Session U28: Vortex Dynamics: Wakes II

Analysis of the wake of an AR 4 square cylinder using time-domain spectral proper orthogonal decomposition

The near-wake of a cantilevered square cylinder of height-to-width ratio h/d = 4 protruding a thin laminar boundary layer of thickness δ/d = 0.21 is investigated using time-resolved stereoscopic particle image velocimetry (PIV) at a Reynolds number of 10600. PIV data are processed using time-domain spectral proper orthogonal decomposition (SPOD), which offers greater flexibility through constraining the spectral bandwidth for coherent contributions. Simultaneously acquired wall-pressure measurements are used to synchronize planar PIV data for 3D reconstructions of the coherent velocity field using a pressure-based estimator. Unlike POD, SPOD modes tend to contain only one dominant frequency, allowing for a better modal separation of the coherent field dynamics and improved estimator performance. Here, near the ground plane, spectral analysis show fluctuating energy concentration at the vortex shedding frequency (f_s), as well as weaker contributions at 2f_s, a low-frequency instability at 0.1f_s, inter-harmonics of interactions at 0.9f_s and 1.1f_s. Of particular interest, for illustrating the benefits of the SPOD approach, is a broadband spectral concentration at 0.4f_s, which could be related to interactions between shed vortices and the horseshoe vortex system.

An experimental study on flow-induced vibration of a flexible cylinder with an attached flexible splitter plate

Flow-induced vibration of a flexible circular cylinder with an attached flexible splitter plate is studied, experimentally. Dynamic response of the system was studied for three different splitter plate widths of 1D, 2D, and 3D, where D is the cylinder's diameter. At a low reduced velocity range at which the bare cylinder without a splitter plate experienced oscillations at its first two bending modes, up to 70% reduction in amplitudes of oscillations was observed for the cylinder with the splitter compared to those of the bare cylinder. At this region, frequencies of oscillations monotonically increased from values close to 0.5 times to twice the first bending natural frequency. At a higher reduced velocity range, amplitudes of oscillation increased for all three cases, but they still stayed smaller than those of the bare cylinder for splitter widths of 1D and 2D. For the case of splitter width of 3D, the amplitudes of oscillations monotonically increased, exceeding those of the bare cylinder with maximum amplitudes as large as 2.6 times those of the bare cylinder's oscillations. While the response exhibited mainly mono-frequency oscillations at this range for the splitter plate width of 1D, multi-frequency oscillations dominated the response for wider splitter plate cases.   

Wake of falling axisymmetric bluff body in quiescent liquid

The wake of an axisymmetric rigid body (a spherical cap of base diameter D and height H) in a quiescent liquid is studied experimentally. The study considers the axisymmetric bluff body freely falling in a fluid at rest. PLIF technique is used to visualize the wake. Mass ratio m∗ (defined as the relative density of the model compared to the fluid) is always greater than one in the present study. Liquid viscosity and base diameter are varied to achieve different Reynolds numbers. As reported in literature, the sphere (mass ratio> 1) always falls without vibration. However, we observed the falling hemisphere with shedding wake to have spiral or zigzag path. We present wake dynamics of rigid spherical cap for different mass ratios (1.13, 2.7, 8.73). We further investigate the mass ratio threshold for vibrating and non-vibrating regimes and report detailed wake analysis using PIV experiment.   

Do vortex streets remember their birth?

Even foils with symmetric oscillations can generate asymmetric wakes. As a result, a foil can feel a net lateral force despite having laterally-symmetric kinematics. Is this asymmetry simply a lingering memory of initial conditions, or something more? We answered this question with a physical model that is the first to 1) predict wake deflection a priori based on kinematic inputs, and 2) explain the dynamics of wake deflection, e.g. the evolution of a vortex wake from a deflected to straight state. We used water channel experiments to both validate the model and demonstrate for the first time that wake deflection angle can decay slowly, sometimes over 200+ oscillation cycles. We found that wake deflection is a supercritical pitchfork bifurcation governed by a parameter that we named the “relative dipole angle”, and we show how a model of this bifurcation offers design and control guidelines for foil-based applications like fish-inspired robots.   

Wake interactions in the flow past side-by-side elliptic cylinders

The wake resulting from an incident flow over two elliptic cylinders involves complex interactions of the separated flow with the inner/outer shear layers and the gap flow close to the cylinders as well as vortex street interactions further downstream. The wake dynamics in such configurations can help understand bio-inspired locomotion, forces and moments on offshore structures, among other applications. This study uses experiments and computations to characterize the wake structures in the flow over two side-by-side ellipses of various eccentricities at different gaps (the shortest distance between cylinder surfaces) and Reynolds numbers. The experiments are conducted in a water tunnel, where the flow structures are investigated using dye visualization as well as Particle Image Velocimetry (PIV) measurements. The computations in the incompressible regime help expand the parameter space for the investigation. Based on the gap size at a given Reynolds number, the wake flow regimes can be classified into single, asymmetric, or coupled wakes. At small gap sizes, the two ellipses act as a single bluff body leading to one vortex street. With an increase in the gap size, vortex shedding from individual ellipses forms two vortex streets. At intermediate gap values, the wake is asymmetric with one cylinder wake dominating over the other. Further increase in the gap leads to coupled wakes where vortex streets with in-phase or anti-phase shedding are observed. The parameter values for transition between these wake regimes will be discussed for different ellipse eccentricities.   

Numerical Investigation to Determine Optimal Inline Semi-Circular Cylinder Configurations for Coherent Karman Vortex Streets

 Recent studies showed that fishes exploit the energy of vortices shed by bluff bodies to swim efficiently. When swimming in such a coherent vortex structure, fish adopt a behavior known as 'Kármán Gait'. Therefore, a fishway could be contrived with a row of cylinders in order to reduce the energy expenditure of fish  and thus favor upstream migration. However, it is unclear, given the diameter, which cylinder spacing to adopt to ensure that counter-rotating vortices interact in a constructive manner and create a coherent vortex street.

In this work, we use computational fluid dynamics to solve the flow around a row of semi-circular cylinders (SCC) with the number of cylinders ranging from 1 to 5. We characterize a coherent vortex street based on the peakedness of the energy spectrum of the spanwise velocity. We employ a state-of-the-art optimization technique to determine the cylinder spacing which maximizes the spectrum peakedness. Our findings show that, in order to generate a coherent vortex street, the SCC should be positioned within a specific range of cylinder spacing values. We further observed that the optimal SCC spacing values for coherent vortex street generation lies within the reattachment vortex shedding regime.   

Experimental application of neural operators for prediction of bluff body wakes

Capable of learning to map between infinite-dimensional functional spaces, neural operators are an exciting and powerful machine learning toolset. The underlying principles of these methods, first applied by Lu et al. (2019) as the Deep Operator Network (DeepONet), have been shown to enable data-driven time-efficient solvers for families of partial differential equations. Fourier Neural Operators (FNOs), introduced by Li et al. (2020), have been previously shown able to learn accurate solution operators based on synthetic data generated by the Navier-Stokes equation. Once trained, FNOs can produce full-field approximations in just milliseconds. In this talk we apply FNOs to experimental flow data, trying to predict the temporal development of several bluff-body wake configurations. We also explore the generalizability of the learned operator networks by testing the performance of fully trained FNOs on wake configurations different from those used for training.

    

Unsteady Wake Effects on Power Generation in Oscillating Foil-Arrays

A predictive model is developed to quantify the effects of wake-foil interactions in the performance of oscillating foils arrays for energy harvesting. The wake dynamics behind flapping foils is particularly important since the coherent structures can cause constructive and/or destructive interference with downstream foils. This work numerically explores a wide range of foil kinematics and array configurations, with the goal of quantifying the power generation difference between foils affected by different wake structures. Due to the wake deficit caused by the leading foil, the power generation from downstream foils are normalized by an averaged wake velocity, then compared directly with the baseline power generation profile. The difference between the time averaged power curves represents the effects of the unsteadiness in the wake. This data is used to build a predictive model for downstream foil performance and hence provide insight for optimizing foil arrays configurations for energy harvesting.   

Fluid-structure interaction of a two-degree-of-freedom flat plate in the vicinity of the free surface

Fluid-structure-surface interaction response of a flexibly mounted rigid flat plate near a free surface was studied through a set of water tunnel experiments combined with time-resolved volumetric quantitative flow measurements to understand the interaction between the flow, free surface and the structure. The plate had two degrees of freedom (DoF) in the pitching and plunging directions. The effects of proximity of the plate to the free surface of the water on the flow-induced instabilities of the plate were investigated for cases ranging from when the flat plate was fully submerged to when its centerline was parallel to the water's free surface. For fully submerged cases at both 1DoF in the pitching direction and 2DoF, the plate experienced divergence instability at lower reduced velocities that later transitioned to periodic limit cycle oscillations at higher reduced velocities. The limit cycle amplitudes of oscillations increased by increasing the flow velocity. As the submerged depth decreased, the limit cycle amplitudes of oscillations decreased, and the onset of oscillation was shifted towards higher reduced velocities. For the 2DOF system in the vicinity of the water surface the asymmetry in the flow field around the plate led to only divergence instability of the plate.   

Drag and lift predictions for vortex-dominated bluff body wakes

The forces on a wake-producing body in an otherwise uniform flow can be calculated by applying linear momentum conservation to a control volume that encompasses the body and passes through the mid-wake region. With some simplifying assumptions regarding the mid-wake flow structure, the result can be a mathematical prediction of lift and drag. This approach was used famously by von Kármán (1912) to predict the time-averaged drag on a cylinder when the wake is modeled as a singly-periodic array of two point vortices; various formulations can be found in the textbooks by Goldstein (1938), Milne-Thompson (1968), et al. We generalize this approach to consider a variety of flows for which the wake can be approximated by coherent vortices embedded in potential flow. In particular, we present a closed-form estimation of drag and lift forces when the wake is approximated as periodic collections of N point vortices, with von Kármán's "drag law" being a special case for N=2.   

Flow dynamics and wake past nature-inspired obstacle arrangements: an experimental study

Spatial arrangements of solid structures obstructing a flow plays an important role in determining the force experienced by the members of the arrangement as well as in affecting the downstream wake. Such spatial arrangements are vital to understand fish schools, bird flight formations, or flow around vegetation patches in flood plains. A systematic study of flow past such an array of obstacles can help optimize airplane/drone flight formations. In this talk, we present an experimental investigation of flow past arrays of 3D-printed rigid cylinders with square and airfoil-like cross-sections. Measurements are done in a water tunnel and velocity field and forces on the objects are obtained simultaneously using high resolution particle image velocimetry (PIV) and a 2-axis load cell. For each cross-sectional shape, effects of array population, packing density, and orientation (regular vs. staggered) are studied at various freestream speeds. The velocity field obtained is used to determine the contribution of the viscous and pressure effects on the forces on the cylinders, and the total drag force is verified using the load-cell. Near-field and far-field wakes are studied qualitatively as well as quantitatively by analyzing various terms of turbulent kinetic energy transport. Turbulent transport for the flow within the cylinder array is also analyzed. This study aims to achieve two objectives: first, establish empirical relations showing functional dependence of total drag on parameters of interest, and second, obtain high resolution velocity field measurements to study turbulent transport which can also be used for further theoretical and numerical modeling.   

Topological Data Analysis of the flow field patterns in vortex wakes generated by pitching and heaving plates

The application of topological data analysis (TDA) to detect patterns in fluid dynamics as they evolve in the topological space of an unsteady or vortex-dominated flow field, is a relatively new endeavor. The technique used to decipher complex data by detecting and tracking topological features is called persistent homology (PH). We apply methods of TDA to the vortex wakes generated by pitching and heaving flat plates as models of bio-inspired propulsion. Two such datasets are studied: a 2D discrete vortex method simulation and velocity fields from stereoscopic particle image velocimetry. The results are analyzed using cubical PH to establish the relationship between the topological connectivity of the field and dynamic fluid phenomena. For example, analysis of PH features of the vorticity field identifies vortex core centers and vortex boundaries as representatives of the zeroth and first homology groups. The analysis is also applied to different derived properties including the velocity and the finite-time Lyapunov exponent, among others. Other topological characteristics of these flow fields, such as Betti numbers, persistence diagrams/barcodes, and CROCKER plots, are interpreted and connected to the physical structures in the flows. Results show that using TDA and PH to analyze these flow field interactions will enable a better understanding of turbulent flow and may provide a reduced set of features that could be used in network methods and machine learning.