Nonhyperbolicity of Conservation Equations of RELAP5 Two-Fluid Model in Nuclear Reactor Safety Results (Investigation and Eigenvalue Analysis)

Abstract

The RELAP5 code simulates the thermal-hydraulic characteristics of nuclear reactors by the use of a two-fluid one-dimensional, nonequilibrium, nonhomogeneous two-phase flow model. This model consists of six governing equations to describe the mass, energy, and momentum of the two fluids. The scope of this work comprises the study of the mathematical nature of the code model and to predict the accuracy of the model in the nuclear reactor safety analysis. The method of characteristics (MOC) is applied to check the nonhyperbolic nature of conservation equations for all normal and accident conditions of light water reactors (LWRs). The analysis also gives information about the soundness of the model and to identify the regions where the solutions obtained from it will be numerically convergent. The characteristics of equations of nonhyperbolic nature are complex. It implies that results thus obtained (by finite difference method) have to be interpreted very carefully in view of the sensitive nature of reactor safety analysis. The present analysis shows that governing equations of the code exhibit complex characteristics for some operating conditions thus implying nonhyperbolicity under those conditions. Results are less accurate under such conditions, so sensitivity analysis plays an important role. The sensitivity of closure relationship on the conservation equation's stability is also checked. The analysis is performed in matlab environment for three different systems, (a) pressurized water reactor (PWR), boiling water reactor (BWR), and (c) natural circulation reactor or advance heavy water reactor (AHWR). These results can also be extended to other thermal-hydraulic systems. The different values of the coefficient of closure relationship are taken for different flow regimes. It is observed that the coefficient of virtual mass (for momentum equation) has a significant effect on the hyperbolicity of the system. It is recommended that further development of the RELAP5 model be performed to identify changes that would reduce the region of complex characteristics. The importance of MOC (in nuclear reactor thermal-hydraulic safety analysis) is evident here. In addition, a detailed analysis for operating pressures range of 0.1–22.5 MPa is also performed to find out the nonhyperbolic regions of code model and realistic data of the different type of reactors is used as input of the code. It is also observed here that RELAP5 results are less accurate when system pressure exceeds 19.5 MPa.