Skip to main content

Investigation of the Effect of Injection from a Yawed Plate with the Spanwise-Varied Base Pressure on the Disturbance Propagation in the Regime of Strong Interaction


Flow in the three-dimensional boundary layer on a yawed plate of finite length from which a gas is injection along the normal is considered in the case of the regime of strong viscous-inviscid interaction. In order to investigate the upstream disturbance propagation, the flow functions are expanded in four-term series in the neighborhood of the leading edge of plate under the assumption that the base pressure which depends on the transverse coordinate is given on the plate trailing edge. It is shown that these expansions contain an undefined function and its first and second derivatives with respect to the transverse coordinate. The corresponding boundary-value problems are formulated and numerically solved and the eigenvalues are found. It is shown that the possibility of downstream influence becomes significantly higher with increase in both the yawing angle and the intensity of gas injection. The influence of the constitutive parameters on the flow characteristics in the three-dimensional boundary layer is investigated.

This is a preview of subscription content, access via your institution.

Fig. 1.
Fig. 2.
Fig. 3.
Fig. 4.
Fig. 5.
Fig. 6.
Fig. 7.


  1. Lees, L., On the boundary-layer equations in hypersonic flow and their approximate solutions, J. Aeronaut. Sci., 1953, no. 20(2), pp. 143–145.

  2. Stewartson, K., On the motion of a flat plate at high speed in a viscous compressible fluid. II. Steady motion, J. Aeronaut. Sci., 1955, no. 22(5), pp. 303–309.

  3. Neiland, V.Ya., Propagation of perturbations upstream with interaction between a hypersonic flow and a boundary layer, Fluid Dyn., 1970, vol. 5, no. 4, pp. 559–566.

    ADS  Article  Google Scholar 

  4. Neiland, V.Ya., Bogolepov, V.V., Dudin, G.N., and Lipatov, I.I., Asymptotic Theory of Supersonic Viscous Gas Flows, Amsterdam: Elsevier, 2007; Moscow: Fizmatlit, 2003.

  5. Brown, S.N. and Stewartson, K., A non-uniqueness of the hypersonic boundary layer, Q. J. Mech. Appl. Math., 1975, vol. 28, pt. 1, pp. 75–90.

    Article  Google Scholar 

  6. A. A. Kovalenko, Investigation of boundary layer separation under strong interaction with a hypersonic gas flow, Uch. Zap. TsAGI, 1974, vol. 5, no. 6, pp. 39–47.

    Google Scholar 

  7. Dudin, G.N. and Neiland, V.Ya., Generation of three-dimensional disturbances in a boundary layer on strong interaction with a supersonic flow, Fluid Dyn., 2018, vol. 53, no. 1, pp. 86–94.

    ADS  MathSciNet  Article  Google Scholar 

  8. Dudin, G.N. and Neiland, V.Ya., Influence of the plate surface temperature on the propagation of disturbances in a hypersonic flow, TsAGI Sci. J., 2018, vol. 49, no. 5, pp. 477–494.

  9. Whalen, R.J., Boundary-layer interaction on a yawed infinite wing in hypersonic flow, JASS, 1959, vol. 26, no. 12, pp. 839–841.

    MATH  Google Scholar 

  10. Kozlova, I.G., and Mikhailov, V.V., Strong viscous interaction on triangular and slipping wings, Fluid Dyn. 1970, vol. 5, no. 6, pp. 982–986.

    ADS  Article  Google Scholar 

  11. Dudin, G.N. and Neiland, V.Ya., Propagation of disturbances on a yawed plate in a regime of strong interaction, Doklady Physics, 2018, vol. 63, no. 11, pp. 467–470.

    ADS  Article  Google Scholar 

  12. Dudin, G.N. and Neiland, V.Y., Some features of hypersonic flow past a yawed plate, Dokl. Ross. Akad. Nauk, 2019, vol. 487, no. 1, pp. 23–26.

    Google Scholar 

  13. Dudin, G.N. and Neiland, V.Y., Temperature factor effect on the disturbance propagation in hypersonic flow past a yawed flat plate, Fluid Dyn., 2019, vol. 54, no. 5, pp. 647–657.

    ADS  MathSciNet  Article  MATH  Google Scholar 

  14. Neiland, V.Y., Gas injection in hypersonic flow, Uch. Zap. TsAGI, 1972, vol. 3, no. 6, pp. 32–39.

    Google Scholar 

  15. Lipatov, I.I., Distributed gas injection in hypersonic flow, J. Prikl. Mekh. Tekh. Fiz., 1987, no. 6, pp. 57–61.

  16. Dudin, G.N., Gas injection from the surface of a triangular plate in a hypersonic flow, Fluid Dyn., 2000, vol. 35, no. 1, pp. 101–107.

    ADS  Article  MATH  Google Scholar 

  17. Balashov, A.A. and Dudin, G.N., Flow past a plate in the regime of strong interaction in the presence of mass transfer, Tr. MFTI, 2015, vol. 7, no. 1, pp. 16–27.

    Google Scholar 

  18. Dudin, G.N. and Neiland, V.Y., Influence of injection from the wedge surface on propagation of disturbances in hypersonic flow, Uch. Zap. TsAGI, 2019, vol. 50, no. 6, pp. 17–32.

    Google Scholar 

  19. Hayes, W.D. and Probstein, R.F., Hypersonic Flow Theory, N.Y.; L.: Academic Press, 1959.

  20. Stollery, J.L., Laminar and turbulent boundary layer studies at hypersonic speeds, ICAS Paper, 1972, no. 72−09.

  21. Dudin, G.N., Treugol’nye kryl’ya v vyazkom giperzvukovom potoke (Delta Wings in a Viscous Hypersonic Flow), Moscow: Moscow Institute of Physics and Technology, 2011.

Download references

Author information

Authors and Affiliations


Corresponding author

Correspondence to G. N. Dudin.

Additional information

Translated by E.A.Pushkar

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Dudin, G.N. Investigation of the Effect of Injection from a Yawed Plate with the Spanwise-Varied Base Pressure on the Disturbance Propagation in the Regime of Strong Interaction. Fluid Dyn 57, 247–260 (2022).

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI:


  • three-dimensional boundary layer
  • yawed plate
  • strong interaction
  • injection
  • temperature factor