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

• Main Authors: Hui Xiao, Wei Liu
• Format: Article
• Language: English
• Published: MDPI AG 2021-03-01
• Series: Energies
• Subjects: pressure equation; pressure boundary condition; pressure-velocity coupling method; algorithm; circular tube
• Online Access: https://www.mdpi.com/1996-1073/14/5/1507

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.