Angular momentum transport and flow organization in Taylor-Couette flow at radius ratio of η=0.357

2019 ◽  
Vol 4 (8) ◽  
Author(s):  
Andreas Froitzheim ◽  
Sebastian Merbold ◽  
Rodolfo Ostilla-Mónico ◽  
Christoph Egbers
Keyword(s):  
Angular Momentum ◽  
Couette Flow ◽  
Radius Ratio ◽  
Momentum Transport ◽  
Angular Momentum Transport ◽  
Taylor Couette ◽  
Taylor Couette Flow

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.

scholarly journals Heat transport in Rayleigh–Bénard convection and angular momentum transport in Taylor–Couette flow: a comparative study

2017 ◽  
Vol 375 (2089) ◽  
pp. 20160079 ◽  
Author(s):  
Hannes J. Brauckmann ◽  
Bruno Eckhardt ◽  
Jörg Schumacher
Keyword(s):  
Angular Momentum ◽  
Couette Flow ◽  
Nusselt Numbers ◽  
Bénard Convection ◽  
Benard Convection ◽  
Taylor Couette ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard ◽  
Good Agreement ◽  
Taylor Couette Flow

Rayleigh–Bénard convection and Taylor–Couette flow are two canonical flows that have many properties in common. We here compare the two flows in detail for parameter values where the Nusselt numbers, i.e. the thermal transport and the angular momentum transport normalized by the corresponding laminar values, coincide. We study turbulent Rayleigh–Bénard convection in air at Rayleigh number Ra =10 7 and Taylor–Couette flow at shear Reynolds number Re S =2×10 4 for two different mean rotation rates but the same Nusselt numbers. For individual pairwise related fields and convective currents, we compare the probability density functions normalized by the corresponding root mean square values and taken at different distances from the wall. We find one rotation number for which there is very good agreement between the mean profiles of the two corresponding quantities temperature and angular momentum. Similarly, there is good agreement between the fluctuations in temperature and velocity components. For the heat and angular momentum currents, there are differences in the fluctuations outside the boundary layers that increase with overall rotation and can be related to differences in the flow structures in the boundary layer and in the bulk. The study extends the similarities between the two flows from global quantities to local quantities and reveals the effects of rotation on the transport. This article is part of the themed issue ‘Toward the development of high-fidelity models of wall turbulence at large Reynolds number’.

scholarly journals Stratorotational instability in Taylor–Couette flow heated from above

2009 ◽  
Vol 623 ◽  
pp. 375-385 ◽  
Author(s):  
M. GELLERT ◽  
G. RÜDIGER
Keyword(s):  
Angular Momentum ◽  
Temperature Gradient ◽  
Axisymmetric Flow ◽  
Boussinesq Approximation ◽  
Momentum Transport ◽  
Angular Momentum Transport ◽  
Axial Temperature ◽  
Small Temperature Gradient ◽  
Taylor Couette ◽  
Set Up

We investigate the instability and nonlinear saturation of temperature-stratified Taylor–Couette flows in a finite height cylindrical gap and calculate angular momentum transport in the nonlinear regime. The model is based on an incompressible fluid in Boussinesq approximation with a positive axial temperature gradient applied. While both ingredients, the differential rotation as well as the stratification due to the temperature gradient, are stable themselves, together the system becomes subject of the stratorotational instability and a non-axisymmetric flow pattern evolves. This flow configuration transports angular momentum outwards and will therefore be relevant for astrophysical applications. The belonging coefficient of β viscosity is of the order of unity if the results are adapted to the size of an accretion disk. The strength of the stratification, the fluid's Prandtl number and the boundary conditions applied in the simulations are well suited too for a laboratory experiment using water and a small temperature gradient around 5 K. With such a set-up the stratorotational instability and its angular momentum transport could be measured in an experiment.

scholarly journals Double maxima of angular momentum transport in small gap Taylor–Couette turbulence

2020 ◽  
Vol 900 ◽  
Author(s):  
Rodrigo Ezeta ◽  
Francesco Sacco ◽  
Dennis Bakhuis ◽  
Sander G. Huisman ◽  
Rodolfo Ostilla-Mónico ◽  
...  
Keyword(s):  
Angular Momentum ◽  
Momentum Transport ◽  
Angular Momentum Transport ◽  
Taylor Couette ◽  
Image Position

Abstract

scholarly journals Optimal Taylor–Couette flow: radius ratio dependence

2014 ◽  
Vol 747 ◽  
pp. 1-29 ◽  
Author(s):  
Rodolfo Ostilla-Mónico ◽  
Sander G. Huisman ◽  
Tim J. G. Jannink ◽  
Dennis P. M. Van Gils ◽  
Roberto Verzicco ◽  
...  
Keyword(s):  
Couette Flow ◽  
Scaling Laws ◽  
Reynolds Numbers ◽  
Radius Ratio ◽  
System Response ◽  
Rossby Number ◽  
Theoretical Predictions ◽  
Taylor Couette ◽  
Set Up ◽  
Taylor Couette Flow

AbstractTaylor–Couette flow with independently rotating inner ($i$) and outer ($o$) cylinders is explored numerically and experimentally to determine the effects of the radius ratio $\eta $ on the system response. Numerical simulations reach Reynolds numbers of up to $\mathit{Re}_i=9.5\times 10^3$ and $\mathit{Re}_o=5\times 10^3$, corresponding to Taylor numbers of up to $\mathit{Ta}=10^8$ for four different radius ratios $\eta =r_i/r_o$ between 0.5 and 0.909. The experiments, performed in the Twente Turbulent Taylor–Couette ($\mathrm{T^3C}$) set-up, reach Reynolds numbers of up to $\mathit{Re}_i=2\times 10^6$ and $\mathit{Re}_o=1.5\times 10^6$, corresponding to $\mathit{Ta}=5\times 10^{12}$ for $\eta =0.714\mbox{--}0.909$. Effective scaling laws for the torque $J^{\omega }(\mathit{Ta})$ are found, which for sufficiently large driving $\mathit{Ta}$ are independent of the radius ratio $\eta $. As previously reported for $\eta =0.714$, optimum transport at a non-zero Rossby number $\mathit{Ro}=r_i |\omega _i-\omega _o |/[2(r_o-r_i)\omega _o]$ is found in both experiments and numerics. Here $\mathit{Ro}_{opt}$ is found to depend on the radius ratio and the driving of the system. At a driving in the range between $\mathit{Ta}\sim 3\times 10^{8}$ and $\mathit{Ta}\sim 10^{10}$, $\mathit{Ro}_{opt}$ saturates to an asymptotic $\eta $-dependent value. Theoretical predictions for the asymptotic value of $\mathit{Ro}_{opt}$ are compared to the experimental results, and found to differ notably. Furthermore, the local angular velocity profiles from experiments and numerics are compared, and a link between a flat bulk profile and optimum transport for all radius ratios is reported.

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