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Sample records for accurate two-phase approximate

  1. 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.

  2. 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.

  3. Approximate Analytic Solutions for the Two-Phase Stefan Problem Using the Adomian Decomposition 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.

  4. 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)

  5. A Quadratic Spline based Interface (QUASI) reconstruction algorithm for accurate tracking of two-phase flows

    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.

  6. 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

  7. Characteristics and stability analyses of transient one-dimensional two-phase flow equations and their finite difference approximations

    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)

  8. 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.

  9. A Two-Phase Space Resection Model for Accurate Topographic Reconstruction from Lunar Imagery with PushbroomScanners.

    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

  10. A Two-Phase Space Resection Model for Accurate Topographic Reconstruction from Lunar Imagery with PushbroomScanners

    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.

  11. 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.

  12. 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

  13. Comparison of iterative methods and preconditioners for two-phase flow in porous media using exact and approximate Jacobians

    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

  14. Numerical treatment of two-phase flow in capillary heterogeneous porous media by finite-volume approximations

    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...

  15. Two-Phase Iteration for Value Function Approximation and Hyperparameter Optimization in Gaussian-Kernel-Based Adaptive Critic Design

    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.

  16. 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.

  17. 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.

  18. 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.

  19. The technique of calculation of non-equilibrium two-phase flows in pin bundles using quasi-two-dimensional approaches and subchannel approximation

    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

  20. Approximate Riemann solvers and flux vector splitting schemes for two-phase flow; Solveurs de Riemann approches et schemas de decentrement de flux pour les ecoulements diphasiques

    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)

  1. Approximate Model of Viscous and Squeeze-film Damping Ratios of Heat Exchanger Tubes Subjected to Two-Phase Cross-Flow

    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

  2. A fourth-order accurate curvature computation in a level set framework for two-phase flows subjected to surface tension forces

    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.

  3. 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...

  4. An improved thin film approximation to accurately determine the optical conductivity of graphene from infrared transmittance

    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

  5. 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.

  6. 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...

  7. Accurate approximate solution to nonlinear oscillators in which the restoring force is inversely proportional to the dependent variable

    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%

  8. Accurate gradient approximation for complex interface problems in 3D by an improved coupling interface method

    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

  9. 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

  10. 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, ...

  11. 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

  12. Two phase sampling

    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...

  13. Covariance approximation for fast and accurate computation of channelized Hotelling observer statistics

    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

  14. 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

  15. 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...

  16. Numerically accurate linear response-properties in the configuration-interaction singles (CIS) approximation.

    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

  17. A trigonometric approximation for the tension in the string of a simple pendulum accurate for all amplitudes

    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)

  18. 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.

  19. 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

  20. 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.

  1. An Accurate Approximation to the Distribution of the Sum of Equally Correlated Nakagami-m Envelopes and its Application in Equal Gain Diversity Receivers

    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.

  2. The slow-scale linear noise approximation: an accurate, reduced stochastic description of biochemical networks under timescale separation conditions

    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

  3. 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...

  4. 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.

  5. Two-Phase Galaxy Formation

    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...

  6. Two-phase potential flow

    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.

  7. 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

  8. Accurate evaluation of pressure effects on the electronic stopping cross section and mean excitation energy of atomic hydrogen beyond the Bethe approximation

    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.

  9. 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

  10. Efficient and accurate local approximations to coupled-electron pair approaches: An attempt to revive the pair natural orbital method

    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

  11. 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

  12. 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

  13. 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

  14. Improvements in Neutronics/Thermal-Hydraulics Coupling in Two-Phase Flow Systems Using Stochastic-Mixture Transport Models

    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...

  15. 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

  16. 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.

  17. 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.

  18. 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

  19. 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

  20. Optoelectronic properties of XIn2S4 (X = Cd, Mg) thiospinels through highly accurate all-electron FP-LAPW method coupled with modified approximations

    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

  1. Fast and accurate Monte Carlo modeling of a kilovoltage X-ray therapy unit using a photon-source approximation for treatment planning in complex media

    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.

  2. 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.

  3. Production Decline Analysis for Two-Phase Flow in Multifractured Horizontal Well in Shale Gas Reservoirs

    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, ...

  4. 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.)

  5. 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.

  6. 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.

  7. 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

  8. 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)

  9. 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.

  10. 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)

  11. 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

  12. 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

  13. 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.)

  14. Two-phase flow of ferrofluids

    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...

  15. 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...

  16. 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.)

  17. 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.

  18. 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

  19. 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.

  20. 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.)

  1. 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.

  2. 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.

  3. 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

  4. Accurate solutions of the Schrödinger and Dirac equations of H2+, HD+, and HT+: With and without Born–Oppenheimer approximation and under magnetic field

    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

  5. Production Decline Analysis for Two-Phase Flow in Multifractured Horizontal Well in Shale Gas Reservoirs

    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.

  6. Accurate and Efficient Solution of the Electronic Schr\\"odinger Equation with the Coulomb Singularity by the Distributed Approximating Functional Method

    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 ...

  7. The near-equivalence of five species of spectrally-accurate radial basis functions (RBFs): Asymptotic approximations to the RBF cardinal functions on a uniform, unbounded grid

    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.

  8. 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.

  9. 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.)

  10. 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

  11. 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

  12. 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)

  13. 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

  14. 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...

  15. 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

  16. 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.)

  17. 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

  18. 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

  19. 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}

  20. 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.

  1. 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

  2. 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)

  3. 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.

  4. 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.

  5. 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)

  6. 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...

  7. 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...

  8. 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

  9. 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.

  10. 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)

  11. 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.

  12. 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...

  13. 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

  14. 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)

  15. 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.

  16. 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

  17. 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.

  18. 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)

  19. 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.

  20. 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

  1. 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

  2. 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.

  3. 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.

  4. 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.

  5. 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

  6. 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)

  7. 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.

  8. 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

  9. 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.

  10. 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...

  11. 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...

  12. 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...

  13. 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....

  14. 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,...

  15. 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

  16. 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...

  17. 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

  18. Optoelectronic properties of XIn{sub 2}S{sub 4} (X = Cd, Mg) thiospinels through highly accurate all-electron FP-LAPW method coupled with modified approximations

    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

  19. 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

  20. 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)

  1. 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.)

  2. 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.)

  3. 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

  4. 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)

  5. 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...

  6. 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

  7. The characteristic finite difference fractional steps methods for compressible two-phase displacement problem

    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.

  8. 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.

  9. 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)

  10. 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

  11. 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.

  12. 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.)

  13. 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.

  14. 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.

  15. 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

  16. 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)

  17. 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...

  18. 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...

  19. 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)

  20. 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

  1. Transient numerical simulation and two-phase flow instability prediction of convective boiling in vertical up-flow tube

    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)

  2. 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

  3. 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.

  4. 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

  5. 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)

  6. 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

  7. 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.

  8. 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...

  9. 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...

  10. 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

  11. 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)

  12. 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.)

  13. 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

  14. 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)

  15. 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.

  16. 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

  17. 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)

  18. 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)

  19. 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)

  20. 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.

  1. 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.

  2. 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....

  3. 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)

  4. 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.)

  5. 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)

  6. 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.

  7. 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

  8. 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

  9. 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

  10. 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

  11. 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)

  12. 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.)

  13. 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.

  14. 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.

  15. 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

  16. Convergence of Discontinuous Galerkin Methods for Incompressible Two-Phase Flow in Heterogeneous Media

    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.

  17. 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

  18. 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)

  19. 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.

  20. 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

  1. 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

  2. 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)

  3. 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...

  4. 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

  5. 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.

  6. 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

  7. 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

  8. 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)

  9. 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.

  10. 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)

  11. 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...

  12. 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...

  13. 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...

  14. 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...

  15. 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

  16. 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...

  17. 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...

  18. 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...

  19. 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. ...

  20. 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...

  1. 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...

  2. 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.

  3. 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

  4. 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...

  5. 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.

  6. 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)

  7. 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)

  8. 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

  9. 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.)

  10. 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

  11. 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

  12. 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.

  13. Development of subchannel void measurement sensor and multidimensional two-phase flow dynamics in rod bundle

    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)

  14. 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.

  15. 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

  16. 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)

  17. 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

  18. 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.

  19. 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.

  20. 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

  1. 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.

  2. 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)

  3. 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.

  4. 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.

  5. 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

  6. The Modified Upwind Finite Difference Fractional Steps Method for Compressible Two-phase Displacement Problem

    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.

  7. 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).

  8. 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

  9. 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.

  10. A general unified non-equilibrium model for predicting saturated and subcooled critical two-phase flow rates through short and long tubes

    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.