Comparison of combined kinetic-hydrodynamic models of different orders on the example of the Couette flow

DOI: 10.34759/trd-2020-110-8

Аuthors

Berezko M. E.^*, Nikitchenko Y. A.^**

Moscow Aviation Institute (National Research University), 4, Volokolamskoe shosse, Moscow, А-80, GSP-3, 125993, Russia

*e-mail: maxberezko@yandex.ru
**e-mail: nikitchenko7@yandex.ru

Abstract

Boundary conditions formulating on a solid surface for moment equations systems represents significant complexities.

A strict formulation of such boundary conditions was obtained only for the Navier-Stokes-Fourier model (NSF) being an incomplete system of second-order moment equations. Under high non-equilibrium conditions, the NSF model with its corresponding boundary conditions significantly overestimates the coefficient of friction on the streamlined surface. Previously, the authors proposed a combined flow model supplementing the NSF model in the near-wall region with a kinetic equation with appropriate boundary conditions. This combination of hydrodynamic and kinetic models allowed significantly improving the solution in the near-wall region.

The presented article proposes a combined physical and mathematical flow model, employing model kinetic equation for polyatomic gases within the Knudsen layer, and the third-order system of moment equations (M3) within the rest of the computational domain. In the region of models concatenation approximating distribution function, representing a decomposition of the Maxwell equilibrium distribution function by the thermal velocity degrees, is being restored. Parameters of decomposition (non-equilibrium stresses and third-order moments) are determined in the M3 model approximation.

The example of the test problem solving for Couette flow demonstrates that this option of the combined model yields smooth solutions in the field of models’ concatination and allows a satisfactory accuracy of the flow field description in a wide range of Knudsen and Mach numbers. Both options of the combined model were compared. Analysis of the results revealed M3 hydrodynamic component employing in the combined model allowed enhancing the acceptable range of Knudsen numbers approximately by an order, while the Mach numbers could be increased up to hypersonic values.

Keywords:

moment equations, kinetic equation, nonequilibrium flows, Couette flow

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