Abstract
The goal of this study is to present a first step towards establishing criteria aimed at assessing whether a particular adverse-pressure-gradient (APG) turbulent boundary layer (TBL) can be considered well-behaved, i.e., whether it is independent of the inflow conditions and is exempt of numerical or experimental artifacts. To this end, we analyzed several high-quality datasets, including in-house numerical databases of APG TBLs developing over flat-plates and the suction side of a wing section, and five studies available in the literature. Due to the impact of the flow history on the particular state of the boundary layer, we developed three criteria of convergence to well-behaved conditions, to be used depending on the particular case under study. (i) In the first criterion, we develop empirical correlations defining the Re\U0001d703-evolution of the skin-friction coefficient and the shape factor in APG TBLs with constant values of the Clauser pressure-gradient parameter β = 1 and 2 (note that β = δ∗/τwdPe/dx, where δ∗ is the displacement thickness, τw the wall-shear stress and dPe/dx the streamwise pressure gradient). (ii) In the second one, we propose a predictive method to obtain the skin-friction curve corresponding to an APG TBL subjected to any streamwise evolution of β, based only on data from zero-pressure-gradient TBLs. (iii) The third method relies on the diagnostic-plot concept modified with the shape factor, which scales APG TBLs subjected to a wide range of pressure-gradient conditions. These three criteria allow to ensure the correct flow development of a particular TBL, and thus to separate history and pressure-gradient effects in the analysis.
Highlights
Fundamental studies of wall-bounded turbulence require accurate representations of the flow case under consideration
In the present work we analyze a total of six in-house APG turbulent boundary layer (TBL) and five additional highquality databases of PG TBLs available in the literature [16, 25,26,27,28]
These TBLs, which exhibit very different albeit relatively simple flow histories, are used to define several criteria to assess the convergence of APG TBLs to well-behaved conditions
Summary
Fundamental studies of wall-bounded turbulence require accurate representations of the flow case under consideration. Sanmiguel Vila et al [22] evaluated their method with various tripping configurations, and characterized the development length under such different inflow conditions in wind-tunnel experiments of ZPG TBLs. In the present article, we extend their work to adverse-pressure-gradient (APG) TBLs where, as discussed by Bobke et al [24], the effect of the flow history is crucial, and develop the corresponding criteria to assess whether a particular TBL can be considered well-behaved or not. We extend their work to adverse-pressure-gradient (APG) TBLs where, as discussed by Bobke et al [24], the effect of the flow history is crucial, and develop the corresponding criteria to assess whether a particular TBL can be considered well-behaved or not These criteria are, in particular, important in the case of wind-tunnel experiments, where the lack of accurate measurements everywhere in the domain of interest requires the use of such methods in order to ensure an adequate boundary-layer development.
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