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 fully attached, while the wall-shear stress on the crest of the bars and in the separated region behind the bars is unaffected. The spanwise laminar flow obtained by neglecting the nonlinear terms involving the turbulent velocity fluctuations is used to compute the power spent for oscillating the fluid along the spanwise direction and an excellent agreement is found with the power spent obtained by the averaged turbulent flow. A marginal or negative net power saved is found by subtracting the power employed for controlling the flow from the power saved thanks to the transverse flow. The control reduces the total drag as the integral of the Reynolds stresses along the horizontal line connecting the corners of two consecutive bars is decreased, which in turn impacts on the pressure and wall-shear stress reductions.
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 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…
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…
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 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…
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 kinematics of a gliding flat-plate with spanwise oscillation has been optimized to enhance the power efficiency by using Bayesian optimization method, in which the portfolio allocation framework consists of a Gaussian process probabilistic surrogate and a hybrid acquisition strategy. We tune three types of acquisition function in the optimization framework and assign three different balance parameters to each acquisition function. The design variables are set as the dimensionless oscillating amplitude and reduced frequency of the spanwise oscillation. The object function is to maximize the…
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…
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…
Data from direct numerical simulation of open channel flow over a geometrically rough wall at a bulk Reynolds number of 2900, generated by Chan-Braun et al. ["Force and torque acting on particles in a transitionally rough open-channel flow", J. Fluid Mech. 684, 441--474 (2011), 10.1017/jfm.2011.311] are further analysed with respect to the time and length scales of force and torque acting on the wall-mounted spheres. For the two sizes of spheres in a square arrangement (11 and 49 wall units in diameter, yielding hydraulically smooth and transitionally rough flow, respectively), the spatial str…
Superhydrophobic surfaces (SHSs) can reduce the friction drag in turbulent flows. In the laminar regime, it has been shown that trace amounts of surfactant can negate this drag reduction, at times rendering these surfaces no better than solid walls (Peaudecerf et al., Proc. Natl. Acad. Sci. USA 114(28), 7254-9, 2017). However, surfactant effects on the drag-reducing properties of SHSs have not yet been studied under turbulent flow conditions, where predicting the effects of surfactant in direct numerical simulations remains expensive by today's standards. We present a model for turbulent flow …
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…
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…
Numerical study of friction reduction and underlying mechanism of air film via parallel and tandem injections on a hypersonic flat plate at high altitude
The effect of a uniform spanwise magnetic field on a turbulent channel flow is investigated for the case of low magnetic Reynolds number. DNS and LES computations are performed for two values of the hydrodynamic Reynolds number (10^4 and 2\times 10^4) and the Hartmann number varying in a wide range. It is shown that the main effect of the magnetic field is the suppression of turbulent velocity fluctuations and momentum transfer in the wall-normal direction. This leads to drag reduction and transformation of the mean flow profile. The centerline velocity grows, the mean velocity gradients near …
Drag penalty during relaminarization and Kelvin-Helmholtz-promoted retransition in an accelerating turbulent boundary layer over initially drag-reducing riblets
Department of Mechanical Engineering, University of Mississippi（密西西比大学机械工程系）
The background of this work is the problem of reducing the aerodynamic turbulent friction drag, which is an important source of energy waste in innumerable technological fields. We develop a theoretical framework aimed at predicting the behaviour of existing drag reduction techniques when used at the large values of Re which are typical of applications. We focus on one recently proposed and very promising technique, which consists in creating at the wall streamwise-travelling waves of spanwise velocity. A perturbation analysis of the Navier-Stokes equations that govern the fluid motion is carr…
We compute, model, and predict drag reduction of an actuated turbulent boundary layer at a momentum thickness based Reynolds number of Reθ = 1000. The actuation is performed using spanwise traveling transversal surface waves parameterized by wavelength, amplitude, and period. The drag reduction for the set of actuation parameters is modeled using 71 large-eddy simulations (LES). This drag model allows to extrapolate outside the actuation domain for larger wavelengths and amplitudes. The modeling novelty is based on combining support vector regression for interpolation, a parameterized ridgelin…
Turbulent mixed convection in channel flows with heterogeneous surfaces is studied using direct numerical simulations. The relative importance between buoyancy and shear effects, characterized by the bulk Richardson number $Ri_b$, is varied in order to cover the flow regimes of forced, mixed and natural convection, which are associated with different large-scale flow organization. The heterogeneous surface consists of streamwise-aligned ridges, which are known to induce secondary motion in case of forced convection. The large-scale streamwise rolls emerging under smooth-wall mixed convection c…
We consider the influence of transverse confinement on the instability properties of velocity and density distributions reminiscent of those pertaining to exchange flows in stratified inclined ducts, such as the recent experiment of Lefauve et al. (J. Fluid Mech. 848, 508-544, 2018). Using a normal mode streamwise and temporal expansion for flows in ducts with various aspect ratios $B$ and non-trivial transverse velocity profiles, we calculate two-dimensional (2D) dispersion relations with associated eigenfunctions varying in the 'crosswise' direction, in which the density varies, and the span…
Turbulent flow over a surface with streamwise-elongated rough and smooth stripes is studied by means of direct numerical simulation (DNS) in a periodic plane open channel with fully resolved roughness. The goal is to understand how the mean height of roughness affects the characteristics of the secondary flow formed above a spanwise-heterogeneous rough surface. To this end, while the statistical properties of roughness texture as well as the width and spacing of the rough stripes are kept constant, the elevation of the smooth stripes is systematically varied in different simulation cases. Util…
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…
Highly turbulent Taylor-Couette flow with spanwise-varying roughness is investigated experimentally and numerically (direct numerical simulations (DNS) with an immersed boundary method (IBM)) to determine the effects of the spacing and axial width $s$ of the spanwise varying roughness on the total drag and {on} the flow structures. We apply sandgrain roughness, in the form of alternating {rough and smooth} bands to the inner cylinder. Numerically, the Taylor number is $\mathcal{O}(10^9)$ and the roughness width is varied between $0.47\leq \tilde{s}=s/d \leq 1.23$, where $d$ is the gap width. E…
Models of cylinders in the oscillatory flow can be found virtually everywhere in the marine industry, such as pump towers experiencing sloshing load in a LNG ship liquid tank. However, compared to the problem of a cylinder in the uniform flow, a cylinder in the oscillatory flow is less studied, let alone multiple cylinders. Therefore, we experimentally and numerically studied two identical circular cylinders oscillating in the still water with either a side-by-side or a tandem configuration for a wide range of Keulegan-Carpenter number and Stokes number $β$. The experiment result shows that th…
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…
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…
A bird-feather-inspired herringbone riblet texture was investigated for turbulent drag reduction. The texture consists of blade riblets in a converging/diverging or herringbone pattern with spanwise wavelength $Λ_f$. The aim is to quantify the drag change for this texture as compared to a smooth wall and to study the underlying mechanisms. To that purpose, Direct Numerical Simulations of turbulent flow in a channel with height $L_z$ were performed. The FIK-identity for drag decomposition was extended to textured walls and was used to study the drag change mechanisms. For $Λ_f/L_z \gtrsim O(10)…
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…
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…
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…
This study seeks to characterise the breakdown of the steady 2D solution in the flow around a 180-degree sharp bend to infinitesimal 3D disturbances using a linear stability analysis. The stability analysis predicts that 3D transition is via a synchronous instability of the steady flows. A highly accurate global linear stability analysis of the flow was conducted with Reynolds number $Re<1150$ and bend opening ratio (ratio of bend width to inlet height) $0.2\leqβ\leq5$. This range of $Re$ and $β$ captures both steady-state 2D flow solutions as well as the inception of unsteady 2D flow. For $0.…
High-fidelity simulations are performed to study active flow control techniques for alleviating deep dynamic stall of a SD7003 airfoil in plunging motion. The flow Reynolds number is $Re=60{,}000$ and the freestream Mach number is $M=0.1$. Numerical simulations are performed with a finite difference based solver that incorporates high-order compact schemes for differentiation, interpolation and filtering on a staggered grid. A mesh convergence study is conducted and results show good agreement with available data in terms of aerodynamic coefficients. Different spanwise arrangements of actuator…
The presence of a no-slip, impermeable, adiabatic, sloped boundary in an otherwise quiescent, stably stratified, Boussinesq flow generates baroclinic vorticity within a diffusive boundary layer. Such conditions are typical of the oscillating boundary layers on adiabatic abyssal slopes, sloped lake bathymetry, and sloped coastal bathymetry in the absence of high-wavenumber internal waves, mean flows, far-field turbulence on larger scales, and resonant tidal-bathymetric interaction. We investigate the linear stability of the oscillating flow within non-dimensional parameter space typical of the …
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 effect of the variations of the permeability tensor on the close-to-the-wall behaviour of a turbulent channel flow bounded by porous walls is explored using a set of direct numerical simulations. It is found that the total drag can be either reduced or increased by more than $20\%$ by adjusting the permeability directional properties. Drag reduction is achieved for the case of materials with permeability in the vertical direction lower than the one in the wall-parallel planes. This configuration limits the wall normal velocity at the interface while promoting an increase of the tangential …
The onset of turbulent flow around an oscillating sphere is known to occur at a critical velocity vc ~ sqrt(kappa omega) where kappa is the circulation quantum and omega is the oscillation frequency. However, in a small interval of driving force amplitudes F (or corresponding velocity amplitudes of few percent above vc) the turbulent flow is found to be unstable. The flow pattern switches intermittently between potential flow and turbulence. The lifetimes of the turbulent phases have an exponential distribution and the mean lifetimes tau grow very rapidly with increasing driving force, namely …
