Computation of three-dimensional three-phase flow of carbon dioxide using a high-order WENO scheme

TL;DR

This paper introduces a high-order WENO numerical scheme for simulating complex three-phase CO2 flows in 3D, achieving high accuracy and close agreement with experimental data.

Contribution

The paper presents a novel high-order WENO-based numerical method for 3D multiphase CO2 flow simulation using a general equation of state.

Findings

Achieved near fifth-order convergence for advection-diffusion and smooth flows.

Demonstrated quantitative agreement with experimental data for CO2 jet flows.

Validated the method's accuracy with real-world flow simulations.

Abstract

We have developed a high-order numerical method for the 3D simulation of viscous and inviscid multiphase flow described by a homogeneous equilibrium model and a general equation of state. Here we focus on single-phase, two-phase (gas-liquid or gas-solid) and three-phase (gas-liquid-solid) flow of CO2 whose thermodynamic properties are calculated using the Span-Wagner reference equation of state. The governing equations are spatially discretized on a uniform Cartesian grid using the finite-volume method with a fifth-order weighted essentially non-oscillatory (WENO) scheme and the robust first-order centered (FORCE) flux. The solution is integrated in time using a third-order strong-stability-preserving Runge-Kutta method. We demonstrate close to fifth-order convergence for advection-diffusion and for smooth single- and two-phase flows. Quantitative agreement with experimental data is obtained for a direct numerical simulation of an air jet flowing from a rectangular nozzle. Quantitative agreement is also obtained for the shape and dimensions of the barrel shock in two highly underexpanded CO2 jets.