Benchmark for scale-resolving simulation with curved walls: the Taylor Couette flow

AbstractFlow between rotating concentric cylinders, or the Taylor Couette flow, has been studied extensively because of its rich physics, ranging from axisymmetric steady laminar flow, to fully developed turbulent flow. In the present study, we advocate the use of this problem as a benchmark case for scale-resolving simulation, such as large eddy simulation (LES) and direct numerical simulation (DNS). The problem is attractive because of its simple geometry, simple boundary conditions, and complex physics involving wall-shear induced and centrifugal instability. Unlike the well-known fully developed channel flow, this problem has a curved wall boundary, and it is unnecessary to add a source term to the governing equations to sustain the fully developed turbulent flow. A p-refinement study for Re = 4000 is performed first to establish DNS data, including the time history of enstrophy, which can be used as an accuracy and resolution indicator to evaluate numerical methods, and is orders of magnitude faster than using the mean flow quantities and Reynolds stresses to evaluate solution quality. Finally, an hp-refinement study is performed to establish the relative accuracy and efficiency of high-order schemes of various accuracy.

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Measurements of mean flow and turbulence characteristics in high-Reynolds number counter-rotating Taylor-Couette flow

Physics of Fluids ◽

10.1063/1.3643738 ◽

2011 ◽

Vol 23 (10) ◽

pp. 105102 ◽

Cited By ~ 11

Author(s):

R. van Hout ◽

J. Katz

Keyword(s):

Reynolds Number ◽

Couette Flow ◽

High Reynolds Number ◽

Mean Flow ◽

Turbulence Characteristics ◽

Taylor Couette ◽

High Reynolds ◽

Taylor Couette Flow

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Direction reversal of a rotating wave in Taylor–Couette flow

Journal of Fluid Mechanics ◽

10.1017/s0022112008002176 ◽

2008 ◽

Vol 607 ◽

pp. 199-208 ◽

Cited By ~ 5

Author(s):

J. ABSHAGEN ◽

M. HEISE ◽

Ch. HOFFMANN ◽

G. PFISTER

Keyword(s):

Aspect Ratio ◽

Couette Flow ◽

Numerical Study ◽

Propagation Speed ◽

Vortex State ◽

Mean Flow ◽

Rotating Wave ◽

Taylor Couette ◽

Direction Reversal ◽

Taylor Couette Flow

In Taylor–Couette systems, waves, e.g. spirals and wavy vortex flow, typically rotate in the same direction as the azimuthal mean flow of the basic flow which is mainly determined by the rotation of the inner cylinder. In a combined experimental and numerical study we analysed a rotating wave of a one-vortex state in small-aspect-ratio Taylor–Couette flow which propagates either progradely or retrogradely in the inertial (laboratory) frame, i.e. in the same or opposite direction as the inner cylinder. The direction reversal from prograde to retrograde can occur at a distinct parameter value where the propagation speed vanishes. Owing to small imperfections of the rotational invariance, the curves of vanishing rotation speed can broaden to ribbons caused by coupling between the end plates and the rotating wave. The bifurcation event underlying the direction reversal is of higher codimension and is unfolded experimentally by three control parameters, i.e. the Reynolds number, the aspect ratio, and the rotation rate of the end plates.

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Experimental investigation of laminar turbulent intermittency in pipe flow

Journal of Fluid Mechanics ◽

10.1017/jfm.2011.189 ◽

2011 ◽

Vol 681 ◽

pp. 193-204 ◽

Cited By ~ 30

Author(s):

DEVRANJAN SAMANTA ◽

ALBERTO DE LOZAR ◽

BJÖRN HOF

Keyword(s):

Couette Flow ◽

Regular Sequence ◽

Flow Speed ◽

Mean Flow ◽

Interaction Length ◽

Low Frequencies ◽

Interaction Distance ◽

Perturbation Frequency ◽

Taylor Couette ◽

Taylor Couette Flow

In shear flows, turbulence first occurs in the form of localized structures (puffs/spots) surrounded by laminar fluid. We here investigate such spatially intermittent flows in a pipe experiment showing that turbulent puffs have a well-defined interaction distance, which sets their minimum spacing as well as the maximum observable turbulent fraction. Two methodologies are employed. Starting from a laminar flow, puffs are first created by locally injecting a jet of fluid through the pipe wall. When the perturbation is applied periodically at low frequencies, as expected, a regular sequence of puffs is observed where the puff spacing is given by the ratio of the mean flow speed to the perturbation frequency. At large frequencies however puffs are found to interact and annihilate each other. Varying the perturbation frequency, an interaction distance is determined which sets the highest possible turbulence fraction. This enables us to establish an upper bound for the friction factor in the transitional regime, which provides a well-defined link between the Blasius and the Hagen-Poiseuille friction laws. In the second set of experiments, the Reynolds number is reduced suddenly from fully turbulent to the intermittent regime. The resulting flow reorganizes itself to a sequence of constant size puffs which, unlike in Couette and Taylor–Couette flow are randomly spaced. The minimum distance between the turbulent patches is identical to the puff interaction length. The puff interaction length is found to be in agreement with the wavelength of regular stripe and spiral patterns in plane Couette and Taylor–Couette flow.

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Momentum transport in Taylor–Couette flow with vanishing curvature

Journal of Fluid Mechanics ◽

10.1017/jfm.2015.737 ◽

2016 ◽

Vol 790 ◽

pp. 419-452 ◽

Cited By ~ 20

Author(s):

Hannes J. Brauckmann ◽

Matthew Salewski ◽

Bruno Eckhardt

Keyword(s):

Couette Flow ◽

Outer Boundary ◽

Momentum Transport ◽

Vortical Flow ◽

Neutral Stability ◽

Mean Flow ◽

Counter Rotation ◽

The Mean ◽

Taylor Couette ◽

Taylor Couette Flow

We numerically study turbulent Taylor–Couette flow (TCF) between two independently rotating cylinders and the transition to rotating plane Couette flow (RPCF) in the limit of infinite radii. By using the shear Reynolds number$Re_{S}$and rotation number$R_{{\it\Omega}}$as dimensionless parameters, the transition from TCF to RPCF can be studied continuously without singularities. Already for radius ratios${\it\eta}\geqslant 0.9$we find that the simulation results for various radius ratios and for RPCF collapse as a function of$R_{{\it\Omega}}$, indicating a turbulent behaviour common to both systems. We observe this agreement in the torque, mean momentum transport, mean profiles and turbulent fluctuations. Moreover, in TCF and RPCF for$R_{{\it\Omega}}>0$, the profiles in the central region are found to conform with inviscid neutral stability. Intermittent bursts, that have been observed in the outer boundary layer and have been linked to the formation of a torque maximum for counter-rotation, are shown to disappear as${\it\eta}\rightarrow 1$. The corresponding torque maximum disappears as well. Instead, two new maxima of different origin appear for${\it\eta}\geqslant 0.9$and RPCF, a broad and a narrow one, in contrast to the results for smaller${\it\eta}$. The broad maximum at$R_{{\it\Omega}}=0.2$is connected with a strong vortical flow and can be reproduced by streamwise-invariant simulations. The narrow maximum at$R_{{\it\Omega}}=0.02$only emerges with increasing$Re_{S}$and is accompanied by an efficient and correlated momentum transport by the mean flow. Since the narrow maximum is of larger amplitude for$Re_{S}=2\times 10^{4}$, our simulations suggest that it will dominate at even higher$Re_{S}$.

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