

Article
History effects and nearequilibrium in adversepressuregradient turbulent boundary layers
Authors: 
Bobke, A.B., Vinuesa, R., Örlü, R., Schlatter, P. 
Document Type: 
Article 
Pubstate: 
Published 
Journal: 
Journal of Fluid Mechanics 
Volume: 
820
667692 
Year: 
2017 
AbstractTurbulent boundary layers under adverse pressure gradients are studied using wellresolved largeeddy simulations (LESs) with the goal of assessing the influence of the streamwise pressuregradient development. Nearequilibrium boundary layers were characterized through the Clauser pressuregradient parameter. In order to fulfil the nearequilibrium conditions, the freestream velocity was prescribed such that it followed a powerlaw distribution. The turbulence statistics pertaining to cases with a constant value of $\bet$a (extending up to approximately 40 boundarylayer thicknesses) were compared with cases with nonconstant $\beta$ distributions at matched values of $\beta$ and friction Reynolds number $Re_{\tau}$ . An additional case at matched Reynolds number based on displacement thickness $Re_{\delta^{*}}$ was also considered. It was noticed that nonconstant $\beta$ cases appear to approach the conditions of equivalent constant cases after long streamwise distances (around 7 boundarylayer thicknesses). The relevance of the constant cases lies in the fact that they define a “canonical” state of the boundary layer, uniquely characterised by $\beta$ and $Re$. The investigations on the flat plate were extended to the flow around a wing section overlapping in terms of $\beta$ and $Re$. Comparisons with the flatplate cases at matched values of $\beta$ and $Re$ revealed that the different development history of the turbulent boundary layer on the wing section leads to a less pronounced wake in the mean velocity as well as a weaker second peak in the Reynolds stresses. This is due to the weaker accumulated effect of the history. Furthermore, a scaling law suggested by Kitsios et al. (Int. J. Heat Fluid Flow, 2016), proposing the edge velocity and the displacement thickness as scaling parameters, was tested on two constantpressuregradient parameter cases. The mean velocity and Reynoldsstress profiles were found to be dependent on the downstream development. The present work is the first step towards assessing history effects in adversepressuregradient turbulent boundary layers and highlights the fact that the values of the Clauser pressuregradient parameter and the Reynolds number are not sufficient to characterise the state of the boundary layer.

