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 Se nsitivity Model (ASM-REL/TF) corresponding to the two-fluid model with nonc ondensable(s) used in RELAP5/MOD3.2. This validation has been carried out b y 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-Loop s with Pumps" sample problem supplied with RELAP5/MOD3.2 has been used to v erify the accuracy and stability of the numerical solution of the ASM-REL/T F when only the liquid phase is present. Furthermore, the "Edwards Pipe" sa mple 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 bo th (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 w hen 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 f luids, respectively, were replaced with pure steam. The results obtained fo r these sample problems depict typical sensitivities of junction velocities and volume-averaged pressures to perturbations in initial conditions and i ndicate 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 cod es for light water reactors. The well-known 2993 ASME Steam Tables are used to present typical analytical and numerical results for sensitivities of t he thermodynamic properties of water to the numerical parameters that appea r in the mathematical formulation of these properties. Particularly highlig hted are the very large sensitivities displayed by the specific isobaric fl uid 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 coeff icient for gas beta(g); and the isothermal coefficient for gas k(g). The de pendence 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 sensitiviti es 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 enthal py h(g), and the isothermal coefficient of compressibility for fluid k(f) t o the parameters that appear in their respective mathematical formulas are quite small. Finally, it is noted that such deterministically calculated se nsitivities can be used to rank the respective parameters according to thei r importance, to assess the effects of nonlinearities and, more generally, to perform comprehensive sensitivity/uncertainty analyses of thermal-hydrau lic codes that use a water substance as the working fluid.