Fluid Dynamics

, Volume 53, Issue 5, pp 690–701 | Cite as

Mach Wave Effect on Laminar-Turbulent Transition in Supersonic Flow over a Flat Plate

  • Q. H. Din
  • I. V. EgorovEmail author
  • A. V. Fedorov


The effect of a Mach wave (N wave) on laminar-turbulent transition induced by the first instability mode (Tollmien–Schlichting wave) in the flat-plate boundary layer is investigated on the basis of the numerical solution of Navier–Stokes equations at the freestream Mach number of 2.5. In accordance with the experiment, the N wave is generated by a two-dimensional roughness at the computation domain boundary corresponding to the side wall of the test section of a wind tunnel. It is shown that the disturbance induced by the backward front of the N wave in the boundary layer has no effect on the beginning of transition but displaces downstream the nonlinear stage of the first mode development. The disturbance induced by the forward front of the N wave displaces the beginning of transition upstream.


numerical modeling quasistationary wake Mach waves Tollmien–Schlichting waves supersonic flow boundary layer 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    S. R. Pate, “On Boundary-Layer Transition in Supersonic-HypersonicWind Tunnels. Theory and Application,” AEDC-TR-77-107, Arnold Engineering Development Center, Tennessee (1978).Google Scholar
  2. 2.
    A. V. Vaganov, Yu. G. Ermolaev, G. L. Kolosov, A. D. Kosinov, A. V. Panina, and N. V. Semenov, “Effect of an Incident MachWave on the Fluctuation Field in the Boundary Layer in Flow over a Planar DeltaWing,” Vestn. Novosibirsk Gos. Un-ta, Ser. Fizika 9 (1), 29 (2014).Google Scholar
  3. 3.
    A. V. Vaganov, Yu. G. Ermolaev, A. D. Kosinov, A. V. Panina, and V. I. Shalaev, “Experimental Investigation of the Flow Structure and Transition in the Boundary Layer on a DeltaWing with Blunted Leading Edges at Mach Numbers 2, 2.5, and 4,” Tr.MFTI 5 (3), 164 (2013).Google Scholar
  4. 4.
    A. V. Vaganov, Yu. G. Ermolaev, G. L. Kolosov, A. D. Kosinov, A. V. Panina, N. V. Semionov, and A. A. Yatskikh, “Impact of Incident Mach Wave on Supersonic Boundary Layer,” Thermophysics Aeromechanics 23 (1), 43 (2016).ADSCrossRefGoogle Scholar
  5. 5.
    Q. H. Din, I. V. Egorov, and A. V. Fedorov, “Interaction between Mach Waves and the Boundary Layer in Supersonic Flow past a Plate with a Sharp Leading Edge,” Uch. Zap. TsAGI 48 (4), 10 (2017).Google Scholar
  6. 6.
    L. M. Mack, “Boundary-Layer Stability Theory,” Jet Propulsion Lab., Pasadena, Ca, Internal Document 900–277 (1969).Google Scholar
  7. 7.
    I. V. Egorov and A. V. Novikov, “Direct Numerical Simulation of Laminar-Turbulent Flow past a Flat Plate at Hypersonic Velocities,” Zh. Vychisl.Mat.Mat. Fiz. 56 (6), 1064 (2016).zbMATHGoogle Scholar
  8. 8.
    G.-S. Jiang and C.-W. Shu, “Efficient Implementation ofWeighted ENO Schemes,” J. Comput. Phys. 126 (1), 202 (1996).ADSMathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    A. Novikov and I. Egorov, “Direct Numerical Simulations of Transitional Boundary Layer over a Flat Plate in Hypersonic Free-Stream,” AIAA Paper No. 3952 (2016).Google Scholar
  10. 10.
    A. Novikov, I. Egorov, and A. Fedorov, “Direct Numerical Simulation of Wave Packets in Hypersonic Compression-Corner Flow,” AIAA J. 54 (7), 2034 (2016).ADSGoogle Scholar
  11. 11.
    C. S. J. Mayer, D. A. von Terzi, and H. F. Fazel, “DNS of Complete Transition to Turbulence via Oblique Breakdown atMach 3,” AIAA Paper No. 4398 (2008).Google Scholar
  12. 12.
    H. Schlichting and K. Gersten, Boundary Layer Theory (Springer, New York, 2000).CrossRefzbMATHGoogle Scholar

Copyright information

© Pleiades Publishing, Inc. 2018

Authors and Affiliations

  1. 1.Moscow Institute of Sciences and Technology InstitutskiiDolgoprudnyi, Moscow oblastRussia
  2. 2.Central Aerohydrodynamic Institute (TsAGI)Zhukovskii, Moscow oblastRussia

Personalised recommendations