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The structure of two-dimensional separation

Published online by Cambridge University Press:  26 April 2006

Laura L. Pauley
Affiliation:
The Pennsylvania State University, University Park, PA 16802, USA
Parviz Moin
Affiliation:
Stanford University, Stanford, CA 94305, USA and NASA/Ames Research Center, Moffett Field, CA 94035, USA
William C. Reynolds
Affiliation:
Stanford University, Stanford, CA 94305, USA and NASA/Ames Research Center, Moffett Field, CA 94035, USA

Abstract

The separation of a two-dimensional laminar boundary layer under the influence of a suddenly imposed external adverse pressure gradient was studied by time-accurate numerical solutions of the Navier–Stokes equations. It was found that a strong adverse pressure gradient created periodic vortex shedding from the separation. The general features of the time-averaged results were similar to experimental results for laminar separation bubbles. Comparisons were made with the ‘steady’ separation experiments of Gaster (1966). It was found that his ‘bursting’ occurs under the same conditions as our periodic shedding, suggesting that bursting is actually periodic shedding which has been time-averaged. The Strouhal number based on the shedding frequency, local free-stream velocity, and boundary-layer momentum thickness at separation was independent of the Reynolds number and the pressure gradient. A criterion for onset of shedding was established. The shedding frequency was the same as that predicted for the most amplified linear inviscid instability of the separated shear layer.

Type
Research Article
Copyright
© 1990 Cambridge University Press

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References

Bestek, H., Gruber, K. & Fasel, H., 1989 Self-excited unsteadiness of laminar separation bubbles caused by natural transition. In The Prediction and Exploitation of Separated Flow. The Royal Aeronautical Society.
Briley, W. R.: 1971 A numerical study of laminar separation bubbles using the Navier–Stokes equations. J. Fluid Mech. 47, 713736.Google Scholar
Curle, N. & Skan, S. W., 1957 Approximate methods for predicting separation properties of laminar boundary layers. Aero. Q. 8, 257268.Google Scholar
Despard, R. A. & Miller, J. A., 1971 Separation in oscillating boundary-layer flows. J. Fluid Mech. 47, 2131.Google Scholar
Dobbinga, E., Van Ingen, J. L. & Kooi, J. W., 1972 Some research on two-dimensional laminar separation bubbles. AGARD CP-4, p. 102.Google Scholar
Elliott, J. W. & Smith, F. T., 1987 Dynamic stall due to unsteady marginal separation. J. Fluid Mech. 179, 489512.Google Scholar
Gaster, M.: 1966 The structure and behavior of laminar separation bubbles. AGARD CP-4, pp. 813854.Google Scholar
Gruber, K., Bestek, H. & Fasel, H., 1987 Interaction between a Tollmien–Schlichting wave and a laminar separation bubble. AIAA-87-1256.Google Scholar
Henk, R. W.: 1990 An experimental study of the fluid mechanics of an unsteady, three-dimensional separation. Ph.D. thesis, Stanford University.
Horton, H. P.: 1968 Laminar separation bubbles in two- and three-dimensional incompressible flow. Ph.D. thesis, University of London.
Kim, J. & Moin, P., 1985 Application of a fractional-step method to incompressible Navier–Stokes equations. J. Comput. Phys. 59, 308323.Google Scholar
Koromilas, C. A. & Telionis, D. P., 1980 Unsteady laminar separation: an experimental study. J. Fluid Mech. 97, 347384.Google Scholar
Mccullough, G. B. & Gault, D. E., 1949 Boundary-layer and stalling characteristics of the NACA 64 A 006 Airfoil Section. NACA TN 1894.Google Scholar
Michalke, A.: 1964 On the inviscid instability of the hyperbolic-tangent velocity profile. J. Fluid Mech. 19, 543556.Google Scholar
Monkewitz, P. A. & Huerre, P., 1982 Influence of the velocity ratio on the spatial instability of mixing layers. Phys. Fluids 25, 11371143.Google Scholar
Pauley, L. L., Moin, P. & Reynolds, W. C., 1988 A numerical study of unsteady laminar boundary-layer separation. Rep. TF-34, Department of Mechanical Engineering, Stanford University, Stanford, CA.
Peake, D. T. & Tobak, M., 1982 Three-dimensional interactions and vortical flows with emphasis on high speeds. AGARDograph 252.Google Scholar
Smith, F. T.: 1979 Laminar flow of an incompressible fluid past a bluff body: the separation, reattachment, eddy properties and drag. J. Fluid Mech. 92, 171205.Google Scholar
Smith, F. T.: 1985 A structure for laminar flow past a bluff body at high Reynolds number. J. Fluid Mech. 155, 175191.Google Scholar
Stewartson, K., Smith, F. T. & Kaups, K., 1982 Marginal separation. Stud. Appl. Maths 67, 4561.Google Scholar
Tani, L.: 1964 Low-speed flows involving bubble separations. Prog. Aero. Sci. 5, 70103.Google Scholar
Thwaites, B.: 1949 Approximate calculation of the laminar boundary layer. Aero. Q. 14, 6185.Google Scholar