Implicitly solving phase appearance and disappearance problems using two-fluid six-equation model

Abstract

Phase appearance and disappearance issue presents serious numerical challenges in two-phase flow simulations using the two-fluid six-equation model. Numerical challenges arise from the singular equation system when one phase is absent, as well as from the discontinuity in the solution space when one phase appears or disappears. In this work, a high-resolution spatial discretization scheme on staggered grids and fully implicit methods were applied for the simulation of two-phase flow problems using the two-fluid six-equation model. A Jacobian-free Newton-Krylov (JFNK) method was used to solve the discretized nonlinear problem. An improved numerical treatment was proposed and proved to be effective to handle the numerical challenges. The treatment scheme is conceptually simple, easy to implement, and does not require explicit truncations on solutions, which is essential to conserve mass and energy. Various types of phase appearance and disappearance problems relevant to thermal-hydraulics analysis have been investigated, including a sedimentation problem, an oscillating manometer problem, a noncondensable gas injection problem, a single-phase flow with heat addition problem and a subcooled flow boiling problem. Successful simulations of these problems demonstrate the capability and robustness of the proposed numerical methods and numerical treatments. Volume fraction of the absent phase can be calculated effectively as zero.

Additional Model Datasets and Results to Accelerate the Verification and Validation of RELAP-7

“…It is noted, however, the result shows the small fluctuations of void fraction around α vap =0.5 at t=20 and 40 [sec] before the equilibrium is reached at the end. These fluctuations are not usually observed in the validation test of the same problem with six-equation based two fluid model [4,5], implying that more tests are required to better understand this behavior.…”

A fully‐implicit numerical algorithm of two‐fluid two‐phase flow model using Jacobian‐free Newton–Krylov method

“…Zou [20][21][22][23][24] has conducted investigations using the JFNK method to fully-implicitly solve the two-fluid two-phase flow problem. The PETSc toolkit was used to provide the preconditioner.…”

“…Zou utilized similar method in his recent work. 22 Currently, most of the researches on the fully-implicit numerical algorithm based on the JFNK method for two-phase flow focus on the drift-flux two-phase flow model. Researches on the JFNK method for two-fluid two-phase flow model are few and not mature.…”

“…These treatments avoid the numerical difficulties and provide continuous interfacial heat transfer and interfacial drag. Zou utilized similar method in his recent work 22 …”