A novel algorithm to detect coherent structures with sparse Lagrangian particle tracking data, using Voronoi tessellation and techniques from spectral graph theory, is tested. Neighbouring tracer particles are naturally identified through the Voronoi tessellation of the tracers' distribution. The method examines the \textit{neighbouring time} of tracer trajectories, defined as the total flow time two Voronoi cells share a common Voronoi edge, by converting this information into a Cartesian distance in the graph representation of the Voronoi diagram. Coherence is assigned to groups of Voronoi cells whose neighbouring time remains high throughout the time interval of analysis. The technique is first tested on the two-dimensional synthetic data of a double-gyre flow, and then with challenging, large-scale three-dimensional Lagrangian particle tracking data behind a bluff body at high Reynolds number. The tested technique proves to be successful at identifying coherence with realistic experimental data. Specifically, it is shown that coherent tracer motion is identifiable for mean inter-particle distances of the order of the largest length scales in the flow.

Abstract: A novel method for three-dimensional particle tracking velocimetry (PTV) is proposed that enables flow measurements in large volumes [V= O(10 m³)] using a single camera. Flow is seeded with centimeter-sized soap bubbles, when combined with suitable illumination, produce multiple glare points. The spacing between the two brightest glare points for each bubble is then utilized to reconstruct its depth. While the use of large soap bubbles comes at the expense of non-Stokesian behaviour, the excellent ray optics allow for large volume illumination when coupled with for instance pulsed LED banks. Possible error sources and the out-of-plane accuracy are discussed before the feasibility of the method is tested in an industrial-scale wind tunnel facility (test section of cross section 9.1 m × 9.1 m). In particular, the vortical structure in the wake of a 30%-scale tractor-trailer model at a 9 ^∘ yaw angle is captured in a 4.0 m × 1.5 m × 1.5 m measurement volume. Long tracks of up to 80 time steps are extracted in three-dimensional space via a single perspective. The successful proof-of-concept confirms the potential of the novel approach for three-dimensional measurements in volumes of industrial scale. Graphic abstract: [Figure not available: see fulltext.]

The concept of added (virtual) mass is applied to a vast array of unsteady fluid-flow problems; however, its origins in potential-flow theory may limit its usefulness in separated flows. A robust framework for modeling instantaneous fluid forces is proposed, named Energized Mass. The energized-mass approach is tested experimentally by acquiring the fluid kinetic-energy history around an accelerating sphere at both subcritical and supercritical terminal velocities. By tracking the energized-mass volume, the force response is shown to be related to changes in shear-layer growth as a function of acceleration moduli and Reynolds number. The energized-mass framework is then used to develop a low-order force model, requiring only body geometry and kinematics as input. An analytical expression for the instantaneous force on a sphere due to energized-mass growth is derived based on shear-layer mass flux arguments. Instantaneous forces determined experimentally, and modeled using the energized-mass approach, show strong agreement with direct force measurements. The results of this investigation thus demonstrate that the energized-mass framework provides a viable low-order modeling approach, and in tandem, can provide new insights into the origin of forces on accelerating bodies.

Abstract: In this study, vortical structures are detected on sparse Shake-The-Box data sets using the Coherent-Structure Colouring (CSC) algorithm. The performance of this Lagrangian approach is assessed by comparing the CSC-coloured tracks with the baseline vorticity field. The ability to extract vortical structures from sparse data is accessed on two Lagrangian particle tracking data sets: the flow past an Ahmed body and a swirling jet flow. The effects of two normalized parameters on the identification of vortical structures were defined and studied: the mean track length and the mean inter-particle distance. The accuracy of the vortical-structure detection problem through CSC is shown to improve with decreasing inter-particle distance values, whereas little dependence on the mean track length is observed at all. Overall, the CSC algorithm showed to yield accurate detection of coherent structures for inter-particle distances smaller than 15% of the characteristic dimension of the structure. However, the results quickly deteriorate for sparser Lagrangian data. Graphic abstract: [Figure not available: see fulltext.]

The Energized-Mass approach [1] offers a simple and robust framework for modeling forces in separated flow, requiring only kinematics, Reynolds-number, and geometry-based inputs. To this end, an energized-mass-based force model has been developed to describe the force response of a generic gust-body interaction, and is tested against numerical simulations of an accelerating sphere at moderate-to-high sub-critical Reynolds numbers. An analytic expression for the instantaneous force due to energized-mass growth is derived based on shear-layer mass flux arguments. The forming vortex ring is controlled by the Reynolds-number-dependent boundary layer thickness, which in turn, governs the energized-mass accumulated by the body. Entrainment effects are increasingly significant at greater Reynolds number as vortex formation transitions from laminar to turbulent, promoting mass flux beyond the predictions of shear-layer feeding arguments. Model predictions of instantaneous energized mass and resultant forces exhibit strong agreement with simulated results, suggesting energized-mass growth in sub-critical regimes is well-described by laminar-boundary-layer feeding. Thus, the current study provides a framework for future low-order force models, using the kinematics, Reynolds number and geometry to describe energized-mass time evolution.

It remains unclear to what extent inviscid added-mass theory accounts for the forces exerted on an accelerating body subjected to separated flow. In this study, reactant forces and velocity-field data are systematically acquired using experimental measurements and simulations of an accelerating circular flat plate. Cases accelerated from rest are compared to cases accelerated from a steady flow state. When the added-mass forces predicted by potential theory and the resistance forces associated with the instantaneous plate velocity are accounted for, the remaining (residual) forces comprise approximately 20% of the peak force, even at high accelerations. In addition, the computed residual forces during accelerations both from rest and steady-state cases yield good collapse with respect to one another, indicating that the total forces are not a strong function of the initial state of the wake. These results suggests that inviscid added-mass theory is inadequate to predict the full reactant force even in the ‘ideal’ condition of impulsive motion from rest.

A kinetic-energy-based, semi-empirical model for unsteady force estimation has been de-veloped, inspired by the concept of the Darwinian drift volume. The limitations of potential flow added mass and vortex impulse approaches were explored, and compared to experimental results. An optical towing tank facility was used to measure the forces and flow around a circular flat plate normal to the free-stream for an acceleration moduli of 4. Lagrangian particle tracks were produced using Eulerian vector-fields and synthetic particle tracking velocimetry. Forces predicted by potential flow added mass theory and vortex impulse modelling exhibited poor agreement compared to measured forces. The kinetic-energy-based approach showed strong agreement with measured forces, and allowed for the direct calculation of an “energized mass”, analogous to added mass derived from potential flow. Contrary to classical theory, the energized mass was not constant in time, which contributed to additional work done by the body. Forces on the body predicted using the semi-empirical model captured the major trends present in the measured forces. The component of the force due to the rate of change of energized mass is shown to be a significant contribution to the total force.

Three model motions were developed to replicate the aerodynamic response of a transverse gust. These motions included a pure plunging and two three-degree-of-freedom motions that approximated the angle-of-attack distribution produced by the gust. Using inviscid models and viscous flow simulations, the responses of the gust and model motions were compared as a function of the nondimensional reduced frequency. The inviscid model was found to overestimate the influence of the rotational added mass in the three-degree-of-freedom motions. In contrast, the viscous flow simulations showed that the two primary sources of discrepancy between the gust and model motions lie in the nonlinear angle-of-attack distribution caused by the gust and the wake development during the model motions. Flow simulations showed that all three motions experienced greater than90%agreement in lift for gusts with reduced frequencies less than 0.5, indicating that, under this reduced frequency, 1) the effect of the gust convection is minimal, and 2) a pure-plunging motion may suffice for modeling gusts. However, at higher reduced frequencies, the pureplunging motion experiences greater than 10% worse agreement than the three-degree-of-freedom motions. Overall, the motions provide a good approximation with greater than90%accuracy in lift for gusts of reduced frequencies less than k = 0.75.

A test case for pressure field reconstruction from particle image velocimetry (PIV) and Lagrangian particle tracking (LPT) has been developed by constructing a simulated experiment from a zonal detached eddy simulation for an axisymmetric base flow at Mach 0.7. The test case comprises sequences of four subsequent particle images (representing multi-pulse data) as well as continuous time-resolved data which can realistically only be obtained for low-speed flows. Particle images were processed using tomographic PIV processing as well as the LPT algorithm ‘Shake-The-Box’ (STB). Multiple pressure field reconstruction techniques have subsequently been applied to the PIV results (Eulerian approach, iterative least-square pseudo-tracking, Taylor’s hypothesis approach, and instantaneous Vortex-in-Cell) and LPT results (FlowFit, Vortex-in-Cell-plus, Voronoi-based pressure evaluation, and iterative least-square pseudo-tracking). All methods were able to reconstruct the main features of the instantaneous pressure fields, including methods that reconstruct pressure from a single PIV velocity snapshot. Highly accurate reconstructed pressure fields could be obtained using LPT approaches in combination with more advanced techniques. In general, the use of longer series of time-resolved input data, when available, allows more accurate pressure field reconstruction. Noise in the input data typically reduces the accuracy of the reconstructed pressure fields, but none of the techniques proved to be critically sensitive to the amount of noise added in the present test case.

In a large variety of fluid-dynamic problems, it is often impossible to directly measure the instantaneous aerodynamic or hydrodynamic forces on a moving body. Examples include studies of propulsion in nature, either with mechanical models or living animals, wings, and blades subjected to significant surface contamination, such as icing, sting blockage effects, etc. In these circumstances, load estimation from flow-field data provides an attractive alternative method, while at the same time providing insight into the relationship between unsteady loadings and their associated vortex-wake dynamics. Historically, classical control-volume techniques based on time-averaged measurements have been used to extract the mean forces. With the advent of high-speed imaging, and the rapid progress in time-resolved volumetric measurements, such as Tomo-PIV and 4D-PTV, it is becoming feasible to estimate the instantaneous forces on bodies of complex geometry and/or motion. For effective application under these conditions, a number of challenges still exist, including the near-body treatment of the acceleration field as well as the estimation of pressure on the outer surfaces of the control volume. Additional limitations in temporal and spatial resolutions, and their associated impact on the feasibility of the various approaches, are also discussed. Finally, as an outlook towards the development of future methodologies, the potential application of Lagrangian techniques is explored.

A perching bird is able to rapidly decelerate while maintaining lift and control, but the underlying aerodynamic mechanism is poorly understood. In this work we perform a study on a simultaneously decelerating and pitching aerofoil section to increase our understanding of the unsteady aerodynamics of perching. We first explore the problem analytically, developing expressions for the added-mass and circulatory forces arising from boundary-layer separation on a flat-plate aerofoil. Next, we study the model problem through a detailed series of experiments at \mathit{Re}=22\,000 and two-dimensional simulations at \mathit{Re}=2000. Simulated vorticity fields agree with particle image velocimetry measurements, showing the same wake features and vorticity magnitudes. Peak lift and drag forces during rapid perching are measured to be more than 10 times the quasi-steady values. The majority of these forces can be attributed to added-mass energy transfer between the fluid and aerofoil, and to energy lost to the fluid by flow separation at the leading and trailing edges. Thus, despite the large angles of attack and decreasing flow velocity, this simple pitch-up manoeuvre provides a means through which a perching bird can maintain high lift and drag simultaneously while slowing to a controlled stop.

A perching bird is able to rapidly decelerate at a high angle of attack while maintaining lift and control. However, the underlying aerodynamic mechanism is poorly understood. We perform a study on a simultaneously decelerating and pitching airfoil section as a simple perching model. First, we use analytic arguments to establish the inertial non-circulatory force on a wing section, and its dependence on the shape change number, τ*, the ratio between the rate of change of frontal dimension and the initial translational velocity. Next, we report that forces measured on a towed and pitched airfoil at Re = 22000, and forces from simulations at Re = 2000, are found to be well above non-circulatory predictions, exhibiting high lift and drag. Flow-field visualizations, both from Particle Image Velocimetry and simulations, reveal strong coherent vortical structures in the wake and near the body. At a higher shape change number, vortices in the wake convect more quickly than at a lower shape change number, generating higher drag. Additionally, separation of the LEV and positive vorticity near the body is reduced at a higher shape change number, increasing lift. Thus wake manipulation through rapid area change provides a means through which a perching bird can maintain high lift and drag simultaneously while slowing to a controlled stop.

If a moving body were made to vanish within a fluid, its boundary-layer vorticity would be released into the fluid at all locations simultaneously, a phenomenon we call global vorticity shedding. We approximate this process by studying the related problem of rapid vorticity transfer from the boundary layer of a body undergoing a quick change of cross-sectional and surface area. A surface-piercing foil is first towed through water at constant speed, U, and constant angle of attack, then rapidly pulled out of the fluid in the spanwise direction. Viewed within a fixed plane perpendicular to the span, the cross-sectional area of the foil seemingly disappears. The rapid spanwise motion results in the nearly instantaneous shedding of the boundary layer into the surrounding fluid. Particle image velocimetry measurements show that the shed layers quickly transition from free shear layers to form two strong, unequal-strength vortices, formed within non-dimensional time t* = 0:03, based on the foil chord and forward velocity. These vortices are connected to, and interact with, the foil's tip vortex through additional streamwise vorticity formed during the rapid pulling of the foil. Numerical simulations show that two strong spanwise vortices form from the shed vorticity of the boundary layer. The three-dimensional effects of the foil removal process are restricted to the tip of the foil. This method of vorticity transfer may be used for quickly introducing circulation to a fluid to provide forcing for biologically inspired flow control.