Since the review of periodic flow phenomena by Berger & Wille (1972) in this journal, over twenty years ago, there has been a surge of activity regarding bluff body wakes. Many of the questions regarding wake vortex dynamics from the earlier review have now been answered in the literature, and perhaps an essential key to our new understandings (and indeed to new questions) has been the recent focus, over the past eight years, on the three-dimensional aspects of nominally two-dimensional wake flows. New techniques in experiment, using laser-induced fluorescence and PIV (Particle-Image-Velocimetry), are vigorously being applied to wakes, but interestingly, several of the new discoveries have come from careful use of classical methods. There is no question that strides forward in understanding of the wake problem are being made possible by ongoing three- dimensional direct numerical simulations, as well as by the surprisingly successful use of analytical modeling in these flows, and by secondary stability analyses. These new developments, and the discoveries of several new phenomena in wakes, are presented in this review.

Vortex Dynamics in the Cylinder Wake

Digital particle image velocimetry (DPIV) is a non-intrusive analysis technique that is very popular for mapping flows quantitatively. To get accurate results, in particular in complex flow fields, a number of challenges have to be faced and solved: The quality of the flow measurements is affected by computational details such as image pre-conditioning, sub-pixel peak estimators, data validation procedures, interpolation algorithms and smoothing methods. The accuracy of several algorithms was determined and the best performing methods were implemented in a user-friendly open-source tool for performing DPIV flow analysis in Matlab.

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PIVlab – Towards User-friendly, Affordable and Accurate Digital Particle Image Velocimetry in MATLAB

The structure of energy-containing turbulence in the outer region of a zero-pressure-
 gradient boundary layer has been studied using particle image velocimetry (PIV) to measure the instantaneous velocity fields in a streamwise-wall-normal plane. Experiments performed at three Reynolds numbers in the range 930 0) that occur on a locus inclined at 30–60° to the wall.In the outer layer, hairpin vortices occur in streamwise-aligned packets that propagate with small velocity dispersion. Packets that begin in or slightly above the buffer layer are very similar to the packets created by the autogeneration mechanism (Zhou, Adrian & Balachandar 1996). Individual packets grow upwards in the streamwise direction at a mean angle of approximately 12°, and the hairpins in packets are typically spaced several hundred viscous lengthscales apart in the streamwise direction. Within the interior of the envelope the spatial coherence between the velocity fields induced by the individual vortices leads to strongly retarded streamwise momentum, explaining the zones of uniform momentum observed by Meinhart & Adrian (1995). The packets are an important type of organized structure in the wall layer in which relatively small structural units in the form of three-dimensional vortical structures are arranged coherently, i.e. with correlated spatial relationships, to form much longer structures. The formation of packets explains the occurrence of multiple VITA events in turbulent ‘bursts’, and the creation of Townsend's (1958) large-scale inactive motions. These packets share many features of the hairpin models proposed by Smith (1984) and co-workers for the near-wall layer, and by Bandyopadhyay (1980), but they are shown to occur in a hierarchy of scales across most of the boundary layer.In the logarithmic layer, the coherent vortex packets that originate close to the wall frequently occur within larger, faster moving zones of uniform momentum, which may extend up to the middle of the boundary layer. These larger zones are the induced interior flow of older packets of coherent hairpin vortices that originate upstream and over-run the younger, more recently generated packets. The occurence of small hairpin packets in the environment of larger hairpin packets is a prominent feature of the logarithmic layer. With increasing Reynolds number, the number of hairpins in a packet increases.

Vortex organization in the outer region of the turbulent boundary layer

Small-scale turbulence has been an area of especially active research in the recent past, and several useful research directions have been pursued. Here, we selectively review this work. The emphasis is on scaling phenomenology and kinematics of small-scale structure. After providing a brief introduction to the classical notions of universality due to Kolmogorov and others, we survey the existing work on intermittency, refined similarity hypotheses, anomalous scaling exponents, derivative statistics, intermittency models, and the structure and kinematics of small-scale structure—the latter aspect coming largely from the direct numerical simulation of homogeneous turbulence in a periodic box.

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The phenomenology of small-scale turbulence

Originally introduced in the fluid mechanics community, dynamic mode decomposition (DMD) has emerged as a powerful tool for analyzing the dynamics of nonlinear systems.
 However, existing DMD theory deals primarily with sequential time series for which the measurement dimension is much larger than the number of measurements taken.
 We present a theoretical framework in which we define DMD as the eigendecomposition of an approximating linear operator.
 This generalizes DMD to a larger class of datasets, including nonsequential time series.
 We demonstrate the utility of this approach by presenting novel sampling strategies that increase computational efficiency and mitigate the effects of noise, respectively.
 We also introduce the concept of linear consistency, which helps explain the potential pitfalls of applying DMD to rank-deficient datasets, illustrating with examples.
 Such computations are not considered in the existing literature but can be understood using our more general framework.
 In addition, we show that our theory strengthens the connections between DMD and Koopman operator theory.
 It also establishes connections between DMD and other techniques, including the eigensystem realization algorithm (ERA), a system identification method, and linear inverse modeling (LIM), a method from climate science.
 We show that under certain conditions, DMD is equivalent to LIM.

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On dynamic mode decomposition: Theory and applications

The flow over a hemisphere-cylinder has been studied at various angles of attack (AoA): 10, 20 and 25 and at Reynolds number between 1000 and 3000. This paper presents an experimental approach to characterise turbulent flow structure generated by such axisymmetric body. Time-resolved particle image velocimetry (PIV) measurement has been conducted to provide both spatial and temporal information of the flow field. Proper orthogonal decomposition (POD) has been performed on such experimental result to identify the dominant features in the flow.

Investigation on the flow over a hemisphere-cylinder

Investigation of accelerated flow over an airfoil at an angle of attack using multigrid cross-correlation digital PIV

Elasto-inertial turbulence is a new state of turbulence found in ows with polymer additives . The dynamicsof turbulence generated and controlled by such additives is investigated from the perspective of the couplingbetween polymer dynamics and ow structures. Direct numerical simulations of channel ow with Reynoldsnumbers ranging from 1000 to 6000 (based on the bulk and the channel height) are used to study the formationand dynamics of elastic instabilities and their e ects on the ow. The resulting mechanism of interactionsbetween polymer dynamics and the ow helps resolve a long-standing controversy in the understanding ofpolymer drag reduction and explains the phenomenon of early turbulence, or onset of turbulence at lowerReynolds numbers than for Newtonian ows, previously observed in polymeric ows. Polymers also point outan interesting analogy with the forward and backward energy cascade in two-dimensional turbulence.

ow helps resolve a long-standing controversy in the understanding of polymer drag reduction and explains the phenomenon of early turbulence, or onset of turbulence at lower Reynolds numbers than for Newtonian ows, previously observed in polymeric ows. Polymers also point out an interesting analogy with the forward and backward energy cascade in two-dimensional turbulence.

Linear stability analysis (LSA) of a self-similar adverse pressure gradient (APG) turbulent boundary layer (TBL) is explored in order to identify coherent structures. An eddy viscosity model (EV) is implemented via the Boussinesq hypothesis [8] to model the nonlinear coherent-turbulent interactions. Direct numerical simulations (DNS) by Kitsios et al. [3, 6] are used for the database of this study. A weak APG and strong APG (on the verge of separation) are studied with dimensionless streamwise pressure gradients (β) of 1 and 39 respectively. Their Reynolds numbers based on the momentum thickness (δ2) within their respective regions of interest are 3,100− 3,400 and 10,000− 12,300. For the strong APG, the most unstable eigen-solution produces a wave resembling a Kelvin-Helmholtz (KH) instability located near the displacement thickness (δ1) height. This position coincides with the inflection point (IP) in the mean flow profile. The IP satisfies Rayleigh’s and Fjortoft’s criterion for the existence of an inviscid instability [9]. Positive growth rate is seen for non-dimensional angular frequencies of 0.08 ≤ ω̂ ≤ 0.51, with the maximum growth occurring at ω̂ = 0.26. The weak APG also contains a KH like wave, however for all ω̂, the growth rates are negative. Spanwise wavenumber ˆ kxr and phase velocity ĉr increase monotonically for both β cases. Comparisons with a quasi-laminar analysis are also made.

Stability of a self-similar adverse pressure gradient turbulent boundary layer

Purpose: Computational Fluid Dynamics (CFD) simulations are performed to investigate the impact of adding a grid to a two-inlet dry powder inhaler (DPI). The purpose of the paper is to show the importance of the correct choice of closure model and modeling approach, as well as to perform validation against particle dispersion data obtained from in-vitro studies and flow velocity data obtained from particle image velocimetry (PIV) experiments. Methods: CFD simulations are performed using the Ansys Fluent 2020R1 software package. Two RANS turbulence models (realisable $k - \epsilon$ and $k - \omega$ SST) and the Stress Blended Eddy Simulation (SBES) models are considered. Lagrangian particle tracking for both carrier and fine particles is also performed. Results: Excellent comparison with the PIV data is found for the SBES approach and the particle tracking data are consistent with the dispersion results, given the simplicity of the assumptions made. Conclusions: This work shows the importance of selecting the correct turbulence modelling approach and boundary conditions to obtain good agreement with PIV data for the flow-field exiting the device. With this validated, the model can be used with much higher confidence to explore the fluid and particle dynamics within the device.

Julio Soria

Papers

Investigation on the flow over a hemisphere-cylinder

Investigation of accelerated flow over an airfoil at an angle of attack using multigrid cross-correlation digital PIV

Stability of a self-similar adverse pressure gradient turbulent boundary layer

On the Use of Computational Fluid Dynamics (CFD) Modelling to Design Improved Dry Powder Inhalers