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

Turbulence of the round jet has been assessed using invariants of the velocity gradient tensor. Experimental data, obtained using Tomographic Particle Image Velocimetry (Tomo-PIV), using four PCO-4000 cameras with 11 megapixel resolution, is presented for a seeded free air jet, operating in the turbulent regime and the Re number based on the diameter of the nozzle is 10000. Using the acquired 3-D velocity fields, the local statistical and geometrical structure of three-dimensional turbulent flow can be described by properties of the velocity gradient tensor. The invariants of the velocity gradient (R and Q), rate-of-strain ( s R and s Q ), and rate-of-rotation ( w Q ) tensors are analyzed across the turbulent expanding regions at different distances from the nozzle outlet. More specifically, the JPDF of invariants is computed, which allows a detailed statistical characterization of the dynamics, geometry and topology of the flow during the entrainment process. It should be noted that the results obtained are indicative of the preliminary work in this area.

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Studying the invariants of the velocity-gradient tensor of a round turbulent jet using Tomo-PIV

Bio-oil is a promising alternative fuel which contains a wide range of chemical components, including high molecular mass, organic compounds and a significant amount of water. This chemical structure can lead to a slow evaporation rate with the low boiling point compounds like water evaporating away from the surface while significant proportions still remain in the droplet core due to the relatively slow rate of liquid diffusion. As the droplet temperature increases, this water trapped in the core can reach a sufficiently high temperature to cause it to vapourise resulting in the droplet exploding. This study presents a numerical model of a stationary spherically symmetric evaporating bio-oil droplet in a hot ambient atmosphere. A diffusion limited model is used to investigate the effect of the large number components, including high boiling point chemicals, on the droplet evaporation rate. The numerical model simulates transient behaviour in the liquid and vapour phases by solving diffusion and heat transport equations in both phases using temperature dependent fluid properties.

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Numerical simulations of an evaporating bio-oil droplet

The prediction of turbulent boundary layer (TBL) flow over a convex surface as in aircraft wings or gas turbine blades is a challenging problem. Finding a universal scaling law of turbulence statistics of TBLs over a wide range of adverse pressure gradients (APG) remains unresolved. Here, we introduce characteristic length and velocity scales for APG-TBLs and nondimensionalise the turbulence statistics of the recent canonical self-similar APG-TBLs by Kitsios {\it et al.} ({\it J. Fluid Mech.}, vol.829, 2018, pp. 392--419). The characteristic length scale, which is termed the `shear thickness', $\delta^\ast$, is defined as the location which corresponds to the end of an actively sheared region in a turbulent shear flow, where the nondimensional shear rate normalised by the kinetic energy and the dissipation rate is approximately constant. Next, we show a universal scaling using a mixed velocity, termed the `friction-pressure velocity', $u^\ast$, which is based on total shear stress. It is revealed that the velocity fluctuations and the Reynolds stresses in TBLs over a wide range of APGs agree well with those in TBLs with zero-pressure-gradient (ZPG). The present scaling is used to scale the kinetic energy balance in TBLs, and compare them to other shear flows. Furthermore, a scaling for small-scale properties, i.e. vorticities, using $\delta^\ast$ and $u^\ast$ is also obtained assuming the local equilibrium in the inertial range. The present scaling for wall-bounded shear flows, including TBLs over a wide range of pressure gradients, implies that the underlying instantaneous turbulence structures have common features under a proper scaling and is key to the development and application of turbulent models.

Outer scaling of self-similar adverse-pressure-gradient turbulent boundary layers

Impinging jets from a thin and infinite lipped nozzle at a Nozzle Pressure Ratio (NPR) of 3.4 and plate spacing of 5.0D are investigated. The dominant modes of the jets are studied using particle image velocimetry. First and second order statistics are generated for each flow to allow for a basic comparison. A peak in transverse variance at the shock cell locations is noted for the thin lip nozzle, but not for the infinite lip case. This is associated with the existence of a global asymmetric mode for the thin lip jet and an axisymmetric mode for the infinite lip nozzle. For the infinite lip jet, this correlates with a large region of high axial variance present at the standoff shock, which is indicative of an axisymmetric mode. This difference in modes is confirmed through proper orthogonal decomposition, which shows a dominant symmetric mode for the thin lip jet and an asymmetric mode for the infinite lip case. Using the high specific energy POD modes, triple decomposition is performed on the jet flows, allowing each high variance region to be associated with its respective dominant global mode for each of the jets.

Effects of nozzle lip thickness on the global modes of an impinging supersonic jet

Particle-fluid interactions in supersonic flows are relevant in many different applications e.g. the cold gas-dynamic spray process. The optimal application of the process is hindered by a lack of understanding of the particle-fluid interactions. To obtain detailed information on the particle-fluid interactions in these high-speed flows special high performance techniques are required. The present work is an investigation into the applicability of magnified digital in-line holography with ultra-high-speed recording for the study of three-dimensional supersonic particle-laden flows. An optical setup for magnified digital in-line holography is created, using an ultrahigh-speed camera capable of frame rates of up to 1.0MHz. To test the new technique an axisymmetric supersonic underexpanded particle-laden jet is investigated. The results show that the new technique allows for the acquisition of time resolved qualitative and quantitative data on the fluid and particle dynamics. The potential for determining the three-dimensional particle positions using holographic reconstruction is also investigated. Five different focus functions used for depthwise location are tested using two different planar targets, a 10 × 10mm calibration grid and 120μm particles on a glass plate. In the case with the calibration grid it is found that accurate determination of the depthwise position is possible. However, when applying the same technique to the particle target, significant problems are encountered.

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Julio Soria

Papers

Studying the invariants of the velocity-gradient tensor of a round turbulent jet using Tomo-PIV

Numerical simulations of an evaporating bio-oil droplet

Outer scaling of self-similar adverse-pressure-gradient turbulent boundary layers

Effects of nozzle lip thickness on the global modes of an impinging supersonic jet

Ultra-high-speed digital in-line holography system applied to particle-laden supersonic underexpanded jet flows