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 turbulence on the mean velocity and skin-friction drag. For triangular riblets, our simulation-free approach reliably predicts drag-reducing trends as well as mechanisms that lead to performance deterioration for large riblets. We investigate the effect of height and spacing on drag reduction and demonstrate a correlation between energy suppression and drag-reduction for appropriately sized riblets. We also analyze the effect of riblets on drag reduction mechanisms and turbulent flow structures including very large scale motions. Our results demonstrate the utility of our approach in capturing the effect of riblets on turbulent flows using models that are tractable for analysis and optimization.
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 $Λ_f/L_z \gtrsim O(10)…
Riblets and superhydrophobic surfaces are two demonstrated passive drag reduction techniques. We describe a method to fabricate surfaces that combine both of these techniques in order to increase drag reduction properties. Samples have been tested with a cone-and-plate rheometer system, and have demonstrated significant drag reduction even in the transitional-turbulent regime. Direct Numerical Simulations have been performed in order to estimate the equivalent slip length at higher rotational speed. The sample with 100~$μ$m deep grooves has been performing very well, showing drag reduction var…
Drag penalty during relaminarization and Kelvin-Helmholtz-promoted retransition in an accelerating turbulent boundary layer over initially drag-reducing riblets
Emulating natural mechanisms in technology has become a very efficient technique to optimize and improve the current machinery. Riblets are such kinds of bio-inspired surface patterns which are seen on Sharks. Their geometric properties induce secondary flows resulting in lower drag, allowing Sharks to achieve such high speeds. Secondary flows are broadly subcategorized into Prandtls first and second kind; the secondary flows induced by riblets belong primarily to Prandtls second kind. These secondary flows have been proven to delay the boundary layer separation by reducing momentum losses. Th…
In this report we briefly summarize the set-up and results for direct numerical simulations (DNS) of turbulent channel flows with riblets. The DNS are carried out with OpenFOAM which allows the use of an unstructured mesh. The present results were presented at the European Drag Reduction and Flow Control Meeting in 2015.
This paper extends the resolvent formalism for wall turbulence proposed by McKeon and Sharma(2010) to account for the effect of streamwise-constant riblets. Under the resolvent formulation, the Navier-Stokes equations are interpreted as a forcing-response system: the nonlinear convective term is interpreted as a feedback forcing on the remaining linear terms, which generates a velocity and pressure response. A gain-based decomposition of the linear forcing-response transfer function --- the resolvent operator --- yields highly amplified velocity and pressure modes, which can be considered key …
In this work, low Reynolds number turbulent flow through a corrugated channel, formed by standard V-groove riblets, are investigated via direct numerical simulations (DNS). The simulations attempt to assess the variation of flow dynamics caused by a change in the characteristic size of the V-groove riblets. Such characterization of size effects provides a means to identify the local flow features arising from fluid-riblet interaction, and to investigate their relevance to the change in viscous drag and turbulence statistics. The present simulations confirmed an improved variation trend when th…
Handling geometric singularities efficiently with the immersed-boundary method: application to riblets
Institute of Fluid Mechanics, Karlsruhe Institute of Technology（卡尔斯鲁厄理工学院流体力学研究所）；Dept. of Aerospace Engineering, Politecnico di Milano（米兰理工大学航空航天工程系）；Dip. di Ingegneria Industriale, Università di Salerno（萨莱诺大学工业工程系）
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 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…
Superhydrophobic surfaces dramatically reduce skin friction of overlying liquid flows. These surfaces are complex and numerical simulations usually rely on models for reducing this complexity. One of the simplest consists in finding an equivalent boundary condition through an homogenisation procedure, which in the case of channel flow over oriented riblets, leads to the presence of a small spanwise component in the homogenized base flow velocity. This work aims at investigating the influence of such a three-dimensionality of the base flow on stability and transition in a channel with walls cov…
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 …
We report measurements of turbulent drag reduction of two different polyelectrolyte solutions: DNA and hydrolyzed Polyacrylamide. Changing the salt concentration in the solutions allows us to change the flexibility of the polymer chains. For both polymers the amount of drag reduction was found to increase with the flexibility. Rheological studies reveal that the elongational viscosity of the solutions increases simultaneously. Hence we conclude that the elongational viscosity is the pertinent macroscopic quantity to describe the ability of a polymer to cause turbulent drag reduction.
Experiments are presented that demonstrate how liquid-infused surfaces can reduce turbulent drag significantly in Taylor-Couette flow. The test liquid was water, and the test surface was composed of square microscopic grooves measuring 100 $μ$m to 800 $μ$m, filled with alkane liquids with viscosities from 0.3 to 1.4 times that of water. We achieve drag reduction exceeding 35\%, four times higher than previously reported for liquid-infused surfaces in turbulent flow. The level of drag reduction increased with viscosity ratio, groove width, fluid area fraction, and Reynolds number. The optimum g…
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 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…
In this review, we describe turbulent drag reduction in a variety of flows using a universal framework of energy flux. In a turbulent flow with dilute polymers and magnetic field, the kinetic energy injected at large scales cascades to the velocity field at intermediate scales, as well as to the polymers and magnetic field at all scales. Consequently, the kinetic energy flux, $ Π_u(k) $, is suppressed in comparison to the pure hydrodynamic turbulence. We argue that the suppression of $Π_u(k)$ is an important factor in the reduction of the inertial force $\langle {\bf u \cdot \nabla u} \rangle$…
We address the "Additive Equivalence" discovered by Virk and coworkers: drag reduction affected by flexible and rigid rodlike polymers added to turbulent wall-bounded flows is limited from above by a very similar Maximum Drag Reduction (MDR) asymptote. Considering the equations of motion of rodlike polymers in wall-bounded turbulent ensembles, we show that although the microscopic mechanism of attaining the MDR is very different, the macroscopic theory is isomorphic, rationalizing the interesting experimental observations.
The modification of dominant coherent structures that extend through the log-region of a drag reduced turbulent boundary layer is studied via examination of two-point correlations from time-resolved particle-image-velocimetry. Measurements were acquired in polymer oceans (uniform concentration) at drag reduction levels corresponding to the low drag reduction regime (< 40%), the high drag reduction (HDR) regime (>40%), and at an intermediate level (46%). The mean velocity profiles and two-point correlations were compared with that of water (Newtonian, DR = 0%). These results show that with incr…
We report on the modification of drag by neutrally buoyant spherical particles in highly turbulent Taylor-Couette flow. These particles can be used to disentangle the effects of size, deformability, and volume fraction on the drag, when contrasted with the drag for bubbly flows. We find that rigid spheres hardly change the drag of the system beyond the trivial viscosity effects caused by replacing the working fluid with particles. The size of the particle has a marginal effect on the drag, with smaller diameter particles showing only slightly lower drag. Increasing the particle volume fraction…
Injection of dilute polymer in a turbulent flow suppresses frictional drag. This challenging and technologically important problem remains primarily unresolved due to the complex nature of the flow. An important factor in the drag reduction is the energy transfer from the velocity field to the polymers. In this paper we quantify this process using energy fluxes, as well as show its universality in diverse flows such as magnetohydrodynamics, quasi-static magnetohydrodynamics, and bubbly turbulence. We show that in such flows, the transfer from kinetic energy to elastic energy leads to a reducti…
Nonlinear traveling waves that are precursors to laminar-turbulent transition and capture the main structures of the turbulent buffer layer have recently been found to exist in all the canonical parallel flow geometries. We study the effect of polymer additives on these "exact coherent states" (ECS), in the plane Poiseuille geometry. Many key aspects of the turbulent drag reduction phenomenon are found, including: delay in transition to turbulence; drag reduction onset threshold; diameter and concentration effects. Furthermore, examination of the ECS existence region leads to a distinct predic…
What is the turbulent drag force experienced by an object moving in a rotating fluid? This open and fundamental question can be addressed by measuring the torque needed to drive an impeller at constant angular velocity $ω$ in a water tank mounted on a platform rotating at a rate $Ω$. We report a dramatic reduction in drag as $Ω$ increases, down to values as low as $12$\% of the non-rotating drag. At small Rossby number $Ro = ω/Ω$, the decrease in drag coefficient $K$ follows the approximate scaling law $K \sim Ro$, which is predicted in the framework of nonlinear inertial wave interactions and…
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…
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 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…
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 …
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…
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 …
The phenomenon of drag reduction induced by injection of bubbles into a turbulent carrier fluid has been known for a long time; the governing control parameters and underlying physics is however not well understood. In this paper, we use three dimensional numerical simulations to uncover the effect of deformability of bubbles injected in a turbulent Taylor-Couette flow on the overall drag experienced by the system. We consider two different Reynolds numbers for the carrier flow, i.e. $Re_i=5\times 10^3$ and $Re_i=2\times 10^4$; the deformability of the bubbles is controlled through the Weber n…
Drag reduction by microbubbles is a promising engineering method for improving ship performance. A fundamental theory of the phenomenon is lacking however, making actual design quite uphazard. We offer here a theory of drag reduction by microbubbles in the limit of very small bubbles, when the effect of the bubbles is mainly to normalize the density and the viscosity of the carrier fluid. The theory culminates with a prediction of the degree of drag reduction given the concentration profile of the bubbles. Comparisons with experiments are discussed and the road ahead is sketched.
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 …
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…
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…
Nontrivial steady flows have recently been found that capture the main structures of the turbulent buffer layer. We study the effects of polymer addition on these "exact coherent states" (ECS) in plane Couette flow. Despite the simplicity of the ECS flows, these effects closely mirror those observed experimentally: Structures shift to larger length scales, wall-normal fluctuations are suppressed while streamwise ones are enhanced, and drag is reduced. The mechanism underlying these effects is elucidated. These results suggest that the ECS are closely related to buffer layer turbulence.
Drag reduction by polymers in turbulent wall-bounded flows exhibits universal and non-universal aspects. The universal maximal mean velocity profile was explained in a recent theory. The saturation of this profile and the crossover back to the Newtonian plug are non-universal, depending on Reynolds number Re, concentration of polymer $c_p$ and the degree of polymerization $N_p$. We explain the mechanism of saturation stemming from the finiteness of extensibility of the polymers, predict its dependence on $c_p$ and $N$ in the limit of small $c_p$ and large Re, and present the excellent comparis…
Reversible in operando control of friction is an unsolved challenge crucial to industrial tribology. Recent studies show that at low sliding velocities, this control can be achieved by applying an electric field across electrolyte lubricants. However, the phenomenology at high sliding velocities is yet unknown. In this paper, we investigate the hydrodynamic friction across electrolytes under shear beyond the transition to turbulence. We develop a novel, highly parallelised, numerical method for solving the coupled Navier-Stokes Poisson-Nernest-Planck equation. Our results show that turbulent d…
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, …
Long-chained, viscoelastic surfactant solutions (VES) have been widely employed in the oil and gas industry, particularly in hydraulic fracturing and gravel-packing operations, where turbulence is commonly reached due to high pumping rates. With this motivation, we experimentally investigate the turbulent duct flow of an under-studied class of wormlike micellar solutions that forms a gel at room temperature. The fluid is characterized via rotational rheometry, and the turbulent velocity and Reynolds stress profiles are measured via Laser Doppler Anemometry (LDA). Three surfactant concentration…
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 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 investigate the mechanisms by which inertial particles dispersed at semi-dilute conditions cause significant drag-reduction in a turbulent channel flow at $\mathrm{Re}_τ= 180$. We consider a series of four-way coupled Euler-Lagrange simulations where particles having friction Stokes number $\mathrm{St}^+ = 6$ or 30 are introduced at progressively increasing mass loading from $M=0.2$ to 1.0. The simulations show that $\mathrm{St}^+ = 30$ particles cause large drag-reduction by up to 19.74\% at $M=1.0$, whereas $\mathrm{St}^+ = 6$ particles cause large drag increase by up to 16.92\% at $M=1.0…
We study the effect of droplet coalescence on turbulent wall-bounded flows, by means of direct numerical simulations. In particular, the volume-of-fluid and front-tracking methods are used to simulate turbulent channel flows containing coalescing and non-coalescing droplets, respectively. We find that coalescing droplets have a negligible effect on the drag, whereas the non-coalescing ones steadily increase drag as the volume fraction of the dispersed phase increases: indeed, at 10\% volume fraction, the non-coalescing droplets show a 30\% increase in drag, whereas the coalescing droplets show…
In hydrodynamic turbulence, the kinetic energy injected at large scales cascades to the inertial range, leading to a constant kinetic energy flux. In contrast, in magnetohydrodynamic (MHD) turbulence, a fraction of kinetic energy is transferred to the magnetic energy. Consequently, for the same kinetic energy injection rate, the kinetic energy flux in MHD turbulence is reduced compared to its hydrodynamic counterpart. This leads to relative weakening of the nonlinear term ($\la | ({\bf u}\cdot \nabla) {\bf u} | \ra$, where ${\bf u}$ is the velocity field) and turbulent drag, but strengthening …
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…
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 …
Using the Taylor--Couette geometry we experimentally investigate the effect of salt on drag reduction caused by bubbles present in the flow. We combine torque measurements with optical high-speed imaging to relate the bubble size to the drag experienced by the flow. Previous findings have shown that a small percentage of air (4%) can lead to dramatic drag reduction (40%). In contrast to previous laboratory experiments, which mainly used fresh water, we will vary the salinity from fresh water to the average salinity of ocean water. We find that the drag reduction is increasingly more inhibited …
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…
