Nichtlineare Stadien der Transition in einer verzögerten Flügel-Grenzschichtströmung bei kontrolliertem, kontinuierlichen und bei natürlichen Störspektrum
Final Report Abstract
The main goal of the present project was the investigation of nonlinear stages of transition initiated by complex-spectrum TS-waves developing in 2D boundary layers, first of all on airfoil sections. When designing subsonic natural-laminar-flow airfoils the computer codes used for boundary-layer transition prediction are usually based on primary linear stability theory. The accuracy of such approaches gets worse when the role of nonlinear interactions increases. The lack of accuracy of transition predictions restricts the abilities of designing improved airfoils with long regions of laminar flow. It is known that resonant interactions between various TS-modes very often play a predominant role at initial nonlinear stages of transition. The present project concentrated on a detailed, systematic study of nonlinear TS-wave interactions occurring in a boundary layer on an airfoil at disturbance conditions, which correspond to the practically important case of so-called ”natural” transition. For deeper physical insight into the problem, a combined experimental, numerical, and theoretical investigation has been carried out. The project involved a cooperation between DFG (Germany) and RFBR (Russia). The experiments devoted to weakly-nonlinear TS-wave interactions have been conducted at the Institute for Aerodynamics und Gasdynamics (IAG), University of Stuttgart, with participation of collaborators from the Institute of Theoretical and Applied Mechanics (ITAM). The theoretical study has been carried out in Novosibirsk, the direct numerical simulations (DNS) have been performed at the IAG. Complementary experimental investigations of late stages of transition and post transitional turbulence have been conducted at the ITAM. The main investigations in Stuttgart were carried out on an airfoil section designed for a long laminar run. The wind-tunnel model was equipped with a newly designed, universal disturbance source that enables the introduction of controlled disturbances into the boundary-layer flow. Phaselocked data acquisition with hot-wires provide complete sets of stationary and fluctuation flow field data. Detailed investigations of transition phenomenon were performed with excitation of controlled TS-waves with various initial frequency-wavenumber spectra. The experimental, theoretical and numerical data are in agreement with each other and support the important conclusions of the present study: The modulation of TS-waves, present in ”natural” transition scenarios, is able to accelerate the boundary-layer transition through nonlinear interactions (non-resonant ones) by providing the flow with seeds of quasi-subharmonic modes, which can feed potentially either the linear-instability amplification of these modes or their amplification due to frequency-detuned subharmonic-type resonant interactions. The importance of such a mechanisms is proven for conditions that are very close to those typical for ”natural” boundarylayer transition. The possibility of excitation of wave bands with a strictly limited width in the spanwise-frequency wavenumber spectra provided a new route to the quantitative investigation of complex wave interactions occurring at continuous disturbance spectra. Together with the numerical capabilities of the DNS and the weakly nonlinear theory a deeper physical understanding of the transition process could be gained. This can be used as a solid basis for the development of improved en methods of transition prediction.
Publications
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Deterministic Turbulence and Its Application. Abstracts of the 7th EUROMECH Fluid Mechanics Conference, University of Manchester, 14-18 September 2008. - Manchester, UK: University of Manchester, 2008, p. 33
V.I. Borodulin, Y.S. Kachanov and A.P. Roschektayev
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Experimental study of multi-wave resonant interactions in a non-self-similar boundary layer on an airfoil. Proc. XIV International Conference on Methods of Aerophysical Research. Ed. V.M. Fomin - Novosibirsk: ITAM SB RAS 2008. - 8 pp.
I. B. de Paula, D. Sartorious, W. Würz, E. Krämer, Y.S. Kachanov
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Application of the deterministic turbulence method to study of LEBU-device mechanism. In: Advances in Turbulence XII. Springer Proceedings in Physics 132, Proceedings of the 12th EUROMECH European Turbulence Conference, September 7-10, 2009, Marburg, Germany / B. Eckhardt, ed. - Berlin, Heidelberg: Springer, 2009, pp. 313-316
V.I. Borodulin, Y.S. Kachanov, A.P. Roschektayev
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The deterministic turbulence (Invited Talk). Abstracts of the International Symposium on Turbulence, September 21-25, 2009, Beijing, China. - Beijing: Peking University, pp. 49-50
V.I. Borodulin, Y.S. Kachanov, A.P. Roschektayev
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Experimental study of resonant interactions of modulated waves in a non self-similar boundary layer. Proc. Seventh IUTAM Symposium on Laminar-Turbulent Transition, Stockholm, Sweden, 2009. Series: IUTAM Bookseries, Vol. 18 / P. Schlatter and D.S. Henningson (Eds.). - Berlin: Springer, 2010, pp. 274-279
I.B. de Paula, W. Würz, E. Krämer, V.I. Borodulin, Y.S. Kachanov
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Production of Seeds for Subharmonic Resonance in the Evolution of Modulated TS-waves on an Airfoil Boundary Layer. Abstracts of the 8th EUROMECH Fluid Mechanics Conference. September 13 - 16, 2010. Bad Reichenhall, Germany, p. S1-37
I.B. de Paula, W. Würz, E. Krämer, V.I. Borodulin, Y.S. Kachanov
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Experimental detection of deterministic turbulence. J. Turbulence Vol. 12, N23, 2011
V.I. Borodulin, Y.S. Kachanov and A.P. Roschektayev
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Nonlinear instabilities of a non-self-similar boundary layer on an airfoil: experiments, DNS, and theory. European Journal of Mechanics - B/Fluids Vol. 31, 102-108, 2012
W. Würz, D. Sartorius, M. Kloker, V.I. Borodulin, Y.S. Kachanov and B.V. Smorodsky
