A Solution to Pressure Equation with Its Boundary Condition of Combining Tangential and Normal Pressure Relations

Hui Xiao and Wei Liu
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Hui Xiao: School of Energy and Power Engineering, Huazhong University of Science and Technology, Wuhan 430074, China
Wei Liu: School of Energy and Power Engineering, Huazhong University of Science and Technology, Wuhan 430074, China

Energies, 2021, vol. 14, issue 5, 1-15

Abstract: Pressure is a physical quantity that is indispensable in the study of transport phenomena. Previous studies put forward a pressure constitutive law and constructed a partial differential equation on pressure to study the convection with or without heat and mass transfer. In this paper, a numerical algorithm was proposed to solve this pressure equation by coupling with the Navier-Stokes equation. To match the pressure equation, a method of dealing with pressure boundary condition was presented by combining the tangential and normal direction pressure relations, which should be updated dynamically in the iteration process. Then, a solution to this pressure equation was obtained to bridge the gap between the mathematical model and a practical numerical algorithm. Through numerical verification in a circular tube, it is found that the proposed boundary conditions are applicable. The results demonstrate that the present pressure equation well describes the transport characteristics of the fluid.

Keywords: pressure equation; pressure boundary condition; pressure-velocity coupling method; algorithm; circular tube (search for similar items in EconPapers)
JEL-codes: Q Q0 Q4 Q40 Q41 Q42 Q43 Q47 Q48 Q49 (search for similar items in EconPapers)
Date: 2021
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