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Shock Waves

, Volume 29, Issue 1, pp 135–151 | Cite as

Modal decomposition of turbulent supersonic cavity

  • R. K. Soni
  • N. Arya
  • A. DeEmail author
Original Article

Abstract

Self-sustained oscillations in a Mach 3 supersonic cavity with a length-to-depth ratio of three are investigated using wall-modeled large eddy simulation methodology for \(\hbox {Re}_{D} = 3.39\times 10^{5}\). The unsteady data obtained through computation are utilized to investigate the spatial and temporal evolution of the flow field, especially the second invariant of the velocity tensor, while the phase-averaged data are analyzed over a feedback cycle to study the spatial structures. This analysis is accompanied by the proper orthogonal decomposition (POD) data, which reveals the presence of discrete vortices along the shear layer. The POD analysis is performed in both the spanwise and streamwise planes to extract the coherence in flow structures. Finally, dynamic mode decomposition is performed on the data sequence to obtain the dynamic information and deeper insight into the self-sustained mechanism.

Keywords

LES Supersonic cavity Proper orthogonal decomposition Dynamic mode decomposition 

Notes

Acknowledgements

Financial support for this research is provided through IITK-Space Technology Cell (STC) (Grant No. STC/AE/20130054). Also, the authors would like to acknowledge the High-Performance Computing (HPC) Facility at IIT Kanpur.

References

  1. 1.
    Plentovich, E., Stallings Jr., R., Tracy, M.: Experimental cavity pressure measurements at subsonic and transonic speeds. Technical Paper 3358, NASA (1993)Google Scholar
  2. 2.
    Rossiter, J.E.: The effects of cavities on the buffeting of aircraft. Royal Aircraft Establishment, Technical Memorandum No. Aero 754, RAE Farnborough (1962)Google Scholar
  3. 3.
    Stallings Jr., R.L., Wilcox Jr., F.J.: Experimental cavity pressure distributions at supersonic speeds. Technical Report 2683, NASA (1987)Google Scholar
  4. 4.
    Tracy, M.B., Plentovich, E.B., Chu, J.: Measurements of fluctuating pressure in a rectangular cavity in transonic flow at high Reynolds numbers. Technical Memorandum 4363, NASA (1992)Google Scholar
  5. 5.
    Rossiter, J.E.: Wind tunnel experiments on the flow over rectangular cavities at subsonic and transonic speeds. Ministry of Aviation; Royal Aircraft Establishment, RAE Farnborough (1964)Google Scholar
  6. 6.
    Rossiter, J.E.: A preliminary investigation into armament bay buffet at subsonic and transonic speeds. Royal Aircraft Establishment, TM AERO 679 (1960)Google Scholar
  7. 7.
    Rossiter, J.E.: A note on periodic pressure fluctuations in the flow over open cavities. Technical Memorandum No. Aero 743, Royal Aircraft Establishment (1961)Google Scholar
  8. 8.
    Rossiter, J.E., Kurn, A.G.: Wind tunnel measurements of the unsteady pressures in and behind a bomb bay (Canberra). HM Stationery Office (1965)Google Scholar
  9. 9.
    Heller, H., Holmes, D.G., Covert, E.E.: Flow-induced pressure oscillations in shallow cavities. J. Sound Vib. 18(4), 545–553 (1971).  https://doi.org/10.1016/0022-460X(71)90105-2 CrossRefGoogle Scholar
  10. 10.
    Heller, H., Bliss, D.: Aerodynamically induced pressure oscillations in cavities—physical mechanisms and suppression concepts. Technical Report AFFDL-TR-74-133, Air Force Flight Dynamics Laboratory (1975)Google Scholar
  11. 11.
    Heller, H., Bliss, D.: The physical mechanism of flow-induced pressure fluctuations in cavities and concepts for their suppression. In: 2nd Aeroacoustics Conference, AIAA Paper 1975-491 (1975). https://doi.org/10.2514/6.1975-491
  12. 12.
    Heller, H., Delfs, J.: Cavity pressure oscillations: The generating mechanism visualized. J. Sound Vib. 196(2), 248–252 (1996).  https://doi.org/10.1006/jsvi.1996.0480 CrossRefGoogle Scholar
  13. 13.
    Zhang, X., Rona, A., Edwards, J.A.: An observation of pressure waves around a shallow cavity. J. Sound Vib. 214(4), 771–778 (1998).  https://doi.org/10.1006/jsvi.1998.1635 CrossRefGoogle Scholar
  14. 14.
    Arunajatesan, S., Sinha, N.: Hybrid RANS–LES modeling for cavity aeroacoustics predictions. Int. J. Comput. Aeroacoust. 2(1), 65–93 (2003).  https://doi.org/10.1260/147547203322436944 CrossRefGoogle Scholar
  15. 15.
    Rizzetta, D.P., Visbal, M.R.: Large-eddy simulation of supersonic cavity flow-fields including flow control. AIAA J. 41(8), 1452–1462 (2003).  https://doi.org/10.2514/2.2128 CrossRefGoogle Scholar
  16. 16.
    Zhuang, N., Alvi, F.S., Alkislar, M.B., Shih, C.: Supersonic cavity flows and their control. AIAA J. 44(9), 2118–2128 (2006).  https://doi.org/10.2514/1.14879 CrossRefGoogle Scholar
  17. 17.
    Tam, C.K., Block, P.J.: On the tones and pressure oscillations induced by flow over rectangular cavities. J. Fluid Mech. 89(2), 373–399 (1978).  https://doi.org/10.1017/S0022112078002657 MathSciNetCrossRefzbMATHGoogle Scholar
  18. 18.
    Lumley, J.L.: The structure of inhomogeneous turbulent flows. In: Yaglom, A.M., Tatarsky, V.I. (eds.) Atmospheric Turbulence and Radio Wave Propagation, pp. 166–178. Nauka, Moscow (1967)Google Scholar
  19. 19.
    Sirovich, L.: Turbulence and the dynamics of coherent structures. I—Coherent structures. II—Symmetries and transformations. III—Dynamics and scaling. Q. Appl. Math. 45, 561–571 (1987).  https://doi.org/10.1090/qam/910462 CrossRefzbMATHGoogle Scholar
  20. 20.
    Soni, R.K., De, A.: Investigation of mixing characteristics in strut injectors using modal decomposition. Phys. Fluids 30(1), 016108 (2018).  https://doi.org/10.1063/1.5006132 CrossRefGoogle Scholar
  21. 21.
    Das, P., De, A.: Numerical investigation of flow structures around a cylindrical after body under supersonic condition. Aerosp. Sci. Technol. 47, 195–209 (2015).  https://doi.org/10.1016/j.ast.2015.09.032 CrossRefGoogle Scholar
  22. 22.
    Das, P., De, A.: Numerical study of flow physics in supersonic base-flow with mass bleed. Aerosp. Sci. Technol. 58, 1–17 (2016).  https://doi.org/10.1016/j.ast.2016.07.016 CrossRefGoogle Scholar
  23. 23.
    Kumar, G., De, A., Gopalan, H.: Investigation of flow structures in a turbulent separating flow using hybrid RANS–LES model. Int. J. Numer. Methods Heat Fluid Flow 27(7), 1430–1450 (2016).  https://doi.org/10.1108/HFF-03-2016-0134 CrossRefGoogle Scholar
  24. 24.
    Rowley, C.W., Mezić, I., Bagheri, S., Schlatter, P., Henningson, D.S.: Spectral analysis of nonlinear flows. J. Fluid Mech. 641, 115–127 (2009).  https://doi.org/10.1017/S0022112009992059 MathSciNetCrossRefzbMATHGoogle Scholar
  25. 25.
    Schmid, P.J.: Dynamic mode decomposition of numerical and experimental data. J. Fluid Mech. 656, 5–28 (2010).  https://doi.org/10.1017/S0022112010001217 MathSciNetCrossRefzbMATHGoogle Scholar
  26. 26.
    Mezić, I.: Spectral properties of dynamical systems, model reduction and decompositions. Nonlinear Dyn. 41(1–3), 309–325 (2005).  https://doi.org/10.1007/s11071-005-2824-x MathSciNetzbMATHGoogle Scholar
  27. 27.
    Zhang, C., Wan, Z., Sun, D.: Model reduction for supersonic cavity flow using proper orthogonal decomposition (POD) and Galerkin projection. Appl. Math. Mech. 38(5), 723–736 (2017).  https://doi.org/10.1007/s10483-017-2195-9 MathSciNetCrossRefzbMATHGoogle Scholar
  28. 28.
    Yoshizawa, A.: Statistical theory for compressible turbulent shear flows, with the application to subgrid modeling. Phys. Fluids 29(7), 2152–2164 (1986).  https://doi.org/10.1063/1.865552 CrossRefzbMATHGoogle Scholar
  29. 29.
    Germano, M., Piomelli, U., Moin, P., Cabot, W.H.: A dynamic subgrid-scale eddy viscosity model. Phys. Fluids 3(7), 1760–1765 (1991).  https://doi.org/10.1063/1.857955 CrossRefzbMATHGoogle Scholar
  30. 30.
    Moin, P., Squires, K.D., Cabot, W.H., Lee, S.: A dynamic subgrid-scale model for compressible turbulence and scalar transport. Phys. Fluids A 3, 2746–2757 (1991).  https://doi.org/10.1063/1.858164 CrossRefzbMATHGoogle Scholar
  31. 31.
    Soni, R.K., Arya, N., De, A.: Characterization of turbulent supersonic flow over a backward-facing step. AIAA J. 55(5), 1511–1529 (2017).  https://doi.org/10.2514/1.J054709 CrossRefGoogle Scholar
  32. 32.
    Lagha, M., Kim, J., Eldredge, J.D., Zhong, X.: A numerical study of compressible turbulent boundary layers. Phys. Fluids 23(1), 015106 (2011).  https://doi.org/10.1063/1.3541841 CrossRefGoogle Scholar
  33. 33.
    Guarini, S.E., Moser, R.D., Shariff, K., Wray, A.: Direct numerical simulation of a supersonic turbulent boundary layer at Mach 2.5. J. Fluid Mech. 414, 1–33 (2000).  https://doi.org/10.1017/S0022112000008466 CrossRefzbMATHGoogle Scholar
  34. 34.
    Poinsot, T.J.A., Lele, S.K.: Boundary conditions for direct simulations of compressible viscous flows. J. Comput. Phys. 101(1), 104–129 (1992).  https://doi.org/10.1016/0021-9991(92)90046-2 MathSciNetCrossRefzbMATHGoogle Scholar
  35. 35.
    Greenshields, C.J., Weller, H.G., Gasparini, L., Reese, J.M.: Implementation of semi-discrete, non-staggered central schemes in a colocated, polyhedral, finite volume framework, for high-speed viscous flows. Int. J. Numer. Methods Fluids 63(1), 1–21 (2010).  https://doi.org/10.1002/fld.2069 MathSciNetzbMATHGoogle Scholar
  36. 36.
    Kurganov, A., Tadmor, E.: New high-resolution central schemes for nonlinear conservation laws and convection–diffusion equations. J. Comput. Phys. 160(1), 241–282 (2000).  https://doi.org/10.1006/jcph.2000.6459 MathSciNetCrossRefzbMATHGoogle Scholar
  37. 37.
    Rony T., Zeidan, D.: An unstaggered central scheme on nonuniform grids for the simulation of a compressible two-phase flow model. In: AIP Conference Proceedings, vol. 1738, no. 1. AIP Publishing (2016).  https://doi.org/10.1063/1.4951788
  38. 38.
    Zeidan, D.: Numerical resolution for a compressible two-phase flow model based on the theory of thermodynamically compatible systems. Appl. Math. Comput. 217(11), 5023–5040 (2011).  https://doi.org/10.1016/j.amc.2010.07.053 MathSciNetzbMATHGoogle Scholar
  39. 39.
    Zeidan, D.: Drag force simulation in explosive volcanic flows. In: AIP Conference Proceedings, vol. 1648, no. 1. AIP Publishing (2015).  https://doi.org/10.1063/1.4912324
  40. 40.
    Gruber, M.R., Baurle, R.A., Mathur, T., Hsu, K.Y.: Fundamental studies of cavity-based flameholder concepts for supersonic combustors. J. Propul. Power 17(1), 146–153 (2001).  https://doi.org/10.2514/2.5720 CrossRefGoogle Scholar
  41. 41.
    Celik, I.B., Cehreli, Z.N., Yavuz, I.: Index of resolution quality for large eddy simulations. J. Fluids Eng. 127(5), 949–958 (2005).  https://doi.org/10.1115/1.1990201 CrossRefGoogle Scholar
  42. 42.
    Ben-Yakar, A., Hanson, R.K.: Cavity flame-holders for ignition and flame stabilization in scramjets: An overview. J. Propul. Power 17(4), 869–877 (2001).  https://doi.org/10.2514/2.5818 CrossRefGoogle Scholar
  43. 43.
    Arya, N., Soni, R.K., De, A.: Investigation of flow characteristics in supersonic cavity using LES. Am. J. Fluid Dyn. 5(3A), 24–32 (2015).  https://doi.org/10.5923/s.ajfd.201501.04 Google Scholar
  44. 44.
    Li, W., Nonomura, T., Fujii, K.: On the feedback mechanism in supersonic cavity flows. Phys. Fluids 25(5), 056101 (2013).  https://doi.org/10.1063/1.4804386 CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Aerospace EngineeringIndian Institute of Technology KanpurKanpurIndia

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