Application of discrete adjoint method to sensitivity and uncertainty analysis in steady-state two-phase flow simulations

Adjoint method is efficient for computing sensitivities of a response to a large number of input parameters; however, a successful application of adjoint method to sensitivity analysis in two-phase flow simulations is rare. In this article, a discrete adjoint sensitivity analysis framework is developed for steady-state two-phase flow problems. The new framework is based on a new implicit forward solver. The residual function of the discretized forward governing equation is used to formulate the adjoint problem. The framework is verified with the faucet flow problem and the Boiling Water Reactor Full-size Fine-mesh Bundle Test (BFBT) benchmark. For the faucet flow problem, adjoint sensitivities are shown to match analytical sensitivities very well. For the BFBT benchmark, the adjoint sensitivities are shown to match the sensitivities calculated with a perturbation equation. The adjoint sensitivities are also used to propagate uncertainties in input parameters to the uncertainty in the response. The uncertainty propagation with the adjoint method is verified with the Monte Carlo method and is shown to be accurate and efficient.