Session M04: Turbulence: Wall-Bounded Flows IV: Drag Reduction, Compliant Walls and Surface Roughness

A driving mechanism of near-wall turbulence subject to adverse pressure gradient

A turbulent Couette flow is considered for several values of constant adverse pressure gradient (APG) in the lower wall region to study the APG effect on near-wall turbulence. A DNS in a large computational box shows that near the lower wall at strong APG the flow remains turbulent, while the near-wall streaks disappear and the cross-flow fluctuations intensify. A linear analysis shows that APG inhibits the generation of near-wall streaks due to the significant reduction of the mean shear in the near lower wall region. According to a DNS in a minimal flow unit, at strong APG the near-wall self-sustaining process is strongly weakened or destroyed, and the turbulent fluctuations become more isotropic and localized. Using a conditional averaging analysis, a new near-wall turbulent production mechanism, initiated by the wall-normal nonlinear transport of a wall-normal velocity fluctuation to the near-wall region under strong APG is uncovered. The transported wall-normal velocity fluctuation is amplified by the Orr mechanism, leading to the non-zero turbulent production with spatially localized vortical structures. This mechanism is confirmed by the strong correlation between the wall-normal nonlinear transport and turbulent production observed in a DNS with large computational box.   

Wall-bounded turbulent flow and equilibrium states in plane Couette flow under spanwise wall oscillation

This talk concerns skin-friction drag of turbulent and equilibrium states in plane Couette flow subjected to spanwise-wall oscillations. We set the configuration to the minimal flow unit at $Re=400$ ($\lambda_z^+\approx 110$ the spanwise wavelength in viscous units) to maintain only one integral length scale dynamics. We use HKW box (Hamilton 1995) as it sustains turbulence for a very long time at $Re=400$. The control is parametrized by the amplitude $A_w$ and the period $T$. The wall oscillation provokes a significant drag reduction for the fully developed turbulence. As a consequence, the control delays the transition to turbulence and reduces the turbulence lifetime. We have considered three equilibrium solutions EQ$1$, EQ$4$, and EQ$7$, each of which has a lower and upper branch that rises from a saddle-node bifurcation. The control over a wide range of $Re$ induces a significant drag reduction for the upper solution and has a minor effect on the lower branch. Near the saddle-node bifurcation, the lower branch skin-friction increases with control—that of the upper branch decreases to merge with the lower solution at the optimal $A_w$ and disappear. Therefore, the critical Reynolds number $Re_c$ of the saddle-node bifurcations moves to a higher $Re$.   

Visualization of instantaneous and filtered turbulent pipe flow data with and without drag reduction by spanwise wall oscillations at moderately high Reynolds number

Turbulent pipe flow with and without azimuthal wall oscillations has been simulated.  Drag reduction manifested by an increased volumetric flow rate is observed with the prescribed wall oscillation parameters.  Instantaneous realizations of the flow field are sampled and filtered to observe changes to the structure of turbulence in a drag reduced as opposed to a non-drag reduced pipe flow.  Optimal filtering in space is taken as the streamwise-azimuthal power spectra of the streamwise velocity fluctuation, and the results are presented in both the standard and drag-reduced case. This filter acts as a low pass filter in space allowing only the most energetic large scales of motion through.  This filter can be inverted to act as a high pass filter allowing for the visualization of most energetic small scales.  The organization of large-scale structures with and without drag reduction is analyzed to understand how the reduction of small scales effects the convection of structures downstream.   

Direct Numerical Simulation of a Fluid-Structure Interaction in a Turbulent Channel over a Finite-thickness Hyper-elastic Wall at Reτ=180

This study is concerned with the simulation of a Re_τ=180 turbulent flow in a channel interacting with a nonlinear compliant wall via Direct Numerical Simulations. The simulation is performed using high-order spectral-element solver Nek5000 with explicit partitioned fluid-structure interaction (FSI) coupling based on Robin-Neumann boundary conditions via Arbitrary Lagrangian-Eulerian Method. The study is focused on analyzing surface drag, surface motion,  turbulent mixing, and turbulent statistics. Strong FSI interactions and active interface motions are observed when the stiffness of the solid material is relatively low. Turbulence statistics, such as mean stream-wise velocity, turbulent kinetic energy, Reynolds stress, and other statistical quantities, are altered dramatically by such compliant surface under selected material properties.   

Wave-turbulence interactions in flow over compliant wall

Direct numerical simulations of turbulent channel flows with one rigid and one compliant wall were performed. We adopt an Euler-Euler approach with a level-set method to simulate the incompressible turbulent flow interacting with an incompressible viscous hyper-elastic wall. The compliant wall sustains the propagation of Rayleigh waves whose phase speed depends on the shear modulus of elasticity and whose dominant wavelength depends on the compliant layer thickness. When the phase speed of Rayleigh waves is commensurate with the advection speed of near-wall pressure fluctuations, strong two-way coupling between the surface and the flow is established. Inflectional instabilities and shear-layer detachment downstream of the surface waves leads to a sharp phase difference between the deformation and pressure. The instabilities are due to the inflectional velocity profiles near the troughs, and are controlled by the net vorticity flux at the elastic surface. This flux is due to pressure gradient at the wave surface and an additional contribution due to an out-of-phase surface acceleration. We will discuss how the choice of material properties affects the balance between these two contributions, and how it will in turn impact the location and intensity of instabilities above the surface.   

Energy balance in lubricated drag-reduced turbulent channel flow

We use direct numerical simulation to study the problem of drag reduction in a lubricated channel, a flow instance in which a thin layer of a lubricating fluid (density ρ1, viscosity η1, thickness h1) is injected in the near-wall region of a plane channel, so to favor the transportation of a primary fluid (density ρ2, viscosity η2, thickness h2). The primary and lubricating fluids have the same density but different viscosity, such that a viscosity ratio λ =η1 /η2 can be defined. Building on a sound flow characterization, we show that significant drag reduction (DR) can be achieved. Reportedly, the observed DR is a non-monotonic function of λ and, in the present case, is maximum for λ = 1 . 00 (~= 13 % flow rate increase). For the cases λ <= 1 . 00 (low-viscosity lubricating fluid), and confirming previous investigations, we show the existence of two different DR mechanisms: when the two fluids have the same viscosity, DR is purely due to the effect of the surface tension. When the viscosity of the lubricating layer is reduced, turbulence can be sustained in the lubricating layer and DR is simply due to the smaller viscosity of the lubricating layer that acts to decrease the corresponding wall friction.   

Direct Numerical Simulations of Bristled Shark Denticles in Turbulent Channel Flows

The mechanisms by which dermal scales (i.e., `denticles') reduce drag for sharks are still under debate. Recently, reduction of form drag and maneuver load by bristled denticles has been observed in a few experiments using real shark skin samples. To investigate how bristled denticles can change the dynamics of a turbulent boundary layer, we performed DNS of open channel flows over arrays of shark denticle replicas. Representative denticles from Isurus oxyrinchus are modeled using an immersed-boundary method. The complete 3D denticle features including the enameloid crown, neck, and the base at which the scale is anchored are considered. The denticle replicas are inclined at 0, 15, and 30 degrees in this study. Both forward and reversed flow directions of the open channel are examined given that bristling may be caused by bending of the fish body and/or local flow reversal. The total drag is increased for all the simulated arrangements despite that the width between keels on top of the crown matches the optimum value for drag-reduction riblets. Complex vortical structures are observed as the bristled denticles interact with the boundary layer. The region under the crown of the denticle acts as a porous media with a variable porosity determined by the bristling and flow direction. The authors acknowledge support from NSF Grant 2039433.   

Onsager approach to wall bounded turbulence

Turbulent drag laws observed with both smooth and rough walls imply divergences of velocity gradients at the wall and/or in the flow interior in the infinite-Re limit. The fluid motions cannot then be understood as strong solutions of the PDE’s. To obtain a valid dynamical description, regularization of the divergences is necessary. Coarse-graining the Navier-Stokes equation filters out eddies of size <ℓ and a windowing function is needed to remove eddies of distance <h to the wall, thus introducing two arbitrary regularization length-scales. The regularized equations for resolved eddies correspond to the weak formulation of Navier-Stokes equation and contain, in addition to the usual turbulent stress, an inertial drag force modeling momentum exchange with unresolved near-wall eddies. By an Onsager-type argument, we derive for smooth-wall channel flow an upper bound on skin friction by a Blasius -1/4 law. Our result is a deterministic version of Prandtl’s relation with the 1/7 power-law profile of the mean streamwise velocity, with also an assumption on scaling of the Reynolds stress with wall distance. Our approach of filtering small-scale motions and windowing out near-wall eddies offers a rigorous framework for large-eddy simulation modeling in the presence of solid walls.   

Direct Numerical Simulations of rough wall-bounded turbulence over unsteady channel flow

Direct Numerical Simulations of unsteady channel flow has been performed over a regular rough surface in order to investigate the physics involved near the wall vicinity and unsteady effect of pulse applied periodically. Unsteady flow has been initiated by applying an unsteady nonzero mean forcing in the form of a time-varying pressure gradient. Forcing frequencies categorized into low to high amplitude of oscillations ranging from 5% to 10% of mean centerline velocity. The simulation of two different Re_τ of 180 and 395 was performed and compared with the near-wall turbulence statistics. Our aim is to investigate the difference in turbulence statistics of the smooth side with the rough side such as mean statistics, phase averaging of the unsteady channel wall. Further extending the findings of the streaks response for both the Reynolds number on the rough turbulent surface vicinity. The current simulation indicates the difference in a structure near the wall as the Reynolds number increase. Due to roughness, small and strong vorticity was observed between the viscous sublayer and buffer layer for the Re_τ of 395 compared to Re_τ of 180. The viscous sublayer for the higher Re_τ shows a higher turbulent structure over the rough wall but that structure has minimal to no contribution over the buffer layer.   

DNS of turbulent plane-Couette flow with surface roughness

Turbulent plane-Couette flow (pCf) between two smooth walls in relative motion is one of the classical problems in fluid mechanics. In practice, however, walls of pCf are never smooth and will have varying degrees of roughness. Barring the lone experimental study of Aydin and Leutheusser (1991), no information on turbulent pCf with surface roughness exists in the literature. In this work, a direct numerical simulation (DNS) of fully-developed turbulent pCf, where the bottom-wall is held stationary and the top-wall moves with a constant velocity U_w in its own plane, is considered to investigate roughness effects. The gap between the two walls is set as 2h. The Reynolds number, based on half the velocity difference between the walls and the channel half-height h, is set to Re = U_wh/2ν = 1300. Two-dimensional rods are periodically arranged with streamwise pitches s = 5r and 10r on the stationary wall and the roughness height is r = 0.2h. The present selection of s = 5r and 10r was made to obtain configurations of d-type and k-type roughness, respectively (Perry et al. 1969). The results have been compared with those of the turbulent pCf with smooth pCf. In each of the rough pCf cases, turbulent statistics collapsed above the channel centerline indicating a localized statistical homogeneity in the streamwise direction. Further, secondary roll cells with streamwise orientation that characterize the core region of smooth pCf are also visible in the current rough pCf cases. Upon roughening a wall, one would anticipate increased turbulence levels only in the near vicinity of the roughness elements. However, in the current rough pCf cases, it has been observed that turbulent kinetic energy (TKE) is increased near both the rough- and the smooth-walls. Further, TKE is higher near the smooth wall than the rough wall. This phenomenon is further elaborated upon using the budget of TKE.