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Linear Stability of the Boundary Layer of Relaxing Gas on a Plate

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Abstract

The development of inviscid and viscous two-dimensional subsonic disturbances in the supersonic flat-plate boundary layer of a vibrationally excited gas is investigated on the basis of the linear stability theory. The system of two-temperature gas dynamics which includes the Landau-Teller relaxation equation is used as the initial model. Undisturbed flow is described by the self-similar boundary-layer solution for a perfect gas. It is shown that in the inviscid approximation excitation decreases the maximum growth rate of the most unstable second mode by 10–12% as compared with an ideal gas. The neutral stability curves are calculated for the first and second most unstable modes at the Mach numbers M = 2.2, 4.5, and 4.8. For both modes the critical Reynolds numbers at maximum excitation are greater by 12–13% than the corresponding values for the perfect gas.

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References

  1. Kneser, H.O., The interpretation of the anomalous sound-absorption in air and oxygen in terms of molecular collisions, J. Acoust. Soc. America, 1933, vol. 5, pp. 122–126.

    Article  ADS  MATH  Google Scholar 

  2. Leontovich, M.A., Remarks to the sound adsorption theory, Zh. Eksper. Teor. Fiz., 1936. vol. 6, no. 6, pp. 561–576.

    Google Scholar 

  3. Landau, L. and Teller, E., On the theory of sound dispersion, in Collected Papers of L.D. Landau, Oxford: Pergamon, 1965, pp. 147–153.

    Google Scholar 

  4. Fujii, K. and Hornung, H.G., Experimental investigation of high-enthalpy effects on attachment-line boundary layer, AIAA J., 2003. vol. 41, no. 7, pp. 1282–1291. https://doi.org/10.2514/2.2096

    Article  ADS  Google Scholar 

  5. Beierholm, A.K.-W., Leyva, I.A., Laurence, S.J., Jewell, J.S., and Hornung, H.G., Transition Delay in a Hypervelocity Boundary Layer using Nonequilibrium CO 2 Injection. GALCIT Technical Report FM 2008.001. Pasadena: California Institute of Technology, 2008.

    Book  Google Scholar 

  6. Bertolotti, F.B., The influence of rotational and vibrational energy relaxation on boundary-layer stability, J. Fluid Mech., 1998, vol. 372, pp. 93–118. https://doi.org/10.1017/S0022112098002353

    Article  ADS  MathSciNet  MATH  Google Scholar 

  7. Johnson, H.B., Seipp, T., and Candler, G.V., Numerical study of hypersonic reacting boundary layer transition on cones, Phys. Fluids, 1998, vol. 10, pp. 2676–2685. https://doi.org/10.1063/L869781

    Article  ADS  Google Scholar 

  8. Wagnild, R.M., Candler, G.V., Leyva, I.A., Jewell, J.S., and Hornung, H.G., Carbon dioxide injection for hypervelocity boundary layer stability, AIAA Paper 2010-1244, January 2010, pp. 1–16.

  9. Mack, L.M., On the inviscid acoustic-mode instability of supersonic shear layer. Part 1: Two-dimensional waves, Theoretical and Computational Fluid Dynamics, 1990. vol. 2, no. 2, pp. 97–123. https://doi.org/10.19910033977

    ADS  MATH  Google Scholar 

  10. Grigoryev, Yu.N. and Ershov, I.V., Stability and Suppression of Turbulence in Relaxing Molecular Gas Flows, Cham: Springer Intern. Publishing, 2017. https://doi.org/10.1007/978-3-319-55360-3

    Book  Google Scholar 

  11. Molevich, N.E., Asymptotic analysis of the stability of a plane-parallel compressible relaxing boundary layer, Fluid Dynamics, 1999. vol. 34, no. 5, pp. 675–680.

    MATH  Google Scholar 

  12. Zavershinskii, I.P. and Knestyapin, V.N., Stability of three-dimensional low-amplitude perturbations in the nonequilibrium compressible boundary layer, Teplofizika Vysokikh Temperatures, 2007. vol. 45, no. 2, pp. 235–242.

    Google Scholar 

  13. Ferziger, J.H. and Kaper, H.G., Mathematical Theory of Transport Processes in Gases, Amsterdam-London: North Holland publishing company, 1972.

    Google Scholar 

  14. Dunn D.W. and Lin, C.C., On the stability of the laminar boundary layer in a compressible fluid, J. Aeron. Sciences, 1955. vol. 22, no. 7, pp. 455–477. https://doi.org/10.2514/8.3374

    Article  MathSciNet  MATH  Google Scholar 

  15. Lin, C.C., The Theory of Hydrodynamics Stability, Cambridge: Cambridge Univ. Press, 1955.

    Google Scholar 

  16. Gaponov, S.A. and Maslov, A.A., Razvitie vozmushchenii v szhimaemykh potokakh (Development of Perturbations in Compressible Flows), Novosibirsk: Nauka, Siberian Branch, 1980.

    Google Scholar 

  17. Mack, L.M., Boundary Layer Stability Theory, Preprint of JPL Technical Report, Document 900-277, Rev. A. Pasadena: California Institute of Technology, 1969.

    Google Scholar 

  18. Grigor’ev, Yu.N. and Ershov, I.V., Linear stability of supersonic Couette flow of a molecular gas under the conditions of viscous stratification and excitation of the vibrational mode, Fluid Dynamics, 2017. vol. 52, no. 1, pp. 9–24. https://doi.org/10.7868/S0568528117010078

    Article  MathSciNet  MATH  Google Scholar 

  19. Kaye, G.W. and Laby, T.H., Tables of Physical and Chemical Constants. London, New York, Toronto: Longmans, Green & Co., 1958.

    MATH  Google Scholar 

  20. Loitsyanskii, L.G., Mechanics of Liquids and Gases, Oxford, London, Edinburgh, New York, Toronto, Paris, Frankfurt: Pergamon, 1966.

    MATH  Google Scholar 

  21. Canuto, C., Hussaini, M.Y., Quarteroni, A., and Zang, T.A., Spectral Methods in Fluid Dynamics, Berlin, Heidelberg: Springer-Verlag, 1988. https://doi.org/10.1007/978-3-642-84108-8

    Book  MATH  Google Scholar 

  22. Trefethen, L.N., Spectral Methods in Matlab, Philadelphia: Society for Industrial and Applied Mathematics, 2000.

    Book  MATH  Google Scholar 

  23. Malik, M.R., Numerical methods for hypersonic boundary layer stability, J. Comp. Phys., 1990, vol. 86, pp. 376–413. https://doi.org/10.1016/0021-9991(90)90106-B

    Article  ADS  MATH  Google Scholar 

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Authors and Affiliations

  1. Institute of Computational Technologies of the Siberian Branch of the Russian Academy of Sciences, pr. Akademika Lavrentieva 6, Novosibirsk, 630090, Russia

    Yu. N. Grigor’ev & I. V. Ershov

  2. Novosibirsk State University, ul. Pirogova 2, Novosibirsk, 630090, Russia

    Yu. N. Grigor’ev

  3. Novosibirsk State Agrarian University, ul. Dobrolyubova 160, Novosibirsk, 630090, Russia

    I. V. Ershov

Authors
  1. Yu. N. Grigor’ev
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  2. I. V. Ershov
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Correspondence to Yu. N. Grigor’ev or I. V. Ershov.

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Russian Text © The Author(s), 2019, published in Izvestiya RAN. Mekhanika Zhidkosti i Gaza, 2019, No. 3, pp. 3–15.

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Grigor’ev, Y.N., Ershov, I.V. Linear Stability of the Boundary Layer of Relaxing Gas on a Plate. Fluid Dyn 54, 295–307 (2019). https://doi.org/10.1134/S0015462819030054

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  • DOI: https://doi.org/10.1134/S0015462819030054

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