Dimples are small concavities imprinted on a flat surface, known to affect heat transfer and also flow separation and aerodynamic drag on bluff bodies when acting as a standard roughness. Recently, dimples have been proposed as a roughness pattern that is capable to reduce the turbulent drag of a flat plate, by providing a reduction of skin friction that compensates the dimple-induced pressure drag, and leads to a global benefit.
The question whether dimples do actually work to reduce friction drag is still unsettled. In this paper, we provide a comprehensive review of the available information, touching upon the many parameters that characterize the problem. A number of reasons that contribute to explaining the contrasting literature information are discussed. We also provide guidelines for future studies, by highlighting key methodological steps required for a meaningful comparison between a flat and dimpled surface in view of drag reduction.
In this article, the mechanics of drag reduction on an axisymmetric body of revolution by shallow dimples is presented by using the high-fidelity Reynolds Stress Modeling based simulations. Experimental results of drag evolution from published literature at different Reynolds numbers are used to validate the model predictions. The numerical predictions show good agreement with the experimental results. It is observed that the drag of the body is reduced by a maximum of $31\%$ with such shape modification (for the depth to diameter ratio of $7.5\%$ and coverage ratio of $52.8\%$). This arises d…
We investigate drag reduction due to the flow-induced reconfiguration of a flexible thin plate in presence of skin friction drag at low Reynolds Number. The plate is subjected to a uniform free stream and is tethered at one end. We extend existing models in the literature to account for the skin friction drag. The total drag on the plate with respect to a rigid upright plate decreases due to flow-induced reconfiguration and further reconfiguration increases the total drag due to increase in skin friction drag. A critical value of Cauchy number ($Ca$) exists at which the total drag on the plate…
The quest for reductions in fuel consumption and CO2 emissions in transport has been a powerful driving force for scientific research into methods that might underpin drag-reducing technologies for a variety of vehicular transport on roads, by rail, in the air, and on or in the water. In civil aviation, skin-friction drag accounts for around 50% of the total drag in cruise conditions, thus being a preferential target for research. With laminar conditions excluded, skin friction is intimately linked to the turbulence physics in the fluid layer closest to the skin. Thus, research into drag reduc…
A numerical investigation of two locally applied drag reducing control schemes is carried out in the configuration of a spatially developing turbulent boundary layer (TBL). One control is designed to damp near-wall turbulence and the other induces constant mass flux in the wall-normal direction. Both control schemes yield similar local drag reduction rates within the control region. However, the flow development downstream of the control significantly differs: persistent drag reduction is found for the uniform blowing case whereas drag increase is found for the turbulence damping case. In orde…
This paper examines how increasing the value of the Reynolds number $Re$ affects the ability of spanwise-forcing techniques to yield turbulent skin-friction drag reduction. The considered forcing is based on the streamwise-travelling waves of spanwise wall velocity (Quadrio {\em et al. J. Fluid Mech.}, vol. 627, 2009, pp. 161--178). The study builds upon an extensive drag-reduction database created with Direct Numerical Simulation of a turbulent channel flow for two, 5-fold separated values of $Re$, namely $Re_τ=200$ and $Re_τ=1000$. The sheer size of the database, which for the first time sys…
The skin of Tursiops Truncatus is corrugated with small, quasi-periodic ridges running circumferentially about the torso. These ridges extend into the turbulent boundary layer and affect the evolution of coherent structures. The development and evolution of coherent structures over a surface is described by the formation and dynamics of vortex filaments. The dynamics of these filaments over a flat, non-ridged surface is determined analytically, as well as through numerical simulation, and found to agree with the observations of coherent structures in the turbulent boundary layer. The calculati…
Direct numerical simulations of fully-developed turbulent channel flows with wavy walls are undertaken. The wavy walls, skewed with respect to the mean flow direction, are introduced as a means of emulating a Spatial Stokes Layer (SSL) induced by in-plane wall motion. The transverse shear strain above the wavy wall is shown to be similar to that of a SSL, thereby affecting the turbulent flow, and leading to a reduction in the turbulent skin-friction drag. The pressure- and friction-drag levels are carefully quantified for various flow configurations, exhibiting a combined maximum overall-drag …
Flow control for turbulent skin-friction drag reduction is applied to a transonic airfoil to improve its aerodynamic performance. The study is based on direct numerical simulations (with up to 1.8 billions cells) of the compressible turbulent flow around a supercritical airfoil, at Reynolds and Mach numbers of $Re_\infty= 3 \times 10^5$ and $M_\infty =0.7$. Control via spanwise forcing is applied over a fraction of the suction side of the airfoil. Besides locally reducing friction, the control modifies the shock wave and significantly improves the aerodynamic efficiency of the airfoil by incre…
Wall-roughness induces extra drag in wall-bounded turbulent flows. Mapping any given roughness geometry to its fluid dynamic behaviour has been hampered by the lack of accurate and direct measurements of skin-friction drag. Here the Taylor-Couette (TC) system provides an opportunity as it is a closed system and allows to directly and reliably measure the skin-friction. However, the wall-curvature potentially complicates the connection between the wall friction and the wall roughness characteristics. Here we investigate the effects of a hydrodynamically fully rough surface on highly turbulent, …
Inspired by the lotus effect, many studies in the last decade have focused on micro- and nano-patterned surfaces. They revealed that patterns at the micro-scale combined with high contact angles can significantly reduce skin drag. However, the mechanisms and parameters that control drag reduction, e.g. Reynolds number and pattern geometry, are still unclear. We propose an effective medium representation of the micro-features, that treats the latter as a porous medium, and provides a framework to model flow over patterned surfaces in both Cassie and Wenzel states. Our key result is a closed-for…
The multiphase flow mechanism in miscible displacement through porous media is an important topic in various applications, such as petroleum engineering, low Reynolds number suspension flows, dusty gas dynamics, and fluidized beds. To simulate such flows, volume averaging spatial operators are considered to incorporate pressure drag and skin friction experienced by a porous medium. In this work, a streamline-based Lagrangian methodology is extended for an efficient numerical approach to handle dispersion and diffusion of solvent saturation during a miscible flow. Overall pressure drag on the d…
If a body in a stream is provided with small ridges aligned in the local flow direction, a remarkable drag reduction can be reached under turbulent flow conditions. This surprising phenomenon is called the 'shark skin effect'. We demonstrate, that a reduction of resistance can also be reached in creeping flows if the ridges are aligned perpendicular to the flow direction. We especially consider in gravity-driven film flows the effect of the bottom topography on the mean transport velocity.
This work studies the effects of skin-friction drag reduction in a turbulent flow over a curved wall, with a view to understanding the relationship between the reduction of friction and changes to the total aerodynamic drag. Direct numerical simulations (DNS) are carried out for an incompressible turbulent flow in a channel where one wall has a small bump; two bump geometries are considered, that produce mildly separated and attached flows. Friction drag reduction is achieved by applying streamwise-travelling waves of spanwise velocity (StTW). The local friction reduction produced by the StTW …
An oscillating spanwise pressure gradient is imposed numerically to control the flow separation and reduce the drag of a turbulent flow in a channel with square bars. The transverse flow produces a maximum drag reduction of 25\%, due to lower pressure and skin-friction drag forces. The pressure drag reduction reaches a maximum of 22\% and is due to a decrease of the positive high pressure in front of the bars and an increase of the low negative pressure behind the bars. The skin-friction drag reduction is caused by a lower wall-shear stress along the cavity between the bars where the flow is f…
The drag on a golf ball can be reduced by dimpling the surface. There have been few studies, primarily experimental, that provide quantitative information on the details of the drag reduction mechanisms. To illuminate the underlying mechanisms, Direct Numerical Simulation (DNS) is applied to the flow around a golf ball using an immersed boundary method. Computations are performed using up to 500 processors on a range of mesh resolutions from 61 million points to 1.2 billion points. Results are presented from simulations performed at a Reynolds number of Re = $1.1\times 10^5$ using a grid of 1.…
A new turbulent Taylor-Couette system consisting of two independently rotating cylinders has been constructed. The gap between the cylinders has a height of 0.927 m, an inner radius of 0.200 m, and a variable outer radius (from 0.279 to 0.220 m). The maximum angular rotation rates of the inner and outer cylinder are 20 and 10 Hz, respectively, resulting in Reynolds numbers up to 3.4 x 10^6 with water as working fluid. With this Taylor-Couette system, the parameter space (Re_i, Re_o, η) extends to (2.0 x 10^6, {\pm}1.4 x 10^6, 0.716-0.909). The system is equipped with bubble injectors, temperat…
We explore the ability of anisotropic permeable substrates to reduce turbulent skin-friction, studying the influence that these substrates have on the overlying turbulence. For this, we perform DNSs of channel flows bounded by permeable substrates. The results confirm theoretical predictions, and the resulting drag curves are similar to those of riblets. For small permeabilities, the drag reduction is proportional to the difference between the streamwise and spanwise permeabilities. This linear regime breaks down for a critical value of the wall-normal permeability, beyond which the performanc…
A new idea for turbulent skin-friction reduction is proposed, wherein the shape of the solid wall is designed to create the spanwise pressure gradient acting similarly to the well-known method of drag reduction by in-plane spanwise wall motion. Estimates based on the assumption of similarity with drag reduction effect of in-plane wall motion suggest that drag reduction of about 2.4% can be achieved in the flow past a wavy wall, with the crests forming an angle of about 38 degrees with the main flow direction, and the wave period in the main flow direction equal to about 1500 wall units. The re…
Wall-resolved large-eddy simulations are performed to study the impact of spanwise traveling transversal surface waves in zero-pressure gradient turbulent boundary layer flow. Eighty variations of wavelength, period, and amplitude of the space- and time-dependent sinusoidal wall motion are considered for a boundary layer at a momentum thickness based Reynolds number of $Re_θ= 1000$. The results show a strong decrease of friction drag of up to $26\,\%$ and considerable net power saving of up to $10\,\%$. However, the highest net power saving does not occur at the maximum drag reduction. The dra…
Boundary-layer transition is accompanied by a significant increase in skin friction whose origin is rigorously explained using the stochastic Lagrangian formulation of the Navier-Stokes equations. This formulation permits the exact analysis of vorticity dynamics in individual realizations of a viscous incompressible fluid flow. The Lagrangian reconstruction formula for vorticity is here extended for the first time to Neumann boundary conditions (Lighthill source). We can thus express the wall vorticity, and therefore the wall stress, as the expectation of a stochastic Cauchy invariant in backw…
Both experiments and direct numerical simulations have been used to demonstrate that riblets can reduce turbulent drag by as much as $10\%$, but their systematic design remains an open challenge. In this paper, we develop a model-based framework to quantify the effect of streamwise-aligned spanwise-periodic riblets on kinetic energy and skin-friction drag in turbulent channel flow. We model the effect of riblets as a volume penalization in the Navier-Stokes equations and use the statistical response of the eddy-viscosity-enhanced linearized equations to quantify the effect of background turbul…
The effect of streamwise-traveling waves of spanwise wall velocity (StTW) on the quasi-streamwise vortices (QSV) populating the near-wall region of turbulent channels is studied via a conditional averaging technique applied to flow snapshots obtained via Direct Numerical Simulation. The analysis by A. Yakeno, Y. Hasegawa, N. Kasagi, "Modification of quasi-streamwise vortical structure in a drag-reduced turbulent channel flow with spanwise wall oscillation", Phys. Fluids 26, 085109 (2014), where the special case of spatially uniform wall oscillation (OW) was considered, is extended to the gener…
Skin friction prediction for attached flows based on two-dimensional inviscid solutions
School of Aeronautics, Northwestern Polytechnical University（西北工业大学航空学院）；International Joint Institute of Intelligent Fluid Mechanics, Northwestern Polytechnical University（西北工业大学智能流体力学国际联合研究院）；National Key Laboratory of Aircraft Configuration Design（飞机构型设计国家重点实验室）
The underlying mechanisms of three different flow-control strategies on drag reduction in a channel flow are investigated by direct numerical simulations at friction Reynolds numbers ranging from 65 to 85. These strategies include the addition of long-chain polymers, the incorporation of slip surfaces, and the application of an external body force. While it has been believed that such methods lead to a skin-friction reduction by controlling near-wall flow structures, the underlying mechanisms at play are still not as clear. In this study, a temporal analysis is employed to elucidate underlying…
A fundamental problem in the field of turbulent skin-friction drag reduction is to determine the performance of the available control techniques at high values of the Reynolds number $Re$. We consider active, predetermined strategies based on spanwise forcing (oscillating wall and streamwise-traveling waves applied to a plane channel flow), and explore via Direct Numerical Simulations (DNS) up to $Re_τ=2100$ the rate at which their performance deteriorates as $Re$ is increased. To be able to carry out a comprehensive parameter study, we limit the computational cost of the simulations by adjust…
We show that the Fukagata et al. (2002)'s identity for free-stream boundary layers simplifies to the von Karman momentum integral equation relating the skin-friction coefficient and the momentum thickness when the upper bound in the integrals used to obtain the identity is taken to be asymptotically large. If a finite upper bound is used, the terms of the identity depend spuriously on the bound itself. Differently from channel and pipe flows, the impact of the Reynolds stresses on the wall-shear stress cannot be quantified in the case of free-stream boundary layers because the Reynolds stresse…
In order to generalize the well-known spanwise-oscillating-wall technique for drag reduction, non-sinusoidal oscillations of a solid wall are considered as a means to alter the skin-friction drag in a turbulent channel flow. A series of Direct Numerical Simulations is conducted to evaluate the control performance of nine different temporal waveforms, in addition to the usual sinusoid, systematically changing the wave amplitude and the period for each waveform. The turbulent average spanwise motion is found to coincide with the laminar Stokes solution that is constructed, for the generic wavefo…
Flow control with the goal of reducing the skin friction drag on the fluid-solid interface is an active fundamental research area, motivated by its potential for significant energy savings and reduced emissions in the transport sector. Customarily, the performance of drag reduction techniques in internal flows is evaluated under two alternative flow conditions, i.e. at constant mass flow rate or constant pressure gradient. Successful control leads to reduction of drag and pumping power within the former approach, whereas the latter leads to an increase of the mass flow rate and pumping power. …
Harmonic oscillations of the walls of a turbulent plane channel flow are studied by direct numerical simulations to improve our understanding of the physical mechanism for skin-friction drag reduction. The simulations are carried out at constant pressure gradient in order to define an unambiguous inner scaling: in this case, drag reduction manifests itself as an increase of mass flow rate. Energy and enstrophy balances, carried out to emphasize the role of the oscillating spanwise shear layer, show that the viscous dissipations of the mean flow and of the turbulent fluctuations increase with t…
