Application of Preconditioning Method to Gas-Liquid Two-Phase Flow Computations

2003 ◽  
Author(s):  
Byeong Rog Shin ◽  
Satoru Yamamoto ◽  
Xin Yuan
Keyword(s):  
Numerical Method ◽  
Incompressible Flows ◽  
Two Phase Flow ◽  
Tvd Scheme ◽  
Phase Flow ◽  
Internal Flows ◽  
Two Phase ◽  
Time Stepping ◽  
Dual Time Stepping ◽  
Preconditioning Method

A preconditioned numerical method for gas-liquid two-phase flows is applied to solve cavitating flow. The present method employs a finite-difference method of dual time-stepping integration procedure and Roe’s flux difference splitting approximation with MUSCL-TVD scheme. A homogeneous equilibrium cavitation model is used. The present density based numerical method permits simple treatment of the whole gas-liquid two-phase flow field including wave propagation, large density changes and incompressible flows characteristics at low Mach number. By this method, two-dimensional internal flows through a backward-facing step duct, a venturi tube and decelerating cascades are computed. Comparisons of predicted results with experiments are provided and discussed.

Application of Preconditioning Method to Gas-Liquid Two-Phase Flow Computations

2004 ◽  
Vol 126 (4) ◽  
pp. 605-612 ◽  
Author(s):  
Byeong Rog Shin ◽  
Satoru Yamamoto ◽  
Xin Yuan
Keyword(s):  
Numerical Method ◽  
Two Phase Flow ◽  
Flow Characteristics ◽  
Tvd Scheme ◽  
Phase Flow ◽  
Internal Flows ◽  
Two Phase ◽  
Time Stepping ◽  
Dual Time Stepping ◽  
Preconditioning Method

A preconditioned numerical method for gas-liquid two-phase flows is applied to solve cavitating flow. The present method employs a finite-difference method of the dual time-stepping integration procedure and Roe’s flux difference splitting approximation with the MUSCL-TVD scheme. A homogeneous equilibrium cavitation model is used. The present density-based numerical method permits simple treatment of the whole gas-liquid two-phase flow field, including wave propagation, large density changes and incompressible flow characteristics at low Mach number. Two-dimensional internal flows through a backward-facing step duct, convergent-divergent nozzles and decelerating cascades are computed using this method. Comparisons of predicted and experimental results are provided and discussed.

A Numerical Method for Two-Phase Flow Consisting of Separate Compressible and Incompressible Regions

2001 ◽  
Vol 166 (1) ◽  
pp. 1-27 ◽  
Author(s):  
Rachel Caiden ◽  
Ronald P. Fedkiw ◽  
Chris Anderson
Keyword(s):  
Numerical Method ◽  
Two Phase Flow ◽  
Phase Flow ◽  
Two Phase

Variational multi-scale finite element method for the two-phase flow of polymer melt filling process

2019 ◽  
Vol 30 (3) ◽  
pp. 1407-1426 ◽  
Author(s):  
Xuejuan Li ◽  
Ji-Huan He
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Numerical Method ◽  
Two Phase Flow ◽  
Polymer Melt ◽  
Phase Flow ◽  
Filling Process ◽  
Two Phase ◽  
Content Type ◽  
Element Method

Purpose The purpose of this paper is to develop an effective numerical algorithm for a gas-melt two-phase flow and use it to simulate a polymer melt filling process. Moreover, the suggested algorithm can deal with the moving interface and discontinuities of unknowns across the interface. Design/methodology/approach The algebraic sub-grid scales-variational multi-scale (ASGS-VMS) finite element method is used to solve the polymer melt filling process. Meanwhile, the time is discretized using the Crank–Nicolson-based split fractional step algorithm to reduce the computational time. The improved level set method is used to capture the melt front interface, and the related equations are discretized by the second-order Taylor–Galerkin scheme in space and the third-order total variation diminishing Runge–Kutta scheme in time. Findings The numerical method is validated by the benchmark problem. Moreover, the viscoelastic polymer melt filling process is investigated in a rectangular cavity. The front interface, pressure field and flow-induced stresses of polymer melt during the filling process are predicted. Overall, this paper presents a VMS method for polymer injection molding. The present numerical method is extremely suitable for two free surface problems. Originality/value For the first time ever, the ASGS-VMS finite element method is performed for the two-phase flow of polymer melt filling process, and an effective numerical method is designed to catch the moving surface.

A Numerical Method for the Analysis of a New Model for Two-Phase Bubbly Flow in Elastic Pipes

2002 ◽  
Author(s):  
D. Kim
Keyword(s):  
Numerical Method ◽  
Surface Deformation ◽  
Two Phase Flow ◽  
Numerical Technique ◽  
Bubbly Flow ◽  
Neumann Boundary ◽  
Phase Flow ◽  
Two Phase ◽  
Tube Cross Section ◽  
Elastic Pipes

A new approach and numerical method for study gas-liquid two-phase flows in elastic pipes is suggested. “A nonlinear wave dynamical model for liquid containing gas bubbles” is applied to derive governing equations for two-phase flow-filled pipelines. On assuming the hydraulic approximation the continuity and momentum equations of two-phase flow in a pipe are obtained for the first time. From these equations the inhomogeneous wave equation of Lighthill-type for two-phase flow in pipelines is derived. The shear stress at the tube surface, deformation of the tube cross-section, and liquid’s phase compressibility are taken into account. A high effectively and accurate finite difference technique for the exact solution of the basic equations in the case of Neumann boundary conditions is developed. Based on the proposed algorithm various numerical experiments have been carried out to investigate the major fluid dynamical features of hydraulic shocks and shock waves in the horizontal pipes. Comparisons with both the experimental data and computational results obtained with a second-order accurate predictor-corrector method support our numerical technique as well as the model.

Upwind Solutions for Two-Phase Flow Problems Using a Hyperbolic Two-Fluid Model

2011 ◽  
Author(s):  
Moon-Sun Chung ◽  
Youn-Gyu Jung ◽  
Sung-Jae Yi
Keyword(s):  
Numerical Method ◽  
Two Phase Flow ◽  
Fluid Model ◽  
Equation System ◽  
Benchmark Problems ◽  
Phase Flow ◽  
Two Phase ◽  
Flow Problems ◽  
Complete Set ◽  
Two Fluid Model

This study discusses on the implementation of an upwind method for a new 2-dimensional 2-fluid model including the surface tension effect in the momentum equations. This model consists of a complete set of 8 equations including 2-mass, 4-momentum, and 2-internal energy conservation equations having all real eigenvalues. Based on this equation system with upwind numerical method, the present authors first make a pilot 2-dimensional code and then solve some benchmark problems to verify whether this model and numerical method is able to properly solve some fundamental one-dimensional two-phase flow problems or not.

An Implicit Second-Order Numerical Method for Three-Dimensional Two-Phase Flow Calculations

1998 ◽  
Vol 130 (2) ◽  
pp. 213-225 ◽  
Author(s):  
I. Toumi ◽  
D. Caruge
Keyword(s):  
Numerical Method ◽  
Two Phase Flow ◽  
Three Dimensional ◽  
Second Order ◽  
Phase Flow ◽  
Two Phase

Study on the transition process of a molten salt pump transporting media with crystalline particles by modeling test and numerical simulation

2019 ◽  
Vol 29 (9) ◽  
pp. 3263-3289
Author(s):  
Chunlei Shao ◽  
Aixia He ◽  
Zhongyuan Zhang ◽  
Jianfeng Zhou
Keyword(s):  
Numerical Model ◽  
Molten Salt ◽  
Numerical Method ◽  
Two Phase Flow ◽  
Transition Process ◽  
Test Method ◽  
Phase Flow ◽  
Two Phase ◽  
Content Type ◽  
Outlet Pressure

Purpose The purpose of this paper is to study the transition process from the crystalline particles appearing before the pump inlet to the stable operation of the pump. Design/methodology/approach Firstly, a modeling test method was put forward for the high-temperature molten salt pump. Then, according to a modeling test scheme, the experiment of the solid–liquid two-phase flow was carried out by using a model pump similar to the prototype pump. Meanwhile, the numerical method to simulate the transition process of a molten salt pump was studied, and the correctness of the numerical model was verified by the experimental results. Finally, the transition process of the molten salt pump was studied by the verified numerical model in detail. Findings In the simulation of the transition process, it is more accurate to judge the end of the transition process based on the unchanged particle volume fraction (PVF) at the pump outlet than on the periodic fluctuation of the outlet pressure. The outlet pressure is closely related to the PVF in the pump. The variation of the outlet pressure is slightly prior to that of the PVF at the pump outlet and mainly affected by the PVF in the impeller and volute. After 0.63 s, the PVF at each monitoring point changes periodically, and the time-averaged value does not change with time. Practical implications This study is of great significance to further improve the design method of molten salt pump and predict the abrasion characteristic of the pump due to interactions with solid particles. Originality/value A numerical method is established to simulate the transition process of a molten salt pump, and a method is proposed to verify the numerical model of two-phase flow by modeling test.

Accuracy Study of the Flux-Corrected Transport Numerical Method Applied to Transient Two-Phase Flow Simulations in Gas Pipelines

2012 ◽  
Author(s):  
Aline B. Figueiredo ◽  
David E. G. P. Bueno ◽  
Renan M. Baptista ◽  
Felipe B. F. Rachid ◽  
Gustavo C. R. Bodstein
Keyword(s):  
Numerical Method ◽  
Flow Pattern ◽  
Two Phase Flow ◽  
Second Order ◽  
Phase Flow ◽  
Specific Class ◽  
Gas Pipelines ◽  
Time Step ◽  
Two Phase ◽  
Flux Corrected Transport

The ability to produce accurate numerical simulations of transient two-phase flows in gas pipelines has long been an important issue in the oil industry. A reliable prediction of such flows is a difficult task to accomplish due to the numerous sources of uncertainties, such as the basic two-phase flow model, the flow-pattern models, the initial condition and the numerical method used to solve the system of partial differential equations. Several numerical methods, conservative or not, of first- and second-order accuracies may be used to discretize the problem. In this paper we use the flux-corrected transport (FCT) finite-difference method to solve a one-dimensional single-pressure four-equation two-fluid model for the two-phase flow that occurs in a nearly horizontal pipeline characterized by the stratified-flow pattern. Because the FCT algorithm is of indeterminate order, we use a test case to assess the spatial and time accuracies for the specific class of hyperbolic problem that we obtain with the modeling employed here. The results show that the method is first order in time and second order in space, which have important consequences on the choice of mesh spacing and time step for a desired accuracy.

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