Stability of finite difference approximations of two fluid, two phase flow equations
- North Carolina State Univ., Raleigh, NC (United States)
It is well known that the basic single pressure, two fluid model for two phase flow has complex characteristics and is dynamically unstable. Nevertheless, common nuclear reactor thermal-hydraulics codes use variants of this model for reactor safety calculations. In these codes, the non-physical instabilities of the model may be damped by the numerical method and/or additional momentum interchange terms. Both of these effects are investigated using the linearized Von Neumann stability analysis. The stability of the semi-implicit method is of primary concern, because of its computational efficiency and popularity. It is shown that there is likely no completely stable numerical method, including fully implicit methods, for the basic single pressure model. Additionally, the momentum interchange terms commonly added to the basic single pressure model do not result in stable numerical methods for all the physically interesting reference conditions. Although practical stable approximations may be realized on a coarse computational grid, it is concluded that the assumption of instantaneously equilibrated phasic pressures must be relaxed in order to develop a generally stable numerical solution of a two fluid model. The numerical stability of the semi-implicit discretization of the true two pressure models of Ransom and Hicks, and Holm and Kupershmidt is analyzed. The semi-implicit discretization of these models, which possess real characteristics, are found to be numerically stable as long as certain convective limits are satisfied. Based on the form of these models, the general form of a numerically stable, basic two pressure model is proposed. The evolution equation required for closure is a volume fraction transport equation, which may possibly be determined based on void wave propagation considerations.
- Research Organization:
- Oak Ridge Inst. for Science and Education, TN (United States)
- Sponsoring Organization:
- USDOE Assistant Secretary for Nuclear Energy
- DOE Contract Number:
- AC05-76OR00033
- OSTI ID:
- 505672
- Report Number(s):
- DOE/OR/00033-T692; ON: DE97053103; TRN: 97:004580
- Resource Relation:
- Other Information: TH: Thesis (Ph.D.); PBD: 1995
- Country of Publication:
- United States
- Language:
- English
Similar Records
Two-fluid modeling of two-phase flow in BWR cores
RELAP-7 Application and Enhancement for FLEX Strategies and ATF Behavior under Extended Loss of AC Power Conditions