Abstract
The work is devoted to the study of weakly non-linear interactions of Tollmien-Schlichting waves in an incompressible 2D airfoil boundary layer. Selected resonant regimes are investigated with emphasis to the regimes where more than one fundamental T-S wave is present in the flow. The results show that amplification rates of the effective sub-harmonic modes are not affected by modulations in time of the fundamental wave. In addition, modulations of the fundamental wave tend to generate additional modes at the modulation frequency via nonlinear wave interaction. These low frequency modes can act as self generated seeds for subharmonic resonance. The nature of these modes and their downstream evolution is investigated in detail. The observations are in agreement with results obtained for much more complicated case of wave bands. The observed mechanism seems to be a possible route for transition in the case of Natural Laminar Flow airfoils under ‘natural’ environment disturbance conditions.
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References
Crouch, J.D.: Modeling transition physics for laminar flow control. In: 38th AIAA Fluid Dynamics Conference and Exhibit, 2008–3832, Seattle, USA, pp. (2008)
Gaster, M., Grant, I.: An experimental investigation of the formation and development of a wave packet in a laminar boundary layer. Proc. of Royal Society of London-A 347, 253–269 (1975)
Cohen, J., Breuer, M.: On the evolution of a wave packet in a laminar boundary layer. J. Fluid Mech. 225, 575–606 (1991)
Medeiros, M.A.F., Gaster, M.: The production of subharmonic waves in nonlinear evolution of wavepackets in boundary layers. J. Fluid Mech. 399, 301–318 (1999)
Healey, J.J.: Wave envelope steepening in Blasius boundary layer. Eur. J. Mech. B-Fluids 19, 871–888 (2000)
Craik, A.A.D.: A model for subharmonic resonance within wavepackets in unstable boundary layers. J. Fluid Mech. 432, 409–418 (2001)
Medeiros, M.A.F.: The nonlinear evolution of a wavetrain emanating from a point source in a boundary layer. J. Fluid Mech. 508, 287–317 (2004)
Sartorius, D.: Experimental investigation of weakly nonlinear interactions of instability waves in a non self-similar boundary layer on an airfoil. Dissertation, IAG, Universität Stuttgart, Deutschland (2007)
De Paula, I.B., Würz, W., Krämer, E., Borodulin, V.I., Kachanov, Y.S.: Experimental study of multi-wave resonant interactions of modulated waves in a non-self-similar boundary layer. In: Schlatter, P., Henningson, D.S. (eds.) Proc. 7th IUTAM symposium on Laminar-Turbulent Transition, Stockholm, Springer (2010)
Kachanov, Y.S., Levchenko, V.Y.: Resonant interaction of disturbances at laminar-turbulent transition in a boundary layer. J. Fluid Mech. 138, 209–247 (1984)
Borodulin, V.I., Kachanov, Y.S., Koptsev, D.B., Roschektayev, A.P.: Experimental study of resonant interactions of instability waves in a self-similar boundary layer with an adverse pressure gradient: II. Detuned resonances. Journal of Turbulence v3 63, 1–22 (2002)
Medeiros, M.A.F., Gaster, M.: The influence of phase on the nonlinear evolution of wavepackets in boundary layers. J. Fluid Mech. 397, 259–283 (1999)
Cherubini, S., Robinet, C., Bottaro, A., De Palma, P.: Optimal wave packets in a boundary layer and initial phases of a turbulent spot. J. Fluid Mech. 656, 231–259 (2010)
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De Paula, I.B., Würz, W., Krämer, E., Borodulin, V.I., Kachanov, Y.S. (2013). Introduction of Initial Seeds for Subharmonic Resonance by Modulation of T-S Waves in an Airfoil Boundary Layer. In: Dillmann, A., Heller, G., Kreplin, HP., Nitsche, W., Peltzer, I. (eds) New Results in Numerical and Experimental Fluid Mechanics VIII. Notes on Numerical Fluid Mechanics and Multidisciplinary Design, vol 121. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35680-3_30
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DOI: https://doi.org/10.1007/978-3-642-35680-3_30
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