Revisiting History Effects in Adverse-Pressure-Gradient Turbulent Boundary Layers Articles uri icon

publication date

  • December 2017

start page

  • 565

end page

  • 587


  • 3-4


  • 99

International Standard Serial Number (ISSN)

  • 1386-6184

Electronic International Standard Serial Number (EISSN)

  • 1573-1987


  • 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 R e (oee integral) -evolution of the skin-friction coefficient and the shape factor in APG TBLs with constant values of the Clauser pressure-gradient parameter beta = 1 and 2 (note that beta = delta (au)/tau (w) dP (e) /dx, where delta (au) is the displacement thickness, tau (w) the wall-shear stress and dP (e) /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 beta, 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.


  • Aeronautics


  • turbulent boundary layer; pressure gradient; flow history; numerical simulation