Symposium on Advanced Sensors and Modeling Techniques for Nuclear Reactor Safety

Investigation of non-hyperbolicity of conservation equations of RELAP/SCADAPSIM in nuclear reactor safety results by method of characteristics

The RELAP/SCADAPSIM code simulates the thermal-hydraulic characteristics of nuclear reactors by use of a two-fluid one dimensional, non-equilibrium, non-homogeneous 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 of the study of mathematical nature of the code model (not physics) and to predict the accuracy of the model in nuclear reactor safety analysis by RELAP/SCDAPSIM. Method of characteristics is applied to check the non-hyperbolic nature of conservation equations for all normal and accident conditions of LWR. 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 stable or unstable. The characteristics of equations of non-hyperbolic nature are complex. The exact implications of a model possessing complex characteristics imply that initial values and all finite difference schemes consistent with the differential equations are unstable. The analysis shows that governing equations of the code are non-hyperbolic for some operating conditions (evidenced by complex characteristics). Results are less accurate under such conditions so sensitivity analysis play an important role. The sensitivity of closure relationship on conservation equation's stability is also checked. The analysis is performed in MATLAB environment for system pressures 15.5, 7.0 and 0.7 MPa for Pressurized Water Reactor (PWR), Boiling Water Reactor (BWR) and Natural circulation reactor respectively. A detailed analysis for operating pressure of 0.1 MPa to 22.5 MPa is also performed to find out the non-hyperbolic region of code model. Realistic data of different type of reactors is used as input of the code. These results can also be extended for other thermal hydraulic systems. The different values of the coefficient of closure relationship (C) are taken for different flow regimes. It is checked that the coefficient of virtual mass for momentum equation has significant effect on the hyperbolicity of the system. It is recommended that further development of the RELAP model be performed to identify changes that would reduce the region of complex characteristics. The importance of method of characteristics (in reactor thermal safety analysis) is clearly evident here.