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

Jacobian-Free Newton-Krylov (JFNK) method is a stable and high-efficiency method to solve the multi-physics coupling problem for the modeling and simulation (M&S) of nuclear reactors. However, for the two-fluid two-phase flow model, the large number of constitutive models for different flow regimes as well as their discontinuities between different flow regimes present a huge challenge to solve the equations with JFNK method. Nevertheless, in this research, a fully-implicit numerical algorithm was proposed to solve the two-fluid two-phase flow model based on the JFNK method. The field equations were fully-implicitly discretized based on the second-order backward time and Van Albada high-order spatial difference schemes. A semi-implicit-scheme-based preconditioner was constructed to improve the calculation efficiency. The V-shaped linear advection test, water faucet test and the oscillating manometer test were simulated to evaluate the accuracy of the numerical algorithm and the performance of the numerical treatments with phase appearance and disappearance. By simulating the Bartolomei subcooled boiling experiment, Becker and Bennett dry out and post-dry out experiments, the performances of the developed numerical algorithm for single-phase flow, two-phase flow and transition from the single-phase flow to the two-phase flow were validated. The single-phase natural circulation and Edwards blowdown experiments were simulated to study the capability of the current fully-implicit numerical algorithm for slow and quick transients, respectively. The results demonstrate good performance of the proposed algorithm and validate the accuracy of such algorithm. The comparisons of numerical efficiency show that the fully-implicit numerical algorithm spends more time than the semi-implicit numerical algorithm because the calculation of the inverse precondition matrix is time consuming. But the numerical stability of the fully-implicit numerical algorithm is not influenced by the time step. In the practical simulations based on the fully-implicit numerical algorithm, a large time step can be used to obtain a stable prediction and comparable or higher calculation efficiency and accuracy with respect to the semi-implicit numerical algorithm.