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The effect of counterflow on the development of compressible shear layers

Published online by Cambridge University Press:  26 April 2006

P. J. Strykowski ,
A. Krothapalli  and
S. Jendoubi
P. J. Strykowski
Affiliation:
Department of Mechanical Engineering, University of Minnesota, Minneapolis, MN 55455, USA
A. Krothapalli
Affiliation:
Department of Mechanical Engineering, Florida A&M University and Florida State University, Tallahassee, FL 32316, USA
S. Jendoubi
Affiliation:
Department of Mechanical Engineering, University of Minnesota, Minneapolis, MN 55455, USA
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Abstract

A compressible countercurrent shear layer was investigated experimentally by establishing reverse flow around the perimeter of a supersonic jet. Measurements demonstrate that spatial growth rates of the countercurrent shear layer significantly exceed those of the classical coflowing layer at comparable density ratios and levels of compressibility. Experiments also reveal the presence of coherent three-dimensional structures in the countercurrent shear layer at convective Mach numbers where similar structures are not present in coflowing layers. It is argued that these kinematic differences are responsible for the enhanced diffusion of the shear layer with counterflow. The spatio-temporal theory is used to examine the connection between the experimental observations and the existence of a transition from convective to absolute instability in high-speed shear layers.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 308 , 10 February 1996 , pp. 63 - 96
Copyright
© 1996 Cambridge University Press

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References

Akhierzer, A. I. & Polovin, R. V. 1971 Criteria for wave growth. Sov. Phys. Uspek. 14, 278.Google Scholar
Arnette, S. A., Samimy, M. & Elliot, G. S. 1993 On streamwise vortices in high Reynolds number supersonic axisymmetric jets. Phys. Fluids A 5, 187–202.Google Scholar
Berman, C. H. & Ffowcs Williams, J. E. 1970 Instability of a two-dimensional compressible jet. J. Fluid Mech. 42, 151–159.Google Scholar
Bers, A. 1983 Space-time evolution of plasma instabilities — absolute and convective. In Handbook of Plasma Physics I. (ed. M. N. Rosenbluth & R. Z. Sagdeev). North-Holland.
Birch, S. F. & Eggers, J. M. 1973 A critical review of the experimental data for developed free turbulent shear layers. NASA SP-321, pp. 11–40.
Bogdanoff, D. W. 1983 Compressibility effects in turbulent shear layers. AIAA J. 21, 926–927.Google Scholar
Briggs, R. J. 1964 Electron-stream interaction with plasmas. Research Monograph 29. MIT.
Brown, G. L. & Roshko, A. 1974 On density effects and large scale structure in turbulent mixing layers. J. Fluid Mech. 64, 775–816.Google Scholar
Chinzei, N., Masuya, G., Komuro, T., Murakami, A. & Kudou, K. 1986 Spreading of two-stream supersonic mixing layers. Phys. Fluid 29, 1345–1347.Google Scholar
Chomaz, J. M., Huerre, P. & Redekopp, L. G. 1988 Bifurcations to local and global modes in spatially-developing flows. Phys. Rev. Lett. 60, 25–28.Google Scholar
Clemens, N. T. & Mungal, M. G. 1991 A planar Mie scattering technique for visualizing supersonic mixing flows. Exps. Fluids 11, 175–185.Google Scholar
Clemens, N. T. & Mungal, M. G. 1992 Two- and three-dimensional effects in the supersonic mixing layer. AIAA J. 30, 973–981.Google Scholar
Elliot, G. & Samimy, M. 1990 Compressibility effects in free shear layers. AIAA Paper 90-0705.
Fourguette, D. C., Mungal, M. G. & Dibble, R. W. 1991 Time evolution of the shear layer of a supersonic axisymmetric jet. AIAA J. 29, 1123–1130.Google Scholar
Freymuth, P. 1966 On the transition in a separated laminar boundary layer. J. Fluid Mech. 25, 683–704.Google Scholar
Goebel, S. G. & Dutton, J. C. 1991 Experimental study of compressible turbulent mixing layers. AIAA J. 29, 538–546.Google Scholar
Gropengiesser, H. 1970 Study of the stability of boundary layers in compressible fluids. NASA TT-F-12, p. 786.
Gutmark, E., Schadow, K. C. & Wilson, K. J. 1991 Effect of convective Mach number on mixing of coaxial circular and rectangular jets. Phys. Fluids A 3, 29–36.Google Scholar
Hannemann, K. & Oertel, H. 1989 Numerical simulation of the absolutely and convectively unstable wake. J. Fluid Mech. 199, 55–88.Google Scholar
Ho, C.-M. & Huerre, P. 1984 Perturbed free shear layers. Ann. Rev. Fluid Mech. 16, 365–424.Google Scholar
Huerre, P. & Monkewitz, P. A. 1985 Absolute and convective instabilities in free shear layers. J. Fluid Mech. 159, 151–168.Google Scholar
Huerre, P. & Monkewitz, P. A. 1990 Local and global instabilities in spatially developing flows. Ann. Rev. Fluid Mech. 22, 473–537.Google Scholar
Humphrey, J. A. C. & Li, S. 1981 Tilting, stretching, pairing and collapse of vortex structures in confined counter-current flows. Trans. ASME I: J. Fluids Engng 101, 466–470.Google Scholar
Jackson, T. L. & Grosch, C. E. 1989 Inviscid spatial stability of a compressible mixing layer. J. Fluid Mech. 208, 609–637.Google Scholar
Jackson, T. L. & Grosch, C. E. 1990 Absolute/convective instabilities and the convective Mach number in a compressible mixing layer. Phys. Fluids A 2, 949.Google Scholar
Jendoubi, S. & Strykowski, P. J. 1994 Absolute and convective instability of axisymmetric jets with external flow. Phys. Fluids 6, 3000–3009.Google Scholar
King, C. J., Krothapalli, A. & Strykowski, P. J. 1994 Streamwise vorticity generation in supersonic jets with minimal thrust loss. AIAA Paper 94-0661.
King, C. J., Krothapalli, A. & Strykowski, P. J. 1995 The effect of annular counterflow on supersonic jet noise. In Proc. 1st Joint CEAS/AIAA Aeroacoustic Conference, Munich, Germany, June 12–15, vol. 2, pp. 1151–1158.
Koch, W. 1985 Local instability characteristics and frequency determination of self-excited wake flows. J. Sound Vib. 99, 53–83.Google Scholar
Krothapalli, A., Buzyna, G. & Lourenco, L. 1991 Streamwise vortices in an underexpanded axisymmetric jet. Phys. Fluids A 3, 1848–1851.Google Scholar
Krothapalli, A., Hsia, Y., Baganoff, D. & Karamcheti, K. 1986 The role of screech tones on mixing of an underexpanded rectangular jet. J. Sound Vib. 106, 119–143.Google Scholar
Kyle, D. & Sreenivasan, K. R. 1993 The instability and breakdown of a round variable-density jet. J. Fluid Mech. 249, 619–664.Google Scholar
Lepicovsky, J., Ahuja, K. K., Brown, W. H., Salikuddin, M. & Morris, P. J. 1988 Acoustically excited heated jets. NASA CR-4129.
Mathis, C., Provansal, M. & Boyer, L. 1984 The Bénard-von Kármán instability: an experimental study near the threshold. J. Phys. Lett. 45, 483–491.Google Scholar
Messersmith, N. L., Dutton, J. C. & Krier, H. 1991 Experimental investigation of large scale structure in compressible mixing layers. AIAA Paper 91-0244.
Michalke, A. 1971 Instabilität eines kompressiblen runden Freistrahls under Berücksichtigung des Einflusses der Strahlgrenzschichtdicke. Z. Flugwiss. 19, 319.Google Scholar
Moffett, R. J. 1982 Contributions to the theory of single-sample uncertainty analysis. Trans. ASME I: J. Fluids Engng 104, 250–260.Google Scholar
Monkewitz, P. A. 1988 The absolute and convective nature of instability in two-dimensional wakes at low Reynolds numbers. Phys. Fluids 31, 999–1006.Google Scholar
Monkewitz, P. A., Bechert, D. W., Barsikow, B. & Lehmann, B. 1990 Self-excited oscillations and mixing in a heated round jet. J. Fluid Mech. 213, 611–639.Google Scholar
Monkewitz, P. A., Lehmann, B., Barsikow, B. & Bechert, D. W. 1989 The spreading of selfexcited hot jets by side jets. Phys. Fluids A 1, 446–448.Google Scholar
Monkewitz, P. A. & Nguyen, L. N. 1987 Absolute instability in the near wake of two-dimensional bluff bodies. J. Fluids Struct. 1, 165–184.Google Scholar
Monkewitz, P. A. & Sohn, K. D. 1988 Absolute instability in hot jets. AIAA J. 26, 911–916.Google Scholar
Novopashin, S. A. & Perepelkin, A. L. 1989 Axial symmetry loss of a supersonic preturbulent jet. Phys. Lett. A 135, 290–293.Google Scholar
Papamoschou, D. 1989 Structure of the compressible turbulent shear layers. AIAA Paper 89-0126.
Papamoschou, D. & Roshko, A. 1988 The compressible turbulent mixing layer: an experimental study. J. Fluid Mech. 197, 453–477.Google Scholar
Pavithran, S. & Redekopp, L. G. 1989 The absolute-convective transition in subsonic mixing layers. Phys. Fluids A 1, 1736–1739.Google Scholar
Peroomian, O. & Kelly, R. E. 1994 Absolute and convective instabilities in compressible confined mixing layers. Phys. Fluids 6, 3192–3194.Google Scholar
Powell, A. 1953 On the mechanism of choked jet noise. Proc. Phys. Soc. Lond. B 66, 1039.Google Scholar
Raman, G., Hailye, M. & Rice, E. J. 1992 The flip flop nozzle extended to supersonic flows. AIAA Paper 92-2724.
Raman, G., Rice, E. J. & Mankbadi, R. R. 1988 Saturation and the limit of jet mixing enhancement by single frequency plane wave excitation: experiment and theory. In Proc. AIAA/ASME/SIAM/APS 1st National Fluid Dynamics Congress, pp. 1000–1007. ASME.
Ramshankar, R. 1988 The dynamics of countercurrent mixing layers. PhD, thesis, Yale University.
Ross, C. B., Lourenco, L. & Krothapalli, A. 1994 Particle image velocimetry measurements in a shock-containing supersonic flow. AIAA Paper 94-0047.
Russ, S., Strykowski, P. J. & Pfender, E. 1994 Mixing in plasma and low density jets. Exps. Fluids 16, 297–307.Google Scholar
Samimy, M., Erwin, D. W. & Elliot, G. S. 1989 Compressibility and shock wave interaction effects on free shear layers. AIAA Paper 89-2460.
Samimy, M. & Lele, S. K. 1990 Particle laden compressible free shear layers. AIAA Paper 90-1977.
Samimy, M., Reeder, M. F. & Elliot, G. S. 1992 Compressibility effects on large structures in free shear flows. Phys. Fluids 4, 1251–1258.Google Scholar
Samimy, M., Zaman, K. B. M. Q. & Reeder, M. F. 1991 Supersonic jet mixing enhancement by vortex generators. AIAA Paper 91-2263.
Sandham, N. & Reynolds, W. C. 1990 Compressible mixing layer: linear theory and direct simulation. AIAA J. 28, 618–624.Google Scholar
Sandham, N. & Reynolds, W. C. 1991 Three-dimensional simulations of large eddies in the compressible mixing layer. J. Fluid Mech. 224, 133–158.Google Scholar
Scharton, T. D., White, P. H. & Rentz, P. H. 1973 Supersonic jet noise investigation using jet fluctuating pressure probes. Air Force Aero Prop. Lab. Rep. AFAPL-TR-73–35.
Schlichting, H. 1978 Boundary Layer Theory, 7th edn. McGraw-Hill.
Shau, Y. R. & Dolling, D. S. 1989 Experimental study of spreading rate enhancement of high Mach number turbulent shear layers. AIAA Paper 89-2458.
Shau, Y. R., Dolling, D. S. & Choi, K. Y. 1993 Organized structure in a compressible turbulent shear layer. AIAA J. 31, 1398–1405.Google Scholar
Sreenivasan, K. R., Raghu, S. & Kyle, D. 1989 Absolute instability in variable density round jets. Exps. Fluids 7, 309–317.Google Scholar
Strykowski, P. J. 1986 The control of absolutely and convectively unstable shear flows. PhD thesis, Yale University.
Strykowski, P. J. & Krothapalli, A. 1993 The countercurrent mixing layer: strategies for shear layer control. AIAA Paper 93-3260.
Strykowski, P. J., Krothapalli, A. & Forliti, D. J. 1995 Fluidic thrust vectoring of a supersonic rectangular jet using counterflow. AIAA J. (under review).
Strykowski, P. J., Krothapalli, A. & Wishart, D. 1993 Enhancement of mixing in high-speed heated jets using a counterflowing nozzle. AIAA J. 31, 2033–2038.Google Scholar
Strykowski, P. J. & Niccum, D. L. 1991 The stability of countercurrent mixing layers in circular jets. J. Fluid Mech. 227, 309–343.Google Scholar
Strykowski, P. J. & Niccum, D. L. 1992 The influence of velocity and density ratio on the dynamics of spatially developing mixing layers. Phys. Fluids A 4, 770–781.Google Scholar
Strykowski, P. J. & Wilcoxon, R. K. 1993 Mixing enhancement due to global oscillations in jets with annular counterflow. AIAA J. 31, 564–570.Google Scholar
Thorpe, A. S. 1968 A method of producing a shear flow in a stratified fluid. J. Fluid Mech. 32, 693–704.Google Scholar
Thorpe, A. S. 1971 Experiments on instability and turbulence in a stratified shear flow: miscible fluids. J. Fluid Mech. 46, 299–319.Google Scholar
Yu, K., Gutmark, E. & Schadow, K. C. 1993 Passive control of coherent vortices in compressible mixing layers. AIAA Paper 93-3262.
Yu, K., Kraeutle, K., Wilson, K., Parr, T., Smith, R., Gutmark, E. & Shadow, K. C. 1992 Supersonic flow mixing and combustion using a ramp nozzle. AIAA Paper 92-3840.
Zapryagaey, V. I. & Solotchin, A. V. 1988 Spatial structure of flow in the initial section of a supersonic underexpanded jet. Acad. Sci. USSR, No. 23–88.