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Shock stability in magnetogasdynamic channel flows

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Abstract

The question of shock stability in a perfect-gas channel flow was examined in [1] in the onedimensional approximation under various assumptions: the disturbances are not reflected from the channel exit section, weak shock, etc. The results were found to coincide for two specific forms of the boundary conditions at the channel exit, from which it was concluded that the shock was not sensitive to the exit boundary condition. In [2] the question of shock stability was studied numerically in relation to a conducting-gas flow in a flat channel of constant cross section in the presence of a magnetic field (zero electric field intensity). It was established that the shock stability is significantly affected by the form of the conductivity law. A condition for the limiting regime between the stable and unstable regions was also given for flow with a shock wave. It was assumed that the pressure in the channel exit section is given. In this paper the effect of the exit boundary condition on shock stability in gasdynamic and magnetogasdynamic flows is demonstrated for small magnetic Reynolds numbers. Stability criteria are obtained for shocks near the channel exit for a specific exit condition. The influence of electromagnetic effects (conductivity law, electric load factor) on shock stability is investigated.

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Literature cited

  1. 1.

    Fundamentals of Gas Dynamics, Princeton Univ. Press., 1959.

  2. 2.

    A. V. Gubarev, L. M. Degtyarev, and A. P. Favorskii, “Some characteristics of a supersonic conducting gas flow in a MHD channel,” Izv. AN SSSR, MZhG [Fluid Dynamics], no. 3, 1969.

  3. 3.

    K. V. Brushlinskii, “Growth of the solution of the mixed problem for incomplete eigenfunctions,” Izv. AN SSSR, ser. matem.,23, no. 6, 1959.

  4. 4.

    F. A. Slobodkina, “Stability of quasi one-dimensional MHD flows,” PMM,31, no. 2, 1967.

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Additional information

Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, Vol. 11, No. 1, pp. 16–23, January–February, 1970.

The author is grateful to A. G. Kulikovskii for discussing his work.

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Slobodkina, F.A. Shock stability in magnetogasdynamic channel flows. J Appl Mech Tech Phys 11, 14–20 (1970). https://doi.org/10.1007/BF01102668

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Keywords

  • Shock Wave
  • Reynolds Number
  • Channel Flow
  • Electric Field Intensity
  • Weak Shock