7 results
Examination of outer-layer similarity in wall turbulence over obstructing surfaces
- Zishen Chen, Ricardo García-Mayoral
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- Journal:
- Journal of Fluid Mechanics / Volume 973 / 25 October 2023
- Published online by Cambridge University Press:
- 19 October 2023, A31
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Turbulent flows over canopies of rigid filaments with different densities are studied using direct numerical simulations at moderate Reynolds numbers $Re_\tau \approx 550\unicode{x2013}1000$. The canopies have heights $h^+\approx 110\unicode{x2013}220$, and are used as an instance of obstructing substrate for the assessment of outer-layer similarity. We show that conventional methods used to determine the zero-plane displacement $\Delta y$ can be at odds with proper outer-layer similarity and may not be applicable for flows at moderate $Re_\tau$. Instead, we determine $\Delta y$ and the length and velocity scales that recover outer-layer similarity by minimising the difference between the smooth-wall and canopy diagnostic function everywhere above the roughness sublayer, not just in the logarithmic layer. In addition, we explore the possibility of the zero-plane displacement and the friction velocity being set independently, but find that outer-layer similarity is recovered more consistently when they are coupled. We observe that although the Kármán constant, $\kappa$ may not have smooth-wall-like values, the flow statistics are smooth-wall-like in the logarithmic layer and above if the surface effect is limited within the near-wall region. This suggests a modified outer-layer similarity, where $\kappa$ is not 0.39, but turbulence is otherwise smooth-wall-like. When the canopy is dense, the flow above the tips is essentially smooth-wall-like, with smooth-wall-like $\kappa \approx 0.39$ and origin essentially at the tip plane. For canopies with intermediate density, the overlying flow perceives a deeper zero-plane displacement into the canopy, which is consistent with observations reported by previous studies, but exhibits a lower Kármán constant, $\kappa \approx 0.34\unicode{x2013}0.36$. For sparse canopies, $\kappa$ tends back to its smooth-wall value, and the zero-plane displacement height is at the canopy bed. For all canopies studied, the decrease in $\kappa$ never exceeds $15\,\%$, which is significantly less than that obtained in some previous works using conventional methods to assess outer-layer similarity.
The smooth-wall-like behaviour of turbulence over drag-altering surfaces: a unifying virtual-origin framework
- Joseph I. Ibrahim, Garazi Gómez-de-Segura, Daniel Chung, Ricardo García-Mayoral
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- Journal:
- Journal of Fluid Mechanics / Volume 915 / 25 May 2021
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- 18 March 2021, A56
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We examine the effect on near-wall turbulence of displacing the apparent, virtual origins perceived by different components of the overlying flow. This mechanism is commonly reported for drag-altering textured surfaces of small size. For the particular case of riblets, Luchini et al. (J. Fluid Mech., vol. 228, 1991, pp. 87–109) proposed that their effect on the overlying flow could be reduced to an offset between the origins perceived by the streamwise and spanwise velocities, with the latter being the origin perceived by turbulence. Later results, particularly in the context of superhydrophobic surfaces, suggest that this effect is not determined by the apparent origins of the tangential velocities alone, but also by the one for the wall-normal velocity. To investigate this, the present paper focuses on direct simulations of turbulent channels imposing different virtual origins for all three velocity components using Robin, slip-like boundary conditions, and also using opposition control. Our simulation results support that the relevant parameter is the offset between the virtual origins perceived by the mean flow and turbulence. When using Robin, slip-like boundary conditions, the virtual origin for the mean flow is determined by the streamwise slip length. Meanwhile, the virtual origin for turbulence results from the combined effect of the wall-normal and spanwise slip lengths. The slip experienced by the streamwise velocity fluctuations, in turn, has a negligible effect on the virtual origin for turbulence, and hence the drag, at least in the regime of drag reduction. This suggests that the origin perceived by the quasi-streamwise vortices, which induce the cross-flow velocities at the surface, is key in determining the virtual origin for turbulence, while that perceived by the near-wall streaks, which are associated with the streamwise velocity fluctuations, plays a secondary role. In this framework, the changes in turbulent quantities typically reported in the flow-control literature are shown to be merely a result of the choice of origin, and are absent when using as origin the one experienced by turbulence. Other than this shift in origin, we demonstrate that turbulence thus remains essentially smooth-wall-like. A simple expression can predict the virtual origin for turbulence in this regime. The effect can also be reproduced a priori by introducing the virtual origins into a smooth-wall eddy-viscosity framework.
Turbulent flows over dense filament canopies
- Akshath Sharma, Ricardo García-Mayoral
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- Journal:
- Journal of Fluid Mechanics / Volume 888 / 10 April 2020
- Published online by Cambridge University Press:
- 06 February 2020, A2
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Turbulent flows over dense canopies consisting of rigid filaments of small size are investigated using direct numerical simulations. The effect of the height and spacing of the canopy elements on the flow is studied. The flow is composed of an element-coherent, dispersive flow and an incoherent flow, which includes contributions from the background turbulence and from the flow arising from the Kelvin–Helmholtz-like, mixing-layer instability typically reported over dense canopies. For the present canopies, with spacings $s^{+}\approx 3{-}50$, the background turbulence is essentially precluded from penetrating within the canopy. As the elements are ‘tall’, with height-to-spacing ratios $h/s\gtrsim 1$, the roughness sublayer of the canopy is determined by their spacing, extending to $y\approx 2{-}3s$ above the canopy tips. The dispersive velocity fluctuations are observed to also depend mainly on the spacing, and are small deep within the canopy, where the footprint of the Kelvin–Helmholtz-like instability dominates. The instability is governed by the canopy drag, which sets the shape of the mean velocity profile, and thus the shear length near the canopy tips. For the tall canopies considered here, this drag is governed by the element spacing and width, that is, the planar layout of the canopy. The mixing length, which determines the length scale of the instability, is essentially the sum of its height above and below the canopy tips. The former remains roughly the same in wall units and the latter is linear with $s$ for all the canopies considered. For very small element spacings, $s^{+}\lesssim 10$, the elements obstruct the fluctuations and the instability is inhibited. Within the range of $s^{+}$ of the present canopies, the obstruction decreases with increasing spacing and the signature of the Kelvin–Helmholtz-like rollers intensifies. For sparser canopies, however, the intensification of the instabilities can be expected to cease as the assumption of a spatially homogeneous mean flow would break down. For the present, dense configurations, the canopy depth also has an influence on the development of the instability. For shallow canopies, $h/s\sim 1$, the lack of depth blocks the Kelvin–Helmholtz-like rollers. For deep canopies, $h/s\gtrsim 6$, the rollers do not perceive the bottom wall and the effect of the canopy height on the flow saturates. Some of the effects of the canopy parameters on the instability can be captured by linear analysis.
Scaling and dynamics of turbulence over sparse canopies
- Akshath Sharma, Ricardo García-Mayoral
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- Journal:
- Journal of Fluid Mechanics / Volume 888 / 10 April 2020
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- 06 February 2020, A1
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Turbulent flows within and over sparse canopies are investigated using direct numerical simulations at moderate friction Reynolds numbers $Re_{\unicode[STIX]{x1D70F}}\approx 520$ and 1000. The height of the canopies studied is $h^{+}\approx 110{-}200$, which is typical of some engineering canopies but much lower than for most vegetation canopies. The analysis of the effect of Reynolds number in our simulations, however, suggests that the dynamics observed would be relevant for larger Reynolds numbers as well. In channel flows, the distribution of the total stress is linear with height. Over smooth walls, the total stress is the sum of the viscous and the Reynolds shear stresses, the ‘fluid stress’ $\unicode[STIX]{x1D70F}_{f}$. In canopies, in turn, there is an additional contribution from the canopy drag, which can dominate within. Furthermore, the full Reynolds shear stress has contributions from the dispersive, element-induced flow and from the background turbulence, the part of the flow that remains once the element-induced flow is filtered out. For the present sparse canopies, we find that the ratio of the viscous stress and the background Reynolds shear stress to their sum, $\unicode[STIX]{x1D70F}_{f}$, is similar to that over smooth walls at each height, even within the canopy. From this, a height-dependent scaling based on $\unicode[STIX]{x1D70F}_{f}$ is proposed. Using this scaling, the background turbulence within the canopy shows similarities with turbulence over smooth walls. This suggests that the background turbulence scales with $\unicode[STIX]{x1D70F}_{f}$, rather than the conventional scaling based on the total stress. This effect is essentially captured when the canopy is substituted by a drag force that acts on the mean-velocity profile alone, aiming to produce the correct $\unicode[STIX]{x1D70F}_{f}$, without the discrete presence of the canopy elements acting directly on the fluctuations. The proposed mean-only forcing is shown to produce better estimates for the turbulent fluctuations compared to a conventional, homogeneous-drag model. These results suggest that a sparse canopy acts on the background turbulence primarily through the change it induces on the mean-velocity profile, which in turn sets the scale for turbulence, rather than through a direct interaction of the canopy elements with the fluctuations. The effect of the element-induced flow, however, requires the representation of the individual canopy elements.
Modulation of near-wall turbulence in the transitionally rough regime
- Nabil Abderrahaman-Elena, Chris T. Fairhall, Ricardo García-Mayoral
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- Journal:
- Journal of Fluid Mechanics / Volume 865 / 25 April 2019
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- 01 March 2019, pp. 1042-1071
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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.
Turbulent flows over superhydrophobic surfaces: flow-induced capillary waves, and robustness of air–water interfaces
- Jongmin Seo, Ricardo García-Mayoral, Ali Mani
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- Journal:
- Journal of Fluid Mechanics / Volume 835 / 25 January 2018
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- 27 November 2017, pp. 45-85
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Superhydrophobic surfaces can retain gas pockets within their microscale textures when submerged in water. This property reduces direct contact between water and solid surfaces and presents opportunities for improving hydrodynamic performance by decreasing viscous drag. In most realistic applications, however, the flow regime is turbulent and retaining the gas pockets is a challenge. In order to overcome this challenge, it is crucial to develop an understanding of physical mechanisms that can lead to the failure of superhydrophobic surfaces in retaining gas pockets when the overlying liquid flow is turbulent. We present a study of the onset of failure in gas retention by analysing direct numerical simulations (DNS) of turbulent flows over superhydrophobic surfaces coupled with the deformation of air–water interfaces that hold the gas pockets. The superhydrophobic surfaces are modelled as periodic textures with patterned slip and no-slip boundary conditions on the overlying water flow. The liquid–gas interface is modelled via a linearized Young–Laplace equation, which is solved coupled with the overlying turbulent flow. A wide range of texture sizes and interfacial Weber numbers are considered in this study. Our analysis identifies flow-induced upstream-travelling capillary waves that are coherent in the spanwise direction as one mechanism for failure in retention of gas pockets. To confirm physical understanding of these waves, a semianalytical inviscid linear analysis is developed; the wave speeds obtained from the space–time correlations in the DNS data were found to match with the predictions of the semianalytical model. The magnitude of the pressure fluctuations due to these waves was found to increase with decreasing surface tension, and increase with a much stronger dependence on the slip velocity, when all numbers are reported in wall units. Based on a fitted scaling, a threshold criterion for the failure of superhydrophobic surfaces is developed that is based on estimates of the onset condition required for the motion of contact lines. The second contribution of this work is the development of boundary maps that identify stable and unstable zones in a parameter space consisting of working parameter and design parameters including texture size and material contact angle. We provide a brief description of previously identified failure modes of superhydrophobic surfaces, namely the stagnation pressure and shear-driven drainage mechanisms. In an overlay map, the stable and unstable zones due to each mechanism are presented. For various input conditions, we provide scaling laws that identify the most critical mechanism limiting the stability of gas retention by superhydrophobic surfaces.
Hydrodynamic stability and breakdown of the viscous regime over riblets
- RICARDO GARCÍA-MAYORAL, JAVIER JIMÉNEZ
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- Journal:
- Journal of Fluid Mechanics / Volume 678 / 10 July 2011
- Published online by Cambridge University Press:
- 19 April 2011, pp. 317-347
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The interaction of the overlying turbulent flow with a riblet surface and its impact on drag reduction are analysed. The ‘viscous regime’ of vanishing riblet spacing, in which the drag reduction produced by the riblets is proportional to their size, is reasonably well understood, but this paper focuses on the behaviour for spacings s+ ≃ 10–20, expressed in wall units, where the viscous regime breaks down and the reduction eventually becomes an increase. Experimental evidence suggests that the two regimes are largely independent, and, based on a re-evaluation of existing data, it is shown that the optimal rib size is collapsed best by the square root of the groove cross-section, ℓg+=Ag+1/2. The mechanism of the breakdown is investigated by systematic DNSs with increasing riblet sizes. It is found that the breakdown is caused by the appearance of long spanwise rollers below y+ ≈ 20, with typical streamwise wavelengths λx+ ≈ 150, that develop from a two-dimensional Kelvin–Helmholtz-like instability of the mean streamwise flow, similar to those over plant canopies and porous surfaces. They account for the drag breakdown, both qualitatively and quantitatively. It is shown that a simplified linear instability model explains the scaling of the breakdown spacing with ℓg+.