History effects and near-equilibrium in adverse-pressure-gradient 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   667-692
Year: 2017


Turbulent boundary layers under adverse pressure gradients are studied using wel-lresolved large-eddy simulations (LESs) with the goal of assessing the influence of the streamwise pressure-gradient development. Near-equilibrium boundary layers were characterized through the Clauser pressure-gradient parameter. In order to fulfil the near-equilibrium conditions, the freestream velocity was prescribed such that it followed a power-law distribution. The turbulence statistics pertaining to cases with a constant value of $\bet$a (extending up to approximately 40 boundary-layer thicknesses) were compared with cases with non-constant $\beta$ 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 non-constant $\beta$ cases appear to approach the conditions of equivalent constant cases after long streamwise distances (around 7 boundary-layer 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 flat-plate 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 constant-pressure-gradient parameter cases. The mean velocity and Reynolds-stress profiles were found to be dependent on the downstream development. The present work is the first step towards assessing history effects in adverse-pressure-gradient turbulent boundary layers and highlights the fact that the values of the Clauser pressure-gradient parameter and the Reynolds number are not sufficient to characterise the state of the boundary layer.