Azimuthal Velocity Profiles Research Articles

Subcritical transition and spiral turbulence in circular Couette flow

AbstractWe present new observations of a controlled transition to turbulence in a fundamental but little-studied regime: circular Couette flow with only the outer cylinder rotating. Our apparatus consists of an outer cylinder of fixed radius and three inner cylinders having different radii that are used interchangeably to study the effect of flow curvature. With the smallest inner cylinder the end-cap configuration (vertical boundary conditions) may also be varied. The turbulent transition is found to be sensitive to both gap width and end-cap configuration, with wider gaps transitioning at higher rotation rates. All configurations are observed to transition with hysteresis and intermittency. A laser Doppler velocimetry (LDV)-based study of the azimuthal velocity profile as a function of gap width and rotation rate reveals that turbulence, once initiated, is confined to regions of significant shear. For wider gap widths, the radial location of these shear layers is determined by the chosen end-cap configuration. This, in turn, affects the transition Reynolds number, which we posit to be radially dependent. The narrow-gap case in particular features spiral turbulence, whose properties are found to be similar to observations of the phenomenon in related shear flows. The velocity profile in this case is correlated with overlapping boundary layers, suggesting a coupling mechanism for the origin of laminar-turbulent banding phenomena.

Laser induced fluorescence measurements of ion velocity and temperature of drift turbulence driven sheared plasma flow in a linear helicon plasma device

Using laser induced fluorescence (LIF), radial profiles of azimuthal ion fluid velocity and ion temperature are measured in the controlled shear de-correlation experiment (CSDX) linear helicon plasma device. Ion velocities and temperatures are derived from the measured Doppler broadened velocity distribution functions of argon ions. The LIF system employs a portable, high power (>300 mW), narrowband (∼1 MHz) tunable diode laser-based system operating at 668.614 nm. Previous studies in CSDX have shown the existence of a radially sheared azimuthal flow as measured with time delay estimation methods and Mach probes. Here, we report the first LIF measurements of sheared plasma fluid flow in CSDX. Above a critical magnetic field, the ion fluid flow profile evolves from radially uniform to peaked on axis with a distinct reversed flow region at the boundary, indicating the development of a sheared azimuthal flow. Simultaneously, the ion temperature also evolves from a radially uniform profile to a profile with a gradient. Measurements in turbulent and coherent drift wave mode dominated plasmas are compared.

Comparison of azimuthal ion velocity profiles using Mach probes, time delay estimation, and laser induced fluorescence in a linear plasma device

We compare measurements of radially sheared azimuthal plasma flow based on time delay estimation (TDE) between two spatially separated Langmuir probes, Mach probes and laser induced fluorescence (LIF). TDE measurements cannot distinguish between ion fluid velocities and phase velocities. TDE and Mach probes are perturbative, so we compare the results against LIF, a non-perturbative, spatially resolved diagnostic technique that provides direct measurements of the ion velocity distribution functions. The bulk ion flow is determined from the Doppler shift of the Argon absorption line at 668.6139 nm. We compare results from all the three diagnostics, at various magnetic fields, which acts as a control knob for development of drift wave turbulence. We find that while Mach probes and LIF give similar profiles, TDE measurements typically overestimate the velocities and are also sensitive to the drift wave modes being investigated.

Applying laser Doppler anemometry inside a Taylor–Couette geometry using a ray-tracer to correct for curvature effects

In the present work it will be shown how the curvature of the outer cylinder affects laser Doppler anemometry measurements inside a Taylor–Couette apparatus. The measurement position and the measured velocity are altered by curved surfaces. Conventional methods for curvature correction are not applicable to our setup, and it will be shown how a ray-tracer can be used to solve this complication.By using a ray-tracer the focal position can be calculated, and the velocity can be corrected. The results of the ray-tracer are verified by measuring an a priori known velocity field, and after applying refractive corrections good agreement with theoretical predictions are found. The methods described in this paper are applied to measure the azimuthal velocity profiles in high Reynolds number Taylor–Couette flow for the case of outer cylinder rotation.

Observations of ferrofluid flow under a uniform rotating magnetic field in a spherical cavity

Flow of a ferrofluid in spherical and cylindrical geometries were measured under the influence of a uniform rotating magnetic field produced by two perpendicular spherical coils, a so-called fluxball, excited by quadrature currents. Using an ultrasound velocity profile technique and a commercial oil based ferrofluid (EFH1, Ferrotec) we observed rotational flow around the z-axis. In comparison, the radial component of the flow was found to be negligible. Results show that the magnitude of the azimuthal velocity profile increases as the applied magnetic field amplitude increases. This behavior is also observed for ferrofluid in a cylindrical container placed inside the fluxball cavity and inside a two-pole stator winding. These results indicate that inhomogeneities in the magnetic field produced by slots and finite height of the stator winding used in prior experiments are not the source of previously observed flows produced by a two pole stator winding. The experiments reported here either point to the existence of non-uniform demagnetizing magnetic fields due to the finite height of the cylindrical container, the existence of couple stresses and spin viscosity in ferrofluids, or to the need to develop alternate governing and constitutive equations capable of describing the experimental observations.

Measurements of mean flow and turbulence characteristics in high-Reynolds number counter-rotating Taylor-Couette flow

Particle image velocimetry was used for measuring the velocity and Reynolds stress distributions in the latitudinal plane of counter-rotating Taylor-Couette flow at high Reynolds numbers (Re). The ratio of outer to inner cylinder angular velocity, μ, varied between −10.79 and −0.68, and Rei based on the inner cylinder velocity ranged between 2635 and 40 446, substantially extending previously available data. The results were used for examining scaling trends, especially the effects of Re and μ on the mean flow and turbulence statistics. We showed that using a kind of “inner wall” scaling, μ was the primary parameter controlling the normalized profiles of mean velocity, Reynolds stresses, TKE production and dissipation rates. Re effects on the scaled profiles were much smaller. Increasing μ flattened the mean azimuthal velocity profiles in the center of the annulus, increased the radial velocity gradients near the walls, and moved the radial point at which the velocity changed sign towards the outer cylinder. The flow also became more turbulent and a log layer with increasing extent developed near the inner wall. All the Reynolds stress components, along with the TKE production and dissipation rates peaked near the inner wall. Raising μ extended the high turbulence levels deeper into the annulus. At low μ, the stabilizing effect of the outer cylinder kept the flow in the outer regions laminar. Only when the magnitude of the inner cylinder angular velocity equaled or exceeded that of the outer one, the Reynolds stresses remained significant across the entire measurement range, and started increasing also near the outer cylinder. The azimuthal energy spectra confirmed these trends and showed that the changes to turbulence levels occurred at a broad range of scales. Furthermore, for low μ, the instantaneous vorticity fields were dominated by nearly parallel, elongated, counter-rotating vorticity contours, reminiscent of inclined counter-rotating vortex pairs. At high μ, more randomly distributed structures were generated near both walls, and eventually filled the whole annulus.

Effect of plumes on measuring the large scale circulation in turbulent Rayleigh-Bénard convection

We studied the properties of the large-scale circulation (LSC) in turbulent Rayleigh-Bénard (RB) convection by using results from direct numerical simulations in which we placed a large number of numerical probes close to the sidewall. The LSC orientation is determined by either a cosine or a polynomial fit to the azimuthal temperature or azimuthal vertical velocity profile measured with the probes. We study the LSC in Γ = D/L = 1/2 and Γ = 1 samples, where D is the diameter and L is the height. For Pr = 6.4 in an aspect ratio Γ = 1 sample at Ra = 1 × 108 and 5 × 108, the obtained LSC orientation is the same, irrespective of whether the data of only 8 or all 64 probes per horizontal plane are considered. In a Γ = 1/2 sample with Pr = 0.7 at Ra = 1 × 108, the influence of plumes on the azimuthal temperature and azimuthal vertical velocity profiles is stronger. Due to passing plumes and/or the corner flow, the apparent LSC orientation obtained using a cosine fit can result in a misinterpretation of the character of the large-scale flow. We introduce the relative LSC strength, which we define as the ratio between the energy in the first Fourier mode and the energy in all modes that can be determined from the azimuthal temperature and azimuthal vertical velocity profiles, to further quantify the large-scale flow. For Ra = 1 × 108, we find that this relative LSC strength is significantly lower in a Γ = 1/2 sample than in a Γ = 1 sample, reflecting that the LSC is much more pronounced in a Γ = 1 sample than in a Γ = 1/2 sample. The determination of the relative LSC strength can be applied directly to available experimental data to study high Rayleigh number thermal convection and rotating RB convection.

Structure of trailing vortices: Comparison between particle image velocimetry measurements and theoretical models

The velocity field of the trailing vortex behind a wing at different angles of attack has been measured through the stereo particle image velocimetry technique in a water tunnel for Reynolds numbers between 20 000 and 40 000, and for several distances to the wing tip. After filtering out the vortex meandering, the radial profiles of the axial and the azimuthal velocity components and of the radial profiles of the vorticity were compared to the theoretical models for trailing vortices by [G. K. Batchelor, J. Fluid Mech. 20, 645 (1964)] and by [D. W. Moore and P. G. Saffman, Proc. R. Soc. London, Ser. A 333, 491 (1973)], whose main features are conveniently summarized. We take into account the downstream evolution of these profiles from just a fraction of the wing chord to more than ten chords. The radial profiles of the vorticity and the azimuthal velocity are shown to fit quite well to Moore and Saffman’s trailing vortex model, while Batchelor’s model does not fit so well, especially in the tails of the profiles. At the downstream distances considered, the radial profiles of the axial velocity do not adjust so well to Moore and Saffman’s model as the azimuthal velocity profiles do, but the disagreement with Batchelor’s model is quite manifested, especially at the axis. Thus, the details of the flow structure are in better agreement with the predictions of Moore and Saffman’s model. The downstream evolution of several key features of the measured velocity profiles is also in agreement with the predictions of Moore and Saffman’s model, within the dispersion of the experimental data, but up to the largest axial distance considered in this work we cannot decide if they follow the asymptotic behavior predicted by this model.

Confined swirling jet impingement on a flat plate at moderate Reynolds numbers

The behavior of a swirling jet issuing from a pipe and impinging on a flat smooth wall is analyzed numerically by means of axisymmetric simulations. The axial velocity profile at the pipe outlet is assumed flat while the azimuthal velocity profile is a Burger’s vortex characterized by two non-dimensional parameters; a swirl number S and a vortex core length δ. We concentrate on the effects of these two parameters on the mechanical characteristics of the flow at moderate Reynolds numbers. Our results for S=0 are in agreement with Phares et al. [J. Fluid Mech. 418, 351 (2000)], who provide a theoretical determination of the wall shear stress under nonswirling impinging jets at high Reynolds numbers. In addition, we show that the swirl number has an important effect on the jet impact process. For a fixed nozzle-to-plate separation, we found that depending on the value of δ and the Reynolds number Re, there is a critical swirl number, S=S∗(δ,Re), above which recirculating vortex breakdown bubbles are observed in the near axis region. For S>S∗, the presence of these bubbles enhances the transition from a steady to a periodic regime. For S<S∗, the flow remains steady and the results show that the introduction of swirl reduces the maximum pressure and radial skin-friction coefficients over the wall.

Theoretical and experimental investigation of the structure of azimuthal source–sink flow in a rotating shallow water layer

The structure of source–sink flow in a rotating shallow water layer is studied both theoretically and experimentally. Theoretical calculations are carried out in the framework of the nonlinear model of Ekman boundary layer based on the description of advective terms in the geostrophic momentum approximation. The radial profiles of azimuthal velocity are derived analytically in the small Rossby number limit. It has been shown that the structure of these profiles varies essentially when changing the direction of a radial flow. The velocity profile is strictly monotonic for cyclonic flow (radial flow is directed to the centre) and non-monotonic with maximum near the source—for anticyclonic flow. These results are in agreement with theoretical results by Danilov, Sazonov, derived in the framework of vertically integrated model. The experimental part of the work is carried out on the special experimental apparatus at Abastumani Astrophysical Observatory. The measured radial profiles of the fluid depth and azimuthal velocity produced by concentric sources and sinks located at the bottom of the rotating parabolic vessel are presented. The dependence of these profiles on the intensity of the source–sink system is investigated. It is shown that theoretical results reproduce the main features of the profiles measured in experiments.

Integrated campaign to study the stationary inertial Alfvén wave in the laboratory and space regimes

A small, off-axis mesh-anode electrode at one plasma-column end is used to create a paraxial channel of electron current and depleted density in the large plasma device upgrade at UCLA. We show that the on-axis, larger, surrounding-plasma column rotates about its cylindrical axis because a radial electric field is imposed by a multiple-segmented-disc termination electrode on the same end as the mesh-anode electrode. The radial profile of azimuthal velocity is shown to be consistent with predictions of rigid-body rotation. Launched inertial Alfvén waves are shown to concentrate in the off-axis channel of electron current and depleted plasma density. In the absence of launched waves, time varying boundary conditions, or spatially structured boundary conditions, a non-fluctuating, non-traveling pattern in the plasma density is shown to arise spontaneously in the channel, but only in the combined presence of electron current, density depletion, and spontaneously in the channel, cross-field convection (i.e. rotation). These results may be relevant to the stationary Alfvén wave in the inertial regime in space and laboratory plasmas.

On the stability of vortex streets in a stratified fluid

On the basis of the perturbation theory developed previously by the authors for localized hydrodynamic vortices, the influence of a specified jet flow and of the structure of individual vortices on the stability of the Karman street is investigated. It is shown that, for a street of vortices with a power law of decrease in the azimuthal velocity, the jet flow suppresses instability only with respect to perturbations with wavelengths from a certain range determined by the parameters of the flow. At the same time, for streets formed from vortices with a Gaussian profile of the azimuthal velocity, even in the absence of a specified flow, there is a certain region of the street’s parameters in which the street is stable against perturbations of all scales. Thus, for the purposes of modeling quasi-two-dimensional flows in a stratified fluid by a sequence of localized vortices, which is discussed in this study, vortices with a Gaussian profile of the azimuthal velocity turn out to be preferable. The results of this study are consistent with numerous experiments on the structure of a quasi-two-dimensional wake behind a body in a stratified fluid at large Reynolds and Froude numbers.

Making a fluid rotate: Circular flow of a weakly conducting fluid induced by a Lorentz body force

We describe the magnetohydrodynamic (MHD) flow of a viscous, electrically conducting, and incompressible fluid driven by the Lorentz body force inside the annulus between two stationary coaxial cylindrical electrodes under imposed electric and magnetic fields. The azimuthal velocity profile is found for axisymmetrical, fully developed laminar and steady flow at arbitrary annulus curvature and different values of the Hartmann number Ha. It is shown that for Ha⩽1, the MHD annular flow behaves as a conventional hydrodynamic fluid driven by an azimuthal Lorentz body force.

Torque and Bulk Flow of Ferrofluid in an Annular Gap Subjected to a Rotating Magnetic Field

We report analysis and measurements of the torque and flow of a ferrofluid in a cylindrical annulus subjected to a rotating magnetic field perpendicular to the cylinder axis. The presence of the inner cylinder results in a nonuniform magnetic field in the annulus. An asymptotic analysis of the ferrohydrodynamic torque and flow assuming linear magnetization and neglecting the effect of couple stresses indicated that the torque should have a linear dependence on field frequency and quadratic dependence on field amplitude. To the order of approximation of the analysis, no bulk flow is expected in the annular gap between stationary cylinders. Experiments measured the torque required to restrain a polycarbonate spindle surrounded by ferrofluid in a cylindrical container and subjected to the rotating magnetic field generated by a two-pole magnetic induction motor stator, as a function of the applied field amplitude and frequency, and for various values of the geometric aspect ratios of the problem. The ultrasound velocity profile method was used to measure the azimuthal and axial velocity profiles in the ferrofluid contained in the annular gap of the apparatus. Flow measurements show the existence of a bulk azimuthal ferrofluid flow between stationary coaxial cylinders with a negligible axial velocity component. The fluid was found to corotate with the applied magnetic field. Both the torque and flow measurements showed power-of-one dependence on frequency and amplitude of the applied magnetic field. This analysis and these experiments indicate that the action of antisymmetric stresses is responsible for the torque measured on the inner cylinder, whereas the effect of body couples is likely responsible for bulk motion of the ferrofluid.

Hysteresis in flow patterns in annular swirling jets

This study investigates the influence of swirl on the mean cold flowfield of an annular jet with a stepped-conical expansion. Both the axial and azimuthal velocity components are measured using a two component Laser Doppler Anemometry system in forward scattering mode. A detailed description of the radial profiles of both mean axial and azimuthal velocity as well as three components of the Reynolds stress are given. Four different jets are identified as a function of the swirl number: ‘Closed Jet Flow’, ‘Open Jet Flow Low Swirl’, ‘Open Jet Flow High Swirl’ and ‘Coanda Jet Flow’. These flow patterns change with varying swirl number and there exists hysteresis when increasing and subsequently decreasing the swirl. Also a method for jet identification based upon pressure measurements is presented to replace the time consuming LDA measurements.

Axisymmetric stability of the flow between two exactly counter-rotating disks with large aspect ratio

We study the first bifurcation in the axisymmetric flow between two exactly counter-rotating disks with very large aspect ratio is developed, in which curvature is neglected, but the centrifugal acceleration term is retained. The Navier–Stokes equations then reduce to leading order to those in a Cartesian frame, and the axisymmetric base flow to a parallel flow. This allows us locally to use a Fourier decomposition along the radial direction. In this framework, we explain the physical mechanism of the instability invoking the linear azimuthal velocity profile and the effect of centrifugal acceleration.

Cubic eddy‐viscosity turbulence models for strongly swirling confined flows with variable density

AbstractAn investigation on the predictive performance of cubic eddy‐viscosity turbulence models for strongly swirling confined flows with variable density is presented. Comparisons of the prediction with the experiments show some improvements of cubic models over the linear k–ε model. The linear k–ε model does not contain any mechanism to represent the interaction of swirl and density variation and as a consequence it performs poorly. With appropriate modelling, two‐equation cubic turbulence models can capture the subcritical nature of the flow, represent the azimuthal velocity profiles of combined forced‐free vortex motion, and predict the combined effects of swirl and density variation fairly well. However, the calibration of model coefficients is still a topic of investigation. Further amendments are also needed for the equations of k and ε to take into account the effects of swirl and density gradients correctly. Copyright © 2004 John Wiley & Sons, Ltd.

A model for the azimuthal plasma velocity in Saturn's magnetosphere

We present a model for Saturn's magnetospheric azimuthal plasma velocities measured by Voyager 1 and 2. The observed velocity profiles deviate from full corotation and show two dips slightly outside the orbits of Dione and Rhea. Our velocity model includes as sources for the deviation: radial mass transport, friction between magnetospheric ions and neutrals, and ion pickup. We combine the latter two processes in a quantity called magnetospheric conductance ΣM. We find that inside of 12 Saturn radii (RS) the magnetospheric conductance dominates the slowing of magnetospheric plasma as compared to the effect of radial mass transport. The magnetospheric conductance peaks twice, i.e., slightly outside the orbit of Dione (6.4 RS) and Rhea (8.8 RS), respectively. These two peaks result from a combination of the radially varying magnetic field magnitude, the radial plasma density distribution, and the neutral density distribution. A key finding of our work is that the two magnetospheric conductance maxima can explain the two dips in the observed azimuthal velocity profile that occur at roughly similar locations. Mismatches in the dip locations can be used to retrieve neutral gas profiles. We achieve reasonable agreement with the observations for very small effective Pedersen conductances, ΣI ∼ 0.014 S (Voyager 1) and ΣI ∼ 0.035 S (Voyager 2) in Saturn's ionosphere, for a total magnetospheric mass source of 40 kg s−1. Larger mass sources require appropriately higher ionospheric conductances. We also find that mass cannot leave, on average, the ≤10 RS regions as plasma. It must be mostly lost via conversion to neutrals.

Mapping of the Lateral Flow Field in Typical Subchannels of a Support Grid With Vanes

Lateral flow fields in four subchannels of a model rod bundle fuel assembly are experimentally measured using particle image velocimetry. Vanes (split-vane pairs) are located on the downstream edge of the support grids in the rod bundle fuel assembly and generate swirling flow. Measurements are acquired at a nominal Reynolds number of 28,000 and for seven streamwise locations ranging from 1.4 to 17.0 hydraulic diameters downstream of the grid. The streamwise development of the lateral flow field is divided into two regions based on the lateral flow structure. In Region I, multiple vortices are present in the flow field and vortex interactions occur. Either a single circular vortex or a hairpin shaped flow structure is formed in Region II. Lateral kinetic energy, maximum lateral velocity, centroid of vorticity, radial profiles of azimuthal velocity, and angular momentum are employed as measures of the streamwise development of the lateral flow field. The particle image velocimetry measurements of the present study are compared with laser Doppler velocimetry measurements taken for the identical support grids and flow condition.

Mode selection in swirling jet experiments: a linear stability analysis

The primary goal of the study is to identify the selection mechanism responsible for the appearance of a double-helix structure in the pre-breakdown stage of so-called screened swirling jets for which the circulation vanishes away from the jet. The family of basic flows under consideration combines the azimuthal velocity profiles of Carton & McWilliams (1989) and the axial velocity profiles of Monkewitz (1988). This model satisfactorily represents the nozzle exit velocity distributions measured in the swirling jet experiment of Billant et al. (1998). Temporal and absolute/convective instability properties are directly retrieved from numerical simulations of the linear impulse response for different swirl parameter settings. A large range of negative helical modes, winding with the basic flow, are destabilized as swirl is increased, and their characteristics for large azimuthal wavenumbers are shown to agree with the asymptotic analysis of Leibovich & Stewartson (1983). However, the temporal study fails to yield a clear selection principle. The absolute/convective instability regions are mapped out in the plane of the external axial flow and swirl parameters. The absolutely unstable domain is enhanced by rotation and it remains open for arbitrarily large swirl. The swirling jet with zero external axial flow is found to first become absolutely unstable to a mode of azimuthal wavenumber , winding with the jet. It is suggested that this selection mechanism accounts for the experimental observation of a double-helix structure.