Sander G. Huisman

Torque Scaling in Turbulent Taylor-Couette Flow with Co- and Counterrotating Cylinders

We analyze the global transport properties of turbulent Taylor-Couette flow in the strongly turbulent regime for independently rotating outer and inner cylinders, reaching Reynolds numbers of the inner and outer cylinders of Re(i) = 2×10(6) and Re(o) = ±1.4×10(6), respectively. For all Re(i), Re(o), the dimensionless torque G scales as a function of the Taylor number Ta (which is proportional to the square of the difference between the angular velocities of the inner and outer cylinders) with a universal effective scaling law G ∝ Ta(0.88), corresponding to Nu(ω) ∝ Ta(0.38) for the Nusselt number characterizing the angular velocity transport between the inner and outer cylinders. The exponent 0.38 corresponds to the ultimate regime scaling for the analogous Rayleigh-Bénard system. The transport is most efficient for the counterrotating case along the diagonal in phase space with ω(o) ≈ -0.4ω(i).

Ultimate Turbulent Taylor-Couette Flow

The flow structure of strongly turbulent Taylor-Couette flow with Reynolds numbers up to Re(i)=2×10(6) of the inner cylinder is experimentally examined with high-speed particle image velocimetry (PIV). The wind Reynolds numbers Re(w) of the turbulent Taylor-vortex flow is found to scale as Re(w)∝Ta(1/2), exactly as predicted by Grossmann and Lohse [Phys. Fluids 23, 045108 (2011).] for the ultimate turbulence regime, in which the boundary layers are turbulent. The dimensionless angular velocity flux has an effective scaling of Nu(ω)∝Ta(0.38), also in correspondence with turbulence in the ultimate regime. The scaling of Nu(ω) is confirmed by local angular velocity flux measurements extracted from high-speed PIV measurements: though the flux shows huge fluctuations, its spatial and temporal average nicely agrees with the result from the global torque measurements.

Multiple states in highly turbulent Taylor-Couette flow

The ubiquity of turbulent flows in nature and technology makes it of utmost importance to fundamentally understand turbulence. Kolmogorovs 1941 paradigm suggests that for strongly turbulent flows with many degrees of freedom and large fluctuations, there would only be one turbulent state as the large fluctuations would explore the entire higher dimensional phase space. Here we report the first conclusive evidence of multiple turbulent states for large Reynolds number, Re = O(10(6)) (Taylor number Ta = O(10(12))) Taylor-Couette flow in the regime of ultimate turbulence, by probing the phase space spanned by the rotation rates of the inner and outer cylinder. The manifestation of multiple turbulent states is exemplified by providing combined global torque- and local-velocity measurements. This result verifies the notion that bifurcations can occur in high-dimensional flows (that is, very large Re) and questions Kolmogorovs paradigm.

Optimal Taylor-Couette flow: radius ratio dependence

Taylor–Couette flow with independently rotating inner (i) & outer (o) cylinders is explored numerically and experimentally to determine the effects of the radius ratio η on the system response. Numerical simulations reach Reynolds numbers of up to Rei = 9.5·10 3 and Reo = 5·10 3 , corresponding to Taylor numbers of up to Ta = 10 8 for four different radius ratios η = ri/ro between 0.5 and 0.909. The experiments, performed in the Twente Turbulent Taylor–Couette (T 3 C) setup, reach Reynolds numbers of up to Rei = 2·10 6 and Reo = 1.5·10 6 , corresponding to Ta = 5·10 12 for η = 0.714−0.909. Effective scaling laws for the torque J ω (Ta) are found, which for sufficiently large drivingTa are independent of the radius ratio η. As previously reported for η = 0.714, optimum transport at a non–zero Rossby number Ro = ri|ωi − ωo|/[2(ro − ri)ωo] is found in both experiments and numerics. Roopt is found to depend on the radius ratio and the driving of the system. At a driving in the range between Ta ∼ 3·10 8 and Ta ∼ 10 10 , Roopt saturates to an asymptotic η-dependent value. Theoretical predictions for the asymptotic value of Roopt 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.

Applying laser Doppler anemometry inside a Taylor-Couette geometry using a ray-tracer to correct for curvature effects

In the present work it will be shown how the curvature of the outer cylinder affects laser Doppler anemometry measurements inside a Taylor?Couette apparatus. The measurement position and the measured velocity are altered by curved surfaces. Conventional methods for curvature correction are not applicable to our setup, and it will be shown how a ray-tracer can be used to solve this complication. By using a ray-tracer the focal position can be calculated, and the velocity can be corrected. The results of the ray-tracer are verified by measuring an a priori known velocity field, and after applying refractive corrections good agreement with theoretical predictions are found. The methods described in this paper are applied to measure the azimuthal velocity profiles in high Reynolds number Taylor?Couette flow for the case of outer cylinder rotation.

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

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

Wall roughness induces asymptotic ultimate turbulence

\eta = 0.716

Statistics of turbulent fluctuations in counter-rotating Taylor-Couette flows

, an aspect-ratio of

Taylor–Couette turbulence at radius ratio η=0.5: scaling, flow structures and plumes

\Gamma = 11.74

Interaction and coalescence of large bubbles rising in a thin gap

, 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. The regime is linearly stable and is characterized by radially increasing specific angular momentum. We present several Rayleigh-stable profiles for shear Reynolds numbers