An effective method for modeling 1D two-phase two-fluid six-equation model with automatic differentiation approach

The modeling of the two-fluid model with plenty of realistic closure correlations has been a tough problem because of the difficulty of forming the Jacobian matrix manually. To predict the phase appearance/disappearance in two-phase flow problems, the high-order spatial and fully implicit temporal discretization typically should be adopted. However, considering the requirement of a fairly accurate evaluation of the Jacobian matrix, the implementation of high-order schemes is a challenging task. In this study, the automatic differentiation (AD) method was employed to overcome these difficulties, which seems the first demonstration of the high-order scheme and the AD method in the two-fluid model with realistic relations. With the AD method, the high-order fully implicit scheme, and the preconditioned Jacobian-free Newton-Krylov (PJFNK) method, the two-fluid code was developed to solve the two-phase flow and heat transfer problems in this study. Through simulations of a series of hydrodynamics two-phase flow problems, this code was verified and validated in both transients and boiling conditions. Meanwhile, code-to-code comparisons with well-validated code, RELAP5, were presented. The results demonstrate the promising performance of the developed code for solving 1D two-phase flow problems.