Hostname: page-component-77c89778f8-vsgnj Total loading time: 0 Render date: 2024-07-16T09:54:35.887Z Has data issue: false hasContentIssue false
  • English
  • Français

The effect of interaction on the boundary layer induced by a convected rectilinear vortex

Published online by Cambridge University Press:  26 April 2006

Fu-Sheng Chuang  and
A. T. Conlisk
Fu-Sheng Chuang
Affiliation:
Department of Mechanical Engineering, National Taiwan Institute of Technology, Taipei, Taiwan, ROC
A. T. Conlisk
Affiliation:
Department of Mechanical Engineering, The Ohio State University, Columbus, OH 43210, USA
Get access Rights & Permissions [Opens in a new window]

Abstract

The effect of interaction on the boundary layer induced by a convected rectilinear vortex is considered. Two schemes are employed in the numerical discretization of the edge interaction condition; the first, developed by Veldman (1981) is useful at larger Reynolds numbers but fails to capture the interactive phase of the motion for Reynolds numbers less than 8 × 104. A scheme devised by Napolitano, Werlé & Davis (1978) is employed at smaller Reynolds numbers and yields similar results to Veldman's scheme at higher Reynolds numbers, while exhibiting greater numerical stability during the interactive phase of the motion. The effect of interaction is found to be negligible during much of the motion, even for a strong vortex, but during the latter stages of the calculations, interaction appears to round off the top of the eddy and delays breakdown for all Reynolds numbers studied when compared with the non-interactive results of Doligalski & Walker (1984). In addition, in the latter stages of the calculations, and during the early stages of the interactive phase, a third eddy is formed with vorticity of the same sign as the main eddy spawned deep within the boundary layer. Such a tertiary eddy has been observed in the experimental work of Walker et al. (1987) in their study of the boundary layer induced by a vortex ring. During the interactive phase of the motion a streamwise lengthscale emerges whose length is approximately $O(Re^{-\frac{3}{11}})$, broadly in line with the analytical predictions of Elliott, Cowley & Smith (1983). A novel feature of the computations is the use of a pseudospectral method (Burggraf & Duck 1982) in the streamwise direction which requires no special coding in reversed-flow regions.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 200 , March 1989 , pp. 337 - 365
Copyright
© 1989 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

Burggraf, O. R.: 1982 Interacting boundary layer solutions for laminar separated flow past airfoils. NASA Rep. NS61622.Google Scholar
Burggraf, O. R. & Duck, P. W., 1982 Spectral computation of triple deck flows. In Numerical and Physical Aspects of Aerodynamic Flows (ed. T. Cebeci), p. 145. Springer.
Burggraf, O. R., Rizzetta, D., Werle, M. J. & Vatsa, V. N., 1979 Effect of Reynolds number of laminar separation of a supersonic stream. AIAA J. 17, 336.Google Scholar
Conlisk, A. T.: 1989 The pressure field in intense vortex/boundary layer interaction. AIAA-89–0293.Google Scholar
Cooley, J. W. & Tukey, J. W., 1965 Maths Comput. 19, 297.
Davis, R. T. & Werle, M. J., 1982 Progress in interacting boundary layer computations at high Reynolds number. In Numerical and Physical Aspects of Aerodynamic Flows (ed. T. Cebeci), p. 187. Springer.
Doligalski, T. L. & Walker, J. D. A. 1984 The boundary layer induced by a convected rectilinear vortex. J. Fluid Mech. 139, 1.Google Scholar
Duck, P. W. & Burggraf, O. R., 1986 Spectral solutions for three dimensional triple-deck flow over surface topography. J. Fluid Mech. 162, 1.Google Scholar
Elliott, J. W., Cowley, S. J. & Smith, F. T., 1983 Breakdown of boundary layers: (i) on moving surfaces; (ii) in self-similar unsteady flow; (iii) in fully unsteady flow. Geophys. Astrophys. Fluid Dyn. 25, 77.Google Scholar
Harvey, J. K. & Perry, F. J., 1971 Flowfield produced by trailing vortices in the vicinity of the ground. AIAA J. 9, 1659.Google Scholar
Henkes, R. A. W. M. & Veldman, A. E. P. 1987 On the breakdown of steady and unsteady interacting boundary layer description. J. Fluid Mech. 179, 513.Google Scholar
Milne-Thompson, L. M.: 1960 Theoretical Hydrodynamics, 4th edn. Macmillan.
Napolitano, M., Werle, M. J. & Davis, R. T., 1978 Numerical solutions of the triple-deck equations for supersonic and subsonic flow past a hump. David Taylor Naval Ship Research and Development Center, Rep. AFL 78–6–42.Google Scholar
Nelson, E. S.: 1986 Phase averaged measurements of vortex interaction with a solid surface and the breakaway proces. M. Sc. thesis, Illinois Institute of Technology.
Perridier, V., Smith, F. T. & Walker, J. D. A. 1988 Methods for the calculation of unsteady separation. AIAA-88–0604.Google Scholar
Riley, N.: 1982 Non-uniform slot injection into a laminar boundary layer. J. Engng Maths 15, 299.Google Scholar
Rosenhead, L.: 1963 Laminar Boundary Layers. Oxford University Press.
Sears, W. R. & Telionis, D. P., 1975 Boundary layer separation in unsteady flow. SIAM J. Appl. Maths 28, 215.Google Scholar
Smith, F. T.: 1988 Finite time breakup can occur in any interacting boundary layer. Mathematica (to appear).Google Scholar
Smith, F. T. & Bodonyi, R. J., 1985 On the short-scale inviscid instabilities in flow past surface mounted obstacles and other non-parallel motions. Aero. J. 89, 205.Google Scholar
Smith, F. T. & Burggraf, O. F., 1985 On the development of large sized short-scaled disturbances in boundary layers. Proc. R. Soc. Lond. A 399, 25.Google Scholar
Van Dommelen, L. L. 1981 Unsteady boundary layer separation. Ph.D. thesis, Cornell University.
Van Dyke, M. 1975 Perturbation Methods in Fluid Mechanics. Parabolic.
Veldman, A. E. P.: 1981 New, quasi-simultaneous method to calculate interacting boundary layers. AIAA J. 19, 79.Google Scholar
Walker, J. D. A.: 1978 The boundary layer due to a rectilinear vortex. Proc. R. Soc. Lond. A 359, 167.Google Scholar
Walker, J. D. A., Smith, C. R., Cerra, A. W. & Doligalski, T. L., 1987 Impact of a vortex ring on a wall. J. Fluid Mech. 181, 99.Google Scholar