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

Handle URI:
http://hdl.handle.net/10754/626560
Title:
Thermodynamically consistent simulation of nonisothermal diffuse-interface two-phase flow with Peng-Robinson equation of state
Authors:
Kou, Jisheng; Sun, Shuyu ( 0000-0002-3078-864X )
Abstract:
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, and thereby derive 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.
KAUST Department:
Computational Transport Phenomena Lab; Physical Sciences and Engineering (PSE) Division
Publisher:
arXiv
Issue Date:
6-Dec-2017
ARXIV:
arXiv:1712.03090
Type:
Preprint
Additional Links:
http://arxiv.org/abs/1712.03090v1; http://arxiv.org/pdf/1712.03090v1
Appears in Collections:
Other/General Submission; Physical Sciences and Engineering (PSE) Division; Computational Transport Phenomena Lab

Full metadata record

DC FieldValue Language
dc.contributor.authorKou, Jishengen
dc.contributor.authorSun, Shuyuen
dc.date.accessioned2017-12-28T07:32:16Z-
dc.date.available2017-12-28T07:32:16Z-
dc.date.issued2017-12-06en
dc.identifier.urihttp://hdl.handle.net/10754/626560-
dc.description.abstractIn 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, and thereby derive 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.en
dc.publisherarXiven
dc.relation.urlhttp://arxiv.org/abs/1712.03090v1en
dc.relation.urlhttp://arxiv.org/pdf/1712.03090v1en
dc.rightsArchived with thanks to arXiven
dc.titleThermodynamically consistent simulation of nonisothermal diffuse-interface two-phase flow with Peng-Robinson equation of stateen
dc.typePreprinten
dc.contributor.departmentComputational Transport Phenomena Laben
dc.contributor.departmentPhysical Sciences and Engineering (PSE) Divisionen
dc.eprint.versionPre-printen
dc.contributor.institutionSchool of Mathematics and Statistics, Hubei Engineering University, Xiaogan 432000, Hubei, China.en
dc.identifier.arxividarXiv:1712.03090en
kaust.authorSun, Shuyuen
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