Abstract
The paper reports results of experimental investigations of the wake — boundary layer interaction in the region of transition on a flat plate in a wind tunnel of low level of turbulence, Tu≤0.0008. Correlation analysis of velocity fluctuations across the induced boundary layer has revealed a region where a phase shift of external disturbances takes place. Spectral analysis of velocity fluctuations showed also strong attenuation of wakes harmonics in this region. The region exists for values of the Reynolds number Rex from 8.104to 2.105, is located at yc = 0.32 and has thickness dc = 0.22, which corresponds to the mean velocity (U/Uc)c equal to 0.74 in the boundary layer. The location of this region (higher than the highest possible critical layer location for the Tollmien-Schlichting waves) and the level of external disturbances e which is equal to 0.03 suggest that could be the nonlinear critical layer which has been analysed in the solution of the nonlinear Orr-Sommerfeld equation for the parameter λ=1/(Re* ε3/2) = O(1) (Benney&Bergeron, 1969, and Haberman, 1972).
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References
Benney, D.J., Bergeron, R.F., 1969, A New Class of Nonlinear Waves in Parallel Flows. Studies Appl. Math, 48, 181–204.
Boiko, A.V., Westin, K.J.A., Klingman, B.G.B., Kozlov, V.V., Alfredson, P.H., 1994, Experiments in a boundary layer subjected to free stream turbulence, Part 2. The role of TS waves in the transition process, J. Fluid Mech., 281, 219–245.
Drazin, P.G., Reid, W.H., 1981, Hydrodynamic Stability, Cambridge, University Press.
Haberman, R., 1972, Critical Layers in Parallel Flows. Studies in Appl. Math., LI. No.2, 139–161.
Hammerton, P.W., Kerschen, E.J., 1996. Boundary — layer receptivity for a parabolic leading edge. J. Fluid Mech., 310, 243–267.
Hcaley, J.J., 1995, On the natural curve of the flat-plate boundary layer: comparison between experiment, Orr-Sommerfeld theory and asymtotic theory, J. Fluid Mech., 288, 59-73.
Jordinson, R., 1970, The flat plate boundary layer. Part 1. Numerical integration of the Orr-Sommerfeld equation, J. Fluid Mechanics. 43, 801–811.
Juszyna, L., Wierciński. Z., 1995b, Measurements of the mean velocity and velocity fluctuation profiles in a region of natural transition in a boundary layer of a flat plate. IMP PAN, Rep. Nr 246/95. IMP PAN, Gdańsk (in Polish).
Landau, L.D., 1944, On turbulence problem, C.R. Acad. Sci. URSS. Vol. 44. pp. 311 (in Rushian).
Lewczenko, W. Ja., Wolodin, A.G., Gaponow, S.A., 1975. Stability charakteristics of boundary layers. Nauka, Nowosibirsk, (in Russian).
Maslowe, S.A., 1986, Critical layers in shear flows. Ann. Rev. Fluid Mech., 18, 405–432.
Nishioka, M., Morkovin, M.V., 1986, Boundary layer receptivity to unsteady pressure gradients: experiments and overview, J. Fluid Mech., 171, 219–261.
Reshotko, E., 1976, Boundary Layer Stability and Transition, Ann. Rev. Fluid Mechanics, 311-349.
Schlichting, H., 1965, Grenzschicht-Theorie, Verlag G. Braun, Karlsruhe,.
Suprun, T., Wierciński, Z., 1995, Investigation of the unsteady boundary layer on the flat plate, Part I: Boundary induced by the wake of the moving cylinder, IMP PAN, Rep. Nr 93/95, Gdansk, (in Polish).
Suprun, T., Wierciński, Z., 1996, Measurements of the velocity profiles in the Pohlhausen boundary layer on the flat plate, MP PAN, Rep. Nr 273/96, Gdansk, (in Polish).
Wierciński, Z., 1994a, Auswirkungen der Nachlaufdellen hinter einem quer zur Strömung pendelnden Zylinder auf den laminar-turbulenten Umschlag der Grenzschicht auf der flachen Platte, VDI Berichte, Nr. 1109, 1994.
Wierciński. Z., 1995a, Measurement of the coefficient C, in the turbulent boundary layer on a flat plate by means of the Preston tube, IMP PAN. Rep. Nr 310/95, Gdańsk,(in Polish).
Wierciński, Z. 1995b, The Influence of the Periodic Wake Behind a Cylinder Pendulating in the Cross-Stream Direction on the Laminar-Turbulent Transition in the Boundary Layer of a Flat Plate, in Unsteady Aerodynamics and Aeroelasticity of Turbomachines, Elsevier, Amsterdam, Eds. Y. Tanida, M. Namba, pp. 461–479.
Wierciński, Z., 1996, Measurements of the spectra of velocity fluctuations in the boundary layer induced by the wakes, IMP PAN, Rep. Nr 517/96, Gdansk, (in Polish).
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Wierciński, Z. (1998). Nonlinear Critical Layer in the Unsteady Boundary Layer Induced on a Flat Plate by Wakes. In: Fransson, T.H. (eds) Unsteady Aerodynamics and Aeroelasticity of Turbomachines. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-5040-8_2
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DOI: https://doi.org/10.1007/978-94-011-5040-8_2
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