Transition induced by free-stream turbulence

Abstract

Free-stream turbulence (FST) is perhaps the most important source inducing by-pass transition in boundary layer flows. The present study describes the initial energy growth of streamwise-oriented disturbances in the boundary layer originating from the presence of FST with intensities between 1.4% and 6.7%, but the study is mainly focused on the modelling of the transition zone. For this study three passive and one active turbulence-generating grids were used. The active grid was used in order to vary the turbulence intensity ($Tu$) without changing the setup in the test section. It is shown that the initial disturbance energy in the boundary layer is proportional to $Tu^2$. The experiments also show that the energy grows in linear proportion to the Reynolds number based on the downstream distance. Furthermore the transitional Reynolds number is shown to be inversely proportional to $Tu^2$ for the whole range of $Tu$ studied. The intermittency in the transitional zone was determined and it was shown that the intermittency function has a universal shape if the downstream distance is scaled with the length of the transition zone. The Reynolds number based on this transition zone length was found to increase linearly with the transition Reynolds number; however it was also noted that this non-dimensional length has a minimum value. With these results we were able to formulate an expression for the spot production rate which has a better physical base than previous models.

Transition of transient channel flow after a change in Reynolds number

“…It is clear that the growth rate increases with increase of Tu, which is consistent with the trend exhibited in the experiments by Fransson et al (2005). Inspired by figure 10(a), the energy growth in terms of E = max y {(u rms − u rms,0 ) 2 /(U b1 − U b0 ) 2 } is plotted against t +0 ( figure 11b).…”

“…Again, the data from the series S0X practically collapse on top of each other whereas the data from S1X have some deviations from the overall trend but still follow it rather closely. At the very early stage, there is a 'delay' in the increase of the energy, which was also noted by Fransson et al (2005), who attributed it to an early receptivity stage when the flow adjusts itself to the boundary layer. Following this stage, the energy growth is linear, which in many cases extends much beyond the point of the onset of transition.…”

“…The proportionality constants, however, vary from one experiment to another. Based on an extensive set of measurements of turbulence levels (Tu) ranging from 1.4 to 6.7 %, Fransson, Matsubara & Alfredsson (2005) attempted to establish semi-empirical correlations for modelling the transition zone. They have shown that the initial disturbance energy in the boundary layer is proportional to Tu 2 and that the transitional Reynolds number (Re x,cr ) is proportional to Tu −2 .…”

“…It has been well established through both theoretical and experimental investigations that Re cr ∼ Tu −2 0 for a spatially developing boundary layer (Andersson et al 1999;Brandt et al 2004;Fransson et al 2005;Ovchinnikov et al 2008). In particular, Andersson et al (1999) proposed…”

“…In addition, in contrast to the Re t,cr used herein, which is based on the onset of the transition, Re x,cr in the above equation is defined as the location at an intermittency level of 0.5, that is, halfway between the onset and the completion of the transition. More recently, Fransson et al (2005) proposed an alternative formulation based on a large number of experimental data:…”