REVIEW ON MATHEMATICAL ANALYSIS OF SOME TWO-PHASE FLOW MODELS

The two-phase flow models are commonly used in industrial applications, such as nuclear, power, chemical-process, oil-and-gas, cryogenics, bio-medical, micro-technology and so on. This is a survey paper on the study of compressible nonconservative two-fluid model, drift-flux model and viscous liquid-gas two-phase flow model. We give the research developments of these three two-phase flow models, respectively. In the last part, we give some open problems about the above models.

Numerical simulation on centrifugal pump compressible flow field with different gas volume fractions

In order to study the influence of gas-liquid two-phase flow on the performance and internal flow field of a centrifugal pump,the steady three-dimensional flow with different gas volume fractions was simulated by applying the Reynolds-average N-S equation and mixture gas-liquid two-phase flow model,and the compressibility of gas was taken into consideration in the simulation. Then the centrifugal pump characteristic and the gas distribution law in different gas volume fractions were analyzed. The computational results show that gas volume fraction has a certain influence on the performance of the centrifugal pump,and the efficiency and head of the pump are on the decline with the increase of it.Static pressure in the impeller increases in the radial direction,but the pressure gradient in the flow direction is different under the different gas volume fractions. The gas volume is distributed mainly in the ipsilateral direction of impeller back shroud in the flow channel of the volute. On the suction side of the blade inlet there is an obvious low-pressure area,which causes bubbles agglutination and higher gas volume fraction. With the gas entering passage flow,gas volume fraction in the suction decreases and the pressure surface rises gradually. Higher gas volume fraction causes air blocking phenomenon in the flow passage and the discharge capacity reduces. The increase of gas volume makes the turbulent motion within the impeller more and more intense,which leads to more and more energy loss.

Simulation of Compressible Two-Phase Flows Using a Void Ratio Transport Equation

A compressible and multiphase flows solver has been developed for the study of liquid/gas flows involving shock waves and strong expansion waves leading to cavitation.This solver has a structure similar to those of the one-fluid Euler solvers,differing from them by the presence of a void ratio transport-equation.The model and the system of equations to be simulated are presented.Results are displayed for shock and expansion tube problems,shock-bubble interaction and underwater explosion.Close agreement with reference solutions,obtained from explicit finite volume approaches,is demonstrated.Different numerical methods are additionally displayed to provide comparable and improved computational efficiency to the model and the system of equations.The overall procedure is therefore very well suited for use in general two-phase fluid flow simulations.

On the Liquid-Vapor Phase-Change Interface Conditions for Numerical Simulation of Violent Separated Flows

Numerous models have been proposed in the literature to include phase change into numerical simulations of two-phase flows.This review paper presents the modeling options that have been taken in order to obtain a model for violent separated flows with application to sloshing wave impacts.A relaxation model based on linear non-equilibrium thermodynamics has been chosen to compute the rate of phase change.The integration in the system of partial differential equations is done through a non-conservative advection term.For each of these modelling choices,some alternative models from the literature are presented and discussed.The theoretical framework for all phase change model(conservation equations and entropy growth)is also summarized.

A High-Order Localized Artificial Diffusivity Scheme for Discontinuity Capturing on 1D Drift-Flux Models for Gas-Liquid Flows

A computational code is developed for the numerical solution of onedimensional transient gas-liquid flows using drift-flux models,in isothermal and also with phase change situations.For these two-phase models,classical upwind schemes such as Roe-and Godunov-type schemes are generally difficult to derive and expensive to use,since there are no treatable analytic expressions for the Jacobian matrix,eigenvalues and eigenvectors of the system of equations.On the other hand,the highorder compact finite difference scheme becomes an attractive alternative on these occasions,as it does not make use of any wave propagation information from the system of equations.The present paper extends the localized artificial diffusivity method for high-order compact finite difference schemes to solve two-phase flows with discontinuities.The numerical method has simple formulation,straightforward implementation,low computational cost and,most importantly,high-accuracy.The numerical methodology proposed is validated by solving several numerical examples given in the literature.The simulations are sixth-order accurate and it is shown that the proposed numerical method provides accurate approximations of shock waves and contact discontinuities.This is an essential property for simulations of realistic mass transport problems relevant to operations in the petroleum industry。