Turbulent plane Couette flow subject to strong system rotation

1997 ◽  
Vol 347 ◽  
pp. 289-314 ◽  
Author(s):  
KNUT H. BECH ◽  
HELGE I. ANDERSSON
Keyword(s):  
Flow Field ◽  
Couette Flow ◽  
Turbulence Level ◽  
Streamwise Vortices ◽  
Plane Couette Flow ◽  
Mean Flow ◽  
Cell Pattern ◽  
System Rotation ◽  
The Mean ◽  
Turbulent Plane

System rotation is known to substantially affect the mean flow pattern as well as the turbulence structure in rotating channel flows. In a numerical study of plane Couette flow rotating slowly about an axis aligned with the mean vorticity, Bech & Andersson (1996a) found that the turbulence level was damped in the presence of anticyclonic system rotation, in spite of the occurrence of longitudinal counter-rotating roll cells. Moreover, the turbulence anisotropy was practically unaffected by the weak rotation, for which the rotation number Ro, defined as the ratio of twice the imposed angular vorticity Ω to the shear rate of the corresponding laminar flow, was ±0.01. The aim of the present paper is to explore the effects of stronger anticyclonic system rotation on directly simulated turbulent plane Couette flow. Turbulence statistics like energy, enstrophy and Taylor lengthscales, both componental and directional, were computed from the statistically steady flow fields and supplemented by structural information obtained by conditional sampling.The designation of the imposed system rotation as ‘high’ was associated with a reversal of the conventional Reynolds stress anisotropy so that the velocity fluctuations perpendicular to the wall exceeded those in the streamwise direction. It was observed that the anisotropy reversal was accompanied by an appreciable region of the mean velocity profile with slope ∼2Ω, i.e. the absolute mean vorticity tended to zero. It is particularly noteworthy that these characteristic features were shared by two fundamentally different flow regimes. First, the two-dimensional roll cell pattern already observed at Ro=0.01 became more regular and energetic at Ro=0.10 and 0.20, whereas the turbulence level was reduced by about 50%. Then, when Ro was further increased to 0.50, a disordering of the predominant roll cell pattern set in during a transient period until the flow field settled at a new statistically steady state substantially less affected by the roll cells. This was accompanied by a substantial amplification of the streamwise turbulent vorticity and an anomalous variation of the mean turbulent kinetic energy which peaked in the middle of the channel rather than near the walls. While the predominant flow structures of the non-rotating flow were longitudinal streaks, system rotation generated streamwise vortices, either ordered secondary flow or quasi-streamwise vortices. Eventually, at Ro=1.0, the turbulent fluctuations were completely suppressed and the flow field relaminarized.

Analysis of Transitional and Fully Turbulent Plane Couette Flow

1983 ◽  
Vol 105 (3) ◽  
pp. 364-368 ◽  
Author(s):  
J. R. Missimer ◽  
L. C. Thomas
Keyword(s):  
Couette Flow ◽  
Flow Analysis ◽  
Wall Region ◽  
Turbulent Regime ◽  
Plane Couette Flow ◽  
Burst Frequency ◽  
Mean Velocity ◽  
The Mean ◽  
Turbulent Plane ◽  
Turbulent Burst

The two-dimensional, incompressible, fully-developed, turbulent plane Couette flow is a limiting case of circular Couette flow. As such, plane Couette flow analyses have been used in lubrication theory to analyze the lubrication flow in an unloaded journal bearings. A weakness of existing analyses, other than the turbulent burst analysis, is that they are not capable of characterizing the transitional turbulent regime. The objective of the proposed paper is to develop a model of the turbulent burst phenomenon for momentum in transitional turbulent and fully turbulent plane Couette flow. Model closure is obtained by specification of the mean turbulent burst frequency and, for moderate to high Reynolds numbers, by interfacing with classical eddy diffusivity models for the turbulent core. The analysis is shown to produce predictions for the mean velocity profile and friction factor that are in good agreement with published experimental data for transitional turbulent and fully turbulent flow. This approach to modeling the wall region involves a minimum level of empiricism and provides a fundamental basis for generalization. The use of the present analysis extends the applicability of plane Couette flow analysis in lubrication problems to the transitional turbulent regime.

Nonlinear vorticity-banding instability in granular plane Couette flow: higher-order Landau coefficients, bistability and the bifurcation scenario

2013 ◽  
Vol 718 ◽  
pp. 131-180 ◽  
Author(s):  
Priyanka Shukla ◽  
Meheboob Alam
Keyword(s):  
Couette Flow ◽  
Volume Fraction ◽  
Critical Density ◽  
Higher Order ◽  
Jump Discontinuity ◽  
Linear Growth Rate ◽  
Plane Couette Flow ◽  
Mean Flow ◽  
Dense Flows ◽  
The Mean

AbstractThe rapid granular plane Couette flow is known to be unstable to pure spanwise perturbations (i.e. perturbations having variations only along the mean vorticity direction) below some critical density (volume fraction of particles), resulting in the banding of particles along the mean vorticity direction: this is dubbed ‘vorticity banding’ instability. The nonlinear state of this instability is analysed using quintic-order Landau equation that has been derived from the pertinent hydrodynamic equations of rapid granular fluid. We have found analytical solutions for related modal/harmonic equations of finite-size perturbations up to quintic order in perturbation amplitude, leading to an exact calculation of both first and second Landau coefficients. This helped to identify the bistable nature of nonlinear vorticity-banding instability for a range of densities spanning from moderately dense to dense flows. For perturbations with small spanwise wavenumbers, the bifurcation scenario for vorticity banding unfolds, with increasing density from the dilute limit, as supercritical pitchfork $\rightarrow $ subcritical pitchfork $\rightarrow $ subcritical Hopf bifurcations. The transition from supercritical to subcritical pitchfork bifurcations is found to occur via the appearance of a degenerate/bicritical point (at which both the linear growth rate and the first Landau coefficient are simultaneously zero) that divides the critical line into two parts: one representing the first-order and the other the second-order phase transitions. Both subcritical oscillatory and stationary solutions have also been uncovered for dilute and dense flows, respectively, when the spanwise wavenumber is large. In all cases, the nonlinear solutions correspond to inhomogeneous states of shear stress and pressure along the vorticity direction, and hence are analogues of vorticity banding in other complex fluids. The quartic-order mean-flow resonance is evidenced in the parameter space for which the second Landau coefficient undergoes a jump discontinuity of infinite order. The importance of retaining higher-order terms to calculate the second Landau coefficient and their possible effects on the nature of bifurcations are elucidated.

scholarly journals Mean flow of turbulent–laminar patterns in plane Couette flow

2007 ◽  
Vol 576 ◽  
pp. 109-137 ◽  
Author(s):  
DWIGHT BARKLEY ◽  
LAURETTE S. TUCKERMAN
Keyword(s):  
Reynolds Number ◽  
Couette Flow ◽  
Full Range ◽  
Force Balance ◽  
Computational Domain ◽  
Plane Couette Flow ◽  
Mean Flow ◽  
The Mean ◽  
The Relationship ◽  
And Diffusion

A turbulent–laminar banded pattern in plane Couette flow is studied numerically. This pattern is statistically steady, is oriented obliquely to the streamwise direction, and has a very large wavelength relative to the gap. The mean flow, averaged in time and in the homogeneous direction, is analysed. The flow in the quasi-laminar region is not the linear Couette profile, but results from a non-trivial balance between advection and diffusion. This force balance yields a first approximation to the relationship between the Reynolds number, angle, and wavelength of the pattern. Remarkably, the variation of the mean flow along the pattern wavevector is found to be almost exactly harmonic: the flow can be represented via only three cross-channel profiles as U(x, y, z) ≈ U0(y) + Uc(y) cos(kz) + Us(y) sin(kz). A model is formulated which relates the cross-channel profiles of the mean flow and of the Reynolds stress. Regimes computed for a full range of angle and Reynolds number in a tilted rectangular periodic computational domain are presented. Observations of regular turbulent–laminar patterns in other shear flows – Taylor–Couette, rotor–stator, and plane Poiseuille – are compared.

Secondary flow in weakly rotating turbulent plane Couette flow

1996 ◽  
Vol 317 ◽  
pp. 195-214 ◽  
Author(s):  
Knut H. Bech ◽  
Helge I. Andersson
Keyword(s):  
Kinetic Energy ◽  
Secondary Flow ◽  
Couette Flow ◽  
Three Dimensional ◽  
Wall Turbulence ◽  
Plane Couette Flow ◽  
Mean Flow ◽  
Comparable Amount ◽  
Flow Vorticity ◽  
Turbulent Plane

As in the laminar case, the turbulent plane Couette flow is unstable (stable) with respect to roll cell instabilities when the weak background angular velocity Ωk is antiparallel (parallel) to the spanwise mean flow vorticity (-dU/dy)k. The critical value of the rotation number Ro, based on 2Ω and dU/dy of the corresponding laminar flow, was estimated as 0.0002 at a low Reynolds number with fully developed turbulence. Direct numerical simulations were performed for Ro = ±0.01 and compared with earlier results for non-rotating Couette flow. At the low rotation rates considered, both senses of rotation damped the turbulence and the number of near-wall turbulence-generating events was reduced. The destabilized flow was more energetic, but less three-dimensional, than the non-rotating flow. In the destabilized case, the two-dimensional roll cells extracted a comparable amount of kinetic energy from the mean flow as did the turbulence, thereby decreasing the turbulent kinetic energy. The turbulence anisotropy was practically unaffected by weak spanwise rotation, while the secondary flow was highly anisotropic due to its inability to contract and expand in the streamwise direction.

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

2017 ◽  
Vol 835 ◽  
pp. 421-443 ◽  
Author(s):  
S. Kraheberger ◽  
S. Hoyas ◽  
M. Oberlack
Keyword(s):  
Boundary Conditions ◽  
Couette Flow ◽  
Transpiration Rate ◽  
Plane Couette Flow ◽  
Simulation Data ◽  
Mean Velocity ◽  
Logarithmic Region ◽  
The Mean ◽  
Turbulent Plane ◽  
Transpiration Velocity

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.

An Upper Bound on the Stress in Plane Couette Flow

1973 ◽  
Vol 95 (4) ◽  
pp. 528-532 ◽  
Author(s):  
E. C. Nickerson
Keyword(s):  
Boundary Layer ◽  
Couette Flow ◽  
Upper Bound ◽  
Energy Integral ◽  
Plane Couette Flow ◽  
Mean Velocity ◽  
Boundary Layer Approximation ◽  
The Mean ◽  
Turbulent Plane ◽  
Consistent Constraint

An absolute upper bound on the momentum number in turbulent plane Couette flow is obtained proportional to the two-thirds power of the Reynolds number. The derivation is based upon the energy integral and the specification of an internally consistent constraint on the fluctuating velocity field. A boundary layer approximation for the mean velocity profile is also obtained and the results are found to be consistent with the two-thirds power law.

scholarly journals Instability wave models for the near-field fluctuations of turbulent jets

2011 ◽  
Vol 689 ◽  
pp. 97-128 ◽  
Author(s):  
K. Gudmundsson ◽  
Tim Colonius
Keyword(s):  
Flow Field ◽  
Large Scale ◽  
Microphone Array ◽  
Near Field ◽  
Turbulent Jets ◽  
Instability Wave ◽  
Mean Flow ◽  
Velocity Fluctuations ◽  
The Mean ◽  
Scale Structures

AbstractPrevious work has shown that aspects of the evolution of large-scale structures, particularly in forced and transitional mixing layers and jets, can be described by linear and nonlinear stability theories. However, questions persist as to the choice of the basic (steady) flow field to perturb, and the extent to which disturbances in natural (unforced), initially turbulent jets may be modelled with the theory. For unforced jets, identification is made difficult by the lack of a phase reference that would permit a portion of the signal associated with the instability wave to be isolated from other, uncorrelated fluctuations. In this paper, we investigate the extent to which pressure and velocity fluctuations in subsonic, turbulent round jets can be described aslinearperturbations to the mean flow field. The disturbances are expanded about the experimentally measured jet mean flow field, and evolved using linear parabolized stability equations (PSE) that account, in an approximate way, for the weakly non-parallel jet mean flow field. We utilize data from an extensive microphone array that measures pressure fluctuations just outside the jet shear layer to show that, up to an unknown initial disturbance spectrum, the phase, wavelength, and amplitude envelope of convecting wavepackets agree well with PSE solutions at frequencies and azimuthal wavenumbers that can be accurately measured with the array. We next apply the proper orthogonal decomposition to near-field velocity fluctuations measured with particle image velocimetry, and show that the structure of the most energetic modes is also similar to eigenfunctions from the linear theory. Importantly, the amplitudes of the modes inferred from the velocity fluctuations are in reasonable agreement with those identified from the microphone array. The results therefore suggest that, to predict, with reasonable accuracy, the evolution of the largest-scale structures that comprise the most energetic portion of the turbulent spectrum of natural jets, nonlinear effects need only be indirectly accounted for by considering perturbations to the mean turbulent flow field, while neglecting any non-zero frequency disturbance interactions.

An Investigation of Flow Fields Over Multi-Element Aerofoils

2001 ◽  
Vol 124 (1) ◽  
pp. 154-165 ◽  
Author(s):  
S. R. Maddah ◽  
H. H. Bruun
Keyword(s):  
Flow Field ◽  
Computational Study ◽  
Separated Flow ◽  
Mean Flow ◽  
Model Configuration ◽  
Attached Flow ◽  
The Mean ◽  
Flap Deflection ◽  
Comparative Results ◽  
Lift And Drag

This paper presents results obtained from a combined experimental and computational study of the flow field over a multi-element aerofoil with and without an advanced slat. Detailed measurements of the mean flow and turbulent quantities over a multi-element aerofoil model in a wind tunnel have been carried out using stationary and flying hot-wire (FHW) probes. The model configuration which spans the test section 600mm×600mm, is made of three parts: 1) an advanced (heel-less) slat, 2) a NACA 4412 main aerofoil and 3) a NACA 4415 flap. The chord lengths of the elements were 38, 250 and 83 mm, respectively. The results were obtained at a chord Reynolds number of 3×105 and a free Mach number of less than 0.1. The variations in the flow field are explained with reference to three distinct flow field regimes: attached flow, intermittent separated flow, and separated flow. Initial comparative results are presented for the single main aerofoil and the main aerofoil with a nondeflected flap at angles of attacks of 5, 10, and 15 deg. This is followed by the results for the three-element aerofoil with emphasis on the slat performance at angles of attack α=10, 15, 20, and 25 deg. Results are discussed both for a nondeflected flap δf=0deg and a deflected flap δf=25deg. The measurements presented are combined with other related aerofoil measurements to explain the main interaction of the slat/main aerofoil and main aerofoil/flap both for nondeflected and deflected flap conditions. These results are linked to numerically calculated variations in lift and drag coefficients with angle of attack and flap deflection angle.

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