Hostname: page-component-cd9895bd7-jkksz Total loading time: 0 Render date: 2024-12-19T08:56:59.982Z Has data issue: false hasContentIssue false
  • English
  • Français

The response of a compressible turbulent boundary layer to short regions of concave surface curvature

Published online by Cambridge University Press:  21 April 2006

Mohan Jayaram ,
Margaret W. Taylor  and
Alexander J. Smits
Mohan Jayaram
Affiliation:
Gas Dynamics Laboratory, Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ 08544, USA
Margaret W. Taylor
Affiliation:
Gas Dynamics Laboratory, Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ 08544, USA
Alexander J. Smits
Affiliation:
Gas Dynamics Laboratory, Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ 08544, USA
Get access Rights & Permissions [Opens in a new window]

Abstract

Experiments were performed to investigate the supersonic flow of a turbulent boundary layer over short regions of concave surface curvature. Upstream of each curved wall, the free-stream Mach number was 2.87, and the incoming boundary layer was typical of a two-dimensional, zero-pressure-gradient, high-Reynolds-number flow. Two different curvatures were used, with radii of curvature equal to 10 and 50 initial boundary-layer thicknesses (Models I and II, respectively). The turning angle was 8° in each case. As the boundary layer passed through the curved region, it experienced a strong adverse pressure gradient, as well as the destabilizing influences of bulk compression and concave curvature. Downstream of the curved walls, the flow relaxed on a short plane wall. The mean and turbulent field for each flow was investigated, using normal and inclined hot wires to measure the turbulent fluctuations. Wherever possible, the results were compared with those from a corresponding 8° ramp. The ramp and Model I exhibited a very similar behaviour: turbulence levels increased significantly, and there was a marked increase in structural parameters such as the stress ratio $-\overline{u^{\prime}v^{\prime}}/\overline{u^{\prime 2}}$ and the length- and timescales of the turbulent motions. Model II behaved quite differently: although the turbulence levels increased, structural parameters were essentially unchanged. The similarities between the ramp and Model I results suggest that the perturbation in both cases is ‘rapid’ in that the perturbation can be described in terms of total strains rather than local strains. In contrast, the flow in Model II is sensitive to the local variations in the strain rate.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 175 , February 1987 , pp. 343 - 362
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

Acharya, M., Kussoy, M. I. & Horstman, C. C. 1978 Reynolds number and pressure gradient effects on compressible turbulent boundary layer. AIAA J. 16, 1217–1218.Google Scholar
Ardonceau, P. L., Lee, D. H., Alziary De Roquefort, T. & Goethals, R. 1979 Turbulence behaviour in shock wave/boundary layer interaction. AGARD Conf. Proc. 271, paper 8.
Bradshaw, P. 1973 Streamline curvature effects in turbulent flow. AGARD Dograph 169.
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., Ferriss, D. H. & Atwell, N. P. 1967 Calculation of boundary layer development using the turbulent energy equation. J. Fluid Mech. 28, 593–616.Google Scholar
Degani, D. & Smits, A. J. 1985 Numerical study of the response of a compressible turbulent boundary layer to a short region of surface curvature. AIAA paper 85–1667.Google Scholar
Dussauge, J.-P. & Gaviglio, J. 1981 Bulk dilatation effects on Reynolds stress in the rapid expansion of a turbulent boundary layer at supersonic speed. Proc. Symp. Turbulent Shear Flows, Davis, Calif. vol. 2, pp. 33–38.
Fernholz, H. H. & Finley, P. J. 1980 A critical commentary on mean flow data for two-dimensional compressible turbulent boundary layers. AGARDograph 253.
Gootzait, E. & Childs, M. E. 1977 Turbulence measurements in axisymmetric supersonic boundary layer flow in adverse pressure gradients. AIAA paper 77–129.Google Scholar
Hopkins, E. J. & Keener, E. R. 1966 Study of surface Pitots for measuring turbulent skin friction at supersonic Mach numbers-adiabatic wall. NASA Tech. Note D-3478.Google Scholar
Hoydysh, W. G. & Zakkay, V. 1969 An experimental investigation of hypersonic turbulent boundary layers in adverse pressure gradient. AIAA J. 7, 105–116.Google Scholar
Hunt, J. C. R. 1977 A review of the theory of rapidly distorted turbulent flows and its applications. Proc. Bienn. Fluid Dyn. Symp., 13th, Warsaw, Poland, pp. 121–152.Google Scholar
Jayaram, M., Dussauge, J. P. & Smits, A. J. 1985 Analysis of a rapidly distorted, supersonic, turbulent boundary layer. Proc. 5th Symp. on Turbulent Shear Flows, Cornell University, Ithaca, NY.
Klebanoff, P. S. 1955 Characteristics of turbulence in a boundary layer with zero pressure gradient. NACA Rep. 1247.Google Scholar
Laderman, A. J. 1980 Adverse pressure gradient effects on supersonic boundary-layer turbulent. AIAA J. 18, 1186–1195.Google Scholar
Launder, B. E., Reece, G. J. & Rodi, W. 1975 Progress in the development of a Reynoldsstress turbulence closure. J. Fluid Mech. 68, 537–566.Google Scholar
Lumley, J. L. 1975 Lecture, Von Karman Inst., Rhodes-St Genese.
McLafferty, G. H. & Barber, R. E. 1962 The effect of adverse pressure gradient on the characteristics of turbulent boundary layers in supersonic streams. J. Aero. Sci. 29, 1–10.Google Scholar
Morkovin, M. V. 1962 Effects of compressibility on turbulent flows. In Mécanique de la Turbulence (ed. A. Favre, pp. 367–380. Paris: CNRS.
Muck, K.-C. 1982 Turbulent boundary layers on mildly curved surfaces. PhD. thesis, University of London, UK.
Naot, D., Shavit, A. & Wolfshtein, M. 1970 Interactions between components of the turbulent velocity correlation tensor. Israel J. Tech. 8, 259.Google Scholar
Peake, D. J., Brakmann, G. & Romeskie, J. M. 1971 Comparisons between some high Reynolds number turbulent boundary layer experiments at Mach 4 and various recent calculation procedures. AGARD Conf. Proc. 93–71, paper 11.
Perry, A. E., Lim, K. L. & Henbest, S. M. 1985 A spectral analysis of smooth flat-plate boundary layers. Proc. 5th Symp. on Turbulent Shear Flows Cornell University, Ithaca, NY, pp. 9.29–9.34.
Ramaprian, B. R. & Shivaprasad, B. G. 1978 The structure of turbulent boundary layers along mildly curved surfaces. J. Fluid Mech. 85, 273–303.Google Scholar
Rong, B. S., Tan, D. K. M. & Smits, A. J. 1985 Calibration of the constant-temperature normal hot-wire anemometer in transonic flow. Princeton University Dept. Mech. & Aero. Engng Rep. no. 1696.Google Scholar
Rosen, R., Roshko, A. & Parish, D. L. 1980 A two-layer calculation for the initial interaction region of an unseparated supersonic turbulent boundary layer with a ramp. AIAA paper 80–0135.Google Scholar
Roshko, A. & Thomke, G. J. 1969 Supersonic turbulent boundary-layer interaction with a compression corner at very high Reynolds number. Proc. ARL Symp. on Viscous Interaction Phenomena in Supersonic and Hypersonic Flow, pp. 109–138. Ohio: University of Dayton Press.
Sandborn, V. A. 1974 A review of turbulence measurements in compressible flow. NASA TMX-62337.
Settles, G. S., Fitzpatrick, T. J. & Bogdonoff, S. M. 1979 Detailed study of attached and separated compression corner flowfields in high Reynolds number supersonic flow. AIAA J. 17, 579–585.Google Scholar
Shih, T.-H. & Lumley, J. L. 1987 Modelling of pressure correlation terms in Reynolds-stress and scalar flux equations. J. Fluid Mech. (submitted).Google Scholar
Smits, A. J., Eaton, J. A. & Bradshaw, P. 1979 The response of a turbulent boundary layer to lateral divergence. J. Fluid Mech. 94, 243–268.Google Scholar
Smits, A. J. & Joubert, P. N. 1982 Turbulent boundary layers on bodies of revolution. J. Ship Res. 26, 135–147.Google Scholar
Smits, A. J. & Muck, K. C. 1984 Constant-temperature hot-wire anemometer practice in supersonic flows. Part 2. The inclined wire. Expts in Fluids 2, 33–41.Google Scholar
Smits, A. J., Muck, K. C. & Hayakawa, K. 1983 Constant-temperature hot-wire anemometer practice in supersonic flows. Part 1. The normal wire. Expts in Fluids 1, 83–92.Google Scholar
Smits, A. J. & Muck, K. C. 1987 Experimental study of three shock-wave/turbulent boundary-layer interactions. J. Fluid Mech. (to appear).Google Scholar
Smits, A. J. & Wood, D. H. 1985 The response of turbulent boundary layers to sudden perturbations. Ann. Rev. Fluid Mech. 17, 321–358.Google Scholar
Smits, A. J., Young, S. T. B. & Bradshaw, P. 1979 The effect of short regions of high surface curvature on turbulent boundary layers. J. Fluid Mech. 94, 209–242.Google Scholar
So, R. M. C. & Mellor, G. L. 1972 An experimental investigation of turbulent boundary layers along curved surfaces. NASA CR-1940.
Sturek, W. B. & Danberg, J. E. 1972a Supersonic turbulent boundary layer in adverse pressure gradient. Part 1. The experiment. AIAA J. 10, 475–480.Google Scholar
Sturek, W. B. & Danberg, J. E. 1972b Supersonic turbulent boundary layer in adverse pressure gradient. Part 2. Data analysis. AIAA J. 10, 630–635.Google Scholar
Taylor, M. W. 1984 A supersonic turbulent boundary layer on concavely curved surfaces. M. Sc. thesis, Princeton University. (available as Dept. Mech. Aerosp. Engng Rept. 1684).
Thomann, H. 1968 Effect of streamwise wall curvature on heat transfer in a turbulent boundary layer. J. Fluid Mech. 33, 283–292.Google Scholar
Townsend, A. A. 1976 The Structure of Turbulent Shear Flow, 2nd edn., 429 pp. Cambridge University Press.
Van Driest, E. R. 1951 Turbulent boundary layer in compressible fluids. J. Aero. Sci. 18, 145–160.Google Scholar
Waltrup, P. J. & Schetz, J. A. 1973 Supersonic turbulent boundary layer subjected to adverse pressure gradients. AIAA J. 11, 50–58.Google Scholar
Wyngaard, J. C. 1968 Measurements of small-scale turbulence structure with hot-wires. J. Phys. E: Sci. Instrum. 1, 1105Google Scholar