Highly turbulent Taylor-Couette flow

The research issues addressed in this mostly experimental thesis concern highly\ud turbulent Taylor-Couette (TC) flow (Re>105, implying Ta>1011). We study it on\ud a fundamental level to aid our understanding of (TC) turbulence and to make predictions towards astrophysical disks, and at a practical level as applications can be found in bubble-induced skin-friction drag reduction on ships. In PART I we introduce the new TC facility of our Physics of Fluids group, called the Twente turbulent Taylor-Couette (T3C) facility. It features two independently rotating cylinders of variable radius ratio with accurate rotation rate and temperature control, torque sensing, bubble injection and it is equipped with several local sensors. It is able to reach Reynolds numbers up to 3:4�106. In PART II we focus on highly turbulent single-phase TC flow. We measure the global torque as a function of the driving parameters and we provide local angular velocity measurements. The results are interpreted as the transport of angular velocity, based on the model proposed by Eckhardt, Grossmann & Lohse (2007). Furthermore, we study the turbulence transport in quasi-Keplerian profiles, mimicking astrophysical disks. In PART III we study the effect of bubbles on highly turbulent TC flow, focusing not only on\ud global drag reduction, but also on the local bubble distribution and angular velocity profiles. We find that drag reduction is a boundary layer effect and that the deformability of bubbles is crucial for strong drag reduction in bubbly turbulent TC flow

Optimal Taylor-Couette turbulence

Strongly turbulent Taylor-Couette flow with independently rotating inner and outer cylinders with a radius ratio of \eta = 0.716 is experimentally studied. From global torque measurements, we analyse the dimensionless angular velocity flux Nu_\omega(Ta, a) as a function of the Taylor number Ta and the angular velocity ratio a = -\omega_o/\omega_i in the large-Taylor-number regime 10^{11} \lesssim Ta \lesssim 10^{13}. We analyse the data with the common power-law ansatz for the dimensionless angular velocity transport flux Nu_\omega(Ta, a) = f(a)Ta^\gamma, with an amplitude f(a) and an exponent \gamma. The data are consistent with one effective exponent \gamma = 0.39\pm0.03 for all a. The amplitude of the angular velocity flux f(a) = Nu_\omega(Ta, a)/Ta^0.39 is measured to be maximal at slight counter-rotation, namely at an angular velocity ratio of a_opt = 0.33\pm0.04. This value is theoretically interpreted as the result of a competition between the destabilizing inner cylinder rotation and the stabilizing but shear-enhancing outer cylinder counter-rotation. With the help of laser Doppler anemometry, we provide angular velocity profiles and identify the radial position r_n of the neutral line. While for moderate counter-rotation -0.40 \omega_i \lesssim \omega_o < 0, the neutral line still remains close to the outer cylinder and the probability distribution function (p.d.f.) of the bulk angular velocity is observed to be monomodal. For stronger counter-rotation the neutral line is pushed inwards towards the inner cylinder; in this regime the p.d.f. of the bulk angular velocity becomes bimodal, reflecting intermittent bursts of turbulent structures beyond the neutral line into the outer flow domain, which otherwise is stabilized by the counter-rotating outer cylinder. Finally, a hypothesis is offered allowing a unifying view for all these various results.Comment: 30 pages, 22 figure

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-turbulenc

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 Rei=2×106 and Reo=±1.4×106, respectively. For all Rei, Reo, 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∝Ta0.88, corresponding to Nuω∝Ta0.38 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 ωo≈-0.4ωi

Optimal Taylor-Couette flow: radius ration dependence

Taylor–Couette flow with independently rotating inner (i) and 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=9.5×103 and Reo=5×103, corresponding to Taylor numbers of up to Ta=108 for four different radius ratios η=ri/ro between 0.5 and 0.909. The experiments, performed in the Twente Turbulent Taylor–Couette (T3C) set-up, reach Reynolds numbers of up to Rei=2×106 and Reo=1.5×106, corresponding to Ta=5×1012 for η=0.714--0.909. Effective scaling laws for the torque Jω(Ta) are found, which for sufficiently large driving Ta 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. Here Roopt is found to depend on the radius ratio and the driving of the system. At a driving in the range between Ta∼3×108 and Ta∼1010, 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