Linear stability analysis of RELAP5 two-fluid model in nuclear reactor safety results

Abstract

System thermal-hydraulic code RELAP5 is based on a two-fluid, non-equilibrium, and non-homogeneous hydrodynamic model for simulation of transient two-phase behavior. The code model includes six governing equations to incorporate the mass, energy, and momentum of the two fluids. In this paper, linear stability analysis is performed to check the ill-posedness of the RELAP5 specific two-fluid model (TFM) for all normal and accident conditions of a standard pressurized water reactor (PWR). The analysis gives information about the soundness of the model and identifies the range of parameters where the solutions obtained from the model will be numerically convergent. The linear two-phase fluid dynamic stability (by dispersion analysis) of the RELAP5 one-dimensional two-fluid model and numerical stability of the difference equation formulation (by Von Neumann method) is presented. The present analysis shows that the two-fluid model becomes ill-posed for some fluid conditions, where the results are less accurate, so sensitivity analysis plays an important role. The ill-posed nature implies that results thus obtained (by finite difference method) have to be interpreted carefully because of the sensitive nature of reactor safety analysis. It is also identified that the variation in various parameters (like slip ratio, system pressure, void fraction, and phasic velocities) can affect the error growth rates. It has been demonstrated that the basic system of one-dimensional two-phase flow equations, that possesses complex characteristics, exhibits unbounded instabilities in the short-wavelength limit and constitutes an improperly posed initial value problem. The semi-implicit numerical method, which is unconditionally stable for hyperbolic systems, becomes unstable for non-hyperbolic systems. For some of the fluid conditions, even after the introduction of artificial viscosity terms (in the difference equation formulation) that damp the high-frequency spatial components of the solution, are not sufficient for regularization of the two-fluid model. Thus, there is a need for the addition of newer terms, e.g. bubble collision, so that the existing incomplete model provides better results. It is also demonstrated that the basic TFM of RELAP5 with additional collision term makes the system unconditionally well-posed which are originally conditionally well-posed. Excellent agreement is obtained between the predicted and computed growth rates of harmonic disturbances. It is found that the instability associated with the two-fluid model discretized system of equations is related to the instability associated with the ill-posedness of the two-fluid model but is quantitatively different.