We investigate the effects of superhydrophobic surfaces (SHS) carrying streamwise grooves on the flow dynamics and the resultant drag reduction in a fully developed turbulent channel flow. The SHS is modelled as a flat boundary with alternating no-slip and free-slip conditions, and a series of direct numerical simulations is performed with systematically changing the spanwise periodicity of the streamwise grooves. In all computations, a constant pressure gradient condition is employed, so that the drag reduction effect is manifested by an increase of the bulk mean velocity. To capture the flow properties that are induced by the non-homogeneous boundary conditions the instantaneous turbulent flow is decomposed into the spatial-mean, coherent and random components. It is observed that the alternating no-slip and free-slip boundary conditions lead to the generation of Prandtl’s second kind of secondary flow characterized by coherent streamwise vortices. A mathematical relationship between the bulk mean velocity and different dynamical contributions, i.e. the effective slip length and additional turbulent losses over slip surfaces, reveals that the increase of the bulk mean velocity is mainly governed by the effective slip length. For a small spanwise periodicity of the streamwise grooves, the effective slip length in a turbulent flow agrees well with the analytical solution for laminar flows. Once the spanwise width of the free-slip area becomes larger than approximately 20 wall units, however, the effective slip length is significantly reduced from the laminar value due to the mixing caused by the underlying turbulence and secondary flow. Based on these results, we develop a simple model that allows estimating the gain due to a SHS in turbulent flows at practically high Reynolds numbers.

Secondary flows can develop in turbulent boundary layers that grow over surfaces with spanwise inhomogeneities. In this article, we demonstrate the formation of secondary flows in both experimental and numerical tests and dissect the instantaneous structure and topology of these secondary motions. We show that the formation of secondary flows is not very sensitive to the Reynolds number range investigated, and direct numerical simulations and experiments produce similar results in the mean flow as well as the dispersive and turbulent stress distributions. The numerical methods capture time-resolved features of the instantaneous flow and provide insight into the near-wall flow structures, that were previously obscured in the experimental measurements. Proper orthogonal decomposition was shown to capture the essence of the secondary flows in relatively few modes and to be useful as a filter to analyse the instantaneous flow patterns. The secondary flows are found to create extended regions of high Reynolds stress away from the wall that comprise predominantly sweeps similar to what one would expect to see near the wall and which are comparable in magnitude to the near-wall stress. Analysis of the instantaneous flow patterns reveals that the secondary flows are the result of a non-homogeneous distribution of mid-size vortices.

The effects of several surface parameters on equivalent sand roughness (ks) in fully rough regime are investigated by means of direct numerical simulation (DNS) of flow in channels with different wall geometries at Reτ≅500. The roughness geometry is generated by randomly distributing roughness elements of random size and prescribed shape on a flat surface. The roughness generation approach allows systematic variation of moments of surface height probability density function (PDF), size distribution of roughness peaks, and surface slope. A total number of 38 cases are solved. It is understood that a correlation based on surface height skewness and effective slope (ES) can satisfactorily predict ks normalized with maximum peak-to-valley roughness height within a major part of the studied parameter space. Such a correlation is developed based on the present data points and a number of complementary data points from the literature. It is also shown that the peak size distribution can independently influence the skin friction; at fixed values of rms surface height, skewness, kurtosis, and ES, a surface with uniform size peaks causes higher skin friction compared to one with nonuniform peak sizes. Additionally, it is understood that a roughness generated by regular arrangement of roughness elements may lead to a significantly different skin friction compared to a random arrangement. A staggered and an aligned regular arrangement are examined in this paper and it is observed that the former produces significantly closer results to the corresponding random arrangement.

Turbulent flow over a surface with streamwise-elongated rough and smooth stripes is studied by means of direct numerical simulation (DNS) in a periodic plane open channel with fully resolved roughness. The goal is to understand how the mean height of roughness affects the characteristics of the secondary flow formed above a spanwise-heterogeneous rough surface. To this end, while the statistical properties of roughness texture as well as the width and spacing of the rough stripes are kept constant, the elevation of the smooth stripes is systematically varied in different simulation cases. Utilizing this variation three configurations representing protruding, recessed and an intermediate type of roughness are analysed. In all cases secondary flows are present and the skin friction coefficients calculated for all the heterogeneous rough surfaces are meaningfully larger than what would result from the area-weighted average of those of homogeneous smooth and rough surfaces. This drag increase appears to be linked to the strength of the secondary flow. The rotational direction of the secondary motion is shown to depend on the relative surface elevation. The present results suggest that this rearrangement of the secondary flow is linked to the spatial distribution of the spanwise-wall-normal Reynolds stress component which carries opposing signs for protruding and recessed roughness.

We carried out high-fidelity large-eddy simulations to investigate the effects of uniform blowing and uniform suction on the aerodynamic efficiency of a NACA4412 airfoil at the moderate Reynolds number based on chord length and incoming velocity of Re c = 200,000 . We found that uniform blowing applied at the suction side reduces the aerodynamics efficiency, while uniform suction increases it. This result is due to the combined impact of blowing and suction on skin friction, pressure drag and lift. When applied to the pressure side, uniform blowing improves aerodynamic efficiency. The Reynoldsnumber dependence of the relative contributions of pressure and friction to the total drag for the reference case is analysed via Reynolds-averaged Navier-Stokes simulations up to Re c = 10,000,000 . The results suggest that our conclusions on the control effect can tentatively be extended to a broader range of Reynolds numbers.