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On the origin of the inflectional instability of a laminar separation bubble

  • SOURABH S. DIWAN (a1) and O. N. RAMESH (a1)

This is an experimental and theoretical study of a laminar separation bubble and the associated linear stability mechanisms. Experiments were performed over a flat plate kept in a wind tunnel, with an imposed pressure gradient typical of an aerofoil that would involve a laminar separation bubble. The separation bubble was characterized by measurement of surface-pressure distribution and streamwise velocity using hot-wire anemometry. Single component hot-wire anemometry was also used for a detailed study of the transition dynamics. It was found that the so-called dead-air region in the front portion of the bubble corresponded to a region of small disturbance amplitudes, with the amplitude reaching a maximum value close to the reattachment point. An exponential growth rate of the disturbance was seen in the region upstream of the mean maximum height of the bubble, and this was indicative of a linear instability mechanism at work. An infinitesimal disturbance was impulsively introduced into the boundary layer upstream of separation location, and the wave packet was tracked (in an ensemble-averaged sense) while it was getting advected downstream. The disturbance was found to be convective in nature. Linear stability analyses (both the Orr–Sommerfeld and Rayleigh calculations) were performed for mean velocity profiles, starting from an attached adverse-pressure-gradient boundary layer all the way up to the front portion of the separation-bubble region (i.e. up to the end of the dead-air region in which linear evolution of the disturbance could be expected). The conclusion from the present work is that the primary instability mechanism in a separation bubble is inflectional in nature, and its origin can be traced back to upstream of the separation location. In other words, the inviscid inflectional instability of the separated shear layer should be logically seen as an extension of the instability of the upstream attached adverse-pressure-gradient boundary layer. This modifies the traditional view that pegs the origin of the instability in a separation bubble to the detached shear layer outside the bubble, with its associated Kelvin–Helmholtz mechanism. We contend that only when the separated shear layer has moved considerably away from the wall (and this happens near the maximum-height location of the mean bubble), a description by the Kelvin–Helmholtz instability paradigm, with its associated scaling principles, could become relevant. We also propose a new scaling for the most amplified frequency for a wall-bounded shear layer in terms of the inflection-point height and the vorticity thickness and show it to be universal.

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Alam M. & Sandham N. D. 2000 Direct numerical simulation of ‘short’ laminar separation bubbles with turbulent reattachment. J. Fluid Mech. 410, 128.
Bendat J. S. & Piersol A. G. 1966 Measurement and Analysis of Random Data. John Wiley & Sons.
Betchov R. & Criminale W. O. 1967 Stability of Parallel Flows. Academic.
Betchov R. & Szewczyk A. 1963 Stability of a shear layer between parallel streams. Phys. Fluids 6 (10), 13911396.
Boiko A. V., Grek G. R., Dovgal A. V. & Kozlov V. V. 2002 The Origin of Turbulence in Near-Wall Flows. Springer.
Cantwell B. J., Coles D. & Dimotakis P. E. 1978 Structure and entrainment in the plane of symmetry of a turbulent spot. J. Fluid Mech. 87, 641672.
Das D. 1998 Evolution and instability of unsteady boundary-layers with reverse flow. PhD thesis, Department of Mechanical Engineering, Indian Institute of Science, Bangalore, India.
Dovgal A. V., Kozlov V. V. & Michalke A. 1994 Laminar boundary layer separation: instability and associated phenomena. Prog. Aerosp. Sci. 30, 6194.
Drazin P. G. & Reid W. H. 1981 Hydrodynamic Stability. Cambridge University Press.
Eaton J. K. & Johnston J. P. 1980 Turbulent flow reattachment: an experimental study of the flow and structure behind a backward-facing step. Tech Rep. MD-39. Deparment of Mechanical Engineering, Stanford University.
Fitzgerald E. J. & Mueller T. J. 1990 Measurements in a separation bubble on an airfoil using laser velocimetry. AIAA J. 28 (4), 584592.
Gaster M. 1967 The structure and behaviour of separation bubbles. ARC London R&M (3595).
Gaster M. & Grant I. 1975 An experimental investigation of the formation and development of a wave packet in a laminar boundary layer. Proc. R. Soc. Lond. A 347, 253269.
Haggmark C. P., Bakchinov A. A. & Alfredsson P. H. 2000 Experiments on a two-dimensional laminar separation bubble. Phil. Trans. R. Soc. Lond. A 358, 31933205.
Hammond D. A. & Redekopp L. G. 1998 Local and global instability properties of separation bubbles. Eur. J. Mech. B 17 (2), 145164.
Hatman A. & Wang T. 1998 Separated-flow transition. Part 1. Experimental methodology and mode classification. Paper 98-GT-461. ASME.
Healey J. J. 1998 Characterizing boundary-layer instability at finite Reynolds numbers. Eur. J. Mech. B 17 (2), 219237.
Herbert T. 1988 Secondary instability of boundary layers. Annu. Rev. Fluid Mech. 20, 487526.
Horton H. P. 1969 A semi-empirical theory for the growth and bursting of laminar separation bubbles. ARC London (C.P. No. 1073).
Lang M., Rist U. & Wagner S. 2004 Investigations on controlled transition development in a laminar separation bubble by means of LDA and PIV. Exp. Fluids 36, 4352.
Langston L. S. & Boyle M. T. 1982 A new surface-streamline flow-visualisation technique. J. Fluid Mech. 125, 5357.
Marxen O., Lang M., Rist U. & Wagner S. 2003 A combined experimental/ numerical study of unsteady phenomena in a laminar separation bubble. Flow Turbul. Combust. 71, 133146.
Maslowe S. A. 1986 Critical layers in shear flows. Annu. Rev. Fluid Mech. 18, 405432.
Maucher U., Rist U. & Wagner S. 1999 Transitional structures in a laminar separation bubble. In New Results in Numerical and Experimental Fluid Mechanics II (ed. Nitsche W., Heinemann H. J. & Hilbig R.), vol. 72, pp. 307314. Vieweg.
Michalke A. 1964 On the inviscid instability of the hyperbolic-tangent velocity profile. J. Fluid Mech. 19, 543556.
Monkewitz P. A. & Huerre P. 1982 Influence of the velocity ratio on the spatial instability of mixing layers. Influence of the velocity ratio on the spatial instability of mixing layers 25 (7), 11371143.
Narasimha R. & Prasad S. N. 1994 Leading edge shape for flat plate boundary layer studies. Leading edge shape for flat plate boundary layer studies 17 (5), 358360.
Nayfeh A. H., Ragab S. A. & Masad J. A. 1990 Effect of a bulge on the subharmonic instability of boundary layers. Phys. Fluids A 2 (6), 937948.
Niew T. R. 1993 The stability of the flow in a laminar separation bubble. PhD thesis, St John's College, Cambridge.
Pauley L. L., Moin P. & Reynolds W. C. 1990 The structure of two-dimensional separation. J. Fluid Mech. 220, 397411.
Ramesh O. N., Hodson H. P. & Harvey N. W. 2001 Separation control in ultra-high lift aerofoils by unsteadiness and surface roughness. In Proc. of the Intl Society of Airbreathing Engines ISABE-1096, Bangalore, India.
Rist U., Maucher U. & Wagner S. 1996 Direct numerical simulation of some fundamental problems related to transition in laminar separation bubbles. In Computational Fluid Dynamics '96 (ed. Desideri J. A., Hirsch C., Tallec P. Le, Pandolfi M. & Periaux J.), pp. 319325. John Wiley & Sons.
Schlichting H. 1960 Boundary Layer Theory. McGraw-Hill.
Sinha S. N., Gupta A. K. & Oberai M. M. 1981 Laminar separating flow over backsteps and cavities. Part 1. Backsteps. AIAA J. 19, 15271530.
Spalart P. R. & Strelets M. Kh. 2000 Mechanisms of transition and heat transfer in a separation bubble. J. Fluid Mech. 403, 329349.
Taghavi H. & Wazzan A. R. 1974 Spatial stability of some Falkner–Skan profiles with reversed flow. Spatial stability of some Falkner–Skan profiles with reversed flow 17 (12), 21812183.
Tani I. 1964 Low speed flows involving bubble separations. Prog. Aerosp. Sci. 5, 70103.
Theofilis V., Hein S. & Dallmann U. 2000 On the origins of unsteadiness and three-dimensionality in a laminar separation bubble. Phil. Trans. R. Soc. Lond. A 358, 32293246.
VanDyke M. 1982 An Album of Fluid Motion. Parabolic.
Villermaux E. 1998 On the role of viscosity in shear instabilities. On the role of viscosity in shear instabilities 10 (2), 368373.
Watmuff J. H. 1999 Evolution of a wave packet into vortex loops in a laminar separation bubble. J. Fluid Mech. 397, 119169.
Zaman K. B. M. Q. & Hussain A. K. M. F. 1981 Turbulence suppression in free shear flows by controlled excitation. J. Fluid Mech. 103, 133159.
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Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
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