We derive the gas-dynamic equations in the Navier-Stokes approximation for weak excitation of molecular vibrational states. We determine the distribution function for the density of the numbers determining occupancy of the vibrational states of the molecules. We show that the relaxational pressure is proportional to the deviation of the vibrational energy density from its local-equilibrium value for the temperature of the translational and rotational degrees of freedom of the molecules.
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V. N. Zhigulev, “On the equations of physical aerodynamics,” Inzh. Zh.,3, No. 1 (1963).
V. N. Zhigulev, “On the equations of motion of a nonequilibrium medium with radiation taken into account,” Inzh. Zh.,4, Nos. 2, 3 (1964).
M. N. Kogan, “The equations of nonequilibrium gas flows,” Zh. Prikl. Mekhan. i Tekh. Fiz., No. 1 (1965).
E. V. Stupochenko, S. A. Losev, and A. I. Osipov, Relaxational Processes in Shock Waves [in Russian], Fizmatgiz, Moscow (1965).
S. V. Valander, I. A. Egorova, and M. I. Rydalevskaya, “Extension of the Chapman-Enskog method to a mixture of gases with internal degrees of freedom and chemical reactions,” in: Aerodynamics of Rarefied Gases, Vol. 2 [in Russian], Leningrad State University, Leningrad (1965), pp. 122–162.
L. A. Pokrovskii, “Deviation of the equations of relaxational nonlinear hydrodynamics using a non-equilibrium statistical operator method, I,” Teoret. i Matem. Fiz.,2, No. 1 (1970).
B. J. Berne, J. Jortner, and R. Gordon, “Vibrational relaxation of diatomic molecules in gases and liquids,” J. Chem. Phys.,47, No. 5 (1967).
L. Waldman, “Transporterscheinungen in Gasen von Mittlerem Druck,” in: Handbuch der Physik, Vol. 12, Göttingen-Heidelberg, Springer-Verlag, Berlin (1958), pp. 295–514.
M. L. Goldberger and K. M. Watson, Collision Theory, Wiley, New York (1964).
L. D. Landau and E. M. Lifshits, Quantum Mechanics, Addison-Wesley, Reading, Mass. (1966).
G. Ludwig and M. Heil, “Boundary layer theory with dissociation and ionization,” in: Adv. Appl. Mech., Vol. 6, Academic Press, New York (1960), pp. 39–118.
V. S. Galkin and M. N. Kogan, “On the equations of nonequilibrium flows of polyatomic gases in the Euler approximation,” in: Problems of Hydrodynamics and Mechanics of a Continuous Medium [in Russian], Nauka, Moscow (1969), pp. 119–128.
V. M. Kuznetsov, “A theory of volume viscosity,” Izv. Akad. Nauk SSSR, Mekhan. Zhidk. i Gaza, No. 6 (1967).
Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 4, pp. 8–17, July–August, 1972.
In conclusion, the author thanks V. N. Zhigulev and V. S. Galkin for a discussion of his results.
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Pal'tsev, L.A. Gas-dynamic equations involving vibrational relaxation. J Appl Mech Tech Phys 13, 437–445 (1972). https://doi.org/10.1007/BF00850382
- Mathematical Modeling
- Distribution Function
- Energy Density
- Mechanical Engineer
- Industrial Mathematic