Joint of kinetic and hydrodynamic models by the example of the Couette flow
Fluid, gas and plasma mechanics
Аuthors
^{*}, ^{**}, ^{***}Moscow Aviation Institute (National Research University), 4, Volokolamskoe shosse, Moscow, А80, GSP3, 125993, Russia
*email: maxberezko@yandex.ru
**email: nikitchenko7@yandex.ru
***email: tikhalena@gmail.com
Abstract
The problem of setting the boundary conditions on a solid surface for the viscous heatconducting gas equations becomes very relevant in the case of hypersonic and moderately rarefied flows. The statement of the boundary conditions at the level of gasdynamic variables results in significant errors for relatively large Mach values (M) and Knudsen (Kn) numbers. Physically adequate formulation of the boundary conditions on active (absorbing or releasing the gas) surfaces is impossible without considering molecular processes.
The kinetic models describing the gas flow at the molecular level make it possible to set the physically adequate conditions on the surfaces with different properties for any flow regime. However, the kinetic calculation of the flow field of complex geometry by is rather inefficient.
The purpose of this work is the development of a physicalmathematical flow model (KIN_NSF) containing the NavierStokesFourier model (NSF), «joined» to the kinetic model equation of polyatomic gases. The kinetic model is used in the nearwall Knudsen layer. The remaining flow range is described by the NSF model. In the range of the model, joining the approximating velocity distribution function of molecules is recovered by the parameters determined by the NSF model. It represents the expansion of the localbalanced distribution function in terms of the thermal velocity. The expansion coefficients (unbalanced stresses and heat fluxes) are presented in the NavierStokes approximation.
The developed KIN_NSF model is efficient enough for the practical applications and at the same time allows setting the boundary conditions at the kinetic level of the gas with the surface interaction processes description.
A series of test calculations has been performed on the example of a flat Couette flow in the intervals . The kinetic model equation for polyatomic gases, NSF and KIN_NSF models were tested.
The results of the calculations revealed that the KIN_NSF model is not much inferior in accuracy to the kinetic model, and it substantially exceeds it in the efficiency. With the KIN_NSF model required a few dozen times less CPU time than the kinetic model.
When describing flows of the dense gases, the economy of the KINNSF model does not depend on the Kn number and depends weakly on the M number, which is typical for the NSF model.
Keywords:
boundary conditions, NavierStokesFourier model, kinetic equation, joining the models, Couette flowReferences

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