Thermodynamically consistent simulation of nonisothermal diffuse-interface two-phase flow with Peng-Robinson equation of state

JOURNAL OF COMPUTATIONAL PHYSICS

卷:371

Article

Kou, Jisheng¹  Sun, Shuyu² 

[1] Hubei Engn Univ, Sch Math & Stat, Xiaogan 432000, Hubei, Peoples R China

[2] King Abdullah Univ Sci & Technol, Div Phys Sci & Engn, Computat Transport Phenomena Lab, Thuwal 239556900, Saudi Arabia

关键词: Diffuse-interface model;    Nonisothermal flow;    Gas-liquid flow;    Thermodynamical consistency;    Peng-Robinson equation of state;    Convex-concave splitting;   

DOI  :  10.1016/j.jcp.2018.05.047

来源: Elsevier

【 摘 要 】

In this paper, we consider a diffuse-interface gas-liquid two-phase flow model with inhomogeneous temperatures, in which we employ the Peng-Robinson equation of state and the temperature-dependent influence parameter instead of the van der Waals equation of state and the constant influence parameter used in the existing models. As a result, our model can characterize accurately the physical behaviors of numerous realistic gas-liquid fluids, especially hydrocarbons. Furthermore, we prove a relation associating the pressure gradient with the gradients of temperature and chemical potential, thereby deriving a new formulation of the momentum balance equation, which shows that gradients of the chemical potential and temperature become the primary driving force of the fluid motion. It is rigorously proved that the new formulations of the model obey the first and second laws of thermodynamics. To design efficient numerical methods, we prove that Helmholtz free energy density is a concave function with respect to the temperature under certain physical conditions. Based on the proposed modeling formulations and the convex-concave splitting of Helmholtz free energy density, we propose a novel thermodynamically stable numerical scheme. We rigorously prove that the proposed method satisfies the first and second laws of thermodynamics. Finally, numerical tests are carried out to verify the effectiveness of the proposed simulation method. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

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