Rapid Distortion Approximations (RDA) may be used to simplify the Reynolds stress equations in rapidly distorted flows, as suggested by Dussauge and Gaviglio (1987). These approximations neglect diffusive and dissipative terms while retaining the production and pressure terms. The retained terms are then modeled as functions of the Reynolds stress tensor and gradients of the mean flow. The models for the pressure-strain term as developed by Lumley (1978) and Shih and Lumley (1985) are evaluated by comparing the calculated results with experimental data for the case of a Mach 2.84 turbulent boundary layer in a 20° centered expansion. The agreement between computed and experimentally obtained Reynolds stresses was found to be encouraging.
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Batchelor, G.K., and Proudman, I. (1952). The effect of rapid distortion of a fluid in turbulent motion. Quart J. Mech. Appl. Math., 7, 83–103.
Donovan, J.F. (1989). The structure of supersonic turbulent boundary layers subjected to concave surface curvature. Ph.D. Thesis, Princeton University.
Dussauge, J.P., and Gaviglio, J. (1987). The rapid expansion of a supersonic turbulent flow: role of bulk dilatation. J. Fluid Mech., 174, 81–112.
Dussauge, J.P., Debieve, J.F., and Smits, A.J. (1989). Rapidly Distorted Compressible Boundary Layers. AGARDograph No. 315 (Fernholz, H., Smits, A.J., Dussauge, J.P. and Finley, P.J., eds.). North Atlantic Treaty Organization, Brussels.
Fernando, E.M., and Smits, A.J. (1990). A supersonic turbulent boundary layer in an adverse pressure gradient. J. Fluid Mech., 211, 285–307.
Hanjalic, K., and Launder, B.E., (1972). A Reynolds stress model of turbulence and its application to thin shear flows. J. Fluid Mech., 52, 609–638.
Hunt, J.C.R. (1977). A review of the theory of rapidly distorted turbulent flows and its applications. Proc. 13th Biennial Fluid Dynamics Symposium, Warsaw, pp. 121–152. Fluid Dynamics Transactions, Vol. 9.
Jayaram, M., Donovan, J.F., Dussauge, J.P., and Smits, A.J. (1989). Analysis of a rapidly distorted, supersonic, turbulent boundary layer. Phys. Fluids, 11, 1855–1864.
Launder, B.E., Reece, G.J., and Rodi, W. (1975). Progress in the development of a Reynolds stress turbulence closure. J. Fluid Mech., 68, 537–566.
Lumley, J.L. (1978). Computational modeling of turbulent flows. Adv. Appl. Mech., 18, 124–176.
Lumley, J.L. (1979). Prediction Methods for Turbulent Flows. Lecture Notes for von Karman Institute, AGARD Lecture Series, No. 1979-2. North Atlantic Treaty Organization, Brussels.
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. In Mechanique de la Turbulence (ed. A. Favre), pp. 367–380. CNRS.
Ribner, H.S., and Tucker, M. (1952). Spectrum of turbulence in a contracting stream. NACA TN 2606.
Rotta, J.C. (1951). Statistiche theorie nichthomogener turbulenz. Z. Phys., 129, 547.
Savill, A.M., (1987). Recent developments in rapid distortion theory. Ann. Rev. Fluid Mech., 19, 531–575.
Shih, T.H., and Lumley, J.L. (1985). Modeling of pressure correlation terms in Reynolds stress and scalar flux equations. Report FDA-85-3, Sibley School of Mechanical and Aerospace Engineering, Cornell University.
Smits, A.J., and Wood, D.H., (1985). The response of turbulent boundary layers to sudden perturbations. Ann. Rev. Fluid Mech., 17, 321–358.
Smits, A.J., Hayakawa, K., and Muck K.C. (1983). Constant temperature hot-wire anemometer practice in supersonic flows. Exp. Fluids, 1, 83–92.
van Driest, E.R. (1951). Turbulent boundary layer in compressible fluids. J. Aero. Sci., 18, 145–160.
Dedicated to Professor J.L. Lumley on the occasion of his 60th birthday.
This work was supported by the U.S. Air Force under AFOSR Contract 89-0420. Monitored by Dr. James McMichael.
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Smith, D.R., Smits, A.J. The rapid expansion of a turbulent boundary layer in a supersonic flow. Theoret. Comput. Fluid Dynamics 2, 319–328 (1991). https://doi.org/10.1007/BF00271471
- Experimental Data
- Boundary Layer
- Stress Tensor
- Mathematical Method
- Calculated Result