scholarly journals Turbulent Taylor–Couette flow with stationary inner cylinder

2016 ◽  
Vol 799 ◽  
Author(s):  
R. Ostilla-Mónico ◽  
R. Verzicco ◽  
D. Lohse
Keyword(s):  
Angular Momentum ◽  
Large Scale ◽  
Outer Cylinder ◽  
Reynolds Numbers ◽  
Law Of The Wall ◽  
Large Scale Structures ◽  
Large Gradient ◽  
The Mean ◽  
Taylor Couette ◽  
Cylinder Rotation

A series of direct numerical simulations were performed of Taylor–Couette (TC) flow, the flow between two coaxial cylinders, with the outer cylinder rotating and the inner one fixed. Three cases were considered, where the Reynolds number of the outer cylinder was $Re_{o}=5.5\times 10^{4}$, $Re_{o}=1.1\times 10^{5}$ and $Re_{o}=2.2\times 10^{5}$. The ratio of radii ${\it\eta}=r_{i}/r_{o}$ was fixed to ${\it\eta}=0.909$ to mitigate the effects of curvature. Axially periodic boundary conditions were used, with the aspect ratio of vertical periodicity ${\it\Gamma}$ fixed to ${\it\Gamma}=2.09$. Being linearly stable, TC flow with outer cylinder rotation is known to have very different behaviour than TC flow with pure inner cylinder rotation. Here, we find that the flow nonetheless becomes turbulent, but the torque required to drive the cylinders and level of velocity fluctuations was found to be smaller than those for pure inner cylinder rotation at comparable Reynolds numbers. The mean angular momentum profiles showed a large gradient in the bulk, instead of the constant angular momentum profiles of pure inner cylinder rotation. The near-wall mean and fluctuation velocity profiles were found to coincide only very close to the wall, showing large deviations from both pure inner cylinder rotation profiles and the classic von Karman law of the wall elsewhere. Finally, transport of angular velocity was found to occur mainly through intermittent bursts, and not through wall-attached large-scale structures as is the case for pure inner cylinder rotation.

Axisymmetric Couette flow at large Taylor numbers

1984 ◽  
Vol 144 ◽  
pp. 329-362 ◽  
Author(s):  
A. A. Townsend
Keyword(s):  
Angular Momentum ◽  
Flow Velocity ◽  
Flow Separation ◽  
Large Scale ◽  
Outer Cylinder ◽  
Axial Flow ◽  
Reynolds Numbers ◽  
Small Scale ◽  
Large Scale Motion ◽  
Scale Motion

Measurements have been made in flow between concentric cylinders with only the inner one rotating, for Reynolds numbers (based on flow gap) from 17 000 to 120 000, corresponding to Taylor numbers from 8 × 107 to 4 × 109. At the lower speeds (Reynolds numbers less than 30 000), the large-scale motion consists of toroidal eddies, highly uniform in spacing and intensity and convected by a slow axial flow past fixed sensors. By synchronizing an external oscillator with the passage frequency, flow velocity and small-scale turbulent intensity may be sampled at defined stages of the passage cycle and averaged to provide maps of the velocity fields and the associated distributions of small-scale intensity and Reynolds stress.At higher speeds, the passage of toroidal eddies becomes too irregular to establish the passage cycle, but, by comparing the velocity fluctuations from four inclined hot wires placed near the outer cylinder, the current location of large-scale flow separation from the outer cylinder can be approximately determined. Statistics of the temporal variations of the location show that the large-scale motion still approximates to the toroidal form, but that there are azimuthal variations of separation position and velocity that indicate a change from toroidal to helical eddies. Conditional averages of flow velocity and small-scale turbulent intensity, based on relative distance from the position of flow separation, are very similar in form and magnitude to phase-selected averages obtained at lower speeds.The considerable changes in the large-scale motion that occur as the Reynolds number increases from 300 to 1200 times the critical value are believed to arise from increase in the ‘turbulent Taylor number’ of the central flow, based on variation of angular momentum and on the eddy diffusion coefficients for linear and angular momentum. Effects on the motion of the slow axial flow, always less than 1% of the peripheral flow velocity, are also discussed.

scholarly journals The near-wall region of highly turbulent Taylor–Couette flow

2015 ◽  
Vol 788 ◽  
pp. 95-117 ◽  
Author(s):  
Rodolfo Ostilla-Mónico ◽  
Roberto Verzicco ◽  
Siegfried Grossmann ◽  
Detlef Lohse
Keyword(s):  
Angular Velocity ◽  
Large Scale ◽  
Outer Cylinder ◽  
Axial Flow ◽  
Reynolds Numbers ◽  
Wall Region ◽  
Reynolds Stresses ◽  
Velocity Fluctuations ◽  
Taylor Couette ◽  
Near Wall

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 ${\it\eta}=r_{i}/r_{o}=0.909$, an aspect ratio of ${\it\Gamma}=L/d=2{\rm\pi}/3$, and a stationary outer cylinder. Three inner cylinder Reynolds numbers of $1\times 10^{5}$, $2\times 10^{5}$ and $3\times 10^{5}$ were simulated, corresponding to frictional Reynolds numbers between $Re_{{\it\tau}}\approx 1400$ and $Re_{{\it\tau}}\approx 4000$. An additional case with a large gap, ${\it\eta}=0.5$ and driving of $Re=2\times 10^{5}$ was also investigated. 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 was also conducted with inner cylinder Reynolds number of $Re=1\times 10^{5}$ and fixed outer cylinder with an externally imposed axial flow of comparable strength to the wind of the TRs. The axial flow was found to convect the TRs without any weakening effect. For small-gap TC flow, evidence was found for the existence of logarithmic velocity fluctuations, and of an overlap layer, in which the velocity fluctuations collapse in outer units. Profiles consistent with a logarithmic dependence were also found for the angular velocity in large-gap TC flow, albeit in a very reduced range of scales. Finally, the behaviour of both small- and large-gap TC flow was compared to other canonical flows. Small-gap TC flow has similar behaviour in the near-wall region to other canonical flows, while large-gap TC flow displays very different behaviour.

Turbulent flow between counter-rotating concentric cylinders: a direct numerical simulation study

2008 ◽  
Vol 615 ◽  
pp. 371-399 ◽  
Author(s):  
S. DONG
Keyword(s):  
Turbulent Flow ◽  
Large Scale ◽  
Outer Cylinder ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Taylor Vortex ◽  
Small Scale ◽  
Mean Flow ◽  
Concentric Cylinders ◽  
High Reynolds

We report three-dimensional direct numerical simulations of the turbulent flow between counter-rotating concentric cylinders with a radius ratio 0.5. The inner- and outer-cylinder Reynolds numbers have the same magnitude, which ranges from 500 to 4000 in the simulations. We show that with the increase of Reynolds number, the prevailing structures in the flow are azimuthal vortices with scales much smaller than the cylinder gap. At high Reynolds numbers, while the instantaneous small-scale vortices permeate the entire domain, the large-scale Taylor vortex motions manifested by the time-averaged field do not penetrate a layer of fluid near the outer cylinder. Comparisons between the standard Taylor–Couette system (rotating inner cylinder, fixed outer cylinder) and the counter-rotating system demonstrate the profound effects of the Coriolis force on the mean flow and other statistical quantities. The dynamical and statistical features of the flow have been investigated in detail.

scholarly journals Azimuthal velocity profiles in Rayleigh-stable Taylor–Couette flow and implied axial angular momentum transport

2015 ◽  
Vol 774 ◽  
pp. 342-362 ◽  
Author(s):  
Freja Nordsiek ◽  
Sander G. Huisman ◽  
Roeland C. A. van der Veen ◽  
Chao Sun ◽  
Detlef Lohse ◽  
...  
Keyword(s):  
Angular Momentum ◽  
Couette Flow ◽  
Outer Cylinder ◽  
Azimuthal Velocity ◽  
Velocity Profiles ◽  
Body Rotation ◽  
Solid Body Rotation ◽  
Angular Momentum Transport ◽  
Taylor Couette ◽  
Taylor Couette Flow

We present azimuthal velocity profiles measured in a Taylor–Couette apparatus, which has been used as a model of stellar and planetary accretion disks. The apparatus has a cylinder radius ratio of ${\it\eta}=0.716$, an aspect ratio of ${\it\Gamma}=11.74$, and the plates closing the cylinders in the axial direction are attached to the outer cylinder. We investigate angular momentum transport and Ekman pumping in the Rayleigh-stable regime. This regime is linearly stable and is characterized by radially increasing specific angular momentum. We present several Rayleigh-stable profiles for shear Reynolds numbers $\mathit{Re}_{S}\sim O(10^{5})$, for both ${\it\Omega}_{i}>{\it\Omega}_{o}>0$ (quasi-Keplerian regime) and ${\it\Omega}_{o}>{\it\Omega}_{i}>0$ (sub-rotating regime), where ${\it\Omega}_{i,o}$ is the inner/outer cylinder rotation rate. None of the velocity profiles match the non-vortical laminar Taylor–Couette profile. The deviation from that profile increases as solid-body rotation is approached at fixed $\mathit{Re}_{S}$. Flow super-rotation, an angular velocity greater than those of both cylinders, is observed in the sub-rotating regime. The velocity profiles give lower bounds for the torques required to rotate the inner cylinder that are larger than the torques for the case of laminar Taylor–Couette flow. The quasi-Keplerian profiles are composed of a well-mixed inner region, having approximately constant angular momentum, connected to an outer region in solid-body rotation with the outer cylinder and attached axial boundaries. These regions suggest that the angular momentum is transported axially to the axial boundaries. Therefore, Taylor–Couette flow with closing plates attached to the outer cylinder is an imperfect model for accretion disk flows, especially with regard to their stability.

LDV and PIV Velocity Results in a Thermosiphon

2003 ◽  
Author(s):  
J. Kulman ◽  
D. Gray ◽  
S. Sivanagere ◽  
S. Guffey
Keyword(s):  
Large Scale ◽  
Single Phase ◽  
Flow Characteristics ◽  
Reynolds Numbers ◽  
Flow Patterns ◽  
Laser Doppler Velocimeter ◽  
Mean Velocity ◽  
Developed Turbulence ◽  
The Mean ◽  
Good Agreement

Heat transfer and flow characteristics have been determined for a single-phase rectangular loop thermosiphon. The plane of the loop was vertical, and tests were performed with in-plane tilt angles ranging from 3.6° CW to 4.2° CCW. Velocity profiles were measured in one vertical leg of the loop using both a single-component Laser Doppler Velocimeter (LDV), and a commercial Particle Image Velocimeter (PIV) system. The LDV data and PIV data were found to be in good agreement. The measured average velocities were approximately 2–2.5 cm/s at an average heating rate of 70 W, and were independent of tilt angle. Significant RMS fluctuations of 10–20% of the mean velocity were observed in the test section, in spite of the laminar or transitional Reynolds numbers (order of 700, based on the hydraulic diameter). These fluctuations have been attributed to vortex shedding from the upstream temperature probes and mitre bends, rather than to fully developed turbulence. Animations of the PIV data clearly show these large scale unsteady flow patterns. Multiple steady state flow patterns were not observed.

scholarly journals Optimal Taylor–Couette flow: direct numerical simulations

2013 ◽  
Vol 719 ◽  
pp. 14-46 ◽  
Author(s):  
Rodolfo Ostilla ◽  
Richard J. A. M. Stevens ◽  
Siegfried Grossmann ◽  
Roberto Verzicco ◽  
Detlef Lohse
Keyword(s):  
Angular Velocity ◽  
Couette Flow ◽  
Scaling Laws ◽  
Outer Cylinder ◽  
Reynolds Numbers ◽  
Velocity Profiles ◽  
Experimental Result ◽  
Counter Rotation ◽  
Taylor Couette ◽  
Taylor Couette Flow

AbstractWe numerically simulate turbulent Taylor–Couette flow for independently rotating inner and outer cylinders, focusing on the analogy with turbulent Rayleigh–Bénard flow. Reynolds numbers of $R{e}_{i} = 8\times 1{0}^{3} $ and $R{e}_{o} = \pm 4\times 1{0}^{3} $ of the inner and outer cylinders, respectively, are reached, corresponding to Taylor numbers $Ta$ up to $1{0}^{8} $. Effective scaling laws for the torque and other system responses are found. Recent experiments with the Twente Turbulent Taylor–Couette (${T}^{3} C$) setup and with a similar facility in Maryland at very high Reynolds numbers have revealed an optimum transport at a certain non-zero rotation rate ratio $a= - {\omega }_{o} / {\omega }_{i} $ of about ${a}_{\mathit{opt}} = 0. 33$. For large enough $Ta$ in the numerically accessible range we also find such an optimum transport at non-zero counter-rotation. The position of this maximum is found to shift with the driving, reaching a maximum of ${a}_{\mathit{opt}} = 0. 15$ for $Ta= 2. 5\times 1{0}^{7} $. An explanation for this shift is elucidated, consistent with the experimental result that ${a}_{\mathit{opt}} $ becomes approximately independent of the driving strength for large enough Reynolds numbers. We furthermore numerically calculate the angular velocity profiles and visualize the different flow structures for the various regimes. By writing the equations in a frame co-rotating with the outer cylinder a link is found between the local angular velocity profiles and the global transport quantities.

A supersonic turbulent boundary layer in an adverse pressure gradient

1990 ◽  
Vol 211 ◽  
pp. 285-307 ◽  
Author(s):  
Emerick M. Fernando ◽  
Alexander J. Smits
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Pressure Gradient ◽  
Pressure Distribution ◽  
Large Scale ◽  
Adverse Pressure Gradient ◽  
Large Scale Structures ◽  
Streamline Curvature ◽  
The Mean ◽  
Scale Structures

This investigation describes the effects of an adverse pressure gradient on a flat plate supersonic turbulent boundary layer (Mf ≈ 2.9, βx ≈ 5.8, Reθ, ref ≈ 75600). Single normal hot wires and crossed wires were used to study the Reynolds stress behaviour, and the features of the large-scale structures in the boundary layer were investigated by measuring space–time correlations in the normal and spanwise directions. Both the mean flow and the turbulence were strongly affected by the pressure gradient. However, the turbulent stress ratios showed much less variation than the stresses, and the essential nature of the large-scale structures was unaffected by the pressure gradient. The wall pressure distribution in the current experiment was designed to match the pressure distribution on a previously studied curved-wall model where streamline curvature acted in combination with bulk compression. The addition of streamline curvature affects the turbulence strongly, although its influence on the mean velocity field is less pronounced and the modifications to the skin-friction distribution seem to follow the empirical correlations developed by Bradshaw (1974) reasonably well.

Vortex-Excited Response of Large-Scale Cylinders in Sheared Flow

1988 ◽  
Vol 110 (3) ◽  
pp. 272-277 ◽  
Author(s):  
J. A. Humphries ◽  
D. H. Walker
Keyword(s):  
Large Scale ◽  
Shear Velocity ◽  
Reynolds Numbers ◽  
Hydrodynamic Drag ◽  
Flow Induced Vibration ◽  
Sheared Flow ◽  
Drag Forces ◽  
Linear Shear ◽  
Series Of Experiments ◽  
The Mean

A series of experiments were performed to measure the vortex-excited response of a 0.168-m-dia slender circular cylinder in a range of linear shear velocity profiles. Reynolds numbers of up to 2.5 × 105 were achieved. The results clearly showed that regular large-amplitude cylinder vibrations occurred well within the critical drag transition region. It was found that increasing the linear shear profile decreased the peak amplitude response but broadened the range of lock-on over which large oscillations occurred. The flow-induced vibration of the cylinder caused amplification of the mean hydrodynamic drag forces acting on the cylinder when compared with those expected for a similar rigid cylinder.

scholarly journals Transient growth in linearly stable Taylor–Couette flows

2014 ◽  
Vol 742 ◽  
pp. 254-290 ◽  
Author(s):  
Simon Maretzke ◽  
Björn Hof ◽  
Marc Avila
Keyword(s):  
Linear Stability ◽  
Reynolds Numbers ◽  
Transition To Turbulence ◽  
Transient Growth ◽  
Energy Growth ◽  
Transient Energy ◽  
Taylor Couette ◽  
Semi Empirical ◽  
Essential Prerequisite ◽  
Cylinder Rotation

AbstractNon-normal transient growth of disturbances is considered as an essential prerequisite for subcritical transition in shear flows, i.e. transition to turbulence despite linear stability of the laminar flow. In this work we present numerical and analytical computations of linear transient growth covering all linearly stable regimes of Taylor–Couette flow. Our numerical experiments reveal comparable energy amplifications in the different regimes. For high shear Reynolds numbers$\mathit{Re}$, the optimal transient energy growth always follows a$\mathit{Re}^{2/3}$scaling, which allows for large amplifications even in regimes where the presence of turbulence remains debated. In co-rotating Rayleigh-stable flows, the optimal perturbations become increasingly columnar in their structure, as the optimal axial wavenumber goes to zero. In this limit of axially invariant perturbations, we show that linear stability and transient growth are independent of the cylinder rotation ratio and we derive a universal$\mathit{Re}^{2/3}$scaling of optimal energy growth using Wentzel–Kramers–Brillouin theory. Based on this, a semi-empirical formula for the estimation of linear transient growth valid in all regimes is obtained.

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