A revisit to the hicks’ hyperbolic two-pressure two-phase flow model

Hicks’ two-phase flow model represents one of the earliest hyperbolic two-pressure two-phase flow models developed in the early 1980s. This model was developed under the separated flow condition, but could be potentially generalized for more realistic flow conditions that are of interest to reactor safety analysis (e.g., bubbly flow). This model is mathematically hyperbolic and therefore well-posed, as eigenvalues from the characteristic analysis found to be all real. Many currently popular two-pressure models are formulated similarly to Hicks’ two-pressure model, with the inclusion of a void fraction transport equation. The void fraction transport equation is closed using the knowledge of transverse velocity on the two-phase interface, which is assumed to be the solution of a Riemann problem in the transverse direction. Numerical experiments on two phenomenological test problems, i.e., the two-phase water faucet problem and the sedimentation problem, were performed using the Hicks’ model, as well as the single-pressure two-phase flow model. Numerical results demonstrate that the channel size, which appears in the void fraction transport equation, has significant impact on the behavior of the Hicks’ model. By comparing to single-pressure model results and available analytical solutions, it was found that Hicks’ model with very small channel width behaves similarly to the single-pressure model. On the contrary, Hicks’ model with large channel width, however, constantly leads to unphysical liquid-phase pressure. These numerical experiments indicate that using the Riemann problem to close the equation system in Hicks’ derivation might be a questionable approach. Further investigations are necessary to explore different approaches that will properly close the equation system without leading to unphysical behaviors.