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.

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.

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.

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 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.

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.

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 $Re=O(10^3)$.

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.

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.

The present study focuses on the performance of a novel high-shear atomizer with a discrete radial-jet fuel nozzle to overcome the constraints associated with the simplex-pressure-swirl and duplex-fuel nozzles at the high-end power demand of a gas turbine combustor. The high-shear atomizer consists of multiple inner and outer radial swirlers with interchangeable flare and fuel nozzle. The performance of the atomizer with discrete radial-jet fuel nozzle is elucidated at ALR (mass ratio of air to liquid) 14.1 through variations in geometrical design parameters of the swirl cup. The parameters of interest are the split ratio (γ), relative swirl direction of inner and outer swirler (co- and counter-rotation), flare angle (θ) and flare mixing length (η). Spray characteristics at ALR 4.72, 7.08 and 9.44 are also presented for an atomizer by freezing the geometrical design. The particle image velocimetry diagnostic technique is employed to capture the spray flow field. The non-dimensional radial (W/Df; W, radial width of CTRZ (in mm) and Df, exit diameter of flare (mm)) and axial (L/Df) sizes of the central toroidal recirculation zone and near field swirl number (SN5) of the flow are explored. Further, variations in the droplet size distribution of the atomizer across all the ALR are discussed in detail. The Sauter mean diameter across all the test cases is found to be in the range of 9–30 μm, 15–37 μm, 15–50 μm and 23–75 μm at ALR 14.1, 9.44, 7.08 and 4.72 respectively, which shows good atomization capability of the atomizer with discrete jets. The spatial distribution of the spray volume/mass in an azimuthal plane is examined in the circumferential and radial directions, which shows consistent and excellent azimuthal symmetry of the spray even with a decrease in ALR value. The overall mean and dynamic spray characteristics of the atomizer suggest that high-shear atomizer in combination with a discrete radial-jet fuel nozzle would be a better candidate than an atomizer with a simplex pressure-swirl fuel nozzle in rich-quench-lean concept-based gas turbine combustors.

A high-fidelity large-eddy simulation and unsteady flamelet combustion model construct is deployed to numerically investigate the effects of crosswind magnitude and pool fire shape on large-scale pool fire attributes. These include general flame dynamics, flame shape and radiative flux magnitude in and around the fire. Three pool fire shapes at a nominal length scale of 10 m are subjected to four crosswind magnitudes between 0 and 20 m s$^{-1}$. The pool shapes studied are circular, square and rectangular. The study includes the sensitivity of parameters to mesh and time step refinement. Results demonstrate that the rectangular shape, under crosswind, has low-levels of vertical velocity induction, resulting in a plume that is closer to the ground. In the quiescent regime, under-resolved meshes provide a higher radiative heat flux prediction compared with the most refined mesh. However, as crosswind increases, low mesh resolutions underpredicted radiative flux. This is due to the coarse mesh resolution not capturing small-scale vortical features that increased mixing and combustion efficiency. A transition of peak radiative flux with respect to crosswind occurs from the leeward- to windward-side of the pool, while sharp pool features result in larger radiative heat fluxes concentrated in regions of high scalar dissipation rate.

The effect of sharp forward-facing steps on boundary-layer transition is systematically investigated in this work in combination with the influence of variations in Mach number, Reynolds number and streamwise pressure gradient. Experiments have been conducted in a quasi-two-dimensional flow at Mach numbers up to 0.77 and chord Reynolds numbers up to 13 million in the Cryogenic Ludwieg-Tube Göttingen. The adopted experimental set-up allows an independent variation of the aforementioned parameters and enables a decoupling of their respective effects on the boundary-layer transition, which has been measured accurately and non-intrusively by means of a temperature-sensitive paint. The functional relations determined between a non-dimensional transition parameter and the non-dimensional step parameters allow the step effect on transition to be isolated from the influence of variations in Mach number, Reynolds number and pressure gradient. Criteria for acceptable heights of forward-facing steps on natural laminar flow surfaces for the examined test conditions are derived from the present functional relations. The measured transition locations are also correlated with the results of linear, local stability analysis for the smooth configuration, enabling the estimation of the step-induced increment of the amplification factor ΔN of Tollmien–Schlichting waves, which can be incorporated in the eN transition prediction method.

The mixing of immiscible oil and water by a pitched blade turbine in a cylindrical vessel is studied numerically. Three-dimensional simulations combined with a hybrid front-tracking/level-set method are employed to capture the complex flow and interfacial dynamics. A large eddy simulation approach, with a Lilly–Smagorinsky model, is employed to simulate the turbulent two-phase dynamics at large Reynolds numbers $Re=1802{-}18\ 026$. The numerical predictions are validated against previous experimental work involving single-drop breakup in a stirred vessel. For small $Re$, the interface is deformed but does not reach the impeller hub, assuming instead the shape of a Newton's Bucket. As the rotating speed increases, the deforming interface attaches to the impeller hub which leads to the formation of long ligaments that subsequently break up into small droplets. For the largest $Re$ studied, the system dynamics becomes extremely complex wherein the creation of ligaments, their breakup and the coalescence of drops occur simultaneously. The simulation outcomes are presented in terms of spatio-temporal evolution of the interface shape and vortical structures. The results of a drop size analysis in terms of the evolution of the number of drops, and their size distribution, is also presented as a parametric function of $Re$.

We present high-fidelity numerical simulations of the interaction of an oblique shock impinging on the turbulent boundary layer developed over a rectangular flexible panel, replicating wind tunnel experiments by Daub et al. (AIAA Journal, vol. 54, 2016, pp. 670–678). The incoming free-stream Mach and unit Reynolds numbers are $M_{\infty } = 3$ and $Re_{\infty }=49.4\times 10^6 {\rm m}^{-1}$, respectively. The reference boundary layer thickness upstream of the interaction with the shock is $\delta _0 = 4$ mm. The oblique shock is generated with a rotating wedge initially parallel to the flow that increases the deflection angle up to $\theta _{{max}} = 17.5^{\circ }$ within approximately $15$ ms. A loosely coupled partitioned flow–structure interaction simulation methodology is used, combining a finite-volume flow solver of the compressible wall-modelled large-eddy simulation equations, an isoparametric finite-element solid mechanics solver and a spring-system-based mesh deformation solver. Simulations are conducted with rigid and flexible panels, and the results compared to elucidate the effects of panel flexibility on the interaction. Three-dimensional effects are evaluated by conducting simulations with both full ($50 \delta _0$) and reduced ($5\delta _0$) spanwise panel width, the latter enforcing spanwise periodicity. Panel flexibility is found to increase the separation bubble size and modify its spectral dynamics. Time- and spanwise-averaged streamwise profiles of the wall pressure exhibit a drop over the flexible panel prior to the interaction and a reduced peak pressure in comparison with the rigid case. Spectral analyses of wall pressure data indicate that the low-frequency motions have a similar spectral distribution for the rigid and flexible cases, but the flexible case shows a wider region dominated by low-frequency motions and traces of the panel vibration on the wall pressure signal. The sensitivity of the interaction to small variations in the wedge extent and incoming boundary layer thickness is evaluated. Predictions obtained from lower-fidelity modelling simplifications are also assessed.

A novel experiment is presented to study the initial disturbances on a free surface due to the constant acceleration of liquid around a submerged obstacle. The surface response to different obstacle sizes, initial surface heights and fluid velocities is measured using high-speed videography. Perturbations observed on the surface are classified into either jetting or gravity waves by measuring the steepness of growing liquid columns. A classification phase map between these two regimes is obtained and compared with analytical results by Martín Pardo and Nedić (2021). The agreement between decision boundaries is good for high Froude numbers (high fluid velocities) but deteriorates at lower velocities, where viscosity and surface tension effects (not considered in the analytical model) have a greater predominance. The surface profile and perturbation amplitude measured in experiments are also compared against this analytical model. In all cases, the model accurately predicts the corresponding experimental results at the beginning of the motion, but the prediction error increases with time. It is also observed that faster moving surfaces that lead to the onset of jetting have greater prediction accuracies and longer validity times of the predictions.