We conduct a well-controlled model experiment for a wide variety of canopy flows. Examples of these include engineering flows such as wind flow, dispersion of scalars through and over urban areas, and the convective heat transfer in many heat exchangers, as well as natural canopies such as flows through terrestrial or aquatic vegetation. We aim to shed the light on fundamental flow and transport phenomena common to these applications. Specifically, the characteristics of mean flow and scalar concentration characteristics of a turbulent boundary layer flow impinging on a canopy, which comprises a cluster of tall obstacles (this 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 $\phi$ (the total planar area covered by cylinders), which is systematically varied ($0.098 \leq \phi \leq 1$) by increasing the number of cylinders in a patch ($N_c$). A point source is placed at ground level upstream of the patch and its transport over and around the patch is examined. Time-averaged velocity and scalar fields, obtained from simultaneous planar particle image velocimetry-planar laser-induced fluorescence (PIV-PLIF) measurements, reveal that the characteristics of wake and flow above porous patches are heavily influenced by $\phi$. In particular, we observe that the horizontal and vertical extent of the wake and scalar concentration downstream of the patches decreases and increases with $\phi$, respectively. Here, the recirculation bubble is shifted closer to the trailing edge (TE) of the patches as $\phi$ increases, limiting the flow from convecting downstream, decreasing the scalar concentration and virtually ‘extending’ the patch in the streamwise direction. As the bubble forms in the TE, vertical bleeding increases and hence the concentration increases above the patch where the cylinders appear to ‘extend’ vertically towards the freestream.

Large-eddy simulation (LES) using an unstructured overset numerical method is performed to study the flow around a ducted marine propeller for the highly unsteady off-design condition called crashback. Known as one of the most challenging propeller states to analyse, the propeller rotates in the reverse direction to yield negative thrust while the vehicle is still in forward motion. The LES results for the marine propeller David Taylor Model Basin 4381 with a neutrally loaded duct are validated against experiments, showing good agreement. The simulations are performed at Reynolds number of 561 000 and an advance ratio $J=-0.82$. The flow field around the different components (duct, rotor blades and stator blades) and their impact on the unsteady loading are examined. The side-force coefficient $K_S$ is mostly generated from the duct surface, consistent with experiments. The majority of the thrust and torque coefficients $K_T$ and $K_Q$ arise from the rotor blades. A prominent contribution to $K_Q$ is also produced from the stator blades. Tip-leakage flow between the rotor blade tips and duct surface is shown to play a major role in the local unsteady loads on the rotor blades and duct. The physical mechanisms responsible for the overall unsteady loads and large side-force production are identified as globally, the vortex ring and locally, leading-edge separation as well as tip-leakage flow which forms blade-local recirculation zones.

We present a method that leverages projected light patterns as a mechanism for freeform deformation of a thin liquid film via the thermocapillary effect. We developed a closed-form solution for the inverse problem of the thin-film evolution equation, allowing us to obtain the projection pattern required in order to achieve a desired topography. We experimentally implement the method using a computer controlled light projector, which illuminates any desired pattern onto the bottom of a fluidic chamber patterned with heat–absorbing metal pads. The resulting heat map induces surface tension gradients in the liquid–air interface, giving rise to thermocapillary flow that deforms the liquid surface. If a polymer is used for the liquid film, it can then be photocured to yield a solid device. Based on the inverse-problem solutions and using this system, we demonstrate the fabrication of several diffractive optical elements, including phase masks for extended depth of field imaging, and for three-dimensional localization microscopy. The entire process, from projection to solidification, is completed in less than five minutes, and yields a sub-nanometric surface quality without any post-processing.

The placement of a scaled-down Savonius (drag) vertical-axis wind turbine on model buildings is analysed experimentally by the use of turbine performance and flow field measurements in a wind tunnel. The set-up consists of two surface mounted cubes aligned in the flow direction. The turbine is tested at six different streamwise positions – three on each cube. Velocity field measurements are performed with particle image velocimetry along the centreline of the cubes with and without the turbine. The performance at each position is evaluated based on measurements of the produced torque and the rotational speed of the turbine. It is demonstrated that the common practice of estimating wind resources based on the urban flow field without the turbine present is insufficient. The turbine has a substantial influence on the flow field and thus also on the available power. The performance is found to be optimal in the front and centre of the first building with a significant drop-off to the back. This trend is reversed for the downstream building. Holistically, for more generic geometries and varying wind directions, the results suggest the central position on a building is a good compromise.

When manufacturing a turbine engine, the combustor annulus and the turbine annulus are created as separate parts and assembled. This leads to an inter-platform gap between the two components, which must be supplied with leakage air to prevent ingestion of the extremely hot combustion gases into the interior of the engine. The combustor and the turbine are likely to misalign because of differential thermal expansion or assembly tolerances. This paper presents a direct numerical simulation study of inter-platform misalignment with leakage flow supplied at the junction of the platforms. The geometry is two misaligned plates with a cross-flow and a leakage flow simulated as a slot jet. The misalignment of the two plates gives rise to a forward misalignment configuration and a backward misalignment configuration, and the jet/cross-flow gives rise to a windward mixing layer and a leeward mixing layer. Compared with the aligned configuration, the cooling effectiveness immediately downstream of the gap decreases in the forward misalignment configuration and increases in the backward misalignment configuration; this response amplifies as the flow rate through the gap increases. In addition to the cooling effectiveness, we report flow statistics, including the velocity, the temperature, the turbulent kinetic energy and the relevant turbulent fluxes. We find strong turbulence generation in the leeward mixing layer and high turbulence level as a result. Mixing of the thermal energy, on the other hand, occurs predominantly in the windward mixing layer. The eddy viscosity and the eddy conductivity that are critical to turbulence modelling are also reported. We find negative eddy viscosity at regions where the incoming boundary layer starts to mix with the leakage jet. The analysis shows that the negative eddy viscosity is a result of flow hysteresis: it takes time, or travel distance, before the eddies in the incoming boundary layer and the eddies in the leakage jet come to an equilibrium, thereby favouring a transport Reynolds stress model over a local eddy viscosity type model. The novelty of this paper lies in the direct numerical simulations, which provide direct access to the near-wall flow field and clarify the effects of blowing ratio and platform misalignment on heat transfer. The novelty also lies in the data analysis, which sheds light on how this flow should be modelled.

We present a series of experiments to illustrate the dynamics of positively or negatively buoyant particle-laden plumes in a cross-flow, with relevance for the discharge of sediment into the ocean during deep-sea mining operations. In an unstratified ambient fluid, our experiments identify three different regimes, corresponding to (i) a dense particle-laden plume, host to relatively dense saline fluid, in which the particles separate from the descending plume as the flow speed falls below the particle settling speed; (ii) a dense particle-laden plume, host to buoyant fluid, in which the fluid gradually rises from the sinking plume of particles, to form a second rising plume of source fluid; and (iii) a buoyant particle-laden plume, host to buoyant fluid, which rises from the discharge pipe, and from which particles gradually sediment. Classical models of single-phase plumes describe the initial motion of the plumes in cases (i) and (iii), but as the flow speed falls below the particle fall speed, sedimentation leads to a change in the averaged buoyancy, and, hence, the plume speed. Our data also suggest that the sedimentation leads to a reduction in the rate of entrainment of ambient fluid, compared with the classical single-phase plumes. We also show that with a density stratified ambient fluid, the stratification may arrest the plume prior to significant particle sedimentation, and in this case, the plume tends to spread downstream at the level of neutral buoyancy where particle sedimentation proceeds. The bulk density of the residual plume fluid may then remain intermediate between the density of the upper and lower layer fluid, or may become less dense than the upper layer fluid, in which case, following sedimentation, the plume fluid rises through the upper layer. While the dynamics of deep-sea mining plumes in the ocean are more complex, for example, owing to background turbulence and mixing, the results of our new laboratory experiments highlight the range of flow processes which may influence the initial dispersion and sedimentation of particles in such plumes following release into the water, depending on the initial conditions, the ambient density and the particle fall speed. We also discuss the relevance of our work in the context of ash dispersal by volcanic plumes.

Cohesive particulate flows play an important role in environmental fluid dynamics, as well as in a wide variety of civil and process engineering applications. However, the scaling laws, constitutive equations and continuum field descriptions governing such flows are currently less well understood than for their non-cohesive counterparts. Grain-resolved simulations represent an essential tool for addressing this shortcoming, along with theoretical investigations, laboratory experiments and field studies. Here we provide a tutorial introduction to simulations of fine-grained sediments in viscous fluids, along with an overview of some representative insights that this approach has yielded to date. After a brief review of the key physical concepts governing van der Waals forces as the main cohesive effect for subaqueous sediment suspensions, we discuss their incorporation into particle-resolved simulations based on the immersed boundary method. We subsequently describe simulations of cohesive particles in several model turbulent flows, which demonstrate the emergence of a statistical equilibrium between the growth and break-up of aggregates. As a next step, we review the influence of cohesive forces on the settling behaviour of dense suspensions, before moving on to submerged granular collapses. Throughout the article, we highlight open research questions in the field of cohesive particulate flows whose investigation may benefit from grain-resolved simulations.

Underwater explosions are inherently complex and unique physical phenomena markedly distinct from those occurring above the surface. This distinctiveness is primarily attributed to the relatively incompressible nature of water, which fundamentally alters the propagation and impact of shock waves. The study of underwater explosions is paramount in applications such as underwater demolitions for construction and salvage operations. These applications require a comprehensive understanding in order to mitigate the disturbances’ impact on marine structures and ecosystems. Studying underwater explosions and their mitigation encompasses various disciplines, including fluid mechanics, materials science and structural engineering. The work reviewed in this study contributes significantly to enhancing safety measures in marine structures by providing critical insights into the behaviour of structures under extreme conditions. This includes understanding the behaviour of gas bubbles formed by explosions, the transmission of shock waves through different media and the resultant forces exerted on structures submerged in water. Consequently, this review is meant to aid in designing robust and resilient marine systems capable of withstanding severe loading conditions caused by underwater explosions by providing key engineering considerations. The continuous evolution of this research area is essential for advancing maritime technology, ensuring the safety of undersea operations and protecting marine environments from the adverse effects of extreme subaqueous loadings.

Strongly coupled sequences of shock waves, known as shock trains, are present in high-speed propulsion systems, where the presence of sidewalls substantially modifies the boundary layer thickness, skin friction and streamwise pressure distribution. In the present contribution, scale-resolved numerical simulations are performed on supersonic channel (infinite span) and square duct flows to evaluate the effect of sidewall confinement with and without shock trains. Comparable secondary flow vortices are observed in the duct case with and without the presence of the shock train. The absence of a separation region at the leading shock of the duct case results in lower flow deflection compared with the channel case, leading to a reduced shock strength. The principal effect of the sidewalls is to cause a shock train that is approximately twice as long and composed of a larger number of shocks. A modification of previous models, based on a momentum thickness-based blockage parameter, leads to an improved collapse of the channel and duct cases.

Mathematical models promise new insights into the mechanisms underlying the emergence of collective behaviour in fish. Here, we establish a mathematical model to examine collective behaviour of zebrafish, a popular animal species in preclinical research. The model accounts for social and hydrodynamic interactions between individuals, along with the burst-and-coast swimming style of zebrafish. Each fish is described as a system of coupled stochastic differential equations, which govern the time evolution of their speed and turn rate. Model parameters are calibrated using experimental observations of zebrafish pairs swimming in a shallow water tank. The model successfully captures the main features of the collective response of the animals, by predicting their preference to swim in-line, with one fish leading and the other trailing. During in-line swimming, the animals share the same orientation and keep a distance from each other, owing to hydrodynamic repulsion. Hydrodynamic interaction is also responsible for an increase in the speed of the pair swimming in-line. By linearizing the equations of motion, we demonstrate local stability of in-line swimming to small perturbations for a wide range of model parameters. Mathematically backed results presented herein support the application of dynamical systems theory to unveil the inner workings of fish collective behaviour.

Atmospheric turbulent velocity fluctuations are known to increase wind turbine structural loading and accelerate wake recovery, but the impact of vortical coherent structures in the atmosphere on wind turbines has not yet been evaluated. The current study uses flow imaging with natural snowfall with a field of view spanning the inflow and near wake. Vortical coherent structures with diameters of the order of 1 m are identified and characterized in the flow approaching a 2.5 MW wind turbine in the region spanning the bottom blade tip elevation to hub height. Their impact on turbine structural loading, power generation and wake behaviour are evaluated. Long coherent structure packets $(\mathrm{\ \mathbin{\lower.3ex\hbox{$\buildrel> \over {\smash{\scriptstyle\sim}\vphantom{_x}}$}}\ }200\;\textrm{m)}$ are shown to increase fluctuating stresses on the turbine support tower. Large inflow vortices interact with the turbine blades, leading to deviations from the expected power generation. The sign of these deviations is related to the rotation direction of the vortices, with rotation in the same direction as the circulation on the blades leading to periods of power surplus, and the opposite rotation causing power deficit. Periods of power deficit coincide with wake contraction events. These findings highlight the importance of considering coherent structure properties when making turbine design and siting decisions.

This paper sets out to investigate the vortex flow of spinnaker yacht sails, which are low-aspect-ratio highly cambered wings used to sail downwind. We tested three model-scale sails with the same sections but different twists over a range of angles of attack in a water tunnel at a Reynolds number of 21 000. We measured the forces with a balance and the velocity field with particle image velocimetry. The sails experience massively separated three-dimensional flow and leading-edge vortices convect at half of the free-stream velocity in a turbulent shear layer. Despite the massive flow separation, the twist of the sail does not change the lift curve slope, in agreement with strip theory. As the angle of attack and the twist vary, flow reattachment might occur in the time-average sense, but this does not necessarily result in a higher lift to drag ratio as the vorticity field is marginally affected. Finally, we investigated the effect of secondary vorticity, vortex stretching and diffusion on the vorticity fluxes. Overall, these results provide new insights into the vortex flow and associated force generation mechanism of wings with massively separated flow.

Displacement ventilation, where cool external air enters a room through low-level vents and warmer air leaves through high-level vents, is characterised by vertical gradients in pressure arising from the warmer indoor temperatures. Models usually assume that horizontal variations of temperature difference are small in comparison and are, therefore, unimportant. Small-scale laboratory experiments and computational fluid dynamics were used to examine these flows, driven by a uniformly heated floor. These experiments and simulations show that the horizontal variations of temperature difference can be neglected for predictions of the bulk ventilation rate; however, they also evidence that these horizontal variations can be significant and play a critical role in establishing the pattern of flow within the room – this renders the horizontal position of the low- and high-level vents (relative to one another) important. We consider two cases: single-ended (where inlet and outlet are at the same end of the room) and opposite-ended. In both cases the ventilation flow rate is the same. However, in the opposite-ended case a dead zone is established in the upper part of the room which results in significant horizontal variations. We consider the formation of this dead zone by examining the streamline patterns and the age of air within the room. We discuss the implications for occupant exposure to pollutants and airborne disease.

We present a theoretical model and experimental demonstration of thin liquid film deformations due to a dielectric force distribution established by surface electrodes. We model the spatial electric field produced by a pair of parallel electrodes and use it to evaluate the stress on the liquid–air interface through Maxwell stresses. By coupling this force with the Young–Laplace equation, we obtain the deformation of the interface. To validate our theory, we design an experimental set-up which uses microfabricated electrodes to achieve spatial dielectrophoretic actuation of a thin liquid film, while providing measurements of microscale deformations through digital holographic microscopy. We characterize the deformation as a function of the electrode-pair geometry and film thickness, showing very good agreement with the model. Based on the insights from the characterization of the system, we pattern conductive lines of electrode pairs on the surface of a microfluidic chamber and demonstrate the ability to produce complex two-dimensional deformations. The films can remain in liquid form and be dynamically modulated between different configurations or polymerized to create solid structures with high surface quality.

In submerged sandy slopes, soil is frequently eroded as a combination of two main mechanisms: breaching, which refers to the retrogressive failure of a steep slope forming a turbidity current, and instantaneous sliding wedges, known as shear failure, that also contribute to shape the morphology of the soil deposit. Although there are several modes of failures, in this paper we investigate breaching and shear failures of granular columns using the two-fluid approach. The numerical model is first applied to simulate small-scale granular column collapses (Rondon et al., Phys. Fluids, vol. 23, 2011, 073301) with different initial volume fractions to study the role of the initial conditions in the main flow dynamics. For loosely packed granular columns, the porous medium initially contracts and the resulting positive pore pressure leads to a rapid collapse. Whereas in initially dense-packing columns, the porous medium dilates and negative pore pressure is generated stabilizing the granular column, which results in a slow collapse. The proposed numerical approach shows good agreement with the experimental data in terms of morphology and excess of pore pressure. Numerical results are extended to a large-scale application (Weij, doctoral dissertation, 2020, Delft University of Technology; Alhaddad et al., J. Mar. Sci. Eng., vol. 11, 2023, 560) known as the breaching process. This phenomenon may occur naturally at coasts or on dykes and levees in rivers but it can also be triggered by humans during dredging operations. The results indicate that the two-phase flow model correctly predicts the dilative behaviour and the subsequent turbidity currents associated with the breaching process.

Over the years, many facilities have been developed to study turbulent flow in the laboratory. Homogeneous isotropic turbulence (HIT) with zero mean flow provides a unique environment for investigating fundamental aspects and specific applications of turbulent flow. We provide an extensive overview of laboratory facilities that generate incompressible zero-mean-flow HIT using different types of actuators and configurations. Reviewed facilities cover a variety of geometries and sizes, as well as forcing style (e.g. symmetric versus asymmetric and unsteady versus steady). We divide facilities into four categories, highlighting links between their geometries and the statistics of the flows they generate. We then compare published data to uncover similarities and differences among various turbulence-generation mechanisms. We also compare the decay of turbulence in zero-mean-flow facilities with that observed in wind and water tunnels, and we analyse the connections between flow characteristics and physical aspects of the facilities. Our results emphasize the importance of considering facility geometry and size together with the strength and type of actuators when studying zero-mean-flow HIT. Overall, we provide insight into how to optimally design and build laboratory facilities that generate zero-mean-flow HIT.

An on-demand painting system with a simple structure device that ejects highly viscous liquids as microjets is introduced. An impulsive motion of the container results in the ejection of a viscous liquid jet from the nozzle. This system enabled us to paint letters on a section of a car body using commercial car paint with a zero-shear viscosity of 100 $\textrm {Pa} \cdot \textrm {s}$. To understand the jet velocity, we conducted systematic experiments. Experimental results showed that the jet velocity increases with the ratio between the liquid depths in the container and the nozzle, up to approximately 30 times faster than the initial velocity. However, a linear relation between the jet velocity and the ratio predicted by the previous model, which considers only the pressure impulse, does not hold for the high length ratios since the actual position of the stagnation point is different from the position predicted by the previous model. By solving the Laplace equation and using the model proposed by Gordillo et al. (J. Fluid Mech., vol. 894, 2020, pp. A3–11), we reproduce the non-monotonic behaviour of the jet velocity as a function of the length ratio. For practical use, we improve the jet-velocity model by considering mass conservation as well as the pressure impulse.

We consider the mixing dynamics of an air–liquid system driven by the rotation of a pitched blade turbine (PBT) inside an open, cylindrical tank. To examine the flow and interfacial dynamics, we use a highly parallelised implementation of a hybrid front-tracking/level-set method that employs a domain-decomposition parallelisation strategy. Our numerical technique is designed to capture faithfully complex interfacial deformation, and changes of topology, including interface rupture and dispersed phase coalescence. As shown via transient, a three-dimensional (3-D) LES (large eddy simulation) using a Smagorinsky–Lilly turbulence model, the impeller induces the formation of primary vortices that arise in many idealised rotating flows as well as several secondary vortical structures resembling Kelvin–Helmholtz, vortex breakdown, blade tip vortices and end-wall corner vortices. As the rotation rate increases, a transition to ‘aeration’ is observed when the interface reaches the rotating blades leading to the entrainment of air bubbles into the viscous fluid and the creation of a bubbly, rotating, free surface flow. The mechanisms underlying the aeration transition are probed as are the routes leading to it, which are shown to exhibit a strong dependence on flow history.

In this case study, we examine the effect of airfoil shape/camber on the formation and existence of stall cells. A series of experiments using a NACA0012 wing with a trailing-edge flap has been carried out over a range of angles of attack ($11.5^\circ$–$21^\circ$), flap angles ($0^\circ$, $5^\circ$, $10^\circ$) and chord-length-based Reynolds numbers (100 000–500 000). The influence of these parameters on stall cell formation has been explored. Tufts have been used to identify the flow behaviour near the surface, while forces have been measured to relate the surface flow behaviour and wing performance. The results from the tuft analysis on the wing indicated that two different Reynolds-number regimes exist with respect to stall cell formation criteria. A preliminary estimate of the airfoil shape influence on stall cell formation is presented. A data-driven approach is used to relate the aerodynamic parameters (lift coefficient and lift-curve slope) to the formation criteria of stall cells for the wing (and flap angles). The lift coefficient can be used to implicitly take into account the change in airfoil shape in addition to the angle of attack and the Reynolds number. It is hoped that the results presented in this case study could be extended to various other airfoil shapes and that the stall cell formation angle of attack can be deduced from just the mean lift behaviour.

Vertical-axis wind turbines are excellent candidates to diversify wind energy technology, but their aerodynamic complexity limits industrial deployment. To improve the efficiency and lifespan of vertical-axis wind turbines, we desire data-driven models and control strategies that take into account the timing and duration of subsequent events in the unsteady flow development. Here, we aim to characterise the chain of events that leads to dynamic stall on a vertical-axis wind turbine blade and to quantify the influence of the turbine operation conditions on the duration of the individual flow development stages. We present time-resolved flow and unsteady load measurements of a wind turbine model undergoing dynamic stall for a wide range of tip-speed ratios. Proper orthogonal decomposition is used to identify dominant flow structures and to distinguish six characteristic stall stages: the attached flow, shear-layer growth, vortex formation, upwind stall, downwind stall and flow reattachment stage. The timing and duration of the individual stages are best characterised by the non-dimensional convective time. Dynamic stall stages are also identified based on aerodynamic force measurements. Most of the aerodynamic work is done during the shear-layer growth and the vortex formation stage which underlines the importance of managing dynamic stall on vertical-axis wind turbines.