Upstream history quantification and scale-decomposed energy analysis for weak-to-strong adverse-pressure-gradient turbulent boundary layers

Abstract

The present study delineates the effects of pressure gradient history and local disequilibration on the small and large-scale energy in turbulent boundary layers (TBLs) imposed with a broad range of adverse-pressure-gradients (APG). This is made possible by analyzing four published high-fidelity APG TBL databases, which span weak to strong APGs and cover dynamic conditions ranging from near-equilibrium to strong disequilibrium. The influence of PG history on TBL statistics is quantified by the accumulated PG parameter ($\overline{\beta }$), proposed previously by Vinuesa et al. (2017) to study integral quanitites, which is compared here between cases at matched local PG strength ($\beta$), Reynolds number ($Re$) and $\mathrm{d}\beta /\mathrm{d}Re$ at nominally similar orders of magnitude. While the effects of local disequilibration ($\mathrm{d}\beta /\mathrm{d}Re$) are investigated by considering TBL cases at matched $\beta$, $Re$, and fairly matched $\overline{\beta }$. It is found that $\overline{\beta }$ cannot unambiguously capture history effects when $\mathrm{d}\beta /\mathrm{d}Re$ levels are significantly high, as it does not account for the delayed response of the mean flow and turbulence, nor the attenuation of the pressure gradient effect with distance. In two comparisons of APG TBLs under strong non-equilibrium, the values of $\overline{\beta }$ and $\mathrm{d}\beta /\mathrm{d}Re$ expressed using Zagarola-Smits scaling were found to be consistent with the trends in mean velocity defect and Reynolds stresses noted previously for weak APG TBLs. While an increase in $\overline{\beta }$ is associated with energisation of both the small and large scales in the outer regions of APG TBLs, it affects only the large scales in the near-wall region. This confirms the ability of near-wall small scales to rapidly adjust to changes in PG strength.

15 pages, 9 figures, accepted for publication in the International Journal of Heat and Fluid Flow

References in corpus (6)

• Direct numerical simulation of a self-similar adverse pressure gradient turbulent boundary layer at the verge of separation
• Energy transfer mechanisms in adverse pressure gradient turbulent boundary layers
• Reynolds-number effects on the outer region of adverse-pressure-gradient turbulent boundary layers
• Turbulent boundary layer response to uniform changes of the pressure force contribution
• Streamwise energy-transfer mechanisms in zero- and adverse-pressure-gradient turbulent boundary layers
• Effects of pressure gradient histories on skin friction and mean flow of high Reynolds number turbulent boundary layers over smooth and rough walls