Turbulent Couette Flow

1974 ◽  
Vol 96 (3) ◽  
pp. 265-271 ◽  
Author(s):  
A. K. Wang ◽  
L. W. Gelhar
Keyword(s):  
Energy Balance ◽  
Couette Flow ◽  
Outer Cylinder ◽  
Mixing Length ◽  
Plane Couette Flow ◽  
Rotating Cylinders ◽  
Mean Velocity ◽  
Balance Hypothesis ◽  
The Mean ◽  
Theoretical Results

Turbulent flow between concentric rotating cylinders is analyzed using an energy balance hypothesis proposed by Zagustin. Predictions of the mean velocity profiles are obtained without any additional assumptions regarding the distribution of mixing length. The theoretical results compare favorably with previous observations with only the inner or outer cylinder rotating, and with new data for counter-rotating cylinders. The theoretical results are also consistent with observed features of plane Couette flow.

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.

ON FULLY DEVELOPED TURBULENT FLOW IN CURVED CHANNELS

1956 ◽  
Vol 34 (11) ◽  
pp. 1134-1146 ◽  
Author(s):  
A. W. Marris
Keyword(s):  
Experimental Data ◽  
Turbulent Flow ◽  
Velocity Distribution ◽  
Radius Of Curvature ◽  
Mixing Length ◽  
Mean Velocity ◽  
Curved Channels ◽  
Fully Developed Turbulent Flow ◽  
The Mean ◽  
Theoretical Results

Formulae for the radial distribution of velocity and vorticity for the case of fully developed turbulent flow in the channel between concentric and infinitely long cylinders are developed on a similarity vorticity transfer theory, by postulating an Eulerian mixing length function dependent on both position and radius of curvature. The theoretical results obtained for the mean velocity distribution across the channel compare satisfactorily with existing experimental data when the curvature dependent parameters are given appropriate numerical values.

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.

Optimal energy growth in stably stratified turbulent Couette flow

2021 ◽  
Author(s):  
Grigory Zasko ◽  
Andrey Glazunov ◽  
Evgeny Mortikov ◽  
Yuri Nechepurenko ◽  
Pavel Perezhogin
Keyword(s):  
Boundary Layer ◽  
Turbulent Flow ◽  
Couette Flow ◽  
Large Scale ◽  
Thin Layers ◽  
Plane Couette Flow ◽  
Turbulent Layer ◽  
Wide Range ◽  
The Mean ◽  
Optimal Disturbances

<p>In this report, we will try to explain the emergence of large-scale organized structures in stably stratified turbulent flows using optimal disturbances of the mean turbulent flow. These structures have been recently obtained in numerical simulations of turbulent stably stratified flows [1] (Ekman layer, LES) and [2] (plane Couette flow, DNS and LES) and indirectly confirmed by field measurements in the stable boundary layer of the atmosphere [1, 2]. In instantaneous temperature fields they manifest themselves as irregular inclined thin layers with large gradients (fronts), spaced from each other by distances comparable to the height of the entire turbulent layer, and separated by regions with weak stratification.</p><p>Optimal disturbances of a stably stratified turbulent plane Couette flow are investigated in a wide range of Reynolds and Richardson numbers. These disturbances were computed based on a simplified linearized system of equations in which turbulent Reynolds stresses and heat fluxes were approximated by isotropic viscosity and diffusion with coefficients obtained from DNS results. It was shown [3] that the spatial scales and configurations of the inclined structures extracted from DNS data coincide with the ones obtained from optimal disturbances of the mean turbulent flow.</p><p>Critical value of the stability parameter is found starting from which the optimal disturbances resemble inclined structures. The physical mechanisms that determine the evolution, energetics and spatial configuration of these optimal disturbances are discussed. The effects due to the presence of stable stratification are highlighted.</p><p>Numerical experiments with optimal disturbances were supported by the RSF (grant No. 17-71-20149). Direct numerical simulation of stratified turbulent Couette flow was supported by the RFBR (grant No. 20-05-00776).</p><p>References:</p><p>[1] P.P. Sullivan, J.C. Weil, E.G. Patton, H.J. Jonker, D.V. Mironov. Turbulent winds and temperature fronts in large-eddy simulations of the stable atmospheric boundary layer // J. Atmos. Sci., 2016, V. 73, P. 1815-1840.</p><p>[2] A.V. Glazunov, E.V. Mortikov, K.V. Barskov, E.V. Kadantsev, S.S. Zilitinkevich. Layered structure of stably stratified turbulent shear flows // Izv. Atmos. Ocean. Phys., 2019, V. 55, P. 312–323.</p><p>[3] G.V. Zasko, A.V. Glazunov, E.V. Mortikov, Yu.M. Nechepurenko. Large-scale structures in stratified turbulent Couette flow and optimal disturbances // Russ. J. Num. Anal. Math. Model., 2010, V. 35, P. 35–53.</p>

scholarly journals Exploring the phase diagram of fully turbulent Taylor–Couette flow

2014 ◽  
Vol 761 ◽  
pp. 1-26 ◽  
Author(s):  
Rodolfo Ostilla-Mónico ◽  
Erwin P. van der Poel ◽  
Roberto Verzicco ◽  
Siegfried Grossmann ◽  
Detlef Lohse
Keyword(s):  
Phase Diagram ◽  
Reynolds Number ◽  
Couette Flow ◽  
Parameter Space ◽  
Coriolis Force ◽  
Scaling Laws ◽  
Outer Cylinder ◽  
Rotating Cylinders ◽  
Aspect Ratios ◽  
Cylinder Rotation

AbstractDirect numerical simulations of Taylor–Couette flow, i.e. the flow between two coaxial and independently rotating cylinders, were performed. Shear Reynolds numbers of up to $3\times 10^{5}$, corresponding to Taylor numbers of $\mathit{Ta}=4.6\times 10^{10}$, were reached. Effective scaling laws for the torque are presented. The transition to the ultimate regime, in which asymptotic scaling laws (with logarithmic corrections) for the torque are expected to hold up to arbitrarily high driving, is analysed for different radius ratios, different aspect ratios and different rotation ratios. It is shown that the transition is approximately independent of the aspect and rotation ratios, but depends significantly on the radius ratio. We furthermore calculate the local angular velocity profiles and visualize different flow regimes that depend both on the shearing of the flow, and the Coriolis force originating from the outer cylinder rotation. Two main regimes are distinguished, based on the magnitude of the Coriolis force, namely the co-rotating and weakly counter-rotating regime dominated by Rayleigh-unstable regions, and the strongly counter-rotating regime where a mixture of Rayleigh-stable and Rayleigh-unstable regions exist. Furthermore, an analogy between radius ratio and outer-cylinder rotation is revealed, namely that smaller gaps behave like a wider gap with co-rotating cylinders, and that wider gaps behave like smaller gaps with weakly counter-rotating cylinders. Finally, the effect of the aspect ratio on the effective torque versus Taylor number scaling is analysed and it is shown that different branches of the torque-versus-Taylor relationships associated to different aspect ratios are found to cross within 15 % of the Reynolds number associated to the transition to the ultimate regime. The paper culminates in phase diagram in the inner versus outer Reynolds number parameter space and in the Taylor versus inverse Rossby number parameter space, which can be seen as the extension of the Andereck et al. (J. Fluid Mech., vol. 164, 1986, pp. 155–183) phase diagram towards the ultimate regime.

A resonance mechanism in plane Couette flow

1980 ◽  
Vol 98 (1) ◽  
pp. 149-159 ◽  
Author(s):  
L. HÅKan Gustavsson ◽  
Lennart S. Hultgren
Keyword(s):  
Reynolds Number ◽  
Couette Flow ◽  
Velocity Component ◽  
Three Dimensional ◽  
Phase Speed ◽  
Maximum Amplitude ◽  
Streamwise Velocity ◽  
Plane Couette Flow ◽  
Mean Velocity ◽  
Streamwise Velocity Component

The temporal evolution of small three-dimensional disturbances on viscous flows between parallel walls is studied. The initial-value problem is formally solved by using Fourier–Laplace transform techniques. The streamwise velocity component is obtained as the solution of a forced problem. As a consequence of the three-dimensionality, a resonant response is possible, leading to algebraic growth for small times. It occurs when the eigenvalues of the Orr–Sommerfeld equation coincide with the eigenvalues of the homogeneous operator for the streamwise velocity component. The resonance has been investigated numerically for plane Couette flow. The phase speed of the resonant waves equals the average mean velocity. The wavenumber combination that leads to the largest amplitude corresponds to structures highly elongated in the streamwise direction. The maximum amplitude, and the time to reach this maximum, scale with the Reynolds number. The aspect ratio of the most rapidly growing wave increases with the Reynolds number, with its spanwise wavelength approaching a constant value of about 3 channel heights.

Weakly nonlinear theory of shear-banding instability in a granular plane Couette flow: analytical solution, comparison with numerics and bifurcation

2010 ◽  
Vol 666 ◽  
pp. 204-253 ◽  
Author(s):  
PRIYANKA SHUKLA ◽  
MEHEBOOB ALAM
Keyword(s):  
Couette Flow ◽  
Shear Banding ◽  
Base Flow ◽  
Plane Couette Flow ◽  
Weakly Nonlinear ◽  
Subcritical Bifurcation ◽  
Supercritical Bifurcation ◽  
Weakly Nonlinear Theory ◽  
Pitchfork Bifurcations ◽  
The Mean

A weakly nonlinear theory, in terms of the well-known Landau equation, has been developed to describe the nonlinear saturation of the shear-banding instability in a rapid granular plane Couette flow using the amplitude expansion method. The nonlinear modes are found to follow certain symmetries of the base flow and the fundamental mode, which helped to identify analytical solutions for the base-flow distortion and the second harmonic, leading to an exact calculation of the first Landau coefficient. The present analytical solutions are used to validate a spectral-based numerical method for the nonlinear stability calculation. The regimes of supercritical and subcritical bifurcations for the shear-banding instability have been identified, leading to the prediction that the lower branch of the neutral stability contour in the (H, φ0)-plane, where H is the scaled Couette gap (the ratio between the Couette gap and the particle diameter) and φ0 is the mean density or the volume fraction of particles, is subcritically unstable. The predicted finite-amplitude solutions represent shear localization and density segregation along the gradient direction. Our analysis suggests that there is a sequence of transitions among three types of pitchfork bifurcations with increasing mean density: from (i) the bifurcation from infinity in the Boltzmann limit to (ii) subcritical bifurcation at moderate densities to (iii) supercritical bifurcation at larger densities to (iv) subcritical bifurcation in the dense limit and finally again to (v) supercritical bifurcation near the close packing density. It has been shown that the appearance of subcritical bifurcation in the dense limit depends on the choice of the contact radial distribution function and the constitutive relations. The scalings of the first Landau coefficient, the equilibrium amplitude and the phase diagram, in terms of mode number and inelasticity, have been demonstrated. The granular plane Couette flow serves as a paradigm that supports all three possible types of pitchfork bifurcations, with the mean density (φ0) being the single control parameter that dictates the nature of the bifurcation. The predicted bifurcation scenario for the shear-band formation is in qualitative agreement with particle dynamics simulations and the experiment in the rapid shear regime of the granular plane Couette flow.

The Ultimate Asymptote and Mean Flow Structure in Toms’ Phenomenon

1970 ◽  
Vol 37 (2) ◽  
pp. 488-493 ◽  
Author(s):  
P. S. Virk ◽  
H. S. Mickley ◽  
K. A. Smith
Keyword(s):  
Velocity Profile ◽  
Drag Reduction ◽  
Flow Structure ◽  
Viscous Sublayer ◽  
Mixing Length ◽  
Mean Flow ◽  
Mean Velocity ◽  
Law Of The Wall ◽  
Length Constant ◽  
The Mean

The maximum drag reduction in turbulent pipe flow of dilute polymer solutions is ultimately limited by a unique asymptote described by the experimental correlation: f−1/2=19.0log10(NRef1/2)−32.4 The semilogarithmic mean velocity profile corresponding to and inferred from this ultimate asymptote has a mixing-length constant of 0.085 and shares a trisection (at y+ ∼ 12) with the Newtonian viscous sublayer and law of the wall. Experimental mean velocity profiles taken during drag reduction lie in the region bounded by the inferred ultimate profile and the Newtonian law of the wall. At low drag reductions the experimental profiles are well correlated by an “effective slip” model but this fails progressively with increasing drag reduction. Based on the foregoing a three-zone scheme is proposed to model the mean flow structure during drag reduction. In this the mean velocity profile segments are (a) a viscous sublayer, akin to Newtonian, (b) an interactive zone, characteristic of drag reduction, in which the ultimate profile is followed, and (c) a turbulent core in which the Newtonian mixing-length constant applies. The proposed model is consistent with experimental observations and reduces satisfactorily to the Taylor-Prandtl scheme and the ultimate profile, respectively, at the limits of zero and maximum drag reductions.

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