Hostname: page-component-8448b6f56d-cfpbc Total loading time: 0 Render date: 2024-04-16T21:27:07.165Z Has data issue: false hasContentIssue false

Response of a laminar separation bubble to impulsive forcing

Published online by Cambridge University Press:  12 May 2017

Theodoros Michelis*
Affiliation:
Department of Aerodynamics, Delft University of Technology, 2629 HS, Delft, The Netherlands
Serhiy Yarusevych
Affiliation:
Fluid Mechanics Research Laboratory, University of Waterloo, N2L 3G1, Waterloo, Canada
Marios Kotsonis
Affiliation:
Department of Aerodynamics, Delft University of Technology, 2629 HS, Delft, The Netherlands
*
Email address for correspondence: t.michelis@tudelft.nl

Abstract

The spatial and temporal response characteristics of a laminar separation bubble to impulsive forcing are investigated by means of time-resolved particle image velocimetry and linear stability theory. A two-dimensional impulsive disturbance is introduced with an alternating current dielectric barrier discharge plasma actuator, exciting pertinent instability modes and ensuring flow development under environmental disturbances. Phase-averaged velocity measurements are employed to analyse the effect of imposed disturbances at different amplitudes on the laminar separation bubble. The impulsive disturbance develops into a wave packet that causes rapid shrinkage of the bubble in both upstream and downstream directions. This is followed by bubble bursting, during which the bubble elongates significantly, while vortex shedding in the aft part ceases. Duration of recovery of the bubble to its unforced state is independent of the forcing amplitude. Quasi-steady linear stability analysis is performed at each individual phase, demonstrating reduction of growth rate and frequency of the most unstable modes with increasing forcing amplitude. Throughout the recovery, amplification rates are directly proportional to the shape factor. This indicates that bursting and flapping mechanisms are driven by altered stability characteristics due to variations in incoming disturbances. The emerging wave packet is characterised in terms of frequency, convective speed and growth rate, with remarkable agreement between linear stability theory predictions and measurements. The wave packet assumes a frequency close to the natural shedding frequency, while its convective speed remains invariant for all forcing amplitudes. The stability of the flow changes only when disturbances interact with the shear layer breakdown and reattachment processes, supporting the notion of a closed feedback loop. The results of this study shed light on the response of laminar separation bubbles to impulsive forcing, providing insight into the attendant changes of flow dynamics and the underlying stability mechanisms.

Type
Papers
Copyright
© 2017 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

Alam, M. & Sandham, N. D. 2000 Direct numerical simulation of ‘short’ laminar separation bubble with turbulent reattachment. J. Fluid Mech. 410, 128.CrossRefGoogle Scholar
Amitay, M., Smith, D. R., Kibens, V., Parekh, D. E. & Glezer, A. 2001 Aerodynamic flow control over an unconventional airfoil using synthetic jet actuators. AIAA J. 39 (3), 361370.CrossRefGoogle Scholar
Bake, S., Meyer, D. G. W. & Rist, U. 2002 Turbulence mechanism in Klebanoff transition: a quantitative comparison of experiment and direct numerical simulation. J. Fluid Mech. 459, 217243.CrossRefGoogle Scholar
Benard, N. & Moreau, E. 2014 Electrical and mechanical characteristics of surface AC dielectric barrier discharge plasma actuators applied to airflow control. Exp. Fluids 55 (11), 1846.Google Scholar
Boiko, A. V., Grek, G. R., Dovgal, A. V & Kozlov, V. V. 2002 The Origin of Turbulence in Near-Wall Flows. Springer.Google Scholar
Boutilier, M. S. H. & Yarusevych, S. 2012 Separated shear layer transition over an airfoil at a low Reynolds number. Phys. Fluids 24, 084105.Google Scholar
Brevdo, L. & Bridges, T. J. 1997 Local and global instabilities of spatially developing flows: cautionary examples. Proc. R. Soc. Lond. A 453 (1962), 13451364.Google Scholar
Corke, T. C., Enloe, C. L. & Wilkinson, S. P. 2010 Dielectric barrier discharge plasma actuators for flow control. Annu. Rev. Fluid Mech. 42, 505529.CrossRefGoogle Scholar
Daubechies, I. 1992 Ten Lectures on Wavelets, CBMS-NSF Regional Conference Series in Applied Mathematics, vol. 61. SIAM.Google Scholar
Diwan, S. S. & Ramesh, O. N. 2009 On the origin of the inflectional instability of a laminar separation bubble. J. Fluid Mech. 629, 263298.Google Scholar
Dovgal, A. V & Boiko, A. V. 1994 Effect of harmonic excitation on instability of a laminar separation bubble on an airfoil. In Laminar-Turbulent Transition (ed. Fasel, H. F. & Saric, W. S.), pp. 675680. Springer.Google Scholar
Dovgal, A. V., Kozlov, V. V. & Michalke, A. 1994 Laminar boundary layer separation: instability and associated phenomena. Prog. Aerosp. Sci. 30 (1), 6194.Google Scholar
Farge, M. 1992 Wavelet transforms and their applications to turbulence. Annu. Rev. Fluid Mech. 24, 395457.CrossRefGoogle Scholar
Gaster, M.1967 The structure and behaviour of laminar separation bubbles. Tech. Rep. 3595. Aeronautical Research Council Reports and Memoranda.Google Scholar
Gaster, M. 1992 Instability, Transition, and Turbulence. Stability of Velocity Profiles with Reverse Flow, pp. 212215. Springer.CrossRefGoogle Scholar
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.Google Scholar
Häggmark, C. P., Hildings, C. & Henningson, D. S. 2001 A numerical and experimental study of a transitional separation bubble. Aerosp. Sci. Technol. 5 (5), 317328.Google Scholar
Hain, R., Kähler, C. J. & Radespiel, R. 2009 Dynamics of laminar separation bubbles at low-Reynolds-number aerofoils. J. Fluid Mech. 630, 129153.CrossRefGoogle Scholar
Ho, C. M. & Huerre, P. 1984 Perturbed free shear layers. Annu. Rev. Fluid Mech. 16, 365424.Google Scholar
Hunt, J. C. R., Wray, A. A. & Moin, P.1988 Eddies, stream, and convergence zones in turbulent flows. Tech. Rep. CTR-S88. Center For Turbulence Research.Google Scholar
van Ingen, J. L. 2008 The e N method for transition prediction. Historical review of work at TU Delft. In 38th AIAA Fluid Dynamics Conference and Exhibit.Google Scholar
van Ingen, J. L. & Kotsonis, M. 2011 A two-parameter method for e N transition prediction. In 6th AIAA Theoretical Fluid Mechanics Conference.Google Scholar
Jones, L. E., Sandbergh, R. D. & Sandham, N. D. 2008 Direct numerical simulation of forced and unforced separation bubbles on an airfoil at incidence. J. Fluid Mech. 602, 175207.Google Scholar
Jones, L. E., Sandberg, R. D. & Sandham, N. D. 2010 Stability and receptivity characteristics of a laminar separation bubble on an aerofoil. J. Fluid Mech. 648, 257296.Google Scholar
Kähler, C. J., Scharnowski, S. & Cierpka, C. 2012 On the resolution limit of digital particle image velocimetry. Exp. Fluids 52, 16291639.Google Scholar
von Kerczek, C. & Davis, S. H. 1974 Linear stability theory of oscillatory stokes layers. J. Fluid Mech. 62, 753773.CrossRefGoogle Scholar
Kotsonis, M. 2015 Diagnostics for characterisation of plasma actuators. Meas. Sci. Technol. 26 (9), 092001.Google Scholar
Kotsonis, M., Ghaemi, S., Veldhuis, L. L. M. & Scarano, F. 2011 Measurement of the body force field of plasma actuators. J. Phys. D: Appl. Phys. 44 (4), 045204.Google Scholar
Kurelek, J. W., Lambert, A. R. & Yarusevych, S. 2016 Coherent structures in the transition process of a laminar separation bubble. AIAA J. 54 (8), 22952309.Google Scholar
LeBlanc, P., Blackwelder, R. & Liebeck, R. 1989 A Comparison Between Boundary Layer Measurements in a Laminar Separation Bubble Flow and Linear Stability Theory Calculations. pp. 189205. Springer.Google Scholar
Lengani, D., Simoni, D., Ubaldi, M. & Zunino, P. 2014 POD analysis of the unsteady behavior of a laminar separation bubble. Exp. Therm. Fluid Sci. 58, 7079.Google Scholar
Lin, N., Reed, H. L. & Saric, W. S. 1992 Effect of Leading-Edge Geometry on Boundary-Layer Receptivity to Freestream Sound, Instability, Transition and Turbulence. Springer.Google Scholar
Mack, L. M.1984 Boundary-layer linear stability theory. AGARD Tech. Rep. 709.Google Scholar
Marxen, O. & Henningson, D. S. 2011 The effect of small-amplitude convective disturbances on the size and bursting of a laminar separation bubble. J. Fluid Mech. 671, 133.CrossRefGoogle Scholar
Marxen, O., Kotapati, R. B., Mital, R. & Zaki, T. 2015 Stability analysis of separated flows subject to control by zero-net-mass-flux jet. Phys. Fluids 27 (2), 024107.CrossRefGoogle Scholar
Marxen, O., Lang, M. & Rist, U. 2013 Vortex formation and vortex breakup in a laminar separation bubble. J. Fluid Mech. 728, 5890.CrossRefGoogle Scholar
Marxen, O., Lang, M., Rist, U., Levin, O. & Henningson, D. S. 2009 Mechanisms for spatial steady three-dimensional disturbance growth in a non-parallel and separating boundary layer. J. Fluid Mech. 634, 165189.Google Scholar
Marxen, O. & Rist, U. 2010 Mean flow deformation in a laminar separation bubble: separation and stability characteristics. J. Fluid Mech. 660, 3754.Google Scholar
Monkewitz, P. A. & Huerre, P. 1982 The influence of the velocity ratio on the spatial instability of mixing layers. Phys. Fluids 25, 11371143.Google Scholar
Niew, T. R.1993 The stability of the flow in a laminar separation bubble. PhD thesis, Cambridge University.Google Scholar
Owen, P. R. & Klanfer, L.1955 On the laminar boundary layer separation from the leading edge of a thin airfoil. Tech. Rep. C.P. 220. Aeronautical Reseach Council, UK.Google Scholar
Pauley, L. L., Moin, P. & Reynolds, W. C. 1990 The structure of two-dimensional separation. J. Fluid Mech. 220, 397411.Google Scholar
Pereira, R., Ragni, D. & Kotsonis, M. 2014 Effect of external flow velocity on momentum transfer of dielectric barrier discharge plasma actuators. J. Appl. Phys. 116 (10), 103301.Google Scholar
Pröbsting, S. & Yarusevych, S. 2015 Laminar separation bubble development on an airfoil emitting tonal noise. J. Fluid Mech. 780, 167191.Google Scholar
Reed, H. L., Saric, W. S. & Arnal, D. 1996 Linear stability theory applied to boundary layers. Annu. Rev. Fluid Mech. 28, 389428.Google Scholar
Reynolds, W. C. & Hussain, A. K. M. F. 1972 The mechanics of an organised wave in turbulent shear flow. Part 3. Theoretical models and comparisons with experiments. J. Fluid Mech. 54, 263288.Google Scholar
Rist, U. & Augustin, K. 2006 Control of laminar separation bubbles using instability waves. AIAA J. 44 (10), 22172223.Google Scholar
Rist, U. & Maucher, U. 2002 Investigations of time-growing instabilities in laminar separation bubbles. Eur. J. Mech. (B/Fluids) 21 (5), 495509.CrossRefGoogle Scholar
Sandham, N. D. 2008 Transitional separation bubbles and unsteady aspects of aerofoil stall. Aeronaut. J. 112, 395404.Google Scholar
Saric, W. S. & White, E.1998 Influence of high-amplitude noise on boundary-layer transition to turbulence. In 29th AIAA Fluid Dynamics Conference, AIAA Paper 98-2645.Google Scholar
Scarano, F. & Riethmuller, M. L. 2000 Advances in iterative multigrid PIV image processing. Exp. Fluids 29 (SUPPL. 1), S51S60.Google Scholar
Serna, J. & Lázaro, B. J. 2014 The final stages of transition and the reattachment region in transitional separation bubbles. Exp. Fluids 55 (4), 1695.Google Scholar
Serna, J. & Lázaro, B. J. 2015 On the bursting condition for transitional separation bubbles. Aerosp. Sci. Technol. 44, 4350.Google Scholar
Simoni, D., Ubaldi, M., Zunino, P. & Bertini, F. 2012a Transition mechanisms in laminar separation bubbles with and without incoming wakes and synthetic jets. Exp. Fluids 53, 173186.CrossRefGoogle Scholar
Simoni, D., Ubaldi, M., Zunino, P., Lengani, D. & Bertini, F. 2012b An experimental investigation of the separated-flow transition under high-lift turbine blade pressure gradients. Flow Turbul. Combust. 88, 4562.Google Scholar
Sirovich, L. 1987 Turbulence and the dynamics of coherent structures. I – Coherent structures. II – Symmetries and transformations. III – Dynamics and scaling. Q. Appl. Maths 45, 561571; 573–590.Google Scholar
Tani, I. 1964 Low-speed flows involving bubble separations. Prog. Aerosp. Sci. 5, 70103.Google Scholar
Theofilis, V. 2011 Global linear instability. Annu. Rev. Fluid Mech. 43, 319352.Google Scholar
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 (1777), 32293246.CrossRefGoogle Scholar
Watmuff, J. H. 1999 Evolution of a wave packet into vortex loops in a laminar separation bubble. J. Fluid Mech. 397, 119169.Google Scholar
Welch, P. 1967 The use of fast Fourier transform for the estimation of power spectra: a method based on time averaging over short, modified periodograms. IEEE Trans. Audio Electroacoust. 15, 7073.Google Scholar
Wieneke, B. 2015 PIV uncertainty quantification from correlation statistics. Meas. Sci. Technol. 26 (7), 074002.Google Scholar
Yang, Z. & Voke, P. R. 2001 Large-eddy simulation of boundary-layer separation and transition at a change of surface curvature. J. Fluid Mech. 439, 305333.Google Scholar
Yarusevych, S. & Kotsonis, M. 2017 Effect of local DBD plasma actuation on transition in a laminar separation bubble. Flow Turbul. Combust. 98, 195216.CrossRefGoogle Scholar
Yarusevych, S., Sullivan, P. E. & Kawall, J. G. 2007 Effect of acoustic excitation amplitude on airfoil boundary layer and wake development. AIAA J. 45 (4), 760771.Google Scholar
Yarusevych, S., Sullivan, P. E. & Kawall, J. G. 2009 On vortex shedding from and airfoil in low-Reynolds-number flows. J. Fluid Mech. 632, 245271.Google Scholar
Zaman, K. B. M. Q., McKinzie, D. J. & Rumsey, C. L. 1989 Natural low-frequency oscillation of the flow over an airfoil near stalling conditions. J. Fluid Mech. 202, 403442.Google Scholar

Michelis et al. supplementary movie

Phase-averaged vorticity within the forcing cycle

Download Michelis et al. supplementary movie(Video)
Video 18.4 MB