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FREE-STREAM TURBULENCE AND ITS INFLUENCE ON BOUNDARY-LAYER TRANSITION

Jens H. M. Fransson
Linne Flow Centre Department of Mechanics KTH–Royal Institute of Technology SE–100 44 Stockholm, Sweden

Résumé

Free-stream turbulence (FST) gives, undoubtedly, rise to the most complicated boundary-layer transition-toturbulence scenario. The reason for the complexity is that the boundary layer thickness grows with the downstream distance at the same time as the turbulence intensity (Tu) of the FST decays and the FST characteristic length scales grow. The FST is present everywhere in the free stream, but changes characteristics with the downstream distance. This implies that the actual forcing by the FST on the boundary layer changes gradually, which makes it an intricate receptivity problem. Today, we cannot honestly say that we are capable to accurately predict the transition location subject to FST in the simplest boundary layer flow, namely the one developing over a flat plat under zero-pressure gradient condition.
Based on a set of original experimental data, consisting of 42 unique FST conditions, we here report on a semiempirical transition prediction model, which takes into account both the integral length scale and the turbulence velocity fluctuation at the leading edge. We show that the Tu, used in all existing models, is not the leading variable. Instead, our data show that the necessary ingredients in a successful transition prediction model includes, firstly, a FST Reynolds number (Re) as leading variable, secondly, an FST parameter being the integral length scale Reynolds number (ReΛ) which further accounts for the effect of different length scales and, thirdly, a scale-matching model between the FST and the boundary layer. However, the importance of Tu can still be realized, since it constitutes the quotient of the two Reynolds numbers, namely Tu ≡ Refst / ReΛ, even though Tu does not explicitly appear in the model.