Abstract
Various relaxation stages in high-velocity and high-temperature gases with physicochemical processes are considered on the basis of model kinetic equations. Macroscopic equations are derived in the zero approximation of the modified Chapman–Enskog method and expressions for the flow members of gas-dynamic equations in terms of intensive and extensive parameters are deduced. A formula for the velocity of sound (as the velocity of propagation of small perturbations) is derived using the parameter æ, which is not a constant under the considered conditions.
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S. V. Vallander, E. A. Nagnibeda, and M. A. Rydalevskaya, Some Questions of the Kinetic Theory of the Chemical Reacting Gas Mixture (Leningr. Gos. Univ., Leningrad, 1977; US Air Force, FASTC–ID (RS) TO–0608–93).
E. A. Nagnibeda and E. V. Kustova, Non-Equilibrium Reacting Gas Flows. Kinetic Theory of Transport and Relaxation Processes (St.-Petersb. Gos. Univ., St. Petersburg, 2003; Springer-Verlag, Berlin, 2009).
M. A. Rydalevskaya, Statistical and Kinetic Models in Physical–Chemical Gas Dynamics (S.-Peterb. Gos. Univ., St. Petersburg, 2003) [in Russian].
P. L. Bhatnagar, Gross, E. P., and M. Krook, “A model for collision processes in gases. I. Small amplitude processes in charged and neutral one-component systems,” Phys. Rev. 94, 511–525 (1954). https:/doi.org/10.1103/PhysRev.94.511
E. P. Gross and M. Krook, “Model for collision processes in gases: Small-amplitude oscillations of charged two-component systems,” Phys. Rev. 102, 593–604 (1956). https:/doi.org/10.1103/PhysRev.102.593
F. B. Hanson and T. F. Morse, “Kinetic models for a gas with internal structure,” Phys. Fluids 10, 345–353 (1967). https:/doi.org/10.1063/1.1762114
T. F. Morse, “Kinetic model for gases with internal degrees of freedom,” Phys. Fluids 7, 159–169 (1964). https:/doi.org/10.1063/1.1711128
M. A. Rydalevskaya, “Hierarchy of relaxation times and the model kinetic equations,” Vestn. St.-Petersb. Univ., Ser. 1: Mat., Mekh., Astron., No. 2, 55–62 (2010).
E. Stupochenko, S. Losev, and A. Osipov, Relaxation in Shock Waves (Nauka, Moscow, 1965; Springer-Verlag, Heidelberg, 1967).
D. Bruno and V. Giovangigli, “Relaxation of internal temperature and volume viscosity,” Phys. Fluids 23, 093104 (2011). https:/doi.org/10.1063/1.3640083
M. A. Rydalevskaya, “Modified Chapman–Enskog method in the terms of intensive parameters,” Comput. Math. Math. Phys. 50, 1238–1248 (2010). doi 10.1134/S0965542510070122
M. A. Rydalevskaya, “Kinetic foundation of nonextensive gas dynamics,” AIP Conf. Proc. 762, 1073–1078 (2005). https:/doi.org/10.1063/1.1941677
S. V. Vallander, Lectures on Hydroaeromechanics (S.-Peterb. Gos. Univ., St. Petersburg, 2005) [in Russian].
M. A. Rydalevskaya and Yu. N. Voroshilova, Hydromechanics of an Ideal Fluid. Statement of Problems and Basic Properties (S.-Peterb. Gos. Univ., St. Petersburg, 2016) [in Russian].
L. I. Sedov, A Course on Continuum Mechanics (Wolters-Noordhoff, Groningen, 1971; Nauka, Moscow, 1973), Vol. 2.
Yu. N. Voroshilova and M. A. Rydalevskaya, “Effect of vibrational excitation of molecules on the velocity of sound in a high-temperature diatomic gas,” J. Appl. Mech. Tech. Phys. 49, 369–374 (2008). https:/doi.org/10.1007/s10808-008-0051-1
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Original Russian Text © Yu.N. Voroshilova, 2018, published in Vestnik Sankt-Peterburgskogo Universiteta: Matematika, Mekhanika, Astronomiya, 2018, Vol. 51, No. 2, pp. 273–282.
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Voroshilova, Y.N. Model Kinetic Equations and the Description of Gas Flows at Various Relaxation Stages. Vestnik St.Petersb. Univ.Math. 51, 169–174 (2018). https://doi.org/10.3103/S1063454118020097
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DOI: https://doi.org/10.3103/S1063454118020097