Second-Order Adjoint Sensitivity and Uncertainty Analysis of a Heat Transport Benchmark Problem—II: Computational Results Using G4M Reactor Thermal-Hydraulic Parameters

This work presents numerical results for the second-order sensitivities of the temperature distributions in a paradigm benchmark problem modeling heat transport in a reactor fuel rod and the surrounding coolant channel. The development of this benchmark problem was originally motivated by the need to verify the numerical results for the first-order sensitivities produced by the FLUENT Adjoint Solver for the G4M Reactor preconceptual design and for a test section designed to investigate thermal-hydraulic phenomena of importance to the safety considerations for this reactor. The relative sensitivities computed using the FLUENT Adjoint Solver had significantly large values, of order unity, thereby motivating the need to investigate the impact of nonlinearities, the bulk of which are quantified by the responses’ second-order sensitivities. However, the current FLUENT Adjoint Solver cannot compute second-order sensitivities, which in turn motivated the derivation of these sensitivities for the heat transport benchmark problem by using the recently developed second-order adjoint sensitivity analysis methodology.

The numerical results obtained in this work used thermal-hydraulic parameters having mean values and standard deviations typical of the conditions found in the preliminary conceptual design of the G4M Reactor. These results show that the contributions of the second-order sensitivities to the expected values of the temperature distributions within the rod, on the rod’s surface, and in the coolant are <1% of the corresponding computed nominal values. Similarly, the contributions of the second-order sensitivities to the standard deviations of the temperature distributions within the rod, on the rod’s surface, and in the coolant are also 1%, or less, of the corresponding contributions stemming from the first-order sensitivities, to the respective total standard deviations (uncertainties). These results justify the use of first-order sensitivities for computing expected uncertainties in the temperature distributions within the benchmark problem and, hence, mutatis mutandis, for the test section and G4M Reactor design.

On the other hand, the most important impact of the second-order sensitivities is the positive skewnesses they induce in the temperature distributions within the rod, on the rod’s surface, and in the coolant. This implies that all three temperature distributions, particularly in the heated rod, are non-Gaussian, asymmetric, and skewed toward temperatures higher than the respective mean temperatures.