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).

Bubbly turbulent Taylor-Couette (TC) flow is globally and locally studied at Reynolds numbers of Re = 5 × 10 5 to 2 × 10 6 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 α global over the range 0-4%. We observe a moderate DR of up to 7% for Re = 5.1 × 10 5 . Significantly stronger DR is achieved for Re = 1.0 × 10 6 and 2.0 × 10 6 with, remarkably, more than 40% of DR at Re = 2.0 × 10 6 and α global = 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 × 10 5 in the moderate DR regime and Re = 1.0 × 10 6 in the strong DR regime, both at α global = 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 × 10 6 is ≈ 2.3 times lower than that for Re = 5.1 × 10 5 , 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 (W e) 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 W e ∼ 1. In the strong DR regime at Re = 1.0×10 6 we find W e > 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 × 10 5 we find W e ≈ 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 × 10 6 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. (2005) and from the numerical simulations by Lu, Fernandez & Tryggvason (2005).

The flow structure of strongly turbulent Taylor-Couette flow with Reynolds numbers up to Rei = 2 • 10 6 of the inner cylinder is experimentally examined with high-speed particle image velocimetry (PIV). The wind Reynolds numbers Rew of the turbulent Taylor-vortex flow is found to scale as Rew ∝ T a 1/2 , exactly as predicted [1] for the ultimate turbulence regime, in which the boundary layers are turbulent. The dimensionless angular velocity flux has an effective scaling of N uω ∝ T a 0.38 , also in correspondence with turbulence in the ultimate regime. The scaling of N uω 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.

Strongly turbulent Taylor-Couette flow with independently rotating inner and outer cylinders with a radius ratio of η = 0.716 is experimentally studied. From global torque measurements, we analyse the dimensionless angular velocity flux N u ω (T a, a) as a function of the Taylor number T a and the angular velocity ratio a = −ω o /ω i in the large-Taylor-number regime 10 11 T a 10 13 and well off the inviscid stability borders (Rayleigh lines) a = −η 2 for co-rotation and a = ∞ for counter-rotation. We analyse the data with the common power-law ansatz for the dimensionless angular velocity transport flux N u ω (T a, a) = f (a)T a γ , with an amplitude f (a) and an exponent γ. The data are consistent with one effective exponent γ = 0.39 ± 0.03 for all a, but we discuss a possible a dependence in the co-and weakly counter-rotating regimes. The amplitude of the angular velocity flux f (a) ≡ N u ω (T a, a)/T a 0.39 is measured to be maximal at slight counter-rotation, namely at an angular velocity ratio of a opt = 0.33 ± 0.04, i.e. along the line ω o = −0.33ω i . 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 in particular identify the radial position r n of the neutral line, defined by ω(r n ) t = 0 for fixed height z. For these large T a values the ratio a ≈ 0.40, which is close to a opt = 0.33, is distinguished by a zero angular velocity gradient ∂ω/∂r = 0 in the bulk. While for moderate counter-rotation −0.40ω i ω o < 0, the neutral line still remains close to the outer cylinder and the probability distribution function of the bulk angular velocity is observed to be monomodal. For stronger counterrotation the neutral line is pushed inwards towards the inner cylinder; in this regime the probability distribution function 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 and consistent interpretation for all these various results.

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.