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.

Bernoulli pads can create a significant normal force on an object without contact. The radial outflow which creates this force also imposes a significant shear force on the object. Better understanding this shear force can improve pad designs in order to mitigate material deformation and damage, or allow the pads to be used as shear-based cleaning implements. Here, we use computational fluid dynamics to explore the parameter space and show a power-law relationship between the fluid power at the pad inlet and the maximum shear stress. These simulations are validated by a particle tracking velocimetry experiment. A relationship between the maximum shear stress and the inlet Reynolds number is provided, and some implications of the observed scaling relationships are explored.

A constantly rotating spherical container sustains turbulence of a fluid partially filling it. This simple turbulence generator has the potential for wide engineering applications as a bladeless mixer. Using the coupled level-set and volume of fluid method and the boundary data immersion method, we conduct direct numerical simulations of liquid–gas flow in a spherical container rotating about a horizontal axis to investigate the driving mechanism of turbulence, flow dependence on the filling rate $\varPsi$ and the mixing ability of the sustained turbulence. Even if the Froude number $Fr$ is small enough ($Fr\lesssim 10^{-3}$) for the liquid–gas interface to be undeformed, if the Reynolds number $Re$ is large enough ($Re\gtrsim 10^3$), small-scale turbulent eddies are sustained by being stretched in shear flow around a counter-rotating pair of container-size vortices, whose swirling directions depend on $\varPsi$. We clarify that the angle of flow near the solid wall colliding with the interface controls the swirling direction of these container-size vortices. Furthermore, we track fluid particles in the liquid phase to quantify mixing properties to show that almost perfect mixing occurs after approximately 10 spins of the container for lower $\varPsi$ ($\lesssim 0.5$), whereas the mixing requires less energy consumption for higher $\varPsi$ ($\gtrsim 0.7$) at the examined $Re=O(10^3)$.

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.

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.

We revisit the laminar–turbulent transition of a fine-grained slurry in a large pipe. The combination of long measurement times in an industrial-scale facility and ultrasound imaging allows us to observe and address anomalous trends. Under turbulent conditions, the flow is homogeneous and steady. However, under laminar conditions, two types of long-time-scale transient behaviours are captured. In the first scenario, the system has been homogenized, following which the flow rate is reduced to laminar conditions. The flow rate continues to gradually drop, while particles settle and form a stationary bed. In the second scenario, the system has been shut down for a prolonged period and the flow rate is slowly increased. The flow rate continues to rise while particles are slowly resuspended from the gradually eroding bed. Near the laminar–turbulent transition point, two types of intermittent structures are responsible for resuspension. The equilibrium phase, with steady flow rate, coincides with complete resuspension. These two long-time-scale transients correspond to the phenomena of ‘slow settling’ and ‘self-equilibration’, respectively. While the former can lead to shutdowns, the latter generates a stable system. Being aware of these phenomena is of relevance while operating slurry pipelines near the favourable operating point of the laminar–turbulent transition.

The evolution of midwater sediment plumes associated with deep-sea mining activities is investigated in the passive-transport phase using a simplified advection–diffusion-settling model. Key metrics that characterize the extent of plumes are defined based on a concentration threshold. Namely, we consider the volume flux of fluid that ever exceeds a concentration threshold, the furthest distance from and maximum depth below the intrusion where the plume exceeds the threshold, and the instantaneous volume of fluid in excess of the threshold. Formulas are derived for the metrics that provide insight into the parameters that most strongly affect the extent of the plume. The model is applied to a reference deep-sea mining scenario around which key parameters are varied. The results provide some sense of scale for deep-sea mining midwater plumes, but more significantly demonstrate the importance of the parameters that influence the evolution of midwater plumes. The model shows that the discharge mass flow rate and the concentration threshold play an equal and opposite role on setting the extent of the plume. Ambient ocean turbulence and the settling velocity distribution of particles play a lesser yet significant role on setting the extent, and can influence different metrics in opposing ways.

It is well established that small-scale cross-density (diapycnal) turbulent mixing induced by breaking of overturns in the interior of the ocean plays a significant role in sustaining the deep ocean circulation and in regulating tracer budgets such as those of heat, carbon and nutrients. There has been significant progress in the fluid mechanical understanding of the physics of breaking internal waves. Connection of the microphysics of such turbulence to the larger scale dynamics, however, is significantly underdeveloped. We offer a hybrid theoretical–statistical approach, informed by observations, to make such a link. By doing so, we define a bulk flux coefficient, $\varGamma _B$, which represents the partitioning of energy available to an ‘ocean box’ (such as a grid cell of a coarse resolution climate model), from winds, tides, and other sources, into mixing and dissipation. Here, $\varGamma _B$ depends on both the statistical distribution of turbulent patches and the flux coefficient associated with individual patches, $\varGamma _i$. We rely on recent parametrizations of $\varGamma _i$ and the seeming universal characteristics of statistics of turbulent patches to infer $\varGamma _B$, which is the essential quantity for representation of turbulent diffusivity in climate models. By applying our approach to climatology and global tidal estimates, we show that, on a basin scale, energetic mixing zones exhibit moderately efficient mixing that induces significant vertical density fluxes, while quiet zones (with small background turbulence levels), although highly efficient in mixing, exhibit minimal vertical fluxes. The transition between the less energetic to more energetic zones marks regions of intense upwelling and downwelling of deep waters. We suggest that such upwelling and downwelling may be stronger than previously estimated, which in turn has direct implications for the closure of the deep branch of the ocean meridional overturning circulation as well as for the associated tracer budgets.

We develop and investigate an advection–diffusion-settling model of deep-sea mining collector plumes, building on the analysis of midwater plumes in Part 1. In the case of collector plumes, deposition plays a predominant role in controlling the mass of sediment in suspension, and thus on setting the extent of the plume. We first discuss the competition between settling, which leads to deposition, and vertical turbulent diffusion, which stretches the plume vertically and reduces deposition. The time evolution of the concentration at the seabed is found to be a highly nonlinear function of time that depends non-trivially on the ratio of diffusion to settling time scales. This has direct implications for the three extent metrics considered, namely the instantaneous area of the seabed where a deposition rate threshold is exceeded, the furthest distance from the discharge where the plume exceeds a concentration threshold and the volume flux of fluid in the water column that ever exceeds a concentration threshold. Unlike the midwater plume, the particle velocity distribution of the sediment has the greatest influence on the extent metrics. The turbulence levels experienced by the plume also markedly affects its extent. Expected variability of turbulence and particle settling velocity yields orders of magnitude changes in the extent metrics.

We performed large-eddy simulations in a neutral atmospheric boundary layer to study the interaction between two identical wind farms with 72 turbines each. We demonstrate that the wind farm wake created by the upstream farm affects the entire flow in and around the downstream farm. The vertical entrainment fluxes above the downstream wind farm are strengthened, resulting in a faster wind farm wake recovery behind the downstream farm. These findings illustrate that interaction between extended wind farms affects flow structures beyond the wind farm scale. Furthermore, we demonstrate that wind farm wakes can reduce the power production of turbines throughout the downstream wind farms. We additionally observe that a staggered wind farm extracts more energy from the flow and thus creates a stronger wind farm wake than an aligned wind farm.

Metal additive manufacturing has enabled geometrically complex internal cooling channels for turbine and heat exchanger applications, but the process gives rise to large-scale roughness whose size is comparable to the channel height (which is 500 $\mathrm {\mu }$m). These super-rough channels pose previously unseen challenges for experimental measurements, data interpretation and roughness modelling. First, it is not clear if measurements at a particular streamwise and spanwise location still provide accurate representation of the mean (time- and plane-averaged) flow. Second, we do not know if the logarithmic layer survives. Third, it is unknown how well previously developed rough-wall models work for these large-scale roughnesses. To answer the above practical questions, we conduct direct numerical simulations of flow in additively manufactured super-rough channels. Three rough surfaces are considered, all of which are obtained from computed tomography scans of additively manufactured surfaces. The roughness’ trough to peak sizes are 0.1$h$, 0.3$h$ and 0.8$h$, respectively, where $h$ is the intended half-channel height. Each rough surface is placed opposite a smooth wall and the other two rough surfaces, leading to six rough-wall channel configurations. Two Reynolds numbers are considered, namely $Re_\tau =180$ and $Re_\tau =395$. We show first that measurements at one streamwise and spanwise location are insufficient due to strong mean flow inhomogeneity across the entire channel, second that the logarithmic law of the wall survives despite the mean flow inhomogeneity and third that the established roughness sheltering model remains accurate.

In offshore offloading operations, two vessels in a side-by-side configuration experience actions of both ambient water waves and liquid sloshing in internal tanks. Under the excitation of water waves, complex multibody motions are induced, resulting in liquid sloshing in tanks, and concurrently liquid sloshing can feedback to affect the vessels’ motions. The interaction between waves and two barges in a side-by-side configuration coupled with liquid sloshing effects is investigated for a fixed–free arrangement. A numerical model is developed based on the boundary element method to deal with complex wave induced multibody motions coupled with liquid sloshing in internal tanks. Due to the presence of a narrow gap between two vessels, gap resonance may occur, and a damping surface is introduced to suppress an unrealistic response near resonance. Concurrently, physical experiments with and without liquid sloshing effects are carried out. In-depth discussions on motion characteristics are given, and Stokes and non-Stokes natural frequencies associated with liquid sloshing are discussed. The significance of the present study is twofold. Firstly, the experimental measurements provide reference results for validations of numerical simulations. Secondly, this work gives an insight into wave induced motions with liquid sloshing effects under different wave headings which affect vessel operational safety.

Leidenfrost drops were recently found to host strong dynamics. In the present study, we investigate both experimentally and theoretically the flow structures and stability inside a Leidenfrost water drop as it evaporates, starting with a large puddle. As revealed by infrared mapping, the drop base is warmer than its apex by typically 10 $^{\circ }$C, which is likely to trigger bulk thermobuoyant flows and Marangoni surface flows. Tracer particles unveil complex and strong flows that undergo successive symmetry breakings as the drop evaporates. We investigate the linear stability of the base flows in a non-deformable, quasi-static, levitating drop induced by thermobuoyancy and the effective thermocapillary surface stress, using only one adjustable parameter. The stability analysis of nominally axisymmetric thermoconvective flows, parametrized by the drop radius $R$, yields the most unstable, thus, dominant, azimuthal modes (of wavenumber $m$). Our theory predicts well the radii $R$ for the mode transitions and cascade with decreasing wavenumber from $m=3,\, m=2$, down to $m=1$ (the eventual rolling mode that entails propulsion) as the drop shrinks in size. The effect of the escaping vapour is not taken into account here, which may further destabilize the inner flow and couple to the liquid/vapour interface to give rise to motion (Bouillant et al. Nat. Phys., vol. 14 (12), 2018, pp. 1188–1192; Brandão & Schnitzer Physical Review Fluids, vol. 5 (9), 2020, 091601).

Pulsatile jet propulsion is a highly energy-efficient swimming mode used by various species of aquatic animals that continues to inspire engineers of underwater vehicles. Here, we present a bio-inspired jet propulsor that combines the flexible hull of a jellyfish with the compression motion of a scallop to create individual vortex rings for thrust generation. Similar to the biological jetters, our propulsor generates a nonlinear time-varying exit velocity profile and has a finite volume capacity. The formation process of the vortices generated by this jet profile is analysed using time-resolved velocity field measurements. The transient development of the vortex properties is characterised based on the evolution of ridges in the finite-time Lyapunov exponent field and on local extrema in the pressure field derived from the velocity data. Special attention is directed toward the vortex merging observed in the trailing shear layer. During vortex merging, the Lagrangian vortex boundaries first contract in the streamwise direction before expanding in the normal direction to keep the non-dimensional energy at its minimum value, in agreement with the Kelvin–Benjamin variational principle. The circulation, diameter and translational velocity of the vortex increase due to merging. The vortex merging takes place because the velocity of the trailing vortex is higher than the velocity of the main vortex ring prior to merging. The comparison of the temporal evolution of the Lagrangian vortex boundaries and the pressure-based vortex delimiters confirms that features in the pressure field serve as accurate and robust observables for the vortex formation process.

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.

The performance of horizontal dilution tubes is investigated by Reynolds-averaged Navier–Stokes and large-eddy simulations. The flame gas enters the dilution tube through a pinhole. The orifice flow and the dilution process inside the tube are studied. The volume flow through the orifice is shown to be proportional to the square root of the pressure drop. The discharge coefficient is 0.9 ± 0.3 in the cold air (calibration) case and drops to 0.35 under hot (flame) conditions. The resulting dilution ratio is roughly a factor of five below typical literature data. The gas sample remains in the wall boundary layer and the mixing process is not complete at the end of the dilution tube. Turbulence decays rapidly behind the tube inlet, which shifts the flow into the laminar to turbulent transition regime. Turbulence increases significantly in the outlet section which has much smaller pipe cross-sections. Despite its relatively low Reynolds number, the outlet flow to the particle sizer (or to the gas analyzer) is clearly turbulent, and interactions with the wall are probable. The results are in agreement with previous findings from laminar jets in cross-flow. Guidelines for optimization of the sampling conditions are suggested.

Most medical diagnostic tests are expensive, involve slow turnaround times from centralized laboratories and require highly specialized equipment with seasoned technicians to carry out the assay. To facilitate realization of precision medicine at the point of care, we have developed a mixed-scale nanosensor chip featuring high surface area pillar arrays where solid-phase reactions can be performed to detect and identify nucleic acid targets found in diseased patients. Products formed can be identified and detected using a polymer nanofluidic channel. To guide delivery of this platform, we discuss the operation of various components of the device and simulations (COMSOL) used to guide the design by investigating parameters such as pillar array loading, and hydrodynamic and electrokinetic flows. The fabrication of the nanosensor is discussed, which was performed using a silicon (Si) master patterned with a combination of focused ion beam milling and photolithography with deep reactive ion etching. The mixed-scale patterns were transferred into a thermoplastic via thermal nanoimprint lithography, which facilitated fabrication of the nanosensor chip making it appropriate for in vitro diagnostics. The results from COMSOL were experimentally verified for hydrodynamic flow using Rhodamine B as a fluorescent tracer and electrokinetic flow using single fluorescently labelled oligonucleotides (single-stranded DNAs, ssDNAs).

The SARS-CoV-2 is transmitted not only through coughing, but also through breathing, speaking or singing. We perform direct numerical simulations of the turbulent transport of potentially infectious aerosols in short conversations, involving repetitive phrases separated by quiescent intervals. We estimate that buoyancy effects due to droplet evaporation are small, and neglect them. A two-way conversation is shown to significantly reduce the aerosol exposure compared with a relative monologue by one person and relative silence of the other. This is because of the ‘cancelling’ effect produced by the two interacting speech jets. Unequal conversation is shown to significantly increase the infection risk to the person who talks less. Interestingly, a small height difference is worse for infection spread, due to reduced interference between the speech jets, than two faces at the same level. For small axial separation, speech jets show large oscillations and reach the other person intermittently. We suggest a range of lateral separations between two people to minimize transmission risk. A realistic estimate of the infection probability is provided by including exposure through the eyes and mouth, in addition to the more common method of using inhaled virions alone. We expect that our results will provide useful inputs to epidemiological models and to disease management.

The flow patterns in the heart, in health and disease, have been of great interest for several years. Modern fluid dynamics analyses elucidate how underlying inefficient energetic or mixing characteristics of these flow patterns correlate with adverse effects. Unfortunately, translation of such modern analyses to the clinical stage remains a challenge. In this experimental work, we propose and demonstrate that braids of random and sparse particle trajectories provide an intuitive, global and practical description of cardiovascular flows. Moreover, we expose the flow pattern in an experimental healthy left ventricle model as a highly effective blood mixer at the topological level. Flow topologies that deviate from this pattern are accompanied by a reduction in energetic efficiency, as shown through comparisons with diseased flow models. These results suggest an ideal clinical approach to patient follow-up and the evaluation of the performance of medical devices.

Redox flow batteries (RFBs) are an emerging electrochemical technology envisioned towards storage of renewable energy. A promising sub-class of RFBs utilizes single-flow membraneless architectures in an effort to minimize system cost and complexity. To support multiple functions, including reactant separation and fast reactant transport to electrode surfaces, electrolyte flow must be carefully designed and optimized. In this work, we propose adding a secondary channel adjacent to a permeable battery electrode, solving for the flow field and analysing the effects on the reactant concentration boundary layer at the electrode. We find that an adjacent channel with gradually changing thickness leads to a desired nearly uniform flow through the electrode to the adjacent channel. Consequently, the thickness of the concentration boundary layer is significantly reduced, increasing reactant transport to the electrode surface to 140% of the rate of a battery with a constant width adjacent channel, and 350% of the rate with no adjacent channel. Overall, this theory provides insight into the important role of flow physics for this promising sub-class of flow batteries, and can pave the way to improved energy efficiency of such flow batteries.