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

The statistics of velocity fluctuations of turbulent Taylor-Couette flow are examined. The rotation rate of the inner and outer cylinder are varied while keeping the Taylor number fixed to $1.49 \times 10^{12}$ ($\mathcal{O}(\text{Re})=10^6$). The azimuthal velocity component of the flow is measured using laser Doppler anemometry (LDA). For each experiment $5\times10^6$ datapoints are acquired and carefully analysed. Using extended self-similarity (ESS) \cite{ben93b} the longitudinal structure function exponents are extracted, and are found to weakly depend on the ratio of the rotation rates. For the case where only the inner cylinder rotates the results are in good agreement with results measured by Lewis and Swinney \cite{lew99} using hot-film anemometry. The power spectra shows clear -5/3 scaling for the intermediate angular velocity ratios $-\omega_o/\omega_i \in \{0.6, 0.8, 1.0\}$, roughly -5/3 scaling for $-\omega_o/\omega_i \in \{0.2, 0.3, 0.4, 2.0\}$, and no clear scaling law can be found for $-\omega_0/\omega_i = 0$ (inner cylinder rotation only); the local scaling exponent of the spectra has a strong frequency dependence. We relate these observations to the shape of the probability density function of the azimuthal velocity and the presence of a neutral line

Turbulence strength in ultimate Taylor-Couette turbulence

We provide experimental measurements for the effective scaling of the Taylor-Reynolds number within the bulk $\text{Re}_{\lambda,\text{bulk}}$, based on local flow quantities as a function of the driving strength (expressed as the Taylor number Ta), in the ultimate regime of Taylor-Couette flow. The data are obtained through flow velocity field measurements using Particle Image Velocimetry (PIV). We estimate the value of the local dissipation rate $\epsilon(r)$ using the scaling of the second order velocity structure functions in the longitudinal and transverse direction within the inertial range---without invoking Taylor's hypothesis. We find an effective scaling of $\epsilon_{\text{bulk}} /(\nu^{3}d^{-4})\sim \text{Ta}^{1.40}$, (corresponding to $\text{Nu}_{\omega,\text{bulk}} \sim \text{Ta}^{0.40}$ for the dimensionless local angular velocity transfer), which is nearly the same as for the global energy dissipation rate obtained from both torque measurements ($\text{Nu}_{\omega} \sim \text{Ta}^{0.40}$) and Direct Numerical Simulations ($\text{Nu}_{\omega} \sim \text{Ta}^{0.38}$). The resulting Kolmogorov length scale is then found to scale as $\eta_{\text{bulk}}/d \sim \text{Ta}^{-0.35}$ and the turbulence intensity as $I_{\theta,\text{bulk}} \sim \text{Ta}^{-0.061}$. With both the local dissipation rate and the local fluctuations available we finally find that the Taylor-Reynolds number effectively scales as Re$_{\lambda,\text{bulk}}\sim \text{Ta}^{0.18}$ in the present parameter regime of $4.0 \times 10^8 < \text{Ta} < 9.0 \times 10^{10}$.Comment: 15 pages, 8 figures, J. Fluid Mech. (In press

Heat transfer enhancement in Rayleigh-B\'enard convection using a single passive barrier

In this numerical study on Rayleigh-B\'enard convection we seek to improve the heat transfer by passive means. To this end we introduce a single tilted conductive barrier centered in an aspect ratio one cell, breaking the symmetry of the geometry and to channel the ascending hot and descending cold plumes. We study the global and local heat transfer and the flow organization for Rayleigh numbers $10^5 \leq Ra \leq 10^9$ for a fixed Prandtl number of $Pr=4.3$. We find that the global heat transfer can be enhanced up to $18\%$, and locally around $800\%$. The averaged Reynolds number is always decreased when a barrier is introduced, even for those cases where the global heat transfer is increased. We map the entire parameter space spanned by the orientation and the size of a single barrier for $Ra=10^8$.Comment: 19 pages, 15 figure

High humidity enhances the evaporation of non-aqueous volatile sprays

We experimentally investigate the evaporation of very volatile liquid droplets (Novec 7000 Engineered Fluid) in a turbulent spray. Droplets with diameters of the order of a few micrometers are produced by a spray nozzle and then injected into a purpose-built enclosed dodecahedral chamber, where the ambient temperature and relative humidity in the chamber are carefully controlled. We observe water condensation on the rapidly evaporating droplet, both for the spray and for a single acoustically levitated millimetric Novec 7000 droplet. We further examine the effect of humidity, and reveal that a more humid environment leads to faster evaporation of the volatile liquid, as well as more water condensation. This is explained by the much larger latent heat of water. We extend an analytical model based on Fick's law to quantitatively account for the data

Periodically driven Taylor-Couette turbulence

We study periodically driven Taylor-Couette turbulence, i.e. the flow confined between two concentric, independently rotating cylinders. Here, the inner cylinder is driven sinusoidally while the outer cylinder is kept at rest (time-averaged Reynolds number is $Re_i = 5 \times 10^5$). Using particle image velocimetry (PIV), we measure the velocity over a wide range of modulation periods, corresponding to a change in Womersley number in the range $15 \leq Wo \leq 114$. To understand how the flow responds to a given modulation, we calculate the phase delay and amplitude response of the azimuthal velocity. In agreement with earlier theoretical and numerical work, we find that for large modulation periods the system follows the given modulation of the driving, i.e. the system behaves quasi-stationary. For smaller modulation periods, the flow cannot follow the modulation, and the flow velocity responds with a phase delay and a smaller amplitude response to the given modulation. If we compare our results with numerical and theoretical results for the laminar case, we find that the scalings of the phase delay and the amplitude response are similar. However, the local response in the bulk of the flow is independent of the distance to the modulated boundary. Apparently, the turbulent mixing is strong enough to prevent the flow from having radius-dependent responses to the given modulation.Comment: 12 pages, 6 figure

Scalar transport and nucleation in quasi-two-dimensional starting jets and puffs

We experimentally investigate the early-stage scalar mixing and transport with solvent exchange in quasi-2D jets. We inject an ethanol/oil mixture upward into quiescent water, forming quasi-2D turbulent buoyant jets and triggering the ouzo effect with initial Reynolds numbers, Re_0=420, 840, and 1680. We study starting jets with continuous injection and puffs with finite volume injection. While both modes start with the jet stage, the puff exhibits different characteristics in transport, entrainment, mixing, and nucleation. For the starting jets, the total nucleated mass from the ouzo mixture seems very similar to that of the passive scalar total mass, indicating a primary nucleation site slightly above the virtual origin above the injection needle, supplying the mass flux like the passive scalar injection. With continuous mixing above the primary nucleation site, the mildly increasing nucleation rate suggests the occurrence of secondary nucleation throughout the entire ouzo jet. For the puffs, although the entrainment and nucleation reduce drastically when the injection stops, the mild mixing still leads to non-zero nucleation rates and the reduced decay of the mean puff concentrations for the ouzo mixture. Adapting the theoretical framework established in \citet{Landel2012b} for quasi-2D turbulent jets and puffs, we successfully model the transport of the horizontally-integrated concentrations for the passive scalar. The fitted advection and dispersion coefficients are then used to model the transport of the ouzo mixture, from which the spatial-temporal evolution of the nucleation rate can be extracted. The spatial distribution of the nucleation rate sheds new light on the solvent exchange process in transient turbulent jet flows