A polyatomic gas with slow relaxation of the internal modes in contact with a solid boundary is considered. In a previous paper [K. Aoki, Phys. Rev. E 102, 023104 (2020)10.1103/PhysRevE.102.023104], the two-Temperature Navier-Stokes system, i.e., a set of compressible Navier-Stokes equations with the translational and internal temperatures, was derived from the ellipsoidal-statistical (ES) model of the Boltzmann equation for a polyatomic gas under the assumption that the Knudsen number is small and the ratio of the collisional mean free time to the relaxation time of the internal modes is as small as the Knudsen number. In the present study, the appropriate boundary conditions for the two-Temperature Navier-Stokes system are derived by the analysis of the Knudsen layer on the basis of the ES model for a polyatomic gas and the Maxwell-Type diffuse-specular reflection condition on the boundary. The resulting boundary conditions, which are of the type of slip boundary conditions, are summarized, together with the two-Temperature Navier-Stokes equations, in a form that is applicable to practical applications immediately.
Boundary conditions for two-temperature Navier-Stokes equations for a polyatomic gas
Martalo', Giorgio
2021-01-01
Abstract
A polyatomic gas with slow relaxation of the internal modes in contact with a solid boundary is considered. In a previous paper [K. Aoki, Phys. Rev. E 102, 023104 (2020)10.1103/PhysRevE.102.023104], the two-Temperature Navier-Stokes system, i.e., a set of compressible Navier-Stokes equations with the translational and internal temperatures, was derived from the ellipsoidal-statistical (ES) model of the Boltzmann equation for a polyatomic gas under the assumption that the Knudsen number is small and the ratio of the collisional mean free time to the relaxation time of the internal modes is as small as the Knudsen number. In the present study, the appropriate boundary conditions for the two-Temperature Navier-Stokes system are derived by the analysis of the Knudsen layer on the basis of the ES model for a polyatomic gas and the Maxwell-Type diffuse-specular reflection condition on the boundary. The resulting boundary conditions, which are of the type of slip boundary conditions, are summarized, together with the two-Temperature Navier-Stokes equations, in a form that is applicable to practical applications immediately.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
