Shock Waves

, Volume 28, Issue 2, pp 267–283 | Cite as

Effect of shock interactions on mixing layer between co-flowing supersonic flows in a confined duct

Original Article

Abstract

Experiments are conducted to observe the effect of shock interactions on a mixing layer generated between two supersonic streams of Mach number M \(_\mathrm {1}\) \(=\) 1.76 and M \(_\mathrm {2}\) \(=\) 1.36 in a confined duct. The development of this mixing layer within the duct is observed using high-speed schlieren and static pressure measurements. Two-dimensional, compressible Reynolds averaged Navier–Stokes equations are solved using the k-\(\omega \) SST turbulence model in Fluent. Further, adverse pressure gradients are imposed by placing inserts of small (<7% of duct height) but finite (> boundary layer thickness) thickness on the walls of the test section. The unmatched pressures cause the mixing layer to bend and lead to the formation of shock structures that interact with the mixing layer. The mixing layer growth rate is found to increase after the shock interaction (nearly doubles). The strongest shock is observed when a wedge insert is placed in the M \(_\mathrm {2}\) flow. This shock interacts with the mixing layer exciting flow modes that produce sinusoidal flapping structures which enhance the mixing layer growth rate to the maximum (by 1.75 times). Shock fluctuations are characterized, and it is observed that the maximum amplitude occurs when a wedge insert is placed in the M \(_\mathrm {2}\) flow.

Keywords

Supersonic flows Mixing layers Shock interactions Mixing enhancement 

Notes

Acknowledgements

The authors would like to thank the members of the Propulsion Laboratory in the Muroran Institute of Technology for their help in carrying out experiments.

References

  1. 1.
    Bradshaw, P.: Compressible turbulent shear layers. Annu. Rev. Fluid Mech. 9, 33–54 (1977)CrossRefMATHGoogle Scholar
  2. 2.
    Dimotakis, P.E.: Turbulent free shear layer mixing and combustion. In: Curran, E.T., Murthy, S.N.B. (eds) High-Speed Flight Propulsion Systems. Progress in Astronautics and Aeronautics, pp. 265–340 (1991)Google Scholar
  3. 3.
    Andreopoulos, Y., Agui, J.H., Briassulis, G.: Shock wave-turbulence interactions. Annu. Rev. Fluid Mech. 32, 309–345 (2000)MathSciNetCrossRefMATHGoogle Scholar
  4. 4.
    Delery, J.: Physical introduction. In: Harvey, J.K., Babinsky, H. (eds.) Shock Wave-Boundary-Layer Interactions. Cambridge University Press, Cambridge (2011)Google Scholar
  5. 5.
    Papamoschou, D., Roshko, A.: The compressible turbulent shear layer: an experimental study. J. Fluid Mech. 197, 453–477 (1988)CrossRefGoogle Scholar
  6. 6.
    Clemens, N.T., Mungal, M.G.: Large-scale structure and entrainment in the supersonic mixing layer. J. Fluid Mech. 284, 171–216 (1995)Google Scholar
  7. 7.
    Goebel, S.G., Dutton, J.C., Krier, H., Renie, J.P.: Mean and turbulent velocity measurements of supersonic mixing layers. Exp. Fluids 8, 263–272 (1990)CrossRefGoogle Scholar
  8. 8.
    Olsen, M.G., Dutton, J.C.: Planar velocity measurements in a weakly compressible mixing layer. J. Fluid Mech. 486, 51–77 (2003)CrossRefMATHGoogle Scholar
  9. 9.
    Sarkar, S., Erlebacher, G., Hussaini, M.Y.: Direct simulation of compressible turbulence in a shear flow, NASA Contractor Report 187537 (1991)Google Scholar
  10. 10.
    Freund, J.B., Lele, S.K., Moin, P.: Compressibility effects in a turbulent annular mixing layer. Part 1. Turbulence and growth rate. J. Fluid Mech. 421, 229–267 (2000)MathSciNetCrossRefMATHGoogle Scholar
  11. 11.
    Freund, J.B., Lele, S.K., Moin, P.: Compressibility effects in a turbulent annular mixing layer. Part 2. Mixing of a passive scalar. J. Fluid Mech. 421, 269–292 (2000)MathSciNetCrossRefMATHGoogle Scholar
  12. 12.
    Vreman, A.W., Sandham, N.D., Luo, K.H.: Compressible mixing layer growth rate and turbulence characteristics. J. Fluid Mech. 320, 235–258 (1996)CrossRefMATHGoogle Scholar
  13. 13.
    Kourta, A., Sauvage, R.: Computation of supersonic mixing layers. Phys. Fluids 14(11), 3790–3797 (2002)CrossRefMATHGoogle Scholar
  14. 14.
    Yi, S., Zhao, Y., Tian, L., Cheng, Z.: A flow control study of a supersonic mixing layer via NPLS. Sci. China Ser. G: Phys., Mech. Astron. 52(12), 2001–2006 (2009)CrossRefGoogle Scholar
  15. 15.
    Zhao, Y., Yi, S., Tian, L., He, L., Cheng, Z.: The fractal measurement of experimental images of supersonic turbulent mixing layer. Sci. China Ser. G: Phys., Mech. Astron. 51(8), 1134–1143 (2008)Google Scholar
  16. 16.
    Barre, S., Bonnet, J.P.: Detailed experimental study of a highly compressible supersonic turbulent plane mixing layer and comparison with most recent DNS results: Towards an accurate description of compressibility effects in supersonic free shear flows. Int. J. Heat Fluid Flow 51, 324–334 (2015)Google Scholar
  17. 17.
    Zhang, S., Zhang, Y., Shu, C.: Multistage interaction of a shock wave and a strong vortex. Phys. Fluids 17, 116101-1–116101-13 (2005)MathSciNetMATHGoogle Scholar
  18. 18.
    Rault, A., Chiavassa, G., Donat, R.: Shock–vortex interactions at high Mach numbers. J. Sci. Comput. 19(1–3), 347–371 (2003)Google Scholar
  19. 19.
    Smart, M.K., Kalkhoran, I.M., Popovic, S.: Some aspects of streamwise vortex behavior during oblique shock wave/vortex interaction. Shock Waves 8, 243–255 (1998)CrossRefGoogle Scholar
  20. 20.
    Génin, F., Menon, S.: Studies of shock/turbulent shear layer interaction using Large–Eddy Simulation. Comput. Fluids 39, 800–819 (2010)Google Scholar
  21. 21.
    Parent, B., Sislian, J.P.: Hypersonic mixing enhancement by compression at a high convective mach number. AIAA J. 42(4), 787–795 (2004)Google Scholar
  22. 22.
    Tahsini, A.M., Tadayon Mousavi S.: Investigating the supersonic combustion efficiency for the jet-in-cross-flow. Int. J. Hydrog. Energy 40, 3091–3097 (2015)Google Scholar
  23. 23.
    Yamauchi, H., Cho, B., Kouchi, T., Masuya, G.: Mechanism of Mixing Enhanced by Pseudo-Shock Wave, AIAA Paper 2009-25, 47th AIAA Aerospace Sciences Meeting Including The New Horizons Forum and Aerospace Exposition (2009)Google Scholar
  24. 24.
    Rao, S.M.V., Jagadeesh, G.: Observations on the non-mixed length and unsteady shock motion in a two dimensional supersonic ejector. Phys. Fluids 26, 036103-1–036103-26 (2014)Google Scholar
  25. 25.
    Sugiyama, H., Takeda, H., Zhang, J., Okuda, K., Yamagishi, H.: Locations and oscillation phenomena of pseudo-shock waves in a straight rectangular duct. JSME Int. J. Ser. II 31(1), 9–15 (1988)Google Scholar
  26. 26.
    Li, L., Saito, T.: A survey of performance of fluidic thrust vectoring mechanisms by numerical and experimental studies. Int. J. Aerosp. Innov. 5(3–4), 51–60 (2013)CrossRefGoogle Scholar
  27. 27.
    Stratford, B.S., Beavers, G.S.: The Calculation of the Compressible Turbulent Boundary Layer in an Arbitrary Pressure Gradient–A Correlation of certain previous Methods, Reports and Memoranda No. 3207, Aeronautical Research Council-UK (1961)Google Scholar
  28. 28.
    Tropea, C., Yarin, A.L., Foss, J.F. (eds.): Springer Handbook of Experimental Fluid Mechanics. Springer, New York (2007)Google Scholar
  29. 29.
    Takagi, S., Uemura, T., Hirata, Y., Takada, K.: Humidity effects on unsteady characteristics of supersonic flow. Muroran Inst. Technol. Bull. 64, 61–68 (2015) (in Japanese)Google Scholar
  30. 30.
    Ben-Dor, G.: Oblique Shock Wave Reflections (Chapter 8.1). In: Ben-Dor, G., Igra, O., Elperin, T. (eds.) Handbook of Shock Waves, vol. 2, pp. 67–179. Academic Press, London (2001)Google Scholar
  31. 31.
    Zhang, Y., Wang, B., Zhang, H.: The shock wave refraction in supersonic planar mixing layers. Chin. Phys. Lett. 30(8), 084701-1–4 (2013)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.Department of Aerospace EngineeringIndian Institute of ScienceBengaluruIndia
  2. 2.Department of Aerospace EngineeringMuroran Institute of TechnologyMuroranJapan

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