Session M14: Rotating Flows I

Small Ekman number heat transport in low Prandtl number rotating thermal convection

Heat transport in rotating convection is a complex combination of buoyancy, rotation, and fluid nonlinearity. We report experimental measurements of heat transport in rotating convection with cryogenic helium gas having a Prandtl number $Pr = 0.7$. The convection cell is cylindrical with aspect ratio $\Gamma = 1/2$, and the range of explored control parameters, Rayleigh number $Ra$ and Ekman number $Ek$, is $4 \times 10^9 < Ra < 4 \times 10^{11}$ and $2 \times 10^{-7} < Ek < 3 \times 10^{-5}$ (corresponding to $0.07 < Ro < 5$). We determine the crossover from buoyancy-dominated convection where rotation plays no measurable role in the heat transport to rotation-influenced convection in which the decrease in the heat transport contribution is no greater than 20\% of the non-rotating value. We also determine the crossover conditions $Ra_t = 0.5 Ra Ek^{-7/4}$ from the rotation-influenced state to a regime of geostrophic turbulence where normalized heat transport $Nu$ varies roughly linearly in $Ra$ as opposed to the $Ra^{1/3}$ scaling of the rotation-free state. An overall phase diagram of rotating convection in the space of $Ra/Ra_c$ and $Ek$ is proposed for a range of $Pr$ from 0.7 to 6 by combining our results with other data available in the literature.   

Rotating thermal convection at low Prandtl numbers

We present experimental results for rotating thermal convection in a cylindrical cell of aspect ratio $\Gamma \approx 1$ and Prandtl number $\mbox{Pr} \approx 0.7$. This value of $\mbox{Pr}$ is relevant to atmospheric convection. By using different compressed gases, we covered the Rayleigh-number range from $6\times 10^7$ to $2\times 10^{10}$. We investigated the transported heat, expressed in terms of the Nusselt number, as well as the sidewall temperature, as a function of the dimensionless rotation rate which we expressed in terms of the inverse Rossby number $1/Ro={2\Omega}/{\sqrt{\alpha g \Delta T/L}}$. For small Ra we found an increase of Nu with rotation that reached values about 1.5\% larger than Nu without rotation. This heat-transport enhancement is significantly smaller than it is for larger Pr, since Ekman pumping cannot efficiently transport warm (cold) fluid from the bottom (top) boundary layer. Numerical simulations by Stevens et al. (NJP Vol. 12, 075005 (2010)) did not resolve any Nusselt-number enhancement for our Pr and Ra numbers. Optical access via shadowgraphy allowed us to study how cold plumes became twisted and formed vortices - a precondition for Ekman pumping.   

Ekman and Taylor Vortices' Destruction and Mixing Enhancement in a Taylor--Couette System With Free Surface

Suppression of Ekman and Taylor vortices is desirable in several industrial processes such as cylindrical crystal growth and osmotic/photonic water purification. Inhomogeneities are undesired for the former, and enhanced mixing is sought for the latter. An active flow control strategy is employed to obliterate vortices in a Taylor--Couette flow, and is studied experimentally and numerically. The inner cylinder rotates while the outer one is stationary. The gap between the cylinders is not completely filled with liquid, and thus a free surface is formed below the upper stationary end-cap. The control consists of effecting minute radial pulsatile motion of the inner cylinder cross-section. The superimposed modulations combined with the free surface dynamics suppress both the Ekman and Taylor vortices. Complete destruction of either type of vortices occurs at different pulsatile frequencies, requiring one order of magnitude higher frequency to obliterate the Ekman vortex. When eliminated, fluid particles are no longer trapped within the Ekman or Taylor vortices. This yields significant increase in the axial and azimuthal velocity fluctuations, which results in enhanced flow mixing.   

Stability of the Taylor-Couette flow under a radial thermoelectric body force

A circular Couette flow developed between coaxial two infinite-length cylinders is considered in the case where only the inner cylinder is rotating. A radial temperature gradient and a radial electric field are applied to the flow, their coupling resulting in the dielectrophoretic body force density. This thermoelectric force can stabilize and destabilize the flow, depending on the heating direction. The critical Taylor number, wavenumber and frequency are determined for a wide range of control parameters. The mechanism behind the instability will be discussed.   

Secondary Floquet modes of instability in Taylor-Couette flow with axial and radial through-flows

Injecting a fluid between a fixed outer impermeable cylinder and concentric rotating permeable inner one and driving it axially is a set-up used in some filtration devices or enzymatic reactors, where the rotation of the inner cylinder promotes mixing or prevents accumulation processes. This set-up can be seen as a Taylor-Couette flow with superimposed axial and radial through-flows and a precise knowledge of the flow structures at stake is a prerequisite for improving these devices. We address the instabilities observed after the laminar flow of a pure, Newtonian solvent has undergone its first two transitions. Previous linear stability analysis has shown that critical convective instabilities take the form of travelling toroidal vortices, turning to helical vortices as the axial flow is increased. Moreover, a weakly non-linear analysis have shown that this primary transition can be subcritical as the radial flow is increased. Based on these previous results, the stability of these primary modes is studied by Floquet analysis. Depending on the strength of the axial and radial flows, harmonic or subharmonic secondary modes are found to be the most dangerous ones. The analytical results are compared to direct numerical simulations using a pseudo-spectral method.   

Experimental Study of the Flow in a Rotating CVD Reactor

An experimental model is developed to study the rotating, vertical, impinging chemical vapor deposition reactor. Deposition occurs only when the system has enough thermal energy. Therefore, understanding the fluid flow and thermal characteristics of the system would provide a good basis to model the thin film deposition process. The growth rate and the uniformity of the film are the two most important factors in the CVD process and these depend strongly on the flow and the thermal transport within the system. Operating parameters, such as inflow velocity, susceptor temperature and rotational speed, are used to create different design simulations. Fluid velocities and temperature distributions are recorded to obtain the effects of different operating parameters. Velocities are recorded by using a rotameter and a hot wire anemometer. The temperatures are recorded by using thermocouples and an infrared thermometer. The effects of buoyancy and rotation are examined. The expermental study is also coupled with a numerical study for validation of the numerical model and to expand the domain. Comparisons between the two models are presented, indicating fair agreement. The numerical model also includes simulation of Gallium Nitride (GaN) thin film deposition. This simulation thus includes mass transport and gas kinetics, along with the flow and heat transfer within the system. A three dimensional simulation is needed due to the rotation of the susceptor. The results obtained as well as the underlying fluid flow phenomena are discussed.   

How barotropic and stable are differential-rotation cylindrical flows?

In rotating cylindrical containers it is possible to generate a highly depth-independent vertical shear layer, akin to the layers studied by Stewartson theoretically in 1957, by driving the inner radial part of the fluid at a different speed through rotation of disks embedded in the top and base of a fluid-filled enclosure. This configuration finds laboratory application in the study of shear layers in rotating flows motivated by geophysical flows such as planetary polar vortices and terrestrial hurricanes. We combine high-order axisymmetric computations with a linear stability analysis and three-dimensional simulation to characterize regimes of depth-independent (``barotropic'') flow, and the modes by which both axial (depth-dependent) and azimuthal symmetry are broken in the system. Azimuthal instability produces striking symmetrical polygonal patterns closely resembling patterns seen in atmospheric polar vortices.   

Near-field flow characterization of isothermal coaxial swirling jet

The present experimental investigation concerns study of hydrodynamic instability resulting from vortex breakdown in a coaxial type atmospheric swirl burner. Transition from the first occurrence of pre-vortex breakdown (Pre-VB) flow reversal to a fully-developed central toroidal recirculation zone (CTRZ) is studied for a range of swirl number $S=$0.592 to 0.801.The swirl number was varied progressively by decreasing the mass flow of center jet stream. The physics of the transition is detailed based on modified Rossby number (\textit{Ro}$_{m})$ effect. The decrease in \textit{Ro}$_{m\thinspace }$across the transition (from an initial 3.15 to 0.02) facilitated the penetration of swirl towards center jet, widening the zone of swirl influence. 2D PIV technique employed in meridional and horizontal planes provided rich insight into the existent dynamics. Transverse plane flow field examination at various axial stations revealed the rigid body rotation characteristic of recirculation flow patterns. Although Rayleigh's criteria for centrifugally unstable flow was satisfied by these coherent structures, the transformation was accompanied by a transition in streamwise vorticity from that dominated by centrifugal forces to the solid body core supporting inertial waves.