Hollow fibre membrane bioreactors provide a fast and efficient method for engineering functional tissue for use in medical treatments. Flow is utilised to overcome mass transport limitations by perfusing a nutrient-rich culture medium through the fibre lumen, which can then transport along the fibre lumen or across the porous membrane wall. Cells seeded at the outer membrane wall consume the nutrient and subsequently produce waste metabolites, which are transported away through an external extra-capillary space (ECS) along with excess nutrient. We present and investigate a two-dimensional axisymmetric model for fluid flow and solute transport through a single-fibre bioreactor configuration, with cells seeded to the external fibre wall. Fluid flow is modelled by steady lubrication and Darcy equations, which are coupled to the solute transport problem modelled by a system of advection–diffusion equations, supplemented with a reaction term to model the cell layer. Our model analysis reveals how spatially varying wall permeability distributions can be utilised to provide uniform nutrient delivery to a spatially uniform, homogeneous cell population. We also reveal how maximising the transmural pressure drop across the membrane wall is the dominant mechanism for waste removal rather than traditional experimental methods of flushing the ECS.

Benthic macroalgae (including brown macroalgae or kelp) constitute one of the largest contributors to coastal primary production, but their ability to store and sequester carbon remains uncertain. Here, we use a numerical model of the flow/kelp interactions to study how tidal currents interact with an idealised numerical model of a giant kelp (Macrocystis pyrifera) forest, intending to better understand the potential for kelp growth in nutrient-limited conditions and the export of important tracers such as dissolved organic carbon. We calibrate and test our model using observations of currents within and surrounding a kelp forest in Southern California. By varying the density of kelp in our model, we find that there is a kelp density that maximises the export of tracer released from the kelp forest. Since the tracer advection/diffusion equation is linear with respect to the tracer concentration, the same kelp density corresponds to the maximum uptake for a tracer with a constant far-field concentration. The density at which this maximum occurs coincides with the density typical of natural kelp forests, where kelp growth may be limited by the uptake of dissolved nutrients from the surrounding water. Additionally, the drag induced on the tidal currents by the kelp forest results in a mean circulation through the kelp forest and a mean displacement of the kelp forest canopy.

To accurately calculate the turbulent exchange coefficient, the contribution of multi-scale turbulent transportation needs to be considered, especially in the complex terrain of the coastal area. In September 2019, a comprehensive observation experiment on the offshore atmospheric boundary layer was carried out at the Yangmeikeng Ecological Monitoring Station and Sai Chung Gulf. Through scale decomposition, it is shown that the turbulent motion in the atmospheric boundary layer in the coastal area is affected by the underlying surface, such as that of the coastal land or the sea–land boundary. This is the main reason behind the phenomenon whereby different scales make different contributions to momentum flux. Different multi-scale characteristics of turbulent structures on the underlying surface affect the drag coefficient. Through wavelet transform and finite element method, the characteristics of the multi-scale flow structures produced by the complicated offshore terrain are analysed. It is found that large-scale flow structures enhance the pulsating intensity at the small scale, but the large-scale coherence characteristics are different from those at the small scale. In summary, in comparing these three sites, the flux exchange on the roof is greatest, followed by that on the tower. In the Gulf, the flux exchange is mainly dependent on small-scale structures, which are linked with the smallest values.

This paper investigates the impact of large-scale turbulence on the aerodynamic characteristics of a pitching wind turbine blade at Reynolds number 135 000, whose cross-section is a NACA0012 airfoil with constant chord length. Large-eddy simulations at reduced frequencies, $k_{red} = 0.05$ and 0.1, were validated against reference data from the literature. An efficient method capable of generating synthetic large-scale turbulence at the inlet was applied by using two streamwise integral length scales $L_{x} = 1c$ and 1.5$c$, which represent energetic turbulence eddies at the height where the wind turbine operates. For $k_{red}= 0.1$, the change in the maximum lift coefficient at the dynamic stall angle near the maximum angle of attack is on average 20 % lower and during the downstroke it is on average 22 % lower, compared with the smooth inflow. A higher reduced frequency ($k_{red} = 0.2$) apparently does not further change the lift, drag and moment coefficients, and the inflow turbulence disordered leading-edge vortices. The turbulent shear stress and the phase-averaged dispersive shear stress in the wake are of the same magnitude, but with negative and positive signs, respectively, suggesting that the large-scale phase-averaged fluctuations transfer momentum in the opposite direction compared with the turbulent fluctuations, reducing the drag on the suction-side flow, and subsequently increasing the averaged lift coefficient. This demonstrates the critical importance of the large-scale non-turbulent unsteadiness in the wake of a pitching wing.

Shallowly submerged oscillating structures may be found in wave energy devices or semi-submersible vessels. Predicting the force on such structures is critical for design purposes, but complicated due to nonlinear phenomena which can occur in shallow water, including wave breaking and bore formation. Such effects are particularly important around the first ‘resonance’ frequency of the fluid on top of the device, where linear theory predicts large flows on/off the cylinder and corresponding surface elevations and forces. In an effort to create a reliable and efficient model to predict the hydrodynamic force on a shallowly submerged truncated vertical cylinder, an axisymmetric nonlinear hybrid model is developed for forced heave oscillations. The flow above the cylinder is modelled using the nonlinear shallow water equations, and linear potential flow theory is used in the surrounding fluid. The model is compared with experimental results for forced heave oscillations and performs well for predicting the heave force. It is then used to examine linearised heave force for increasing amplitudes of (prescribed) harmonic heave motion. There is a significant reduction in the peaks of radiation damping and added mass coefficients with increasing amplitude, and associated shifts in the frequencies of the peaks.

The flow dynamics of small-width wall-attached jets generated by a Coand-effect nozzle is investigated by unsteady Reynolds-averaged Navier–Stokes simulations. The data are validated by comparison with hot-wire velocity measurements performed on the same flow configurations. The jets exhibit a complex topology strongly influenced not only by the spanwise vorticity (as usually observed in wall jets) but also by a vorticity component normal to the wall and induced by the shear layer developing on the jet sides. This results in an original U-shaped jet whose characteristics are studied in detail for three different mass flow rates. The robustness of the flow topology on a larger range of injected mass flow rates is finally presented and discussed in terms of the injected momentum near the wall. The resulting flow profiles point out that our injector is expected to be a promising candidate for active flow control in gas-turbine compressors for aeronautical and energy applications.

Flagellated bacteria propel themselves by rotating flexible flagella driven by independent motors. Depending on the rotation direction of the motors and the handedness of the helical filaments, the flagella either pull or push the cell body. Motivated by experimental observations of Magnetococcus marinus, we develop an elastohydrodynamic model to study the locomotion of a bi-flagellated bacterium with one puller flagellum and one pusher flagellum. In this model, the boundary integral technique and Kirchhoff rod model are employed respectively to calculate the hydrodynamic forces on the swimmer and model the elastic deformations of the flagella. Our numerical results demonstrate that the model bacterium travels along a double helical trajectory, which is consistent with the experimental observations. Varying the stiffness, orientations or positions of the flagella significantly changes the swimming characteristics. Notably, when either the applied torque is higher than a critical value or the flagellum stiffness is lower than a critical stiffness, the pusher flagellum exhibits overwhirling motion, resulting in a more complicated swimming style and a lower swimming speed. For a moderate flagellum stiffness, the swimming speed is insensitive to the rest configuration orientation over a wide range of orientation angles as the flagella deform to maintain alignment with the swimming direction.

Motivated by flow interactions in schooling biological swimmers as well as in unmanned underwater vehicle fleets, we investigate the flow past two identical 6 : 1 ellipses using two-dimensional simulations at Reynolds numbers of $\mathcal {O}(10^3)$. When both ellipses move at the same velocity, overall drag reductions of 10 %–20 % can be achieved in staggered formations, with the strongest drag reductions occurring at the smallest lateral distances. In side-by-side configurations, the drag on both bodies increases by 10 %–20 %. Lift coefficients are repulsive and up to four times larger than the total drag coefficients. During overtaking manoeuvres, increasing the relative speed of the overtaking ellipse predominantly affects the forces on the overtaken ellipse. The mean drag force on the overtaken ellipse increases with increasing speed difference. Mean lift forces during the overtaking manoeuvre are repulsive for both bodies; as the speed difference increases, the repulsive force increases on the overtaken body and decreases on the overtaking body. Overall, these results highlight that the lateral forces in hydrodynamic interactions between bodies in formation dominate the hydrodynamic interactions. Further, the results indicate that future work is needed to investigate how viscous and three-dimensional effects change the lateral forces between side-by-side submerged bodies.

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.

Efficient tools for predicting the drag of rough walls in turbulent flows would have a tremendous impact. However, accurate methods for drag prediction rely on experiments or numerical simulations which are costly and time consuming. Data-driven regression methods have the potential to provide a prediction that is accurate and fast. We assess the performance and limitations of linear regression, kernel methods and neural networks for drag prediction using a database of 1000 homogeneous rough surfaces. Model performance is evaluated using the roughness function obtained at a friction Reynolds number $Re_\tau$ of 500. With two trainable parameters, the kernel method can fully account for nonlinear relations between the roughness function $\Delta U^+$ and surface statistics (roughness height, effective slope, skewness, etc.). In contrast, linear regression cannot account for nonlinear correlations and displays large errors and high uncertainty. Multilayer perceptron and convolutional neural networks demonstrate performance on par with the kernel method but have orders of magnitude more trainable parameters. For the current database size, the networks’ capacity cannot be fully exploited, resulting in reduced generalizability and reliability. Our study provides insight into the appropriateness of different regression models for drag prediction. We also discuss the remaining steps before data-driven methods emerge as useful tools in applications.

Proper orthogonal decomposition (POD) is applied to three-dimensional (3-D) velocity fields collected from large-eddy simulations (LES) of a baffled stirred tank. In the LES, the tank operates with a Rushton-type impeller under turbulent conditions (at least in the near-impeller region) and the working fluid exhibits either Newtonian or shear-thinning rheology. The most energetic POD modes are analysed, and a POD reconstruction based on the higher modes is proposed to approximate the fluctuating component of the velocity field. Subsequently, the POD reconstruction is used to identify vortical structures and characterise them in terms of their shape. The structures are identified by considering a frame-invariant formulation of a popular, Eulerian, local-region-type method: the $Q$-criterion. Statistics of shape-related parameters are then investigated to address the morphology of the structures. It is found that: (i) regardless of the working fluid rheology, it seems feasible to decompose the 3-D field into its mean, most energetic periodic and fluctuating components using POD, allowing, for instance, reduced-order modelling of the energetic periodic motions for mixing enhancement purposes, and (ii) vortical structures related to turbulence are mostly tubular. Finding (ii) implies that, as starting point, phenomenological models for the interaction between fluid particles (drops and bubbles) and vortices should consider the latter as cylindrical structures rather than of spherical shape, as classically assumed in these models.

This study presents a direct numerical simulation that investigates the transport mechanisms of sand particles in the neutrally stable atmospheric Ekman boundary layer (AEBL). The simulation models the AEBL in a half-channel flow, taking into account the Earth's rotation and adding a Coriolis term to the Navier–Stokes equations. The Lagrangian point-particle method with one-way coupling is used to track the sand particles. The main objective is to examine the impact of gravity and particle Stokes number on the sand particle dynamics. The results indicate that gravity has a significant effect on large-size sand particles, as seen in the mean and root-mean-square sand velocity profiles. The slip velocity profiles of sand particles relative to the surrounding air show that larger particles experience higher drag forces in the viscous sublayer, which hinders their forward movement. This effect is also amplified by gravity. Furthermore, the mean profiles of the streamwise and spanwise slip velocities exhibit distinct demarcations of the viscous sublayer, buffer layer and log-law region. The spatial and temporal Voronoï analysis reveals that gravity increases the clustering level of sand particles in the entire turbulent Ekman layer and reduces the time for the change of the Voronoï volume, particularly for large-size particles.

Gravure printing is a type of printing method that uses metal cylinders with engraved cells that hold ink. The ink is transferred directly to the paper or other material by pressing it against the cylinder. The flow associated with gravure printing includes a flow in a liquid bridge formed in the contact region of the cylinders and a thin-film coating flow of the ink. The flow is governed by viscous and capillary forces. In many cases, the flow is unstable, which leads to the formation of instability patterns on the printed surfaces. The analysis of these instabilities is a very challenging problem, especially since industrial inks are usually rheologically complex. In this experimental and theoretical study, the flow of inks on a rotating cylinder is analysed, accounting for the shear-rate-dependent liquid viscosity. A theoretical solution for the film flow allows us to predict the width of the liquid bridge between two cylinders. Moreover, it is shown that the measured characteristic size of the printed pattern is of the same order as the predicted liquid bridge width. We observe a nearly linear dependence of pattern size and liquid bridge width.

The importance of buoyancy relative to free-stream flow is described using an adapted Froude number $Fr' = U/f_0^{1/3}$, where $U$ is the flow speed and $f_0$ is the exhaust buoyancy flux per unit length. We varied $Fr'$ by changing the free-stream flow rate, the exhaust flow rate and the buoyancy of the exhaust. We have experimentally identified two flow regimes, depending on the value of $Fr'$. For high $Fr'$ (low buoyancy), dispersion is driven by inertial forces in the wake and the amount of a pollutant in the wake is independent of $Fr'$. For moderate $Fr'$, a wall plume develops up the back of the step, directly feeding the pollutant into the shear layer, but without altering the shape of the wake. This wall plume reduces the amount of pollutant trapped behind the step. We developed an analytic model to describe the quantity of pollutant trapped behind the step. The model predicts the transition from buoyancy being negligible to being the dominant transport mechanism within the wake. We have hypothesised and observed some evidence of a third regime at low $Fr'$, when the buoyancy is sufficient to distort the macrostructure of the shear layer and wake.

The unsteady flow behaviour of two side-by-side rotors in ground proximity is experimentally investigated. The rotors induce a velocity distribution interacting with the ground causing the radial expansion of the rotor wakes. In between the rotors, an interaction of the two wakes takes place, resulting in an upward flow similar to a fountain. Two types of flow topologies are examined and correspond to two different stand-off heights between the rotors and the ground: the first one where the height of the fountain remains below the rotor disks, and a second one where it emerges above, being re-ingested. The fountain unsteadiness is shown to increase when re-ingestion takes place, determining a location switch from one rotor disk to the other, multiple times during acquisition. Consequently, variable inflow conditions are imposed on each of the two rotors. The fountain dynamics is observed at a frequency that is about two orders of magnitude lower than the blade passing frequency. The dominant characteristic time scale is linked to the flow recirculation path, relating this to system parameters of thrust and ground stand-off height. The flow field is analysed using proper orthogonal decomposition, in which coupled modes are identified. Results from the modal analysis are used to formulate a simple dynamic flow model of the re-ingestion switching cycle.

Martian dust storms in the planetary boundary layer share many qualitative similarities to terrestrial sandstorms. Both of these turbulence-driven, particle-laden boundary layer flows are known to generate electric fields due to the transport of differentially charged particles; this charge separation can be strong enough to lead to dielectric breakdown in the form of sparks or lightning. Using wall-modelled large-eddy simulations supplemented with conservation of equations for the charged particle transport, representative simulations of neutrally stable Martian and terrestrial particle-laden boundary layer flows are compared. The simulations, albeit canonical in nature, provide evidence to support previous observations of the less frequent occurrence of lightning on Mars but a higher occurrence of localised electric discharge events due to the much lower breakdown potential. The rarefied Martian atmosphere impedes charged particle transport, resulting in a weaker electric field than the equivalent terrestrial sandstorm. The lower drag force in the rarefied Martian atmosphere means that the electrostatic force plays a more significant role in the particle transport, which results in a self-regulation of the electric field. The strongest Martian dust storms show evidence of significant breakdown events and these discharge events only occur very close to the ground despite the very large boundary layer on Mars.

It is demonstrated how aqueous droplets with volumes down to the sub-femtolitre range can be manipulated, including the withdrawal of minute samples from the droplets. The underlying principle is that of partial coalescence with a liquid reservoir in an applied electric field. Upon partial coalescence, a droplet merges with a reservoir and reappears with a smaller diameter. The droplets studied here perform a reciprocating motion between two reservoirs during which their volume gets reduced. Manipulation of droplets with diameters down to 400 nm is reported. A similarity relation is derived expressing the ratio of droplet diameters before and after partial coalescence as a function of the ratio between electric and interfacial-tension forces. The presented scheme allows the withdrawal of minute samples from small droplets and could prove helpful in various applications where droplets are used as tiny reaction spaces or when the goal is to tailor the size of individual droplets.

Predicting the laminar to turbulent transition is an important aspect of computational fluid dynamics because of its impact on skin friction. Traditional transition prediction methods such as local stability theory or the parabolized stability equation method do not allow for the consideration of strongly non-parallel boundary layer flows, as in the presence of surface defects (bumps, steps, gaps, etc.). A neural network approach, based on an extensive database of two-dimensional incompressible boundary layer stability studies in the presence of gap-like surface defects, is used. These studies consist of linearized Navier–Stokes calculations and provide information on the effect of surface irregularity geometry and aerodynamic conditions on the transition to turbulence. The physical and geometrical parameters characterizing the defect and the flow are then provided to a neural network whose outputs inform about the effect of a given gap on the transition through the ${\rm \Delta} N$ method (where N represents the amplification of the boundary layer instabilities).

Indoor ventilation is underutilized for the control of exposure to infectious pathogens. Occupancy restrictions during the pandemic showed the acute need to control detailed airflow patterns, particularly in heavily occupied spaces, such as lecture halls or offices, and not just to focus on air changes. Displacement ventilation is increasingly considered a viable energy efficient approach. However, control of airflow patterns from displacement ventilation requires us to understand them first. The challenge in doing so is that, on the one hand, detailed numerical simulations – such as direct numerical simulations (DNSs) – enable the most accurate assessment of the flow, but they are computationally prohibitively costly, thus impractical. On the other hand, large eddy simulations (LES) use parametrizations instead of explicitly capturing small-scale flow processes critical to capturing the inhomogeneous mixing and fluid–boundary interactions. Moreover, their use for generalizable insights requires extensive validation against experiments or already validated gold-standard DNSs. In this study, we start to address this challenge by employing efficient monotonically integrated LES (MILES) to simulate airflows in large-scale geometries and benchmark against relevant gold-standard DNSs. We discuss the validity and limitations of MILES. Via its application to a lecture hall, we showcase its emerging potential as an assessment tool for indoor air mixing heterogeneity.

This work explores the relationship between wind speed and time-dependent structural motion response as a means of leveraging the rich information visible in flow–structure interactions for anemometry. We build on recent work by Cardona, Bouman and Dabiri (Flow, vol. 1, 2021, E4), which presented an approach using mean structural bending. Here, we present the amplitude of the dynamic structural sway as an alternative signal that can be used when mean bending is small or inconvenient to measure. A force balance relating the instantaneous loading and instantaneous deflection yields a relationship between the incident wind speed and the amplitude of structural sway. This physical model is applied to two field datasets comprising 13 trees of 4 different species exposed to ambient wind conditions. Model generalization to the diverse test structures is achieved through normalization with respect to a reference condition. The model agrees well with experimental measurements of the local wind speed, suggesting that tree sway amplitude can be used as an indirect measurement of mean wind speed, and is applicable to a broad variety of diverse trees.