Turbulent Plane Couette Flow Research Articles

Stratification effect on extreme-scale rolls in plane Couette flows

The effect of weak stratification on turbulent plane Couette flows is studied by means of direct numerical simulations at the Prandtl number of air. We demonstrate that the stratification tends to reduce the intensity of Couette streamwise streaks in the channel center, eventually breaking the characteristic Couette large-scale rolls. By analyzing the bursting mechanism (i.e. sweeps and ejections) responsible for the vertical momentum transfer, we observe weaker events in a disorganized spatial configuration. This scenario no longer supports the generation of Couette large-scale streaks and rolls in the channel center.

Scale interactions in turbulent plane Couette flows in minimal domains

Abstract

Large-eddy simulation of wall-bounded turbulent flow with high-order discrete unified gas-kinetic scheme

In this paper, we introduce the discrete Maxwellian equilibrium distribution function for incompressible flow and force term into the two-stage third-order Discrete Unified Gas-Kinetic Scheme (DUGKS) for simulating low-speed turbulent flows. The Wall-Adapting Local Eddy-viscosity (WALE) and Vreman sub-grid models for Large-Eddy Simulations (LES) of turbulent flows are coupled within the present framework. Meanwhile, the implicit LES are also presented to verify the effect of LES models. A parallel implementation strategy for the present framework is developed, and three canonical wall-bounded turbulent flow cases are investigated, including the fully developed turbulent channel flow at a friction Reynolds number (Re) about 180, the turbulent plane Couette flow at a friction Re number about 93 and lid-driven cubical cavity flow at a Re number of 12000. The turbulence statistics, including mean velocity, the r.m.s. fluctuations velocity, Reynolds stress, etc. are computed by the present approach. Their predictions match precisely with each other, and they are both in reasonable agreement with the benchmark data of DNS. Especially, the predicted flow physics of three-dimensional lid-driven cavity flow are consistent with the description from abundant literature. The present numerical results verify that the present two-stage third-order DUGKS-based LES method is capable for simulating inhomogeneous wall-bounded turbulent flows and getting reliable results with relatively coarse grids.

Polymer-induced flow relaminarization and drag enhancement in spanwise-rotating plane Couette flow

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Transient states in plane Couette flow

Abstract

DNS of plane Couette flow with surface roughness

Direct numerical simulation of fully developed turbulent plane Couette flow (pCf) has been performed to investigate the effect of surface roughness. Flow characteristics in a statistically stationary field are then compared with the smooth pCf data. The present study considers a case, where the bottom wall is fixed, while the top wall is moving with a constant velocity $$U_{\mathrm{w}}$$ in the flow direction. For roughening, square ribs are placed on the stationary wall with a streamwise pitch $$\lambda = 5k$$, where $$k = 0.2h$$ is the roughness height and h is half the height between the walls. In the present study, we examined the flow and pressure fields around the ribs. For the pitch $$\lambda = 5k$$, a single recirculation zone is observed in the cavity between any two consecutive ribs. In addition, the profiles of the mean data in the channel core region at different streamwise locations are shown to collapse with each other, indicating that the flow is quasi-homogeneous in the streamwise direction. Further, counter-rotating secondary roll cells or Taylor–Gortler-like vortices, which evolve temporally and oriented along the flow direction, are also observed in the rough pCf. In addition, the large-scale turbulent structures are distorted into fine-scale motion around the ribs. Furthermore, the skin friction coefficient and the mean pressure fields are qualitatively similar to a rough Poiseuille flow (with ribs only on one wall).

Direct numerical simulation and statistical analysis of stress-driven turbulent Couette flow with a free-slip boundary

The effects of free-slip boundary on shear turbulence are studied numerically using the direct numerical simulation (DNS) approach. The flow considered in this study is a stress-driven turbulent Couette flow between two flat boundaries. The top boundary has an imposed shear stress in the streamwise direction and a free-slip condition for the streamwise velocity fluctuation and the spanwise velocity, and the bottom boundary satisfies the no-slip condition. This type of flow has a mean flow pattern similar to the turbulent plane Couette flow between a stationary flat plate and a moving flat plate but exhibits considerable differences in turbulence statistics due to the effects of the free-slip boundary. Statistical analysis based on the DNS data and theoretical derivation based on Taylor series expansion show that near the free-slip surface the turbulence variances of the three velocity components vary as quadratic functions of the vertical distance from the boundary while the Reynolds shear stress exhibits a linear behavior, which are very different from the counterparts near the no-slip boundary. The free-slip surface condition also leads to zero horizontal vorticities at the surface but allows nonzero vertical vorticity in the meantime, leading to considerable differences in the near-boundary statistics of vorticities and coherent vortex structures. Comparison of three DNS runs with different grid resolutions shows that smoothly resolving the more energetic turbulent flow structures near the free-slip boundary requires a higher horizontal grid resolution than that used for resolving the structures near the no-slip boundary.

Spectral link and macroscopic non-universality in turbulent plane Couette flow

In fully developed turbulent plane Couette flow the classical experimental data of frictional factor f versus Reynolds number Re display well-known disparities which have long remained unexplained. These disparities are accompanied by previously unnoticed disparities in the wakes, and only in the wakes, of the attendant mean-velocity profiles (MVPs). To help explain these experimental data, we apply the model of the ‘spectral link’ for MVPs to turbulent plane Couette flows. The model links the dissipative range, the inertial range, and the energetic range of the standard phenomenological model of the spectrum of turbulent kinetic energy to, respectively, the buffer layer, the log layer, and the wake of the MVPs. By assessing the empirical data using the spectral model, we argue for the existence, in plane Couette flow, of multiple states of turbulence which differ from one another only at the largest lengthscales in the flow, corresponding to the energetic range, where the spectrum is subject to finite-domain effects. Thus, the multiplicity of turbulent states is entirely consistent with small-scale universality, and the experimental data on plane Couette flow pose no challenge to the phenomenological theory of turbulence. Our findings might apply more broadly to a general class of flows engendered by moving boundaries.

Numerical study of plane Couette flow: turbulence statistics and the structure of pressure–strain correlations

AbstractThe paper presents the results of direct numerical simulation of turbulent plane Couette flow. The calculations were performed for Reynolds numbers Re =U0H/ν(His the height of the channel, ±U0/2 is the motion velocities of the lower and upper walls, respectively,νis the kinematic viscosity) from 5200 (where viscous effects significantly affect the flow structure) to 80000 (where a logarithmic layer is clearly observed). Estimates of terms of the equation for the balance of turbulent Reynolds stresses are obtained, which indicate the importance of the kinetic energy transport by velocity fluctuations. The vertical transport of the turbulent momentum flux is less important and partly compensated by the transport of pressure fluctuations. It is shown that in the logarithmic layer the normal components of the ‘pressure–strain rate’ correlation tensor are described in the framework of the ‘isotropization of production’ model, and in the central part of the channel they are described by the linear Rotta model [29]. The additive model considering both the interaction of the velocity field fluctuation and the influence of the mean velocity gradient is a good approximation only for the off-diagonal component of the tensor entering the balance equation for the turbulent momentum flux.

Dissipation function in turbulent plane Poiseuille and Couette flows subject to spanwise rotations

The dissipation function in turbulent plane Poiseuille flows (PPFs) and plane Couette flows (PCFs) subject to spanwise rotations is analyzed. It is found that, in the PCFs without system rotations, the mean part is constant while the fluctuation part follows a logarithmic law, resulting in a similar logarithmic skin friction law as PPFs. However, if the flow system rotates in the spanwise direction, no obvious dependence on the rotation number can be evaluated. In the PPFs with rotations, the dissipation function shows an increase with the rotation number, while in the PCFs with rotations, when the rotation number increases, the dissipation function first decreases and then increases.

Transport of finite-size particles in a turbulent Couette flow: The effect of particle shape and inertia

The transport of finite-size particles in a turbulent plane Couette flow has been studied by particle-resolved numerical simulations based on the Force Coupling Method. The influence of the deviation of particle shape from sphericity was addressed, using neutrally buoyant spheroids with aspect ratio ranging from 0.5 to 2. The particle transport was compared to the case where the inertia of spherical particles was varied by considering different particle densities (while keeping comparable Stokes number). This work has shown that close to the wall, the symmetry axis of oblate particles is almost parallel to the wall-normal direction and the major axis of prolate particles tends to align in the flow direction. Both types of particles have a kayaking type of rotation in the core region which yields homogeneous collisions. The spatial particle distribution is strongly correlated to coherent structures. However, strong deviations occur for the most inertial particles which accumulate in the near wall region. Successive stages of accumulation and release in the streaks are observed while the regeneration cycle of turbulence proceeds. The case of massless bubbles is characterized by a very strong correlation with the large scale vortices that span over the depth of the Couette gap. Even though the particles do not modify drastically the flow, they have some effect on the fluctuating energy, as suggested from the pdf. This effect is more clear for non-spherical particles compared to the spherical ones with various density ratios.

The mechanism by which nonlinearity sustains turbulence in plane Couette flow

Turbulence in wall-bounded shear flow results from a synergistic interaction between linear non-normality and nonlinearity in which non-normal growth of a subset of perturbations configured to transfer energy from the externally forced component of the turbulent state to the perturbation component maintains the perturbation energy, while the subset of energy-transferring perturbations is replenished by nonlinearity. Although it is accepted that both linear non-normality mediated energy transfer from the forced component of the mean flow and nonlinear interactions among perturbations are required to maintain the turbulent state, the detailed physical mechanism by which these processes interact in maintaining turbulence has not been determined. In this work a statistical state dynamics based analysis is performed on turbulent Couette flow at R = 600 and a comparison to DNS is used to demonstrate that the perturbation component in Couette flow turbulence is replenished by a non-normality mediated parametric growth process in which the fluctuating streamwise mean flow has been adjusted to marginal Lyapunov stability. It is further shown that the alternative mechanism in which the subspace of non-normally growing perturbations is maintained directly by perturbation-perturbation nonlinearity does not contribute to maintaining the turbulent state. This work identifies parametric interaction between the fluctuating streamwise mean flow and the streamwise varying perturbations to be the mechanism of the nonlinear interaction maintaining the perturbation component of the turbulent state, and identifies the associated Lyapunov vectors with positive energetics as the structures of the perturbation subspace supporting the turbulence.

Modeling and numerical simulations of polymer degradation in a drag reducing plane Couette flow

Mechanical molecular scission is the main problem of polymeric drag reducers. The ability to reduce the drag is notably decreased as the molecules break down step by step as time goes on. A number of researchers have given a large part of their time to attempts to further understand the role that some important features play in polymer degradation. Until now, all efforts have been in experimental approaches. This paper is the first attempt to take into account the effect of molecular scission on a drag reducing flow by a direct numerical simulation. We analyse a turbulent plane Couette flow of a FENE-P fluid. Our degradation model is based on the maximum polymer extension length L. Unlike the standard FENE-P model, in which L is a constant, the polymer extension here is a spatio-temporal field L(x, y, z, t). When the molecules are highly stretched, which is measured by the trace of the conformation tensor, their maximum length is locally reduced and, consequently, so is their ability to reduce drag. The degraded L spreads within the domain by means of a transport equation. We show here that with such a simple idea we are able to predict the main aspects of mechanical degradation in the flow, such as the change of the turbulent structures and velocity field, and, consequently, the fall of the drag reduction over time.

Extreme-scale motions in turbulent plane Couette flows

We study the large-scale motions in turbulent plane Couette flows at moderate friction Reynolds number up to $Re_{\unicode[STIX]{x1D70F}}=500$. Direct numerical simulation (DNS) domains were as large as $100\unicode[STIX]{x03C0}\unicode[STIX]{x1D6FF}\times 2\unicode[STIX]{x1D6FF}\times 5\unicode[STIX]{x03C0}\unicode[STIX]{x1D6FF}$, where $\unicode[STIX]{x1D6FF}$ is half the distance between the walls. The results indicate that there are streamwise vortices filling the space between the walls that remain correlated over distances in the streamwise direction and that increase strongly with the Reynolds number, so that for the largest Reynolds number studied here, they are correlated across the entire $100\unicode[STIX]{x03C0}\unicode[STIX]{x1D6FF}$ length of the domain. The presence of these very long structures is apparent in the spectra of all three velocity components and the Reynolds stress. In DNS using a smaller domain, the large structures are constrained, eliminating the streamwise variations present in the larger domain. Near the centre of the domain, these large-scale structures contribute as much as half of the Reynolds shear stress.

Multiple states in turbulent plane Couette flow with spanwise rotation

Turbulence is ubiquitous in nature and engineering applications. Although Kolmogorov’s (C. R. Acad. Sci. URSS, vol. 30, 1941a, pp. 301–305;Dokl. Akad. Nauk URSS, vol. 30, 1941b, pp. 538–540) theory suggested a unique turbulent state for high Reynolds numbers, multiple states were reported for several flow problems, such as Rayleigh–Bénard convection and Taylor–Couette flows. In this paper, we report that multiple states also exist for turbulent plane Couette flow with spanwise rotation through direct numerical simulations at rotation number$Ro=0.2$and Reynolds number$Re_{w}=1300$based on the angular velocity in the spanwise direction and half of the wall velocity difference. With two different initial flow fields, our results show that the flow statistics, including the mean streamwise velocity and Reynolds stresses, show different profiles. These different flow statistics are closely related to the flow structures in the domain, where one state corresponds to two pairs of roll cells, and the other shows three pairs. The present result enriches the studies on multiple states in turbulence.

DNS of a turbulent Couette flow at constant wall transpiration up to

We present a new set of direct numerical simulation data of a turbulent plane Couette flow with constant wall-normal transpiration velocity $V_{0}$, i.e. permeable boundary conditions, such that there is blowing on the lower side and suction on the upper side. Hence, there is no net change in flux to preserve periodic boundary conditions in the streamwise direction. Simulations were performed at $Re_{\unicode[STIX]{x1D70F}}=250,500,1000$ with varying transpiration rates in the range $V_{0}^{+}\approx 0.03$ to 0.085. Additionally, a classical Couette flow case at $Re_{\unicode[STIX]{x1D70F}}=1000$ is presented for comparison. As a first key result we found a considerably extended logarithmic region of the mean velocity profile, with constant indicator function $\unicode[STIX]{x1D705}=0.77$ as transpiration increases. Further, turbulent intensities are observed to decrease with increasing transpiration rate. Mean velocities and intensities collapse only in the cases where the transpiration rate is kept constant, while they are largely insensitive to friction Reynolds number variations. The long and wide characteristic stationary rolls of classical turbulent Couette flow are still present for all present DNS runs. The rolls are affected by wall transpiration, but they are not destroyed even for the largest transpiration velocity case. Spectral information indicates the prevalence of the rolls and the existence of wide structures near the blowing wall. The statistics of all simulations can be downloaded from the webpage of the Chair of Fluid Dynamics.

Modulation of large-scale structures by neutrally buoyant and inertial finite-size particles in turbulent Couette flow

Effect of neutrally buoyant large particles on turbulent plane Couette flow is numerically investigated at $R\phantom{\rule{0}{0ex}}e$ near transition. Second moments of the flow are relatively unchanged. However, slightly inertial particles modulate the streak dynamics and flow intermittency.

Turbulent statistics and flow structures in spanwise-rotating turbulent plane Couette flows

The effects of anticyclonic rotation on turbulent statistics and flow structures are studied through 20 direct numerical simulations, covering many qualitatively different flow regimes, from rotation numbers $R\phantom{\rule{0}{0ex}}o=0$ to $R\phantom{\rule{0}{0ex}}o=0.9$.

Quad-Decomposition of Velocity Field in Spanwise-Rotating Turbulent Plane Couette Flows

AbstractIn this paper, we propose a new quad-decomposition approach for the instantaneous flow field which has the secondary flows. Different from the previously reported quad-decomposition, where the velocity field is decomposed into a mean part, a streamwise part and a cross-flow part of the secondary flow, and the residual three-dimensional fluctuation part, our new quad-decomposition separates the flow field into a mean part, a streamwise streaks-related part, a cross-flow roll-cells-related part and a residual cross-flow fluctuation part. These two decomposition approaches are used to explore the underlying physics of the energy balance and transfer among different shares of the turbulent kinetic energy in spanwise-rotating turbulent plane Couette flows. The new quad-decomposition can provide clear pictures of the energy transfer from the streaks to the residual cross-flow fluctuations due to the system rotation and the correlation between pressure and streamwise velocity fluctuations’ gradient, in addition to the bridge role of the cross-flow roll-cells-related field between the mean field and the residual fluctuation field, which can also be demonstrated by the previous quad-decomposition.

Spreading of turbulence in plane Couette flow.

We investigate the growth in the spanwise direction of turbulent spots invading a laminar flow in a plane Couette flow. Direct numerical simulation is used to track the nucleation of streaks during the spot growth. Experiment and direct numerical simulation allow us to study the velocity of the spot fronts and of the vortices observed at the spots' edges. All these results show that two mechanisms are involved when turbulent spots grow: a formerly proposed local growth occurring at the spot spanwise tips but also in comparable proportion a global growth induced by large-scale advection identified in the present work.