Fast and accurate water and steam properties programs for two-phase flow calculations

Abstract

The athlet code (M.J. Burwell et al., The thermalhydraulic code athlet for analysis of PWR and BWR systems, NURETH-4, Karlsruhe, 1989) is being developed at GRS for the thermohydraulic analysis of the behavior of PWRs and BWRs under postulated transient and accidental conditions. It is used by a number of institutions to perform thermohydraulic analysis in the field of nuclear reactor safety. These analyses are carried out both on mainframes and workstations. In general, these analyses consume hours of computing time on high speed computers. Much of this computing time is used to calculate water and steam properties. It has been found that, in some applications, up to 50% of the computing time is used to evaluate water and steam property routines, depending on the simulation model. In order to cut down computing costs most thermohydraulic codes use specially designed water and steam property packages which run much faster than the very accurate reference package IFC85 by Haar, Gallagher and Kell (NBS/NRC Wasserdampftafeln, London, 1988). At GRS work has been carried out to improve the packages used in the athlet code, which are fast running specially designed subroutines based on cubic and bicubic interpolation. In the reanalysis of the problem of constructing fast and accurate property packages it was found that, by using a sophisticated design of property package, substantial improvement can be achieved. The main points of the new package are as follows. 1. (i) For saturation values depending on pressure: extended range for pressure and temperature (0.01 bar, 6.9°C to 215 bar, 371.5°C); improved accuracy at the same computing effort by optimum selection of nodes; spline-based cubic interpolation leading to continuous second derivatives; common grid for all properties; consistent derivatives calculated by analytical differentiation of the interpolation functions 2. (i) For property values depending on pressure and temperature (subcooled, superheated, coexisting phases): extended range for pressure and temperature (liquid 0.01 bar, 6.9°C to 215 bar, 371.5°C; vapor 0.01 bar, 6.9°C to 215 bar, 2000°C); fast computation of subcooled and superheated values by combining analytical functions and bicubic interpolation; bicubic interpolation-based and 2D spline interpolation on a transformed curvilinear grid; linear continuation into the domain of coexisting phases (thermodynamic nonequilibrium); 2D functions to match the saturation values at the saturation line exactly; common 2D grid for all property functions; consistent derivatives calculated by analytical differentiation of the interpolation functions. The new package calculates only the material properties and leaves aside viscosity, heat capacity, thermal conductivity and surface tension, for which a fast solution is already given by Haar, Gallagher and Kell. The new package has been implemented into the athlet code. Its performance is demonstrated with the help of a typical thermohydraulic problem of a transient fill-up of a vessel. In addition, many numerical recipes and useful insights gained during the development of the new package will be presented, providing useful information for anyone who is planning to replace property packages, complicated correlations, etc. by fast and accurate interpolations/approximations.