Controlling turbulent drag across electrolytes using electric fields

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 drag cannot be controlled across dilute electrolyte using static electric fields alone. The limitations of the Poisson-Nernst-Planck formalism hints at ways in which turbulent drag could be controlled using electric fields.Comment: Accepted by the Faraday Discussions on Chemical Physics of Electroactive Material

Exploring the large-scale structure of Taylor-Couette turbulence through Large-Eddy Simulations

Large eddy simulations (LES) of Taylor-Couette (TC) flow, the flow between two co-axial and independently rotating cylinders are performed in an attempt to explore the large-scale axially-pinned structures seen in experiments and simulations. Both static and dynamic LES models are used. The Reynolds number is kept fixed at Re = 3.4 • 104, and the radius ratio η = ri/ro is set to η = 0.909, limiting the effects of curvature and resulting in frictional Reynolds numbers of around Reτ ≈ 500. Four rotation ratios from Rot =-0.0909 to Rot = 0.3 are simulated. First, the LES of TC is benchmarked for different rotation ratios. Both the Smagorinsky model with a constant of cs = 0.1 and the dynamic model are found to produce reasonable results for no mean rotation and cyclonic rotation, but deviations increase for increasing rotation. This is attributed to the increasing anisotropic character of the fluctuations. Second, "over-damped" LES, i.e. LES with a large Smagorinsky constant is performed and is shown to reproduce some features of the large-scale structures, even when the near-wall region is not adequately modeled. This shows the potential for using over-damped LES for fast explorations of the parameter space where large-scale structures are found

Investigating the origins of fluctuation forces on plates immersed in turbulent flows

A net force can arise on objects which lie in systems with complex energy partitions, even if the system is on average stationary. These forces are usually called fluctuation forces, as they arise due to the objects modifying the character of the fluctuations within the system. We continue the investigation of Spandan \emph{et al.}, \textit{Sci. Adv., 6(14), eaba0461} (2020), who found an attractive fluctuation force between two parallel square plates in homogeneous isotropic turbulence (HIT). We conduct simulations which systematically vary the plate size and Reynolds number. At $Re_\lambda=100$ small plates show a monotonic force dependence, with a maximum force for the smallest plate separations, while medium and large plates show a non-monotonic behaviour of the force with maximum attractive force at intermediate separations. We find that energy-related statistics cannot explain the dependence on plate separation of the force, but that statistics related to vorticity do show qualitative variations around the plate separation corresponding to the maximum force. This suggests that the role of plates in affecting intense vorticity structures is critical to the behaviour of the force. By decreasing $Re_\lambda$, we show that removing vortex stretching decreases the attractive force, but does not completely eliminate it, and find that the local maximum at intermediate distances becomes a local minimum. This confirms that the attractive force is related to vorticity, while suggesting that a second mechanism is present -- supporting the proposal for a two-fold origin from earlier work: the plates both restrict the presence of energy structures in the slit and pack intense vortical structures which stretch each other causing the pressure to drop

The effect of roll number on the statistics of turbulent Taylor-Couette flow

A series of direct numerical simulations in large computational domains has been performed in order to probe the spatial feature robustness of the Taylor rolls in turbulent Taylor-Couette (TC) flow. The latter is the flow between two coaxial independently rotating cylinders of radius $r_i$ and $r_o$, respectively. Large axial aspect ratios $\Gamma = 7$-$8$ (with $\Gamma = L/(r_o-r_i)$, and $L$ the axial length of the domain) and a simulation with $\Gamma=14$ were used in order to allow the system to select the most unstable wavenumber and to possibly develop multiple states. The radius ratio was taken as $\eta=r_i/r_o=0.909$, the inner cylinder Reynolds number was fixed to $Re_i=3.4\cdot10^4$, and the outer cylinder was kept stationary, resulting in a frictional Reynolds number of $Re_\tau\approx500$, except for the $\Gamma=14$ simulation where $Re_i=1.5\cdot10^4$ and $Re_\tau\approx240$. The large-scale rolls were found to remain axially pinned for all simulations. Depending on the initial conditions, stable solutions with different number of rolls $n_r$ and roll wavelength $\lambda_z$ were found for $\Gamma=7$. The effect of $\lambda_z$ and $n_r$ on the statistics was quantified. The torque and mean flow statistics were found to be independent of both $\lambda_z$ and $n_r$, while the velocity fluctuations and energy spectra showed some box-size dependence. Finally, the axial velocity spectra was found to have a very sharp drop off for wavelengths larger than $\lambda_z$, while for the small wavelengths they collapse

Turbulence decay towards the linearly-stable regime of Taylor-Couette flow

Taylor-Couette (TC) flow is used to probe the hydrodynamical stability of astrophysical accretion disks. Experimental data on the subcritical stability of TC are in conflict about the existence of turbulence (cf. Ji et al. Nature, 444, 343-346 (2006) and Paoletti et al., A$\&$A, 547, A64 (2012)), with discrepancies attributed to end-plate effects. In this paper we numerically simulate TC flow with axially periodic boundary conditions to explore the existence of sub-critical transitions to turbulence when no end-plates are present. We start the simulations with a fully turbulent state in the unstable regime and enter the linearly stable regime by suddenly starting a (stabilizing) outer cylinder rotation. The shear Reynolds number of the turbulent initial state is up to $Re_s \sim10^5$ and the radius ratio is $\eta=0.714$. The stabilization causes the system to behave as a damped oscillator and correspondingly the turbulence decays. The evolution of the torque and turbulent kinetic energy is analysed and the periodicity and damping of the oscillations are quantified and explained as a function of shear Reynolds number. Though the initially turbulent flow state decays, surprisingly, the system is found to absorb energy during this decay.Comment: Preprint submitted to PRL, 12 pages, 5 figure

Direct numerical simulation of Taylor-Couette flow with grooved walls: torque scaling and flow structure

We present direct numerical simulations of Taylor-Couette flow with grooved walls at a fixed radius ratio $\eta=r_i/r_o=0.714$ with inner cylinder Reynolds number up to $Re_i=3.76\times10^4$, corresponding to Taylor number up to $Ta=2.15\times10^9$. The grooves are axisymmetric V-shaped obstacles attached to the wall with a tip angle of $90^\circ$. Results are compared to the smooth wall case in order to investigate the effects of grooves on Taylor-Couette flow. We focus on the effective scaling laws for the torque, flow structures, and boundary layers. It is found that, when the groove height is smaller than the boundary layer thickness, the torque is the same as that of the smooth wall cases. With increasing $Ta$, the boundary layer thickness becomes smaller than the groove height. Plumes are ejected from the tips of the grooves and secondary circulations between the latter are formed. This is associated to a sharp increase of the torque and thus the effective scaling law for the torque vs. $Ta$ becomes much steeper. Further increasing $Ta$ does not result in an additional slope increase. Instead, the effective scaling law saturates to the "ultimate" regime effective exponents seen for smooth walls. It is found that even though after saturation the slope is the same as for the smooth wall case, the absolute value of torque is increased, and the more the larger size of the grooves.Comment: Accepted by JFM, 27 pages, 23 figure

Dynamics and evolution of Turbulent Taylor rolls

In many shear- and pressure-driven wall-bounded turbulent flows secondary motions spontaneously develop and their interaction with the main flow alters the overall large-scale features and transfer properties. Taylor-Couette flow, the fluid motion developing in the gap between two concentric cylinders rotating at different angular velocity, is not an exception, and toroidal Taylor rolls have been observed from the early development of the flow up to the fully turbulent regime. In this manuscript we show that under the generic name of ``Taylor rolls'' there is a wide variety of structures that differ for the vorticity distribution within the cores, the way they are driven and their effects on the mean flow. We relate the rolls at high Reynolds numbers not to centrifugal instabilities, but to a combination of shear and anti-cyclonic rotation, showing that they are preserved in the limit of vanishing curvature and can be better understood as a pinned cycle which shows similar characteristics as the self-sustained process of shear flows. By analyzing the effect of the computational domain size, we show that this pinning is not a product of numerics, and that the position of the rolls is governed by a random process with the space and time variations depending on domain size.Comment: Submitted to JF

The near-wall region of highly turbulent Taylor-Couette flow

Direct numerical simulations of the Taylor-Couette (TC) problem, the flow between two coaxial and independently rotating cylinders, have been performed. The study focuses on TC flow with mild curvature (small gap) with a radius ratio of $\eta=r_i/r_o=0.909$, an aspect ratio of $\Gamma=L/d=2\pi/3$, and a stationary outer cylinder. Three inner cylinder Reynolds of $1\cdot10^5$, $2\cdot10^5$ and $3\cdot 10^5$ were simulated, corresponding to frictional Reynolds numbers between $Re_\tau\approx 1400$ and $Re_\tau \approx 4000$. An additional case with a large gap, $\eta=0.5$ and driving of $Re=2\cdot10^5$ was also performed. Small-gap TC was found to be dominated by spatially-fixed large-scale structures, known as Taylor rolls (TRs). TRs are attached to the boundary layer, and are active, i.e. they transport angular velocity through Reynolds stresses. An additional simulation with inner cylinder Reynolds number of $Re=1\cdot10^5$ and fixed outer cylinder with an externally imposed axial flow of comparable strength as the wind of the TRs was also conducted. The axial flow was found to convect the TRs without any weakening effect. For small-gap TC, evidence for the existence of logarithmic velocity fluctuations, and of an overlap layer, in which the velocity fluctuations collapse in outer units, was found. Profiles consistent with a logarithmic dependence were also found for the angular velocity in large-gap TC, albeit in a very reduced range of scales. Finally, the behaviour of both small- and large-gap TC was compared to other canonical flows. Small-gap TC has similar behaviour in the near-wall region to other canonical flows, while large-gap TC displays very different behaviour