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Unsteady separation and heat transfer upstream of obstacles

Published online by Cambridge University Press:  26 April 2006

R. I. Puhak ,
A. T. Degani  and
J. D. A. Walker
R. I. Puhak
Affiliation:
Department of Mechanical Engineering and Mechanics, Lehigh University, Bethlehem, PA 18015, USA
A. T. Degani
Affiliation:
Department of Mechanical Engineering and Mechanics, Lehigh University, Bethlehem, PA 18015, USA
J. D. A. Walker
Affiliation:
Department of Mechanical Engineering and Mechanics, Lehigh University, Bethlehem, PA 18015, USA
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Abstract

The development of a laminar boundary layer upstream of both two- and threedimensional obstacles mounted on a plane wall is considered. The motion is impulsively started from rest, and it is shown that the boundary layer upstream of the obstacle initially develops independently from that on the obstacle itself. Numerical solutions for the unsteady boundary-layer flow on the plane wall are obtained in both Eulerian and Lagrangian coordinates. It is demonstrated that in both situations the flow focuses into a narrow-band eruption characteristic of separation phenomena at high Reynolds number. For the three-dimensional problem, results are obtained on a symmetry plane upstream of the obstacle which indicate the evolution, and subsequent sharp compression, of a spiral vortex in the near-wall flow in a manner consistent with recent experimental studies. The eruptive response of the two-dimensional boundary layer is found to be considerably stronger than the corresponding event in three dimensions. Calculated results for the temperature distribution are obtained for the situation where the wall temperature is constant but different from that of the mainstream. It is shown that a concentrated response develops in the surface heat transfer rate as the boundary layer starts to separate from the surface.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 305 , 25 December 1995 , pp. 1 - 27
Copyright
© 1995 Cambridge University Press

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References

Acarlar, M. S. & Smith, C. R. 1987 A study o hairpin vortices in a laminar boundary layer. Part 1. Hairpin vortices generated by a hemisphere protuberance. J. Fluid Mech. 175, 1–41.Google Scholar
Adams, E. C., Conlisk, A. T. & Smith, F. T. 1995 Adaptive grind scheme for vortex-induced boundary layers. AIAA J 33, 864–870.Google Scholar
Affes, H. Xiao, Z. & Conlisk, A. T. 1994 The boundary-layer flow due to a vortex approaching a cylinder. J. Fluid Mech. 275, 33–57.Google Scholar
Cowley, S. J., Dommelen, L. L. Van & Lam, S. T. 1990 On the use of Lagrangian variables on descriptions of unsteady boundary-layer separation. Phil. Trans. R. Soc. Lond. A 333, 343–378.Google Scholar
Doligalski, T.L. & Walker, J. D. A. 1984 The boundary layer induced by a convected two-dimensional vortex. J. Fluid Mech. 139, 1–28.Google Scholar
Doligalski, T. L., Smith, C. R. & Walker, J. D. A. 1994 Vortex interactions with walls. Ann. Rev. Fluid Mech. 26, 573–616.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, 77–138.Google Scholar
Ersoy, S. & Walker, J. D. A. 1987 The boundary layer due to a three-dimensional vortex loop. J. Fluid Mech. 185, 569–598.Google Scholar
Hung, C. M. Sung, C. H. & Chen, C. L. 1991 Computation of saddle point of attachment. AIAA Paper 91–1713.Google Scholar
Milne-Thomson, L. M. 1960 Theoretical Hydrodynamics 4th edn. Macmillan.
Perdier, V. J., Smith, F. T. & Walker, J. D. A. 1991 Vortex-induced boundary-layer separation. Part 1: The limit problem Re-→∞. J. Fluid Mech. 232, 99–131.Google Scholar
Proudman, I. & Johnson, K. 1962 Boundary-layer growth near a rear stagnation point. J. Fluid Mech. 12, 161–168.Google Scholar
Sears, W. P. & Telonis, D. P. 1975 Boundary-layer separation in unsteady flow. SIAM J. Appl. Maths 28, 215–235.Google Scholar
Smith, C. R. Fitzgerald, J. P. & Greco, J. J. 1991 Cylinder end-wall vortex dynamics. Phys. Fluids A 3, 2031.Google Scholar
Dommelen, L. L. Van & Cowley, S. J. 1990 On the Lagrangian description of the unsteady boundary layer separation. Part 1. General theory. J. Fluid Mech. 210, 593–626.Google Scholar
Dommelen, L. L. Van & Shen, S. F. 1980 The spontaneous generation of the singularity in a separating boundary layer. J. Comput. Phys. 38, 125–140.Google Scholar
Dommelen, L. L. Van & Shen, S. F. 1982 The genesis of separation. In Proc. Symp. on Numerical and Physical Aspects of Aerodynamic Flow (ed. T. Cebeci), Long Beach, California pp. 283–311. Springer.
Dommelen, L. L. Van & Shen, S. F. 1985 The flow at a near stagnation point is eventually determined by exponentially small values of velocity. J. Fluid Mech. 157, 1–16.Google Scholar
Visbal, M R 1991 Structure of laminar juncture flows. AIAA J. 29, 1273–1282.Google Scholar