Abstract
As compared to the two-fluid single-pressure model, the two-fluid seven-equation two-pressure model has been proved to be unconditionally well-posed in all situations, thus existing with a wide range of industrial applications. The classical 1st-order upwind scheme is widely used in existing nuclear system analysis codes such as RELAP5, CATHARE, and TRACE. However, the 1st-order upwind scheme possesses issues of serious numerical diffusion and high truncation error, thus giving rise to the challenge of accurately modeling many nuclear thermal-hydraulics problems such as long term transients. In this paper, a semi-implicit algorithm based on the finite volume method with staggered grids is developed to solve such advanced well-posed two-pressure model. To overcome the challenge from 1st-order upwind scheme, eight high-resolution total variation diminishing (TVD) schemes are implemented in such algorithm to improve spatial accuracy. Then the semi-implicit algorithm with high-resolution TVD schemes is validated on the water faucet test. The numerical results show that the high-resolution semi-implicit algorithm is robust in solving the two-pressure two-fluid two-phase flow model; Superbee scheme and Koren scheme give two highest levels of accuracy while Minmod scheme is the worst one among the eight TVD schemes.
Highlights
In many industrial applications especially in nuclear industries, two-phase flows exist widely and are the most important phenomenon
From the book of De Bertodano et al [1], which is of great reference value for investigating the stability of two-fluid model, the oscillations are caused by the Kelvin–Helmholtz instability (KH)
A semi-implicit numerical algorithm based on the finite volume method associated with staggered grids has been developed to solve the advanced well-posed twofluid seven-equation two-pressure model
Summary
In many industrial applications especially in nuclear industries, two-phase flows exist widely and are the most important phenomenon. Berry et al [6] and Abgrall and Saurel [24] developed the discrete equation method (DEM) with a HLLC scheme to solve the seven-equation model They analyzed two pressure relaxation cases: infinitely fast and bounded with a realistic specific interfacial area. Many current reactor thermal-hydraulics codes like RELAP5 and CATHARE were developed based on classical first-order upwind scheme. Using such low-order scheme to make the convection terms of conservation equations discrete produces excessive numerical diffusion. In all the work mentioned above, the high-order schemes are performed for two-fluid six-equation single-pressure model only; few studies have been done on implementing high-resolution scheme in solving twopressure model.
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