Sensitivity analysis of the 1-D SFR thermal stratification model via discrete adjoint sensitivity method

Abstract This paper presents a parameter sensitivity analysis on a thermal stratification (TS) model by using the discrete sensitivity method. The TS model was recently developed in our research group to efficiently predict the TS phenomenon in pool-type Sodium-cooled Fast Reactors. The fluid temperature gradient was considered as the figure of merit in the sensitivity analysis because it best characterizes the thermal stratification phenomenon. The sensitivities of the fluid temperature gradient with respect to four different parameters were investigated, including jet volumetric flow rate Q jet , jet temperature T jet , heat capacity of the ambient fluid C p , a m b , and static thermal conductivity of the ambient fluid k c , a m b . The sensitivity analysis was conducted through both the conventional forward sensitivity method and the advanced adjoint sensitivity method, which is more effective in cases where the number of outputs is small and the number of input parameters is large. The sensitivities obtained in this study suggested that perturbations in Q jet , C p , a m b , and k c , a m b could introduce either positive or negative changes to the temperature gradient, depending on the axial location and the elapsed time of the experiment. However, an increase in T jet always decreased the temperature gradient. Moreover, the impact of T jet on the maximum temperature gradient was several times higher than that of the other three parameters, which indicated that additional attention may need to be paid to the occurrence of thermal stratification in the sodium pool when the impinging jet has a large temperature change. This study also provides a step-by-step example for the application of the discrete adjoint sensitivity method to the time-dependent nonlinear systems.