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# Article

## Free-stream turbulence boundary layer transition

Authors: Shahinfar, S., Fransson, J. H. M. Conference Published Svenska mekanikdagarna, Göteborg, June 13-15 2011 1   38 2011

### Abstract

In the present work we study the free-stream turbulence (FST) boundary layer transition scenario on the simplest conceivable geometry, namely a flat plate with zero pressure gradient, in order to enhance the fundamental understanding of the influence of the FST characteristics, such as the turbulence intensity (Tu) and the integral length scal($\Lambda _{x}$), on the transitional Reynolds number. The experiments have been performed in the Minimum-Turbulence-Level wind tunnel at KTH and the FST characteristics were varied by means of totally eight turbulence generating grids, six of which were active. So, by varying the counter-flow injection rate in the active grids and the relative position of the grid to the leading edge the FST characteristics were changed. In this investigation over 40 different conditions at the leading edge have been generated, which are quantified in terms of FST characteristics. The range of leading edge Tu and $\Lambda _{x}$ are 2--6 % of the free-stream velocity $U_\infty$ , which has been kept constant at 6 m~s$^{-1}$, and 16--33 mm, respectively. In this study two hot-wire probes, separated in the spanwise direction, are traversed inside the boundary layer and the hot-wire traces are used to calculate the intermittency factor ($\gamma$) distribution in the streamwise direction (same procedure as outlined in \cite{Ref1}). Here we define the onset of transition, the transition location and the end of the transition region as the streamwise location where $\gamma$ is equal to 0.1, 0.5 (or tr) and 0.9, respectively. By introducing the non-dimensional coordinate $\xi = (Re_{x}-Re_{tr}) /\Delta Re_{tr}$ one may show the universality of the intermittency distribution as done in figure~\ref{Figure1}(a), where data from all the grids have been plotted with different symbols. The solid line is a curve fit to the data. The gray region in figure~\ref{Figure1}(b) shows the transition zone $\Delta Re_{tr}$ as a function of $Tu$. The symbols represent the $Re_{tr}$ and the correlation to the Tu-level may be described by the relation $$\label{eq1} Re_{tr} =C\cdot Tu^{-2}+D ,$$ where the first term on the RHS is derived from physical arguments \cite{Ref2} and the second term is given by a minimum $\Delta Re_{tr}$ argumentation.