Session G35: Turbulence: Wakes

Anisotropic character of low-order turbulent flow descriptions with the proper orthogonal decomposition

Proper orthogonal decomposition (POD) is applied to data from distinct sets to characterize the error arising in the description of turbulence. Wind turbine wake experiment data and direct numerical simulation data from a fully developed channel flow are used to illustrate dependence of the anisotropy tensor invariants on the modes used in low-order descriptions. Reduced order flow descriptions via truncated POD bases greatly exaggerate turbulence anisotropy and can lead to a loss of three-dimensionality in extreme cases. Simple corrections to the low-order descriptions significantly reduces the errors. Similar gains are seen in the anisotropy tensor invariants. Corrections of this form reintroduces three-dimensionality to severely truncated POD bases. A threshold for truncating the POD basis based on the equivalent anisotropy factor for each measurement set requires many more modes than a threshold based on energy. The mode requirement to reach the anisotropy threshold after correction is reduced by an order of magnitude for all example data sets, ensuring that economical low-dimensional models in terms of modes included account for the isotropic quality of the turbulence field.   

A Predictive Model for Wind Farms Using Dynamic Mode Decomposition

In this work we extend traditional dynamic mode decomposition (DMD) to develop a linear predictive model for the time evolution of the velocity field for a multiple-turbine wind farm. Traditional DMD identifies a set of DMD modes which can be used to produce a linear system that approximates the dynamics of the original system. Typically, these DMD modes consist of those that both grow and decay, but in order to develop a predictive model we need a system that evolves along a manifold that neither grows nor decays. Here we modify the DMD calculation to build such a model. We then apply this method to three dimensional large eddy simulations (LES) of a multi-turbine wind farm. Our predictive wind farm model is initialized with a small time series of data independent of the original data used to create the system. When initialized in this manner our DMD based model can reproduce the subsequent time evolution of the velocity field over ten inter-turbine convective timescales with a gradual falloff in performance.   

Low dimensional representations of side-by-side cylinders in cross-flow subject to varying freestream turbulence

Particle image velocity is employed to capture the near and intermediate wakes of pairs of side-by-side cylinders in cross-flow with varying levels of incoming freestream turbulence. Four sets of inflow conditions are each applied to three different transverse cylinder-to-cylinder spacing values. The center-to-center distance between the cylinders as well as the turbulence of the inflow heavily impact the mean velocity components as well as the Reynolds stresses. Proper orthogonal decomposition is used to further characterize the influence of freestream turbulence of the inflow on the wakes of each set cylinder transverse spacing.   

Experimental investigation of axially aligned flow past spinning cylinders.

Experimental and numerical results of ongoing subsonic investigations of the flow field about axially aligned spinning cylinders with variable inter-cylinder spacing are presented. The experimental design is capable of investigating wake dynamics of the modeled system up to a Reynolds Number of 300,000 and rotation numbers up to 2. The experimental results are used to validate and confirm numerical simulations with and without the effects of swirl. The focus of the overall effort is an understanding of the dynamics of multi-body problems in a flow field, as such we relate the ongoing effort to previous studies by both the authors and the community at large and our ongoing work in developing accurate plant models for use in engineering analysis and design.   

The Effect of Flow Curvature on the Axisymmetric Wake

The swirling turbulent wake is a perturbation to the canonical axisymmetric turbulent wake. Past studies of the axisymmetric turbulent wake have increased understanding of wake Reynolds number influence on wake characteristics such as centerline wake velocity deficit and wake width. In comparison, the axisymmetric turbulent swirling wake has received little attention. Earlier work by our group has shown that the addition of swirl can change the characteristics of the wake. The goal of this current work is to examine how wake mean flow quantities are related to the wake Reynolds number and the swirl number, where the latter quantity is the ratio of the angular momentum flux to the axial momentum deficit flux. A custom designed swirling wake generator is used in a low turbulence intensity wind tunnel flow to study the turbulent swirling wake in isolation. Stereoscopic Particle Image Velocimetry is used to obtain three component velocity fields in the axial-radial plane. From this data, the wake Reynolds number, the swirl number, centerline velocity decay, wake width, and other relevant wake mean flow quantities are determined. Using these results, the impact of swirl on wake development is discussed.   

Hydrodynamic mechanism behind the suppression of vortex-induced vibration with permeable meshes

Vortex-induced vibration (VIV) induces resonant vibrations on elastic bluff bodies when exposed to a flow. A VIV suppressor called ``\emph{ventilated trousers}'' (VT) -- consisting of a flexible net with tens of \emph{bobbins} fitted every other node -- has been developed as a commercial solution. Only a few experiments in the literature have evaluated the effectiveness of the VT, but very little is know about the underlying mechanism behind the suppression. Experiments have been carried out in a water channel with models of circular cylinders fitted with three different permeable meshes. VIV response and drag were obtained for models free to oscillate in the cross-flow direction with low mass and damping ($Re=5,000$ to 25,000). All meshes achieved an average 50\% reduction of the peak amplitude and reduced the mean drag when compared to that of a bare cylinder. PIV visualization of the wake revealed that the VT produced a much longer vortex-formation length, thus explaining its enhanced efficiency in suppressing VIV and reducing drag. The geometry and distribution of the bobbins proved to be important parameters. PIV also revealed the rich three-dimensional flow structures created by the bobbins that disrupt the formation of a coherent vortex wake.   

Vortex dynamics in the near-wake of tabs with various geometries using 2D and 3D PIV.

The vortex dynamics and turbulence statistics in the near-wake of rectangular, trapezoidal, triangular, and ellipsoidal tabs were studied in a refractive-index-matching channel at Re $=$ 2000 and 13000, based on the tab height. The tabs share the same bulk dimensions including a 17 mm height, a 28 mm base width, and a 24.5o angle. 3D PIV was used to study the mean flow and dominant large-scale vortices, while high-spatial resolution planar PIV was used to quantify high-order statistics. The results show the coexistence of counter-rotating vortex pair (CVP) and hairpin structures. These vortices exhibit distinctive topology and strength across Re and tab geometry. The CVP is a steady structure that grows in strength over a significantly longer distance at the low Re due to the lower turbulence levels and the delayed shedding of the hairpin vortices. These features at the low Re are associated with the presence of K-H instability that develops over three tab heights. The interaction between the hairpins and CVP is measured in 3D for the first time and shows complex coexistence. Although the CVP suffers deformation and splitting at times, it maintains its presence and leads to significant spanwise and wall-normal flows.   

Characterizing cycle-to-cycle variations of the shedding cycle in the turbulent wake of a normal flat plate using generalized phase averages.

Quasi-periodic vortex shedding in the turbulent wake of a thin-flat plate placed normal to a uniform stream at Reynolds number of 6700 is investigated based on Particle Image Velocimetry experiments. The wake structure and vortex formation are characterized using a generalized phase average (GPA), a refinement of the triple decomposition of Reynolds and Hussain (1970) incorporating elements of mean-field theory (Stuart, 1958). The resulting analysis highlights the importance of cycle-to-cycle variations in characterizing vortex formation, wake topology and the residual turbulent Reynolds Stresses. For example, it is shown that during high-amplitude cycles vorticity is strongly concentrated within the well-organized shed vortices, whereas during low-amplitude cycles the shed vortices are highly distorted resulting in significant modulation of the shedding frequency. It is found that high-amplitude cycles contribute more to the coherent Reynolds stress field while the low-amplitude cycles contribute to the residual stress field. It is further shown that traditional phase-averaging techniques lead to an over-estimation of the residual stress field.   

Coherent structures and enstrophy dynamics in highly stratified flow past a sphere at Re = 3700

Vortex dynamics of flow past a sphere in a linearly stratified environment is investigated. Simulations are carried out for a flow with Reynolds number of 3700 and for several Froude numbers ($Fr$) ranging as low as 0.025. Isosurface of Q criterion is used to identify vortical structures whose cross-section and orientation are found to be affected by buoyancy. At low $Fr = 0.025$, pancake eddies and surfboard-like inclined structures emerge in the near wake and have a regular streamwise spacing that is associated with the frequency of vortex shedding from the sphere. Similar to turbulent kinetic energy, the enstrophy in the near wake decreases with decreasing $Fr$ (increasing stratification) until a minimum at $Fr = 0.5$ but the trend reverses in the low-$Fr$ regime. Vortex stretching by fluctuating and mean strain are both responsible for enhancing vorticity with relatively small contribution from the baroclinic term. Decreasing $Fr$ to $O(1)$ values tends to suppress vortex stretching. Upon further reduction of $Fr$ below 0.25, the vortex stretching term takes large values near the sphere.   

Dynamics of flow over a sphere at moderate Re in a highly stratified fluid

Direct numerical simulations (DNS) are performed to investigate the flow past a sphere at $Re = 3700$ and $Fr \in [0.025, 1]$. Unlike previous experimental and numerical studies of flow over a sphere at low $Re$ and low $Fr$, it is found that the fluctuations tend to regenerate at $Fr$ lower than a critical value for moderate $Re = 3700$. High stratification suppress vertical motion and, for a three-dimensional body, the fluid flows horizontally around the sides leading to a new regime of unsteady vortex shedding. Vertically thin layers of shear interspersed between quasi-two dimensional motions undergo secondary Kelvin-Helmholtz (KH) instabilities if the buoyancy Reynolds number, $Re_b \geq O(1)$. The combined effect of unsteady vortex shedding, enhanced horizontal shear, and secondary KH instabilities results in the regeneration of turbulence at low $Fr$. There is an $increase$ in the coefficient of drag $C_d$ at high stratification (low $Fr$), for $Re = 3700$. This result is contrary to previous experiments on flow over sphere at low $Re$ where $C_d$ was found to $decrease$ with increase in stratification in the low-$Fr$ regime.