channel having vertically extending walls forming a continuous channel around a fuel assembly volume, the channel being open at the bottom end for engagement to a lower tie plate and open at the upper end for engagement to an upper tie plate; rods for placement within the chamber, each the rod containing fissile material for producing nuclear reaction when in the presence of sufficient moderated neutron flux; a lower tie plate for supporting the bundle of rods within the channel, the lower tie plate for supporting the bundle of rods within the channel, the lower tie plate joining the bottom of the channel to close the bottom end of the channel, the lower tie plate providing defined apertures for the inflow of water in the channel between the rods for the generating of steam during the nuclear reaction; the plurality of fuel rods extending from the lower tie plate wherein a single phase region of the water in the bundle is defined to an upward portion of the bundle wherein a two phase region of the water and steam in the bundle is defined during nuclear steam generating reaction in the fuel bundle.
Two-phase pressure drop reduction BWR assembly design
This patent describes a boiling water reactor having discrete bundles of fuel rods confined within channel enclosed fuel assemblies, an improvement to a fuel bundle assembly for placement in the reactor. It comprises a fuel channel having vertically extending walls forming a continuous channel around a fuel assembly volume, the channel being open at the bottom end for engagement to a lower tie plate and open at the upper end for engagement to an upper tie plate; rods for placement within the chamber, each the rod containing fissile material for producing nuclear reaction when in the presence of sufficient moderated neutron flux; a lower tie plate for supporting the bundle of rods within the channel, the lower tie plate for supporting the bundle of rods within the channel, the lower tie plate joining the bottom of the channel to close the bottom end of the channel, the lower tie plate providing defined apertures for the inflow of water in the channel between the rods for the generating of steam during the nuclear reaction; the plurality of fuel rods extending from the lower tie plate wherein a single phase region of the water in the bundle is defined to an upward portion of the bundle wherein a two phase region of the water and steam in the bundle is defined during nuclear steam generating reaction in the fuel bundle
A two-phase mixture model of avascular tumor growth
Ozturk, Deniz; Burcin Unlu, M.; Yonucu, Sirin; Cetiner, Ugur
2012-02-01
Interactions with biological environment surrounding a growing tumor have major influence on tumor invasion. By recognizing that mechanical behavior of tumor cells could be described by biophysical laws, the research on physical oncology aims to investigate the inner workings of cancer invasion. In this study, we introduce a mathematical model of avascular tumor growth using the continuum theory of mixtures. Mechanical behavior of the tumor and physical interactions between the tumor and host tissue are represented by biophysically founded relationships. In this model, a solid tumor is embedded in inviscid interstitial fluid. The tumor has viscous mechanical properties. Interstitial fluid exhibits properties of flow through porous medium. Associated with the mixture saturation constraint, we introduce a Lagrange multiplier which represents hydrostatic pressure of the interstitial fluid. We solved the equations using Finite Element Method in two-dimensions. As a result, we have introduced a two-phase mixture model of avascular tumor growth that provided a flexible mathematical framework to include cells' response to mechanical aspects of the tumor microenvironment. The model could be extended to capture tumor-ECM interactions which would have profound influence on tumor invasion.
Wall function approach for boiling two-phase flows
One of the important goals of the NURESIM project is to assess and improve the simulation capability of the three-dimensional two-fluid codes for prediction of local boiling flow processes. The boiling flow is strongly affected by local mechanisms in the turbulent boundary layer near the heated wall. Wall-to-fluid transfer models for boiling flow with the emphasis on near-wall treatment are being addressed in the paper. Since the computational grid of the 3D two-fluid models is too coarse to resolve the variable gradients in the near-wall region, the use of wall functions is a common approach to model the liquid velocity and temperature profile adjacent to the heated wall. The wall function model for momentum, based on the surface roughness analogy has been discussed and implemented in the NEPTUNECFD code. The model has been validated on several upward boiling flow experiments, differing in the geometry, working fluid and operating conditions. The simulations with the new wall function model show an improved prediction of flow parameters over the boiling boundary layer. Furthermore, a wall function model for the energy equation, based on enhanced two-phase wall friction has been derived and validated.
Critical two-phase flow through rough slits
The knowledge of the two-phase mass flow rate through a crack in the wall of nuclear or chemical reactor components is very important under the leak-before-break criterion point of view. For providing a qualified analytical tool for calculating critical mass flow rates through such a crack a detailed test program was carried out using subcooled water up to pressures of 14 MPa. A real crack and several simulated cracks (rough slits) were examined experimentally. The important parameters such as inlet pressure, subcooling temperature of water, slit width, and inner surface roughness were varied in a wide range and the measured data compared with calculated values from different models. The data comparison indicates that the model published by Pana leads to predictions which agree best with the observed data. First calculations were carried out using the friction coefficient ζ, which results from single phase flow measurements. A correlation has been developed to calculate ζ from the geometrical dimensions of the crack and was integrated into an advanced version of the Pana model. The modified Pana model was qualified against some hundreds of test values. The measured data were predicted with a relative standard deviation of less than 20%. (orig.)
Biogasification of solid wastes by two-phase anaerobic fermentation
Municipal, industrial and agricultural solid wastes, and biomass deposits, cause large-scale pollution of land and water. Gaseous products of waste decomposition pollute the air and contribute to global warming. This paper describes the development of a two-phase fermentation system that alleviates methanogenic inhibition encountered with high-solids feed, accelerates methane fermentation of the solid bed, and captures methane (renewable energy) for captive use to reduce global warming. The innovative system consisted of a solid bed reactor packed with simulated solid waste at a density of 160 kg/m3 and operated with recirculation of the percolated culture (bioleachate) through the bed. A rapid onset of solids hydrolysis, acidification, denitrification and hydrogen gas formation was observed under these operating conditions. However, these fermentative reactions stopped at a total fatty acids concentration of 13,000 mg/l (as acetic) at pH 5, with a reactor head-gas composition of 75 percent carbon dioxide, 20 percent nitrogen, 2 percent hydrogen and 3 percent methane. Fermentation inhibition was alleviated by moving the bioleachate to a separate methane-phase fermenter, and recycling methanogenic effluents at pH 7 to the solid bed. Coupled operation of the two reactors promoted methanogenic conversion of the high-solids feed. (author)
Stability of stratified two-phase flows in horizontal channels
Barmak, I.; Gelfgat, A.; Vitoshkin, H.; Ullmann, A.; Brauner, N.
2016-04-01
Linear stability of stratified two-phase flows in horizontal channels to arbitrary wavenumber disturbances is studied. The problem is reduced to Orr-Sommerfeld equations for the stream function disturbances, defined in each sublayer and coupled via boundary conditions that account also for possible interface deformation and capillary forces. Applying the Chebyshev collocation method, the equations and interface boundary conditions are reduced to the generalized eigenvalue problems solved by standard means of numerical linear algebra for the entire spectrum of eigenvalues and the associated eigenvectors. Some additional conclusions concerning the instability nature are derived from the most unstable perturbation patterns. The results are summarized in the form of stability maps showing the operational conditions at which a stratified-smooth flow pattern is stable. It is found that for gas-liquid and liquid-liquid systems, the stratified flow with a smooth interface is stable only in confined zone of relatively low flow rates, which is in agreement with experiments, but is not predicted by long-wave analysis. Depending on the flow conditions, the critical perturbations can originate mainly at the interface (so-called "interfacial modes of instability") or in the bulk of one of the phases (i.e., "shear modes"). The present analysis revealed that there is no definite correlation between the type of instability and the perturbation wavelength.
A two-phase model of aquifer heterogeneity
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
Uncertainty analysis of two-phase flow pressure drop calculations
Siqueira, Cezar A.M.; Costa, Bruno M.P.; Fonseca Junior, Roberto da; Gonalves, Marcelo de A.L. [PETROBRAS, Rio de Janeiro, RJ (Brazil)
2004-07-01
The simulation of multiphase flow in pipes is usually performed by petroleum engineers with two main purposes: design of new pipelines and production systems; diagnosis of flow assurance problems in existing systems. The tools used for this calculation are computer codes that use published pressure drop correlations developed for steady-state two-phase flow, such as Hagedorn-Brown, Beggs and Brill and others. Each one of these correlations is best suited for a given situation and the engineer must find out the best option for each particular case, based on his experience. In order to select the best correlation to use and to analyze the results of the calculation, the engineer must determine the reliability of computed values. The uncertainty of the computation is obtained by considering uncertainties of the correlation adopted, of the calculation algorithm and the input data. This paper proposes a method to evaluate the uncertainties of this type of calculation and presents an analysis of these uncertainties. The uncertainty analysis also allows the identification of the parameters that are more significant for the final uncertainty of the simulation. Therefore it makes possible to determine which are the input parameters that must be determined with higher accuracy and the ones that may have lower accuracy, without reducing the reliability of the results. (author)
A simple volume-of-fluid reconstruction method for three-dimensional two-phase flows
Kawano, Akio
2016-01-01
A new PLIC (piecewise linear interface calculation)-type VOF (volume of fluid) method, called APPLIC (approximated PLIC) method, is presented. Although the PLIC method is one of the most accurate VOF methods, the three-dimensional algorithm is complex. %involves multiple conditional branches, Accordingly, it is hard to develop and maintain the computational code. The APPLIC method reduces the complexity using simple approximation formulae. Three numerical tests were performed to compare the accuracy of the SVOF (simplified volume of fluid), VOF/WLIC (weighed line interface calculation), THINC/SW (tangent of hyperbola for interface capturing/slope weighting), THINC/WLIC, PLIC, and APPLIC methods. The results of the tests show that the APPLIC results are as accurate as the PLIC results and are more accurate than the SVOF, VOF/WLIC, THINC/SW, and THINC/WLIC results. It was demonstrated that the APPLIC method is more computationally efficient than the PLIC method.
This thesis deals with the Baer-Nunziato two-phase flow model. The main objective of this work is to propose some techniques to cope with phase vanishing regimes which produce important instabilities in the model and its numerical simulations. Through analysis and simulation methods using Suliciu relaxation approximations, we prove that in these regimes, the solutions can be stabilised by introducing some extra dissipation of the total mixture entropy. In a first approach, called the Eulerian approach, the exact resolution of the relaxation Riemann problem provides an accurate entropy-satisfying numerical scheme, which turns out to be much more efficient in terms of CPU-cost than the classical and very simple Rusanov's scheme. Moreover, the scheme is proved to handle the vanishing phase regimes with great stability. The scheme, first developed in 1D, is then extended in 3D and implemented in an industrial code developed by EDF. The second approach, called the acoustic splitting approach, considers a separation of fast acoustic waves from slow material waves. The objective is to avoid the resonance due to the interaction between these two types of waves, and to allow an implicit treatment of the acoustics, while material waves are explicitly discretized. The resulting scheme is very simple and allows to deal simply with phase vanishing. The originality of this work is to use new dissipative closure laws for the interfacial velocity and pressure, in order to control the solutions of the Riemann problem associated with the acoustic step, in the phase vanishing regimes. (author)
Two phase flow characteristics of an air lift pump using small diameter tubes
An air lift pump system has been designed, constructed and tested which supplies low volumetric flow through an elevation change of approximately 32 feet. The system is a prototype hydraulic sampler system which is to supply 200-500 cc/min liquid flow from a large storage tank. The two phase flow characteristics are unique in this system since small diameter tubes (order .25 inches) are used in a series of vertical and nearly horizontal flow sections. The system requires separation of the liquid/gas stream into each of its two-phase components at the top of the air lift. Instantaneous pressure measurements were made at six locations along the flow in both vertical and horizontal flow sections. Time traces of pressure along with their spectral characteristics are presented. These results were correlated with visual observations made through quartz tubes and recorded on video tape. In addition, pressure drop data was obtained in both vertical and horizontal flow sections and related to the system parameters
Optical Readout of a Two Phase Liquid Argon TPC using CCD Camera and TGEMs
Mavrokoridis, K; Carroll, J; Lazos, M; McCormick, K J; Smith, N A; Touramanis, C; Walker, J
2014-01-01
This paper presents a preliminary study into the use of CCDs to image secondary scintillation light generated by Thick Gas Electron Multipliers (TGEMs) in a two phase LAr TPC. A Sony ICX285AL CCD chip was mounted above a double TGEM in the gas phase of a 40 litre two-phase LAr TPC with the majority of the camera electronics positioned externally via a feedthrough. An Am-241 source was mounted on a rotatable motion feedthrough allowing the positioning of the alpha source either inside or outside of the field cage. Developed for and incorporated into the TPC design was a novel high voltage feedthrough featuring LAr insulation. Furthermore, a range of webcams were tested for operation in cryogenics as an internal detector monitoring tool. Of the range of webcams tested the Microsoft HD-3000 (model no:1456) webcam was found to be superior in terms of noise and lowest operating temperature. In ambient temperature and atmospheric pressure 1 ppm pure argon gas, the TGEM gain was approximately 1000 and using a 1 msec...
A Hydrodynamic Model for Slug Frequency in Horizontal Gas-Liquid Two-Phase Flow
刘磊; 孙贺东; 胡志华; 周芳德
2003-01-01
The prediction of slug frequency has important significance on gas-liquid two-phase flow. A hydrodynamic model was put forward to evaluate slug frequency for horizontal two-phase flow, based on the dependence of slug frequency on the frequency of unstable interfacial wave. Using air and water, experimental verification of the model was carried out in a large range of flow parameters. Six electrical probes were installed at different positions of a horizontal plexiglass pipe to detect slug frequency development. The pipe is 30 m long and its inner diameter is 24 ram. It is observed experimentally that the interracial wave frequency at the inlet is about i to 3 times the frequency of stable slug. The slug frequencies predicted by the model fit well with Tronconi (1990) model and the experimental data. The combination of the hydrodynamic model and the experimental data results in a conclusion that the frequency of equilibrium liquid slug is approximately half the minimum frequency of interfacial wave.
As part of a study on a two-phase natural circulation flow between the outer reactor vessel and the insulation material in the reactor cavity under an external reactor vessel cooling of APR (Advanced Power Reactor) 1400, a K-HERMES-HALF (Hydraulic Evaluation of Reactor cooling Mechanism by External Self-induced flow-HALF scale) experiment was performed at KAERI (Korea Atomic Energy Research Institute) using an air injection method. This experiment was analyzed to verify and evaluate the experimental results using the RELAP5/MOD3 computer code. In addition, the geometry scaling on full height & full sector, and a material scaling between air-water and steam-water two phase natural circulation flow, have been performed for an application of the experimental results to an actual APR1400. The RELAP5/MOD3 results on the water circulation mass flow rate are very similar to the experimental results, in general. The water circulation mass flow rate of the full height & full sector case is approximately 7.6-times higher than that of the K-HERMEL-HALF case. The water circulation mass flow rate of the air injection case is 20-50 % higher than that of the steam injection case at 20 % of the injection rate. (author)
Molten corium concrete interaction: investigation of heat transfer in two-phase flow
In the context of severe accident research for the second and the third generation of nuclear power plants, there are still open issues concerning some aspects of the concrete cavity ablation during the molten corium - concrete interaction (MCCI). The determination of heat transfer along the interfacial region between the molten corium pool and the ablating basemat concrete is crucial for the assessment of concrete ablation progression and eventually the basemat melt through. For the purpose of experimental investigation of thermal hydraulics inside a liquid pool agitated by gas bubbles, the CLARA project has been launched. The CLARA experiments are performed using simulant materials and they reveal the influence of superficial gas velocity, liquid viscosity and pool geometry on the heat transfer coefficient between the internally heated liquid pool and vertical and horizontal pool walls maintained at uniform temperature. The first test campaign has been conducted with the small pool configuration (50 cm * 25 cm * 25 cm). The tests have been performed with liquids covering a wide range of dynamic viscosity from approximately 1 mPa s to 10000 mPa s and the superficial gas velocity is varied up to 8 cm/s. This thesis comprises a brief description of MCCI phenomenology, literature reviews on the existing heat transfer correlations for two phase flow and the void fraction, a description of CLARA setup, experimental results and their interpretation. The experimental results are compared with existing models and some new models for the assessment of heat transfer coefficient in two-phase flow. (author)
Approximate Representations and Approximate Homomorphisms
Moore, Cristopher; Russell, Alexander
2010-01-01
Approximate algebraic structures play a defining role in arithmetic combinatorics and have found remarkable applications to basic questions in number theory and pseudorandomness. Here we study approximate representations of finite groups: functions f:G -> U_d such that Pr[f(xy) = f(x) f(y)] is large, or more generally Exp_{x,y} ||f(xy) - f(x)f(y)||^2$ is small, where x and y are uniformly random elements of the group G and U_d denotes the unitary group of degree d. We bound these quantities i...
Jakobsen, Arne; Antonius, Jesper; Knudsen, Hans Jørgen Høgaard
1999-01-01
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 as the homogenous model produce a too fast response....
Development of a hybrid particle-mesh method for two-phase flow simulations with phase change
A hybrid particle-mesh method was developed for efficient and accurate simulations of two-phase flows with phase change. In this method, the CIP/MM (constrained interpolated profile/multi-moment finite volume) method is used to calculate the main part of two-phase flows, while the finite volume particle (FVP) method is applied to represent the interface between two phases based on a Lagrangian scheme. The conservation equations are first solved by CIP/MM, and then mass, velocity and energy on the mesh grid are interpolated to numerical particles, which are distributed only on the surface of liquid phase to capture the phase interface by the FVP method. The particles are also used to calculate heat and mass transfers due to phase change on the interface. The phase of each particle is determined according to its enthalpy value interpolated from mesh grids. The mesh and particle methods are combined tightly in a single numerical solution algorithm to improve numerical accuracy and stability. Two benchmark simulations of conventional 1D Stefan problem for a vapor-liquid system and horizontal film boiling behavior demonstrate that this hybrid method is potentially applicable to two-phase flow calculations with phase change occurring at moving interface. (author)
Numerical methods for two-phase flow with contact lines
Walker, Clauido
2012-07-01
This thesis focuses on numerical methods for two-phase flows, and especially flows with a moving contact line. Moving contact lines occur where the interface between two fluids is in contact with a solid wall. At the location where both fluids and the wall meet, the common continuum descriptions for fluids are not longer valid, since the dynamics around such a contact line are governed by interactions at the molecular level. Therefore the standard numerical continuum models have to be adjusted to handle moving contact lines. In the main part of the thesis a method to manipulate the position and the velocity of a contact line in a two-phase solver, is described. The Navier-Stokes equations are discretized using an explicit finite difference method on a staggered grid. The position of the interface is tracked with the level set method and the discontinuities at the interface are treated in a sharp manner with the ghost fluid method. The contact line is tracked explicitly and its dynamics can be described by an arbitrary function. The key part of the procedure is to enforce a coupling between the contact line and the Navier-Stokes equations as well as the level set method. Results for different contact line models are presented and it is demonstrated that they are in agreement with analytical solutions or results reported in the literature.The presented Navier-Stokes solver is applied as a part in a multiscale method to simulate capillary driven flows. A relation between the contact angle and the contact line velocity is computed by a phase field model resolving the micro scale dynamics in the region around the contact line. The relation of the microscale model is then used to prescribe the dynamics of the contact line in the macro scale solver. This approach allows to exploit the scale separation between the contact line dynamics and the bulk flow. Therefore coarser meshes can be applied for the macro scale flow solver compared to global phase field simulations
Simulation of two-phase flows by domain decomposition
This thesis deals with numerical simulations of compressible fluid flows by implicit finite volume methods. Firstly, we studied and implemented an implicit version of the Roe scheme for compressible single-phase and two-phase flows. Thanks to Newton method for solving nonlinear systems, our schemes are conservative. Unfortunately, the resolution of nonlinear systems is very expensive. It is therefore essential to use an efficient algorithm to solve these systems. For large size matrices, we often use iterative methods whose convergence depends on the spectrum. We have studied the spectrum of the linear system and proposed a strategy, called Scaling, to improve the condition number of the matrix. Combined with the classical ILU pre-conditioner, our strategy has reduced significantly the GMRES iterations for local systems and the computation time. We also show some satisfactory results for low Mach-number flows using the implicit centered scheme. We then studied and implemented a domain decomposition method for compressible fluid flows. We have proposed a new interface variable which makes the Schur complement method easy to build and allows us to treat diffusion terms. Using GMRES iterative solver rather than Richardson for the interface system also provides a better performance compared to other methods. We can also decompose the computational domain into any number of sub-domains. Moreover, the Scaling strategy for the interface system has improved the condition number of the matrix and reduced the number of GMRES iterations. In comparison with the classical distributed computing, we have shown that our method is more robust and efficient. (author)
Development of two-phase Flow Model, 'SOBOIL', for Sodium
The objective of this research is to develop a sodium two-phase flow analysis model, 'SOBOIL', for the assessment of the initial stage of the KALIMER HCDA (Hypotherical Core Disruptive Accident). The 'SOBOIL' is basically similar to the multi-bubble slug ejection model used in SAS2A[1]. When a bubble is formed within the liquid slug, the bubble fills the whole cross section of the coolant channel except for a film left on the cladding or on the structure. Up to nine bubbles, separated by the liquid slugs, are allowed in the channel at any time. Each liquid slug flow rate in the model is performed in 2 steps. In the first step, the preliminary flow rate in the liquid slug is calculated neglecting the effect of changes in the vapor bubble pressures over the time step. The temperature and pressure distributions, and interface velocity at the interface between the liquid slug and vapor bubble are also calculated during this process. The new vapor temperature and pressure are then determined from the balance between the net energy transferred into the vapor and the change of the vapor energy. The liquid flow is finally calculated considering the change of the vapor pressure over a time step and the calculation is repeated until specified elapsed time is met. Continuous effort, therefore, must be made on the examination and improvement for the model to become reliable. To this end, much interest must be concentrated in the relevant international collaborations for access to a reference model or test data for the verification
Experimental and Theoretical Studies on Two-Phase Flows.
Koh, Christopher James
This thesis, comprised of two parts, deals with the flow of suspensions. Part I concerns specifically with the stability of a single drop translating through a quiescent, unbounded suspending fluid at low Reynolds number. The evolution of the shape of an initially nonspherical drop as it translates is studied numerically and experimentally. For finite capillary numbers, it is shown that the drop reverts to a sphere provided that the initial deformation is small enough. However, beyond certain critical initial deformation, the drop deforms continuously. For initially prolate shapes, the drop elongates with the formation of a tail; for initially oblate shapes, the drop flattens with the formation of a cavity at its rear. Experiments extend the numerical results. It is found that initially unstable prolate drops break up into multiple droplets, while initially unstable oblate drops deform in double-emulsion drops. Part II of this thesis considers the flow of high concentration solid suspensions through a rectangular channel. By adapting the well-known Laser Doppler Anemometry, an experimental technique is developed to measure the velocity as well as particle volume fraction of the suspension. A crucial element in these experiments is the reduction of the optical turbidity of the suspension. To accomplish this goal, a systematic method based on refractive-index-matching of the two phases is employed. Experimental results show that the velocity profile is blunted while the concentration profile has a maximum near the center. The qualitative features of the experimental data compare reasonably well with theoretical predictions based on the shear-induced particle migration theory.
Characterization and modeling of annular two-phase flows
Three aspects of annular two-phase flow are studied: (a) wave motion on falling films, (b) flow transition from downflow to upflow, and (c) the upflow. For the case of wave motion on falling films, it is shown that the assumption of the Nusselt velocity profile for finite-amplitude waves is solution of the wave profile, wave velocity, and velocity components within the wave is developed. An algorithm based on collocation methods is also detailed and can be applied to extend the model to solve for higher order terms in the velocity profile. Comparisons with experimental studies show good agreement. Flow transition and the upflow experiments are conducted in a 5.08 x 10-2m inner diameter, 6.5m long Plexiglas column. The liquid rates are varied from 0 to 0.126 kg/s and the gas rates from 0 to 0.0524 kg/s. At four measuring stations along the length of the column, an electrical conductance technique which employs two electrodes mounted flush with the wall is utilized to measure film thickness and pressure transducers are used to make the pressure measurements. Flow visualization studies indicate that flooding takes place as a result of entrainment from the crests of large waves. The effect of column length and pore size of the feed device on flooding velocities is studied. No previous correlation or theory is found to be fully adequate. A speculative interaction among system parameters is proposed to form a basis for a physical model for flooding phenomena
Unreddened stars and the two-phase model of the interstellar medium
Two phase models have been computed of the interstellar medium, with cosmic rays and X-rays assumed to be the main ionizing agents, heating due to photoelectron ejection from the interstellar grains. It is shown that it is possible to have a hot and tenuous intercloud medium in pressure equilibrium with the interstellar clouds for a wide range of physical conditions, possibly existing in the interstellar space. The atomic and ionic line observations towards lambda Sco are shown to be consistent with the origin of these lines in the intercloud medium for a range of values of the ionizing flux. It is suggested that the intercloud medium may be predominantly neutral, with ionization rates consistent with the limits imposed by molecular observations. The mean fractional ionization of the intercloud medium is approximately 1%. (Auth.)
THE NONLINEAR BEHAVIOR OF INTERFACE BETWEEN TWO-PHASE SHEAR FLOW WITH LARGE DENSITY RATIOS
DONG Yu-hong
2006-01-01
The Navier-Stokes equations for the two-dimensional incompressible flow are used to investigate the effects of the Reynolds number and the Weber number on the behavior of interface between liquid-gas shear flow.In the present study, the density ratios are fixed at approximately 100-103.The interface between the two phases is resolved using the level-set approach.The Reynolds number and the Weber number, based on the gas, are selected as 400-10000 and 40-5000, respectively.In the past, simulations reappeared the amplitude of interface growth predicted by viscous Orr-Sommerfeld linear theory, verifying the applicability and accuracy of the numerical method over a wide range of density and viscosity ratios; now, the simulations show that the nonlinear development of ligament elongated structures and resulted in the subsequent breakup of the heavier fluid into drops.
Magnetic viscosity in a nanocrystalline two phase composite with enhanced remanence
The intrinsic values of the magnetic viscosity and the fluctuation field in a two phase composite Nd2Fe14B+0.18 vol. αFe were investigated. The composite studied, with equiaxed and isotropically oriented grains had mean grain sizes favoring a strong exchange coupling between the phases. The relations between the intrinsic and the experimentally measured magnitudes are reviewed and the approximations discussed. For applied fields close to the coercivity, the time dependence of the magnetization is not well described by a simple logarithmic law. The intrinsic fluctuation field is found to increase when the reverse internal field increases in all the ranges investigated and two different regimes are identified. These different regimes are discussed considering the distributions of critical fields for nucleation of inverse domains in the hard phase, at hard-soft and hard-hard grain boundaries, respectively
Hydrodynamic Dryout in Two-Phase Flows: Observations of Low Bond Number Systems
Weislogel, Mark M.; McQuillen, John B.
1998-01-01
Dryout occurs readily in certain slug and annular two-phase flows for systems that exhibit partial wetting. The mechanism for the ultimate rupture of the film is attributed to van der Waals forces, but the pace towards rupture is quickened by the surface tension instability (Rayleigh-type) of the annular film left by the advancing slug and by the many perturbations of the free surface present in the Re(sub g) approximately 0(10(exp 3)), Re(sub l) approximately 0(10(exp 4)), and Ca approximately 0(10(exp -1) flows. Results from low-gravity experiments using three different test fluids are presented and discussed. For the range of tests conducted, the effect of increasing viscosity is shown to eliminate the film rupture while the decrease of surface tension via a surfactant additive is shown to dramatically enhance it. Laboratory measurements using capillary tubes are presented which reveal the sensitivity of the dryout phenomena to particulate and surfactant contamination. Rom such observations, dryout due to the hydrodynamic-van der Waals instability can be expected in a certain range of flow parameters in the absence of heat transfer. The addition of heat transfer may only exacerbate the problem by producing thermal transport lines replete with "hot spots." A caution to this effect is issued to future space systems designers concerning the use of partially wetting working fluids.
Effect of fine-dispersed inclusions on the critical velocity analysis in the two-phase flow
Volgina Lyudmila Vsevolodovna
2014-12-01
Full Text Available The co-authors have designated the point for the identification of the critical velocity and intensity of the hydro-abrasive wear within the framework of the two-phase flow mechanics challenges. In this article, the two-phase flow is analyzed as the flow that has the solid phase, including ore particles, concentrates and tailings, solid fuel combustion products, sand, and construction materials, etc., and as the flow containing the liquid phase, or water. The authors have identified the influence produced by the presence of fine-dispersed solid particles in the two-phase flows that transport the milled ore concentrate due to the presence of the water. Variations in critical velocity values, driven by the per-cent clay content in the ore, were exposed to the experimental research performed by the Laboratory of Hydraulic Transportation at the Hydraulics Department, MGSU. The experimental data are consistent with the findings of the analysis of the influence produced by dust fractions on the critical velocity at the Eastern site’s placer of Malyshev deposit. The co-authors offer their methodology for the refinement of the critical velocity analysis depending on varied per cent clay content values; the diagram compiled in relative coordinates, and the approximative correlation required for practical applications. The proposed methodology consisting in feeding fine-dispersed additives into the two-phase flow, reduces the critical velocity.
Xin Chen; Penghuan Xie; Yonghua Xiong; Yong He; Min Wu
2015-01-01
Adaptive Dynamic Programming (ADP) with critic-actor architecture is an effective way to perform online learning control. To avoid the subjectivity in the design of a neural network that serves as a critic network, kernel-based adaptive critic design (ACD) was developed recently. There are two essential issues for a static kernel-based model: how to determine proper hyperparameters in advance and how to select right samples to describe the value function. They all rely on the assessment of sa...
Quantitative analysis of two-phase 3D+time aortic MR images
Zhao, Fei; Zhang, Honghai; Walker, Nicholas E.; Yang, Fuxing; Olszewski, Mark E.; Wahle, Andreas; Scholz, Thomas; Sonka, Milan
2006-03-01
Automated and accurate segmentation of the aorta in 3D+time MR image data is important for early detection of connective tissue disorders leading to aortic aneurysms and dissections. A computer-aided diagnosis method is reported that allows the objective identification of subjects with connective tissue disorders from two-phase 3D+time aortic MR images. Our automated segmentation method combines level-set and optimal border detection. The resulting aortic lumen surface was registered with an aortic model followed by calculation of modal indices of aortic shape and motion. The modal indices reflect the differences of any individual aortic shape and motion from an average aortic behavior. The indices were input to a Support Vector Machine (SVM) classifier and a discrimination model was constructed. 3D+time MR image data sets acquired from 22 normal and connective tissue disorder subjects at end-diastole (R-wave peak) and at 45% of the R-R interval were used to evaluate the performance of our method. The automated 3D segmentation result produced accurate aortic surfaces covering the aorta from the left-ventricular outflow tract to the diaphragm and yielded subvoxel accuracy with signed surface positioning errors of -0.09+/-1.21 voxel (-0.15+/-2.11 mm). The computer aided diagnosis method distinguished between normal and connective tissue disorder subjects with a classification correctness of 90.1 %.
Subcooled boiling is one of the crucial phenomena in nuclear reactor safety, such as the downcomer boiling in the reflood phase of Large-Break Loss-of-Coolant Accident (LBLOCA). Among various models to analyze a subcooled boiling two-phase flow, the two-fluid model is the most appropriate model which is beneficial to treat the transient of each phase separately. The analysis with the two-fluid model requires an accurate prediction for the interfacial area concentration. To estimate the dynamic and multi-dimensional behavior of the interfacial area concentration, an interfacial area transport equation has been derived in previous researchers. In this study, the interfacial area transport equation available for the subcooled boiling flow was developed with a mechanistic model for the wall boiling source term. To evaluate the model, a two phase flow CFD code was developed and the experimental data from the subcooled boiling test was utilized for its validation
Validation of Friction Models in MARS-MultiD Module with Two-Phase Cross Flow Experiment
Choi, Chi-Jin; Yang, Jin-Hwa; Cho, Hyoung-Kyu; Park, Goon-Cher [Seoul National University, Seoul (Korea, Republic of); Euh, Dong-Jin [KAERI, Daejeon (Korea, Republic of)
2015-05-15
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 Friction Models in MARS-MultiD Module with Two-Phase Cross Flow Experiment
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
CERN. Geneva
2015-01-01
Most physics results at the LHC end in a likelihood ratio test. This includes discovery and exclusion for searches as well as mass, cross-section, and coupling measurements. The use of Machine Learning (multivariate) algorithms in HEP is mainly restricted to searches, which can be reduced to classification between two fixed distributions: signal vs. background. I will show how we can extend the use of ML classifiers to distributions parameterized by physical quantities like masses and couplings as well as nuisance parameters associated to systematic uncertainties. This allows for one to approximate the likelihood ratio while still using a high dimensional feature vector for the data. Both the MEM and ABC approaches mentioned above aim to provide inference on model parameters (like cross-sections, masses, couplings, etc.). ABC is fundamentally tied Bayesian inference and focuses on the “likelihood free” setting where only a simulator is available and one cannot directly compute the likelihood for the dat...
Schmidt, Wolfgang M
1980-01-01
"In 1970, at the U. of Colorado, the author delivered a course of lectures on his famous generalization, then just established, relating to Roth's theorem on rational approxi- mations to algebraic numbers. The present volume is an ex- panded and up-dated version of the original mimeographed notes on the course. As an introduction to the author's own remarkable achievements relating to the Thue-Siegel-Roth theory, the text can hardly be bettered and the tract can already be regarded as a classic in its field."(Bull.LMS) "Schmidt's work on approximations by algebraic numbers belongs to the deepest and most satisfactory parts of number theory. These notes give the best accessible way to learn the subject. ... this book is highly recommended." (Mededelingen van het Wiskundig Genootschap)
One-dimensional two-phase moving boundary problem
This paper presents the results of mathematically modeling a first-order phase change for the melting of a solid. The mathematical model will be validated against an experiment. The experiment will be the melting of paraffin as it undergoes a phase change from solid to liquid. The authors approximate the partial differential equation describing the enthalpy balance by a variable grid finite difference algorithm. This work will not address interface melting where phase change is occurring at a sharp interface, and is limited to the analysis of a first-order phase change for a homogeneous mixture where mass transfer, crystal growth and reactions are neglected
Experimental Investigation of Two-Phase Flow in Rock Salt
Malama, Bwalya; Howard, Clifford L.
2014-07-01
This Test Plan describes procedures for conducting laboratory scale flow tests on intact, damaged, crushed, and consolidated crushed salt to measure the capillary pressure and relative permeability functions. The primary focus of the tests will be on samples of bedded geologic salt from the WIPP underground. However, the tests described herein are directly applicable to domal salt. Samples being tested will be confined by a range of triaxial stress states ranging from atmospheric pressure up to those approximating lithostatic. Initially these tests will be conducted at room temperature, but testing procedures and equipment will be evaluated to determine adaptability to conducting similar tests under elevated temperatures.
An improved CFD tool to simulate adiabatic and diabatic two-phase flows
With increasing computer capabilities, numerical modeling of two-phase flows has developed significantly over the last few years. Although there are two main categories, namely ‘one’ fluid and ‘two’ fluid methods, the ‘one’ fluid methods are more commonly used for tracking or capturing the interface between two fluids. Level set (LS), volume-of-fluid (VOF), front tracking, marker-and-cell (MAC) and lattice Boltzmann (LB) methods are all ‘one’ fluid methods. It is clear that there is no perfect method; each method has advantages and disadvantages which make it more appropriate for one kind of problem than for others. For instance, a LS method will accurately compute the curvature and the normal to the interface, but tends to loss mass which is physically incorrect. On the other hand, a VOF method will conserve mass up to machine precision, but the computation of the curvature and normal to the interface is not as accurate. In order to minimize the disadvantages of these methods, several authors have used two or more methods together to model two-phase flows. This is the case for the CLSVOF (Couple Level Set Volume Of Fluid) method, where LS and VOF are coupled together in order to better capture the interface. In CLSVOF, the level set function is used to compute the interface curvature and normal to the interface, while the volume of fluid function is used to capture the interface. For two-phase flows in microchannels, surface tension forces play an important role in determining the dynamics of bubbles whereas gravitational forces are generally negligible. Also it is very important to consider the interaction between the boundaries and the fluids by prescribing or computing the correct contact angle between them. The commercial CFD code FLUENT allows the use of static constant angles, or the use of User Defined Functions (UDF) to compute the dynamic contact angles. It is inappropriate to use a static contact angle to model cases involving moving
Concurrent growth of two phases in 2D space
A.A. Burbelko
2008-12-01
Full Text Available The kinetics of phase transformations has been studied within the framework of the Kolmogorov-Johnson-Mehl-Avrami (KJMA theory. This theory accurately describes only the parallel growth of anisotropic products with identical convex shape. The identical growth velocity distribution at an interface is the indispensable condition for the above restriction. The proposed earlier extension of KJMA theory (statistical theory of the screened growth enlarges the scope of its application and eliminates the above limitation. The results of the application of this extension were compared with the results obtained during modelling of the concurrent growth of the two types of circular particles on a plane, where the said particles were characterised by different growth rates and modelling was carried out by the method of cellular automata (CA.
Bubble Dynamics in a Two-Phase Medium
Jayaprakash, Arvind; Chahine, Georges
2010-01-01
The spherical dynamics of a bubble in a compressible liquid has been studied extensively since the early work of Gilmore. Numerical codes to study the behavior, including when large non-spherical deformations are involved, have since been developed and have been shown to be accurate. The situation is however different and common knowledge less advanced when the compressibility of the medium surrounding the bubble is provided mainly by the presence of a bubbly mixture. In one of the present works being carried out at DYNAFLOW, INC., the dynamics of a primary relatively large bubble in a water mixture including very fine bubbles is being investigated experimentally and the results are being provided to several parallel on-going analytical and numerical approaches. The main/primary bubble is produced by an underwater spark discharge from two concentric electrodes placed in the bubbly medium, which is generated using electrolysis. A grid of thin perpendicular wires is used to generate bubble distributions of vary...
Improvement of gas-liquid two-phase flow simulation methodology on unstructured grid
A high-precision gas-liquid two-phase flow simulation methodology has been developed based on a volume-of-fluid algorithm to simulate gas entrainment (GE) phenomena in sodium-cooled fast reactors. Since the GE is known to be strongly dependent on local velocity distribution formed by local structural configuration, an unstructured grid is employed in our simulation methodology to achieve an accurate modeling of system configuration. On unstructured grids, basic differential equations are usually discretized based on the collocated variable arrangement. However, it is well-known that the collocated variable arrangement often cause unphysical behaviors. We found that unphysical behaviors were induced near gas-liquid interfaces in two-phase simulations by the collocated variable arrangement. In this study, we first show that the unphysical behaviors are derived from inappropriate formulations of the momentum and velocity-pressure coupling equations. Then, improved formulations are mechanistically formulated considering the balance conditions of physical quantities. In the improved formulations, the velocities at interfacial regions are calculated using the volume fraction values and each phase's velocities. In addition, the pressure forces at the interfacial regions are calculated considering the balance with the surface tension forces. These new formulations were verified by simulating a rising air bubble in water. As the results, the improved formulations succeeded in eliminating unphysical velocity and pressure distributions near the bubble interface induced by the conventional formulations and gave the simulation results of the rising bubble shapes agreed well with experimental results. The simulations were conducted also on the unstructured grid and similar results with the results on the structured grid were obtained. (author)
Anti-diffusion method for interface steepening in two-phase incompressible flow
So, K. K.; Hu, X. Y.; Adams, N. A.
2011-06-01
In this paper, we present a method for obtaining sharp interfaces in two-phase incompressible flows by an anti-diffusion correction, that is applicable in a straight-forward fashion for the improvement of two-phase flow solution schemes typically employed in practical applications. The underlying discretization is based on the volume-of-fluid (VOF) interface-capturing method on unstructured meshes. The key idea is to steepen the interface, independently of the underlying volume-fraction transport equation, by solving a diffusion equation with reverse time, i.e. an anti-diffusion equation, after each advection time step of the volume fraction. As the solution of the anti-diffusion equation requires regularization, a limiter based on the directional derivative is developed for calculating the gradient of the volume fraction. This limiter ensures the boundedness of the volume fraction. In order to control the amount of anti-diffusion introduced by the correction algorithm we propose a suitable stopping criterion for interface steepening. The formulation of the limiter and the algorithm for solving the anti-diffusion equation are applicable to 3-dimensional unstructured meshes. Validation computations are performed for passive advection of an interface, for 2-dimensional and 3-dimensional rising-bubbles, and for a rising drop in a periodically constricted channel. The results demonstrate that sharp interfaces can be recovered reliably. They show that the accuracy is similar to or even better than that of level-set methods using comparable discretizations for the flow and the level-set evolution. Also, we observe a good agreement with experimental results for the rising drop where proper interface evolution requires accurate mass conservation.
Eulerian two-phase computational fluid dynamics for boiling water reactor core analysis
Traditionally, the analysis of two-phase boiling flows has relied on experimentally-derived correlations. This approach provides accurate predictions of channel-averaged temperatures and void fractions and even peak assembly temperatures within an assembly. However, it lacks the resolution needed to predict the detailed intra-channel distributions of temperature, void fraction and steaming rates that are needed to address the fuel reliability concerns which result from longer refueling cycles and higher burnup fuels, particularly for the prediction of potential fuel pin cladding failures resulting from growth of tenacious crud. As part of the ongoing effort to develop a high-fidelity, full-core, pin-by-pin, fully-coupled neutronic and thermal hydraulic simulation package for reactor core analysis], capabilities for Eulerian-Eulerian two-phase simulation within the commercial Computational Fluid Dynamics code Star-CD are being extended and validated for application to Boiling Water Reactor (BWR) cores. The extension of the existing capability includes the development of wall heat partitioning and bubble growth models, implementation of a topology map based approach that provides the necessary capability to switch between the liquid and vapor as the continuous phase on a cell-by-cell basis and the development of appropriate models for the inter-phase forces that influence the movement of bubbles and droplets. Two applications have been identified as an initial demonstration and validation of the implemented methodology. First, the model is being applied to an Atrium-10 fuel assembly from Cycle 11 of the River Bend Nuclear Power Plant. Second, the model is being applied to an international benchmark problem for validation of BWR assembly analysis methods. (authors)
Highlights: • Additional pressure drop caused by rolling motion is theoretically analyzed. • Fluctuation amplitude of pressure drop increases with increasing rolling amplitude. • Mass flux fluctuation varies with the fluctuation of frictional pressure drop. • Time average pressure drop under rolling motion is equal to that under steady state. • Phase lag between fluctuation of mass flux and pressure drop is 1/4 rolling period. - Abstract: In order to investigate the two-phase frictional pressure drop characteristics of boiling flow in a rectangular narrow channel under rolling motion, a series of experiments and theoretical analysis are performed. The results demonstrate that the total additional pressure drop fluctuation has the same period with the rolling motion, and the fluctuation amplitude increases with the increase of rolling amplitude and rolling frequency. The time average additional pressure drop is 2–3 orders of magnitude smaller than that of frictional pressure drop in the boiling region. The fluctuation amplitude of the two-phase frictional pressure drop increases with increasing rolling amplitude, rolling period and heat flux, while it decreases with the increase of system pressure. Compared with the additional pressure drop in two-phase regions the outlet quality of channel and the space variation of the experimental loop are the main reasons that induce the fluctuation of two-phase frictional pressure drop. The mass flux fluctuation varies with the fluctuation of two-phase frictional pressure drop, and the fluctuation amplitude of mass flux increases with the increase of rolling amplitude and rolling period. The phase lag between the fluctuation of mass flux and frictional pressure drop is approximately equal to 1/4 rolling period
Fracture toughness of two phase WC-Co cermets
The present analysis is an attempt to show that fracture toughness of cermets based on WC-Co and the like can be predicted with reasonable accuracy from a simple fracture mechanics relationship. The resistance to fracture has been considered to manifest primarily from the plastic deformation of Co phase. The constrained deformation behavior of the ductile Co phase between the rigid WC grains, approximated to the behavior of ideal plastic flow of a ductile layer sandwiched between rigid platens, has been incorporated into the fracture toughness predictions. Reasonable assumptions on in situ flow and fracture behavior of Co phase have been made in such estimations. Comparison of the calculated fracture toughness values with the experimental data of a large number of WC-Co systems of varying microstructural conditions, indicates reasonable agreement
Prestack wavefield approximations
Alkhalifah, Tariq
2013-09-01
The double-square-root (DSR) relation offers a platform to perform prestack imaging using an extended single wavefield that honors the geometrical configuration between sources, receivers, and the image point, or in other words, prestack wavefields. Extrapolating such wavefields, nevertheless, suffers from limitations. Chief among them is the singularity associated with horizontally propagating waves. I have devised highly accurate approximations free of such singularities which are highly accurate. Specifically, I use Padé expansions with denominators given by a power series that is an order lower than that of the numerator, and thus, introduce a free variable to balance the series order and normalize the singularity. For the higher-order Padé approximation, the errors are negligible. Additional simplifications, like recasting the DSR formula as a function of scattering angle, allow for a singularity free form that is useful for constant-angle-gather imaging. A dynamic form of this DSR formula can be supported by kinematic evaluations of the scattering angle to provide efficient prestack wavefield construction. Applying a similar approximation to the dip angle yields an efficient 1D wave equation with the scattering and dip angles extracted from, for example, DSR ray tracing. Application to the complex Marmousi data set demonstrates that these approximations, although they may provide less than optimal results, allow for efficient and flexible implementations. © 2013 Society of Exploration Geophysicists.
Optical Measurement of Mass Flow of a Two-Phase Fluid
Wiley, John; Pedersen, Kevin; Koman, Valentin; Gregory, Don
2008-01-01
An optoelectronic system utilizes wavelength-dependent scattering of light for measuring the density and mass flow of a two-phase fluid in a pipe. The apparatus was invented for original use in measuring the mass flow of a two-phase cryogenic fluid (e.g., liquid hydrogen containing bubbles of hydrogen gas), but underlying principles of operation can readily be adapted to non-cryogenic two-phase fluids. The system (see figure) includes a laser module, which contains two or more laser diodes, each operating at a different wavelength. The laser module also contains beam splitters that combine the beams at the various wavelengths so as to produce two output beams, each containing all of the wavelengths. One of the multiwavelength output beams is sent, via a multimode fiberoptic cable, to a transmitting optical coupler. The other multiwavelength output beam is sent, via another multimode fiber-optic cable, to a reference detector module, wherein fiber-optic splitters split the light into several multiwavelength beams, each going to a photodiode having a spectral response that is known and that differs from the spectral responses of the other photodiodes. The outputs of these photodiodes are digitized and fed to a processor, which executes an algorithm that utilizes the known spectral responses to convert the photodiode outputs to obtain reference laser-power levels for the various wavelengths. The transmitting optical coupler is mounted in (and sealed to) a hole in the pipe and is oriented at a slant with respect to the axis of the pipe. The transmitting optical coupler contains a collimating lens and a cylindrical lens that form the light emerging from the end of the fiber-optic cable into a fan-shaped beam in a meridional plane of the pipe. Receiving optical couplers similar to the transmitting optical couplers are mounted in the same meridional plane at various longitudinal positions on the opposite side of the pipe, approximately facing the transmitting optical
Presented are calculated dependences for adiabatic compressibility, isoentropy coefficient and thermodynamic sound velocity of a two-phase media with homogeneous disperse structure being in a state of equilibrium. The character of the change of the values mentioned for vapor water media at the change of vapor mass composition in the mixture from zero to 1 is shown. Comparison of the calculated data as to dependences obtained with the experimental ones for critical regimes of vapor-water flow outflow through short and long cylindrical channels with sharp entrance rims. The calculation error does not exceed approximately 12%. Analysis of the results obtained showed that at outflow through short channels of metastable vapor liquid flow the main characteristics, like at outflow through long channels, are determined by the pressure in the exit cross section, mass vapor content and specific volume of the mixture, which are calculated with account for real overheating of the liquid to the exit cross section. At critical regime of outflow through the very long channels, when one can not neglect hydraulic resistance in the channel and the process is not isoentropic, the pressure and mass vapor content in the exit cross section also unambiguously determine the value of adiabatic compressibility of two-phase media, sound velocity and isoentropy coefficient in the cross section. Conclusion is made that the dependences obtained can be used with sufficient for practical purposes accuracy when solving different engineering problems, as well as for the calculations of the mixture consumption at flow of the reactor contours NAI with WWR
Controlling the long-range corrections in atomistic Monte Carlo simulations of two-phase systems.
Goujon, Florent; Ghoufi, Aziz; Malfreyt, Patrice; Tildesley, Dominic J
2015-10-13
The long-range correction to the surface tension can amount to up to 55% of the calculated value of the surface tension for cutoffs in the range of 2.1-6.4 σ. The calculation of the long-range corrections to the surface tension and to the configurational energy in two-phase systems remains an active area of research. In this work, we compare the long-range corrections methods proposed by Guo and Lu ( J. Chem. Phys. 1997 , 106 , 3688 - 3695 ) and Janeček ( J. Phys. Chem. B 2006 , 110 , 6264 - 6269 ) for the calculation of the surface tension and of the coexisting densities in Monte Carlo simulations of the truncated Lennard-Jones potential and the truncated and shifted Lennard-Jones potential models. These methods require an estimate of the long-range correction at each step in the Monte Carlo simulation. We apply the full version of the Guo and Lu method, which involves the calculation of a double integral that contains a series of density differences, and we compare these results with the simplified version of the method which is routinely used in two-phase simulations. We conclude that the cutoff dependencies of the surface tension and coexisting densities are identical for the full versions of Guo and Lu and Janeček methods. We show that it is possible to avoid applying the long-range correction at every step by using the truncated Lennard-Jones potential with a cutoff rc ≥ 5 σ. The long-range correction can then be applied at the end of the simulation. The limiting factor in the accurate calculation of this final correction is an accurate estimate of the coexisting densities. Link-cell simulations performed using a cutoff rc = 5.5 σ require twice as much computing time as those with a more typical cutoff of rc = 3.0 σ. The application of the Janeček correction increases the running time of the simulation by less than 10%, and it can be profitably applied with the shorter cutoff. PMID:26574249
Order parameters of two phase transitions in ES-mixtures
Our model is the ES-mixture of ellipsoidal (E) and spherical (S) molecules dispersed on b.c.c. lattice with a ratio of concentration different from 1:1. Minimizing numerically the effective thermodynamic potential, obtained in the usual molecular-field approximation, we have studied the variation of the orientational and positional order parameters for different values of concentration, molecular parameter (of ellipsoidal molecules) and interaction constants. We have checked also the coupling effects arising from the interplay between orientational and positional degree of freedom. Determining the critical temperatures for two kinds of transitions we have obtained the (critical temperatures-concentration) phase diagram, where the transition lines define four regions corresponding to the completely disordered mixture, the only positionally ordered mixture, the only orientationally ordered mixture and the positionally and orientationally ordered mixture. Thus, in large line, our model of ES-mixture reproduces qualitatively some features of the behaviour of plastic and liquid crystals. (author). 20 refs, 7 figs
Understanding and predicting two-phase flow and heat transfer in porous media is of fundamental interest for a number of engineering applications. Examples include thermal technologies for remediation of contaminated subsurfaces, the extraction of geothermal energy from vapor-dominated reservoirs, and the assessment of high-level nuclear waste repositories. A numerical and experimental study is reported for two-phase flow and heat transfer in a horizontal porous formation with water through flow and partial heating from below. Based on a newly developed two-phase mixture model, numerical results of the temperature distribution, liquid saturation, liquid and vapor phase velocity fields are presented for three representative cases with varying inlet velocities. It is found that the resulting two-phase structure and flow patterns are strongly dependent upon the water inlet velocity and the bottom heat flux. The former parameter measures the flow along the horizontal direction, while the latter creates a relative motion between the phases in the vertical direction. Experiments are also performed to measure temperature distributions and to visualize the two-phase flow patterns. Qualitative agreement between experiments and numerical predictions is achieved. Overall, this combined experimental and numerical study has provided new insight into conjugate single- and two-phase flow and heat transfer in porous media, although future research is required if accurate modeling of these complex problems is to be accomplished
Touma, Rony; Zeidan, Dia
2016-06-01
In this paper we extend a central finite volume method on nonuniform grids to the case of drift-flux two-phase flow problems. The numerical base scheme is an unstaggered, non oscillatory, second-order accurate finite volume scheme that evolves a piecewise linear numerical solution on a single grid and uses dual cells intermediately while updating the numerical solution to avoid the resolution of the Riemann problems arising at the cell interfaces. We then apply the numerical scheme and solve a classical drift-flux problem. The obtained results are in good agreement with corresponding ones appearing in the recent literature, thus confirming the potential of the proposed scheme.
Ma, C.; Bothe, D.
2013-01-01
A one-field model is derived from the sharp interface continuum mechanical balances for two-phase evaporative and thermocapillary flows. Emphasis is put on a clear distinction of the different velocities at the interface which appear due to phase transfer. The one-field model is solved numerically within a Finite Volume scheme and the interface is captured using an extended Volume of Fluid method, where the interface is reconstructed linearly with the PLIC technique. The numerical heat transfer is based on a two-scalar approach where two separate temperature fields are used for the temperature inside the two phases. This results in an accurate treatment of the interfacial heat transfer, specifically the interface temperature which is crucial numerically, both for evaporation and thermocapillarity. The method is validated for two-phase heat conduction, with analytical solution in case of no evaporation and with experimental measurement in case of incorporated evaporation effect. The method is applied to realistic cases dealing with non-uniformly heated thin liquid films, i.e. liquid films on (i) structured heated substrates and (ii) locally heated substrates. The numerical predictions in terms of flow pattern, surface deformation, temperature and velocity are compared with experiments conducted at the Université Libre de Bruxelles for (i) and at the Technische Universität Darmstadt for (ii). Qualitative agreement is achieved and shows the potential of this approach to simulate thermocapillary flows with dynamically deformable interfaces combined with evaporation.
Characteristics of low-mass-velocity vertical gas-liquid two-phase flow
Low-mass-velocity two-phase flow in a vertical pipe shows lower void fraction than high-mass-velocity two-phase flow even though their qualities are the same. In order to clarify the flow characteristics of the low-mass-velocity two-phase flow, air-water two-phase flow experiments were conducted under the froth or annular flow conditions. Experimental results show that wall shear stress is positive even though both gas and liquid superficial velocities are positive. Measured water film average velocity is negative under this condition. These results indicate that local flow reversal should exist along the channel wall. This local flow reversal gives to the low void fraction in low-mass-velocity two-phase flow. It is also clarified that the drift flux model can be applied to the low-mass-velocity two-phase flow with local reversal. (author)
Highlights: ► A numerical technique for transient two-phase flow in a vertical channel using the Drift Flux Model is presented. ► The proposed model was validated for wide range two-phase flow parameters. ► Good agreement between the predicted void fraction, RELAP5 code and the experimental data was obtained. ► The analysis lead to a better understanding of the basic mechanism of sub-cooled flow boiling. ► It was concluded that the model predicts the void fraction in two phase flow with sufficient accuracy. - Abstract: This paper presents a numerical solution of one-dimensional transient two-phase flow in a vertical channel using the Drift Flux Model (DFM). The DFM treats the two phases as a mixture, but allows slippage between the gas and the liquid phase. The DFM was used for the calculation of velocity and fraction of each phase, combined with the most relevant closure relationships models for condensation, wall evaporation, and phasic velocities. The solution of the three conservation equations for the mixture and a continuity equation for the gas phases is obtained by a semi-implicit numerical method. A finite volume method is used to discretize the governing equations on a staggered grid in the computational domain. Satisfactory agreement is shown between predicted void fraction, RELAP5 code and available experimental data under both transient and steady state conditions. Numerical solution was also obtained for a wide two-phase flow conditions: system pressure, surface heat flux, mass flow rate and inlet sub-cooling to check the model ability to predict void fraction accurately. It is concluded, therefore, that the DFM is able to predict void fraction in subcooled flow boiling with sufficient accuracy. For pressures lower than 30 bars, the DFM overestimated the void fraction in comparison with the experimental data by about 15%. The model requires less computational power to simulate than other approaches and has no limitations on the nodalization
Towards accurate modeling of moving contact lines
Holmgren, Hanna
2015-01-01
The present thesis treats the numerical simulation of immiscible incompressible two-phase flows with moving contact lines. The conventional Navier–Stokes equations combined with a no-slip boundary condition leads to a non-integrable stress singularity at the contact line. The singularity in the model can be avoided by allowing the contact line to slip. Implementing slip conditions in an accurate way is not straight-forward and different regularization techniques exist where ad-hoc procedures ...
EXPERIMENTAL STUDY OF AIR-WATER TWO-PHASE FLOW IN PARALLEL HELICALLY COILED PIPES
Panella, Bruno
2012-01-01
The air-water two-phase flow in a 12 mm inner diameter parallel helically coiled pipes is investigated with three different coils diameters. Void fraction, flow rate distribution and two-phase pressure drops along the pipes in the parallel channels are measured. The test two-phase pressure drops are compared with theoretical ones, in terms of multipliers and friction factors. The instabilities arisen during the experimental tests are investigated and are related to the void fraction and flow ...
Development of methods for mass flow measurement of non-stationary two-phase flows
The topics of the present work are: 1) functioning and testing of a True Mass Flow Meter (TMFM), 2) development of an infra-red absorption measuring process to determine the single components and the mass flows in a non-stationary air/water two-phase flow, 3) presentation of a radionuclide measuring method to measure two-phase mass flow, 4) description of a test stand to calibrate various two-phase mass flow measuring methods. (RW/LH)
On the Existence of Two-Phase Fluid in Good Communication with Liquid Water
Grant, Malcolm A.
1980-12-16
It has been argued that wells of high discharge enthalpy (two-phase wells) at Baca must be isolated from communication with an extensive liquid reservoir. It is shown that such communication has existed, and been maintained, during the history of Wairakei and Broadlands fields. Interpretation of downhole measurements in two-phase fields, and the nature of the two-phase reservoir fluid, is also treated.
Mathematical models for two-phase stratified pipe flow
Biberg, Dag
2005-06-01
The simultaneous transport of oil, gas and water in a single multiphase flow pipe line has for economical and practical reasons become common practice in the gas and oil fields operated by the oil industry. The optimal design and safe operation of these pipe lines require reliable estimates of liquid inventory, pressure drop and flow regime. Computer simulations of multiphase pipe flow have thus become an important design tool for field developments. Computer simulations yielding on-line monitoring and look ahead predictions are invaluable in day-to-day field management. Inaccurate predictions may have large consequences. The accuracy and reliability of multiphase pipe flow models are thus important issues. Simulating events in large pipelines or pipeline systems is relatively computer intensive. Pipe-lines carrying e.g. gas and liquefied gas (condensate) may cover distances of several hundred km in which transient phenomena may go on for months. The evaluation times associated with contemporary 3-D CFD models are thus not compatible with field applications. Multiphase flow lines are therefore normally simulated using specially dedicated 1-D models. The closure relations of multiphase pipe flow models are mainly based on lab data. The maximum pipe inner diameter, pressure and temperature in a multiphase pipe flow lab is limited to approximately 0.3 m, 90 bar and 60{sup o}C respectively. The corresponding field values are, however, much higher i.e.: 1 m, 1000 bar and 200{sup o}C respectively. Lab data does thus not cover the actual field conditions. Field predictions are consequently frequently based on model extrapolation. Applying field data or establishing more advanced labs will not solve this problem. It is in fact not practically possible to acquire sufficient data to cover all aspects of multiphase pipe flow. The parameter range involved is simply too large. Liquid levels and pressure drop in three-phase flow are e.g. determined by 13 dimensionless parameters
The design of a two-phase radiolabelled meal for gastric emptying studies
A meal intended for use in gastric emptying studies must be highly reproducible, must provide a normal physiological stimulus in terms of bulk, calorie content and composition and must employ stable radiotracers which accurately reflect in their biodistribution, the fate of the two-phases. This is particularly important in a field, such as gastric emptying, where so many variables may influence the results. A conventional pancake and orange juice were chosen as suitable vehicles for the solid and liquid phases. 111In-labelled resin beads were used as the solid-phase marker and a variety of 99Tcm-labelled radiopharmaceuticals including pertechnetate, DTPA and colloid forms were investigated as liquid-phase markers. Prior to administration to patients, the stability of the phases and their interactions in vitro were investigated. The use of 99Tcm-DTPA resulted in a loss of 111In from solid to liquid phase. All non-colloidal markers exhibited a tendency for adsorption onto solid phase. Colloidal markers including rhenium and antimony sulphide colloids showed the truest delineation of the liquid phase. (author)
Migration of rigid particles in two-phase shear flow of viscoelastic fluids
Anderson, Patrick; Jaensson, Nick; Hulsen, Martien
2015-11-01
In the Stokes regime, non-Brownian, rigid particles in a shear flow will not migrate across streamlines if the fluid is Newtonian. In viscoelastic fluids, however, particles will migrate across streamlines away from areas of higher elastic stresses, e.g. towards the outer cylinder in a wide-gap Couette flow. This migration is believed to be due to a difference in normal stresses. We simulate the two-phase case where this difference in normal stresses is not due to the flow field, but rather due to the properties of the fluids. We apply the diffuse-interface model for the interface between the two fluids, which can naturally handle a changing topology of the interface, e.g. during particle adsorption. Furthermore, the diffuse-interface model includes an accurate description of surface tension and can be used for a moving contact line. A sharp interface is assumed between the particles and the fluids. Initially, a particle is placed close to an interface of two fluids with different viscoelastic properties in a shear flow. We show that based on the properties of the fluids and the interfacial tension, four regimes can be defined: 1) migration away from the interface, 2) halted migration towards the interface, 3) adsorption of the particle at the interface and 4) penetration of the particle into the other fluid. This research forms part of the research programme of the Dutch Polymer Institute (DPI), Project #746.
Gradient-augmented hybrid interface capturing method for incompressible two-phase flow
Zheng, Fu; Shi-Yu, Wu; Kai-Xin, Liu
2016-06-01
Motivated by inconveniences of present hybrid methods, a gradient-augmented hybrid interface capturing method (GAHM) is presented for incompressible two-phase flow. A front tracking method (FTM) is used as the skeleton of the GAHM for low mass loss and resources. Smooth eulerian level set values are calculated from the FTM interface, and are used for a local interface reconstruction. The reconstruction avoids marker particle redistribution and enables an automatic treatment of interfacial topology change. The cubic Hermit interpolation is employed in all steps of the GAHM to capture subgrid structures within a single spacial cell. The performance of the GAHM is carefully evaluated in a benchmark test. Results show significant improvements of mass loss, clear subgrid structures, highly accurate derivatives (normals and curvatures) and low cost. The GAHM is further coupled with an incompressible multiphase flow solver, Super CE/SE, for more complex and practical applications. The updated solver is evaluated through comparison with an early droplet research. Project supported by the National Natural Science Foundation of China (Grant Nos. 10972010, 11028206, 11371069, 11372052, 11402029, and 11472060), the Science and Technology Development Foundation of China Academy of Engineering Physics (CAEP), China (Grant No. 2014B0201030), and the Defense Industrial Technology Development Program of China (Grant No. B1520132012).
Determination of volume fractions in two-phase flows from sound speed measurement
Chaudhuri, Anirban [Los Alamos National Laboratory; Sinha, Dipen N. [Los Alamos National Laboratory; Osterhoudt, Curtis F. [University of Alaska
2012-08-15
Accurate measurement of the composition of oil-water emulsions within the process environment is a challenging problem in the oil industry. Ultrasonic techniques are promising because they are non-invasive and can penetrate optically opaque mixtures. This paper presents a method of determining the volume fractions of two immiscible fluids in a homogenized two-phase flow by measuring the speed of sound through the composite fluid along with the instantaneous temperature. Two separate algorithms are developed by representing the composite density as (i) a linear combination of the two densities, and (ii) a non-linear fractional formulation. Both methods lead to a quadratic equation with temperature dependent coefficients, the root of which yields the volume fraction. The densities and sound speeds are calibrated at various temperatures for each fluid component, and the fitted polynomial is used in the final algorithm. We present results when the new algorithm is applied to mixtures of crude oil and process water from two different oil fields, and a comparison of our results with a Coriolis meter; the difference between mean values is less than 1%. Analytical and numerical studies of sensitivity of the calculated volume fraction to temperature changes and calibration errors are also presented.
Zeng, Chao-Xi; Xin, Rui-Pu; Qi, Sui-Jian; Yang, Bo; Wang, Yong-Hua
2016-02-01
Aqueous two-phase systems, based on the use of natural quaternary ammonium compounds, were developed to establish a benign biotechnological route for efficient protein separation. In this study, aqueous two-phase systems of two natural resources betaine and choline with polyethyleneglycol (PEG400/600) or inorganic salts (K2 HPO4 /K3 PO4 ) were formed. It was shown that in the K2 HPO4 -containing aqueous two-phase system, hydrophobic interactions were an important driving force of protein partitioning, while protein size played a vital role in aqueous two-phase systems that contained polyethylene glycol. An extraction efficiency of more than 90% for bovine serum albumin in the betaine/K2 HPO4 aqueous two-phase system can be obtained, and this betaine-based aqueous two-phase system provided a gentle and stable environment for the protein. In addition, after investigation of the cluster phenomenon in the betaine/K2 HPO4 aqueous two-phase systems, it was suggested that this phenomenon also played a significant role for protein extraction in this system. The development of aqueous two-phase systems based on natural quaternary ammonium compounds not only provided an effective and greener method of aqueous two-phase system to meet the requirements of green chemistry but also may help to solve the mystery of the compartmentalization of biomolecules in cells. PMID:26447826
Clive R McMahon
Full Text Available Generally, sigmoid curves are used to describe the growth of animals over their lifetime. However, because growth rates often differ over an animal's lifetime a single curve may not accurately capture the growth. Broken-stick models constrained to pass through a common point have been proposed to describe the different growth phases, but these are often unsatisfactory because essentially there are still two functions that describe the lifetime growth. To provide a single, converged model to age animals with disparate growth phases we developed a smoothly joining two-phase nonlinear function (SJ2P, tailored to provide a more accurate description of lifetime growth of the macropod, the Tasmanian pademelon Thylogale billardierii. The model consists of the Verhulst logistic function, which describes pouch-phase growth--joining smoothly to the Brody function, which describes post-pouch growth. Results from the model demonstrate that male pademelons grew faster and bigger than females. Our approach provides a practical means of ageing wild pademelons for life history studies but given the high variability of the data used to parametrise the second growth phase of the model, the accuracy of ageing of post-weaned animals is low: accuracy might be improved with collection of longitudinal growth data. This study provides a unique, first robust method that can be used to characterise growth over the lifespan of pademelons. The development of this method is relevant to collecting age-specific vital rates from commonly used wildlife management practices to provide crucial insights into the demographic behaviour of animal populations.
This thesis is devoted to the study of the Riemann problem and the construction of Godunov type numerical schemes for one or two dimensional two-phase flow models. In the first part, we study the Riemann problem for the well-known Drift-Flux, model which has been widely used for the analysis of thermal hydraulics transients. Then we use this study to construct approximate Riemann solvers and we describe the corresponding Godunov type schemes for simplified equation of state. For computation of complex two-phase flows, a weak formulation of Roe's approximate Riemann solver, which gives a method to construct a Roe-averaged jacobian matrix with a general equation of state, is proposed. For two-dimensional flows, the developed methods are based upon an approximate solver for a two-dimensional Riemann problem, according to Harten-Lax-Van Leer principles. The numerical results for standard test problems show the good behaviour of these numerical schemes for a wide range of flow conditions
Dahms, Rainer N.
2016-04-01
A generalized framework for multi-component liquid injections is presented to understand and predict the breakdown of classic two-phase theory and spray atomization at engine-relevant conditions. The analysis focuses on the thermodynamic structure and the immiscibility state of representative gas-liquid interfaces. The most modern form of Helmholtz energy mixture state equation is utilized which exhibits a unique and physically consistent behavior over the entire two-phase regime of fluid densities. It is combined with generalized models for non-linear gradient theory and for liquid injections to quantify multi-component two-phase interface structures in global thermal equilibrium. Then, the Helmholtz free energy is minimized which determines the interfacial species distribution as a consequence. This minimal free energy state is demonstrated to validate the underlying assumptions of classic two-phase theory and spray atomization. However, under certain engine-relevant conditions for which corroborating experimental data are presented, this requirement for interfacial thermal equilibrium becomes unsustainable. A rigorously derived probability density function quantifies the ability of the interface to develop internal spatial temperature gradients in the presence of significant temperature differences between injected liquid and ambient gas. Then, the interface can no longer be viewed as an isolated system at minimal free energy. Instead, the interfacial dynamics become intimately connected to those of the separated homogeneous phases. Hence, the interface transitions toward a state in local equilibrium whereupon it becomes a dense-fluid mixing layer. A new conceptual view of a transitional liquid injection process emerges from a transition time scale analysis. Close to the nozzle exit, the two-phase interface still remains largely intact and more classic two-phase processes prevail as a consequence. Further downstream, however, the transition to dense-fluid mixing
Celia, Michael A.; Binning, Philip John
1992-01-01
A numerical algorithm for simulation of two-phase flow in porous media is presented. The algorithm is based on a modified Picard linearization of the governing equations of flow, coupled with a lumped finite element approximation in space and dynamic time step control. Numerical results indicate......'s equation is valid. Numerical results also demonstrate the potential importance of air phase advection when considering contaminant transport in unsaturated soils. Comparison to several other numerical algorithms shows that the modified Picard approach offers robust, mass conservative solutions to the...
Multi-scale diffuse interface modeling of multi-component two-phase flow with partial miscibility
Kou, Jisheng
2016-05-10
In this paper, we introduce a diffuse interface model to simulate multi-component two-phase flow with partial miscibility based on a realistic equation of state (e.g. Peng-Robinson equation of state). Because of partial miscibility, thermodynamic relations are used to model not only interfacial properties but also bulk properties, including density, composition, pressure, and realistic viscosity. As far as we know, this effort is the first time to use diffuse interface modeling based on equation of state for modeling of multi-component two-phase flow with partial miscibility. In numerical simulation, the key issue is to resolve the high contrast of scales from the microscopic interface composition to macroscale bulk fluid motion since the interface has a nanoscale thickness only. To efficiently solve this challenging problem, we develop a multi-scale simulation method. At the microscopic scale, we deduce a reduced interfacial equation under reasonable assumptions, and then we propose a formulation of capillary pressure, which is consistent with macroscale flow equations. Moreover, we show that Young-Laplace equation is an approximation of this capillarity formulation, and this formulation is also consistent with the concept of Tolman length, which is a correction of Young-Laplace equation. At the macroscopical scale, the interfaces are treated as discontinuous surfaces separating two phases of fluids. Our approach differs from conventional sharp-interface two-phase flow model in that we use the capillary pressure directly instead of a combination of surface tension and Young-Laplace equation because capillarity can be calculated from our proposed capillarity formulation. A compatible condition is also derived for the pressure in flow equations. Furthermore, based on the proposed capillarity formulation, we design an efficient numerical method for directly computing the capillary pressure between two fluids composed of multiple components. Finally, numerical tests
Multi-scale diffuse interface modeling of multi-component two-phase flow with partial miscibility
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
Bubble Generation in a Flowing Liquid Medium and Resulting Two-Phase Flow in Microgravity
Pais, S. C.; Kamotani, Y.; Bhunia, A.; Ostrach, S.
1999-01-01
The present investigation reports a study of bubble generation under reduced gravity conditions, using both a co-flow and a cross-flow configuration. This study may be used in the conceptual design of a space-based thermal management system. Ensuing two-phase flow void fraction can be accurately monitored using a single nozzle gas injection system within a continuous liquid flow conduit, as utilized in the present investigation. Accurate monitoring of void fraction leads to precise control of heat and mass transfer coefficients related to a thermal management system; hence providing an efficient and highly effective means of removing heat aboard spacecraft or space stations. Our experiments are performed in parabolic flight aboard the modified DC-9 Reduced Gravity Research Aircraft at NASA Lewis Research Center, using an air-water system. For the purpose of bubble dispersion in a flowing liquid, we use both a co-flow and a cross-flow configuration. In the co-flow geometry, air is introduced through a nozzle in the same direction with the liquid flow. On the other hand, in the cross-flow configuration, air is injected perpendicular to the direction of water flow, via a nozzle protruding inside the two-phase flow conduit. Three different flow conduit (pipe) diameters are used, namely, 1.27 cm, 1.9 cm and 2.54 cm. Two different ratios of nozzle to pipe diameter (D(sub N))sup * are considered, namely (D(sub N))sup * = 0.1 and 0.2, while superficial liquid velocities are varied from 8 to 70 cm/s depending on flow conduit diameter. It is experimentally observed that by holding all other flow conditions and geometry constant, generated bubbles decrease in size with increase in superficial liquid velocity. Detached bubble diameter is shown to increase with air injection nozzle diameter. Likewise, generated bubbles grow in size with increasing pipe diameter. Along the same lines, it is shown that bubble frequency of formation increases and hence the time to detachment of a
Two-phase flow research using the DC-9/KC-135 apparatus
McQuillen, John B.; Neumann, Eric S.; Shoemaker, J. Michael
1996-01-01
Low-gravity gas-liquid flow research can be conducted aboard the NASA Lewis Research Center DC-9 or the Johnson Space Center KC-135. Air and water solutions serve as the test liquids in cylindrical test sections with constant or variable inner diameters of approximately 2.54 cm and lengths of up to 3.0 m. Superficial velocities range from 0.1 to 1.1 m/sec for liquids and from 0.1 to 25 m/sec for air. Flow rate, differential pressure, void fraction, film thickness, wall shear stress, and acceleration data are measured and recorded at data rates of up to 1000 Hz throughout the 20-sec duration of the experiment. Flow is visualized with a high-speed video system. In addition, the apparatus has a heat-transfer capability whereby sensible heat is transferred between the test-section wall and a subcooled liquid phase so that the heat-transfer characteristics of gas-liquid two-phase flows can be determined.
Unsteady MHD two-phase Couette flow of fluid-particle suspension in an annulus
Basant K. Jha
2011-12-01
Full Text Available The problem of two-phase unsteady MHD flow between two concentric cylinders of infinite length has been analysed when the outer cylinder is impulsively started. The system of partial differential equations describing the flow problem is formulated taking the viscosity of the particle phase into consideration. Unified closed form expressions are obtained for the velocities and the skin frictions for both cases of the applied magnetic field being fixed to either the fluid or the moving outer cylinder. The problem is solved using a combination of the Laplace transform technique, D’Alemberts and the Riemann-sum approximation methods. The solution obtained is validated by comparisons with the closed form solutions obtained for the steady states which has been derived separately. The governing equations are also solved using the implicit finite difference method to verify the present proposed method. The variation of the velocity and the skin friction with the dimensionless parameters occuring in the problem are illustrated graphically and discussed for both phases.
A new treatment of capillarity to improve the stability of IMPES two-phase flow formulation
Kou, Jisheng
2010-12-01
In this paper, we present an efficient numerical method for two-phase immiscible flow in porous media with different capillarity pressures. In highly heterogeneous permeable media, the saturation is discontinuous due to different capillary pressure functions. One popular scheme is to split the system into a pressure and a saturation equation, and to apply IMplicit Pressure Explicit Saturation (IMPES) approach for time stepping. One disadvantage of IMPES is instability resulting from the explicit treatment for capillary pressure. To improve stability, the capillary pressure is usually incorporated in the saturation equation which gradients of saturation appear. This approach, however, does not apply to the case of different capillary pressure functions for multiple rock-types, because of the discontinuity of saturation across rock interfaces. In this paper, we present a new treatment of capillary pressure, which appears implicitly in the pressure equation. Using an approximation of capillary function, we substitute the implicit saturation equation into the pressure equation. The coupled pressure equation will be solved implicitly and followed by the explicit saturation equation. Five numerical examples are provided to demonstrate the advantages of our approach. Comparison shows that our proposed method is more efficient and stable than the classical IMPES approach. © 2010 Elsevier Ltd.
Sorting microparticles into lateral streams using a two-phase rectangular electrokinetic array
In this paper, we study microparticles in liquid suspension streaming around a closed rectangular track and present lateral sorting of the particles into focused streams. The track consists of a two-phase interdigitated electrode array with symmetric electrodes but asymmetric electrode spacing. We demonstrate the ability to consistently focus an initially scattered suspension of mono-size polystyrene particles into a single narrow stream traveling around the circuit. We also demonstrate the ability of the device to separate suspensions of multiple sphere sizes into distinct streams according to size. We report that focusing positions are generally consistent for a given particle size, regardless of the presence of other particles in the suspension, and that particles sort by decreasing size from the center to the edge of the track. These results are compared with finite element analysis of the steady-state electric field and analytical approximations of the electrokinetic forces. We hypothesize that the sorting is due to a balance between phase-based and gradient-based dielectrophoretic forces
On Internet Traffic Classification: A Two-Phased Machine Learning Approach
Taimur Bakhshi
2016-01-01
Full Text Available Traffic classification utilizing flow measurement enables operators to perform essential network management. Flow accounting methods such as NetFlow are, however, considered inadequate for classification requiring additional packet-level information, host behaviour analysis, and specialized hardware limiting their practical adoption. This paper aims to overcome these challenges by proposing two-phased machine learning classification mechanism with NetFlow as input. The individual flow classes are derived per application through k-means and are further used to train a C5.0 decision tree classifier. As part of validation, the initial unsupervised phase used flow records of fifteen popular Internet applications that were collected and independently subjected to k-means clustering to determine unique flow classes generated per application. The derived flow classes were afterwards used to train and test a supervised C5.0 based decision tree. The resulting classifier reported an average accuracy of 92.37% on approximately 3.4 million test cases increasing to 96.67% with adaptive boosting. The classifier specificity factor which accounted for differentiating content specific from supplementary flows ranged between 98.37% and 99.57%. Furthermore, the computational performance and accuracy of the proposed methodology in comparison with similar machine learning techniques lead us to recommend its extension to other applications in achieving highly granular real-time traffic classification.
Research on network model of gas-liquid two-phase
A general modeling approach of the two-phase flow network system is studied. Based on the homogeneous phase model, a model of non-loss and mean friction two-phase flow network model and parameter-impedance and admittance are given. The advice to the non-homogeneous phase model is given
Mass flow rate measurements in two-phase mixtrues with stagnation probes
Applications of stagnation probes to the measurement of mass flow rate in two-phase flows are discussed. Descriptions of several stagnation devices, which have been evaluated at the Idaho National Engineering Laboratory, are presented along with modeling techniques and two-phase flow data
刘洋; 魏修成
2003-01-01
Based on Biot theory of two-phase anisotropic media and Hamilton theory about dynamic problem, finite elementequations of elastic wave propagation in two-phase anisotropic media are derived in this paper. Numerical solutionof finite element equations is given. Finally, properties of elastic wave propagation are observed and analyzedthrough FEM modeling.
Interchannel stability analysis of oscillatory instable parallel channel two phase flow regimes
Conditions for interchannel hydrodynamic stability of oscillatory unstable parallel channel two-phase flow regimes are being analysed. For experimental determined transfer functions Nyquist diagrams for one-phase and two-phase flow regimes are being considered. The results are presented show interchannel stability oscillatory unstable linear experimental regimes and interchannel instability nonlinear experimental regimes
Symmetrical components and power analysis for a two-phase microgrid system
Alibeik, M.; Santos Jr., E. C. dos; Blaabjerg, Frede
2014-01-01
This paper presents a mathematical model for the symmetrical components and power analysis of a new microgrid system consisting of three wires and two voltages in quadrature, which is designated as a two-phase microgrid. The two-phase microgrid presents the following advantages: 1) constant power...
A Matrix Converter Producing Two Phase Supply From Single Phase Supply
Trupti.L.Bonde
2014-02-01
Full Text Available Abstract-This paper describes a matrix converter which gives a two phase supply as an output. The said matrix converter is devoid of any energy storage element. This output is used for running two phase induction motor.
Mass flow rate measurements in two-phase mixtrues with stagnation probes. [PWR
Fincke, J.R.; Deason, V.A.
1979-01-01
Applications of stagnation probes to the measurement of mass flow rate in two-phase flows are discussed. Descriptions of several stagnation devices, which have been evaluated at the Idaho National Engineering Laboratory, are presented along with modeling techniques and two-phase flow data.
Numerical simulation for gas-liquid two-phase flow in pipe networks
The complex pipe network characters can not directly presented in single phase flow, gas-liquid two phase flow pressure drop and void rate change model. Apply fluid network theory and computer numerical simulation technology to phase flow pipe networks carried out simulate and compute. Simulate result shows that flow resistance distribution is non-linear in two phase pipe network
Numerical Simulation Of Hydrothermal Processes In Lake Drukshiai: 5. The Two-Phase Model
The state of two-phase 'liquid-gas' flow has been modeled numerically by the three-dimensional method of a complex research of heat and mass transfer. This allows examining the interaction of some transfer processes in a natural cooling basin (Lake Drukshiai): the power and direction of the wind, the variable density of the water, the heat conduction and heat transfer coefficients of the water-air interface. The combined effect of these natural actions determines the heat amount that the basin is able to dissipate to the surrounding atmospheric medium in thermal equilibrium (no change in the mean water temperature). This article presents a number of most widely used expressions for vertical and horizontal heat transfer coefficients. Basing on the stream velocity and mean temperature profiles measured in the cooling pond, as well as on then-time variations, suggestions are made that the mixing rate at the water surface is caused by the natural space-time variation of the wind and can be described by the value of the eddy viscosity coefficient - 1 m2/s (in numerical modeling 0.9-1.3 m2/s were used). The wind influence on the surface of the lake, according to the experimental data, is 1-3% of the mean wind velocity. The model is applied for a moderate wind, approximately 1-5 m/s of the mean wind velocity. A comparison of the experimental and numerical results showed a qualitative agreement. For a better quantitative approximation it is necessary to have more boundary conditions variable with time and to solve the unsteady set equations for transfer processes. (author)
A MODEL FOR PREDICTING PHASE INVERSION IN OIL-WATER TWO-PHASE PIPE FLOW
GONG Jing; LI Qing-ping; YAO Hai-yuan; YU Da
2006-01-01
Experiments of phase inversion characteristics for horizontal oil-water two-phase flow in a stainless steel pipe loop (25.7 mm inner diameter,52 m long) are conducted. A new viewpoint is brought forward about the process of phase inversion in oil-water two-phase pipe flow. Using the relations between the total free energies of the pre-inversion and post-inversion dispersions, a model for predicting phase inversion in oil-water two-phase pipe flow has been developed that considers the characteristics of pipe flow. This model is compared against other models with relevant data of phase inversion in oil-water two-phase pipe flow. Results indicate that this model is better than other models in terms of calculation precision and applicability. The model is useful for guiding the design for optimal performance and safety in the operation of oil-water two-phase pipe flow in oil fields.
Geometric effects of 90-degree vertical elbows on global two-phase flow parameters
Geometric effects of 90-degree vertical elbows on global two-phase flow parameters, in particular pressure drop and flow regime transition are investigated. Pressure measurements are obtained along the test section over a wide range of flow conditions in both single-phase and two-phase flow conditions. A two-phase pressure drop correlation analogous to Lockhart-Martinelli correlation is proposed to predict the minor loss across the elbows. Flow visualization is performed to study the effect of elbows on the two-phase flow regime transition. Modified flow regime maps for horizontal and vertical-downward two-phase flow are obtained which demonstrate that downstream of the elbows flow regime transition boundaries deviate significantly from the conventional flow regime transition boundaries. (author)
Michal Prazenica; Branislav Dobrucky; Peter Sekerak; Lukas Kalamen
2011-01-01
This paper deals with the two-stage two-phase electronic systems with orthogonal output voltages and currents - DC/AC/AC. Design of two-stage DC/AC/AC high frequency converter with two-phase orthogonal output using single-phase matrix converter is also introduced. Output voltages of them are strongly nonharmonic ones, so they must be pulse-modulated due to requested nearly sinusoidal currents with low total harmonic distortion. Simulation experiment results of matrix converter for both steady...
Hasan, Abbas; Lucas, Gary
2007-01-01
In two phase flow, differential pressures technique can be used to measure the volume fraction of the gas phase. In the case where no restriction is available in the pipeline, the differential pressure technique can be used only in vertical or inclined pipelines. Two phase air-water pressure drop across a Venturi meter may change its sign from positive to negative due to change in the compressibility of the gas phase. In other words, the inlet of the venturi (upstream section) is not...
Stability of two phase natural convection in a rectangular loop with a vertical three rod heater
Full text of publication follows: Nuclear Reactors are being designed which incorporate the concept of two-phase natural convection for removing heat generated in the core. Stability of natural convection systems is, in general, an important consideration. Much of the experimental data available for stability of natural convection systems is at high pressures while during startup pressures may be quite small; also, data with single annular heater elements are mostly reported. An experimental study is conducted here for determining the stability limits for two-phase natural convection in a rectangular loop with two types of heaters - an annulus heater and a three-rod cluster heater. The experimental test setup consists of a vertical heated section, a condenser section and a vertical downcomer section. The experiments were performed at atmospheric conditions and the test section is transparent for easy visualization of the flow. The steady state natural convection data matched well with that reported in the literature. The stability boundaries of the system were experimentally determined at different values of the input power and inlet subcooling and represented in terms of the appropriate non-dimensional numbers. The stability characteristics of the rectangular loop were numerically evaluated using the nonlinear stability analysis reported in the literature. The one dimensional mass, momentum and energy equations integrated in the spatial dimension using a linear enthalpy approximation within a control volume were solved numerically in the time domain to obtain the stability characteristics of the loop. A single-phase characterization of the loop was performed to obtain the frictional pressure drop inputs required for the calculations. The average friction from all the heater elements and the overall heat per unit length was used for the numerical calculations in the three rod heater case. The experimental results were closer to the numerically calculated results
Analysis of free-surface flows through energy considerations: Single-phase versus two-phase modeling
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.
Two-phase flow and transport in the air cathode of proton exchange membrane fuel cells
Wang, Z. H.; Wang, C. Y.; Chen, K. S.
Two-phase flow and transport of reactants and products in the air cathode of proton exchange membrane (PEM) fuel cells is studied analytically and numerically. Single- and two-phase regimes of water distribution and transport are classified by a threshold current density corresponding to first appearance of liquid water at the membrane/cathode interface. When the cell operates above the threshold current density, liquid water appears and a two-phase zone forms within the porous cathode. A two-phase, multicomponent mixture model in conjunction with a finite-volume-based computational fluid dynamics (CFD) technique is applied to simulate the cathode operation in this regime. The model is able to handle the situation where a single-phase region co-exists with a two-phase zone in the air cathode. For the first time, the polarization curve as well as water and oxygen concentration distributions encompassing both single- and two-phase regimes of the air cathode are presented. Capillary action is found to be the dominant mechanism for water transport inside the two-phase zone of the hydrophilic structure. The liquid water saturation within the cathode is predicted to reach 6.3% at 1.4 A cm -2 for dry inlet air.
Two-Dimensional Numerical Simulation of Boiling Two-Phase Flow of Liquid Nitrogen
Ishimoto, Jun; Oike, Mamoru; Kamijo, Kenjiro
Two-dimensional characteristics of the boiling two-phase flow of liquid nitrogen in a duct flow are numerically investigated to contribute to the further development of new high-performance cryogenic engineering applications. First, the governing equations of the boiling two-phase flow of liquid nitrogen based on the unsteady drift-flux model are presented and several flow characteristics are numerically calculated taking account the effect of cryogenic flow states. Based on the numerical results, a two-dimensional structure of the boiling two-phase flow of liquid nitrogen is shown in detail, and it is found that the phase change of liquid nitrogen occurs in quite a short time interval compared with that of two-phase pressurized water at high temperature. Next, it is clarified that the distributions of pressure and the void fraction in a two-phase flow show a tendency different from those of fluids at room temperature because of the decrease in sound velocity due to large compressibility and the rapid phase change velocity in a cryogenic two-phase mixture flow. According to these numerical results, the fundamental characteristics of the cryogenic two-phase flow are predicted. The numerical results obtained will contribute to advanced cryogenic industrial applications.
Two-phase aqueous micellar systems: an alternative method for protein purification
Rangel-Yagui C. O.
2004-01-01
Full Text Available Two-phase aqueous micellar systems can be exploited in separation science for the extraction/purification of desired biomolecules. This article reviews recent experimental and theoretical work by Blankschtein and co-workers on the use of two-phase aqueous micellar systems for the separation of hydrophilic proteins. The experimental partitioning behavior of the enzyme glucose-6-phosphate dehydrogenase (G6PD in two-phase aqueous micellar systems is also reviewed and new results are presented. Specifically, we discuss very recent work on the purification of G6PD using: i a two-phase aqueous micellar system composed of the nonionic surfactant n-decyl tetra(ethylene oxide (C10E4, and (ii a two-phase aqueous mixed micellar system composed of C10E4 and the cationic surfactant decyltrimethylammonium bromide (C10TAB. Our results indicate that the two-phase aqueous mixed (C10E4/C10TAB micellar system can improve significantly the partitioning behavior of G6PD relative to that observed in the two-phase aqueous C10E4 micellar system.
Experimental study of flow monitoring instruments in air-water, two-phase downflow
The performance of a turbine meter, target flow meter (drag disk), and a gamma densitometer was studied in air-water, two-phase vertical downflow. Air and water were metered into an 0.0889-m-ID (3.5-in.) piping system; air flows ranged from 0.007 to 0.3 m3/sec (16 to 500 scfm) and water flows ranged from 0.0006 to 0.03 m3/sec (10 to 500 gpm). The study included effects of flow rate, quality, flow regime, and flow dispersion on the mean and fluctuating components of the instrument signals. Wire screen flow dispersers located at the inlet to the test section had a significant effect on the readings of the drag disk and gamma densitometer, but had little effect on the turbine. Further, when flow dispersers were used, mass flow rates determined from the three instrument readings and a two-velocity, slip flow model showed good agreement with actual mass flow rate over a three-fold range in quality; mass flows determined with the drag disk and densitometer readings assuming homogeneous flow were nearly as accurate. However, when mass flows were calculated using the turbine and densitometer or turbine and drag disk readings assuming homogeneous flow, results were scattered and relatively inaccurate compared to the actual mass flows. Turbine meter data were used with a two-velocity turbine model and continuity relationships for each phase to determine the void fraction and mean phase velocities in the test section. The void fraction was compared with single beam gamma densitometer results and fluid momentum calculated from a two-velocity model was compared with drag disk readings
An analytical method for modeling two-phase gravity-driven drainage systems in BOP applications
Highlights: ► An actual gravity drainage system in an operating power plant is described. ► A drain flow oscillation exists in the system, which is replicated using RELAP5. ► The RELAP model identifies that steam binding due to poor venting is the cause. ► The RELAP model shows that new vent piping prevents the flow oscillations. ► The revised vent piping is installed in the plant and resolves the flow oscillations. - Abstract: Two-phase gravity-driven drainage systems are used in many applications within nuclear power Balance of Plant (BOP) applications such as the drain lines for moisture separator re-heaters (MSRs) and feedwater heaters. Design of these systems is typically based on industry-oriented guidelines and operator-based experience. Changes in plant operation, such as uprates and equipment modification and/or replacement, are relatively common as plants seek to generate more power with greater efficiency. These plant modifications may inadvertently change system operation from design conditions and impose undesirable system transients. This paper seeks to provide a method for analyzing BOP drainage systems in an effort to characterize and mitigate drain flow transients. Previous methodologies diagnose and evaluate drain instability through measurement, empirical analysis, and operational experience. This paper identifies methods that can be utilized to generate computational models of discrete plant drainage systems that decrease the level of speculation involved in previous analyses. Additionally, a real-world application of this method is presented to demonstrate how computer modeling can accurately mimic plant transients.
CFD modelling of wall steam condensation by a two-phase flow approach
Condensation heat transfer in the presence of non-condensable gases is a relevant phenomenon in many industrial applications. The present work is focused on the condensation heat transfer that plays a dominant role in many accident scenarios postulated to occur in the containment of nuclear reactors. The aim of the study is to contribute to the understanding of the heat and mass transfer mechanisms involved in the problem. The modelling proposed in the paper assumes that liquid droplets form along the wall at nucleation sites. Vapor condensation on droplets makes them to grow. Once the droplet diameter reaches a critical value, gravitational forces compensate surface tension force and then droplets slide over the wall. Droplets can also join the surrounding droplets and form a film layer. As a consequence of the modelling adopted in the paper, the starting point is the balance of heat and mass transfer between droplets and the gas mixture surrounding the droplet. So, the flow in the simulation domain is modelled as a two-phase flow. This approach allows taking into account simultaneously heat and mass transfer on droplets in the core of the flow and condensation or evaporation phenomena at the wall. Two tests were performed to validate the condensation model against experimental data: the COPAIN experiment (CEA Grenoble) and the TOSQAN ISP47 experiment (IRSN Saclay). Calculated profiles compare favourably with experimental results particularly for the helium and steam volume fraction. Nevertheless the cross-comparison of the gas velocities profiles should be improved in plume-jet configuration. Hence more investigations are needed in turbulence modelling for accurate predictions of heat transfer in the whole containment. (author)
Highlights: • Development of optimization rules for S2 quadrature sets. • Studying the dependency of optimized S2 quadratures on composition and geometry. • Demonstrating S2 procedures preserving the features of higher approximations. - Abstract: Discrete ordinates method relies on approximating the integral term of the transport equation with the aid of quadrature summation rules. These quadratures are usually based on certain assumptions which assure specific symmetry rules and transport/diffusion limits. Generally, these assumptions are not problem-dependent which results in inaccuracies in some instances. Here, various methods have been developed for more accurate estimation of the independent angle in S2 approximation, as it is tightly related to valid estimation of the diffusion coefficient/length. We proposed and examined a method to reduce a complicated problem that usually is consisting many energy groups and discrete directions (SN) to an equivalent one-group S2 problem while it mostly preserves general features of the original model. Some numerical results are demonstrated to show the accuracy of proposed method
Study of two-phase flow thermal-hydraulics during bottom reflooding of nuclear reactor cores
Based on experimental observation of two-phase flow void fraction behavior during reflooding, and empirical correlation is proposed for fitting reflooding two-phase void fraction distribution. The empirical void fraction distribution is used to correct Hsu's transition boiling correlation for the effect of local void fraction. The UCLA Multi-Channel Reflood Model for analysis of reflooding thermal hydraulics is reviewed. Simple methods proposed for treatment of two-phase phenomena and core multi-dimensional effects are shown to be adequate. The model predictions are shown to be adequate. The model predictions are shown to compare well with experiment
Simulation of throttle flow with two phase and single phase homogenous equilibrium model
Koukouvinis, P.; Gavaises, M.
2015-12-01
This paper aims to compare the results of two commonly used methods for the simulation of cavitating flows; one is the two phase mass transfer approach and the other is a homogenous equilibrium model. Both methodologies are compared in a shock tube and a throttle flow, which resembles the constrictions in Diesel injector passages. The mass transfer rate in the two phase model plays the fundamental role in affecting how close to equilibrium the model is; by increasing the mass transfer the two phase model comes close to the homogenous equilibrium model.
The capability of RELAP5 to model single and two-phase acoustic waves is demonstrated with the use of fine temporal and spatial discretizations. Two cases were considered: a single phase air shock tube problem and pressure waves observed by Takeda and Toda in a two-phase decompression experiment in a pipe. Whereas the agreement for the single phase case is excellent, some discrepancies were observed in the two-phase case. However, RELAP5 produced markedly better results after adjusting the bubble size and the choked flow area. These results illustrate the need of a dynamic model for the interfacial area concentration (i.e., the bubble size). (author)
Measurement of local two-phase flow parameters of nanofluids using conductivity double-sensor probe
Park Yu sun; Chang Soon
2011-01-01
Abstract A two-phase flow experiment using air and water-based γ-Al2O3 nanofluid was conducted to observe the basic hydraulic phenomenon of nanofluids. The local two-phase flow parameters were measured with a conductivity double-sensor two-phase void meter. The void fraction, interfacial velocity, interfacial area concentration, and mean bubble diameter were evaluated, and all of those results using the nanofluid were compared with the corresponding results for pure water. The void fract...
Single and two-phase flow fluid dynamics in parallel helical coils
De Salve, M.; Orio, M.; Panella, B.
2014-04-01
The design of helical coiled steam generators requires the knowledge of the single and two-phase fluid dynamics. The present work reports the results of an experimental campaign on single-phase and two phase pressure drops and void fraction in three parallel helicoidal pipes, in which the total water flow rate is splitted by means of a branch. With this test configuration the distribution of the water flow rate in the helicoidal pipes and the phenomena of the instability of the two-phase flow have been experimentally investigated.
Two-phase flow measurements with advanced instrumented spool pieces and local conductivity probes
A series of two-phase, air-water and steam-water tests performed with instrumented spool pieces and with conductivity probes obtained from Atomic Energy of Canada, Ltd. is described. The behavior of the three-beam densitometer, turbine meter, and drag flowmeter is discussed in terms of two-phase models. Application of some two-phase mass flow models to the recorded spool piece data is made and preliminary results are shown. Velocity and void fraction information derived from the conductivity probes is presented and compared to velocities and void fractions obtained using the spool piece instrumentation
Highlights: • Reduced order model for LiFePO4 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
Measurement of off-diagonal transport coefficients in two-phase flow in porous media.
Ramakrishnan, T S; Goode, P A
2015-07-01
The prevalent description of low capillary number two-phase flow in porous media relies on the independence of phase transport. An extended Darcy's law with a saturation dependent effective permeability is used for each phase. The driving force for each phase is given by its pressure gradient and the body force. This diagonally dominant form neglects momentum transfer from one phase to the other. Numerical and analytical modeling in regular geometries have however shown that while this approximation is simple and acceptable in some cases, many practical problems require inclusion of momentum transfer across the interface. Its inclusion leads to a generalized form of extended Darcy's law in which both the diagonal relative permeabilities and the off-diagonal terms depend not only on saturation but also on the viscosity ratio. Analogous to application of thermodynamics to dynamical systems, any of the extended forms of Darcy's law assumes quasi-static interfaces of fluids for describing displacement problems. Despite the importance of the permeability coefficients in oil recovery, soil moisture transport, contaminant removal, etc., direct measurements to infer the magnitude of the off-diagonal coefficients have been lacking. The published data based on cocurrent and countercurrent displacement experiments are necessarily indirect. In this paper, we propose a null experiment to measure the off-diagonal term directly. For a given non-wetting phase pressure-gradient, the null method is based on measuring a counter pressure drop in the wetting phase required to maintain a zero flux. The ratio of the off-diagonal coefficient to the wetting phase diagonal coefficient (relative permeability) may then be determined. The apparatus is described in detail, along with the results obtained. We demonstrate the validity of the experimental results and conclude the paper by comparing experimental data to numerical simulation. PMID:25748636
Development of gas-liquid two-phase flow interfacial structure in a confined bubbly flow
In gas-liquid two-phase flow systems, the interfacial structure specifies the geometric capability of the interfacial transfer of mass, momentum, and energy between the two phases. In view of this, extensive experiments have been carried out in an air-water upward two-phase flow through a test section of 20-cm in width and 1-cm in gap. In it, the local two-phase flow parameters were acquired by the double-sensor conductivity probe at three different elevations in a wide range of the bubbly flow conditions. The acquired local parameters include void fraction ( α), interfacial area concentration (ai), bubble velocity (Ub), bubble Sauter mean diameter (Dsm) and bubble frequency. By taking advantage of the transparent two-dimensional flow path, the flow regime map was constructed through flow visualization. Examination of the measured parameters reveals the development of the interfacial structure due to bubble interactions. (author)
Research of Characteristics of Gas-liquid Two-phase Pressure Drop in Microreactor
Li Dan
2015-01-01
Full Text Available With the research system of nitrogen and deionized water, this paper researches the pressure drop of gas-liquid two-phase flow in the circular microchannel with an inner diameter which is respectively 0.9mm and 0.5mm, analyzes the effect of microchannel diameter on gas-liquid two-phase frictional pressure drop in the microchannel reactor, and compares with the result of frictional pressure drop and the predicting result of divided-phase flow pattern. The result shows that, the gas-liquid two-phase frictional pressure drop in the microchannel significantly increases with the decreasing microchannel diameter; Lockhart-Martinelli relationship in divided-phase flow pattern can preferably predict the gas-liquid two-phase frictional pressure drop in the microchannel, but the Tabular constant needs to be corrected.
Development of One Dimensional Hyperbolic Coupled Solver for Two-Phase Flows
Kim, Eoi Jin; Kim, Jong Tae; Jeong, Jae June
2008-08-15
The purpose of this study is a code development for one dimensional two-phase two-fluid flows. In this study, the computations of two-phase flow were performed by using the Roe scheme which is one of the upwind schemes. The upwind scheme is widely used in the computational fluid dynamics because it can capture discontinuities clearly such as a shock. And this scheme is applicable to multi-phase flows by the extension methods which were developed by Toumi, Stadtke, etc. In this study, the extended Roe upwind scheme by Toumi for two-phase flow was implemented in the one-dimensional code. The scheme was applied to a shock tube problem and a water faucet problem. This numerical method seems efficient for non oscillating solutions of two phase flow problems, and also capable for capturing discontinuities.
Falabella, Steven; Meyer, Glenn A; Tang, Vincent; Guethlein, Gary
2014-06-10
A two-phase mixed media insulator having a dielectric fluid filling the interstices between macro-sized dielectric beads packed into a confined volume, so that the packed dielectric beads inhibit electro-hydrodynamically driven current flows of the dielectric liquid and thereby increase the resistivity and breakdown strength of the two-phase insulator over the dielectric liquid alone. In addition, an electrical apparatus incorporates the two-phase mixed media insulator to insulate between electrical components of different electrical potentials. And a method of electrically insulating between electrical components of different electrical potentials fills a confined volume between the electrical components with the two-phase dielectric composite, so that the macro dielectric beads are packed in the confined volume and interstices formed between the macro dielectric beads are filled with the dielectric liquid.
Non-local two phase flow momentum transport in S BWR
The non-local momentum transport equations derived in this work contain new terms related with non-local transport effects due to accumulation, convection, diffusion and transport properties for two-phase flow. For instance, they can be applied in the boundary between a two-phase flow and a solid phase, or in the boundary of the transition region of two-phase flows where the local volume averaging equations fail. The S BWR was considered to study the non-local effects on the two-phase flow thermal-hydraulic core performance in steady-state, and the results were compared with the classical local averaging volume conservation equations. (Author)
Mosdorf Romuald
2015-06-01
Full Text Available The two-phase flow (water-air occurring in square minichannel (3x3 mm has been analysed. In the minichannel it has been observed: bubbly flow, flow of confined bubbles, flow of elongated bubbles, slug flow and semi-annular flow. The time series recorded by laser-phototransistor sensor was analysed using the recurrence quantification analysis. The two coefficients:Recurrence rate (RR and Determinism (DET have been used for identification of differences between the dynamics of two-phase flow patterns. The algorithm which has been used normalizes the analysed time series before calculating the recurrence plots.Therefore in analysis the quantitative signal characteristicswas neglected. Despite of the neglect of quantitative signal characteristics the analysis of its dynamics (chart of DET vs. RR allows to identify the two-phase flow patterns. This confirms that this type of analysis can be used to identify the two-phase flow patterns in minichannels.
Simulation of two-phase flow for compressible and nearly incompressible regimes
A new finite element formulation for compressible and nearly incompressible problems is applied to the analysis of two-phase flows.The method allows the analysis of nearly incompressible flows without resorting to the incompressible fluid model. Thus, the fluid equation of state is not discarded from the model. This feature is of foremost importance for the approach adopted in this work, where the thermodynamic behaviour of the mixture is constructed from the thermodynamic behaviour of the individual phases. Numerical examples of two-phase steam-water mixtures are presented. The models employed to characterise turbulence and the two-phase mixture are rather simple. Nevertheless, the examples presented show good qualitative behaviour and serve to indicate further developments towards the computational simulation of two-phase flows. (author)
Single and two-phase flow pressure drop for CANFLEX bundle
Park, Joo Hwan; Jun, Ji Su; Suk, Ho Chun [Korea Atomic Energy Research Institute, Taejon (Korea, Republic of); Dimmick, G. R.; Bullock, D. E. [Atomic Energy of Canada Limited, Ontario (Canada)
1998-12-31
Friction factor and two-phase flow frictional multiplier for a CANFLEX bundle are newly developed and presented in this paper. CANFLEX as a 43-element fuel bundle has been developed jointly by AECL/KAERI to provide greater operational flexibility for CANDU reactor operators and designers. Friction factor and two-phase flow frictional multiplier have been developed by using the experimental data of pressure drops obtained from two series of Freon-134a (R-134a) CHF tests with a string of simulated CANFLEX bundles in a single phase and a two-phase flow conditions. The friction factor for a CANFLEX bundle is found to be about 20% higher than that of Blasius for a smooth circular pipe. The pressure drop predicted by using the new correlations of friction factor and two-phase frictional multiplier are well agreed with the experimental pressure drop data of CANFLEX bundle within {+-} 5% error. 11 refs., 5 figs. (Author)
Two-phase gas bubble-liquid boundary layer flow along vertical and inclined surfaces
The behavior of a two-phase gas bubble-liquid boundary layer along vertical and inclined porous surfaces with uniform gas injection is investigated experimentally and analytically. Using argon gas and water as the working fluids, a photographical study of the two-phase boundary layer flow has been performed for various angles of inclination ranging from 450 to 1350 and gas injection rates ranging from 0.01 to 0.1 m/s. An integral method has been employed to solve the system of equations governing the two-phase motion. The effects of the gas injection rate and the angle of inclination on the growth of the boundary layer have been determined. The predicted boundary layer thickness is found to be in good agreement with the experimental results. The calculated axial liquid velocity and the void fraction in the two-phase region are also presented along with the observed flow behavior
Critical Regimes of Two-Phase Flows with a Polydisperse Solid Phase
Barsky, Eugene
2010-01-01
This book brings to light peculiarities of the formation of critical regimes of two-phase flows with a polydisperse solid phase. A definition of entropy is formulated on the basis of statistical analysis of these peculiarities. The physical meaning of entropy and its correlation with other parameters determining two-phase flows are clearly defined. The interrelations and main differences between this entropy and the thermodynamic one are revealed. The main regularities of two-phase flows both in critical and in other regimes are established using the notion of entropy. This parameter serves as a basis for a deeper insight into the physics of the process and for the development of exhaustive techniques of mass exchange estimation in such flows. The book is intended for graduate and postgraduate students of engineering studying two-phase flows, and to scientists and engineers engaged in specific problems of such fields as chemical technology, mineral dressing, modern ceramics, microelectronics, pharmacology, po...
Numerical simulation of multi-dimensional two-phase flow based on flux vector splitting
Staedtke, H.; Franchello, G.; Worth, B. [Joint Research Centre - Ispra Establishment (Italy)
1995-09-01
This paper describes a new approach to the numerical simulation of transient, multidimensional two-phase flow. The development is based on a fully hyperbolic two-fluid model of two-phase flow using separated conservation equations for the two phases. Features of the new model include the existence of real eigenvalues, and a complete set of independent eigenvectors which can be expressed algebraically in terms of the major dependent flow parameters. This facilitates the application of numerical techniques specifically developed for high speed single-phase gas flows which combine signal propagation along characteristic lines with the conservation property with respect to mass, momentum and energy. Advantages of the new model for the numerical simulation of one- and two- dimensional two-phase flow are discussed.
Modified Diffusion Flux Model for Analysis of Turbulent Gas-Particle Two-Phase Flows
YANG Ruichang; ZHOU Weiduo; FUKUDA Kenji; JU Zejian; SHANG Zhi
2005-01-01
A modified diffusion flux model (DFM) was developed to analyze turbulent multi-dimensional gas-particle two-phase flows. In the model, the solid particles move in a modified acceleration field, , which includes the effects of various forces on the particles as if all the forces have the same effect on the particles as the gravity. The accelerations due to various forces are then taken into account in the calculation of the diffusion velocities of the solid particles in the gas-particle two-phase flow. The DFM was used to numerically simulate the gas-solid two-phase flow behind a vertical backward-facing step. The numerical simulation compared well with experimental data and numerical results using both the k-ε-Ap and k-ε-kp two-fluid models available in the literature. The comparison shows that the modified diffusion flux model correctly simulates the turbulent gas-particle two-phase flow.
Non-local two phase flow momentum transport in S BWR
Espinosa P, G.; Salinas M, L.; Vazquez R, A., E-mail: gepe@xanum.uam.mx [Universidad Autonoma Metropolitana, Unidad Iztapalapa, Area de Ingenieria en Recursos Energeticos, Apdo. Postal 55-535, 09340 Ciudad de Mexico (Mexico)
2015-09-15
The non-local momentum transport equations derived in this work contain new terms related with non-local transport effects due to accumulation, convection, diffusion and transport properties for two-phase flow. For instance, they can be applied in the boundary between a two-phase flow and a solid phase, or in the boundary of the transition region of two-phase flows where the local volume averaging equations fail. The S BWR was considered to study the non-local effects on the two-phase flow thermal-hydraulic core performance in steady-state, and the results were compared with the classical local averaging volume conservation equations. (Author)
Experimental on two sensors combination used in horizontal pipe gas-water two-phase flow
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
Experimental on two sensors combination used in horizontal pipe gas-water two-phase flow
Wu, Hao; Dong, Feng [Tianjin Key Laboratory of Process Measurement and Control, School of Electrical Engineering and Automation, Tianjin University, Tianjin (China)
2014-04-11
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.
Experimental on two sensors combination used in horizontal pipe gas-water two-phase flow
Wu, Hao; Dong, Feng
2014-04-01
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.
Programs and calculations of heat transfer in two-phase flow
Problems of physical simulation of hydrodynamics and heat exchange processes in two-phase flows of coolants in nuclear reactors are discussed. Programs RELAP-4 and TRAC, used for the analysis of reactor safety, are described
In order to evaluate an influence of earthquake acceleration to the boiling two-phase flow behavior in nuclear reactors, numerical simulations were performed under the simulated earthquake condition. The two-phase flow analysis code, ACE-3D, was modified as the influence of the earth quake acceleration can calculate. To check out if the modification is adequate, a series of calculations were carried out and the following summaries were derived; 1) the void fraction in the fuel bundle receives the influence of the earthquake, 2) the liquid-phase in the two-phase flow moves in the same direction as the direction of oscillation due to the inputted earthquake acceleration, and 3) due to the density difference in comparison with the liquid phase, the gas phase of that moves in the direction opposite to the oscillating direction. This study enabled visualized evaluation of the boiling two-phase flow behavior in the nuclear reactors at the earthquake condition. (author)
Development of an Enhanced Two-Phase Production System at the Geysers Geothermal Field; FINAL
A method was developed to enhance geothermal steam production from two-phase wells at THE Geysers Geothermal Field. The beneficial result was increased geothermal production that was easily and economically delivered to the power plant
Detection of reactor antineutrino coherent scattering off nuclei with a two-phase noble gas detector
Akimov, Dmitri; Bondar, Alexander; Burenkov, Alexander; Buzulutskov, Alexei
2009-01-01
Estimation of the signal amplitudes and counting rates for coherent scattering of reactor antineutrino off atomic nuclei in two-phase xenon and argon detectors has been done. A conceptual design of detector based on the existing technologies and experience has been proposed. It is shown that a condensed xenon/argon two-phase detector possesses the necessary sensitivity for the use in experiment on detection of coherent scattering of the reactor antineutrino off nuclei. It is shown that a two-...
Effective-Medium Theory for Two-Phase Random Composites with an Interfacial Shell
无
2000-01-01
According to the Bruggeman theory and MaxwelI-Garnett theory, the effective dielectric constant of a two-phase random composite with an interfacial shell is presented. The nonlinearity of the theory is obvious. Especially, the theory is suited to study the dielectric properties of two-phase random composites with a spherical interracial shell. The theoretical results on dielectric properkies of polystyrene-barium titanate composites with an interracial shell are in good agreement with experimental data.
Two-phase bounded acceleration traffic flow model: Analytical solutions and applications
LEBACQUE, JP
2003-01-01
The present paper describes a two phase traffic flow model. One phase is traffic equilibrium: flow and speed are functions of density, and traffic acceleration is low. The second phase is characterized by constant acceleration. This model extends first order traffic flow models and recaptures the fact that traffic acceleration is bounded. The paper show how to calculate analytical solutions of the two-phase model for dynamic traffic situations, provides a set of calculation rules, and analyze...
Personal view of educating two-phase flow and human resource development as a nuclear engineer
As an engineer who has devoted himself in the nuclear industry for almost three decades, the author gave a personal view on educating two-phase flow and developing human resources. An expected role of universities in on-going discussions of collaboration among industry-government-academia is introduced. Reformation of two-phase flow education is discussed from two extreme viewpoints, the basic structure of physics and the practical system analysis. (author)
Treatment technologies of liquid and solid wastes from two-phase olive oil mills
Rincón, Bárbara; Raposo, Francisco; Borja, Rafael
2006-01-01
Over the last 10 years the manufacture of olive oil has undergone important evolutionary changes in the equipment used for the separation of olive oil from the remaining components. The latest development has been the introduction of a two-phase centrifugation process in which a horizontally-mounted centrifuge is used for a primary separation of the olive oil fraction from the vegetable solid material and vegetation water. Therefore, the new two-phase olive oil mills produce three identifiabl...
Treatment technologies of liquid and solid wastes from two-phase olive oil mills
Borja Padilla, Rafael; Raposo Bejines, Francisco; Rincón, Bárbara
2006-01-01
Over the last 10 years the manufacture of olive oil has undergone important evolutionary changes in the equipment used for the separation of olive oil from the remaining components. The latest development has been the introduction of a two-phase centrifugation process in which a horizontally-mounted centrifuge is used for a primary separation of the olive oil fraction from the vegetable solid material and vegetation water. Therefore, the new two-phase olive oil mills produce three ident...
Comparison of three-phase modulation with two-phase and four-phase modulation
Pierce, J. R.
1980-01-01
For a constant added noise density at high signal-to-noise ratios and for the same error rate, three-phase PSK requires about 0.75 dB less energy per bit than two-phase or four-phase PSK. However, at very low signal-to-noise ratios, three-phase PSK requires about 0.74 dB more energy per bit of channel capacity than two-phase or four-phase PSK.
Features concerning capillary pressure and the effect on two-phase and three-phase flow
2008-01-01
The effect of capillary pressure related to immiscible WAG (Water Alternate Gas) is studied by use of a numerical simulator. The capillary pressure is found to have a significant effect on the pressure gradient and the total oil production both in two-phase and three-phase flow situations. When the capillary pressure is included in the simulation the total oil production is considerably lower than when the capillary pressure is neglected. Experimentally measured two-phase capil...
Bortolato, Matteo
2014-01-01
This thesis reports the results of many experimental tests conducted to gain a deeper insight on the two-phase heat transfer inside minichannels and to characterize the thermal performance of two refrigerants with low environmental impact: propane (R290) and R1234ze(E). Furthermore, some considerations on the application of the minichannel technology in refrigeration applications and solar concentrators are presented. As pressure drops greatly affect the heat transfer in two-phase flow, th...
Two-phase flow measurements at high void fraction by a Venturi meter
Monni, Grazia; Salve, Mario De; Panella, Bruno
2014-01-01
An experimental investigation of a vertical upward annular two-phase flow across a Venturi flow meter has been performed for the measurement of two-phase flow parameters with reference to the experimental simulation of nuclear accidents, as LOCA, characterized by very high void fraction. The pressure drops between the inlet and throat section and between inlet and outlet (irreversible pressure losses) have been measured and analyzed. The Venturi flow meter is characterized by an inlet diamete...
Two-phase flow and heat transfer symposium-workshop. Proceedings of condensed papers
Two-phase flow applications are found in a wide range of engineering systems, such as boiling water reactors, conventional steam boilers, evaporators of refrigeration systems, and evaporative and condensive heat exchangers in chemical and petroleum industries. Over the past two decades, two-phase flow instability problems have been a challenge to many investigators. Such instabilities could induce boiling crisis, disturb control systems and/or cause mechanical damage. It is important to be able to predict the conditions under which a two-phase flow system will perform without instability. Therefore, the understanding of two-phase flow phenomena is extremely important for the design, control and performance prediction of such systems. Because of the recent energy crisis, many other two-phase flow problems have also become important. Some of them are the modeling of the loss of coolant accident in pressurized water nuclear reactors, scaling up of fluidized bed reactors for converting coal to clean gaseous and liquid fuels, and design of heat exchangers for liquified natural gas, and design of heat exchangers for liquified natural gas. There is a need to provide researchers and engineers in this field with an opportunity to exchange their experience and ideas in order to assess the state-of-the-art of two-phase flow and heat transfer studies, and to establish a basis for identification of areas of future research and application. This symposium provides the latest information on the status of two-phase flow and heat transfer research, development and applications. It also establish a rational basis for identification of areas of two-phase flow and heat transfer for further research and application
NEW STUDYING OF LATTICE BOLTZMANN METHOD FOR TWO-PHASE DRIVEN IN POROUS MEDIA
许友生; 刘慈群; 俞慧丹
2002-01-01
By using the interaction of particles, such as the physical principle of the same attract each other and the different repulse each other, a new model of Lattice Boltzmann to simulate the two-phase driven in porous media was discussed. The result shows effectively for the problem of two-phase driven in porous media. Furthermore, the method economizes on computer time, has less fiuctuation on boundary surface and takes no average measure.
Numerical simulation of two-phase gas-liquid flows in inclined and vertical pipelines
Loilier, P.
2006-01-01
The present thesis describes the advances made in modelling two-phase flows in inclined pipes using a transient one-dimensional approach. The research is a developement of an existing numerical methodology, capable of simulating stratified and slugging two-phase flows in horizontal or inclined single pipes. The aim of the present work is to extend the capabilities of the approach in order (i) to account for the effect of the pipe topography in the numerical solution of the two-...
A research on the mechanisms of transition from annular flow in two-phase pipeline flow
Various kinds mechanisms of transitions from two-phase annular flow in tubes were studied and modelled, and the affection factors on the transitions were also discussed. Some mathematical equations and transition criteria for every mechanisms presented were derived, and an unified general criterion for the annular flow transitions in whole range of pipe inclinations was recommended. The boundaries predicted show good agreement with the air-water two-phase experimental data
CURE OF A MICROGEL-EPOXY RESIN TWO-PHASE POLYMER WITH ETHYLENE DIAMINE
SONG Aiteng; HUANG Wei; YU Yunzhao
1992-01-01
The curing of a microgel-epoxy resin two phase polymer prepared by in situ copolymerization of unsaturated polyester with acrylic monomer was studied. The unsaturated unit reacted with N- H during the cure of the resin with ethylene diamine. The Michael type reaction was ten times more rapid than the addition of N -H to epoxide .This was accounted for the lower apparent activation energy of the curing of the two phase resin.
Bastian, Peter
2013-01-01
In this paper we formulate and test numerically a fully-coupled discontinuous Galerkin (DG) method for incompressible two-phase flow with discontinuous capillary pressure. The spatial discretization uses the symmetric interior penalty DG formulation with weighted averages and is based on a wetting-phase potential / capillary potential formulation of the two-phase flow system. After discretizing in time with diagonally implicit Runge-Kutta schemes the resulting systems of nonlinear algebraic equations are solved with Newton's method and the arising systems of linear equations are solved efficiently and in parallel with an algebraic multigrid method. The new scheme is investigated for various test problems from the literature and is also compared to a cell-centered finite volume scheme in terms of accuracy and time to solution. We find that the method is accurate, robust and efficient. In particular no post-processing of the DG velocity field is necessary in contrast to results reported by several authors for d...
A study of the effects of flashing inception on maximum and minimum critical two-phase flow rates
Critical flow is a common phenomenon that plays an important role in a variety of engineering applications. The prediction of the critical flow rate following a pipe rupture is of paramount importance in the safety analysis of nuclear reactors. Here, the ability to maintain adequate core cooling is highly dependent on the critical mass flux. As the local pressure decreases along the flow length to below saturation, the fluid becomes metastable and begins to flash. The location where this occurs defines the onset of two-phase flow (flashing inception point) within the pipe. The results of an experimental study of critical two-phase flow of saturated and subcooled water through long tubes are reported. The location of flashing inception was accurately controlled through the use of a new device. This allowed for a systematic study of the effects of the location of flashing inception on the critical mass flux. Data were obtained for different stagnation temperatures, pressures and test section length. The results show that a range in the critical mass flux exists for each stagnation condition. This range was dependent on the location of flashing inception. The critical mass flux was found to increase with a decrease in the superheat at flashing inception. A decrease in this superheat also occurred as the location of flashing inception was moved upstream
Lee, Pilhwa; Wolgemuth, Charles W.
2016-01-01
The swimming of microorganisms typically involves the undulation or rotation of thin, filamentary objects in a fluid or other medium. Swimming in Newtonian fluids has been examined extensively, and only recently have investigations into microorganism swimming through non-Newtonian fluids and gels been explored. The equations that govern these more complex media are often nonlinear and require computational algorithms to study moderate to large amplitude motions of the swimmer. Here, we develop an immersed boundary method for handling fluid-structure interactions in a general two-phase medium, where one phase is a Newtonian fluid and the other phase is viscoelastic (e.g., a polymer melt or network). We use this algorithm to investigate the swimming of an undulating, filamentary swimmer in 2D (i.e., a sheet). A novel aspect of our method is that it allows one to specify how forces produced by the swimmer are distributed between the two phases of the fluid. The algorithm is validated by comparing theoretical predictions for small amplitude swimming in gels and viscoelastic fluids. We show how the swimming velocity depends on material parameters of the fluid and the interaction between the fluid and swimmer. In addition, we simulate the swimming of Caenorhabditis elegans in viscoelastic fluids and find good agreement between the swimming speeds and fluid flows in our simulations and previous experimental measurements. These results suggest that our methodology provides an accurate means for exploring the physics of swimming through non-Newtonian fluids and gels.
Three-dimensional multi-relaxation-time lattice Boltzmann front-tracking method for two-phase flow
Hai-Qiong, Xie; Zhong, Zeng; Liang-Qi, Zhang
2016-01-01
We developed a three-dimensional multi-relaxation-time lattice Boltzmann method for incompressible and immiscible two-phase flow by coupling with a front-tracking technique. The flow field was simulated by using an Eulerian grid, an adaptive unstructured triangular Lagrangian grid was applied to track explicitly the motion of the two-fluid interface, and an indicator function was introduced to update accurately the fluid properties. The surface tension was computed directly on a triangular Lagrangian grid, and then the surface tension was distributed to the background Eulerian grid. Three benchmarks of two-phase flow, including the Laplace law for a stationary drop, the oscillation of a three-dimensional ellipsoidal drop, and the drop deformation in a shear flow, were simulated to validate the present model. Project supported by the National Natural Science Foundation of China (Grant No. 11572062), the Fundamental Research Funds for the Central Universities, China (Grant No. CDJZR13248801), the Program for Changjiang Scholars and Innovative Research Team in University, China (Grant No. IRT13043), and Key Laboratory of Functional Crystals and Laser Technology, TIPC, Chinese Academy of Sciences.
Application of non-equilibrium thermodynamics to two-phase flows with a change of phase
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)
Structural developments of turbulent two-phase flow in large pipes
In connection with the thermohydraulic problems of two-phase flow that may be encountered under certain operating conditions in piping systems containing heat sources and sinks such as a CANDU reactor heat transport system, this study investigates some of the turbulent characteristics of both cocurrent air-water two-phase flow and single phase flow in large pipes with horizontal orientation. Pitot tubes together with hot film anemometry have been shown to be an adequate measurement system in turbulent dispersed two-phase flow. A practical semi-empirical formula has been developed to predict local mixture velocity as a function of differential head read by Pitot tube, local void fraction, flow pattern constant, gas-liquid properties, momentum transfer factor and two-phase flow quality. The structural developments of the dispersed mixture velocity was studied along a straight horizontal PVC run and expressed in terms of the radial distance and the pipeline length. A correlation is introduced to determine the local mixture velocity in terms of radial and streamwise distance, two-phase flow quality, gas and liquid densities. A similar correlation is presented to predict the local developments of the void fraction. In addition to those normalized correlations, hypothetical interpretations of the experienced phenonema are presented. It was found that the mixture velocity is significantly influenced by the volumetric mixing ratio of both phases. Conclusions are drawn in the special cases of turbulent single and two-phase flow
Mixed Model for Silt-Laden Solid-Liquid Two-Phase Flows
唐学林; 徐宇; 吴玉林
2003-01-01
The kinetic theory of molecular gases was used to derive the governing equations for dense solid-liquid two-phase flows from a microscopic flow characteristics viewpoint by multiplying the Boltzmann equation for each phase by property parameters and integrating over the velocity space. The particle collision term was derived from microscopic terms by comparison with dilute two-phase flow but with consideration of the collisions between particles for dense two-phase flow conditions and by assuming that the particle-phase velocity distribution obeys the Maxwell equations. Appropriate terms from the dilute two-phase governing equations were combined with the dense particle collision term to develop the governing equations for dense solid-liquid turbulent flows. The SIMPLEC algorithm and a staggered grid system were used to solve the discretized two-phase governing equations with a Reynolds averaged turbulence model. Dense solid-liquid turbulent two-phase flows were simulated for flow in a duct. The simulation results agree well with experimental data.
IMPROVED SUBGRID SCALE MODEL FOR DENSE TURBULENT SOLID-LIQUID TWO-PHASE FLOWS
TANG Xuelin; QIAN Zhongdong; WU Yulin
2004-01-01
The dense solid-phase governing equations for two-phase flows are obtained by using the kinetic theory of gas molecules. Assuming that the solid-phase velocity distributions obey the Maxwell equations, the collision term for particles under dense two-phase flow conditions is also derived.In comparison with the governing equations of a dilute two-phase flow, the solid-particle's governing equations are developed for a dense turbulent solid-liquid flow by adopting some relevant terms from the dilute two-phase governing equations. Based on Cauchy-Helmholtz theorem and Smagorinsky model,a second-order dynamic sub-grid-scale (SGS) model, in which the sub-grid-scale stress is a function of both the strain-rate tensor and the rotation-rate tensor, is proposed to model the two-phase governing equations by applying dimension analyses. Applying the SIMPLEC algorithm and staggering grid system to the two-phase discretized governing equations and employing the slip boundary conditions on the walls, the velocity and pressure fields, and the volumetric concentration are calculated. The simulation results are in a fairly good agreement with experimental data in two operating cases in a conduit with a rectangular cross-section and these comparisons imply that these models are practical.
Highlights: • Analysis of the two-phase flow structure in minichannel. • Innovative use of stereology methods and hi-speed photography. • Application of stereological parameters to flow monitoring. - Abstract: The paper describes a method of two-phase flow structure evaluation for minichannels. The two-phase flow structure appears in gas–liquid mixture. The research is based on innovative approach, with the use of stereology methods. Evaluation of the flow structure is made by image analysis. The images are obtained with high-speed visualization technique. The applied stereological analysis is based on the linear methods – the random secants method and directed secants method. Development of mini heat exchangers requires knowledge of the two-phase flow phenomena. The major result of conducted research is that for each flow structure there is a set of stereological parameters, enabling the quantitative estimation of the two-phase flow. It has been found that the interrelation of stereological parameters, during the change of the flow structure, can be used for controlling the operating conditions. The basic conclusion is that the knowledge about the character of the changes taking place in the flow structure may be used for constant process adjustment for various two-phase gas–liquid or gas–solid systems
Measurement of local two-phase flow parameters of nanofluids using conductivity double-sensor probe
Park, Yu Sun; Chang, Soon Heung
2011-12-01
A two-phase flow experiment using air and water-based γ-Al2O3 nanofluid was conducted to observe the basic hydraulic phenomenon of nanofluids. The local two-phase flow parameters were measured with a conductivity double-sensor two-phase void meter. The void fraction, interfacial velocity, interfacial area concentration, and mean bubble diameter were evaluated, and all of those results using the nanofluid were compared with the corresponding results for pure water. The void fraction distribution was flattened in the nanofluid case more than it was in the pure water case. The higher interfacial area concentration resulted in a smaller mean bubble diameter in the case of the nanofluid. This was the first attempt to measure the local two-phase flow parameters of nanofluids using a conductivity double-sensor two-phase void meter. Throughout this experimental study, the differences in the internal two-phase flow structure of the nanofluid were identified. In addition, the heat transfer enhancement of the nanofluid can be resulted from the increase of the interfacial area concentration which means the available area of the heat and mass transfer.
Measurement of local two-phase flow parameters of nanofluids using conductivity double-sensor probe
Park Yu sun
2011-01-01
Full Text Available Abstract A two-phase flow experiment using air and water-based γ-Al2O3 nanofluid was conducted to observe the basic hydraulic phenomenon of nanofluids. The local two-phase flow parameters were measured with a conductivity double-sensor two-phase void meter. The void fraction, interfacial velocity, interfacial area concentration, and mean bubble diameter were evaluated, and all of those results using the nanofluid were compared with the corresponding results for pure water. The void fraction distribution was flattened in the nanofluid case more than it was in the pure water case. The higher interfacial area concentration resulted in a smaller mean bubble diameter in the case of the nanofluid. This was the first attempt to measure the local two-phase flow parameters of nanofluids using a conductivity double-sensor two-phase void meter. Throughout this experimental study, the differences in the internal two-phase flow structure of the nanofluid were identified. In addition, the heat transfer enhancement of the nanofluid can be resulted from the increase of the interfacial area concentration which means the available area of the heat and mass transfer.
Numerical study for two phase flow in the near nozzle region of turbine combustors
In the present study flow conditions in the near nozzle region of the combustion chamber have been investigated. There exists two-phase flow in this region. The overall performance and pollutant formation in the combustion chamber have been investigated. There exists two-phase flow in this region. The overall performance and pollutant formation in the combustion zone largely depends on the spray field in the near nozzle region the studies are conducted to determined the effects of multi jets on the flow pattern in the near nozzle region The phase doppler particle analyzer (PDPA) has been used to measure the velocities and sizes of the droplets. The flow field of two-phase liquid drop-air jets is formed from three injectors arranged in t line. Furthermore the two-phase flow field has been analyzed numerically also. The numerical analysis consists of two computational models, namely (i) 3 non-evaporating two-phase jets, (II) 3 evaporating two phase jets. The Eulerian-Eulerian approach in incorporated in both the numerical models. Since the flow is turbulent, a two-equation model (k-Epsilon) is implemented in the numerical analysis. Numerical solution of the conservation equation is obtained using PHOENICS computer code. Boundary conditions are provided from the experimental measurements. Numerical domain for the two models of the analysis starts at some distance (about 10 diameters of the injector orifice) where the atomization process is complete and droplet size and velocity could be measured experimentally. (author)
Lukas Kalamen
2011-01-01
Full Text Available This paper deals with the two-stage two-phase electronic systems with orthogonal output voltages and currents - DC/AC/AC. Design of two-stage DC/AC/AC high frequency converter with two-phase orthogonal output using single-phase matrix converter is also introduced. Output voltages of them are strongly nonharmonic ones, so they must be pulse-modulated due to requested nearly sinusoidal currents with low total harmonic distortion. Simulation experiment results of matrix converter for both steady and transient states for IM motors are given in the paper, also experimental verification under R-L load, so far. The simulation results confirm a very good time-waveform of the phase current and the system seems to be suitable for low-cost application in automotive/aerospace industries and application with high frequency voltage sources.
A theoretical model for predicting the threshold of instability for two phase flow in a natural circulation loop is presented. The model calculates the flow transient caused by a step disturbance of the heat input, and is based upon the conservation laws of mass, momentum and energy in one dimensional form. Empirical correlations are used in the model for estimating the void fractions and the two-phase flow pressure drops. The equations are solved numerically in a finite difference approximation coded for a digital computer. An experimental study of the hydrodynamic instability and dynamic burnout in two-phase flow has been performed in a natural circulation loop in the pressure range from 10 to 70 atg. The test sections were round ducts of 20, 30 and 36 mm inner diameter and 4890 mm heated length. The experimental results showed that within the ranges tested, the stability of the flow increases with increasing pressure and increasing throttling before the test section, but decreases with increasing Inlet subcooling and increasing throttling after the test section. Comparing the natural circulation burnout steam qualities with corresponding forced circulation data shoved that the former data were low by a factor up to 2.5. However, by applying inlet throttling of the flow the burnout values approached and finally coincided with the forced circulation data. The present experimental results as well as data available from other sources have been compared with the stability thresholds obtained with the theoretical model. The comparisons included circular, annular and rod cluster geometries, and the agreement between the experimental and theoretical stability limits was good. Finally the application of the experimental and theoretical results on the assessment of boiling heavy water reactor design is discussed
Xie, Hai-Qiong; Zeng, Zhong; Zhang, Liang-Qi; Liang, Gong-You; Hiroshi, Mizuseki; Yoshiyuki, Kawazoe
2012-12-01
In this paper, an improved incompressible multi-relaxation-time lattice Boltzmann-front tracking approach is proposed to simulate two-phase flow with a sharp interface, where the surface tension is implemented. The lattice Boltzmann method is used to simulate the incompressible flow with a stationary Eulerian grid, an additional moving Lagrangian grid is adopted to track explicitly the motion of the interface, and an indicator function is introduced to update the fluid properties accurately. The interface is represented by using a four-order Lagrange polynomial through fitting a set of discrete marker points, and then the surface tension is directly computed by using the normal vector and curvature of the interface. Two benchmark problems, including Laplace's law for a stationary bubble and the dispersion relation of the capillary wave between two fluids are conducted for validation. Excellent agreement is obtained between the numerical simulations and the theoretical results in the two cases.
Variant of a volume-of-fluid method for surface tension-dominant two-phase flows
G Biswas
2013-12-01
The capabilities of the volume-of-fluid method for the calculation of surface tension-dominant two-phase flows are explained. The accurate calculation of the interface remains a problem for the volume-of-fluid method if the density ratios of the fluids in different phases are high. The simulations of bubble growth is performed in water at near critical pressure for different degrees of superheat using combined levelset and volume-of fluid (CLSVOF) method. The effect of superheat on the frequency of bubble formation was analyzed. A deviation from the periodic bubble release is observed in the case of superheat of 20 K in water. The vapor-jet-like columnar structure is observed. Effect of heat flux on the slender vapor column has also been explained.
Zhang, Hong
2016-01-01
Motivated by observations of saturation overshoot, this paper investigates numerical modeling of two-phase flow incorporating dynamic capillary pressure. The effects of the dynamic capillary coefficient, the infiltrating flux rate and the initial and boundary values are systematically studied using a travelling wave ansatz and efficient numerical methods. The travelling wave solutions may exhibit monotonic, non-monotonic or plateau-shaped behaviour. Special attention is paid to the non-monotonic profiles. The travelling wave results are confirmed by numerically solving the partial differential equation using an accurate adaptive moving mesh solver. Comparisons between the computed solutions using the Brooks-Corey model and the laboratory measurements of saturation overshoot verify the effectiveness of our approach.