Session A21: Vortex Dynamics I

Effects of formation time and flexibility on the starting and stopping vortices in piston-cylinder devices

A computational study has been conducted to address the formation of vortex rings ejected from a weakly flexible nozzle at the end of a piston-cylinder device. The first observation is that, regardless of flexibility, for small enough duration of a push on the piston, the negatively-signed induced vorticity on the outside of the cylinder merges with the stopping vortex and spills into the core and pairs up with the primary (starting) vortex. The second observation is that the flexibility of the exit nozzle affects the behavior of the vortex by changing the effective diameter of the exit. Also, the snapping back of the nozzle strengthens this interaction. To model the flexibility, two approaches have been used in the study. First, the nozzle is modeled using a torsional-spring-mass-rigid system which is allowed to rotate about a hinge and its rotation is coupled with the flow solver. Second, the nozzle is considered as an elastic material and its deflection is solved using a FEM solver. It is hypothesized that the presence of flexibility in the model increases the time scale as well as the thrust as compared with results from rigid nozzle models. A study is conducted to find the highest thrust generated versus the flexural parameters.   

Computational Analysis of Vortex Formation Over a Flat Plate with Gradient-Based Slip Condition

A thorough understanding of small scale aerodynamics is important for the design of micro air vehicles. Since they fly in the same Re regime as that of insects, these animals can provide biologically inspired designs. Butterflies have small scales (on the order of 100 microns in length) that line the surface of their wings; these scales can affect the slip condition over their wings, altering vortex formation and possibly leading to improved flight characteristics. In particular, it is believed that the scales impose a preferential direction for flow over the wing. To test this hypothesis, 2D flow over an infinitely thin flat plate was studied using the CFD software FLUENT. The slip condition was specified by defining an imposed velocity gradient on the plate's surface. Differences in vortex growth and formation are discussed with the goal of ascertaining whether the existence of a preferential flow direction leads to improved flight performance.   

Optimal energy harvesting from long cables in VIV

Vortex-induced vibrations (VIV) of flexible structures in steady flows may result in large amplitude self-sustained oscillations of the solid, making it an attractive mechanism for energy harvesting. Here, we investigate the possibility of harvesting energy using long tensioned cables in VIV with localized energy extraction. The non-linear fluid-solid dynamics is described using a classical Van der Pol wake oscillator and the energy harvesting device is represented by a discrete damping distribution (dashpots). The cable extracts energy from the flow along its entire length, but it is also responsible for the transport of the harvested energy toward the dashpots. Focusing on the permanent saturated regime, we study this energy transfer along the cable, and determine the optimal damping distribution that maximizes the harvested energy.   

Phase drift between the in-line and cross-flow vortex-induced vibrations of a long flexible cylinder in shear flow

Long flexible structures with bluff cross-sections placed in cross-flow exhibit vortex- induced vibrations. The in-line and cross-flow vibrations generally occur with a frequency ratio of two leading to figure-eight orbits in the plane perpendicular to the span. The structure is excited by the flow under a lock-in condition defined as the synchronization between vortex shedding and body displacement. Previously, we have shown that, in sheared current, the region of lock-in is characterized by trajectories where the structure moves upstream at the extremes of the cross-flow motion. Recent experimental and numerical studies have emphasized a phenomenon of phase drift between in-line and cross-flow vibrations dominated by traveling waves, that induces a continuous change in the shape and orientation of the flexible body orbit along the span. In the present work, we elucidate the link between this phenomenon and the departure from a ratio of two between the in-line and cross-flow excited structural wavenumbers and we show, by means of numerical simulation, that the effective added mass in each direction controls the phase drift.   

Numerical simulations of flow past flat plates

The starting vortex in flow past a finite and a semi-infinite plate is studied numerically, using a semi-Lagrangian, compact finite difference method with an implicit time-stepping scheme. The results are compared with those existing in the literature for driven cavity flow and flow past plates. The effects of viscosity on the core trajectory and the shed circulation are investigated. Furthermore, an alternative vortex method is explored which has more flexibility in terms of the fluid domain, and is potentially much faster, provided a fast summation algorithm is used.   

Unsteady vortical structures in porous media flows

The pore scale character of moderate Reynolds number, inertial flow through mono-disperse packed beds of spheres is examined using numerical experiments. Direct numerical simulations are performed for flow through (i) a periodic, $3\times3\times6$ simple cubic arrangement at $Re_p=529$, and (ii) a realistic randomly packed tube containing 326 spheres with $d_{tube}/d_{sp}=5.96$ at $Re_p=600$. At these Reynolds numbers, unsteady vortical regions are dominant features at the pore scale, and can have a profound effect on permeability and dispersion properties at the macro-scale. Despite similar Reynolds numbers and mean void fractions, the vortical structures observed in these two flows are remarkably different. The flow through the arranged packing is characterized by spatially and temporally periodic vortex-ring like structures, while the flow through the random packing contains many elongated helical vortices and a wider spectrum of space and time scales. The sensitive dependence of flow length and time scales and the local pore geometry is investigated using the DNS data.   

POD-based Reduced-order Model for Forced Motion and Vortex-Induced Vibration of a Circular Cylinder

For flow past a cylinder either held fixed, in prescribed harmonic motion perpendicular to the mean flow, or mounted on a linear spring and undergoing vortex-induced vibration (VIV) perpendicular to the mean flow, a finite-element method (FEM) is used to compute high-fidelity solutions of the Navier-Stokes equations at $Re=100$ (based on diameter). By means of proper orthogonal decomposition, the computed velocity field is used to construct a set of orthogonal vector-valued velocity modes. The pressure field is decomposed into a set of nonorthogonal modes. An approximate reduced-order model (ROM) is obtained by projecting the Navier-Stokes equations onto these modes. To stabilize the resulting ordinary differential equation system, we add a ``shift mode'' calculated using the steady symmetric solution for a stationary cylinder. For all three cases (stationary cylinder, prescribed motion, and VIV), the ROM gives velocity and pressure fields in good agreement with the high-fidelity FEM results.   

Passive Suppression of Vortex-Induced Vibration of a Cylinder at $Re=100$

For a Reynolds number (\textit{Re}) based on cylinder diameter of 100 and a ratio of cylinder density to fluid density of 10, we investigate the use of an essentially nonlinear approach to passive suppression of vortex-induced vibration (VIV) of a rigid circular cylinder restrained by a linear spring, and constrained to move perpendicular to the mean flow. The variational multiscale residual-based stabilized finite-element method used to compute approximate solutions of the incompressible Navier-Stokes equations about the moving cylinder is coupled to a simple model of a ``nonlinear energy sink'' (NES), an essentially nonlinear oscillator consisting of a mass, a linear damper, and a strongly nonlinear spring. The NES promotes nearly one-way transfer of energy from the primary structure (the cylinder) to itself, resulting in reduction of the amplitude of the limit cycle oscillation by as much as 75{\%}, depending on the parameters characterizing the NES. Various mechanisms of VIV suppression by the NES are discussed, along with results showing the effectiveness, over a range of \textit{Re}, of passive suppression using an NES whose parameters were selected to work well at $Re=100$.   

Flow around a cylinder fitted with strakes

In this paper, we investigate numerically the mechanism of suppression of vortex-induced vibration by using helical strakes. Although the strakes effectiveness has been assessed, the suppression mechanism is yet not well established. Most works point out that the main aspect on the suppression is the decrease in the vortex shedding correlation along the span. The flow in the spanwise direction induced by the shape of the strakes is also another reason for suppression of vortex-induced vibration. Computational simulation of the flow around a fixed circular cylinder fitted with strakes are carried out for Reynolds number 1,000 and 10,000 in order to ratify that the main aspect on the suppression mechanism is the decrease in the vortex shedding correlation along the span. To support the latter allegation, we employ a spatial correlation of the mean velocity fields, and we also investigate the instantaneous resulting fluid forces on different sections along the body in comparison to experimental measurements. We also observe that the vortex wake is formed farther downstream and we can identify this as a secondary mechanism of vortex-induced vibrations suppression. A comparison of velocity fields from particle image velocimetry with the simulation results is presented in order to support the simulation analysis.