High-Reynolds-number turbulent boundary layers under adverse pressure gradients. Part 1. Decoupling local and upstream pressure gradient effects

Abstract

This study presents a controlled examination of the universality of the von Karman and additive coefficients in the logarithmic law of the mean streamwise velocity profile for high-Reynolds-number turbulent boundary layers under low-to-moderate adverse pressure gradients. The experiments use a method for prescribing pressure gradients along Melbourne's high-Reynolds-number boundary layer wind tunnel, combined with direct friction velocity measurements from oil-film interferometry. This allows systematic variation of upstream pressure-gradient history while maintaining locally matched Reynolds number and Clauser parameter at the measurement location. The configuration therefore separates the effects of Reynolds number, local adverse pressure gradient, and pressure-gradient history on turbulence statistics and energy spectra across the boundary layer. Owing to the high Reynolds number and moderate pressure-gradient conditions, the overlap region is sufficiently extended to assess the logarithmic law. The von Karman coefficient remains invariant within experimental uncertainty, whereas the additive coefficient varies systematically with both local pressure gradient and pressure-gradient history. Local adverse pressure gradients energize both large- and small-scale motions in the wake region around 0.4 delta, while pressure-gradient history also affects large-scale motions down to about 0.25 delta, just above the overlap region. In contrast to lower-Reynolds-number studies, neither effect extends into the inner region. These measurements provide a high-fidelity dataset for improving physical understanding and developing composite mean velocity profile formulations for adverse-pressure-gradient turbulent boundary layers.

Figures (14)

• Figure 1: (a) $\beta(Re_{\tau})$ map of APG TBLs datasets from the literature, including numerical and experimental studies. The yellow-shaded area represents the region of interest for the present study, i.e. high $Re_{\tau}$ and low-to-moderate $\beta$ where a well-defined overlap region is expected. (b) Schematic representation of the different regions of TBL development typically encountered in high-$Re_{\tau}$ APG experiments. (c) Comparison of experimental parameters between the present study and those reported by romero_properties_2022 and knopp2021experimental. $\delta_{\rm{ref}}=\delta(x=x_{\rm{ref}})$.
• Figure 2: (a) Schematic of the experimental setup established in deshpande, to generate high-$Re_{\tau}$ APG TBLs with controlled upstream pressure-gradient histories. Conceptual profile of $C_{P}(x)$ along the test section to investigate a ZPG and APG TBLs with (b) minimal PG history or (c) with a controlled upstream PG perturbation, following the framework of figure \ref{['fig1']}(b).
• Figure 3: $C_P(x)$ profiles measured for the (a) ZPG, Ref. APG3 and Perturbed cases, and the (b) ZPG, APG1 and APG3 cases (see table \ref{['tab:1']} for exact flow conditions). Vertical dashed lines indicate the locations of streamwise velocity and OFI measurements. $\delta_1$ denotes the value of $\delta$ at $x_1$. In the APG regions, $dC_P/dx$ is nominally 0.025 for the APG3 and Perturbed cases and 0.015 for the APG1 case.
• Figure 4: (a) Profiles of mean streamwise velocity, and (b) deviations from the classical log-law for the ZPG and Perturbed cases in the relaxation region. Both cases have locally matched flow conditions, but unique PG histories. Note that the profiles for $x_b$ and $x_c$ are vertically offset.
• Figure 5: (a,b) Profiles of mean streamwise velocity, (c,d) indicator function, and (e,f) deviations from the classical log-law for the ZPG, Ref. APG3 and Perturbed cases in the development region at (left) $x=x_1$ and (right) $x=x_2$. All APG cases have locally matched flow conditions, but unique PG histories. The ZPG cases have locally matched $Re_{\tau}$, for reference.