Comparison of the Navier-Stokes-Fourier model and the two-temperature model on the example of the problem of flow around high- camber surface

DOI: 10.34759/trd-2023-131-09

Аuthors

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

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

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

Abstract

The problem of flow around a surface with a large curvature (sharp edge) is becoming very relevant in connection with the development of modern technologies. In the vicinity of a sharp edge, a highly nonequilibrium gas flow occurs. Depending on the sharpness (curvature of the surface) of the edge, the degree of non-equilibrium of the flow can approach the non-equilibrium in the shock wave.

In the present work, we consider a supersonic flow of a diatomic gas around a plate of infinite span, which is installed parallel to the oncoming flow. The tip of the plate is rounded. The rounding radius characterizes the Knudsen number Кn of the problem being solved. The aim of this work is to estimate the maximum value of Kn at which the solutions of the NSF and M2T models practically coincide.

The calculations were carried out for a diatomic gas at the Mach number M=2. The Knudsen number varied in the range Kn=10^–2 ... 1. In the framework of the problem under consideration, Kn can be considered as the degree of pointedness of the nose, regardless of the degree of rarefaction of the gas, which is traditionally characterized by the number Kn.

The most important gas parameters, from a practical point of view, are the density and temperature in the near-wall region. These parameters mainly determine the processes of erosion of the edge surface, leading to a change in its shape.

The performed calculations show that for Kn>10^–2 both models of the first approximation, which describe the energy exchange between the translational and rotational degrees of freedom in different ways, lead to significantly different temperature distributions. the temperature distributions are fairly close over the entire range of Knudsen numbers considered.

Keywords:

arches, panels, hyperelastic materials, finite differences, nonlinear problems, stabilization method, approximation, boundary conditions

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