Research Progress on Relaxed Two-pressure Two-fluid Model and Algorithm

Abstract

An accurate two-phase flow model is an important basis for nuclear reactor safety analysis. The classical two-fluid six-equation model used in many current thermal-hydraulic programs has an ill-posed problem, if a small disturbance is introduced, the system parameters will oscillate greatly, resulting in unstable calculation results. In the existing researches at home and abroad, the most commonly used solutions to this problem are adding the virtual mass force or additional interphase interface pressure. However, the model can only be improved to a certain extent, and the ill-posedness of the model cannot be completely eliminated. The effective solution is to restore the two-phase pressure nonequilibrium and increase the volume transport differential equation to form a twopressure seven-equation model. In addition, a relaxation term is introduced to describe the multi-dimensional motion phenomenon of the interphase interface, and the concept of a relaxationtype twopressure model is proposed. This paper expounded the establishment method of the relaxation two-pressure model in LWR systems, discussed the processing methods and significance of the interphase interface pressurevelocity relaxation process, summarized the calculation method of the twophase mobile interphase interface, and introduced the numerical solution method of the model. Through eigenvalue analysis, the relaxed twopressure twofluid model studied in the paper is absolutely well-posed, which can solve the ill-posed problem of the original sixequation model. The relaxation term in the model can accurately describe the multi-dimensional motion on the interphase interface. There are two ways to obtain the relaxation coefficient, one is based on the relaxation time scale and the other is based on the acoustic impedance. The expression based on the acoustic impedance is only valid under high-speed flow conditions. For lowspeed flow, the first expression related to the traditional viscous resistance is more appropriate. The Riemann problem solution can be used to approximate the pressure and velocity on the interphase interface to solve the two-phase discontinuity at the interface. In the numerical solution of the model, a large number of existing researches use the step-by-step method to solve the problem, and the solution generates more intermediate variables and occupies a large space. There are also studies which solve the model as a whole, which preprocess the mass conservation equation and momentum conservation equation into the form of sumdifference differential equations to overcome the numerical instability problem caused by the disappearance of vapor/liquid phase. This paper summarized the existing research results and analyzed the future development direction of the relaxation twopressure twophase flow model, in order to provide theoretical reference for subsequent research.

Keywords

• two-fluid
• two-pressure
• velocity relaxation
• pressure relaxation
• well-posedness