| Abstract: |
| In this work, an multiple-relaxation-time (MRT) lattice Boltzmann (LB) equation model with Beam-Warming (B-W) scheme is proposed to simulate multi-phase fluid system with Peng-Robinson (P-R) equation of state (EOS). The mathematical model of the multi-phase fluid flow is derived based on the NVT-based framework, where the Helmholtz free energy of P-R fluid is introduced. The nonideal force in multi-phase flow is directly computed from the free energy so that a more compact formulation of hydrodynamic equations, which is termed as potential form, can be obtained. The MRT-LB model is developed based on the potential form of hydrodynamic equations, which can eliminates the parasitic currents effectively. In addition, to capture the tiny nonconvex perturbation from the linear trend of P-R model precisely, the B-W scheme is utilized in the present MRT-LB model, which leads to an adjustable Courant-Friedrichs-Lewy (CFL) number and the second order accuracy can be naturally achieved by this scheme without any other requirement and numerical boundary conditions. In the numerical experiments, a realistic hydrocarbon component, such as isobutane, in three dimensional space is simulated by the proposed MRT-LB model. Numerical results show that the magnitude of parasitic currents can be significantly reduced by the present MRT-LB model. |
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