Analysis of anisotropically permeable surfaces for turbulent drag reduction

The present work proposes the use of anisotropically permeable substrates as a means to reduce turbulent skin friction. We conduct an a priori analysis to assess the potential of these surfaces, based on the effect of small-scale surface manipulations on near-wall turbulence. The analysis, valid for small permeability, predicts a monotonic decrease in friction as the streamwise permeability increases. Empirical results suggest that the drag-reducing mechanism is however bound to fail beyond a certain permeability. We investigate the development of Kelvin-Helmholtz-like rollers at the surface as a potential mechanism for this failure. These rollers, which are a typical feature of turbulent flows over permeable walls, are known to increase drag, and their appearance to limit the drag-reducing effect. We propose a model, based on linear stability analysis, which predicts the onset of these rollers for sufficiently large permeability, and allows us to bound the maximum drag reduction that these surfaces can achieve

Modulation of near-wall turbulence in the transitionally rough regime

Direct numerical simulations of turbulent channels with rough walls are conducted in the transitionally rough regime. The effect that roughness produces on the overlying turbulence is studied using a modified triple decomposition of the flow. This decomposition separates the roughness-induced contribution from the background turbulence, with the latter essentially free of any texture footprint. For small roughness, the background turbulence is not significantly altered, but merely displaced closer to the roughness crests, with the change in drag being proportional to this displacement. As the roughness size increases, the background turbulence begins to be modified, notably by the increase of energy for short, wide wavelengths, which is consistent with the appearance of a shear-flow instability of the mean flow. A laminar model is presented to estimate the roughness-coherent contribution, as well as the displacement height and the velocity at the roughness crests. Based on the effects observed in the background turbulence, the roughness function is decomposed into different terms to analyse different contributions to the change in drag, laying the foundations for a predictive model

Geometry-induced fluctuations in the transitionally rough regime

Direct numerical simulations of turbulent flows over rough surfaces are conducted to investigate the physics of the transitionally rough regime. Different roughness sizes are analysed within the transitional regime, while keeping the shape of the surface geometry constant. To study the effect of roughness on the flow field, a novel decomposition is used to divide the velocity into two components: a turbulent, geometry-independent contribution, and a geometry-induced contribution, whose intensity is modulated by the overlying turbulence. In the onset of the transitionally rough regime, the turbulent component remains essentially unmodified, and it is anticipated that all the roughness effects can be attributed entirely to the geometry-induced fluctuations. As the roughness size increases further, the turbulent component is also modified, and the fluid-surface interaction becomes more complex.This work was supported by the European Research Council through the II Multiflow Summer Workshop, and by the British Engineering and Physical Sciences Research Council through grant number EP/M506485/1

The effect of slip and surface texture on turbulence over superhydrophobic surfaces

Superhydrophobic surfaces are able to entrap gas pockets in between surface roughness elements when submerged in water. These entrapped gas pockets give these surfaces the potential to reduce drag due to the overlying flow being able to locally slip over the gas pockets, resulting in a mean slip at the surface. In this work we assess the separate effects that surface slip and surface texture have on turbulence over superhydrophobic surfaces. We show that the direct effect of surface slip does not modify the dynamics of the overlying turbulence, which remains canonical or smooth-wall like. The surface drag is governed by the difference between two virtual origins, the virtual origin of the mean flow and the virtual origin experienced by the overlying turbulence, in an extension of the theory from Luchini, Manzo &amp; Pozzi (J. Fluid Mech., vol. 228, 1991, pp. 87–109) for riblets. Streamwise slip deepens the virtual origin of the mean flow, while spanwise slip deepens the virtual origin perceived by the overlying turbulence. Drag reduction is then proportional to the difference between the two virtual origins. We decompose the near-wall flow into background-turbulence and texture-coherent components, and show that the background-turbulence component experiences the surface as homogeneous slip lengths. The validity of the slip-length model can then be extended to larger texture size $L^{+}$ than thought in previous studies. For $L^{+}\gtrsim 25$, however, we observe that a nonlinear interaction with the texture-coherent flow develops that alters the dynamics of the background turbulence, exhibiting a modified distribution of turbulent energy across length scales. This has the effect of reducing the velocity increment \unicode[STIX]{x0394}U^{+} compared to that predicted using homogeneous slip lengths and sets the upper limit of applicability of slip-length models.</jats:p

Analysis of anisotropically permeable surfaces for turbulent drag reduction

The present work proposes the use of anisotropically permeable substrates as a means to reduce turbulent skin friction. We conduct an a priori analysis to assess the potential of these surfaces, based on the effect of small-scale surface manipulations on near-wall turbulence. The analysis, valid for small permeability, predicts a monotonic decrease in friction as the streamwise permeability increases. Empirical results suggest that the drag-reducing mechanism is however bound to fail beyond a certain permeability. We investigate the development of Kelvin-Helmholtz-like rollers at the surface as a potential mechanism for this failure. These rollers, which are a typical feature of turbulent flows over permeable walls, are known to increase drag and their appearance is known to limit the drag-reducing effect. We propose a model, based on linear stability analysis, that predicts the onset of these rollers for sufficiently large permeability and allows us to bound the maximum drag reduction that these surfaces can achieve

Geometry-induced fluctuations in the transitionally rough regime

Direct numerical simulations of turbulent flows over rough surfaces are conducted to investigate the physics of the transitionally rough regime. Different roughness sizes are analysed within the transitional regime, while keeping the shape of the surface geometry constant. To study the effect of roughness on the flow field, a novel decomposition is used to divide the velocity into two components: a turbulent, geometry-independent contribution, and a geometry-induced contribution, whose intensity is modulated by the overlying turbulence. In the onset of the transitionally rough regime, the turbulent component remains essentially unmodified, and it is anticipated that all the roughness effects can be attributed entirely to the geometry-induced fluctuations. As the roughness size increases further, the turbulent component is also modified, and the fluid-surface interaction becomes more complex

Modulation of near-wall turbulence in the transitionally rough regime

Direct numerical simulations of turbulent channels with rough walls are conducted in the transitionally rough regime. The effect that roughness produces on the overlying turbulence is studied using a modified triple decomposition of the flow. This decomposition separates the roughness-induced contribution from the background turbulence, with the latter essentially free of any texture footprint. For small roughness, the background turbulence is not significantly altered, but merely displaced closer to the roughness crests, with the change in drag being proportional to this displacement. As the roughness size increases, the background turbulence begins to be modified, notably by the increase of energy for short, wide wavelengths, which is consistent with the appearance of a shear-flow instability of the mean flow. A laminar model is presented to estimate the roughness-coherent contribution, as well as the displacement height and the velocity at the roughness crests. Based on the effects observed in the background turbulence, the roughness function is decomposed into different terms to analyse different contributions to the change in drag, laying the foundations for a predictive model

The effect of slip and surface texture on turbulence over superhydrophobic surfaces

Superhydrophobic surfaces are able to entrap gas pockets in between surface roughness elements when submerged in water. These entrapped gas pockets give these surfaces the potential to reduce drag due to the overlying flow being able to locally slip over the gas pockets, resulting in a mean slip at the surface. In this work we assess the separate effects that surface slip and surface texture have on turbulence over superhydrophobic surfaces. We show that the direct effect of surface slip does not modify the dynamics of the overlying turbulence, which remains canonical or smooth-wall like. The surface drag is governed by the difference between two virtual origins, the virtual origin of the mean flow and the virtual origin experienced by the overlying turbulence, in an extension of the theory from Luchini, Manzo & Pozzi (J. Fluid Mech., vol. 228, 1991, pp. 87-109) for riblets. Streamwise slip deepens the virtual origin of the mean flow, while spanwise slip deepens the virtual origin perceived by the overlying turbulence. Drag reduction is then proportional to the difference between the two virtual origins. We decompose the near-wall flow into background-turbulence and texture-coherent components, and show that the background-turbulence component experiences the surface as homogeneous slip lengths. The validity of the slip-length model can then be extended to larger texture size than thought in previous studies. For , however, we observe that a nonlinear interaction with the texture-coherent flow develops that alters the dynamics of the background turbulence, exhibiting a modified distribution of turbulent energy across length scales. This has the effect of reducing the velocity increment compared to that predicted using homogeneous slip lengths and sets the upper limit of applicability of slip-length models