Session Y11: Vortex Dynamics and Vortex Flows: Wakes (11:30am - 12:15pm CST)

Three-dimensional unsteady wake dynamics of hydrofoils with combined pitching and heaving motion

The primary and secondary vortex evolution in the wake of an oscillating teardrop foil with combined heaving and pitching motion is investigated using Direct Numerical Simulations at Re$=$8000. Recent experiments of Van Buren et al. (2019) suggested that either high propulsive efficiency or large thrust generation is achieved for limited motion settings. The former case corresponded to Strouhal number (St)$=$0.2, phase difference($\Phi )=$270$^{\mathrm{o}}$ and reduced frequency(f*) $=$0.6, while the settings for the latter were: St$=$0.9, $\Phi =$330$^{\mathrm{o}}$ and f*$=$0.8. In this study we examine how the vortex dynamics differ for these settings. Initial results indicate that the high efficiency system is characterized by a thrust generating 2P wake that transitions to an inverse 2S wake downstream. In contrast, the large thrust generating system depicted the Mode-A asymmetric wake comprising of vortex dipoles. Primary vortex interactions and their transitional features further suggest differences in vortex dislocations. Also, statistical analysis on the identification of secondary vortex characteristics revealed close resemblance to a long wavelength mode. Two new vortex skeleton models are introduced that incorporates the new findings on wake dynamics.   

Near Wake of a Circular Cylinder Undergoing Yaw Oscillation at Subcritical Flow

In this experimental study the near wake of a circular cylinder undergoing yaw oscillation is investigated. The yaw angle is varied from a crossflow ($0^o$) to $30^o$. Two different Reynolds numbers of $5\times10^3$ and $1.5\times10^4$ are considered. Planar Particle Image Velocimetry measurements are used to study the flow topology in the near wake at the midspan of the cylinder, which corresponds to the center of yaw oscillation. Flow field measurements are obtained for a range of reduced frequencies based on the cylinder length, freestream velocity and oscillation frequency. The flow field results and wake parameters are compared to a baseline static cylinder at corresponding yaw angles. It is found that various wake parameters, such as the wake closure length or wake width vary with reduced frequency. As the reduced frequency is increased the wake closure length tends to decrease. For low to moderate reduced frequencies, the vortex shedding can be suppressed at high yaw angles. For the highest values of reduced frequency considered in this study the mean recirculation region can be suppressed throughout the oscillation cycle.   

Using supervised machine learning to predict leading edge vortex growth, detachment, and wake trajectory

The strength and trajectory of a leading edge vortex (LEV) formed by a hydrofoil (chord $c$) pitching and heaving in a water flume is studied. The LEV is identified using the Q-criterion calculated from the 2D velocity field obtained from PIV measurements. The relative angle of attack at mid-stroke, $\alpha_{T/4}$, proves to be an effective method of combining heave ($h_0/c$), pitch ($\theta_0$), and frequency ($fc/U_{\infty}$) into a single variable that predicts the maximum value of Q over a wide range of operating conditions. Once the LEV separates from the foil, it travels downstream and gradually weakens and diffuses and this behavior also seems to scale with $\alpha_{T/4}$. Supervised machine learning is used to create a regression algorithm that predicts the vortex strength and trajectory during growth and after separation. The size and shape of the LEV is parameterized by an ellipse with axes $a$ and $b$, and orientation $\phi$. The machine learning algorithm is trained using these vortex characteristics, along with the operating parameters $h_0/c, \theta_0, fc/U_{\infty}, \alpha_{T/4}, t/T$. During training, Gaussian process regression (GPR) models achieved excellent performance, with the lowest root-mean-square error.   

Transitions in the wake symmetry of side-by-side oscillating foils.

The unsteady hydrodynamics of two oscillating foils in side-by-side configuration is numerically examined for in-phase and out-phase oscillations at Reynolds number of $Re=4000$ and Strouhal numbers of $St=0.25-0.5$ using Direct Numerical Simulations. This study examined the effects of Strouhal number and oscillation phase difference on the propulsive performance and the wake topology. The wake symmetry was preserved throughout oscillations at lower $St$ ($St=0.25$) for both phase angles. In contrast, in-phase and out-of-phase oscillations display entirely opposite characteristics at higher $St$ ($St=0.5$). Wake of the in-phase oscillating foils at higher $St$, which is initially asymmetric, restores the wake symmetry in time. This restoration coincides with the enhancement of the propulsive performance of the foils. For out-of-phase oscillations, however, initial symmetry of the wake transition to asymmetry after several oscillation cycles. The collective propulsive performance of the foils stays still during the transition, even though one of the foils benefits from the absence of the wake symmetry while the other suffers from it.   

Shedding timing of secondary vortices from a rotating plate

Many vortex generators involve the formation of a primary vortex followed by the occurrence of other coherent structures. When a vortex is formed from an accelerated plate or from a piston-cylinder apparatus, it grows up to a limit when it pinches-off. Beyond this point, swirling structures akin to a Kelvin-Helmholtz instability are observed. All the coherent structures generated after the formation of the primary vortex are called secondary vortices. In the present study, we investigate the shedding timing of secondary vortices, generated around a rotating rectangular plate in a quiescent flow. Time-resolved PIV images show that secondary vortices are discretely released from tip during the plate motion and they are not generated from the stretching of an unstable shear layer. Once separated from the plate, secondary vortices evolve in time following a self-similar curve well approximated by Kaden's spiral. From this result, we compute the time position of each secondary vortex along the spiral and fit it with a second order polynomial curve. The parabolic fit allows to estimate the pinch-off moment of secondary vortices and retrieve the timing of the entire shedding process. Between $6$ and $7$ secondary vortices every $20^\circ$ are observed for all the tested Reynolds number.   

Wake observations for a circular cylinder undergoing forced two-degrees-of-freedom motions.

A series of experiments were performed to characterize the wake and forces on a circular cylinder that undergoes forced two-degree-of-freedom sinusoidal motions in a free stream. A comprehensive dataset consisting of 9555 combined in-line and cross-flow motion experiments with force measurement and 819 flow visualization experiments was obtained, varying the in-line amplitude of motion, cross-flow amplitude of motion, reduced velocity, and phase between motions. Experiments were carried out at a constant Reynolds number of 7620. Unique observations are made regarding observed vortex patterns in the wake and force measurements. For example, under certain combinations of motion parameters, unique repeatable patterns of vortex shedding that differ from established patterns are observed. Additionally, non-repeatable patterns may also be observed despite forced periodic motions. A mapping of wake patterns covering the entire parameter space is presented. This map illustrates that there is a large variability in potential wake patterns when a cylinder undergoes combined in-line and cross-flow motion, in contrast to when a cylinder is constrained to cross-flow motion only. We observe that over the range of motion parameters tested and in most cases, when a change in motions results in a sign change in the average power transferred from the cylinder to the fluid, there is a corresponding change in the wake pattern, however this transition is not universally true over the entire database of motions.   

Partial lock-on in the wake of a streamwise-oscillating cylinder

It has been well established for a streamwise-oscillating cylinder that forcing frequencies, $f_f$, of the same order of magnitude as the stationary vortex shedding frequency, $f_0$, can lead to the development of a lock-on state consisting of the synchronization between the forcing and shedding frequency. Although relatively less studied, forcing frequencies multiple orders of magnitude less than the stationary shedding frequency have been shown to cause the development of quasi-steady shedding. Between these two extremes, however, studies have shown the development of sub-harmonic lock-on. In this study, we use Particle Image Velocimetry and fluorescent dye flow visualization to study forcing frequencies between the quasi-steady and lock-on regimes and show that a ``partial lock-on" state can also develop in which one portion of the forcing trajectory corresponds to quasi-steady shedding while the other portion sees the generation of a starting vortex phase-locked to the forcing. Various combinations of forcing frequency and amplitude will be discussed, all with a mean Reynolds number of $Re_0 = 900$.   

Dynamics of Wake-Vortices Deflection Over an Airfoil Using Active Morphing Flaps

Dynamics of wake-vortices structures deflected by active morphing flaps were investigated around a NACA0012 airfoil at a low angle of attack. Two-dimensional direct numerical simulations were performed at the chord Reynolds number of 10,000, where the vortex patterns in controlled and noncontrolled wakes were investigated as well as the effect of an actuation frequency on the control ability. It was found that there is an optimum actuation-frequency regime at around $F^+ = 2.00$ which is normalized by the chord length and freestream velocity. Wake vortices of the well-controlled case is classified as the 2P mode according to the Williamson’s categorization, where the forced frequency corresponds to the natural vortex shedding frequency without control. Meanwhile, the other synchronized modes do not maintain the wake deflection. We also performed a massive parametric study to construct the map of wake vortex structures with respect to actuation frequency and amplitude, which were systematically classified using a proper orthogonal decomposition. The present classification of wake vortex patterns and finding of the optimum frequency regime in the wake deflection control can lead to a more robust design suitable for vortex-induced-vibration (VIV) related engineering systems.   

Particle dispersal induced by coherent flow structures near oscillating leaves

Plant pathogens like rust spores are ongoing issues for agricultural practices. Past studies have shown that liberation of rust spores from leaf surfaces can result from vortices induced by impacting droplets. Our experiments suggest that heaving leaf motions indeed generate shear layers along leaf surfaces with periodic shedding of counter-rotating vortex tubes that enhance particle mixing and spatial transport. We utilize Finite Time Lyapunov Exponents (FTLE) to map out coherent structures that emerge over 2D flow maps on the transverse cross-section of vibration, while investigating particle advection properties owing to such oscillatory, unsteady flow patterns. The vorticities are extracted from smoke visualization data and matched with theoretical predictions based on 2D velocity potentials commonly adopted in oscillatory airfoil theory. We then applied a ballistic model with modification on velocity from vortex tubes and airfoil theory to simulate trajectories of ejected particles from host leaf surfaces. In summary, the study visually captures vortical airflow patterns from induced leaf vibrations, uses FTLE to characterize the coherent flow structures that facilitate dry-advection, and compares experimental data on transport with theoretical estimates.   

Effect of Rotary Oscillations on the Coupled Vortex Wake of Two Cylinders.

In the present investigation, we study the effects of rotational oscillations of the two cylinders in a side-by-side configuration at Reynolds number of 150 and spacing ratio, T/D $=$ 4.0. The two cylinders are forced to oscillate in both in-phase and anti-phase configurations. The oscillation amplitude is varied from 0 to $\pi $ radians and the normalized forcing frequency is varied from FR$=$ 0 to 5, where FR is the ratio of forced oscillation frequency to the vortex shedding frequency of a single stationary cylinder. Planar laser induced fluorescence technique is used for visualization. Time and phase averaged PIV measurements are made to study the flow field quantitatively. It is observed that there is strong interaction between the wake vortices at resonant frequencies corresponding to maximum fluctuation intensity and a peak in the circulation. As FR is increased beyond 1.0, the wake structure switches from the coupled wake structure to the double row mode leading to a decrease in the interaction between the two vortex streets. A drag estimate is also made and it is observed that it gets amplified in the resonant frequency range and decreases significantly at higher frequencies compared to the case of two stationary cylinders at the same spacing.   

Spanwise structures in the wake of a rotationally oscillating tapered cylinder

A linearly tapered cylinder executing rotational oscillations is studied experimentally at a Re number (based on mean diameter) of 250. The tapered cylinder is forced to perform rotational oscillations at various oscillation amplitudes and normalized forcing frequencies, FR, ranging from 0 to 4. Hydrogen bubble technique is used for visualizing the wake structure. The cylinder used in the present study has a taper ratio of 70:1 (ratio of length to difference between cylinder end-diameters) and wetted length (L) of 280 mm. The mean diameter of the cylinder is 8mm. Oblique shedding (with oblique angle of 13.5 degrees) is observed for the stationary cylinder. The oblique angle gradually reduces and eventually modifies to parallel shedding with increase of forcing frequency up to a certain FRT (this FRT value comes out to be different for different case of oscillation amplitude). Further increase in FR again transitions to oblique shedding for oscillation amplitude of 45 degs, whereas for other oscillation amplitudes, it remains parallel. Cellular structures are found to be formed for some specific forcing parameters. For oscillation amplitude of 135 degs and forcing frequency of 2, a new 3-D mode is observed with the span-wise wavelength of 1.6.   

Effect of Forcing Frequency in the Flow past a Rotationally Oscillating Cylinder with an Attached Filament

Marine animals, like tadpoles, propel themselves by moving both their head (which resembles a bluff body) as well as their tail. Their motion can be approximately modelled by a rotationally oscillating cylinder with an attached filament - the focus of the study. In the present work, experimental studies are conducted on a rotationally oscillating cylinder with an attached filament at a Reynolds number of 150. The cylinder is forced to oscillate at prescribed forcing parameters. The diagnostics are flow visualization using laser-induced fluorescence technique and velocity and vorticity field data using planar particle image velocimetry. In the present study, the vortices shedding from the cylinder surface interact with the vortices generated at the filament tip and get shed in the wake. Based on the cylinder forcing parameters, significant changes are observed in the wake structure, including a transition from a K\'{a}rm\'{a}n vortex street (indicative of drag) to a reverse K\'{a}rm\'{a}n vortex street (indicative of thrust generation). The observations on the time averaged velocity and vorticity field data are consistent with the convection of vortex pairs arranged in a particular configuration in the wake, as seen from flow visualization data.   

Mixing process parameterization of a building wake impact on a turbulent jet into a crossflow

As the important components of the modern microgrid system, hydrocarbon-fueled distributed generation (DG) units are usually located near population centers, which requires the assessment of air pollutant concentrations near the DG unit. A common DG unit is a building with short chimneys. The plume from a DG chimney is a turbulent jet into the ambient crossflow and would be disturbed by the wake of the building. This scenario includes two classic fluid dynamics topics, a turbulent jet into a crossflow (TJIF) and a blunt body wake. In this study, we conducted computational fluid dynamics (CFD) of the flow field and the concentration field around a series of box-shape building with a short chimney. The CFD results were evaluated using the USEPA wind tunnel measurement. We proposed a concentration field parameterization method, named the Mixture Model, which is the aggregation of different Gaussian-based distributions. The model parameters were determined by the building and chimney dimensions, plume properties, ambient wind features, and the atmospheric boundary layer stabilities. The new method was evaluated by using the USEPA wind tunnel measurement and the field measurement data of the American Gas Association.   

Effect of Curvature on Whisker-Wake Interactions

California sea lions effectively follow hydrodynamic trails, and have been observed to curve their whiskers forward during tracking. To test whether whisker orientation aids tracking, experiments were conducted in a recirculating water channel. A larger cylinder (1/2'' OD, Re$=$1920) created a wake of known shedding frequency and a smooth smaller cylinder (1/8'' OD, Re$=$ 480) was placed downstream, in the larger cylinder's wake. The smaller cylinder was tested in both straight and curved (90 degree) configurations. Stereoscopic particle image velocimetry (PIV) was used to capture the flow field downstream of the smaller cylinder. Discrete Fourier analysis showed that the spectrum of the curved cylinder was dominated by a single peak, corresponding to the large cylinder's shedding frequency, while the straight cylinder showed two dominant frequencies, the large cylinder's and its own shedding frequency. This suggests that a forward-facing, curved whisker is more effective at decomposing complicated wakes because it reduces the noise the whisker itself produces.