Sensitivity Theory for Reactor Thermal-Hydraulics Problems

A sensitivity theory based on reactor physics experience was successfully developed for a reactor thermal-hydraulics problem. The new theory is derived for the case of nonlinear transient heat and mass transfer in a typical reactor subassembly. Suitable adjoint equations for heat and fluid flow are presented along with methods for deriving the sources and boundary and final conditions for these equations. Expressions for the sensitivity of any integral temperature response to problem input data are also presented. The theory is applied to a sample problem describing the steady-state thermal-hydraulic conditions in a Clinch River Breeder Reactor fuel channel. For this case, sensitivity coefficients are derived for several thermal response functions (i.e., peak clad and peak fuel temperature) for all physical input data (i.e., the heat transfer coefficient, thermal conductivities, etc.). A typical uncertainty analysis for peak clad and peak fuel temperature was also performed using uncertainty information about the physical data. Conclusions are drawn about the applicability of this approach to more general problems, and the procedures for its implementation in conjunction with large safety or thermal-hydraulics codes are outlined. The method is also compared with currently used response surface techniques.