Gas-dynamic equations involving vibrational relaxation

  • L. A. Pal'tsev
Article
  • 18 Downloads

Abstract

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.

Keywords

Mathematical Modeling Distribution Function Energy Density Mechanical Engineer Industrial Mathematic 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Literature cited

  1. 1.
    V. N. Zhigulev, “On the equations of physical aerodynamics,” Inzh. Zh.,3, No. 1 (1963).Google Scholar
  2. 2.
    V. N. Zhigulev, “On the equations of motion of a nonequilibrium medium with radiation taken into account,” Inzh. Zh.,4, Nos. 2, 3 (1964).Google Scholar
  3. 3.
    M. N. Kogan, “The equations of nonequilibrium gas flows,” Zh. Prikl. Mekhan. i Tekh. Fiz., No. 1 (1965).Google Scholar
  4. 4.
    E. V. Stupochenko, S. A. Losev, and A. I. Osipov, Relaxational Processes in Shock Waves [in Russian], Fizmatgiz, Moscow (1965).Google Scholar
  5. 5.
    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.Google Scholar
  6. 6.
    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).Google Scholar
  7. 7.
    B. J. Berne, J. Jortner, and R. Gordon, “Vibrational relaxation of diatomic molecules in gases and liquids,” J. Chem. Phys.,47, No. 5 (1967).Google Scholar
  8. 8.
    L. Waldman, “Transporterscheinungen in Gasen von Mittlerem Druck,” in: Handbuch der Physik, Vol. 12, Göttingen-Heidelberg, Springer-Verlag, Berlin (1958), pp. 295–514.Google Scholar
  9. 9.
    M. L. Goldberger and K. M. Watson, Collision Theory, Wiley, New York (1964).Google Scholar
  10. 10.
    L. D. Landau and E. M. Lifshits, Quantum Mechanics, Addison-Wesley, Reading, Mass. (1966).Google Scholar
  11. 11.
    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.Google Scholar
  12. 12.
    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.Google Scholar
  13. 13.
    V. M. Kuznetsov, “A theory of volume viscosity,” Izv. Akad. Nauk SSSR, Mekhan. Zhidk. i Gaza, No. 6 (1967).Google Scholar

Copyright information

© Consultants Bureau 1974

Authors and Affiliations

  • L. A. Pal'tsev
    • 1
  1. 1.Moscow

Personalised recommendations