An advancement in iterative solution schemes for three-dimensional, two-fluid modeling of two-phase flow in PWR fuel bundles

This paper outlines a fully three-dimensional two-fluid one-pressure model with a semi-implicit finite difference scheme coupled with heat conduction which can be applicable to thermal non-equilibrium two-phase flow field in subchannel geometry of Pressurized Water Reactors (PWR). The system of equations was linearized using the Newton-Raphson method and was collapsed into the pressure equations forming a system of the Poisson type. Then, two-phase flow modeling was combined with Krylov methods as advanced computing techniques to investigate the feasibility of implementing preconditioned Krylov subspace solvers as the numerical scheme to solve pressure equations. Six popular Krylov subspace solvers were considered: GMRES, FGMRES, DQGMRES, CGNR, BCG, and TFQMR combined with the block incomplete LU factorization with a dual truncation strategy (BILUT) preconditioner. These proposed iterative solvers were applied to the constructed linear pressure equations in the inner iteration in combination with the outer-Raphson iteration loop. Evaluation was performed in two stages. First, two-fluid numerical scheme capability was evaluated against OECD/NRC NUPEC PWR Bundle tests (PSBT Benchmark). The results for steady-state (PSBT) bundle show that an overall agreement can be found. At the second stage, convergency, stability, and accuracy of the proposed schemes were studied based on PSBT steady-state data through a comparison of utilized Krylov solvers and the direct inversion method as the pressure solution modeling options. It was found that the Krylov solvers do not introduce deviations to the two-phase flow results. Moreover, the convergence history of candidate Krylov solvers demonstrated that GMRES, FGMRES, and DQGMRES have a more efficient and stable convergence performance.