Development of temporal and spatial high‐order schemes for two‐fluid seven‐equation two‐pressure model and its applications in two‐phase flow benchmark problems

Abstract

Summary Current existing main nuclear thermal‐hydraulics (T‐H) system analysis codes, such as RALAP5, TRACE, and CATHARE, play a crucial role in the nuclear engineering field for the design and safety analysis of nuclear reactor systems. However, two‐fluid model used in these T‐H system analysis codes is ill posed, easily leading to numerical oscillations, and the classical first‐order methods for temporal and special discretization are widely employed for numerical simulations, yielding excessive numerical diffusion. Two‐fluid seven‐equation two‐pressure model is of particular interest due to the inherent well‐posed advantage. Moreover, high‐order accuracy schemes have also attracted great attention to overcome the challenge of serious numerical diffusion induced by low‐order time and space schemes for accurately simulating nuclear T‐H problems. In this paper, the semi‐implicit solution algorithm with high‐order accuracy in space and time is developed for this well‐posed two‐fluid model and the robustness and accuracy are verified and assessed against several important two‐phase flow benchmark tests in the nuclear engineering T‐H field, which include two linear advection problems, the oscillation problem of the liquid column, the Ransom water faucet problem, the reversed water faucet problem, and the two‐phase shock tube problem. The following conclusions are achieved. (1) The proposed semi‐implicit solution algorithm is robust in solving two‐phase flows, even for fast transients and discontinuous solutions. (2) High‐order schemes in both time and space could prevent excessive numerical diffusion effectively and the numerical simulation results are more accurate than those of first‐order time and space schemes, which demonstrates the advantage of using high‐order schemes.

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

“…The V-shaped linear advection test is a benchmark problem that has been widely used to verify the accuracy of numerical algorithms. 27 The main parameters of the test section and test conditions are shown in Table 1. The test section is a horizontal pipe.…”

“…A stable and monotone high‐order discretization scheme can be obtained by using a bounded nonlinear slope limiter which makes the total variation diminish (TVD). Our previous study 27 showed that the Van Albada 28 high‐order spatial scheme, which satisfies the TVD condition, is the most accurate discretization scheme. Thus, it is used in this research and the slope limiter is $$$$ \psi (r)=\frac{r\left(r+1\right)}{r^2+1}.$$…”

Reliable Iterative Methods for Solving Convective Straight and Radial Fins with Temperature-Dependent Thermal Conductivity Problems

“…Many applications of the fluids in sciences or engineering are made such as: the developments of the fluid models where the robustness and accuracy have been checked and evaluated with six major two-phase flow benchmark problems [16]. These problems involve two linear advection problems, the problem of oscillation for the liquid column, the problem of a ransom water faucet, the reversed water faucet problem, and the problem of the two-phase shock tube where all of them are fundamental in the nuclear engineering T-H field.…”