Data-driven decompositions of Particle Image Velocimetry (PIV) measurements are widely used for a variety of purposes, including the detection of coherent features (e.g., vortical structures), filtering operations (e.g., outlier removal or random noise mitigation), data reduction and compression. This work presents the application of a novel decomposition method, referred to as Multiscale Proper Orthogonal Decomposition ( Mendez J Fluid Mech 870:988-1036, 2019) to Time-Resolved PIV (TR-PIV) measurement. This method combines Multiresolution Analysis (MRA) and standard Proper Orthogonal Decomposition (POD) to achieve a compromise between decomposition convergence and spectral purity of the resulting modes.
The selected test case is the flow past a cylinder in both stationary and transient conditions, producing a frequency-varying Karman vortex street. The results of the mPOD are compared to the standard POD, the Discrete Fourier Transform (DFT) and the Dynamic Mode Decomposition (DMD). The mPOD is evaluated in terms of decomposition convergence and time-frequency localization of its modes. The multiscale modal analysis allows for revealing beat phenomena in the stationary cylinder wake, due to the three-dimensional nature of the flow, and to correctly identify the transition from various stationary regimes in the transient test case.
Data-driven decompositions are becoming essential tools in fluid dynamics, allowing for tracking the evolution of coherent patterns in large datasets, and for constructing low order models of complex phenomena. In this work, we analyze the main limits of two popular decompositions, namely the Proper Orthogonal Decomposition (POD) and the Dynamic Mode Decomposition (DMD), and we propose a novel decomposition which allows for enhanced feature detection capabilities. This novel decomposition is referred to as Multiscale Proper Orthogonal Decomposition (mPOD) and combines Multiresolution Analysis …
A Fast Spectral Formulation of the Multiscale Proper Orthogonal Decomposition
Czech Technical University in Prague（布拉格捷克理工大学）；Czech Academy of Sciences（捷克科学院）；The von Karman Institute for Fluid Dynamics（冯·卡门流体力学研究所）；Vrije Universiteit Brussel (VUB)（布鲁塞尔自由大学）；École Polytechnique de Bruxelles, Université Libre de Bruxelles（布鲁塞尔理工学院，布鲁塞尔自由大学）；Universidad Carlos III de Madrid（马德里卡洛斯三世大学）
In this study we focus on the control of the dynamics of 3D turbulent wake downstream a square-back Ahmed body ($Re_H=3.9\times10^5$). The peculiar dynamics of such a wake are first characterized through the trajectories of the pressure barycenter over the rear part of the model as well as the recirculation barycenter in the wake. In particular it is shown that these dynamics allow the definition of three different states: the two so-called reflectional symmetry-breaking (RSB) modes and the transient symmetric (TS) mode. It was shown recently that the time-fluctuations of the pressure barycent…
We present an open-source MATLAB package, entitled OpenPIV-Matlab, for analyzing particle image velocimetry (PIV) data. We extend the PIV analysis with additional tools for post-processing the PIV results including the estimation of aero/hydrodynamic forces from the PIV data of a wake behind an immersed (bluff or streamlined) body. The paper presents a detailed description of the packages, covering the three main parts: generating two-dimensional two component velocity fields from pairs of images (OpenPIV-Matlab), spatial and temporal flow analysis based on the velocity fields (Spatial and Tem…
The wake behind a sphere, rotating about an axis aligned with the streamwise direction, has been experimentally investigated in a low-velocity water tunnel using LIF visualizations and PIV measurements. The measurements focused on the evolution of the flow regimes that appear depending on two control parameters, namely the Reynolds number $Re$ and the dimensionless rotation or swirl rate $Ω$, which is the ratio of the maximum azimuthal velocity of the body to the free stream velocity. In the present investigation, we cover the range of $Re$ smaller than 400 and $Ω$ from 0 and 4. Different wake…
Flows over two side-by-side circular cylinders exhibit fascinating flow physics due to complex interactions between the coupled wakes. However, their mutual interference effects have not been elucidated in a quantitative manner thus far. In this paper, we create a mismatch between the two wakes by introducing a size difference in the cylinder pair, such that the effects of one wake on the other can be distinguished. Depending on the size and gap ratios between the two cylinders, the coupled wake exhibits distinct dynamical features including the quasi-periodic flow, synchronized flow, and chao…
The propulsive dynamics of a flexible undulating foil in a self-propelled swimming configuration near a wall is studied experimentally. Measurements of the swimming speed and the propulsive force are presented, together with image acquisition of the kinematics of the foil and particle image velocimetry (PIV) in its wake. The presence of the wall enhances the cruising velocity in some cases up to 25% and the thrust by a 45%, for swept angles of 160 and 240 degrees. The physical mechanisms underlying this effect are discussed by studying the vorticity dynamics in the wake of the foil. Proper Ort…
The near wake of a small-scale wind turbine is investigated using Particle Image Velocimetry (PIV) experiments at different tip speed ratios ($λ$). The wind turbine model had a nacelle and a tower mimicking real scale wind turbines. The near wake is found to be dominated by multiple coherent structures including the tip vortices, distinct vortex sheddings from the nacelle and tower, and wake meandering. The merging of the tip vortices is found to be strongly dependent on $λ$. A convective length scale ($L_c$) related to the pitch of the helical vortices is defined which is shown to be a better…
The effect of freestream turbulence on the spreading of the near wake of a circular cylinder is investigated through particle image velocimetry (PIV) data. Different ``flavours'' of freestream turbulence, in which the turbulence intensity and integral length scale are independently varied, are subjected to the cylinder. The time-averaged spreading of the near wake is decoupled into the growth through entrainment and the envelope of the spatial extent of the instantaneous wake due to wake ``meandering'', induced by the presence of large-scale coherent structures, i.e. the von Karman vortex stre…
In this research article we study the wake formation behind 3-Dimensional Multi-scale Porous Obstacles (3DMPOs). Particle Imaging Velocimetry (PIV) is used in a non-shallow ($B/h =1.5$) water flume, with measurements carried out across the $x$ - $y$ plane (at $z$ = 130 mm) and with $Re=70,000$ based on the free-stream velocity ($U_{\infty}$). To characterise the downstream wake characteristics of 3DMPOs the obstacles are split into 3 regimes; (1) non-porous, (2) porous with a single internal scale and (3) porous fractals (based on the Sierpinski carpet). The void fraction ($ϕ=0.7$) and externa…
The mechanisms associated with an owls ability to fly silently have been the subject of scientific interest for many decades and a source of inspiration in the context of reducing noise in both flapping and non-flapping flight. Here, we characterize the near wake dynamics and associated flow structures that are produced by flying owls. The goal is to shed light on unique flow features that result from the owls wing morphology and its motion during forward flapping flight. We study the wake of the southern boobook owl (Ninox boobook); a mid-sized owl, which shares the common feature of stealthy…
Particle Image Velocimetry (PIV) estimates velocities through correlations of particle images within interrogation windows, leading to a spatial modulation of the velocity field. Although in principle Particle Tracking Velocimetry (PTV) estimates locally a non-modulated particle displacement, to exploit the scattered data from PTV it is necessary to interpolate these data on a structured grid, which implies a spatial modulation effect that biases the resulting velocity field. This systematic error due to finite spatial resolution inevitably depends on the interrogation window size and on the i…
In this paper I consider the self-excited rotation of an elliptical cylinder towed in a viscous fluid as a canonical model of nonlinear fluid structure interactions with possible applications in the design of sensors and energy extraction devices. First, the self-excited ellipse system is shown to be analogous to the forced bistable oscillators studied in classic chaos theory. A single variable, the distance between the pivot and the centroid, governs the system bifurcation into bi-stability. Next, fully coupled computational fluid dynamics simulations of the motion of the cylinder demonstrate…
Fractal grids generate turbulence by exciting many length scales of different sizes simultaneously rather than using the nonlinear cascade mechanism to obtain multi-scale structures, as it is the case for regular grids. The interest in these grids has been further building up since the surprising findings stemming from the experimental and computational studies conducted on these grids. This work presents experimental wind tunnel and computational fluid dynamics (CFD) studies of the turbulent flow generated by a space-filling fractal square grid. The experimental work includes Particle Image V…
Viscoelastic flow through an abrupt planar contraction geometry above a certain Weissenberg number (Wi) is well known to become unstable upstream of the contraction plane via a central jet separating from the walls and forming vortices in the salient corners. Here, for the first time we consider three-dimensional (3D) viscoelastic contraction flows in a microfabricated glass square-square contraction geometry. We employ state-of-the-art microtomographic particle image velocimetry to produce time-resolved and volumetric quantification of the 3D viscoelastic instabilities arising in a dilute pol…
The strength and trajectory of a leading edge vortex (LEV) formed by a pitching-heaving hydrofoil (chord $c$) is studied. The LEV is identified using the $Q$-criterion method, which is calculated from the 2D velocity field obtained from PIV measurements. The relative angle of attack at mid-stroke, ${α_{T/4}} $, proves to be an effective method of combining heave amplitude ($h_0/c$), pitch amplitude ($θ_0$), and reduced frequency ($f^*$) into a single variable that predicts the maximum value of $Q$ over a wide range of operating conditions. Once the LEV separates from the foil, it travels downs…
We examine the characteristics of mean flow and scalar concentration characteristics of a turbulent boundary layer flow impinging on a cluster of tall obstacles (which can also be interpreted as a porous obstruction). The cluster is created with a group of cylinders of diameter $d$ and height $h$ arranged in a circular patch of diameter $D$.The solidity of the patch/obstruction is defined by $ϕ$ (the total planar area covered by cylinders), which is systematically varied ($0.098 \leq ϕ\leq 1$) by increasing the number of cylinders in a patch ($N_c$). A point source is placed at ground level up…
The wake behind a cube with a face normal to the flow was investigated experimentally in a water tunnel using laser induced fluorescence visualisation (LIF) and particle image velocimetry (PIV) techniques. Measurements were carried out for moderate Reynolds numbers between 100 and 400 and in this range a sequence of two flow bifurcations was confirmed. Values for both onsets were determined in the framework of Landau`s instability model. The measured longitudinal vorticity was separated into three components corresponding to each of the identified regimes. It was shown that the vorticity assoc…
In this paper we present experimental and numerical reference data for a NACA 64A-110 airfoil at two angles of attack for $Ma=0.72$ and a Reynolds number of $Re_c=930.000$ with respect to the chord length. The test cases are designed to provide data for an uninclined airfoil at $0^\circ$ and for the case of a stable, steady shock at $3^\circ$. For both cases we conduct experiments in the trisonic wind tunnel at the RWTH Aachen including PIV data as well as numerical wall-resolved large eddy simulations. The results show matching mean velocities and Reynolds stresses in the wake and boundary la…
We propose a data-driven algorithm for reconstructing the irregular, chaotic flow dynamics around two side-by-side square cylinders from sparse, time-resolved, velocity measurements in the wake. We use Proper Orthogonal Decomposition (POD) to reduce the dimensionality of the problem and then explore two different reconstruction approaches: in the first approach, we use the subspace system identification algorithm n4sid to extract a linear dynamical model directly from the data (including the modelling and measurement error covariance matrices) and then employ Kalman filter theory to synthesize…
Dynamic mode decomposition (DMD) provides a principled approach to extract physically interpretable spatial modes from time-resolved flow field data, along with a linear model for how the amplitudes of these modes evolve in time. Recently, DMD has been extended to work with more realistic data that is under-resolved either in time or space, or with data collected in the same spatial domain over multiple independent time windows. In this work, we develop an extension to DMD to synthesize globally consistent modes from velocity fields collected independently in multiple partially overlapping spa…
The identification of coherent structures from experimental or numerical data is an essential task when conducting research in fluid dynamics. This typically involves the construction of an empirical mode base that appropriately captures the dominant flow structures. The most prominent candidates are the energy-ranked proper orthogonal decomposition (POD) and the frequency ranked Fourier decomposition and dynamic mode decomposition (DMD). However, these methods fail when the relevant coherent structures occur at low energies or at multiple frequencies, which is often the case. To overcome the …
We introduce a novel end-to-end approach to improving the resolution of PIV measurements. The method blends information from different snapshots without the need for time-resolved measurements on grounds of similarity of flow regions in different snapshots. The main hypothesis is that, with a sufficiently large ensemble of statistically-independent snapshots, the identification of flow structures that are morphologically similar but occurring at different time instants is feasible. Measured individual vectors from different snapshots with similar flow organisation can thus be merged, resulting…
