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Flows with Density Variations and Compressibility: Similarities and Differences

  • Conference paper
IUTAM Symposium on Variable Density Low-Speed Turbulent Flows

Part of the book series: Fluid Mechanics and Its Applications ((FMIA,volume 41))

Abstract

Similarities and differences between low speed, variable density flows and compressible flows are discussed. To aid in this comparison, flows of a binary mixture of ideal gases are considered. Under appropriate conditions significant density variations can arise in such systems, with or without compressibility. For simplicity, chemical reactions are excluded from consideration. The effects of density fluctuations and compressibility are examined in the context of the averaged transport equations with emphasis on the physical processes occuring in the flow. The roles of pressure fluctuations, differential acceleration and baroclinic vorticity are highlighted. A synopsis of the behavior of the variable density mixing layer and its compressible counterpart is given. The need for experiments and numerical simulations specifically designed to yield fundamental information about the effects of density variations and compressibility is stressed.

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References

  • Barre, S., Quine, C. and Dussauge, J. P. 1994 Compressibility effects on the structure of supersonic mixing layers: experimental results. J. Fluid Mech. 259, 47–78.

    Article  ADS  Google Scholar 

  • Barre, S. 1994 Estimate of convective velocity in a supersonic turbulent mixing layer. AIAA J. 32, 211–213.

    Article  ADS  Google Scholar 

  • Batchelor, G. K., Canuto, V. M. and Chasnov, J. R. 1992 Homogeneous buoyancy-generated turbulence. J. Fluid Mech. 235, 349–378.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  • Besnard, D., Harlow, F. H., Rauenzahn, R. M. and Zemach, A. C. 1992 Turbulence transport equations for variable-density flows and their relationship to two-fluid models. Los Alamos National Laboratory Report LA-12303-MS.

    Google Scholar 

  • Bilger, R. W. 1989 Turbulent diffusion flames. Annual Rev. Fluid Mech. 21 101–135.

    Article  MathSciNet  ADS  Google Scholar 

  • Blaisdell, G. A., Mansour, N. N., and Reynolds, W. C. 1993 Compressibility effects on the growth and structure of homogeneous turbulent shear flow. J. Fluid Mech. 256, 443–485.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  • Bonnet, J. P., Debisschop, J. R. and Chambres, O. 1993 Experimental studies of the turbulent structure of supersonic mixing layers. AIAA Paper 93–0217.

    Google Scholar 

  • Bonnet, J. P., Chambres, O., Lammari, M., Barre, S. and Braud, P. 1994 Couches de melange turbulentes supersoniques. Rapport final, Contract DRET 91/172, Aout 1994, Univ. Poitiers, CEAT.

    Google Scholar 

  • Bradshaw, P. 1977 Compressible turbulent shear layers. Ann. Rev. Fluid Mech. 9 33–54.

    Article  ADS  Google Scholar 

  • Bray, K. N. C. 1995 Turbulent transport in flames. Proc. Royal Soc. Lond. Ser. A 451 231–256.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  • Breidenthal, R. 1990 The sonic eddy-a model for compressible turbulence. AIAA Paper 90–0495.

    Google Scholar 

  • Brown, G. and Roshko, A. 1974 On density effects and large structure in turbulent mixing layers. J. Fluid Mech. 64, 775–816.

    Article  ADS  Google Scholar 

  • Chassaing, P., Harran, G. and Joly, L. 1994 Density fluctuation correlations in free turbulent binary mixing. J. Fluid Mech. 279, 239–278.

    ADS  MATH  Google Scholar 

  • Clemens, N. T. and Mungal, M. G. 1992 Two-and three-dimensional effects in the supersonic mixing layer. AIAA J. 30, 973–981.

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  MATH  Google Scholar 

  • Dimotakis, P. E. 1986 Two-dimensional shear-layer entrainment. AIAA J. 24, 1791–1796.

    Article  ADS  Google Scholar 

  • Dimotakis, P. A. 1991 Turbulent free shear layer mixing and combustion. In High-speed Flight Propulsion Systems, Prog. in Astronaut. Aeronaut., ed. S. N. B. Murthy, E. T. Curran, AIAA-Washington D. C., 265–340.

    Google Scholar 

  • Djeridane, T., Amielh, M., Anselmet, F. and Fulachier, L. 1996 Velocity turbulence properties in the near-field region of axisymmetric variable density jets. Phys. Fluids 8, 1614–1630.

    Article  ADS  Google Scholar 

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

    Article  ADS  MATH  Google Scholar 

  • Elliot, G. S. and Samimy, M. 1990 Compressibility effects in free shear layers. Phys. Fluids A 2, 1231–1240.

    Article  ADS  Google Scholar 

  • Favre, A. 1969 Statistical equations of turbulent gases. In Problems of hydrodynamics and continuum mechanics, SIAM Philadelphia, 231–266.

    Google Scholar 

  • Fiedler, H. E., Lummer, M. and Nottmeyer, K. 1991. Plane mixing layer between parallel streams of different velocities and different densities. In Advances in Turbulence, eds. H. Branover, Y. Unger, AIAA Series on Progress in Astronautics and Aeronautics 1993, 40–52.

    Google Scholar 

  • Freund, J. B., Lele, S. K. and Moin, P. 1997 Direct simulation of a supersonic round turbulent shear layer. AIAA Paper 97–0760.

    Google Scholar 

  • Gaviglio, J. 1987 Reynolds analogies and experimental study of heat transfer in the supersonic boundary layer. Int. J. Heat Mass Transfer 30, 911–926.

    Article  MATH  Google Scholar 

  • Goebel, S. G. and Dutton, J. C. 1991 Experimental study of compressible turbulent mixing layers. AIAA J. 29, 538–546.

    Article  ADS  Google Scholar 

  • Haas, J. F. and Sturtevant, B. 1987 Interaction of weak shock waves with cylindrical and spherical gas inhomogeneities, J. Fluid Mech. 181, 41–76.

    Article  ADS  Google Scholar 

  • Hall, J. L., Dimotakis, P. E. and Rosemann, H. 1993 Experiments in nonreacting compressible shear layers. AIAA J. 31, 2247–2254.

    Article  ADS  Google Scholar 

  • Hinze, J. O. 1975 Turbulence, 2nd. edn., McGraw Hill.

    Google Scholar 

  • Huang, P. G., Coleman, G. N. and Bradshaw, P. 1995 Compressible turbulent channel flows: DNS results and modeling. J. Fluid Mech. 305, 185–218.

    Article  ADS  MATH  Google Scholar 

  • Jacobs, J. W. 1993 The dynamics of shock accelerated light and heavy gas cylinders. Phys. Fluids A 5, 2239–2247.

    Article  ADS  Google Scholar 

  • Jones, W. P. 1992 Turbulence modeling for combustion flows. In von Karman Institute for Fluid Dynamics Lecture Series 1992–03.

    Google Scholar 

  • Kida, S. and Orszag, S. 1990 Energy and spectral dynamics in forced compressible turbulence. J. Sci. Comput. 5 35–125.

    Article  MathSciNet  Google Scholar 

  • Kuo, K. K. 1986 Principles of Combustion, pp. 161–205. John Wiley.

    Google Scholar 

  • Lee, S., Lele, S. K. and Moin, P. 1991 Eddy shocklets in decaying compressible turbulence. Phys. Fluids A 3 657–664.

    Article  ADS  Google Scholar 

  • Lee, S., Lele, S. K. and Moin, P. 1997 Interaction of isotropic turbulence with shock waves: effect of shock strength. to appear in J. Fluid Mech.

    Google Scholar 

  • Lele, S. K. 1994 Compressibility effects on turbulence. Ann. Rev. Fluid Mech. 26, 211–254.

    Article  MathSciNet  ADS  Google Scholar 

  • Libby, P. A. and Bray, K. N. C. 1981 Countergradient diffusion in premixed flames. AIAA J. 19 205–213.

    Article  ADS  Google Scholar 

  • Lighthill, M. J. 1952 On sound generated aerodynamically: I. General theory. Proc. Roy. Soc. London, Ser. A 221 564–587.

    MathSciNet  ADS  Google Scholar 

  • Lu, G. and Lele, S. K. 1994 On the density ratio effect on the growth rate of a compressible mixing layer. Phys. Fluids 6, 1073–1075.

    Article  ADS  Google Scholar 

  • Mahadevan, R. and Loth, E. 1994 High-speed cinematography of compressible mixing layers. Experiments in Fluids 17, 179–189.

    Article  ADS  Google Scholar 

  • Mahesh, K., Lele, S. K. and Moin, P. 1997 The influence of entropy fluctuations on the interaction of turbulence with a shock wave . J. Fluid Mech. 334, 353–379.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  • McMurtry, P. A., Jou, W. H., Riley, J. J. and Metcalfe, R. W. 1986 Direct numerical simulation of a reacting mixing layer with chemical heat release. AIAA J. 24, 962–970.

    Article  ADS  Google Scholar 

  • Moin, P., Squires, K., Cabot, W. and Lee, S. 1991 A dynamic subgrid scale model for compressible turbulence and scalar transport. Phys. Fluids A 3, 2746–2757.

    Article  ADS  MATH  Google Scholar 

  • Morkovin, M. V. 1961 Effects of compressibility on turbulent flows. In Mecanique de la Turbulence, ed. A. Favre, Paris:CNRS, 367–380.

    Google Scholar 

  • Morkovin, M. V. 1992 Mach number effects on free and wall turbulent structures in light of instability flow interactions. In Studies in Turbulence, ed. Gatski, T. B., Sarkar, S. and Speziale, C. G. Springer-Verlag, 269–284.

    Chapter  Google Scholar 

  • Panchapakesan, N. and Lumley, J. L. 1993 Turbulence measurements in axisymmetric jets of air and helium. Part 1 and 2. J. Fluid Mech. 246, 197–247.

    Article  ADS  Google Scholar 

  • Papamoschou, D. 1991a Structure of the compressible turbulent shear layer. AIAA J. 29 680–681.

    Article  ADS  Google Scholar 

  • Papamoschou, D. 1991b Effect of Mach number on communication between regions of a shear layer. Proc. Eighth Symp. on Turbulent Shear Flows 21–5–1 to 21–5–6.

    Google Scholar 

  • Papamoschou, D. and Roshko, A. 1988 The compressible turbulent mixing layer: an experimental study. J. Fluid Mech. 197, 453–477.

    Article  ADS  Google Scholar 

  • Papamoschou, D. and Lele, S. K. 1993 Vortex-induced disturbance field in a compressible shear layer. Phys. Fluids A 5 1412–1419.

    Article  ADS  Google Scholar 

  • Papamoschou, D. 1995 Evidence of shocklets in a counterflow supersonic shear layer. Phys. Fluids 7, 233–235.

    Article  ADS  Google Scholar 

  • Pope, S. B. 1987 Turbulent premixed flames. Ann. Rev. Fluid Mech. 19 237–270.

    Article  ADS  Google Scholar 

  • Ramaswamy, M., Loth, E. and Dutton, J. C. 1996 Free shear layer interaction with an expansion-compression wave pair. AIAA J. 34, 565–571.

    Article  ADS  Google Scholar 

  • Reynolds, W. C. and Kassinos S. C. 1995 One-point modeling of rapidly deformed homogeneous turbulence. Proc. Roy. Soc. Lond. A 451, 87–104.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  • Ristorcelli, J. R. 1995 A pseudo-sound constitutive relationship and closure for the dilatational covariances in compressible turbulence: an analytical theory. ICASE Report 95–22, submitted to J. Fluid Mech.

    Google Scholar 

  • Samimy, M., Elliot, G. S. and Reeder, M. F. 1992 Compressibility effects on large structures in free shear flows. Phys. Fluids A 4, 1251–1258.

    Article  ADS  Google Scholar 

  • Sandham, N. D. and Reynolds, W. C. 1990 Compressible mixing layer: linear theory and direct simulation. AIAA J. 28 618–624.

    Article  ADS  Google Scholar 

  • Sandoval, D. L. 1995 The dynamics of variable-density turbulence. Thesis, LA-13037-T, Los Alamos National Laboratory.

    Google Scholar 

  • Sarkar, S., Erlebacher, G., Hussaini, M. Y. 1991a Direct simulation of compressible turbulence in a shear flow. Theor. Comput. Fluid Dyn. 2, 291–305.

    Article  MATH  Google Scholar 

  • Sarkar, S., Erlebacher, G., Hussaini, M. Y. and Kreiss, H. O. 1991b The analysis and modeling of dilatational terms in compressible turbulence. J. Fluid Mech. 227, 473–493.

    Article  ADS  MATH  Google Scholar 

  • Sarkar, S. 1992 The pressure-dilatation correlation in compressible flows. Phys. Fluids A 4,2674–2682.

    Article  ADS  Google Scholar 

  • Sarkar, S. 1995 The stabilizing effect of compressibility in turbulent shear flow. J. Fluid Mech. 282, 163–186.

    Article  ADS  MATH  Google Scholar 

  • Shih, T. S., Lumley, J. L. and Janicka, J. L. 1987 Second order modeling of a variable density mixing layer. J. Fluid Mech. 180, 93–116.

    Article  ADS  MATH  Google Scholar 

  • Starner, S. H. and Bilger, R. W. 1980 LDA measurements in a turbulent diffusion flame with axial pressure gradients. Combust. Sci. Technol. 21, 259–276.

    Article  Google Scholar 

  • Staquet, C. 1995 Two-dimensional secondary instabilities in a strongly stratified shear layer. J. Fluid Mech. 296, 73–126.

    Article  MathSciNet  ADS  MATH  Google Scholar 

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

    Article  ADS  MATH  Google Scholar 

  • Williams, F. A. 1985 Combustion Theory, 2nd. edn., pp. 604–627.Addison Wesley.

    Google Scholar 

  • Zank, G. P. and Matthaeus, W. H. 1991 The equations of nearly incompressible fluids. I. Hydrodynamics, turbulence, and waves. Phys. Fluids A 3, 69–82.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  • Zeman, O. 1990 Dilatation dissipation: the concept and application in modeling compressible mixing layers. Phys. Fluids A 3 951–955.

    Article  ADS  Google Scholar 

  • Zeman, O. 1991 On the decay of compressible isotropic turbulence. Phys. Fluids A 3, 951–955.

    Article  ADS  Google Scholar 

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Lele, S.K. (1997). Flows with Density Variations and Compressibility: Similarities and Differences. In: Fulachier, L., Lumley, J.L., Anselmet, F. (eds) IUTAM Symposium on Variable Density Low-Speed Turbulent Flows. Fluid Mechanics and Its Applications, vol 41. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-5474-1_36

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  • DOI: https://doi.org/10.1007/978-94-011-5474-1_36

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