In most settings, from international pipelines to home water supplies, the drag caused by turbulence raises pumping costs many times higher than if the flow were laminar. Drag reduction has therefore long been an aim of high priority. In order to achieve this end, any drag reduction method must modify the turbulent mean flow. Motivated by minimization of the input energy this requires, linearly optimal forcing functions are examined. It is shown that the forcing mode leading to the greatest response of the flow is always of m=1 azimuthal symmetry. Little evidence is seen of the second peak at large m (wall modes) found in analogous optimal growth calculations, which may have implications for control strategies. The model's prediction of large response of the large length-scale modes is verified in full direct numerical simulation of turbulence ($Re=5300$, $Re_τ\approx 180$). Further, drag reduction of over 12% is found for finite amplitude forcing of the largest scale mode, m=1. Significantly, the forcing energy required is very small, being less than 2% of that by the through pressure, resulting in a net energy saving of over 10%.
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…
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…
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…
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…
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…
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…
We investigate open- and closed-loop active control for aerodynamic drag reduction of a car model. Turbulent flow around a blunt-edged Ahmed body is examined at $Re_{H}\approx3\times10^{5}$ based on body height. The actuation is performed with pulsed jets at all trailing edges combined with a Coanda deflection surface. The flow is monitored with pressure sensors distributed at the rear side. We apply a model-free control strategy building on Dracopoulos & Kent (Neural Comput. & Applic., vol. 6, 1997, pp. 214-228) and Gautier et al. (J. Fluid Mech., vol. 770, 2015, pp. 442-457). The optimized c…
The impact of fluidic actuation on the wake and drag of a three-dimensional blunt body is investigated experimentally. Jets blowing tangentially to the main flow allow to force the wake with variable frequency and amplitude. Depending on the forcing conditions, two flow regimes can be distinguished. First, in case of broadband actuation with frequencies comprising the natural wake time scale, the convection of the jet structures enhances wake entrainment, shortens the length of the recirculating flow and increases drag. Secondly, at higher actuation frequencies, shear-layer deviation leads to …
The drag reduction induced by superhydrophobic surfaces is investigated in turbulent pipe flow. Wetted superhydrophobic surfaces are shown to trap gas bubbles in their asperities. This stops the liquid from coming in direct contact with the wall in that location, allowing the flow to slip over the air bubbles. We consider a well defined texture with streamwise grooves at the walls in which the gas is expected to be entrapped. This configuration is modelled with alternating no-slip and shear-free boundary conditions at the wall. With respect to classical turbulent pipe flow, a substantial drag …
Polymer additives can substantially reduce the drag of turbulent flows and the upper limit, the so called "maximum drag reduction" (MDR) asymptote is universal, i.e. independent of the type of polymer and solvent used. Until recently, the consensus was that, in this limit, flows are in a marginal state where only a minimal level of turbulence activity persists. Observations in direct numerical simulations using minimal sized channels appeared to support this view and reported long "hibernation" periods where turbulence is marginalized. In simulations of pipe flow we find that, indeed, with inc…
The results of a comparative analysis based upon a Karhunen-Loève expansion of turbulent pipe flow and drag reduced turbulent pipe flow by spanwise wall oscillation are presented. The turbulent flow is generated by a direct numerical simulation at a Reynolds number $Re_τ= 150$. The spanwise wall oscillation is imposed as a velocity boundary condition with an amplitude of $A^+ = 20$ and a period of $T^+ = 50$. The wall oscillation results in a 27% mean velocity increase when the flow is driven by a constant pressure gradient. The peaks of the Reynolds stress and root-mean-squared velocities shi…
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…
We experimentally assess the capabilities of an active, open-loop technique for drag reduction in turbulent wall flows recently introduced by Quadrio et al. [J. Fluid Mech., v.627, 161, (2009)]. The technique consists in generating streamwise-modulated waves of spanwise velocity at the wall, that travel in the streamwise direction. A proof-of-principle experiment has been devised to measure the reduction of turbulent friction in a pipe flow, in which the wall is subdivided into thin slabs that rotate independently in the azimuthal direction. Different speeds of nearby slabs provide, although i…
This paper considers plane channel flow modified by waves of spanwise velocity applied at the wall and travelling along the streamwise direction. Laminar and turbulent regimes for the streamwise flow are both studied. When the streamwise flow is laminar, it is unaffected by the spanwise flow induced by the waves. This flow is a thin, unsteady and streamwise-modulated boundary layer that can be expressed in terms of the Airy function of the first kind. We name it the generalized Stokes layer because it reduces to the classical oscillating Stokes layer in the limit of infinite wave speed. When t…
Drag reduction and subcritical turbulence in controlled pipe flows
Politecnico di Milano（米兰理工大学）；Univ. Lille, CNRS, ONERA, Arts et Metiers Institute of Technology, Centrale Lille（里尔大学、法国国家科学研究中心、法国航空发展局、巴黎国立高等工艺学院、里尔中央理工学院）；Massachusetts Institute of Technology（麻省理工学院）
Recent simulations indicate that streamwise-preferential porous materials have the potential to reduce drag in wall-bounded turbulent flows(Gomez-de-Segura & Garcia-Mayoral 2019). This paper extends the resolvent formulation to study the effect of such anisotropic permeable substrates on turbulent channel flow. Under the resolvent formulation, the Fourier-transformed Navier-Stokes equations are interpreted as a linear forcing-response system. The nonlinear terms are considered the endogenous forcing in the system that gives rise to a velocity and pressure response. A gain-based decomposition o…
The drag reduction properties of a turbulent channel flow modified by spanwise sinusoidal oscillations of the walls are investigated by direct numerical simulations. The work is based on the linear relation between the drag reduction and the parameter $S$, function of the maximum wall velocity and the period of the oscillation. This quantity has been found through physical arguments pertaining to the action of the oscillating Stokes layer on the near-wall turbulence dynamics. The predictive potential of the scaling parameter is exploited to gain insight into the drag-reducing effects of the os…
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…
Recent experimental observations (Kuehnen et al., 2018) have shown that flattening a turbulent streamwise velocity profile in pipe flow destabilises the turbulence so that the flow relaminarises. We show that a similar phenomenon exists for laminar pipe flow profiles in the sense that the nonlinear stability of the laminar state is enhanced as the profile becomes more flattened. Significant drag reduction is also observed for the turbulent flow when triggered by sufficiently large disturbances. The flattening is produced by an artificial body force designed to mimick a baffle used in the exper…
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…
A composite drag control (CDC) combining the opposition (OC) and spanwise opposed wall-jet forcing (SOJF) methods is studied in a turbulent channel flow via direct numerical simulation of the incompressible Navier-Stokes equations. A maximum drag reduction of about 33% is obtained for CDC -- much higher than that produced by either individual method (namely, 19% for SOJF and 23% for OC). Due to the small power input required for both OC and SOJF methods, a significant net power saving (about 32%) is achieved via CDC. Flow analysis shows that CDC can take advantage of both OC and SOJF methods t…
We study the dynamics of a dilute solution of rigid rodlike polymers in a viscous fluid at low Reynolds number by means of numerical simulations of a simple rheological model. We show that the rotational dynamics of polymers destabilizes the laminar flow and causes the emergence of a turbulent-like chaotic flow with a wide range of active scales. This regime displays an increased flow resistance, corresponding to a reduced mean flow at fixed external forcing, as well as an increased mixing efficiency. The latter effect is quantified by measuring the decay of the variance of a scalar field tran…
We study suspensions of oblate rigid particles in a viscous fluid for different values of the particle volume fractions. Direct numerical simulations have been performed using a direct-forcing immersed boundary method to account for the dispersed phase, combined with a soft-sphere collision model and lubrication corrections for short-range particle-particle and particle-wall interactions. With respect to the single phase flow, we show that in flows laden with oblate spheroids the drag is reduced and the turbulent fluctuations attenuated. In particular, the turbulence activity decreases to lowe…
Particles suspended in a fluid exert feedback forces that can significantly impact the flow, altering the turbulent drag and velocity fluctuations. We study flow modulation induced by particles heavier than the carrier fluid in the framework of an Eulerian two-way coupled model, where particles are represented by a continuum density transported by a compressible velocity field, exchanging momentum with the fluid phase. We implement the model in direct numerical simulations of the turbulent Kolmogorov flow, a simplified setting allowing for studying the momentum balance and the turbulent drag i…
We present direct numerical simulations of the different two-dimensional flow regimes generated by a constant spatially periodic forcing balanced by viscous dissipation and large scale drag with a dimensionless damping rate $1/Rh$. The linear response to the forcing is a $6\times6$ square array of counter-rotating vortices, which is stable when the Reynolds number $Re$ or $Rh$ are small. After identifying the sequence of bifurcations that lead to a spatially and temporally chaotic regime of the flow when $Re$ and $Rh$ are increased, we study the transitions between the different turbulent regi…
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 address a challenge of active flow control: the optimization of many actuation parameters guaranteeing fast convergence and avoiding suboptimal local minima. This challenge is addressed by a new optimizer, called explorative gradient method (EGM). EGM alternatively performs one exploitive downhill simplex step and an explorative Latin hypercube sampling iteration. Thus, the convergence rate of a gradient based method is guaranteed while, at the same time, better minima are explored. For an analytical multi-modal test function, EGM is shown to significantly outperform the downhill simplex me…
Over the last two decades, both experiments and simulations have demonstrated that transverse wall oscillations with properly selected amplitude and frequency can reduce turbulent drag by as much as 40%. In this paper, we develop a model-based approach for designing oscillations that suppress turbulence in a channel flow. We utilize eddy-viscosity-enhanced linearization of the turbulent flow with control in conjunction with turbulence modeling to determine skin-friction drag in a simulation-free manner. The Boussinesq eddy viscosity hypothesis is used to quantify the effect of fluctuations on …
We extend the analysis of the friction factor for turbulent pipe flow reported by G. Gioia, P. Chakraborty and N. Goldenfeld (GCG) (G. Gioia and P. Chakraborty, Phys. Rev. Lett. 96, 044502 (2006), N. Goldenfeld, Phys. Rev. Lett. 96, 044503 (2006)) to the case where drag is reduced by polymer additives.
The problem of oscillating flows inside pipes under periodic forcing of viscoelastic fluids is addressed here. Starting from the linear Oldroyd-B model, a generalized Darcy's law is obtained in frequency domain and an explicit expression for the dependence of the dynamic permeability on fluid parameters and forcing frequency is derived. Previous results in both viscoelastic and Newtonian fluids are here shown to be particular cases of our results. On the basis of our calculations, a possible explanation for the observed damping of local dynamic response as the forcing frequency increases is gi…
Direct numerical simulations (DNSs) of turbulent pipe flow subjected to streamwise-varying wall rotation are performed. This control method is able to achieve drag reduction and even relaminarize the flow under certain control parameters at low Reynolds number. Two control parameters, which are velocity amplitude and wavelength, are considered. An annular boundary layer, called Spatial Stokes Layer (SSL), is formed by the wall rotation. Based on the thickness of SSL, two types of drag reduction scenarios are identified. When the thickness is low, the SSL acts as a spacer layer, obstructing the…
The flow of fluids in channels, pipes or ducts, as in any other wall-bounded flow (like water along the hulls of ships or air on airplanes) is hindered by a drag, which increases many-folds when the fluid flow turns from laminar to turbulent. A major technological problem is how to reduce this drag in order to minimize the expense of transporting fluids like oil in pipelines, or to move ships in the ocean. It was discovered in the mid-twentieth century that minute concentrations of polymers can reduce the drag in turbulent flows by up to 80%. While experimental knowledge had accumulated over t…
We use plate drag to study the response of granular media to localized forcing as a function of volume fraction, $ϕ$. A bifurcation in the force and flow occurs at the onset of dilatancy, $ϕ_c.$ Below $ϕ_c$ rapid fluctuations in the drag force, $F_D,$ are observed. Above $ϕ_c$ fluctuations in $F_D$ are periodic and increase with $ϕ$. Velocity field measurements indicate that the bifurcation in $F_D$ results from the formation of stable shear bands above $ϕ_c$ which are created and destroyed periodically during drag. A friction-based model captures the dynamics for $ϕ>ϕ_c$.
Motivated by the results of recent experiments (Kühnen et al., Flow Turb. Combust., vol. 100, 2018, pp. 919-943), we consider the problem of designing a baffle (an obstacle to the flow) to relaminarise turbulence in pipe flows. Modelling the baffle as a spatial distribution of linear drag $\mathbf{f}(\mathbf{x},t)=-χ(\mathbf{x})\mathbf{u}_{tot}(\mathbf{x},t)$ within the flow ($\mathbf{u}_{tot}$ is the total velocity field and $χ\ge 0$ a scalar field), two different optimisation problems are considered to design $χ$ at a Reynolds number $Re=3000$. In the first, the smallest baffle defined in te…
The changes of a turbulent channel flow subjected to oscillations of wall flush-mounted rigid discs are studied by means of direct numerical simulations. The Reynolds number is $R_τ$=$180$, based on the friction velocity of the stationary-wall case and the half channel height. The primary effect of the wall forcing is the sustained reduction of wall-shear stress, which reaches a maximum of 20%. A parametric study on the disc diameter, maximum tip velocity, and oscillation period is presented, with the aim to identify the optimal parameters which guarantee maximum drag reduction and maximum net…
