Session BI: Vortex Dynamics and 3D Vortex Flows I

Towed-Grid Studies of Quantum Turbulence

We produce Homogeneous Isotropic Quantum Turbulence (HIQT) in liquid helium at 20 mK to compare with classical experiments and theories. Specifically, in the absence of viscosity, through what path does the turbulence decay? To produce HIQT we must quickly accelerate a grid to about 1 m/s in a channel of superfluid helium, tow it for 1 cm at a nearly constant speed, and then stop it equally quickly. To avoid joule and eddy current heating of the liquid helium, a magnetically shielded superconducting linear motor has been built, guided by simulations, along with the current pulses control program written in LabView with an embedded C compiler. The simulations, design process, and the experimental data demonstrating the functioning motor will be presented. We measure the HIQT energy decay mechanism using a calorimetric technique. Recent theory suggests the decay occurs through a Kelvin-wave cascade on the vortex lines which couples the initially large turbulent eddies to the short wavelength phonon spectrum of the liquid, yielding a characteristic rate of temperature rise. Doped germanium thermometers less than 300 $\mu $m diameter immersed in the turbulent helium allow fast calorimetric measurements to be made. The decay of turbulence is detected by the rate of temperature rise in the isolated cell after the grid is pulled.   

Experimental Studies of the Transition to He II using Hydrogen Seed Particles

Experimental studies of the phase transition to superfluidity in $^{4}$He using H$_{2}$ seed particles are presented. A gaseous mixture of hydrogen heavily diluted with helium is injected into the He I phase only a few mK above the lambda transition. The hydrogen gas solidifies into particles typically smaller than a micron, which are imaged by a CMOS camera focused on a thin laser sheet. The system is then evaporatively cooled through the lambda transition. Significant fluctuations and aggregation of the hydrogen particles are observed as the system passes through the phase transition. The fluctuating motions are characterized by particle-tracking. The aggregation is quantified by estimating the particle sizes from the intensity probability distribution function and its evolution. Systematic studies of the effects of quench rapidity and potential causes of these effects are discussed. Bewley G.P., Lathrop D.P., Sreenivasan K.R., \textit{Nature} \textbf{441, }588 (2006)   

High order Lagrangian computations of elliptical electron vortices

Vortex methods are numerical schemes for approximating solutions to the Navier-Stokes equations using a linear combination of moving basis functions to approximate the vorticity field of a fluid. Typically, the basis function velocity is determined through a Biot-Savart integral applied at the basis function centroid. These naturally adaptive methods are advantageous in flows dominated by localized regions of vorticity. The new method is a viscous core spreading algorithm using deforming elliptical Gaussian basis functions that achieve fourth order spatial convergence. This technique is unusual because one must evaluate the Biot-Savart integral of an elliptical Gaussian basis function and basis functions do not move with the physical flow velocity at the basis function centroid. Rather, high order accuracy is obtained when one adds a consistently small flow field curvature correction. To demonstrate the method's efficacy, we have been using these techniques for comparison with electron beam experiments which obey dynamics that are very similar to the Euler equations. In particular, we are exploring the growth of large non-axisymmetric modes and their dependence upon the initial aspect ratio and profile of an elliptical electron vortex.   

Characteristics of Plasma Synthetic Jet Actuators in Crossflow

The plasma synthetic jet actuator (PSJA) consists of two annular electrodes separated by dielectric material that results in a circular region of dielectric barrier discharge plasma. In quiescent conditions, this plasma ring produces a synthetic jet which can be used for active flow control applications. Unsteady pulsing of the actuator results in the formation of multiple primary and secondary vortex rings, the latter remaining fixed or trapped in space. The jet is observed to be formed by the advection and interaction of the primary vortices, resembling a conventional synthetic jet. This presentation examines the operation of the PSJA in a crossflow at three different jet to freestream velocity ratios. PIV measurements in the streamwise and cross-stream planes are used to illustrate the three dimensionality of the jet and associated vortical structures. The strength of the vortex ring is found to vary along its circumference due to interaction with the freestream. The boundary layer characteristics obtained from these experiments suggest that the mechanism of the PSJA in crossflow is similar to an active boundary layer trip. Both the penetration of the jet and effectiveness of the trip action are found to decrease with increase in freestream velocity. The effects of unsteady pulsing and increasing input power on actuator created crossflow vortices will also be presented.   

Effect of induced currents in electrically driven vortices under strong dipolar magnetic fields

A quasi-two-dimensional numerical study of electrically driven vortices in a shallow fluid layer under a dipolar magnetic field is carried out. The flow is produced by an applied Lorentz force created by the interaction of an injected DC electric current with the field produced by a permanent magnet whose dipolar moment points transversally to the fluid layer. In turn, an induced Lorentz force, usually known as Hartmann braking, appears due to the existence of induced currents created by the fluid motion. The flow is governed by two dimensionless parameters: the Reynolds number, $Re$, that is proportional to the magnitude of the injected current, and the Hartmann number, proportional to the magnetic field strength. When $Ha$ is $O(1)$ or smaller, the applied force dominates and a pair of counter-rotating vortices are formed in a wide range of $Re$ ($0.01 \le Re \le 100$). Under these conditions, the flow remains stable even for high values of $Re$. When $Ha>>1$, Hartmann braking is dominant and the flow velocity is reduced. For a high enough $Ha$, the induced force can reverse the main flow direction in the zone of strong magnetic field. In such a case, a monopolar vortex appears in the latter zone, in between the pair of counter-rotating vortices produced by the applied force. Results indicate that flow destabilization can be reached by increasing $Ha$ with intermediate values of $Re$.   

Double-plane stereo-PIV study on Tornado-like vortex in water

We investigated tornado-like vortex induced by a fan similar to Rushton turbine placed under the top surface of a cylindrical water tank. The three-component velocity fields in a cross-section of the tornado-like vortex were measured by stereoscopic PIV. Swirling flow was formed in the tank, and an upward flow was confirmed near the center of vortex. While the vortex core was dominated by an upward flow, abrupt velocity deficit at the center of vortex was observed in the mean axial velocity profile. Temporal fluctuation of the axial velocity indicated the existence of the instantaneous downward flow in the vortex core. By using double laser light sheet stereo-PIV method, axial gradient of vorticity will be investigated to evaluate the fluctuating pressure gradient in the vortex core inducing the axial velocity fluctuation.   

Measurement of Fine Scale Structure in Turbulence by Time-Resolved Dual-Plane Stereoscopic PIV

To investigate fine scale structure of turbulent flows, time-resolved dual-plane stereoscopic particle image velocimetry (TRDPSPIV) has been developed using high-repetition-rate Nd:YAG lasers for industrial processing and high-speed CMOS cameras. This system provides all three velocity components and nine velocity gradients with high spatial and temporal resolution. The developed system was applied to velocity measurements of a turbulent jet. It is shown that probability density functions of the measured nine velocity gradients agree well with those obtained from direct numerical simulation (DNS). From these velocity gradients, various physical quantities such as vorticity vectors and second invariant of velocity gradient tensor are obtained exactly. These quantities allow an eddy identification, which has been used in the analysis of DNS, to investigate fine scale structure of turbulence. The characteristics of the experimentally-detected fine scale eddy coincide with those obtained from DNS.   

Combining PIV and LDA to study 3D instabilities in rotating flows

The swirling flow between a rotating lid and a stationary cylinder is studied experimentally. The flow is governed by two parameters: The ratio of container height to disk radius, h, and the Reynolds number, Re, based on the disk angular velocity, cylinder radius and kinematic viscosity of the working liquid. For the first time the onset of three-dimensional flow behavior is measured by combining the high spatial resolution of Particle Image Velocimetry (PIV) and the temporal accuracy of Laser Doppler Anemometry (LDA). A detailed mapping of the transition scenario from steady and axisymmetric flow to unsteady and non-axisymmetric flow is investigated for h-values in the range from 1 to 3.5. The flow is characterized by the generation of azimuthal modes of different wave numbers. A range of different modes is detected and critical Reynolds numbers and associated frequencies are identified. The results are compared to previous numerical stability analyses. In most cases the measured onset of three-dimensionality is in good agreement with the numerical results and disagreements can be explained by bifurcations not accounted for by the stability analysis. For h=3.4 the experiment revealed the existence of a stable triplet that may explain the steady behavior of the $k$= 3 mode observed in previous computations.