Adjoint sensitivity analysis of the RELAP5/MOD3.2 two-fluid thermal-hydraulic code system - II: Applications

This work presents results that illustrate the validation of the Adjoint Sensitivity Model (ASM-REL/TF) corresponding to the two-fluid model with noncondensable(s) used in RELAP5/MOD3.2. This validation has been carried out by using sample problems involving (a) a liquid phase only, (b) a gas phase only, and (c) a two-phase mixture (of water and steam). Thus, the "Two-Loops with Pumps" sample problem supplied with RELAP5/MOD3.2 has been used to verify the accuracy and stability of the numerical solution of the ASM-REL/TF when only the liquid phase is present. Furthermore, the "Edwards Pipe" sample problem, also supplied with RELAP5/MOD3.2, has been used to verify the accuracy and stability of the numerical solution of the ASM-REL/TF when both (i.e., liquid and gas) phases are present. In addition, the accuracy and stability have been verified of the numerical solution of the ASM-REL/TF when only the gas phase is present by using modified "Two-Loops with Pumps" and the "Edwards Pipe" sample problems in which the liquid- and two-phase fluids, respectively, were replaced with pure steam. The results obtained for these sample problems depict typical sensitivities of junction velocities and volume-averaged pressures to perturbations in initial conditions and indicate that the numerical solution of the ASM-REL/TF is as robust, stable, and accurate as the original RELAP5/MOD3.2 calculations. This work also illustrates the role that sensitivities of the thermodynamic properties of water play for sensitivity analysis of thermal-hydraulic codes for light water reactors. The well-known 2993 ASME Steam Tables are used to present typical analytical and numerical results for sensitivities of the thermodynamic properties of water to the numerical parameters that appear in the mathematical formulation of these properties. Particularly highlighted are the very large sensitivities displayed by the specific isobaric fluid and gas heat capacities C-pf and C-pg, respectively; the specific fluid enthalpy h(f); the specific gas volume V-g; the volumetric expansion coefficient for gas beta(g); and the isothermal coefficient for gas k(g). The dependence of beta(g) and k(g) on the most sensitive parameters turns out to be nonlinear, while the dependence of C-pf, C-pg, h(f), and V-g on the most sensitive parameters turns out to be linear, so the respective sensitivities predict exactly the effects of variations in the respective parameters. On the other hand, the sensitivities of the specific fluid volume V-f, the volumetric expansion coefficient for fluid beta(f), the specific gas enthalpy h(g), and the isothermal coefficient of compressibility for fluid k(f) to the parameters that appear in their respective mathematical formulas are quite small. Finally, it is noted that such deterministically calculated sensitivities can be used to rank the respective parameters according to their importance, to assess the effects of nonlinearities and, more generally, to perform comprehensive sensitivity/uncertainty analyses of thermal-hydraulic codes that use a water substance as the working fluid.