While there have been numerous applications of large eddy simulations (LES) to complex flows, their application to practical engineering configurations, such as full aircraft models, have been limited to date. Recently, however, advances in rapid, high quality mesh generation, low-dissipation numerical schemes and physics-based subgrid-scale and wall models have led to, for the first time, accurate simulations of a realistic aircraft in landing configuration (the Japanese Aerospace Exploration Agency Standard Model) in less than a day of turnaround time with modest resource requirements. In this paper, a systematic study of the predictive capability of LES across a range of angles of attack (including maximum lift and post-stall regimes), the robustness of the predictions to grid resolution and the incorporation of wind tunnel effects is carried out. Integrated engineering quantities of interest, such as lift, drag and pitching moment will be compared with experimental data, while sectional pressure forces will be used to corroborate the accuracy of the integrated quantities. Good agreement with experimental $C_L$ data is obtained across the lift curve with the coefficient of lift at maximum lift, $C_{L,max}$, consistently being predicted to within five lift counts of the experimental value. The grid point requirements to achieve this level of accuracy are reduced compared with recent estimates (even for wall modelled LES), with the solutions showing systematic improvement upon grid refinement, with the exception of the solution at the lowest angles of attack, which will be discussed later in the text. Simulations that include the wind tunnel walls and aircraft body mounting system are able to replicate important features of the flow field noted in the experiment that are absent from free air calculations of the same geometry, namely, the onset of inboard flow separation in the post-stall regime. Turnaround times of the order of a day are made possible in part by algorithmic advances made to leverage graphical processing units. The results presented herein suggest that this combined approach (meshing, numerical algorithms, modelling, efficient computer implementation) is on the threshold of readiness for industrial use in aeronautical design.

A new guideline for mitigating indoor airborne transmission of COVID-19 prescribes a limit on the time spent in a shared space with an infected individual (Bazant & Bush, Proceedings of the National Academy of Sciences of the United States of America, vol. 118, issue 17, 2021, e2018995118). Here, we rephrase this safety guideline in terms of occupancy time and mean exhaled carbon dioxide (${\rm CO}_{2}$) concentration in an indoor space, thereby enabling the use of ${\rm CO}_{2}$ monitors in the risk assessment of airborne transmission of respiratory diseases. While ${\rm CO}_{2}$ concentration is related to airborne pathogen concentration (Rudnick & Milton, Indoor Air, vol. 13, issue 3, 2003, pp. 237–245), the guideline developed here accounts for the different physical processes affecting their evolution, such as enhanced pathogen production from vocal activity and pathogen removal via face-mask use, filtration, sedimentation and deactivation. Critically, transmission risk depends on the total infectious dose, so necessarily depends on both the pathogen concentration and exposure time. The transmission risk is also modulated by the fractions of susceptible, infected and immune people within a population, which evolve as the pandemic runs its course. A mathematical model is developed that enables a prediction of airborne transmission risk from real-time ${\rm CO}_{2}$ measurements. Illustrative examples of implementing our guideline are presented using data from ${\rm CO}_{2}$ monitoring in university classrooms and office spaces.

In recent years, observations of the atmospheric surface layer have greatly promoted research on high-Reynolds-number wall-bounded turbulence, especially observations of wind-blown sand flows/sandstorms, which are typical sand-laden two-phase flows; these successes have advanced the science of gas–solid two-phase wall-bounded turbulence to very-high-Reynolds-number conditions. Based on a review of existing atmospheric surface layer observations and the development process, this paper summarizes the important promoting effect played by these observations in understanding the very-large-scale structure characteristics, turbulent kinetic energy fraction and amplitude modulation effect, and in reconstructing the spatial electric field under high-Reynolds-number wall turbulence. This review focuses on the main successes achieved by the observation of sand-laden two-phase flows and the three-dimensional turbulent flow field, especially in the streamwise direction. Finally, some suggestions and outlooks for further research on particle-laden two-phase wall-bounded turbulence under high-Reynolds-number conditions are presented.

The variety of configurations for vertical-axis wind turbines (VAWTs) make the development of universal scaling relationships for even basic performance parameters difficult. Rotor geometry changes can be characterized using the concept of solidity, defined as the ratio of solid rotor area to the swept area. However, few studies have explored the effect of this parameter at full-scale conditions due to the challenge of matching both the non-dimensional rotational rate (or tip speed ratio) and scale (or Reynolds number) in conventional wind tunnels. In this study, experiments were conducted on a VAWT model using a specialized compressed-air wind tunnel where the density can be increased to over 200 times atmospheric air. The number of blades on the model was altered to explore how solidity affects performance while keeping other geometric parameters, such as the ratio of blade chord to rotor radius, the same. These data were collected at conditions relevant to the field-scale VAWT but in the controlled environment of the lab. For the three highest solidity rotors (using the most blades), performance was found to depend similarly on the Reynolds number, despite changes in rotational effects. This result has direct implications for the modelling and design of high-solidity field-scale VAWTs.

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.

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.

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.

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.

We present a microfluidic method to measure the elastic properties of a population of microcapsules (liquid drops enclosed by a thin hyperelastic membrane). The method is based on the observation of flowing capsules in a cylindrical capillary tube and an automatic inverse analysis of the deformed profiles. The latter requires results from a full numerical model of the fluid–structure interaction accounting for nonlinear membrane elastic properties. For ease of use, we provide them under the form of databases, when the initially spherical capsule has a membrane governed by a neo-Hookean or a general Hooke's law with different surface Poisson ratios. Ultimately, the microfluidic method yields information on the type of elastic constitutive law that governs the capsule wall material together with the value of the elastic parameters. The method is applied to a population of ovalbumin microcapsules and is validated by means of independent experiments of the same capsules subjected to a different flow in a microrheological device. This is of great interest for quality control purposes, as small samples of capsule suspensions can be diverted to a measuring test section and mechanically tested with a 10 % precision using an automated process.

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.

Helical vortex systems, such as those found in the wakes of wind turbines, helicopter rotors and propellers, are subject to instabilities that lead to pairing between adjacent vortex loops. Certain modes of these instabilities can be triggered by an asymmetry in the rotor generating the vortices. In three-vortex systems, like those formed by many industrial rotors, the nonlinear vortex interactions are highly complex, introducing the need for a simple model to predict their dynamics. The current study presents a model for helical vortex systems based on an infinite strip of periodically repeating point vortices, whose motion can be computed using a single equation. This highly simplified model is shown to accurately reproduce the helical vortex dynamics predicted by a more sophisticated filament model and observed in water channel experiments on model rotors. The model is then used to investigate different types of vortex perturbations. Perturbation direction is found to have an important effect on the evolution of the instability, and displacements are observed to induce vortex pairing more quickly than circulation changes. These findings can be used to design asymmetric rotors that induce vortex breakdown more effectively, mitigating detrimental wake effects such as increased fatigue loading on downstream structures.

We review the progress on the applications of the vortex-surface field (VSF). The VSF isosurface is a vortex surface consisting of vortex lines. Based on the generalized Helmholtz theorem, the VSF isosurfaces of the same threshold at different times have strong coherence. As a general flow diagnostic tool for studying vortex evolution, the numerical VSF solution is first constructed in a given flow field by solving a pseudo-transport equation driven by the instantaneous frozen vorticity, and then the VSF evolution is calculated by the two-time method. From the database of numerical simulations or experiments, the VSF can elucidate mechanisms in the flows with essential vortex dynamics, such as isotropic turbulence, wall flow transition, flow past a flapping plate and turbulence–flame interaction. The characterization of VSFs reveals the correlation between robust statistical features and the critical quantities needed to be predicted in engineering applications, such as the friction coefficient in transition, thrust in bio-propulsion and growth rate in interface instability. Since the VSF evolution captures the essential Lagrangian-based dynamics of vortical flows, it inspires novel numerical methods on cutting-edge hardware, e.g. graphic and quantum processors.

Current methods for fabricating lenses rely on mechanical processing of the lens or mould, such as grinding, machining and polishing. The complexity of these fabrication processes and the required specialized equipment prohibit rapid prototyping of optical components. This work presents a simple method, based on free-energy minimization of liquid volumes, which allows us to quickly shape curable liquids into a wide range of spherical and aspherical optical components, without the need for any mechanical processing. After the desired shape is obtained, the liquid can be cured to produce a solid object with nanometric surface quality. We provide a theoretical model that accurately predicts the shape of the optical components, and demonstrate rapid fabrication of all types of spherical lenses (convex, concave, meniscus), cylindrical lenses, bifocal lenses, toroidal lenses, doublet lenses and aspheric lenses. The method is inexpensive and can be implemented using a variety of curable liquids with different optical and mechanical properties. In addition, the method is scale invariant and can be used to produce even very large optical components, without a significant increase in fabrication time. We believe that the ability to easily and rapidly create optical components, without the need for complex and expensive infrastructure, will provide researchers with new affordable tools for fabricating and testing optical designs.

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.

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 propose an improved adjoint-based method for the reconstruction and prediction of the nonlinear wave field from coarse-resolution measurement data. We adopt the data assimilation framework using an adjoint equation to search for the optimal initial wave field to match the wave field simulation result at later times with the given measurement data. Compared with the conventional approach where the optimised initial surface elevation and velocity potential are independent of each other, our method features an additional constraint to dynamically connect these two control variables based on the dispersion relation of waves. The performance of our new method and the conventional method is assessed with the nonlinear wave data generated from phase-resolved nonlinear wave simulations using the high-order spectral method. We consider a variety of wave steepness and noise levels for the nonlinear irregular waves. It is found that the conventional method tends to overestimate the surface elevation in the high-frequency region and underestimate the velocity potential. In comparison, our new method shows significantly improved performance in the reconstruction and prediction of instantaneous surface elevation, surface velocity potential and high-order wave statistics, including the skewness and kurtosis.

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.

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.

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.

Vertical axis turbine (VAT) arrays can achieve larger power generation per land area than their horizontal axis counterparts, due to the positive synergy from clustering VATs in close proximity. The VATs generate a three-dimensional wake that evolves unevenly over the vertical and transverse directions according to two governing length scales, namely the rotor's diameter and height. Theoretical wake models need to capture such a complex wake dynamics to enable reliable array design that maximises energy output. This paper presents two new theoretical VAT wake models based on super-Gaussian and Gaussian shape functions, which account for the three-dimensional velocity deficit distribution in the wake. The super-Gaussian model represents the initial elliptical shape with the superposition of vertical and lateral shape functions that progressively converge into an axisymmetric circular-shaped wake at a downstream distance that depends on the rotor's height-to-diameter aspect ratio. Our Gaussian model improves the initial wake width prediction taking into account the rectangular rotor's cross-section. Our models were well validated with large-eddy simulations (LES) of single VATs with varying aspect ratios and thrust coefficients operating in an atmospheric boundary layer. The super-Gaussian model attained a good agreement with LES in both near and far wake, whilst the Gaussian model represented well the far-wake region.