Dennis P. M. van Gils

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).

On bubble clustering and energy spectra in pseudo-turbulence

Three-dimensional particle tracking velocimetry (PTV) and phase-sensitive constant temperature anemometry in pseudo-turbulence – i.e. flow solely driven by rising bubbles – were performed to investigate bubble clustering and to obtain the mean bubble rise velocity, distributions of bubble velocities and energy spectra at dilute gas concentrations (α ≤ 2.2 %). To characterize the clustering the pair correlation function G(r, θ) was calculated. The deformable bubbles with equivalent bubble diameter db = 4–5 mm were found to cluster within a radial distance of a few bubble radii with a preferred vertical orientation. This vertical alignment was present at both small and large scales. For small distances also some horizontal clustering was found. The large number of data points and the non-intrusiveness of PTV allowed well-converged probability density functions (PDFs) of the bubble velocity to be obtained. The PDFs had a non-Gaussian form for all velocity components and intermittency effects could be observed. The energy spectrum of the liquid velocity fluctuations decayed with a power law of −3.2, different from the ≈ −5/3 found for homogeneous isotropic turbulence, but close to the prediction −3 by Lance & Bataille (J. Fluid Mech., vol. 222, 1991, p. 95) for pseudo-turbulenceThree-dimensional particle tracking velocimetry (PTV) and phase-sensitive constant temperature anemometry in pseudo-turbulence – i.e. flow solely driven by rising bubbles – were performed to investigate bubble clustering and to obtain the mean bubble rise velocity, distributions of bubble velocities and energy spectra at dilute gas concentrations (α ≤ 2.2 %). To characterize the clustering the pair correlation function G(r, θ) was calculated. The deformable bubbles with equivalent bubble diameter db = 4–5 mm were found to cluster within a radial distance of a few bubble radii with a preferred vertical orientation. This vertical alignment was present at both small and large scales. For small distances also some horizontal clustering was found. The large number of data points and the non-intrusiveness of PTV allowed well-converged probability density functions (PDFs) of the bubble velocity to be obtained. The PDFs had a non-Gaussian form for all velocity components and intermittency effects could be observed. The energy spectrum of the liquid velocity fluctuations decayed with a power law of −3.2, different from the ≈ −5/3 found for homogeneous isotropic turbulence, but close to the prediction −3 by Lance & Bataille (J. Fluid Mech., vol. 222, 1991, p. 95) for pseudo-turbulence

The importance of bubble deformability for strong drag reduction in bubbly turbulent Taylor-Couette flow

Bubbly turbulent Taylor–Couette (TC) flow is globally and locally studied at Reynolds numbers of Re=5×105 to 2×106 with a stationary outer cylinder and a mean bubble diameter around 1 mm. We measure the drag reduction (DR) based on the global dimensional torque as a function of the global gas volume fraction αglobal over the range 0–4 %. We observe a moderate DR of up to 7 % for Re=5.1×105. Significantly stronger DR is achieved for Re=1.0×106 and 2.0×106 with, remarkably, more than 40% of DR at Re=2.0×106 and αglobal=4%. To shed light on the two apparently different regimes of moderate DR and strong DR, we investigate the local liquid flow velocity and the local bubble statistics, in particular the radial gas concentration profiles and the bubble size distribution, for the two different cases: Re=5.1×105 in the moderate DR regime and Re=1.0×106 in the strong DR regime, both at αglobal=3±0.5%. In both cases the bubbles mostly accumulate close to the inner cylinder (IC). Surprisingly, the maximum local gas concentration near the IC for Re=1.0×106 is ≈2.3 times lower than that for Re=5.1×105, in spite of the stronger DR. Evidently, a higher local gas concentration near the inner wall does not guarantee a larger DR. By defining and measuring a local bubble Weber number (We) in the TC gap close to the IC wall, we observe that the cross-over from the moderate to the strong DR regime occurs roughly at the cross-over of We∼1. In the strong DR regime at Re=1.0×106 we find We>1, reaching a value of 9(+7,−2) when approaching the inner wall, indicating that the bubbles increasingly deform as they draw near the inner wall. In the moderate DR regime at Re=5.1×105 we find We≈1, indicating more rigid bubbles, even though the mean bubble diameter is larger, namely 1.2(+0.7,−0.1) mm, as compared with the Re=1.0×106 case, where it is 0.9(+0.6,−0.1) mm. We conclude that bubble deformability is a relevant mechanism behind the observed strong DR. These local results match and extend the conclusions from the global flow experiments as found by van den Berg et al. (Phys. Rev. Lett., vol. 94, 2005, p. 044501) and from the numerical simulations by Lu, Fernandez & Tryggvason

The Twente turbulent Taylor-Couette (T3C) facility: Strongly turbulent (multiphase) flow between two independently rotating cylinders

A new turbulent Taylor-Couette system consisting of two independently rotating cylinders has been constructed. The gap between the cylinders has a height of 0.927 m, an inner radius of 0.200 m, and a variable outer radius (from 0.279 to 0.220 m). The maximum angular rotation rates of the inner and outer cylinder are 20 and 10 Hz, respectively, resulting in Reynolds numbers up to 3.4 × 10(6) with water as working fluid. With this Taylor-Couette system, the parameter space (Re(i), Re(o), η) extends to (2.0 × 10(6), ±1.4 × 10(6), 0.716-0.909). The system is equipped with bubble injectors, temperature control, skin-friction drag sensors, and several local sensors for studying turbulent single-phase and two-phase flows. Inner cylinder load cells detect skin-friction drag via torque measurements. The clear acrylic outer cylinder allows the dynamics of the liquid flow and the dispersed phase (bubbles, particles, fibers, etc.) inside the gap to be investigated with specialized local sensors and nonintrusive optical imaging techniques. The system allows study of both Taylor-Couette flow in a high-Reynolds-number regime, and the mechanisms behind skin-friction drag alterations due to bubble injection, polymer injection, and surface hydrophobicity and roughness.

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.

Experimental investigation of heat transport in homogeneous bubbly flow

We present results on the global and local characterisation of heat transport in homogeneous bubbly flow. Experimental measurements were performed with and without the injection of

Optimal Taylor-Couette turbulence

\sim 2.5

Bubbly turbulent drag reduction is a boundary layer effect.

mm diameter bubbles (corresponding to

Torque scaling in turbulent Taylor-Couette flow with co- and counter-rotating cylinders

Re_b \approx 600