Near-wall turbulence and its modulation to the outer flow: From canonical ZPG to wind turbine airfoils

Near-wall turbulence is relevant in a broad range of applications such as turbulence modeling, heat transfer from the surface to the flow and drag considerations among others. In this study near-wall turbulence is studied using numerical and experimental methods for different types of surface modification such as, sand grain surface roughness and a bio-inspired surface coating that shows drag reduction properties. At the beginning, a zero-pressure-gradient turbulent boundary layer flowing over a transitionally rough surface (24-grit sandpaper) with $k+\approx 11$ and Reynolds numbers based on momentum thickness of around 2400 is studied using direct numerical simulation (DNS). Heat transfer between the isothermal rough surface and the turbulent flow with molecular Prandtl number $Pr$=0.71 is simulated. The dynamic multi-scale approach developed by Araya et al. is employed to prescribe realistic time-dependent thermal inflow boundary conditions. In general, the rough surface reduces mean and fluctuating temperature profiles with respect to the smooth surface flow when normalized by Wang et a. inner/outer scaling. It is shown that the Reynolds analogy does not hold for . In this region the value of the turbulent Prandtl number departs substantially from unity. Above this region Reynolds analogy is only approximately valid with the turbulent Prandtl number decreasing from 1 to 0.7 across the boundary layer for rough and smooth walls. In comparison with the smooth wall case, the turbulent transport of heat per unit mass, $v\prime v\prime \theta \prime ―$, toward the wall is enhanced in the buffer layer, but the transport of $v\prime v\prime \theta \prime ―$ away from the wall is reduced in the outer layer for the rough case; similar behaviour is found for the vertical transport of turbulent momentum per unit mass, $v\prime u\prime v\prime ―$. Above the roughness sub-layer ($3-5k$) it is found that most of the temperature field statistics, including higher order moments and conditional averages, are highly similar for the smooth and rough surface flow, showing that the Townsend's Reynolds number similarity hypothesis applies for the thermal field as well as the velocity field for the Reynolds number and $k+$ considered in this study. It is also demonstrated that surface roughness reduces the logarithmic-law (log-law) length of the mean streamwise velocity and temperature profiles; however, it increases the power-law length. This increase in power-law length is a direct result of the increased streamwise inhomogeneity.

Further, two-point cross-correlations at different wall-normal positions are computed to investigate the footprints of structural components of the developing velocity field in the inner and outer layers. Observed features and correlations are compared for the rough and smooth cases for the single point statistics and two-point correlations. The two-point statistics reveal that the Townsend's hypothesis does not hold in the terms of turbulent velocity field structures, specifically for vertical velocity fluctuations in the log-layer and streamwise velocity fluctuations in the outer layer. Even though the single point statistics satisfy the Townsend's hypothesis in the roughness sub-layer ($3k-5k$ away from the wall). The structures of velocity field are slightly affected in the outer layer due to surface roughness mainly for the streamwise velocity fluctuations.

We continue our study by experimentally inspecting the flow over a mushroom-shaped micro-scale coating over a diverging channel that followed the pressure side of a wind turbine blade (S835). High-resolution particle image velocimetry was used to obtain in-plane velocity measurements in a refractive-index-matching flume at Reynolds number $Re\theta \approx 1200$ based on the momentum thickness. Results show that the evolution of the boundary layer thickness, displacement thickness, and shape factor change with the coating, contrary to the expected behavior of an adverse pressure gradient boundary layer over a canonical rough surface. Comparison of the flow with that over a smooth wall revealed that the turbulence production exhibited similar levels in both cases suggesting that the coating does not behave like a typical rough wall, which increases the Reynolds stresses. Proper orthogonal decomposition (POD) was used to decompose the velocity field to investigate the possible structural changes introduced by the wall region. It suggests that large-scale motions in the wall region lead to high-momentum flow over the coated case compared to the smooth counterpart.

Finally, the experimental results of larger structures as the surface coating are discussed. Surfaces coated with the enlarged bio-inspired mushroom-shaped and also cylindrical pillars were tested and higher resolution was achieved near the wall to study the flow interactions with the coated surfaces and compared with the smooth surface. Particle image velocimetry experiments were carried out in a zero-pressure-gradient turbulent boundary layer at Reynolds number $Re\theta \approx 1050$ based on the momentum thickness. The results suggests that the surface coatings has minimal effect on the single-point statistics of the flow, reduces the wall-normal turbulent transports close to the surface and promotes the sweep and ejection events close to the surface. The unique characteristic of the surface coating in modifying the vertical velocity at the surface in an organized way is also shown.