TY - JOUR

T1 - Boundary Conditions for Fluid-Dynamic Parameters of a Single-Component Gas Flow with Vibrational Deactivation on a Solid Wall

AU - Shakurova, L. A.

AU - Kustova, E. V.

N1 - Publisher Copyright: © 2022, Pleiades Publishing, Ltd.

PY - 2022/6/1

Y1 - 2022/6/1

N2 - Abstract: Boundary conditions for fluid-dynamic parameters of a strongly nonequilibrium single-component rarefied gas flow in the slip regime are obtained using the methods of kinetic theory. The gas flow is described in the frame of the state-to-state approach assuming vibrational energy exchange as the slow relaxation process. The set of governing equations, including conservation equations, coupled with additional relaxation equations for vibrational state populations is presented. The gas-solid surface interaction is considered on the basis of the specular-diffusive model, and possible vibrational deactivation/excitation processes on the wall are taken into account. The obtained boundary conditions depend on the accommodation and deactivation coefficients along with the transport coefficients, such as the multicomponent vibrational energy diffusion and thermal diffusion coefficients, the thermal conductivity, the bulk and shear viscosity coefficients and the relaxation pressure. The dependence of boundary conditions on the normal mean stress has been obtained for the first time. In the particular case of the gas without internal degrees of freedom, the slip velocity and the temperature jump can be reduced to the well-known in the literature expressions. Implementation of the state-specific boundary conditions should not cause additional computational costs in numerical simulations of viscous flows in the state-to-state approach since the slip/jump equations depend on the transport coefficients that have to be evaluated regardless of the boundary conditions used in the code.

AB - Abstract: Boundary conditions for fluid-dynamic parameters of a strongly nonequilibrium single-component rarefied gas flow in the slip regime are obtained using the methods of kinetic theory. The gas flow is described in the frame of the state-to-state approach assuming vibrational energy exchange as the slow relaxation process. The set of governing equations, including conservation equations, coupled with additional relaxation equations for vibrational state populations is presented. The gas-solid surface interaction is considered on the basis of the specular-diffusive model, and possible vibrational deactivation/excitation processes on the wall are taken into account. The obtained boundary conditions depend on the accommodation and deactivation coefficients along with the transport coefficients, such as the multicomponent vibrational energy diffusion and thermal diffusion coefficients, the thermal conductivity, the bulk and shear viscosity coefficients and the relaxation pressure. The dependence of boundary conditions on the normal mean stress has been obtained for the first time. In the particular case of the gas without internal degrees of freedom, the slip velocity and the temperature jump can be reduced to the well-known in the literature expressions. Implementation of the state-specific boundary conditions should not cause additional computational costs in numerical simulations of viscous flows in the state-to-state approach since the slip/jump equations depend on the transport coefficients that have to be evaluated regardless of the boundary conditions used in the code.

KW - boundary conditions

KW - concentration jump

KW - nonequilibrium flow

KW - slip velocity

KW - state-to-state approach

KW - temperature jump

UR - http://www.scopus.com/inward/record.url?scp=85133725173&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/d2dae283-6796-303c-b01a-85b2a6e4255a/

U2 - 10.1134/S1063454122020121

DO - 10.1134/S1063454122020121

M3 - Article

AN - SCOPUS:85133725173

VL - 55

SP - 249

EP - 256

JO - Vestnik St. Petersburg University: Mathematics

JF - Vestnik St. Petersburg University: Mathematics

SN - 1063-4541

IS - 2

ER -