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Theoretical and Computational Fluid Dynamics

, Volume 31, Issue 5–6, pp 555–565 | Cite as

Spanwise effects on instabilities of compressible flow over a long rectangular cavity

  • Y. Sun
  • K. Taira
  • L. N. CattafestaIII
  • L. S. Ukeiley
Original Article

Abstract

The stability properties of two-dimensional (2D) and three-dimensional (3D) compressible flows over a rectangular cavity with length-to-depth ratio of \(L/D=6\) are analyzed at a free-stream Mach number of \(M_\infty =0.6\) and depth-based Reynolds number of \(Re_D=502\). In this study, we closely examine the influence of three-dimensionality on the wake mode that has been reported to exhibit high-amplitude fluctuations from the formation and ejection of large-scale spanwise vortices. Direct numerical simulation (DNS) and bi-global stability analysis are utilized to study the stability characteristics of the wake mode. Using the bi-global stability analysis with the time-averaged flow as the base state, we capture the global stability properties of the wake mode at a spanwise wavenumber of \(\beta =0\). To uncover spanwise effects on the 2D wake mode, 3D DNS are performed with cavity width-to-depth ratio of \(W/D=1\) and 2. We find that the 2D wake mode is not present in the 3D cavity flow with \(W/D=2\), in which spanwise structures are observed near the rear region of the cavity. These 3D instabilities are further investigated via bi-global stability analysis for spanwise wavelengths of \(\lambda /D=0.5{-}2.0\) to reveal the eigenspectra of the 3D eigenmodes. Based on the findings of 2D and 3D global stability analysis, we conclude that the absence of the wake mode in 3D rectangular cavity flows is due to the release of kinetic energy from the spanwise vortices to the streamwise vortical structures that develops from the spanwise instabilities.

Keywords

Compressible cavity flow Wake mode Global stability analysis 

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References

  1. 1.
    Åkervik, E., Brandt, L., Henningson, D.S., Hœpffner, J., Marxen, O., Schlatter, P.: Steady solutions of the Navier–Stokes equations by selective frequency damping. Phys. Fluids 18, 068–102 (2006)CrossRefGoogle Scholar
  2. 2.
    Arunajatesan, S., Barone, M.F., Wagner, J.L., Casper, K.M., Beresh, S.J.: Joint experimental/computational investigation into the effects of finite width on transonic cavity flow. AIAA Paper 2014-3027 (2014)Google Scholar
  3. 3.
    Beresh, S.J., Wagner, J.L., Pruett, B.O.M., Henfling, J.F.: Supersonic flow over a finite-width rectangular cavity. AIAA J. 53(2), 296–310 (2015)Google Scholar
  4. 4.
    Brès, G.A.: Numerical simulations of three-dimensional instabilities in cavity flows. Ph.D. thesis, California Institute of Technology (2007)Google Scholar
  5. 5.
    Brès, G.A., Colonius, T.: Three-dimensional instabilities in compressible flow over open cavities. J. Fluid Mech. 599, 309–339 (2008)CrossRefzbMATHGoogle Scholar
  6. 6.
    Brès, G.A., Nichols, J.W., Lele, S.K., Ham, F.E.: Towards best practices for jet noise predictions with unstructured large eddy simulations. In: 42nd AIAA Fluid Dynamics Conference, AIAA Paper 2012-2965 (2012)Google Scholar
  7. 7.
    Cattafesta, L.N., Song, Q., Williams, D.R., Rowley, C.W., Alvi, F.S.: Active control of flow-induced cavity oscillations. Prog. Aerosp. Sci. 44, 479–502 (2008)CrossRefGoogle Scholar
  8. 8.
    Citro, V., Giannetti, F., Brandt, L., Luchini, P.: Linear three-dimensional global and asymptotic stability analysis of incompressible open cavity flow. J. Fluid Mech. 768, 113–140 (2015)CrossRefzbMATHGoogle Scholar
  9. 9.
    Colonius, T.: An overview of simulation, modeling, and active control of flow/acoustic resonance in open cavities. In: 39th Aerospace Sciences Meeting and Exhibit, AIAA Paper 2001-0076 (2001)Google Scholar
  10. 10.
    Ding, Y., Kawahara, M.: Linear stability of incompressible flow using a mixed finite element method. J. Comput. Phys. 139, 243–273 (1998)CrossRefzbMATHMathSciNetGoogle Scholar
  11. 11.
    de Vicente, J., Basley, J., Meseguer-Garrido, F., Soria, J., Theofilis, V.: Three-dimensional instabilities over a rectangular open cavity: from linear stability analysis to experimentation. J. Fluid Mech. 748, 189–220 (2014)CrossRefGoogle Scholar
  12. 12.
    George, B., Ukeiley, L., Cattafesta, L., Taira, K.: Control of three-dimensional cavity flow using leading edge slot blowing. AIAA Paper 2015-1059 (2015)Google Scholar
  13. 13.
    Gharib, M., Roshko, A.: The effect of flow oscillations on cavity drag. J. Fluid Mech. 177, 501–530 (1987)CrossRefGoogle Scholar
  14. 14.
    Krishnamurty, K.: Sound radiation from surface cutouts in high speed flow. Ph.D. thesis, California Institute of Technology (1956)Google Scholar
  15. 15.
    Lawson, S.J., Barakos, G.N.: Review of numerical simulations for high-speed, turbulent cavity flows. Prog. Aerosp. Sci. 47, 186–216 (2011)CrossRefGoogle Scholar
  16. 16.
    Lehoucq, R., Maschhoff, K., Sorensen, D., Yang, C.: ARPACK software (1996–2007). http://www.caam.rice.edu/software/ARPACK/
  17. 17.
    Maull, D.J., East, L.F.: Three-dimensional flow in cavities. J. Fluid Mech. 16, 620–632 (1963)CrossRefzbMATHGoogle Scholar
  18. 18.
    Munday, P., Taira, K.: Private communication (2016)Google Scholar
  19. 19.
    Ramanan, N., Homsy, G.M.: Linear stability of lid-driven cavity flow. Phys. Fluids 6, 2690–2701 (1994)CrossRefzbMATHGoogle Scholar
  20. 20.
    Rockwell, D., Naudascher, E.: Review-self-sustaining oscillations of flow past cavities. J. Fluids Eng. 100, 152–165 (1978)CrossRefGoogle Scholar
  21. 21.
    Rossiter, J.E.: Wind-tunnel experiments on the flow over rectangular cavities at subsonic and transonic speeds. Technical Report 3438, Aeronautical Research Council Reports and Memoranda (1964)Google Scholar
  22. 22.
    Rowley, C.W., Colonius, T., Basu, A.J.: On self-sustained oscillations in two-dimensional compressible flow over rectangular cavities. J. Fluid Mech. 455, 315–346 (2002)CrossRefzbMATHMathSciNetGoogle Scholar
  23. 23.
    Schmid, P.J., Henningson, D.S.: Stability and Transition in Shear Flows. Springer, New York (2001)CrossRefzbMATHGoogle Scholar
  24. 24.
    Sipp, D., Lebedev, A.: Global stability of base and mean flows: a general approach and its applications to cylinder and open cavity flows. J. Fluid Mech. 593, 333–358 (2007)CrossRefzbMATHGoogle Scholar
  25. 25.
    Sun, Y., Nair, A.G., Taira, K., Cattafesta, L.N., Brès, G.A., Ukeiley, L.S.: Numerical simulation of subsonic and transonic open-cavity flows. In: 7th AIAA Theoretical Fluid Mechanics Conference, AIAA Paper 2014-3092 (2014)Google Scholar
  26. 26.
    Sun, Y., Zhang, Y., Taira, K., Cattafesta, L., George, B., Ukeiley, L.: Width and sidewall effects on high speed cavity flows. In: 54th AIAA Aerospace Sciences Meeting, AIAA Paper 2016-1343 (2016)Google Scholar
  27. 27.
    Theofilis, V.: Advances in global linear instability analysis of nonparallel and three-dimensional flows. Prog. Aerosp. Sci. 39, 249–315 (2003)CrossRefGoogle Scholar
  28. 28.
    Theofilis, V.: Global linear instability. Annu. Rev. Fluid Mech. 43, 319–352 (2011)CrossRefzbMATHMathSciNetGoogle Scholar
  29. 29.
    Theofilis, V., Colonius, T.: Three-dimensional instabilities of compressible flow over open cavities: direct solution of the biglobal eigenvalue problem. In: 34th Fluid Dynamics Conference and Exhibit, AIAA Paper 2004-2544 (2004)Google Scholar
  30. 30.
    Theofilis, V., Duck, P.W., Owen, J.: Viscous linear stability analysis of rectangular duct and cavity flows. J. Fluid Mech. 505, 249–286 (2004)CrossRefzbMATHMathSciNetGoogle Scholar
  31. 31.
    Yamouni, S., Sipp, D., Jacquin, L.: Interaction between feedback aeroacoustic and acoustic resonance mechanisms in a cavity flow: a global stability analysis. J. Fluid Mech. 717, 134–165 (2013)CrossRefzbMATHMathSciNetGoogle Scholar
  32. 32.
    Zhang, K., Naguib, A.M.: Dispersion relation and mode selectivity in low-Mach-number cavity flows. In: 36th AIAA Fluid Dynamics Conference, AIAA Paper 2006-3229 (2006)Google Scholar
  33. 33.
    Zhang, K., Naguib, A.M.: Effect of finite cavity width on flow oscillation in a low-Mach-number cavity flow. Exp. Fluids 51(5), 1209–1229 (2011)CrossRefGoogle Scholar
  34. 34.
    Zhang, Y., Sun, Y., Arora, N., Cattafesta, L., Taira, K., Ukeiley, L.: Suppression of cavity oscillations via three-dimensional steady blowing. AIAA Paper 2015-3219 (2015)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringFlorida State UniversityTallahasseeUSA
  2. 2.Department of Mechanical and Aerospace EngineeringUniversity of FloridaGainesvilleUSA

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