Hostname: page-component-745bb68f8f-mzp66 Total loading time: 0 Render date: 2025-02-11T11:07:44.705Z Has data issue: false hasContentIssue false
  • English
  • Français

The rapid expansion of a supersonic turbulent flow: role of bulk dilatation

Published online by Cambridge University Press:  21 April 2006

J. P. Dussauge  and
J. Gaviglio
J. P. Dussauge
Affiliation:
Institut de Mécanique Statistique de la Turbulence, LA CNRS No. 130. Université d'Aix-Marseille II, France
J. Gaviglio
Affiliation:
Institut de Mécanique Statistique de la Turbulence, LA CNRS No. 130. Université d'Aix-Marseille II, France
Get access Rights & Permissions [Opens in a new window]

Abstract

The rapid expansion of a turbulent boundary layer in supersonic flow is studied analytically and experimentally. Emphasis is placed on the effect of bulk dilatation on turbulent fluctuations. The hypotheses made in the analysis are similar to those in the rapid distortion theory and are used to simplify second-order closures. By assuming that the fluctuating velocity is solenoidal an extension of classical subsonic models is proposed. A new variable is defined, which takes into account the mean density variations, and behaves like the Reynolds stress tensor in subsonic flows with weak inhomogeneities and a weak dissipation rate. The results of the analysis are compared with turbulence measurements performed in a supersonic boundary layer subjected to an expansion fan. The proposed approximations describe correctly the evolution of turbulence intensities: bulk dilatation contributes predominantly to the Reynolds stress evolution. The boundary layer is ‘relaminarized’ by the expansion. Downstream of the latter, the layer returns to equilibrium. Measurements show that the turbulence decays slowly in the outer layer and increases rapidly in the inner layer.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 174 , January 1987 , pp. 81 - 112
Copyright
© 1987 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Allen, J. M. 1972 Impact probe displacement in a supersonic turbulent boundary layer. AIAA J. 10 (4), 555–556.Google Scholar
Batchelor, G. K. 1955 The effective pressure exerted by a gas in turbulent motion. Vistas in Astronomy 1, 290–295.Google Scholar
Batchelor, G. K. & Proudman, I. 1954 The effect of rapid distortion of a fluid in turbulent motion. Q. J. Mech. Appl. Maths. 7, 83.Google Scholar
Bestion, D., Debiéve, J. F. & Dussauge, J. P. 1983 Too-rapid distortions in supersonic flows: turbulence-shock wave and turbulence-expansion. Structure of complex turbulent shear flows. IUTAM symposium, Marseille, 1982 (ed. R. Dumas & L. Fulachier), pp. 289–298. Springer.
Bonnet, J. P. & Alziary De Roquefort, T. 1982 Measurement of turbulence correlations in a two-dimensional supersonic wake. Symp. Heat and Mass Transfer and the Structure of Turbulence, Dubrovnik. 1980. Hemisphere.
Bradshaw, P. 1974 The effect of mean compression or dilatation on the turbulence structure of supersonic boundary layers. J. Fluid Mech. 63, 449–464.Google Scholar
Bradshaw, P. 1976 Complex turbulent flows. In Theoretical and Applied Mechanics (ed. W. T. Koiter), pp. 104–113. North-Holland.
Bradshaw, P. 1977 Compressible turbulent shear layers. Ann. Rev. Fluid Mech. 9. 33–54.Google Scholar
Bradshaw, P. & Ferriss, D. H. 1971 Calculation of boundary layer development using the turbulent energy equation: compressible flow on adiabatic walls. J. Fluid Mech. 46, 83–110.Google Scholar
Chew, Y. T. 1978 Two-parameter skin-friction formula for adiabatic compressible flow. AIAA J. 16 186–188.Google Scholar
Chew, Y. T. & Squire, L. C. 1979 The boundary layer development downstream of a shock interaction at an expansion corner. Aeronautical Research Council, R & M no. 3839. London.
Craya, A. 1958 Contribution à I'analyse de la turbulence associée à des vitesses moyennes. PST no. 345. Paris: Ministère de l'Air.Google Scholar
Debieve, J. F. 1983 Etude d'une interaction turbulence–onde de choc. Thése d'Etat, Univ. Aix-Marseille II.
Debieve, J. F., Gouin, M. & Gaviglio, J. 1982 Momentum and temperature fluxes in a shock wave turbulence interaction. Symp. Heat and Mass Transfer and the Structure of Turbulence Dubronik 1980. Hemisphere.
Délery, J. & Masure, B. 1969 Action d'une variation brusque de pression sur une couche limite turbulente et application aux prises d'aire hypersoniques. La Recherche Aérospatiale, no. 129, pp. 3–12.Google Scholar
Demetriades, A. 1976 Turbulence correlations in a compressible wake. J. Fluid Mech. 74, 251–268.Google Scholar
Dussauge, J. P. 1981 Evolution de transferts turbulents dans une détente rapide en écoulement supersonique. Thèse d'Etat, Univ. Aix-Marseille II.
Elena, M., Borel, A. & Gaviglio, J. 1977 Interaction couche limite turbulente – Onde de choc– 1: couche limite initiale. dispositif d'expérience. RT ONERA 15/1455 AN.
Elena, M. & Gaviglio, J. 1983 Confrontation de mesures par anémomètres à laser et à fil chaud, en couches limites turbulentes, à vitesse supersonique. Proc. 20th Collogue d'Aérodynamique Appliquée, Toulouse, France, Novembre 8–10.Google Scholar
Favre, A., Kovasznay, L. S. G., Dumas, R., Gaviglio, J. & Coantic, M. 1976 La Turbulence en Mécanique des Fluides. Gauthier-Villars.
Feiereisen, W. J., Reynolds, W. C. & Ferziger, J. H. 1981 Numerical simulation of a compressible homogeneous turbulent shear flow. Thermoscience Division Rep. no. TF-13, Dept. Mech. Engng, Stanford University.
Fernholz, H. H. & Finley, P. J. 1980 A critical commentry on mean flow data for two-dimensional compressible boundary layers. AGAR Dograph 253.Google Scholar
Fernholz, H. H. & Finley, P. J. 1981 A further compilation of compressible boundary layer data with a survey of turbulence data. AGAR Dograph 263.Google Scholar
Galmes, J. M., Dussauge, J. P. & Dekeyser, I. 1983 Couches limites turbulentes supersoniques soumises à un gradient de pression: calcul à l'aide d'un modèle. K-. J. Méc. 2 (4), 539–558.Google Scholar
Gaviglio, J. 1971 Sur la détermination des sensibilités des anémothermomètres à fil chaud en écoulement supersonique. C. R. Acad. Sci. Paris. A 273, 634–637.Google Scholar
Gaviglio, J. 1978 Sur les méthodes de l'anémomètrie pa fil chaud des écoulements turbulents compressible des gaz. J. Méc. 2 (4), 449–498.Google Scholar
Gaviglio, J., Dussauge, J. P., Debieve, J. F. & Favre, A. 1977 Behavior of a turbulent flow, strongly out of equilibrium, at supersonic speeds. Phys. Fluids 20, 5179–5192.Google Scholar
Gaviglio, J. & Dussauge, J. P. 1977 On reduction of errors arising in hot-wire anemometry of thin turbulent shear layers. National Bureau of Standards Special Publication no. 484 (ed. L. K. Irwin) and TP ONERA no. 1977–168.
Goldstein, M. E. 1978 Unsteady vortical and entropic distortions of potential flows round arbitrary obstacles. J. Fluid Mech. 89, 433–468.Google Scholar
Goldstein, M. E. 1979 Turbulence generated by the interaction of entropy fluctuations with non-uniform mean flows. J. Fluid Mech. 93, 209–224.Google Scholar
Hunt, J. C. R. 1973 A theory of turbulent flow round two-dimensional bluff bodies, J. Fluid Mech. 61, 625–706.Google Scholar
Hunt, J. C. R. 1977 A review of the theory of rapidly distorted turbulent flows and its applications. Fluid Dynamics Transaction, vol. 9, pp. 121–152. Thirteenth Biennial Fluid Dynamics Symposium, Poland.
Johnson, D. A. & Rose, W. C. 1975 Laser velocimeter and hot-wire anemometer comparison in a supersonic boundary layer. AIAA J. 13, 512–515.Google Scholar
Kistler, A. L. 1959 Fluctuations measurements in a supersonic turbulent boundary layer. Phys. Fluids 2, 290–296.Google Scholar
Klebanoff, P. S. 1954 Characteristics of turbulence in a boundary layer with zero pressure gradient. NACA TN 3178. Washington, DC.
Kovasznay, L. S. G. 1953 Turbulence in supersonic flow. J. Aero. Sci. 20, 657–675.Google Scholar
Laufer, J. 1969 Thoughts on compressible turbulent boundary layers. The RAND Corp., Memo RM, 5946 PR. University of California.
Laufer, J. & McClellan, R 1956 Measurements of heat transfer from fine wires in supersonic flows. J. Fluid Mech. 1, 276–289.Google Scholar
Launder, B. E., Reece, G. J. & Rodi, W. 1975 Progress in the development of a Reynolds stress turbulent closure. J. Fluid. Mech. 68, 537–566.Google Scholar
Lumley, J. L. 1975 Prediction methods for turbulent flows introduction. Institut von Kármán, Rhodes-Saint-Genèse, Belgium.
Michel, R. 1960 Résultats sur la couche limite turbulente aux grandes vitesses. Tenth Congrès de Mécanique Appliquée, Stresa. ONERA no. 102.
Moffatt, H. K. 1968 The interaction of turbulence with a strong wind shear. International Colloquium on Atmospheric Turbulence and Radio Wave Propagation, Moscow 1965 (ed. Y. Yaglom & V. I. Tatarsky), pp. 139–150, Moscow: Nauka.
Morkovin, M. V. 1955 Effects of high acceleration on a turbulent supersonic shear layer. Heat Transfer and Fluid Mechanics Institute, Stanford University.
Morkovin, M. V. 1962 Effects of compressibility on turbulent flows. Mécanique de la Turbulence (Ed. A. Favre), pp. 367–380. CNRS.
Moyal, J. E. 1952 The spectra of turbulence in a compressible fluid: eddy turbulence and random noise. Proc. Camb. Phil. Soc. 48, 329.Google Scholar
Naot, D., Shavit, A. & Wolfsthein, M. 1970 Interaction between components of the turbulent velocity correlation tensor due to pressure fluctuations. Israel J. Tech. 8, 259.Google Scholar
Narasimha, R. & Sreenivasan, K. R. 1979 Relaminarization of fluid flows. Adv. Appl. Mech. 19, 221–309.Google Scholar
Narasimha, R. & Viswanath, P. R. 1975 Reverse transition on expansion corner in supersonic flows. AIAA J. 13, 693–695.Google Scholar
Ribner, H. S. & Tucker, M. 1952 Spectrum of turbulence in a contracting stream. NACA TN 2606. Washington.
Rubesin, M. W. 1976 A one-equation model of turbulence for use with the compressible Navier-Stokes equations. NASA TM X-73, 128.
Sabot, J., Renault, J. & Comte-Bellot, G. 1973 Space-time correlations of the transverse velocity fluctuation in pipe-flow. Phys. Fluids. 16, 1403–1405.Google Scholar
Smits, A. J., Hayakawa, K. & Muck, K. C. 1983 Constant temperature hot-wire anemometer practice in supersonic flows. Exp. Fluids. 1, 83–92.Google Scholar
Smits, A. J. & Wood, D. H. 1985 The response of turbulent boundary layer to sudden perturbations. Ann. Rev. Fluid Mech. 17, 321–358.Google Scholar
Sternberg, J. 1954 The transition from a turbulent to a laminar boundary layer. Aberdeen Proving Group, Ballistic Research Lab. MD, USA.
Townsend, A. A. 1980 The response of a sheared turbulence to additional distortion. J. Fluid Mech. 98, 171–192.Google Scholar
Voisinet, R. L. P. & Lee, R. E. 1972 Measurements of a Mach 4.9 zero pressure gradient turbulent boundary layer with heat transfer. NOLTR 72–232.
Wilcox, D. C. & Alber, I. E. 1972 A turbulence model for high speed flows. Heat Transfer and Fluid Mechanics Institute, Stanford University, Stanford, California.
Wilcox, D. C. & Rubesin, M. W. 1980 Progress in turbulence modeling for complex flow field including effects of compressibility. NASA TR 1517.
Yanta, W. J. & Crapo, B. J. 1976 Laser velocimetry applied to transsonic and supersonic aerodynamics. Application of non-intrusive instrumentation in fluid flow-research. AGARD Conf. Proc. 193.Google Scholar
Young, A. D. 1951 The equations of motion and energy and the velocity profile of a turbulent boundary layer in a compressible fluid. College of Aeronautics, Cranfield, England, Rep. no. 42. 42.Google Scholar