Session H10: Instability: Wakes II - Non-Cylindrical Objects and Wind Tunnels

Turbulent axisymmetric swirling wake: equilibrium similarity solution and experiments with a wind turbine as wake generator

An analytical and experimental investigation of the turbulent axisymmetric swirling wake was carried out. An equilibrium similarity theory was derived that obtained scaling functions from conditions for similarity from the equations of motion, leading to a new scaling function for the decay of the swirling velocity component. Axial and azimuthal (swirl) velocity fields were measured in the wake of a single 3-bladed model wind turbine with rotor diameter of 0.91 m, up to 20 diameters downstream, using X-wire constant temperature hot-wire anemometry. The turbine was positioned in the free stream, near the entrance of the UNH Flow Physics Facility, which has a test section of 6m x 2.7m cross section and 72m length. Measurements were conducted at different rotor loading conditions with blade tip-speed ratios up to 2.8. At $U_\infty$=7 m/s, the Reynolds number based on turbine diameter was approximately 5 $\times 10^5$. Both mean velocity deficit and mean swirl were found to persist beyond 20 diameters downstream. First evidence for a new scaling function for the mean swirl, $W_{max}\propto U_o^{3/2}\propto x^{-1}$ was found. The similarity solution thus predicts that in the axisymmetric swirling wake mean swirl decays faster with $x^{-1}$ than mean velocity deficit with $x^{-2/3}$.   

Experimental Investigation of Very Large Model Wind Turbine Arrays

The decrease in energy yield in large wind farms (array losses) and associated revenue losses can be significant. When arrays are sufficiently large they can reach what is known as a fully developed wind turbine array boundary layer, or fully developed wind farm condition. This occurs when the turbulence statistics and the structure of the turbulence, within and above a wind farm, as well as the performance of the turbines remain the same from one row to the next. The study of this condition and how it is affected by parameters such as turbine spacing, power extraction, tip speed ratio, etc. is important for the optimization of large wind farms. An experimental investigation of the fully developed wind farm condition was conducted using a large array of porous disks (upstream) and realistically scaled 3-bladed wind turbines with a diameter of 0.25m. The turbines and porous disks were placed inside a naturally grown turbulent boundary layer in the 6m x 2.5m x 72m test section of the UNH Flow Physics Facility which can achieve test section velocities of up to 14 m/s and Reynolds numbers $\delta^+ = \delta u_\tau / \nu \approx 20,000$. Power, rate of rotation and rotor thrust were measured for select turbines, and hot-wire anemometry was used for flow measurements.   

Stability of a wind turbine wake subject to root vortex perturbations

Results for DNS of a wind turbine wake will be presented. The Tj\ae borg wind turbine geometry is modelled using a spectral element solver in coupled to an actuator line model described by S\o rensen and Shen (2002). The actuator line model considers the flow over the turbine by calculating body forces derived from two-dimensional airfoil data and flow velocity localised at the blade. Using such a model, Ivanell et al.\ (2010) identified instabilities in the tip vortex for sinusoidal perturbations that reduced the streamwise spacing between tip vortices. In work to be presented we consider perturbations to the blade-root vortex of the turbine. We examine whether perturbations to the root vortex can excite instability mechanisms in the tip vortex and potentially modify tip vortex downstream extents. We also explore how changes to the spacing between root and tip vortices modifies these effects. Ivanell et al.\ (2010) \emph{J Wind Energy} \textbf{13}, S\o rensen and Shen. (2002) \emph{J Fluids Eng} \textbf{124}.   

Base Flow Asymmetry Effects on the Absolute Stability of Non-uniform Density Wakes

This work investigates the hydrodynamic stability of bluff body wakes with non-uniform mean density. Such flows are common in bluff body combustors. The absolute/convective stability characteristics of the wake are important, because vortex shedding from the bluff body participates in such processes as mixing, flame blowoff, and combustion instability. Non-uniform density is a sensitive stability parameter for wake flows. Reduction of the wake density relative to the free stream density can stabilize the flow and suppress coherent vortex shedding. Practical bluff body combustors operate at a range of flame density ratios spanning this stability limit. Recent experimental bluff body combustor work by Tuttle et al. investigates wakes with asymmetry in the base flow density profiles. This motivates a hydrodynamic stability model for non-uniform density wakes that includes base flow asymmetry. The model developed in this study investigates the effects of asymmetric base flow velocity and density profiles. It begins with a parameterization of the base flow asymmetries. Results show that base flow asymmetry influences the absolute stability of the flow, and has a strong effect on the most amplified mode shape. The investigation concludes with a comparison to the vorticity equation. Here, we elucidate the physics of the model, and comment on the limitations of such a model.   

The mechanisms of convective and standing wave mode generation in the wake behind very slender asisymmetric bodies by selective excitation of unstable helical modes

Experiments of Asai, et al. (2011) confirm earlier experiments of Sato {\&} Okada (1966), Peterson {\&} Hama (1976) that, for sufficiently slender axisymmetric bodies of revolution placed in a stream parallel to the axes, only convectively unstable modes exist. However, in the downstream nonlinear region, the present theoretical/computational work shows that the imposition of the most unstable helical modes results in the generation of a stationary harmonic-helical mode that persists downstream. This is elucidated from energy transfer mechanism from the mean flow and inter-mode energy transfer via triad interactions. While absolute unstable modes behind bluff bodies of revolution are a natural occurrence according to the linear theory, the presence of such modes behind very slender bodies of revolution is a consequence of downstream nonlinear interactions between the excited helical modes.   

Experimental study of the interaction between the horseshoe system and the vortex shedding of a wall-mounted rectangular cylinder

The interaction between the horseshoe vortex system (HVS) and the shedding of large-scale vortical structures of a wall-mounted rectangular cylinder (height-to-width ratio h/d $=$ 4) is investigated experimentally for both a canonical and a perturbed boundary layers ($\delta $/h $=$ 0.18 and 0.64, respectively). The Reynolds number is Re$_{d} =$ 12000. The 3D flow is reconstructed from uncorrelated 2D snapshots of time-resolved Particle Image Velocimetry data, using proper orthogonal decomposition, a phase-averaging technique and symmetry/antisymmetry decomposition of the flow. It is found that the dynamics of the HVS affects the topology of the vortex shedding near the wall, particularly for the thicker boundary layer. The back-flow and the zero-flow modes of the HVS have particular influence on the symmetry of the horseshoe legs and its momentum content. The orientation and the momentum content of the horseshoe legs can result in the bend of the shedding vortices towards the cylinder back wall. An interaction between the tip and the junction flows is also observed just downstream from the obstacle. A downwash mechanism and a like eruption process are evidenced for the natural boundary layer whether a strong upwash dominate the tip-junction interaction for the thicker boundary layer.   

Path instabilities of heavy bodies in free fall in a viscous fluid: wake dynamics vs. aerodynamic effects

Solid bodies in free fall in a viscous fluid generally fall along a non-straight path, and a variety of periodic (fluttering, tumbling) and non-periodic regimes can be observed. We analyze the structure of the couplings between the fluid and the body, restricting to a linear stability framework. Introducing a simple toy model consisting of a infinitely long plate sliding along a vertical wall, we show that in the limit of large solid-to-fluid masses a decoupling takes place, allowing us to distinguish two kinds of modes: ``wake'' modes in which the body motion has virtually no influence, and ``body'' modes for which the intrinsic wake dynamics can be neglected. Turning to more realistic objects, we show that the ``body'' modes can be described through a rationally derived aerodynamic model (based on quasi-static assumptions), yielding either a static instability, or a dynamic, low-frequency, instability. Considering 2D rectangular rods and 3D disks, we explore the competition between the three kinds of instabilities. For objects elongated in the spanwise direction, it is found that wake instability dominates in case of 2D rectangles and low-frequency instability dominates in case of disks. For objects elongated in the streamwise direction, static instability always dominate.