AbstractsEngineering

A new numerical method and a solver for the two-phase two-fluid model are developed using an innovative high-resolution, Total Variation Diminishing (TVD) scheme. The new scheme is derived first for scalar hyperbolic problems using the method of flux limiters, then extended to the two-phase two-fluid model. A hybridization of the monotone 1st-order upwind scheme and the Quadratic Upstream Interpolation scheme (QUICK) is implemented using a new flux limiter function. The new function is derived in a systematic manner by imposing conditions necessary to ensure the TVD properties of the resulting scheme. For temporal discretization, the theta method is used, and values for the parameter theta are chosen such that the scheme is unconditionally stable (1/2???theta???1). Finite volume techniques with staggered mesh are then used to develop a solver for the one-dimensional two-phase two-fluid model based on different numerical schemes including the new scheme developed here. Linearized equations of state are used as closure relations for the model, with linearization derivatives calculated numerically using water properties based on the IAPWS IF-97 standard. Numerical convergence studies were conducted to verify, first, the new numerical scheme and then, the two-phase two-fluid solver. Numerical scheme results are presented for one-dimensional pure advection problem with smooth and discontinuous initial conditions and compared to those of other classical and high-resolution numerical schemes. Convergence rates for the new scheme are examined and shown to be higher compared to those of other schemes. For smooth solutions, the new scheme was found to exhibit a convergence rate of 1.3 and a convergence rate of 0.82 for discontinuous solutions. The two-phase two-fluid model solver is implemented to analyze numerical benchmark problems for verification and testing its abilities to handle discontinuities and fast transients with phase change. Convergence rates are investigated by comparing numerical results to analytical solutions available in literature for the case of the faucet flow problem. The new solver based on the new TVD scheme is shown to exhibit higher-order accuracy compared to other numerical schemes with convergence rate of 0.8. Mass errors are also examined when phase change occurs for the shock tube problem, and compared to those of the 1st-order upwind scheme implemented in common nuclear thermal-hydraulics codes like TRACE and RELAP5. The solver is shown to exhibit numerical stability when implemented to problems with discontinuous solutions and results of the new solver were free of spurious oscillations.