More conservative governing equations in RELAP5: Derivation of equations

The design and analysis of the thermal/hydraulic systems in nuclear power plants necessitate system codes that can be used in the analysis of steady state and transient conditions. RELAP5 is one of the most commonly used system codes in nuclear organizations. RELAP5 is based on a two-fluid, non-equilibrium, non-homogeneous, hydrodynamic model for the transient simulation of the two-phase system behavior. This model includes six governing equations to describe the mass, energy, and momentum of the two fluids. The “non-conservative” numerical approximation form (which is the current version of RELAP5 code) is obtained through the manipulation of selected derivative terms in the equations including the linearization of the product terms in the time derivatives of the equations. In the non-conservative technique, the truncation errors introduced in the linearization process can produce mass and energy errors for some classes of transients during time advancements, either resulting in (a) automatic reduction of time steps used in the advancement of the equations and increased run times or (b) the growth of unacceptably large errors in the transient results. To eliminate these difficulties, an optional numerical approach has been introduced in RELAP/SCDAPSIM/MOD4.0. This approach uses a more consistent set of “conservative” numerical approximations to solve non-linearized mass and energy governing equations. The RELAP/SCDAPSIM/MOD4.0 code, being developed as part of the international Severe Core Damage Analysis Package (SCDAP) Development and Training Program (SDTP), is the first version of RELAP5 rewritten to FORTRAN 90/95/2000 standards. This paper provides an overview of the original RELAP5 numerical approximations and describes the new theoretical approach. The second article introduces the strategic solution of the more conservative approach and presents some examples of transient problems that have been addressed utilizing this new approach.