Session EO: Separated Flows II

Dynamics of separation over airfoils at low Reynolds numbers, Part I: 2D equilibria and reduced-order models

We present results of a computational study of dynamics of separation over airfoils using an immersed boundary method and a collection of other tools. Computational wrappers are developed to enable the DNS code to perform bifurcation studies (using Newton-GMRES iterations) and linear stability analysis (using Arnoldi's method). These techniques are used to study the flow past a flat plate at large angles of attack and low Reynolds numbers. We compute the unstable steady states and compare them with the periodically shedding unsteady flow. We observe that the unstable steady state resembles the unsteady flow at times corresponding to the minimum lift, in which a strong trailing edge vortex is present, while at maximum lift for the unsteady flow, a stronger leading edge vortex is present. Low-dimensional models of the flow linearized about the stable fixed points at low angles of attack are obtained using an approximate balanced truncation technique and POD modes, and compared with standard POD/Galerkin models.   

Dynamics of separation over airfoils at low Reynolds number, Part II: Three-dimensional effects

Experimental studies of low-aspect ratio flapping and rotating wings at low Reynolds number and high angle-of-attack have highlighted the stabilizing influence of three-dimensionality and rotation on the flow and in particular the leading-edge vortex. For purely translating wings, few measurements have been reported in the literature. We employ a new formulation of the immersed-boundary method to numerically investigate the dynamics and stability of three-dimensional separated flow behind a translating flat plate at low Reynolds number. The computations are validated by comparing forces and velocity fields with experimental measurements in an oil tow tank and a recirculating oil tunnel. Bifurcations from steady flow to vortex shedding are characterized as a function of aspect ratio, angle-of-attack, and Reynolds number. The influence of planform shape on the spanwise transport of vorticity is also investigated.   

Spanwise visualization of the flow around a three-dimensional foil with leading edge protuberances

Studies of model humpback whale fins have shown that leading edge protuberances, or tubercles, can lead to delayed stall and increased lift at higher angles of attack, compared to foils with geometrically smooth leading edges. Such enhanced performance characteristics could prove highly useful in underwater vehicles such as gliders or long range AUVs (autonomous underwater vehicles). In this work, Particle Imaging Velocimetry (PIV) is performed on two static wings in a water tunnel over a range of angles of attack. These three- dimensional, finite-aspect ratio wings are modeled after a humpback whale flipper and are identical in shape, tapered from root to tip, except for the leading edge. In one of the foils the leading edge is smooth, whereas in the other, regularly spaced leading edge bumps are machined to simulate the whale’s fin tubercles. Results from these PIV tests reveal distinct cells where coherent flow structures are destroyed as a result of the leading edge perturbations. Tests are performed at Reynolds numbers $Re \sim$ O($10^5$), based on chordlength, in a recirculating water tunnel. An inline six-axis load cell is mounted to measure the forces on the foil over a range of static pitch angles. It is hypothesized that this spanwise breakup of coherent vortical structures is responsible for the delayed angle of stall. These quantitative experiments complement exiting qualitative studies with two dimensional foils.   

Separation Control on a Hydrofoil Using Leading Edge Protuberances

Experiments were conducted on a series of two dimensional symmetric hydrofoils with leading edge protuberances. The foils were CNC machined, each having sinusoidal protuberances of fixed amplitude and period. The protuberance amplitude ranged from 2.5 to 12{\%} of the chord. The mean chord Reynolds number was 1.8 $\times $ 10$^{5}$, and angles of attack up to 30 degrees were used. Lift and drag of foils with leading edge protuberances were compared to that of a baseline foil. To visualize the flow separation, surface tufts and dye injection were also employed. Mapping of the velocity field in the vicinity of protuberances was accomplished by a two component LDV system. The results indicate that the foils with leading edge protuberances do not experience stall in the same manner as the baseline foil. Moreover, the foils with leading edge protuberances produce greater lift than the baseline foil at post-stall angles of attack with little or no drag penalty. The flow visualization indicates induced streamwise vortex pairs at the shoulders of the protuberances. These streamwise vortices are thought to be responsible for the improved post-stall performance of foils with leading edge protuberances.   

Application of separated flow control over a cylindrical turret

Our research group is working in the development of real time closed loop separation control for aero-optical applications. It is been demonstrated (Jumper et al., 2001) that turbulence causes a reduction in the performance of the optical system. Our approach involves the application of 22 zero net-mass flux actuators created by a 50 mm piezoelectric disks uniformly distributed upstream over a cylindrical turret. Particle Image Velocimetry, PIV, is being used as a tool to capture the velocity field and simultaneously sampled surface pressure around the turret. Low dimensional tools like Proper Orthogonal Decomposition, POD, and Linear Stochastic Estimation, LSE, are also being utilized for the development of real time closed loop control in a similar fashion as Pinier et al. (to appear AIAA Journal) applied these tools to the NACA 4412.   

Control of the Near-Wake of a Cylinder: Effect of a Spanwise Wire

The effect of a single, spanwise surface wire on the overall structure of the near-wake of a cylinder is addressed. The Reynolds number is 10,000, and the wire diameter is approximately one percent of the cylinder diameter. A technique of high-image-density particle image velocimetry allows characterization of the instantaneous and averaged patterns of the flow structure in conjunction with spectral analysis at a large number of points over the flow domain. As the angular position of the wire is altered, relative to the forward stagnation point of the cylinder, patterns of asymmetry of the near-wake structure are induced over a range of angular positions. These patterns of vorticity, streamline topology and Reynolds stress are all interrelated, and a key feature is the relatively early transition to turbulence and thereby production of relatively large Reynolds stress in the separating shear layer from the wire side of the cylinder. A new concept of critical angles of the wire is introduced; these angles are interpreted in terms of extension and contraction of the near-wake.   

Understanding mode transitions in vortex-induced vibrations of a circular cylinders using controlled vibration

In this study we have made extensive measurements of the fluid forces on a cylinder that is controlled to oscillate transverse to a free stream at Re = 4000. These measurements were used to create extremely high-resolution contour plots of the magnitude of the fluid force, and the phase angle between the forces and body motion, in the plane of normalized amplitude and frequency. We find transitions in certain regions of this plane where the character of the fluid forces changes between distinct modes. Interestingly, these transitions correspond well with boundaries separating different vortex shedding modes in the Williamson-Roshko (1988) map. A further fascinating characteristic, which is only observable with very high-resolution data, is the existence of regimes where two modes overlap. By examining the energy transfer from fluid to cylinder we are able to predict the response of an elastically mounted cylinder that agrees surprisingly well with measured the free vibration response of Govardhan {\&} Williamson (2006) at both high and low mass-damping. Furthermore, by looking at the shape of the excitation contours and the transitions between different modes, we are able to exhibit clearly the hysteretic and intermittent switching mode transitions, which occur between different branches of the free vibration response. As part of our ongoing research, we plan to extend our high-resolution data to higher Re.   

Sting-free Unsteady Flowfield, Base Pressure and Force Measurements on Axisymmetric Bluff-Body

To avoid interference of model support, flowfields as well as aerodynamic force and base pressure on blunt short cylinders in axial flow were measured at Re=100,000 with the JAXA 60cm magnetic suspension and balance system. The fineness ratio ranged from 1.27 to 1.79. A digital telemeter system was developed for the base pressure measurement, and the velocity field was obtained using a PIV system. Vortices along separating shear layer and shear layer flappings with or without reattachment on the wall were observed. Downstream the cylinder in the azimuthal plane, PIV snapshots showed large-scale motion of longitudinal vortices. These instantaneous flowfields presented excellent axisymmetry when they were ensemble-averaged. Mean base pressure agreed with the drag variation at different fineness ratios. The present magnetic suspension and balance system allowed evaluation of low frequency unsteady aerodynamic force vector from feedback current to the coils and the detected small model movement. Base pressure fluctuations were compared with the drag fluctuations and discussed in light of overall flowfield phenomena.