Session GR: Vortex Dynamics and 3D Vortex Flows V

Multi-frequency lift forces from vortex shedding behind an oscillating cylinder

Vortex shedding in the wake of a flexibly mounted circular cylinder results in hydrodynamic forces that affect the fatigue life of long cylindrical structures such as cables, risers, and pipelines. Restricting the cylinder to cross-flow vibrations results in forces typically modeled as single frequency sinusoids. We show that this model does not hold when the cylinder is allowed to vibrate in two degrees of freedom (in-line and transverse to the flow). Free vibration motions are replicated in a small towing tank by forcing a cylinder to move in two degrees of freedom with equivalent kinematics to measured free vibrations. Through quantitative flow visualizations and force measurements, we show that over one cycle of transverse free vibration, the relative motion of shed vortices with respect to the cylinder results in large amplitude, multi-frequency harmonic lift forces. The higher harmonics in lift are shown to be enhanced by the in-line motions of the cylinder combined with the phasing between cross-flow and in-line oscillations. A coarse matrix of forced vibration tests is performed with varying in-line amplitude, cross-flow amplitude, phase between in-line and cross-flow motions, and reduced velocity. The database of tests provides a basis for introducing higher harmonic forces into lift coefficient predictions, while showing how in-line motions change the existing coefficients for single frequency sinusoids.   

Particle Image Velocimetry of Vortex Loops in a Laminar Boundary Layer

Time resolved particle image velocimetry (PIV) is used to investigate the development of vortex loops in a laminar boundary layer. Vortex loops are generated in a laminar boundary layer by the impulsive injection of fluid from streamwise aligned slots in the wall. The vortex loops arising from a single slot as well as two slots separated by a small spanwise distance is investigated. A time resolved, phase averaged volume is built up from individual stereoscopic PIV measurement planes. The development of the vortex loops, visualized by the enstrophy of the ensemble averaged velocity fields, reveals a complex interaction of vortex cores between adjacent vortex loops.   

Analysis of the Vortex-Decay Process in the K\'{a}rm\'{a}n Street

In this talk we shall explore the effect of viscosity upon the vorticity distribution and rate of decay of vortex cores in the K\'{a}rm\'{a}n vortex street behind a circular cylinder. We used direct numerical simulation data, which we contrasted against well-known experimental measurements. By decomposing the incompressible velocity field in its solenoidal and harmonic components, we identified the eddy structures associated with the formation, shedding and rearrangement of the vortices into the K\'{a}rm\'{a}n street. We then follow their evolution during the subsequent decay process. This allowed us to extend the conclusions of the partially-viscous model of Hooker (1936), who assumed several simplifying hypothesis: initial infinite-length filament-vortex wake, circular Lamb vortices of equal age at subsequent times, and no overlapping of the vortex cores. We found that the vortex cores exhibit a Gaussian vorticity profile, and a vorticity-stream function scatter-plot clearly consistent with the Lamb-vortex model. The vorticity peak on the core decays downstream with the systematic hyperbolic law given by Lamb's solution, with a rate of decay determined by the amount of circulation contained into the core at the early stages of the street formation.   

The Wake Behind a Rolling Sphere

Experiments were carried out for a sphere translating along a wall with different rates of rotation, ranging from forward rolling, to pure sliding and backwards rolling. Flow visualizations have revealed four distinct flow regimes which exist for Reynolds numbers between 80 and 300. Dramatic changes in wake structure occurred, corresponding to different senses and magnitudes of the imposed rotation. Two steady flow regimes were observed and in this range of Reynolds number, the transition to unsteady flow led to either the shedding of vortex loops, similar to that for the isolated sphere, or an antisymmetric wake composed of a counter-rotating streamwise vortex pair.   

Near wake structure of a wall-mounted finite-length square cylinder

The wake of an `infinite' cylinder has long been extensively studied. While, in various engineering applications, the cylinder-like structures often have a finite length, most with one end free and the other mounted on a flat plate. Due to the three dimensionality caused by the free end, the limited length and the ground-wall boundary layer, the flow structure of a finite cylinder should differ drastically from that of an infinite one. Indeed, such a great difference has been found by quite a number of previous investigations. However, it remains a subject of some debate to date, especially the fundamentals of near wake flow structures. This paper reports an experimental investigation of the near-wake structure of a finite-length square cylinder. The aspect ratio ranges from 3 to 7. Present measurements were carried out mainly in a low-speed wind tunnel at Re=9300, using hot-wire anemometer and PIV. To gain the topology of the wake, PIV measurements were performed in streamwise, lateral and spanwise directions. In addition, flow visualizations were also conducted to demonstrate more clearly the downstream development of the near-wake structure. A new flow model is proposed for the near wake structure based on the present experimental results.   

Lagrangian analysis of vortex shedding behind a 2D airfoil

Identifying the coherent structures and their interactions in the mixing zone is a useful means in designing future flow control strategies. To this end, a Lagrangian analysis of two-dimensional vortex shedding over an Eppler 387 airfoil is presented. Stable and unstable material manifolds in the flow are identified. Unstable manifolds such a the shear layer characterize a barrier to fluid mixing and are easily visualized using dye injection in an experiment. On the other hand, stable manifolds are more difficult to visualize in an experiment. Reattachment lines are examples of such manifolds. As such the existence of these structures in the flow, is presented and how these structures are useful in understanding vortex shedding is explored. The manifold structure is also presented in a time averaged view, allowing a comparison with the traditional separation bubble. Furthermore, lobe dynamic calculation are performed and the fluid entrainment into shedded vortices are investigated. Finally, investigation of correlation between the behavior of the material manifolds and more traditional quantities such as skin friction, flow phase portrait, and pressure is presented.   

On the Decay of Axial Flow in a q-Vortex

A q-vortex is a model isolated vortex flow with both axial and azimuthal velocity components. The presence of an axial flow of sufficient strength results in an instability. Previous direct numerical simulations of a turbulent q-vortex have shown that as the turbulence develops the mean flow changes such that the axial velocity decreases more rapidly than the azimuthal velocity. As the flow becomes swirl dominated, the instability is lost and the turbulence decays. What has been unclear is why the axial velocity decays more rapidly than the azimuthal velocity. Examination of the laminar self-similar solution on which the q-vortex is based reveals a similar behavior. By considering the azimuthal and axial components of vorticity a simple explanation is found for why the axial velocity decays more quickly than the azimuthal velocity. This explanation is valid for the turbulent case as well.   

Axisymmetric interaction between a laminar vortex ring and a sphere -- stationary sphere case.

The interaction between a vortex ring and a neutrally buoyant sphere centered in the axis of travel of the ring is one of the simplest fluid-structure interactions and was commented on by Lord Kelvin. A starting case in order to calculate this case is to have a laminar vortex ring interact with a stationary sphere. In order to calculate this interaction, a high-order 3D immersed boundary flow solver was used. The momentum equations are spatially discretized on a staggered mesh by finite differences and all derivatives are evaluated with implicit 10th order compact finite difference schemes. The fourth order accurate Runge-Kutta scheme was used for temporal discretization. The immersed boundary was implemented through a direct forcing procedure. It is shown that as the vortex approaches the sphere, significant secondary vorticity is generated on the surface of the sphere. As the interaction continues and the vortex ring diameter increases in response to the presence of the sphere, a secondary vorticity ring wraps around the front of the advancing vortex. This secondary ring separates from the surface and breaks up as it interacts with the primary ring. For Reynolds number around 1000, a three-dimensional azimuthal instability, which appears to be of centrifugal nature, grows on the secondary vorticity ring.   

The Vortices Trapped above Low-aspect-ratio Wings

A stationary vortex trapped above the nondelta, low-aspect-ratio wings was first obtained in 3D unsteady numerical simulation. Flow visualization was conducted in water-channel using hydrogen bubble. The results verify that there is a vortex trapped above the low-aspect-ratio wings and the stationary vortex is consisted of two semi-ball, anti-rotation vortices which are different from the leading edge vortices on the delta wing. This stationary vortex trapped above the nondelta, low-aspect-ratio wings is a new phenomenon, which is different from the leading edge vortex on the delta wing. The numerical results show that lift coefficient increase to 0.8 when incidence increases form 0$^{\circ}$ to 30$^{\circ}$, the lift coefficient keeps this value up to 45$^{\circ}$--a very high stall angle. The numerical results indicate that the trapped vortex might be the source of the high stall angle of attack and nonlinear lift at high incidence. Accompanied with the low-aspect-ratio wing, the existence of the stationary vortex is thought to be related to the strong effects of tip vortices. Further experimental and numerical works have been undertaken, the results show that trapped vortices have variant shapes and different critical angels of attack.   

Tilt-induced instability of a vortex in a stratified fluid

The dynamics and stability of a vortex in a linearly stratified fluid is studied experimentally and theoretically when the axis of the vortex is slightly inclined with respect to the direction of stratification. For Froude numbers larger than one, the tilt of the axis induces strong density gradients and an intense axial flow in a rim around the vortex, at the radius where the angular velocity of the vortex is equal to the Brunt-Vaisala frequency. This critical layer can be studied theoretically in the viscous regime, which shows that the axial flow changes from a jet to a shear layer when turning around the vortex, in excellent agreement with the PIV measurements. For high Reynolds numbers, this axial flow creates a Kelvin-Helmholtz instability and a jet instability, leading to secondary vortices rolled-up around the primary vortex. The growth rates of these instabilities have been measured and compared to predictions from a linear stability analysis. These three-dimensional instabilities of the tilted vortex does not lead to the destruction of the vortex, but it decreases its core size if the Froude number is larger but close to one.