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Nonlinear effects on the receptivity of cross-flow in the swept Hiemenz flow

Published online by Cambridge University Press:  18 December 2014

Christian Thomas ,
Philip Hall  and
Christopher Davies
Christian Thomas*
Affiliation:
Department of Mathematics, South Kensington Campus, Imperial College London, London SW7 2AZ, UK
Philip Hall
Affiliation:
Department of Mathematics, South Kensington Campus, Imperial College London, London SW7 2AZ, UK
Christopher Davies
Affiliation:
School of Mathematics, Cardiff University, Cardiff CF24 4AG, UK
*
†Email address for correspondence: c.thomas@imperial.ac.uk
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Abstract

Nonlinear effects on the receptivity of cross-flow in the swept Hiemenz boundary layer are investigated. Numerical simulations are generated using a vorticity form of the Navier–Stokes equations. Steady perturbations are established using surface suction and blowing distributed along the spanwise direction as either a periodic strip or a band of small holes. The method of excitation, the size and the location of the prescribed forcing are shown to have a significant influence on the receptivity of the boundary layer. Blowing holes are found to excite perturbations with considerably larger magnitudes than those generated using a periodic suction and blowing strip. A semi-logarithmic relationship is derived that relates the initial amplitude of the linear-only disturbances with the location at which the absolute magnitude of the chordwise primary Fourier harmonic attains a stationary point or a size of approximately one-tenth of the free-stream spanwise velocity. Furthermore, the size of the physical chordwise velocity perturbation about this position can be estimated directly from the linear-only solutions. This would suggest that, for sufficiently small initial amplitudes, the onset of some nonlinear flow development properties can be predicted directly from a linear receptivity analysis.

JFM classification

Boundary Layers: Boundary layer receptivity Boundary Layers: Boundary layer stability Instability: Nonlinear instability
Type
Papers
Information
Journal of Fluid Mechanics , Volume 763 , 25 January 2015 , pp. 433 - 459
Copyright
© 2014 Cambridge University Press 

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References

Balachandar, S., Streett, C. L. & Malik, M. R. 1992 Secondary instability in rotating-disk flow. J. Fluid Mech. 242, 323–347.Google Scholar
Bonfigli, G. & Kloker, M. J. 2007 Secondary instabilities of crossflow vortices: validation of the stability theory by direct numerical simulation. J. Fluid Mech. 583, 229–272.Google Scholar
Choudhari, M. 1993 Boundary-layer receptivity due to distributed surface imperfections of a deterministic or random nature. Theor. Comput. Fluid Dyn. 4, 101–117.CrossRefGoogle Scholar
Choudhari, M. 1994 Roughness-induced generation of cross-flow vortices in three-dimensional boundary layers. Theor. Comput. Fluid Dyn. 6, 1–30.Google Scholar
Choudhari, M. & Duck, P. W. 1996 Nonlinear excitation of inviscid stationary vortex instabilities in a boundary-layer flow. In Proceedings of the IUTAM Symposium on Nonlinear Instability and Transition in Three-Dimensional Boundary Layers, Manchester, UK (ed. Duck, P. W. & Hall, P.), pp. 409–422. Kluwer Academic.Google Scholar
Collis, S. S. & Lele, S. K. 1999 Receptivity to surface roughness near a swept leading edge. J. Fluid Mech. 380 (1), 141–168.Google Scholar
Crouch, J. D.1993 Receptivity of three-dimensional boundary layers. In 31st AIAA Aerospace Sciences Meeting and Exhibition, Reno, NV, p. 1993. AIAA.Google Scholar
Davies, C. & Carpenter, P. W. 2001 A novel velocity–vorticity formulation of the Navier–Stokes equations with applications to boundary layer disturbance evolution. J. Comput. Phys. 172, 119–165.Google Scholar
Federov, A. V. 1988 Excitation of waves of instability of the secondary flow in the boundary layer on a swept wing. J. Appl. Mech. Tech. Phys. 29, 643–648.Google Scholar
Fischer, T. M. & Dallmann, U. 1991 Primary and secondary stability analysis of a 3D boundary-layer flow. Phys. Fluids A 3, 2378–2391.Google Scholar
Friederich, T. & Kloker, M. J. 2012 Control of the secondary crossflow instability using localized suction. J. Fluid Mech. 706, 470–495.CrossRefGoogle Scholar
Gregory, N., Stuart, J. T. & Walker, W. S. 1955 On the stability of three-dimensional boundary layers with application to the flow due to a rotating disk. Phil. Trans. R. Soc. Lond. A 248, 155–199.Google Scholar
Hall, P., Malik, M. R. & Poll, D. I. A. 1984 On the stability of an infinite swept attachment line boundary layer. Proc. R. Soc. Lond. A 395, 229–245.Google Scholar
Herbert, T. 1988 Secondary instability of boundary layers. Annu. Rev. Fluid Mech. 20, 487–526.Google Scholar
Hosseini, S., Tempelmann, D., Hanifi, A. & Henningson, D. S. 2013 Stabilization of a swept-wing boundary layer by distributed roughness elements. J. Fluid Mech. 718, R1.Google Scholar
Hunt, L. & Saric, W. S.2011 Boundary-layer receptivity of three-dimensional roughness arrays on a swept-wing. In 41st AIAA Fluid Dynamics Conference and Exhibition, 27–30 June 2011, Honolulu, HI, AIAA 2011-3881.Google Scholar
Janke, E. & Balakumar, P. 2000 On the secondary instability of three-dimensional boundary layers. Theor. Comput. Fluid Dyn. 14, 167–194.Google Scholar
Koch, W. 2000 On the spatio-temporal stability of primary and secondary crossflow vortices in a three-dimensional boundary layer. J. Fluid Mech. 456, 85–111.Google Scholar
Kohama, Y. 1984 Study on boundary layer transition of a rotating disk. Acta Mech. 50, 193–199.Google Scholar
Kohama, Y., Onodera, T. & Egami, Y. 1996 Design and control of crossflow instability field. In Proceedings of the IUTAM Symposium on Nonlinear Instability and Transition in Three-Dimensional Boundary Layers, Manchester, UK (ed. Duck, P. W. & Hall, P.), pp. 147–156. Kluwer Academic.Google Scholar
Kohama, Y., Saric, W. S. & Hoos, J. A.1991 A high frequency instability of crossflow vortices that leads to transition. In Proceedings of the Royal Aeronautical Society Conference on Boundary-Layer Transition and Control, Cambridge.Google Scholar
Lovig, E., Downs, R. S. & White, E. B. 2014 Passive laminar flow control at low turbulence levels. AIAA J. 52, 1072–1075.CrossRefGoogle Scholar
Malik, M. R. 1986 The neutral curve for stationary disturbances in rotating-disk flow. J. Fluid Mech. 164, 275–287.Google Scholar
Malik, M. R., Li, F. & Chang, C. L. 1994 Crossflow disturbances in three-dimensional boundary layers: nonlinear development, wave interaction and secondary instability. J. Fluid Mech. 268, 1–36.Google Scholar
Malik, M. R., Li, F., Choudhari, M. M. & Chang, C. L. 1999 Secondary instability of crossflow vortices and swept-wing boundary-layer transition. J. Fluid Mech. 399, 85–115.Google Scholar
Meyer, F. & Kleiser, L.1988 Numerical investigation of transition in 3D boundary layers. In Fluid Dynamics of Three-Dimensional Turbulent Shear Flows and Transition. AGARD-CP-438, pp. 16.1–16.17.Google Scholar
Morkovin, M. V. 1969 On the many faces of transition. In Viscous Drag Reduction (ed. Wells, C. S.), pp. 1–31. Plenum.Google Scholar
Mughal, S. 2012 Advanced Transition Prediction and Development of Linearised Navier–Stokes Receptivity Methods, Validation and Application. Institute for Mathematical Sciences, Imperial College London.Google Scholar
Müller, B. & Bippes, H.1988 Experimental study of instability modes in a three dimensional boundary-layer. In Fluid Dynamics of Three-Dimensional Turbulent Shear Flows and Transition. AGARD-CP-438, pp. 13.1–13.15.Google Scholar
Ng, L. L. & Crouch, J. D. 1999 Roughness-induced receptivity to crossflow vortices on a swept wing. Phys. Fluids 11, 432–438.Google Scholar
Obrist, D., Henniger, R. & Kleiser, L. 2012 Subcritical spatial transition of swept Hiemenz flow. Intl J. Heat Fluid Flow 35, 61–67.Google Scholar
Poll, D. I. A. 1985 Some observations of the transition process on the windward of a long yawed cylinder. J. Fluid Mech. 150, 329–356.Google Scholar
Reibert, M. S., Saric, W. S., Carillo, R. B. & Chapman, K. L.1996 Experiments in nonlinear saturation of stationary crossflow vortices in a swept-wing boundary layer. AIAA Paper 96-0184.Google Scholar
Saric, W., Reed, H. & Kerschen, E. J. 2002 Boundary-layer receptivity to freestream disturbances. Annu. Rev. Fluid Mech. 34, 291–319.Google Scholar
Saric, W., Reed, H. & White, E. 2003 Stability and transition of three-dimensional boundary layers. Annu. Rev. Fluid Mech. 35, 413–440.Google Scholar
Schrader, L., Amin, S. & Brandt, L. 2010 Transition to turbulence in the boundary layer over a smooth and rough swept plate exposed to free-stream turbulence. J. Fluid Mech. 646 (1), 297–325.Google Scholar
Schrader, L. U., Brandt, L. & Henningson, D. S. 2009 Receptivity mechanisms in three-dimensional boundary layer flows. J. Fluid Mech. 618, 209–241.Google Scholar
Spalart, P. R.1988 Direct numerical study of leading edge contamination. In Fluid Dynamics of Three-Dimensional Turbulent Shear Flows and Transition. AGARD-CP-438, pp. 5.1–5.13.Google Scholar
Spalart, P. R. 1990 Direct numerical study of crossflow instability. In Laminar–Turbulent Transition, IUTAM (ed. Arnal, D. & Michel, R.), pp. 621–630. Springer.Google Scholar
Spalart, P. R. 1993 Numerical study of transition induced by suction devices. In Proceedings of Conference on Near-Wall Turbulent Flows, Tempe, AZ (ed. So, R. M. C., Speziale, C. G. & Launder, B. E.), Elsevier Science.Google Scholar
Streett, C.1998 Direct harmonic linear Navier–Stokes methods for efficient simulation of wave packets. AIAA Paper 1998-0784.Google Scholar
Tempelmann, D., Hanifi, A. & Henningson, D. 2012a Swept-wing boundary-layer receptivity. J. Fluid Mech. 700, 490–501.Google Scholar
Tempelmann, D., Schrader, L.-U., Hanifi, A., Brandt, L. & Henningson, D. 2012b Swept wing boundary-layer receptivity to localized surface roughness. J. Fluid Mech. 711, 516–544.Google Scholar
Wassermann, P. & Kloker, M. 2002 Mechanisms and passive control of crossflow-vortex-induced transition in a three-dimensional boundary layer. J. Fluid Mech. 456 (1), 49–84.Google Scholar
Wassermann, P. & Kloker, M. J. 2003 Transition mechanisms induced by travelling crossflow vortices in a three-dimensional boundary layer. J. Fluid Mech. 483, 467–489.Google Scholar