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Compressibility effects in the shear layer over a rectangular cavity

Published online by Cambridge University Press:  26 October 2016

Steven J. Beresh ,
Justin L. Wagner  and
Katya M. Casper
Steven J. Beresh*
Affiliation:
Sandia National Laboratories, Albuquerque, NM 87185, USA
Justin L. Wagner
Affiliation:
Sandia National Laboratories, Albuquerque, NM 87185, USA
Katya M. Casper
Affiliation:
Sandia National Laboratories, Albuquerque, NM 87185, USA
*
†Email address for correspondence: [email protected]
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Abstract

The influence of compressibility on the shear layer over a rectangular cavity of variable width has been studied in a free stream Mach number range of 0.6–2.5 using particle image velocimetry data in the streamwise centre plane. As the Mach number increases, the vertical component of the turbulence intensity diminishes modestly in the widest cavity, but the two narrower cavities show a more substantial drop in all three components as well as the turbulent shear stress. This contrasts with canonical free shear layers, which show significant reductions in only the vertical component and the turbulent shear stress due to compressibility. The vorticity thickness of the cavity shear layer grows rapidly as it initially develops, then transitions to a slower growth rate once its instability saturates. When normalized by their estimated incompressible values, the growth rates prior to saturation display the classic compressibility effect of suppression as the convective Mach number rises, in excellent agreement with comparable free shear layer data. The specific trend of the reduction in growth rate due to compressibility is modified by the cavity width.

JFM classification

Turbulent Flows: Compressible turbulence Aerodynamics: High-speed flow Turbulent Flows: Shear layer turbulence
Type
Papers
Information
Journal of Fluid Mechanics , Volume 808 , 10 December 2016 , pp. 116 - 152
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Copyright
© Cambridge University Press 2016. This is a work of the U.S. Government and is not subject to copyright protection in the United States. 

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References

Ahuja, K. K. & Mendoza, J.1995 Effects of cavity dimensions, boundary layer, and temperature on cavity noise with emphasis on benchmark data to validate computational aeroacoustic codes. NASA Contractor Rep. 4653.Google Scholar
Arunajatesan, S., Barone, M. B., Wagner, J. L., Casper, K. M. & Beresh, S. J.2014 Joint experimental/computational investigation into the effects of finite width on transonic cavity flow. AIAA Paper 2014-3027.Google Scholar
Ashcroft, G. & Zhang, X. 2005 Vortical structures over rectangular cavities at low speed. Phys. Fluids 17 (1), 015104.CrossRefGoogle Scholar
Barone, M. F. & Lele, S. K. 2005 Receptivity of the compressible mixing layer. J. Fluid Mech. 540, 301–335.Google Scholar
Barone, M. F., Oberkampf, W. L. & Blottner, F. G. 2006 Validation case study: prediction of compressible turbulent mixing layer growth rate. AIAA J. 44 (7), 1488–1497.Google Scholar
Barre, S., Quine, C. & Dussauge, J. P. 1994 Compressibility effects on the structure of supersonic mixing layers: experimental results. J. Fluid Mech. 259, 47–78.Google Scholar
Basley, J., Pastur, L. R., Delprat, N. & Lusseyran, F. 2013 Space-time aspects of a three-dimensional multi-modulated open cavity flow. Phys. Fluids 25 (6), 064105.Google Scholar
Basley, J., Pastur, L. R., Lusseyran, F., Faure, T. M. & Delprat, N. 2011 Experimental investigation of global structures in an incompressible cavity flow using time-resolved PIV. Exp. Fluids 50 (4), 905–918.Google Scholar
Basley, J., Pastur, L. R., Lusseyran, F., Soria, J. & Delprat, N. 2014 On the modulating effect of three-dimensional instabilities in open cavity flows. J. Fluid Mech. 759, 546–578.CrossRefGoogle Scholar
Bell, J. H. & Mehta, R. D. 1990 Development of a two-stream mixing layer from tripped and untripped boundary layers. AIAA J. 28 (12), 2034–2042.Google Scholar
Beresh, S. J., Wagner, J. L., Pruett, B. O. M., Henfling, J. F. & Spillers, R. W. 2015a Supersonic flow over a finite-width rectangular cavity. AIAA J. 53 (2), 296–310.Google Scholar
Beresh, S. J., Wagner, J. L., Pruett, B. O. M., Henfling, J. F. & Spillers, R. W. 2015b Width effects in transonic flow over a rectangular cavity. AIAA J. 53 (12), 3831–3834.Google Scholar
Bian, S., Driscoll, J. F., Elbing, B. R. & Ceccio, S. L. 2011 Time resolved flow-field measurements of a turbulent mixing layer over a rectangular cavity. Exp. Fluids 51 (1), 51–63.Google Scholar
Bogdanoff, D. W. 1983 Compressibility effects in turbulent shear layers. AIAA J. 21 (6), 926–927.Google Scholar
Bradshaw, P. 1966 The effect of initial conditions on the development of a free shear layer. J. Fluid Mech. 26 (2), 225–236.CrossRefGoogle Scholar
Brès, G. A. & Colonius, T. 2008 Three-dimensional instabilities in compressible flow over open cavities. J. Fluid Mech. 599, 309–339.CrossRefGoogle Scholar
Chinzei, N., Masuya, G., Komuro, T., Murakami, A. & Kudou, K. 1986 Spreading of two-stream supersonic turbulent mixing layers. Phys. Fluids 29 (5), 1345–1347.Google Scholar
Chung, K.-M. 2001 Three-dimensional effect on transonic rectangular cavity flows. Exp. Fluids 30 (5), 531–536.Google Scholar
Clark, R. L., Kaufman, L. G. II & Maciulaitus, A.1980 Aeroacoustic measurements for Mach .6 to 3.0 flows past rectangular cavities. AIAA Paper 80-0036.Google Scholar
Clemens, N. T. & Mungal, M. G. 1992 Effects of sidewall disturbances on the supersonic mixing layer. AIAA J. 8 (1), 249–251.Google Scholar
Clemens, N. T. & Mungal, M. G. 1995 Large-scale structure and entrainment in the supersonic mixing layer. J. Fluid Mech. 284, 171–216.Google Scholar
Crook, S. D., Lau, T. C. W. & Kelso, R. M. 2013 Three-dimensional flow within shallow, narrow cavities. J. Fluid Mech. 735, 587–612.Google Scholar
Day, M. J., Reynolds, W. C. & Mansour, N. N. 1998 The structure of the compressible reacting mixing layer: insights from linear stability analysis. Phys. Fluids 10 (4), 993–1007.Google Scholar
Debiève, J.-F., Dupont, P., Laurent, H., Menaa, M. & Dussauge, J.-P. 2000 Compressibility and structure of turbulence in supersonic shear layers. Eur. J. Mech. (B/Fluids) 19 (5), 597–614.CrossRefGoogle Scholar
Debisschop, J. R., Chambres, O. & Bonnet, J. P. 1994 Velocity field characteristics in supersonic mixing layers. Exp. Therm. Fluid Sci. 9 (2), 147–155.Google Scholar
Disimile, P. J., Toy, N. & Savory, E. 2000 Effect of planform aspect ratio on flow oscillations in rectangular cavities. Trans. ASME 122 (1), 32–38.Google Scholar
Douay, C. L., Pastur, L. R. & Lusseyran, F. 2016 Centrifugal instabilities in an experimental open cavity flow. J. Fluid Mech. 788, 670–694.Google Scholar
Dudley, J. G. & Ukeiley, L.2011 Detached eddy simulation of a supersonic cavity flow with and without passive flow control. AIAA Paper 2011-3844.Google Scholar
Dutton, J. C.1997 Compressible turbulent free shear layers. AGARD Rep. 819. Turbulence in Compressible Flows, 2-1 to 2-42.Google Scholar
Dutton, J. C., Burr, R. F., Goebel, S. G. & Messersmith, N. L.1990 Compressibility and mixing in turbulent free shear layers. In Proceedings of the Twelfth Biennial Symposium on Turbulence, pp. A22-1 to A22-12.Google Scholar
Elliott, G. S. & Samimy, M. 1990 Compressibility effects in free shear layers. Phys. Fluids A 2 (7), 1231–1240.Google Scholar
Elliott, G. S., Samimy, M. & Arnette, S. A. 1995 The characteristics and evolution of large-scale structures in compressible mixing layers. Phys. Fluids 7 (4), 864–876.Google Scholar
Faure, T. M., Pastur, L., Lusseyran, F., Fraigneau, Y. & Bisch, D. 2009 Three-dimensional centrifugal instabilities development inside a parallelepipedic open cavity of various shape. Exp. Fluids 47 (3), 395–410.CrossRefGoogle Scholar
Forestier, N., Jacquin, L. & Geffroy, P. 2003 The mixing layer over a deep cavity at high-subsonic speed. J. Fluid Mech. 465, 101–145.Google Scholar
Freund, J. B., Lele, S. K. & Moin, P. 2000 Compressibility effects in a turbulent annular mixing layer. Part 1. Turbulence and growth rate. J. Fluid Mech. 421, 229–267.Google Scholar
Gai, S. L., Kleine, H. & Neely, A. J. 2015 Supersonic flow over a shallow open rectangular cavity. J. Aircraft 52 (2), 609–616.Google Scholar
Gharib, M. & Roshko, A. 1987 The effect of flow oscillations on cavity drag. J. Fluid Mech. 177, 501–530.Google Scholar
Goebel, S. G. & Dutton, J. C. 1991 Experimental study of compressible turbulent mixing layers. AIAA J. 29 (4), 538–546.Google Scholar
Grace, S. M., Dewar, W. G. & Wroblewski, D. E. 2004 Experimental investigation of the flow characteristics within a shallow wall cavity for both laminar and turbulent upstream boundary layers. Exp. Fluids 36 (5), 791–804.Google Scholar
Gruber, M. R., Messersmith, N. L. & Dutton, J. C. 1993 Three-dimensional velocity field in a compressible mixing layer. AIAA J. 31 (11), 2061–2067.Google Scholar
Haigermoser, C., Vesely, L., Novara, M. & Onorato, M. 2008 A time-resolved particle image velocimetry investigation of a cavity flow with a thick incoming turbulent boundary layer. Phys. Fluids 20 (10), 105101.Google Scholar
Hall, J. L., Dimotakis, P. E. & Rosemann, H. 1993 Experiments in nonreacting compressible shear layers. AIAA J. 31 (12), 2247–2254.CrossRefGoogle Scholar
Heller, H. H. & Bliss, D. B.1975 The physical mechanism for flow-induced pressure fluctuations in cavities and concepts for their suppression. AIAA Paper 75-491.Google Scholar
Ikawa, H. & Kubota, T. 1975 Investigation of supersonic turbulent mixing layer with zero pressure gradient. AIAA J. 13 (5), 566–572.CrossRefGoogle Scholar
Kang, W., Lee, S. B. & Sung, H. J. 2008 Self-sustained oscillations of turbulent flows over an open cavity. Exp. Fluids 45 (4), 693–702.Google Scholar
Krishnamurty, K.1955 Acoustic radiation from two-dimensional rectangular cut-outs in aerodynamic surfaces. NACA TN 3487.Google Scholar
Larchevêque, L., Sagaut, P., Thien-Hiep, L. & Comte, P. 2004 Large-eddy simulation of a compressible flow in a three-dimensional open cavity at high Reynolds number. J. Fluid Mech. 516, 265–301.CrossRefGoogle Scholar
Larchevêque, L., Sagaut, P. & Labbé, O. 2007 Large-eddy simulation of a subsonic cavity flow including asymmetric three-dimensional effects. J. Fluid Mech. 577, 105–126.Google Scholar
Lele, S. K. 1994 Compressibility effects in turbulence. Annu. Rev. Fluid Mech. 26, 211–254.Google Scholar
Liepmann, H. W. & Laufer, J.1947 Investigations of free turbulent mixing. NACA Tech. Note 1257.Google Scholar
Liu, X. & Katz, J. 2013 Vortex-corner interactions in a cavity shear layer elucidated by time-resolved measurements of the pressure field. J. Fluid Mech. 728, 417–457.Google Scholar
Malone, J., Debiasi, M., Little, J. & Samimy, M. 2009 Analysis of the spectral relationships of cavity tones in subsonic resonant cavity flows. Phys. Fluids 21 (5), 055103.CrossRefGoogle Scholar
Maull, D. J. & East, L. F. 1963 Three-dimensional flow in cavities. J. Fluid Mech. 16, 620–632.Google Scholar
Morris, P. J. & Giridharan, M. G. 1991 The effect of walls on instability waves in supersonic shear layers. Phys. Fluids A 3 (2), 356–358.Google Scholar
Murray, N., Sallstrom, E. & Ukeiley, L. 2009 Properties of subsonic open cavity flow fields. Phys. Fluids 21 (9), 095103.Google Scholar
Murray, R. C. & Elliott, G. S. 2001 Characteristics of the compressible shear layer over a cavity. AIAA J. 39 (5), 846–856.Google Scholar
Ohmichi, Y. & Suzuki, K. 2014 Flow structures and heating augmentation around finite-width cavity in hypersonic flow. AIAA J. 52 (8), 1624–1631.Google Scholar
Olsen, M. G. & Dutton, J. C. 2003 Planar velocity measurements in a weakly compressible mixing layer. J. Fluid Mech. 486, 51–77.CrossRefGoogle Scholar
Papamoschou, D. & Roshko, A. 1988 The compressible turbulent shear layer: an experimental study. J. Fluid Mech. 197, 453–477.Google Scholar
Plumblee, H. E., Gibson, J. S. & Lassiter, L. W.1962 A theoretical and experimental investigation of the acoustical response of cavities in aerodynamic flow. WADD TR-61-75.Google Scholar
Ragab, S. A. & Wu, J. L. 1989 Linear instabilities in two-dimensional compressible mixing layers. Phys. Fluids A 1 (6), 957–966.Google Scholar
Robinet, J.-C., Dussauge, J.-P. & Casalis, G. 2001 Wall effect on the convective-absolute boundary for the compressible shear layer. Theor. Comput. Fluid Dyn. 15 (3), 143–163.Google Scholar
Rockwell, D. & Knisely, C. 1979 The organized nature of flow impingement upon a corner. J. Fluid Mech. 93 (3), 413–432.Google Scholar
Rockwell, D. & Knisely, C. 1980 Observations of the three-dimensional nature of unstable flow past a cavity. Phys. Fluids 23 (3), 425–431.Google Scholar
Rossiter, J. E.1964 Wind-tunnel experiments on the flow over rectangular cavities at subsonic and transonic speeds. Aeronautical Research Council Rep. 3438.Google Scholar
Rossmann, T., Mungal, M. G. & Hanson, R. K. 2002 Evolution and growth of large-scale structures in high compressibility mixing layers. J. Turbul. 3 (1), 9.Google Scholar
Rowley, C. W., Colonius, T. & Basu, A. J. 2002 On self-sustained oscillations in two-dimensional compressible flow over rectangular cavities. J. Fluid Mech. 455, 315–346.Google Scholar
Samimy, M. & Elliott, G. S. 1990 Effects of compressibility on the characteristics of free shear layers. AIAA J. 28 (3), 439–445.Google Scholar
Samimy, M., Reeder, M. F. & Elliott, G. S. 1992 Compressibility effects on large structures in free shear flows. Phys. Fluids A 4 (6), 1251–1258.CrossRefGoogle Scholar
Sandham, N. D. & Reynolds, W. C. 1991 Three-dimensional simulations of large eddies in the compressible mixing layer. J. Fluid Mech. 224, 133–158.CrossRefGoogle Scholar
Sarohia, V. 1977 Experimental investigation of oscillations in flows over shallow cavities. AIAA J. 15 (7), 984–991.Google Scholar
Sirieix, M. & Solignac, J. L.1968 Contribution à l’étude experimental de la couche de mélange turbulente isobare d’un écoulement supersonique. In Symposium on Separated Flows, AGARD CP-4(1), pp. 241–270.Google Scholar
Slessor, M. D., Zhuang, M. & Dimotakis, P. E. 2000 Turbulent shear-layer mixing: growth-rate compressibility scaling. J. Fluid Mech. 414, 35–45.Google Scholar
Smits, A. J. & Dussauge, J.-P. 2006 Turbulent Shear Layers in Supersonic Flow, 2nd edn. pp. 139–178. Springer.Google Scholar
Stallings, R. L. & Wilcox, F. J.1987 Experimental cavity pressure distributions at supersonic speeds. NASA Tech. Paper 2683.Google Scholar
Taylor, J. R. 1997 An Introduction to Error Analysis, 2nd edn. pp. 140–141. University Science Books.Google Scholar
Theofilis, V. 2003 Advances in global linear instability analysis of nonparallel and three-dimensional flows. Prog. Aerosp. Sci. 39 (4), 249–315.Google Scholar
Tracy, M. B. & Plentovich, E. B.1997 Cavity unsteady-pressure measurements at subsonic and transonic speeds. NASA Tech. Paper 3669.Google Scholar
Ukeiley, L. & Murray, N. 2005 Velocity and surface pressure measurements in an open cavity. Exp. Fluids 38 (5), 656–671.Google Scholar
Unalmis, O. H., Clemens, N. T. & Dolling, D. S. 2004 Cavity oscillation mechanisms in high-speed flows. AIAA J. 42 (10), 2035–2041.Google Scholar
Urban, W. D. & Mungal, M. G. 2001 Planar velocity measurements in compressible mixing layers. J. Fluid Mech. 431, 189–222.Google Scholar
de Vicente, J., Basley, J., Meseguer-garrido, F., Soria, J. & Theofilis, V. 2014 Three-dimensional instabilities over a rectangular open cavity: from linear stability analysis to experimentation. J. Fluid Mech. 748, 189–220.Google Scholar
Wagner, R. D.1973 Mean flow and turbulence measurements in a Mach 5 free shear layer. NASA Tech. Note D-7366.Google Scholar
Wagner, J. L., Casper, K. M., Beresh, S. J., Henfling, J. F., Spillers, R. W. & Pruett, B. O. M. 2015a Mitigation of wind tunnel wall interactions in subsonic cavity flows. Exp. Fluids 56 (3), 59.Google Scholar
Wagner, J. L., Casper, K. M., Beresh, S. J., Hunter, P. S., Henfling, J. F., Spillers, R. W. & Pruett, B. O. M. 2015b Fluid-structure interactions in compressible cavity flows. Phys. Fluids 27 (6), 066102.Google Scholar
Wygnanski, I. & Fiedler, H. E. 1970 The two-dimensional mixing region. J. Fluid Mech. 41 (2), 327–361.Google Scholar
Zhang, K. & Naguib, A. M. 2011 Effect of finite cavity width on flow oscillation in a low-Mach-number cavity flow. Exp. Fluids 51 (5), 1209–1229.Google Scholar
Zhang, X. & Edwards, J. A. 1990 An investigation of supersonic oscillatory cavity flows driven by thick shear layers. Aeronaut. J. 94 (940), 355–364.Google Scholar
Zhuang, N., Alvi, F. S., Alkislar, M. B. & Shih, C.2003 Aeroacoustics properties of supersonic cavity flows and their control. AIAA Paper 2003-3101.Google Scholar
Zhuang, N., Alvi, F. S., Alkislar, M. B. & Shih, C. 2006 Supersonic cavity flows and their control. AIAA J. 44 (9), 2118–2128.Google Scholar
Zhuang, M., Dimotakis, P. E. & Kubota, T. 1990 The effect of walls on a spatially growing supersonic shear layer. Phys. Fluids A 2 (4), 599–604.Google Scholar