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The Scientific World Journal
Volume 2013, Article ID 810175, 12 pages
http://dx.doi.org/10.1155/2013/810175
Research Article

Investigation of the Effects of Length to Depth Ratio on Open Supersonic Cavities Using CFD and Proper Orthogonal Decomposition

Department of Mechanical Engineering, TOBB University of Economics and Technology, Sogutozu Cad., No. 43, 06560 Ankara, Turkey

Received 12 April 2013; Accepted 20 May 2013

Academic Editors: A. Hadjadj and E. E. Imrak

Copyright © 2013 Ibrahim Yilmaz et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. S. Aradag, CFD for High Speed Flows in Engineering, VDM Dr. Müller, Saarbrucken, Germany, 2008.
  2. A. Syed, Detached eddy simulation of turbulent flow over an open cavity with and without cover plates [M.S. thesis], Wichita State University, Wichita, Kan, USA, 2010.
  3. S. J. Lawson and G. N. Barakos, “Review of numerical simulations for high-speed, turbulent cavity flows,” Progress in Aerospace Sciences, vol. 47, no. 3, pp. 186–216, 2011. View at Publisher · View at Google Scholar · View at Scopus
  4. J. E. Rossiter, “Wind tunnel experiments on the flow over rectangular cavities at subsonic and transonic speeds,” Tech. Rep. 64037, Royal Aircraft Establishment, Surrey, UK, 1964. View at Google Scholar
  5. H. H. Heller and D. B. Bliss, “The physical mechanism of flow-induced pressure fluctuations in cavities and concepts for their suppression,” in Proceedings of the 2nd Aeroacoustics Conference, AIAA Paper No. 75-491, AIAA, Hampton, Va, 1975.
  6. M. C. Shieh and P. Morris, “Comparison of two and three dimensional turbulent cavity flows,” in Proceedings of the 39th Aerospace Sciences Meeting and Exhibit, AIAA Paper No. 2001-0511, Reno, Nev, USA, 2001.
  7. S. H. Shih, A. Hamed, and J. J. Yeuan, “Unsteady supersonic cavity flow simulations using coupled k-ε and Navier-Stokes equations,” AIAA Journal, vol. 32, no. 10, pp. 2015–2021, 1994. View at Google Scholar · View at Scopus
  8. D. P. Rizzetta, “Numerical simulation of supersonic flow over a three dimensional cavity,” AIAA Journal, vol. 26, no. 7, pp. 799–807, 1988. View at Publisher · View at Google Scholar
  9. X. Zhang and J. A. Edwards, “Analysis of unsteady supersonic cavity flow employing an adaptive meshing algorithm,” Computers and Fluids, vol. 25, no. 4, pp. 373–393, 1996. View at Publisher · View at Google Scholar · View at Scopus
  10. A. Hamed, D. Basu, and K. Das, “Effect of Reynolds number on the unsteady flow and acoustic fields of supersonic cavity,” in Proceedings of the 4th ASME/JSME Joint Fluids Engineering Conference, FEDSM2003-45473, ASME, Honolulu, Hawaii, USA, July 2003. View at Scopus
  11. D. Basu, A. Hamed, and K. Das, “DES, hybrid RANS/LES and PANS models for unsteady separated turbulent flow simulations,” in Proceedings of the ASME Fluids Engineering Division Summer Meeting (FEDSM '05), FEDSM, 2005-77421, ASME, Houston, Tex, USA, June 2005. View at Scopus
  12. G. N. Barakos, S. J. Lawson, R. Steijl, and P. Nayyar, “Numerical simulations of high-speed turbulent cavity flows,” Flow, Turbulence and Combustion, vol. 83, no. 4, pp. 569–585, 2009. View at Publisher · View at Google Scholar · View at Scopus
  13. P. C. Bueno, Ö. H. Unalmis, N. T. Clemens, and D. S. Dolling, “The effects of upstream mass injection on a Mach 2 cavity flow,” in Proceedings of the 40th AIAA Aerospace Sciences Meeting & Exhibit, AIAA Paper No. 2002-0663, AIAA, Reno, Nev, USA, 2002.
  14. Ö. H. Ünalmis, N. T. Clemens, and D. S. Dolling, “Experimental study of shear-layer/acoustics coupling in Mach 5 cavity flow,” AIAA Journal, vol. 30, no. 2, pp. 242–252, 2001. View at Google Scholar · View at Scopus
  15. S. W. Perng, Passive Control of Pressure Oscillations in Hypersonic Cavity Flow [Ph.D. dissertation], University of Texas at Austin, Austin, Tex, USA, 1996.
  16. E. Lazar, G. Elliotts, and N. Glumac, “Control of the shear layer above a supersonic cavity using energy deposition,” AIAA Journal, vol. 46, no. 12, pp. 2987–2997, 2008. View at Publisher · View at Google Scholar · View at Scopus
  17. R. L. Stallings, “Store separations from cavities at supersonic flight speeds,” Journal of Spacecraft and Rockets, vol. 20, no. 2, pp. 129–132, 1983. View at Google Scholar · View at Scopus
  18. Y. Cao, J. Zhu, Z. Luo, and I. M. Navon, “Reduced order modeling of the upper tropical pacific ocean model using proper orthogonal decomposition,” Computers and Mathematics with Applications, vol. 52, no. 8-9, pp. 1373–1386, 2006. View at Publisher · View at Google Scholar · View at Scopus
  19. P. Holmes, J. L. Lumley, and G. Berkooz, Turbulence and Coherent Structures, Dynamical Systems and Symmetry, Cambridge University Press, New York, NY, USA, 1996.
  20. A. Chatterjee, “An introduction to the proper orthogonal decomposition,” Current Science, vol. 78, no. 7, pp. 808–817, 2000. View at Google Scholar · View at Scopus
  21. B. F. Feeny and R. Kappagantu, “On the physical interpretation of proper orthogonal modes in vibrations,” Journal of Sound and Vibration, vol. 211, no. 4, pp. 607–616, 1998. View at Google Scholar · View at Scopus
  22. B. Ravindra, “Comments on ‘on the physical interpretation of proper orthogonal modes in vibrations’,” Journal of Sound and Vibration, vol. 219, no. 1, pp. 189–192, 1999. View at Publisher · View at Google Scholar · View at Scopus
  23. R. Kappagantu and B. F. Feeny, “An “optimal” modal reduction of a system with frictional excitation,” Journal of Sound and Vibration, vol. 224, no. 5, pp. 863–877, 1999. View at Google Scholar · View at Scopus
  24. Y. C. Liang, H. P. Lee, S. P. Lim, W. Z. Lin, K. H. Lee, and C. G. Wu, “Proper orthogonal decomposition and its applications, part I: theory,” Journal of Sound and Vibration, vol. 252, no. 3, pp. 527–544, 2002. View at Publisher · View at Google Scholar · View at Scopus
  25. J. L. Lumley, “The structure of inhomogeneous turbulent flows,” in Atmospheric Turbulence and Radio Propagation, A. M. Yaglom and V. I. Tatarski, Eds., pp. 166–178, Nauka, Moskow, Russia, 1967. View at Google Scholar
  26. N. Aubry, P. Holmes, J. L. Lumley, and E. Stone, “The dynamics of coherent structures in the wall region of a turbulent boundary layer,” Journal of Fluid Mechanics, vol. 192, pp. 115–173, 1988. View at Google Scholar
  27. C. W. Rowley, T. Colonius, and R. M. Murray, “POD based models of self-sustained oscillations in the flow past an open cavity,” in Proceedings of the 6th Aeroacoustics Conference and Exhibit, AIAA Paper No. 2000-1969, AIAA, Lahaina, Hawaii, USA, 2000.
  28. K. K. Nagarajan, L. Cordier, C. Airiau, and A. Kourta, “POD based reduced order modelling of a compressible forced cavity flow,” in Le 19ème Congrès Français de Mécanique, Marseille, France, 2009.
  29. D. M. Bortz, A. D. Rubio, H. T. Banks, A. B. Cain, and R. C. Smith, “Reduced order modeling in control of open cavity acoustics,” Tech. Rep. CRSC-TROO-18, Center for Research in Scientific Computation, North Carolina State University, Rayleigh, NC, USA, 2000. View at Google Scholar
  30. T. Colonius, “An overview of simulation, modeling, and active control of flow/acoustic resonance in open cavities,” in Proceedings of the 39th Aerospace Sciences Meeting and Exhibit, AIAA Paper No. 2001-0076, AIAA, Reno, Nev, USA, 2001.
  31. E. Caraballo, X. Yuan, J. Little et al., “Further development of feedback control of cavity flow using experimental based reduced order model,” in Proceedings of the 35th AIAA Fluid Dynamics Conference and Exhibit, AIAA Paper No. 2005-5269, AIAA, Toronto, Canada, 2006. View at Scopus
  32. C. Kasnakoglu, Reduced order modeling, nonlinear analysis and control methods for flow control problems [Ph.D. thesis], The Ohio State University, Columbus, Ohio, USA, 2007.
  33. G. Berkooz, P. Holmes, and J. L. Lumley, “The proper orthogonal decomposition in the analysis of turbulent flows,” Annual Review of Fluid Mechanics, vol. 25, no. 1, pp. 539–575, 1993. View at Google Scholar · View at Scopus
  34. L. G. Kaufman, A. Maciulaitis, and R. L. Clark, “Mach 0. 6 to 3. 0 flows over rectangular cavities,” Tech. Rep. AFWAL-TR-82-3112, Air Force Wright Aeronautical Labs, New York, NY, USA, 1983. View at Google Scholar
  35. D. C. Wilcox, Turbulence Modeling for CFD, DCW Industries, La Canada, Calif, USA, 1993.
  36. A. J. Newman, “Model reduction via the Karhunen-Loéve expansion part II: some elementary examples,” Tech. Rep. 9633, Institute for Systems Research, University of Maryland, College Park, Md, USA, 1996, http://hdl.handle.net/1903/5752. View at Google Scholar
  37. A. E. Deane, I. G. Kevrekidis, G. E. Karniadakis, and S. A. Orszag, “Low-dimensional models for complex geometry flows: application to grooved channels and circular cylinders,” Physics of Fluids A, vol. 3, no. 10, pp. 2337–2354, 1991. View at Google Scholar · View at Scopus
  38. L. Sirovich, “Turbulence and the dynamics of coherent structures, part 1–3,” Quarterly Applied Mathematics, vol. 45, no. 3, pp. 561–590, 1987. View at Google Scholar
  39. H. V. Ly and H. T. Tran, “Modeling and control of physical processes using proper orthogonal decomposition,” Mathematical and Computer Modelling, vol. 33, no. 1–3, pp. 223–236, 2001. View at Publisher · View at Google Scholar · View at Scopus
  40. T. R. Smith, J. Moehlis, and P. Holmes, “Low-dimensional modelling of turbulence using the proper orthogonal decomposition: a tutorial,” Nonlinear Dynamics, vol. 41, no. 1–3, pp. 275–307, 2005. View at Publisher · View at Google Scholar · View at Scopus
  41. S. Volkwein, 1999, Proper Orthogonal Decomposition and Singular Value Decomposition Bericht Nr. 153 (Graz: Spezialforschungsbereich F003 Optimierung und Kontrolle, Projektbereich Kontinuierliche Optimierung und Kontrolle).
  42. K. Cohen, S. Siegel, and T. McLaughlin, “A heuristic approach to effective sensor placement for modeling of a cylinder wake,” Computers and Fluids, vol. 35, no. 1, pp. 103–120, 2006. View at Publisher · View at Google Scholar · View at Scopus
  43. H. C. Garner et al., “Drag of a rectangular planform cavity in a flat plate with a turbulent boundary layer for Mach numbers up to 3, part II: open and transitional flows,” Tech. Rep., Engineering Science Data Unit 00007, ESDU, London, UK, 2000. View at Google Scholar
  44. E. Ayli, Numerical analysis of supersonic cavity flow [M.S. thesis], TOBB University of Economics and Technology, Ankara, Turkey, 2012.