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 order to account for this difference the formulation of a global drag reduction rate is suggested. It represents the reduction of the streamwise force exerted by the fluid on a finite length plate. Furthermore, it is shown that the far downstream development of the TBL after the control region can be described by a single quantity, namely a streamwise shift of the uncontrolled boundary layer, i.e. a changed virtual origin. Based on this result, a simple model is developed that allows relating for the local drag reduction rate to the global one without the need of conducting expensive simulations or measurements far downstream of the control region.
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…
In this paper, we derive mathematical formulas for the skin friction coefficient in wall-bounded turbulence based on the Reynolds averaged streamwise momentum equation and the total stress. Specially, with the theoretical or empirical relation of the total stress, the skin friction coefficient is expressed in terms of the mean velocity and the Reynolds shear stress in an arbitrary wall-normal region $[h_0, h_1]$. The formulas are validated using the direct numerical simulation data of turbulent channel and boundary layer flows, and the results show that our formulas estimate the skin friction …
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 informatio…
The dynamics in the thin boundary layers of temperature and velocity is the key to a deeper understanding of turbulent transport of heat and momentum in thermal convection. The velocity gradient at the hot and cold plates of a Rayleigh-Bénard convection cell forms the two-dimensional skin friction field and is related to the formation of thermal plumes in the respective boundary layers. Our analysis is based on a direct numerical simulation of Rayleigh-Bénard convection in a closed cylindrical cell of aspect ratio $Γ=1$ and focused on the critical points of the skin friction field. We identify…
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 global approach leading to a self-consistent solution to the Navier-Stokes-Prandtl equations for zero-pressure-gradient boundary layers is presented. It is shown that as $Re_δ\rightarrow \infty$, the dynamically defined boundary layer thickness $δ(x)\propto x/\ln^{2}Re_{x}$ and the skin friction $λ=\frac{2τ_{w}}{ρU_{0}^{2}}\propto 1/\ln^{2}δ(x)$. Here $τ_{w}$ and $U_{0}$ are the wall shear stress and free stream velocity, respectively. The theory is formulated as an expansion in powers of a small dimensionless parameter $\frac{dδ(x)}{dx}\rightarrow 0$ in the limit $x\rightarrow \infty$.
An asymptotic $-1/2$ power-law scaling and a semi-empirical finite-$Re$ model were recently presented by Dixit et al. (2020) for skin friction in zero-pressure-gradient (ZPG) turbulent boundary layers (TBLs). In this work, a new derivation is presented which shows that these relations (i) fundamentally represent a dynamically-consistent scaling of skin friction for nominally two-dimensional ZPG TBLs and fully-developed pipes and channels, and (ii) apply individually to each of these flows. The new theoretical arguments are based on transfer of kinetic energy from mean flow to large eddies of t…
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）
A global approach to analysis of fully developed turbulent flows in pipes/channels and zero pressure gradient boundary layers is proposed. A new dynamic definition of the boundary layer thickness $δ(x)$, where $x$ is the distance to the plate origin, is proposed. The Coles - Fernholtz empirical correlation for skin friction $λ=\frac{2τ_{w}}{ρU_{0}^{2}}\propto 1/\ln^{2}δ(x)$ and $δ(x)\propto x/\ln^{2}(\frac{x}{x_{0}})$ are derived from the Navier-Stokes equations in the limit $Re_{x}\to \infty$. Here $τ_{w}$ and $U_{0}$ are the wall shear stress and free stream velocity, respectively. The theor…
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…
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…
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…
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 …
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 …
The near-wall cycle for skin-friction generation revealed through explainable deep learning
Instituto Universitario de Matemática Pura y Aplicada, Universitat Politècnica de València（纯数学与应用数学大学研究所，瓦伦西亚理工大学）；Department of Aerospace Engineering, University of Michigan（密歇根大学航空航天工程系）
Since it is difficult to apply the existing method of friction and heat flux decomposition on the complex surface, a combined decomposition method of friction and heat flux with clear physical interpretation is proposed, which is based on FIK and RD decomposition method and can be applied to arbitrary surface. Based on this method, the aerothermodynamic characteristics of bistable states of curved compression ramps are analyzed from the perspective of energy transformation. The results show that the decrease of friction in the interaction region of the attachment state and the minimum values o…
The application of drag-control strategies on canonical wall-bounded turbulence, such as periodic channel and zero- or adverse-pressure-gradient boundary layers, raises the question of how to describe control effects consistently for different reference cases. We employ the RD identity (Renard & Deck, J. Fluid Mech., 790, 2016, pp. 339-367) to decompose the mean friction drag and investigate the control effects of uniform blowing and suction applied to a NACA4412 airfoil at chord Reynolds numbers Re_c=200,000 and 400,000. The connection of the drag reduction/increase by using blowing/suction w…
The scope of the present project is to quantify the effects of uniform blowing and body-force damping on turbulent boundary layers subjected to a non-uniform adverse-pressure-gradient distribution. To this end, well-resolved large-eddy simulations are employed to describe the flow around the NACA4412 airfoil at moderate Reynolds number 200, 000 based on freestream velocity and chord length. In the present paper we focus on uniform blowing and the conference presentation will include a comparison with body-force damping applied in the same region. The inner-scaled profiles of the mean velocity …
Two aspects of turbulent flows have been the subject of extensive, split research efforts: macroscopic properties, such as the frictional drag experienced by a flow past a wall, and the turbulent spectrum. The turbulent spectrum may be said to represent the fabric of a turbulent state; in practice it is a power law of exponent α(the "spectral exponent") that gives the revolving velocity of a turbulent fluctuation (or "eddy") of size s as a function of s. The link, if any, between macroscopic properties and the turbulent spectrum remains missing. Might it be found by contrasting the frictional …
We present a physical model for turbulent friction on rough surfaces with regularly distributed roughness elements. Wall shear stresses are expressed as functions of physical quantities. Surfaces with varying roughness densities and roughness elements with different aspect ratios are considered. We propose a straight forward method based on the conservation of momentum to deduce the drag on elements by expressing it as functions of the maximum drag and drag reductions ratios, as the drag on individual elements decreases as packing density increases. A drag reduction effect of momentum redistri…
d'Alembert's paradox is the contradictory observation that for incompressible and inviscid (potential) fluid flow, there is no drag force experienced by a body moving with constant velocity relative to the fluid. This paradox can be straightforwardly resolved by considering Navier's slip boundary condition. Potential flow around a cylinder then solves the Navier--Stokes equations using friction parameter $β=-2ν$. This negative friction parameter can be interpreted physically as the fluid being accelerated by the cylinder wall. This explains the lack of drag. In this paper, we introduce the Nav…
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.
The drag force acting on a body moving in a fluid has two components, friction drag due to fluid viscosity and form drag due to flow separation behind the body. When present, form drag is usually the most significant between the two and in many applications, streamlining efficiently reduces or prevents flow separation. As studied here, when the operating fluid is water, a promising technique for form drag reduction is to modify the walls of the body with superhydrophobic surfaces. These surfaces entrap gas bubbles in their asperities, avoiding the direct contact of the liquid with the wall. Su…
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 power laws in the overlap region of two layer theory of turbulent boundary layer have been obtained by Izakson-Millikan-Kolmogorov hypothesis. The solution of the open functional equation is not unique. The power laws for velocity \& skin friction have equivalence with log laws for velocity \& skin friction, for large Reynolds numbers.
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…
Waves of spanwise velocity imposed at the walls of a plane turbulent channel flow are studied by Direct Numerical Simulations. We consider sinusoidal waves of spanwise velocity which vary in time and are modulated in space along the streamwise direction. The phase speed may be null, positive or negative, so that the waves may be either stationary or traveling forward or backward in the direction of the mean flow. Such a forcing includes as particular cases two known techniques for reducing friction drag: the oscillating wall technique (a traveling wave with infinite phase speed) and the recent…
Numerical study of friction reduction and underlying mechanism of air film via parallel and tandem injections on a hypersonic flat plate at high altitude
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…
The velocity and friction properties of laminar pipe flow of a viscoelastic solution are bounded by the corresponding values for two Newtonian fluids, namely, the solvent and a fluid with a viscosity identical to the total viscosity of the solution. The lower friction factor for the flow of the solution when compared to the latter is tracked to an increased strain rate needed to enhance viscous dissipation. Lastly, we show analytically that the effective viscosity varies similarly to the radial diagonal component of the conformation tensor as observed numerically in turbulent flows, and give a…
Steady forcing at the wall of a channel flow is studied via DNS to assess its ability of yielding reductions of turbulent friction drag. The wall forcing consists of a stationary distribution of spanwise velocity that alternates in the streamwise direction. The idea behind the forcing builds upon the existing technique of the spanwise wall oscillation, and exploits the convective nature of the flow to achieve an unsteady interaction with turbulence. The analysis takes advantage of the equivalent laminar flow, that is solved analytically to show that the energetic cost of the forcing is unaffec…
A theoretical description of the phenomenon of modulation of near-wall turbulence by large scale structures is investigated. The description given is simple in that the effect of large-scale structures is limited to a quasi-steady response of the near-wall turbulence to slow large-scale fluctuations of the skin friction. The most natural and compact form of expressing this mechanism is given by the usual Reynolds-number-independent representation of the total skin friction and velocity, scaled in wall variables, where the mean quantities are replaced by large-scale low-pass-filtered fluctuatin…
The dynamical friction force experienced by a massive gravitating body moving through a gaseous medium is modified by sufficiently strong large-scale magnetic fields. Using linear perturbation theory, we calculate the structure of the wake generated by, and the gravitational drag force on, a body traveling in a straight-line trajectory in a uniformly magnetized medium. The functional form of the drag force as a function of the Mach number (V_0/c_s, where V_0 is the velocity of the body and c_s the sound speed) depends on the strength of the magnetic field and on the angle between the velocity …
We study the direction-dependent drag acting on a cylindrical solid intruder with length $L$ and diameter $D$ as it moves in water-saturated granular beds at constant depth. Polysterene and hydrogel grains with diameter $d$ are used to investigate materials which have high contact friction and those which are nearly frictionless, respectively. The drag on the intruder is measured while oriented perpendicular $F_\perp$ and parallel $F_\parallel$ to its axis as a function of speed $U$ from the quasi-static to the rate-dependent regime. We find that the drag anisotropy $ξ= F_\perp/F_\parallel$ is…
In the present study, we use a fifth-order ordinary differential equation, a generalization of the Blasius equation derived from the Leray-alpha model, to examine the transition to turbulence in rough-wall boundary-layer flows. This equation, combined with a weaker formulation of the von Karman log law modified to include the effects of surface roughness, provides a family of turbulent velocity profiles with two free parameters: the momentum thickness based Reynolds number and the roughness function. As a result, a skin-friction correlation is obtained and predictions of the transitional Reyno…
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…
