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Compressible Turbulence and Energetic Scales: What Is Known from Experiments in Supersonic Flows?

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Abstract

Some properties of large-scale structures in supersonic turbulent flows are examined through experiments. The large eddies considered here include energetic scales, which contribute predominantly to, say, turbulent energy and coherent structures. Different features are presented, such as the level of energy in supersonic free shear flows, the average size of energetic structures, and their characteristic timescales. It is shown that compressibility affects the level of velocity and the size of the energetic eddies, but in many common supersonic situations, the estimation of the timescales can be made from rules valid for solenoidal turbulence. Some implications for compressible turbulence modeling are suggested. Finally, the properties of coherent structures are considered in the case of mixing layers and in a separated shock/boundary layer interaction. Some features relative to the organization of the large eddies are given and the importance of the shock motion is discussed in relation to the shock/layer interaction.

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References

  1. Barre, S., Quine, C. and Dussauge, J.P., Compressibility effects on the structure of supersonic shear layers: Experimental 88 J. Fluid Mech. 259 (1994) 47–78.

    Article  ADS  Google Scholar 

  2. Bellaud, S., Mesures et analyses détaillées des champs turbulents en couches de mélange annulaires supersoniques. Thèse de Doctorat, Université de Poitiers, France (1999).

    Google Scholar 

  3. Bellaud, S., Barre, S. and Bonnet, J.P., Experimental study of annular supersonic mixing layer: Turbulent kinetic energy budget. In: Banerjee, S. and Eaton, J. (eds), “Turbulence and Shear Flow Phenomena 1, Santa Barbara, CA, 12–15 September. Begell House, New York (1999) pp. 457–462.

    Google Scholar 

  4. Bernal, L.P., The statistics of the organized vortical structure in turbulent mixing layers. Phys. Fluids 31(9) (1988) 2533–2543.

    Article  MATH  ADS  Google Scholar 

  5. Bogar, T.J., Sajben, M. and Kroutil, J.C., Characteristic frequencies of transonic diffuser flow oscillations. AIAA J. 21(2) (1983) 1232–1240.

    ADS  Google Scholar 

  6. Chambres, O., Barre, S. and Bonnet, J.P. Detailed turbulence characteristics of a highly compressible supersonic turbulent plane mixing layer. Internal Report, LEA/CEAT, Université de Poitiers, France (1999).

    Google Scholar 

  7. Clemens, N.T. and Mungal, M.G., Large scale structure and entrainment in the supersonic mixing layer. J. Fluid Mech. 284 (1995) 171–216.

    Article  ADS  Google Scholar 

  8. Coleman, G.N., Kim, J. and Moser, R.D., A numerical study of turbulent supersonic isothermal wall channel flow. J. Fluid Mech. 305 (1995) 159–183.

    Article  MATH  ADS  Google Scholar 

  9. Culick, F.E.C. and Rogers, T., The response of normal shocks in diffusers. AIAA J. 21(10) (1983) 1382–1390.

    MATH  ADS  Google Scholar 

  10. Debiève, J.F., Dupont, P., Laurent, H., Menaa, M. and Dussauge, J.P., Compressibility and structure of turbulence in supersonic shear flows. J. Mech., B Fluids 19(5) (2000) 597–614.

    MATH  Google Scholar 

  11. Demetriades, A. and Martindale, W.R., Determination of one-dimensional spectra in highspeed boundary-layers. Phys. Fluids 26 (1983) 397–403.

    Article  ADS  Google Scholar 

  12. Dolling, D.S. and Murphy, M.T., Unsteadiness of the separation shock wave structure in a supersonic compressible ramp flow field. AIAA J. 21 (1983) 1628–1634.

    ADS  Google Scholar 

  13. Dumas, R., Fulachier, L., Arzoumanian, E. and Favre, A., Etude de la structure de la turbulence dans une couche-limite par les corrélations spatio-temporelles. J. Physique (supplement C1, No. 1) 37 (1997) C1 181–184

    Google Scholar 

  14. Dosanjh, D.S. and Weeks, T.M., Interaction of a starting vortex as well as a vortex street with a traveling shock wave. AIAA J. 3(2) (1965) 216–223.

    MATH  Google Scholar 

  15. Durbin, P.A. and Zeman, O., Rapid distortion theory for homogeneous compressed turbulence with application to modelling. J. Fluid Mech. 242 (1992) 349–370.

    Article  MATH  ADS  Google Scholar 

  16. Dupont, P. and Debiève, J.F., Constitution d'une base de données sur des écoulements comportant des chocs. Final Report of Contract ONERA/DSA-SPAé (1999) 95–95–006.

  17. Dupont, P., Muscat, P. and Dussauge, J.P., Localization of large scale structures in a supersonic mixing layer: A new method and first analysis. Flow, Turbulence and Combustion 62 (1999) 335–358.

    Article  MATH  Google Scholar 

  18. Dussauge. J.P. and Smits, A.J., Characteristic scales for energetic eddies in turbulent supersonic boundary layers. Exp. Thermal Fluid Sci. 13(4) (1996) 85–91.

    Google Scholar 

  19. El Baz, A.M. and Launder, B.E., Second moment modeling of compressible mixing layers. In: Rodi, W. and Martelli, F. (eds), Engineering Turbulence Modelling and Experiments 2. Elsevier Science Publishers, Amsterdam (1993) pp. 63–72.

    Google Scholar 

  20. Freund, J.B., Moin, P. and Lele, S.K., Compressibility effect in a turbulent annular mixing layer. Report No. TF-72, Department of Mechanical Engineering, Stanford University, CA (1997).

  21. Girard, S., Étude des charges latérales dans une tuyère supersonique surdétendue. Thèse de Doctorat, Université de Poitiers, France (1999).

  22. Grueber, M.R., Messersmith, N.L. and Dutton, J.C., Three-dimensional velocity field in compressible mixing layers. AIAA J. 31(11) (1993) 2061–2067.

    ADS  Google Scholar 

  23. Ha Minh, H., Vandromme, D. and Kollmann, W., Implicit treatment of multi-equation turbulence models for compressible flows. NASA Report NCC2–186 (A.R.C.) (1983).

  24. Ha Minh, H., Rubesin, M.W., Viegas, J.R. and Vandromme, D.D., On the use of second order closure modelling for the prediction of turbulent boundary layer/shock wave interactions: Physical and numerical aspects. In: Oshima, K. (ed.), Numerical Methods in Fluid Mechanics I, Invited Lectures of the International Symposium on Computational Fluid Dynamics, Tokyo. Science University of Tokyo (1985) pp. 53–60.

  25. Ha Minh, H., Viegas, J.R., Rubesin, M.W., Vandromme, D. and Spalart, P., Physical analysis and second order modelling of an unsteady turbulent flow: The oscillating boundary layer on a 390 J.P. DUSSAUGE flat plate. In: Durst, F. et al. (eds), Proceedings of the 7th Symposium on Turbulent Shear Flow, Stanford, CA, August 21–23. Stanford University (1989) pp. 9–41.

  26. Ha Minh, H., Physique et modélisation de la turbulence. In: Candel, S. (ed.), École de Printemps en Mécanique des Fluides Numériques, Carcan-Maubuisson, CNRS, 9–15 May. CNRS (1993) pp. 1–27.

  27. Ha Minh, H., La modélisation statistique de la turbulence: Ses capacités et ses limitations. C.R. Acad. Sci. Paris, série IIb 327 (1999) 343–358.

    MATH  Google Scholar 

  28. Jacquin, L., Cambon, C. and Blin, E., Turbulence amplification by a shock wave and rapid distortion theory. Phys. Fluids A 5 (1993) 2539–2550.

    Article  MATH  ADS  Google Scholar 

  29. Laurent, H., Turbulence d'une interaction onde de choc/couche limite sur une paroi plane adiabatique ou chauffée. Thèse de Doctorat, Université de la Méditerranée (Aix-Marseille II), France (1996).

    Google Scholar 

  30. Lechner, R., Sesterhenn, J. and Friedrich, R., Turbulent supersonic channel flow. J. Turbulence 2 (2001) 1–31.

    Article  MathSciNet  ADS  Google Scholar 

  31. Lele, S.K. and Moin, P., Direct simulation of shock-turbulence interaction. J. Fluid Mech. 251 (1993) 533–562.

    Article  ADS  Google Scholar 

  32. McGinley, C.B., Spina, E.F. and Sheplak, M., Turbulence measurements in a Mach 11 Helium boundary layer. AIAA Paper 94–2364 (1994).

  33. Mahadevan, R. and Loth, E., High-speed cinematography of compressible mixing layers. Exp. Fluids 17 (1994) 179–189.

    Article  Google Scholar 

  34. Menaa, M., Etude expérimentale d'une couche de mélange turbulente supersonique et analyse des propriétés de similitude. Thèse de Doctorat, Université de Provence, Marseille, France (1998).

    Google Scholar 

  35. Muscat, P., Structures à grandes échelles dans une couche de mélange supersonique. Analyse de Fourier et analyse en ondelettes. Thèse de Doctorat, Université de la Méditerranée (Aix-Marseille II), France (1998).

    Google Scholar 

  36. Muscat, P., Dupont, P. and Dussauge, J.P., Characterization of large scale eddies in a supersonic turbulent mixing layer: Identification and statistical properties. In: Takayama, K. (ed.), Proceedings of the Second International Workshop on Shock Wave/Vortex Interaction, Institute of Fluid Science, University of Tohoku, Sendaï, Japan, October (1997) pp. 31–47.

  37. Papamoschou, D. and Roshko, A., The compressible turbulent shear layer: An experimental study. J Fluid Mech. 197 (1987) 453–477.

    Article  ADS  Google Scholar 

  38. Pantano, C. and Sarkar, S. A study of compressibility effects in the high-speed, turbulent shear layer using direct simulation. J. Fluid Mech. (1999) submitted.

  39. Poggie, J. and Smits, A.J., Wavelet analysis of wall-pressure fluctuations in a supersonic blunt-fin flow. AIAA J. 35 (1997) 1597–1603.

    Google Scholar 

  40. Ristorcelli, J.R., A pseudo-sound constitutive relationship for the dilatational covariances in compressible turbulence. J. Fluid Mech. 347 (1997) 37–70.

    Article  MATH  ADS  Google Scholar 

  41. Robinet, J.C., Stabilité linéaire d'un écoulement présentant une onde de choc. Thèse de Doctorat de l'ENSAE, ENSAE, Toulouse, France (1999).

  42. Robinet, J.C., Étude des instabilités dans une couche limite décollée incompressible et compressible. Rapport IRPHE/CNES, Universités d'Aix-Marseille I et II, Marseille, France (2000).

  43. Robinet, J.C. and Casalis, G., Shock oscillations in diffuser modelled by a selective noise amplification. AIAA J. 37(4) (1999) 453–459.

    Google Scholar 

  44. Sabot, J. and Comte-Bellot, G., Mémoire des fluctuations longitudinales de vitesse en conduite lisse circulaire. C.R. Acad. Sci. Paris 274A (1972) 1647.

    Google Scholar 

  45. Sajben, M., Bogar, T.J. and Kroutil, J.C., Characteristic frequency and length scales in transonic diffuser flow oscillations. AIAA Paper 81–1291 (1981).

  46. Sarkar, S., The stabilizing effect of compressibility in turbulent shear flow. J. Fluid Mech. 282 (1981) 163–186.

    Article  ADS  Google Scholar 

  47. Selig, M.S., Andreopoulos, J., Muck, K.C., Dussauge, J.P. and Smits, A.J., Effect of periodic blowing on attached and separated supersonic turbulent boundary layers. AIAA J. 27 (1989) 862–869.

    Article  ADS  Google Scholar 

  48. Smits, A.J. and Dussauge, J.P., Turbulent Shear Layers in Supersonic Flow. AIP Press, The American Institute of Physics, Woodbury, NY (1996).

    Google Scholar 

  49. Spina, E.F., Smits, A.J. and Robinson, S.K., The physics of supersonic turbulent boundary layers. Ann. Rev. Fluid Mech. 26 (1994) 287–319.

    Article  ADS  Google Scholar 

  50. Spina, E.F. and Smits, A.J., Organized structures in a compressible turbulent boundary layer. J. Fluid Mech. 182 (1994) 85–109.

    Article  ADS  Google Scholar 

  51. Vreman, A.W., Sandham, N.D. and Luo, K.H., Compressible mixing layer growth rate and turbulence characteristics. J. Fluid Mech. 320 (1996) 235–258.

    Article  MATH  ADS  Google Scholar 

  52. Wunenburger, R, Fauchet, G., Shao, L. and Bertoglio, J.P., An improved two-point closure for weakly compressible turbulence and comparisons with LES. In: 11th Symposium on Turbulent Shear Flows, Université de Grenoble, France, September 8–11 (1997) pp. 32–13, 32–18.

  53. Friedrich, R. and Bertolotti, F.P., Compressibility effects due to fluctuations. Appl. Sci. Res. 57 (1997) 165–194.

    MATH  ADS  Google Scholar 

  54. Bonnet, J.P., Alziary de Roquefort, T. Measurements of turbulence correlctions in a twodimensional supersonic wake. In: Zaric, G. (ed.), Symposium on Heat and Mass Transfer and the Structure of Turbulence, Dubrovnik, 1980. Hemishere (1982) pp. 75–81.

  55. Poggie, J. and Smits, A.J., Shock unsteadiness in a reattaching shear layer. J. Fluid Mech. 429 (2001) pp. 155–185.

    Article  MATH  ADS  Google Scholar 

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  1. I.U.S.T.I., U.M.R. Université-CNRS 6595, Groupe Supersonique 12, Avenue Général Leclerc, F-13003, Marseille, France

    J.P. Dussauge

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Dussauge, J. Compressible Turbulence and Energetic Scales: What Is Known from Experiments in Supersonic Flows?. Flow, Turbulence and Combustion 66, 373–391 (2001). https://doi.org/10.1023/A:1013585413220

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