Abstract
The characteristics of turbulent boundary layers (TBLs) subjected to adverse pressure gradients are analysed through well-resolved large-eddy simulations. The geometries under study are the NACA0012 and NACA4412 wing sections, at and angle of attack, respectively, both of them at a Reynolds number based on inflow velocity and chord length of . The turbulence statistics show that adverse pressure gradients (APGs) have a significant effect on the mean velocity, velocity fluctuations and turbulent kinetic energy budget, and this effect is more prominent on the outer region of the boundary layer. Furthermore, the effect of flow history is assessed by means of an integrated Clauser pressure-gradient parameter (Vinuesa et al., Flow Turbul. Combust., vol. 99, 2017, pp. 565–587), through the study of cases with matching local values of and the friction Reynolds number to isolate this effect. Our results show a noticeable effect of the flow history on the outer region, however the differences in the near-wall peak of the tangential velocity fluctuations appear to be mostly produced by the local APG magnitude. The one-dimensional power-spectral density shows energetic small scales in the outer region of APG TBLs, whereas these energetic scales do not appear in zero-pressure-gradient (ZPG) TBLs, suggesting that small scales near the wall are advected towards the outer layer by the APG. Moreover, the linear coherence spectra show that the spectral outer peak of high-Reynolds-number ZPG TBLs is highly correlated with the near-wall region (Baars et al., J. Fluid Mech., vol. 823, 2017, R2), unlike APG TBLs which do not show such a correlation. This result, together with the different two-dimensional spectra of APG and high-Reynolds-number ZPG TBLs, suggests different energisation mechanisms due to APG and increase in Reynolds number. To the authors’ knowledge, this is the first in-depth analysis of the TBL characteristics over wings, including detailed single-point statistics, spectra and coherence.
Highlights
Turbulent boundary layers (TBLs) under the influence of adverse pressure gradients (APGs) are present in many wall-bounded flows of industrial applications such as A8-2Á
In the experiments of Skåre & Krogstad (1994) it was found that the production of turbulent kinetic energy in TBLs exposed to a strong APG shows a second peak located in the outer region
With respect to the results shown in figure 2(a), it can be observed that the pressure side of the NACA4412 shows, for most of the surface, a negative value of β which corresponds to a favourable pressure gradient (FPG)
Summary
Turbulent boundary layers (TBLs) under the influence of adverse pressure gradients (APGs) are present in many wall-bounded flows of industrial applications such as. The main goal of the present study is to analyse the effect of the adverse pressure gradient and the flow history on the turbulent boundary layers developing on the suction side of two airfoils: the cambered NACA4412 and the symmetric NACA0012 both at Rec = 400 000, with 5◦ and 0◦ angle of attack, respectively This can be considered as the continuation of the work by Vinuesa et al (2017a) but comparing two cases with different pressure distributions over the surface of the wing.
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