Hostname: page-component-586b7cd67f-vdxz6 Total loading time: 0 Render date: 2024-11-25T06:25:38.407Z Has data issue: false hasContentIssue false
  • English
  • Français

Comparisons Between Inverse Boundary-Layer Calculations and Detailed Measurements in Laminar Separated Flows

Published online by Cambridge University Press:  07 June 2016

H.P. Horton
H.P. Horton*
Affiliation:
Queen Mary College, University of London
Get access

Summary

A brief description is given of an accurate numerical method for the inverse calculation of both attached and separated laminar, two-dimensional, incompressible boundary-layers with prescribed displacement thickness. The method employs downstream-marching, using an approximation to the convection terms in the reverse-flow region to stabilise the computation. Results of three calculations made by this method, using measured distributions of displacement thickness as input, are presented and compared with the corresponding measured velocity profiles and distributions of external velocity. Very close agreement between theory and experiment is found in general, giving further evidence of the validity of the boundary-layer approximation in separated flows of limited extent.

Type
Research Article
Information
Aeronautical Quarterly , Volume 32 , Issue 3 , August 1981 , pp. 169 - 187
Copyright
Copyright © Royal Aeronautical Society. 1981

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

1 Catherall, D. and Mangier, K.W. The integration of the two-dimensional laminar boundary-layer equations past the point of vanishing skin friction. Journal of Fluid Mechanics, Vol. 26, Part 1, p 163, 1966.Google Scholar
2 Goldstein, S. On laminar boundary-layer flow near a position of separation. Quarterly Journal of Mechanics and Applied Mathematics, Vol. I, p 43, 1948.Google Scholar
3 Smith, A.M.O. and Clutter, D.W. Solution of the incompressible boundary-layer equations. AIAA Journal, Vol. 1, p 2062, 1963.Google Scholar
4 Carter, J.E. Inverse solutions for laminar boundary-layer flows with separation and reattachment. NASA Technical Report TR R-447, 1975.Google Scholar
5 Klineberg, J.M. and Steger, J.L. On laminar boundary-layer separation. AIAA Paper No. 74-94, 1974.Google Scholar
6 Horton, H.P. Separating laminar boundary layers with prescribed wall shear. AIAA Journal, Vol. 12, p 1772, 1974.Google Scholar
7 Horton, H.P. Numerical investigation of regular laminar boundary layer separation. AGARD CP No. 168, 1975.Google Scholar
8 Klineberg, J.M. and Steger, J.L. Calculation of separated flows at subsonic and transonic speeds. Lecture Notes in Physios, Vol. 19, p 161, Springer-Verlag, 1973.Google Scholar
9 Briley, W.R. and McDonald, H. Numerical prediction of incompressible separation bubbles. Journal of Fluid Mechanics, Vol. 69, Part 4, p 631, 1975.Google Scholar
10 Briley, W.R. A numerical study of laminar separation bubbles using the Navier-Stokes equations. Journal of Fluid Mechanics, Vol. 47, Part 4, p 713, 1971.Google Scholar
11 Murphy, J.D. An efficient solution procedure for the incompressible Navier-Stokes equations. AIAA Journal, Vol. 15, p 1307, 1977.Google Scholar
12 Reyhner, T.A. and Flügge-Lotz, I. The interaction of a shock wave with a laminar boundary layer. International Journal of Non-Linear Mechanics, Vol. 3, p 173, 1968.Google Scholar
13 Schubauer, G.B. Air flow in a separating laminar boundary layer. NACA Report 527, 1935.Google Scholar
14 Ntim, B.A. A theoretical and experimental investigation of separation bubbles. Ph.D. Thesis, Queen Mary College, university of London, 1969.Google Scholar
15 Horton, H.P. Laminar separation bubbles in two- and three-dimensional incompressible flow. Ph.D. Thesis, Queen Mary College, University of London, 1968.Google Scholar
16 Görtler, H. A new series for the calculation of steady laminar boundary layer flows. Journal of Mathematics and Mechanics, Vol. 6, No. 1, p1, 1957.Google Scholar
17 Jaffe, N.A. and Smith, A.M.O. Calculation of laminar boundary layers by means of a differential-difference method. Progress in Aerospace Science, Vol. 12, Pergamon Press, p 49, 1971.Google Scholar
18 Meyer, G.H. Initial-value methods for boundary-value problems, Academic Press, 1973,Google Scholar
19 Horton, H.P. Numerical solution of laminar boundary-layer problems using invariant imbedding: Inverse Problems. Queen Mary College, Faculty of Engineering, EP 1039, 1981.Google Scholar
20 Brown, S.N. and Stewartson, K. Laminar separation. Annual Review of Fluid Mechanics, p 45, 1969.Google Scholar
21 Woodward, D.S. An investigation of the flow in separation bubbles. Ph.D. Thesis, Queen Mary College, University of London, 1970.Google Scholar
22 Jones, R.T. Effects of sweepback on boundary layer and separation. NACA Report 884, 1949.Google Scholar
23 Williams, P.G. A reverse flow computation in the theory of self-induced separation. Lecture Notes in Physics, Vol. 35, p 445, Springer-Verlag, 1975.Google Scholar