Container motion along a planar circular trajectory at a constant angular velocity, i.e. orbital shaking, is of interest in several industrial applications, e.g. for fermentation processes or in cultivation of stem cells, where good mixing and efficient gas exchange are the main targets. Under these external forcing conditions, the free surface typically exhibits a primary steady-state motion through a single-crest dynamics, whose wave amplitude, as a function of the external forcing parameters, shows a Duffing-like behaviour. However, previous experiments in laboratory-scale cylindrical containers have revealed that, owing to the excitation of super-harmonics, diverse dynamics are observable in certain driving-frequency ranges. Among these super-harmonics, the double-crest dynamics is particularly relevant, as it displays a notably large amplitude response, which is strongly favoured by the spatial structure of the external forcing. In the inviscid limit and with regards to circular cylindrical containers, we formalize here a weakly nonlinear analysis via a multiple-time-scale method of the full hydrodynamic sloshing system, leading to an amplitude equation suitable for describing such a double-crest swirling motion. The weakly nonlinear prediction is shown to be in fairly good agreement with previous experiments described in the literature. Lastly, we discuss how an analogous amplitude equation can be derived by solving asymptotically for the first super-harmonic of the forced Helmholtz–Duffing equation with small nonlinearities.

Shallow mixing layers (SMLs) behind a splitter plate were studied in a tilted rectangular open-channel flume for a range of flow depths and the initial shear parameter ${\lambda = (U_{2}-U_{1})/(U_{2}+U_{1})}$, where $U_1$ and $U_2$ are streamwise velocities of the slow and fast streams, respectively. The main focus of the study is on (i) key parameters controlling the time-averaged SMLs; and (ii) the emergence and spatial development of Kelvin–Helmholtz coherent structures (KHCSs) and large- and very-large-scale motions (LSMs and VLSMs) and associated turbulence statistics. The time-averaged flow features of the SMLs are mostly controlled by bed-friction length scale $h/c_f$ and shear parameter $\lambda$ as well as by time-averaged spanwise velocities $V$ and momentum fluxes $UV$, where $h$ and $c_f$ are flow depth and bed-friction coefficient, respectively. For all studied cases, the effect of shear layer turbulence on the SML growth is comparatively weak, as the fluxes $UV$ dominate over the spanwise turbulent fluxes. Initially, the emergence of KHCSs and their length scales largely depend on $\lambda$. The KHCSs cannot form if ${\lambda \lessapprox 0.3}$ and the turbulence behind the splitter plate resembles that of free mixing layers. Further downstream, shear layer turbulence becomes dependent on the bed-friction number $S = c_f \delta _v /(4 h \lambda )$, where $\delta _v$ is vorticity thickness. When $S \gtrapprox 0.01$, the KHCSs are longitudinally stretched and the scaled transverse turbulent fluxes decrease with increasing $S$. The presence and streamwise development of LSMs/VLSMs away from the splitter plate depends on the $\lambda$-value, particularly when $\lambda > 0.3$, resembling LSMs/VLSMs in conventional open-channel flows when $\lambda$ is small.

A turbulent drag-reduction method employing synthetic jet sheets in a turbulent channel flow is investigated by direct numerical simulations. The jet sheets are wall-parallel and produced by periodic blowing and suction from pairs of thin slots aligned with the main streamwise flow. By varying the slot height and the jet-sheet angle with respect to the spanwise direction, drag-reduction margins between $10\,\%$ and $30\,\%$ are obtained for jet-sheet angles between $45 ^{\circ }$ and $75 ^{\circ }$, while a drag increase of almost 100 % is computed when the jet sheets are spanwise-oriented. When global skin-friction drag reduction occurs, the wall-shear stress near the jet-sheet exits increases during suction and decreases during blowing, while the velocity fluctuations weaken during suction and intensify during blowing. The global drag-reduction effect is produced by a finite counter flow induced by the nonlinear interaction between the jet-sheet flow and the main flow, although the turbulent intensity and Reynolds shear stresses increase. The power spent to generate the jet sheets is computed by modelling numerically the actuator underneath the channel flow as a piston oscillating sinusoidally along the spanwise direction in a round-shaped cavity from which the fluid is released into the channel through the cavity exits. A power balance leads to the computation of the efficiency of the actuator system, quantifying the portion of the piston power that is lost as internal power fluxes and heat transfer through the cavity walls. For the tested configurations, the power consumed by the piston to generate the jet sheets is larger than the power saved thanks to the drag reduction.

We study a gravity-driven wavy liquid film falling down the inner surface of a narrow cylindrical tube in the presence of an active core gas flow. We employ the model of Dietze and Ruyer-Quil (J. Fluid Mech., vol. 762, 2015, pp. 68–109) to investigate the role of surface waves in the occlusion of the tube. We consider four real working liquids and reproduce several experiments from the literature, focusing on conditions where the Bond number is greater or equal to unity. We prove that occlusion is triggered by spatially growing surface waves beyond the limit of saturated travelling-wave solutions, and delimit three possible regimes for a naturally evolving wavy film: (i) certain occlusion, when the liquid Reynolds number is greater than the limit of the spatially most amplified travelling waves. Occlusion is caused by surface waves emerging from linear wave selection (scenario I); (ii) conditional occlusion, when the most amplified waves possess travelling states but longer waves do not. Occlusion is triggered by secondary instability, generating long waves through nonlinear coarsening dynamics (scenario II); and (iii) impossible occlusion, when travelling waves always exist, no matter how great their wavelength. We show that certain occlusion is delayed by gravity and precipitated by a counter-current gas flow, axial viscous diffusion (high-viscosity liquids) and inertia (low-viscosity liquids). The latter two effects are also found to determine whether the occlusion mechanism is dictated by loss of travelling-wave solutions or absolute instability. Finally, we show that occlusion can be prevented through coherent inlet forcing. As a side benefit, we introduce an augmented version of our model based on a localized additional force term that allows representing stable travelling liquid pseudo-plugs.

We study propulsion of rectangular and rhombic lattices of flapping plates at $O$(10–100) Reynolds numbers in incompressible flow. The fluid dynamics often converges to time periodic in 5–30 flapping periods, facilitating accurate computations of time-averaged thrust force and input power. We classify the propulsive performances of the lattices and the periodicities of the flows with respect to flapping amplitude and frequency, horizontal and vertical spacings between plates, and oncoming flow velocity. Non-periodic states are most common at small streamwise spacing, large lateral spacing and large Reynolds number. Lattices that are closely spaced in the streamwise direction produce intense vortex dipoles between adjacent plates. The flows transition sharply from drag- to thrust-producing as these dipoles switch from upstream to downstream orientations at critical flow speeds. Near these transitions the flows pass through a variety of periodic and non-periodic states, with and without up–down symmetry, and multiple stable self-propelled speeds can occur. As the streamwise spacing increases (and with large lateral spacing), the plates may shed vortex streets that impinge on downstream neighbours. The most efficient streamwise spacing increases with flapping amplitude. With small lateral spacing, the rectangular lattices have Poiseuille-type flows that yield net drag, while the rhombic lattices may shed vortices and generate net thrust, sometimes with relatively high efficiency. As lateral spacing increases to one plate length and beyond, the rectangular lattices begin to shed vortices and generate thrust, eventually with efficiencies similar to the rhombic lattices', as the two types of flows converge. At $Re = 70$, the lattices’ maximum Froude efficiencies are approximately twice those of an isolated plate (only considering nearly periodic lattice flows). As $Re$ decreases, the lattices’ efficiency advantage increases further.

With particle image velocimetry (PIV), cross-correlation and optical flow methods have been mainly adopted to obtain the velocity field from particle images. In this study, a novel artificial intelligence (AI) architecture is proposed to predict an accurate flow field and drone rotor thrust from high-resolution particle images. As the ground truth, the flow fields past a high-speed drone rotor obtained from a fast Fourier transform-based cross-correlation algorithm were used along with the thrusts measured by a load cell. Two deep-learning models were developed, and for instantaneous flow-field prediction, a generative adversarial network (GAN) was employed for the first time. It is a spectral-norm-based residual conditional GAN translator that provides a stable adversarial training and high-quality flow generation. Its prediction accuracy is 97.21 % (coefficient of determination, or R2). Subsequently, a deep convolutional neural network was trained to predict the instantaneous rotor thrust from the flow field, and the model is the first AI architecture to predict the thrust. Based on an input of the generated flow field, the network had an R2 accuracy of 94.57 %. To understand the prediction pathways, the internal part of the model was investigated using a class activation map. The results showed that the model recognized the area receiving kinetic energy from the rotor and successfully made a prediction. The proposed architecture is accurate and nearly 600 times faster than the cross-correlation PIV method for real-world complex turbulent flows. In this study, the rotor thrust was calculated directly from the flow field using deep learning for the first time.

In this work we study experimentally and numerically the stability of hydrodynamic focusing to produce microemulsions. The jetting regime was produced experimentally for the lowest outer viscosity, while microdripping was obtained for the highest outer viscosity. The liquid ejection for small capillary numbers stabilizes as the distance between the feeding capillary and the focusing orifice decreases. The comparison between confined selective withdrawal and stretched flow focusing for the largest outer viscosity shows that confined selective withdrawal significantly enhances the stability of the microdripping mode, which entails a significant reduction of the minimum value of the droplet diameter. When surfactants are dissolved in the inner liquid at sufficiently large concentrations, we observe a significant decrease in both the minimum flow rate leading to tip streaming and the droplet diameter. The surfactant monolayer stabilizes the meniscus and promotes the transition from microdripping to jetting. The global stability analysis shows that jetting via tip streaming becomes unstable due to the growth of an oscillatory perturbation. The unstable perturbation affects the tapering meniscus for the lowest outer viscosity, which explains why the meniscus oscillates in the experiments. The critical flow rate ratio is accurately predicted by the global stability analysis in most of the experiments with the lowest outer viscosity. For the highest outer viscosity, the global stability analysis correctly predicts the microdripping mode and allows one to calculate the droplet emission frequency in that mode.

Gravity-driven size segregation is important in mountain streams where a wide range of grain sizes are transported as bedload. More particularly, vertical size segregation is a multi-scale process that originates in interactions at the scale of particles with important morphological consequences for the river bed. To address this issue, a volume-averaged multi-phase flow model for immersed bi-disperse granular flows was developed based on an interparticle segregation force (Guillard et al., J. Fluid Mech., vol. 807, 2016, R1) and a granular Stokesian drag force (Tripathi & Khakhar, J. Fluid Mech., vol. 717, 2013, pp. 643–669). An advection–diffusion model was derived from this model yielding parametrisations for the advection and diffusion coefficients based on the interparticle interactions. This approach makes it possible to bridge the gap between grain-scale physics and continuum modelling. Both models were successfully tested against existing discrete element model (DEM) simulations of size segregation in bedload transport (Chassagne et al., J. Fluid Mech., vol. 895, 2020, A30). Through a detailed investigation of the granular forces, it is demonstrated that the observed scaling of the advection and diffusion coefficients with the inertial number can be explained by the granular drag force dependency on the viscosity. The drag coefficient is shown to be linearly dependent on the small particle concentration. A new scaling relationship for the segregation force including the small particle concentration and the pressure is proposed. Lastly, adding a size-ratio dependency in the segregation force fairly reproduces the DEM results for a large range of small particle concentrations and size ratios.

We investigate experimentally the coalescence cascade process for a confined swarm of deformable bubbles immersed in a bidimensional vertical cell filled with water. For different gas volume fractions, air bubbles of size $D_0$ larger than the cell thickness are injected at the bottom of the cell. The bubbles swarms transformation is explored using high-speed visualizations. The time evolution of each bubble in the swarm is determined using a specifically developed algorithm, enabling bubble tracking and coalescence detection. We determine the evolution of the bubble size distribution downstream from the injection point, and show that the stages of the coalescence cascade are characterized by the diameter, $D_{V90}$, representative of the largest bubbles. The collision frequency of pairs of bubbles of sizes $D_k$ and $D_{k'}$, $h(D_k, D_{k'})$, and their coalescence efficiency, $\lambda$, are obtained from the experiments. The efficiency is nearly constant, independently of the bubble sizes and of the gas volume fraction. Concerning collision frequency, our results reveal the existence of two different coalescence regimes depending on the capability of the bubbles to deform. Models describing $h(D_k, D_{k'})$ for both regimes are provided. They take into account the specific response of the bubble pair, which depends on the reduced diameter $D_p = 2 D_k D_{k'} / (D_k + D_{k'})$, to the global swarm-induced agitation governed by $D_{V90}$ and the gas volume fraction. In the first regime, occurring for smaller $D_p$, bubbles are brought together by agitation and rapidly coalesce, while for sufficiently large $D_p$, both bubbles are able to deform and spend more time adapting mutually their shapes before coalescing.

Dense, small particles suspended in turbulent smooth-wall flow are known to migrate towards the wall. It is, however, not clear if the particle migration continues in a rough-wall flow and what the responsible mechanism is, especially with changing roughness parameters. Here, we address this using direct numerical simulation of a turbulent pipe flow of a fixed friction Reynolds numbers and changing the roughness size as well as the Stokes number of the particles. The transport and deposition mechanisms of particles are segregated into three different regimes dictated by the Stokes number. Particles with small Stokes number follow the carrier fluid and are affected by the turbulent structures of the rough wall. Flow separation in the wake of the roughness and stagnant flow in the trough of the roughness causes these particles to be trapped in the roughness canopy. Particles with very large Stokes number, on the other hand, are attracted to the wall due to turbophoresis and collide with the rough wall where the frequency of wall collision increases with increasing Stokes number. These ballistic particles are unaffected by the turbulent fluctuations of the flow and their trajectory is determined by the roughness topography. At intermediate Stokes numbers, the transport of the particles is influenced by both the wall collisions and also the turbulent flow. Particles in this range of Stokes number occasionally collide with the wall and are entrained by the turbulent flow. In this regime, the particles may have a mean streamwise velocity that is larger than the bulk flow rate of the fluid. Finally, we observe that bulk particle velocity scale better with a time scale based on the roughness elements rather than the usual viscous time scale.