AUTHORS: Yu. A. Nikitchenko, S. A. Popov, A. V. Tikhonovets
Download as PDF
ABSTRACT: A mathematical model of the flow of a polyatomic gas containing a combination of the NavierStokes-Fourier model (NSF) and the model kinetic equation of polyatomic gases is presented. At the heart of the composed components is a unified physical model, as a result of which the NSF model is a strict first approximation of the model kinetic equation. The model allows calculations of flow fields in a wide range of Knudsen numbers ( Kn ), as well as fields containing regions of high dynamic nonequilibrium. The boundary conditions on a solid surface are set at the kinetic level, which allows, in particular, to formulate the boundary conditions on the surfaces absorbing or emitting gas. The composed model was tested. The example of the problem of the shock wave profile shows that up to Mach numbers M 2 the combined model gives smooth solutions even in those cases where the sewing point is in a high gradient region. For the Couette flow, smooth solutions are obtained at M 5, Kn 0.2 . As a result of research, a weak and insignificant difference between the kinetic region of the composed model and the “pure” kinetic model was established. A model effect was discovered: in the region of high nonequilibrium, there is an almost complete coincidence of the solutions of the kinetic region of the combined model and the “pure” kinetic solution. This work was conducted with the financial support of the Ministry of Education and Science of the Russian Federation, project №9.7170.2017/8.9.
KEYWORDS: polyatomic gases, Navier-Stokes-Fourier model, model kinetic equation, composed model, dynamic nonequilibrium, sorption surfaces.REFERENCES:
1] P. Degond, S. Jin, L. Mieussens, A smooth
transition model between kinetic and hydrodynamic
equations, Journal of Computational Physics,
No.209, 2005, pp. 665–694.
 I.V. Egorov, A.I. Erofeev, Continuum and kinetic approaches to the simulation of the hypersonic flow past a flat plate, Fluid Dynamics, Volume 32, Issue 1, January 1997, pp 112–122.
 G. Abbate, C.R. Kleijn, B.J. Thijsse, Hybrid continuum/molecular simulations of transient gas flows with rarefaction, AIAA Journal, Vol. 47, No. 7, 2009, pp. 1741-1749.
 N. Crouseilles, P. Degond, M. Lemou, A hybrid kinetic-fluid model for solving the gas dynamics Boltzmann-BGK equations, J. Comput. Phys., 199, 2004, pp 776-808.
 N. Crouseilles, P. Degond, M. Lemou, A hybrid kinetic-fluid model for solving the VlasovBGK equations, Journal of Computational Physics, 203, 2005, pp 572-601.
 E.M. Shakhov, Metod issledovaniia dvizhenii razrezhennogo gaza, М.: Nauka, 1975. 207 s.
 O.I. Rovenskaya, G. Croce, Numerical simulation of gas flow in rough micro channels: hybrid kinetic–continuum approach versus Navier– Stokes, Microfluid Nanofluid, 2016, 20:81.
 Yu.A. Nikitchenko, Model Kinetic Equation for Polyatomic Gases, Computational Mathematics and Mathematical Physics, Volume 57, Issue 11, November 2017, pp 1843–1855.
 Yu.A. Nikitchenko, Modeli neravnovesnykh techenii, М.: Izd-vo MAI, 2013. 160 s.
 V.A. Rykov, A model kinetic equation for a gas with rotational degrees of freedom, Fluid Dynamics, Volume 10, Issue 6, November 1975, pp 959–966.
 I.N. Larina, V.A. Rykov, Kinetic model of the Boltzmann equation for a diatomic gas with rotational degrees of freedom, Computational Mathematics and Mathematical Physics, Volume 50, Issue 12, December 2010, pp 2118–2130
 H. Alsmeyer, Density profiles in argon and nitrogen shock waves measured by the absorption of an electron beam, J. Fluid Mech., V. 74, Pt. 3, 1976, pp. 497-513.
 F. Robben, L. Talbot, Experimental study of the rotational distribution function of nitrogen in a shock wave, Phys. Fluids, V. 9, № 4, 1966, pp. 653- 662.
 V.S. Glinkina, Yu.A. Nikitchenko, S.A. Popov, Yu.A. Ryzhov, Drag Coefficient of an Absorbing Plate Set Transverse to a Flow, Fluid Dynamics, November 2016, Volume 51, Issue 6, pp 791–798.
 A.I. Erofeev. Investigation of the Nitrogen Shock Wave Structure on the Basis of Trajectory Calculations of the Molecular Interaction, Fluid Dynamics, Volume 37, Issue 6, November 2002, pp 970–982.
 Elizarova T.G., Khokhlov A.A., Montero S., Numerical simulation of shock wave structure in nitrogen, Physics of Fluids, vol.19 (N 6) 068102, 2007.
 M.E. Berezko, Yu.A. Nikitchenko, A.V. Tikhonovets, Sshivanie kineticheskoi i gidrodinamicheskoi modelei na primere techeniya Kuetta, Trudy MAI, Vyp.№94, http://trudymai.ru/published.php?ID=80922