In this work we propose and demonstrate a Fresnel-lens-inspired method to focus multiple laser-induced shock waves through time-delay superposition at arbitrary locations. While the principle works for any geometry, we demonstrate that this method already achieves focusing with two pairs of photoacoustic shock wave emitters located on a line centred around the acoustic axis ($z$) in a quasi-two-dimensional liquid geometry. Each emitter pair is created by focusing one laser pulse simultaneously at two spots with a spatial light modulator at $z=0\ \mathrm {\mu }$m with $y=\pm 145\ \mathrm {\mu }$m and $y=\pm 75\ \mathrm {\mu }$m. The delays between the emitters necessary to vary the location of the focus from $z\approx 0$ to ${\sim }206\ \mathrm {\mu }$m are $35$ and $0$ ns, respectively. We find that the location of constructive superposition is significantly closer to the origin than what would be expected for linear waves in homogeneous media. This is confirmed with simulations using an Euler solver that shows the importance of finite-amplitude effects. The simulated dynamics are in reasonable agreement with our measurements. Finally, pressure gains at various locations along the acoustic axis are tested with the response of gaseous microbubbles acting as pressure probes. The measurements agree with calculated pressure ratios at different positions.

This article presents a computational approach for determining the optimal slip velocities on any given shape of an axisymmetric micro-swimmer suspended in a viscous fluid. The objective is to minimize the power loss to maintain a target swimming speed, or equivalently to maximize the efficiency of the micro-swimmer. Owing to the linearity of the Stokes equations governing the fluid motion, we show that this PDE-constrained optimization problem reduces to a simpler quadratic optimization problem, whose solution is found using a high-order accurate boundary integral method. We consider various families of shapes parameterized by the reduced volume and compute their swimming efficiency. Among those, prolate spheroids were found to be the most efficient micro-swimmer shapes for a given reduced volume. We propose a simple shape-based scalar metric that can determine whether the optimal slip on a given shape makes it a pusher, a puller or a neutral swimmer.

Centrifugal instability of the boundary layer is known to induce spiral vortices over a rotating slender cone that is facing an axial inflow. This paper shows how a deviation from the symmetry of such axial inflow affects the boundary layer instability over a rotating slender cone with half-angle $\psi =15^\circ$. The spiral vortices are experimentally detected using their thermal footprint on the cone surface for both axial and non-axial inflow conditions. In axial inflow, the onset and growth of the spiral vortices are governed by the local rotational speed ratio $S$ and Reynolds number $Re_l$ in agreement with the literature. During their growth, the spiral vortices significantly affect the mean velocity field as they entrain and bring high-momentum flow closer to the wall. It is found that the centrifugal instability induces these spiral vortices in non-axial inflow as well; however, the asymmetry of the non-axial inflow inhibits the initial growth of the spiral vortices, and they appear at higher local rotational speed ratio and Reynolds number, where the azimuthal variations in the instability characteristics (azimuthal number $n$ and vortex angle $\phi$) are low.

Numerous field observations of tsunami-induced eddies in ports and harbours have been reported for recent tsunami events. We examine the evolution of a turbulent shallow-water monopolar vortex generated by a long wave through a series of large-scale experiments in a rectangular wave basin. A leading-elevation asymmetric wave is guided through a narrow channel to form a flow separation region on the lee side of a straight vertical breakwater, which coupled with the transient flow leads to the formation of a monopolar turbulent coherent structure (TCS). The vortex flow after detachment from the trailing jet is fully turbulent ($Re_h \sim O(10^{4}\text {--}10^{5}$)) for the remainder of the experimental duration. The free surface velocity field was extracted through particle tracking velocimetry over several experimental trials. The first-order model proposed by Seol & Jirka (J. Fluid Mech., vol. 665, 2010, pp. 274–299) to predict the decay and spatial growth of shallow-water vortices fits the experimental data well. Bottom friction is predicted to induce a $t^{-1}$ azimuthal velocity decay and turbulent viscous diffusion results in a $\sqrt {t}$ bulk vortex radial growth, where $t$ represents time. The azimuthal velocity, vorticity and free surface elevation profiles are well described through an idealised geophysical vortex. Kinematic free surface boundary conditions predict weak upwelling in the TCS-centre, followed by a zone of downwelling in a recirculation pattern along the water column. The vertical confinement of the flow is quantified through the ratio of kinetic energy contained in the secondary and primary surface velocity fields and a transition point towards a quasi-two-dimensional flow is identified.

Starting from an alternative decomposition of the turbulent field, a multi-dimensional statistical formalism for the description and understanding of turbulence in free-shear flows is proposed and applied to the symmetries of planar temporal jets. The theoretical framework is based on the exact equation for the second-order moment of the two-point velocity increment and allows us to trace, for the first time, the spatially evolving cascade processes at the basis of turbulence mixing and entrainment. Fascinating reverse energy cascade mechanisms are found to be responsible for the generation of long and wide structures in the interface region. Analogously to two-dimensional turbulence, the energy provided by these spatially ascending reverse cascades is found to be eventually dissipated by viscosity at large scales through friction shearing processes involving a thin cross-flow layer of these large-scale structures. Finally, the external non-turbulent region of the jet is also found to be active from an energetic point of view. It is found that pressure-mediated non-local phenomena of displacement of almost quiescent fluid give rise to non-turbulent fluctuations that in time, through transitional mechanisms, would contribute to the growth of the turbulent jet. Overall, the unexpected paths taken by the scale-energy flux in the combined physical/scale space, which are a substantial novelty with respect to known descriptions of turbulent mixing and entrainment, may have major repercussions on our theoretical understanding and modelling, as anticipated here by reduced equations capable of giving a simple scale-dependent description of the rich dynamics of the flow.

A relation between the ensemble average and the nearest particle statistics is derived. The relation accounts for interactions among all the particles, not only the nearest one, and can be used to study long-range particle interactions without the difficulty of a divergent integral. As an example, this relation is applied to calculate the particle sedimentation velocity to the first order of the particle volume fraction. Using the relation, an important particle–fluid–particle stress is introduced for general multiphase flows.

Flow structure inside and around a rectangular array of emerged cylinders located adjacent to the sidewall of an open channel is investigated using eddy-resolving numerical simulations. This configuration is particularly relevant for understanding how patches of aquatic vegetation developing near a river's banks affect flow and transport. The array of width W = 1.6D and length L = 33D–35D (D is the flow depth) contains rigid cylinders. Simulations with incoming, fully developed turbulent flow (channel Reynolds number, ReD = 12 500) are conducted with different values of the solid volume fraction (0.02 < ϕ < 0.1), frontal area per unit volume of the array, a (0.41 < aW < 1.63), diameter of the solid cylinders (d = 0.1D and 0.2D) and cylinder shape (circular and square). The paper focuses on investigating flow and turbulence structure inside and downstream of the array and the role played by coherent structures (e.g. vortices forming in the horizontal shear layer at the lateral face of the array, vortices shed in the wake of the solid cylinders) in sediment entrainment and transport. Simulation results show that significant upwelling and downwelling motions are generated near the front and lateral faces of the array and inside the shear layer. Moreover, some distance from the front face of the array, the shear layer vortices generate successive regions of high and low streamwise velocity inside the patch. The frequency associated with these wave-like oscillations is approximately half of the frequency associated with the advection of vortices in the downstream part of the shear layer. These streamwise velocity oscillations induce spanwise patches of high and low bed friction velocity that extend over the regions occupied by the array and the horizontal shear layer. For sufficiently high array resistance, horseshoe vortices form around the upstream corner of the array and provide an additional mechanism for sediment entrainment. For aW > 0.5, mean-flow recirculation bubbles form behind the array. For constant aW, the total size of the region containing recirculation bubbles decreases with increasing d/D. Simulations results are used to quantify the effect of varying ϕ, aW, d/D and the cylinders’ shape on the streamwise decay of the mean streamwise velocity inside the array, turbulent kinetic energy distribution, mean streamwise drag forces acting on the cylinders and mean streamwise drag coefficients.

Miniature shock tubes are finding growing importance in a variety of interdisciplinary applications. There is a lack of experimental data to validate the existing shock tube flow models that explain the shockwave attenuation in pressure-driven miniature shock tubes. This paper gives insights into the shock formation and shock propagation phenomena in miniature shock tubes of 2, 6 and 10 mm square cross-sections operated at diaphragm rupture pressure ratios in the range 5–25 and driven section initially at ambient conditions. Pressure measurements and visualization studies are carried out in a new miniature table-top shock tube system using nitrogen and helium as driver gases. The experimental findings are validated using a shock tube model explained in terms of two regions: (i) the shock formation region, dominated by wave interactions due to the diaphragm's finite rupture time; and (ii) the shock propagation region, where the shockwave attenuation occurs mainly due to wall effects and boundary layer growth. Correlations to predict the variation of shock Mach number in the shock formation region and shock propagation region work well for the present findings and experimental data reported in the literature. Similar flow features are observed in the shock tubes at the same dimensionless time stamps. The formation of the planar shock front scales proportionally with the diameter of the shock tube. The peak Mach number attained by the shockwave is higher as the shock tube diameter increases.

The canopy-related terms in the transport equations for momentum, Reynolds stresses, turbulent kinetic energy and its dissipation rate were described by a perturbative expansion around a velocity scale based on the mean total kinetic energy. The quality of the series and the relative magnitude of the first orders were analysed through comparison with the results of large-eddy simulation of three canopy flows representative of real-life applications. The flows in question were those over a horizontally homogeneous forest, a sequence of forest stands and clearings, and a forested hill. The analysis gave both the highest order required for an accurate evaluation of the canopy effects and a mathematical formulation for the canopy-related terms in a Reynolds-averaged Navier–Stokes formulation. This offers a sounder basis and assured consistency for the turbulence modelling of canopy flows between Reynolds-averaged Navier–Stokes and large-eddy simulation frameworks.

Indirect noise generated by the acceleration of synthetic compositional and entropic perturbations through non-isentropic nozzles is measured experimentally. A physics-based analytical low-order model to evaluate the indirect noise generated by non-isentropic compact nozzles is developed and validated with experimental measurements. A one-dimensional model for describing the waves generated by the addition of mass, momentum, energy and species to a steady flow in an entropy and composition wave generator is presented. The transfer functions describing the multiple reflections of acoustic waves in an enclosed environment are derived. This analytical framework allows unambiguous identification and isolation of the experimental direct and indirect noise generated by the injection of helium, methane, argon or carbon dioxide into a flow duct. Experimental data show that entropic and compositional noise make a significant contribution to the overall pressure traces acquired in the entropy generator. Moreover, it is demonstrated that the isentropic modelling assumption is inadequate to capture the experimental behaviour, while the analytical model for non-isentropic nozzles successfully describes the direct and indirect noise transfer functions. The disregard for the compositional contribution and the unjustified use of the isentropic assumption can provide significantly inaccurate noise predictions. This work shows that compositional noise, as well as non-isentropicity in the system, should be considered in future thermoacoustic and combustion noise models.

Single fuel droplet vaporization, with special attention to the case of ethanol, is considered in this study. First, we showed, using an order-of-magnitude analysis and detailed unsteady simulations, that the commonly used quasi-steady assumption is not suitable for an accurate description of the liquid phase during the evaporation process. Second, we demonstrated that an increase in the relative importance of radiation explains the departures of the evaporation rate from the $d^{2}$-law observed experimentally when sufficiently large droplets – initial radius above 0.25 mm – evaporated in ambient temperatures around 800 K. The multicomponent formulation included here, in which the physical properties of both liquid and gas phases depend on the concentration of the different species involved, was validated by comparing our numerical results with experimental data of ethanol, $n$-heptane, ethanol–water and $n$-dodecane–$n$-hexadecane droplets available in the literature. Because of its technological relevance, we dedicated special attention to the effect of the droplet water content and ambient humidity on the evaporation time of ethanol droplets. Our computations showed higher vaporization rates with increasing ambient humidity as a consequence of the extra heat generated during the condensation of moisture on the droplet surface.

In this work, the classic problem of the aeroacoustic instability occurring in deep cavities subject to a low-Mach grazing flow is revisited experimentally and theoretically. This instability is caused by the constructive feedback between the acoustic modes of the cavity and the turbulent shear layer that forms at its opening. Systematic experiments are performed in order to construct a new theoretical model, which describes the aeroacoustic system as two linearly stable oscillators, with linear reactive coupling, nonlinear damping and nonlinear resistive coupling. This model constitutes the basis for a linear stability analysis, and for the prediction of limit cycle amplitudes by using a describing function approach and by searching the fixed points of amplitude equations. Moreover, it is shown that only supercritical Hopf bifurcations are found in this aeroacoustic system, and that, in contrast with many flow-induced vibration problems, frequency lock-in does not occur. In the last part of the paper, the intermittency observed in the vicinity of the supercritical Hopf bifurcations is successfully modelled by adding a coloured multiplicative noise to the grazing flow velocity in order to account for the effect of turbulence. The necessary conditions favouring intermittently stable or intermittently unstable intervals in such systems are identified using stochastic differential equations governing the aeroacoustic oscillations and Fokker–Planck equations ruling the probability density function of the acoustic envelope. This work is relevant for many musical and industrial configurations exhibiting this type of aeroacoustic instability, as well as for thermoacoustic instabilities in turbulent combustors for aeronautic and power generation applications.

During the last fifteen years there has been a paradigm shift in the continuum modelling of granular materials; most notably with the development of rheological models, such as the $\mu (I)$-rheology (where $\mu$ is the friction and I is the inertial number), but also with significant advances in theories for particle segregation. This paper details theoretical and numerical frameworks (based on OpenFOAM) which unify these currently disconnected endeavours. Coupling the segregation with the flow, and vice versa, is not only vital for a complete theory of granular materials, but is also beneficial for developing numerical methods to handle evolving free surfaces. This general approach is based on the partially regularized incompressible $\mu (I)$-rheology, which is coupled to the gravity-driven segregation theory of Gray & Ancey (J. Fluid Mech., vol. 678, 2011, pp. 353–588). These advection–diffusion–segregation equations describe the evolving concentrations of the constituents, which then couple back to the variable viscosity in the incompressible Navier–Stokes equations. A novel feature of this approach is that any number of differently sized phases may be included, which may have disparate frictional properties. Further inclusion of an excess air phase, which segregates away from the granular material, then allows the complex evolution of the free surface to be captured simultaneously. Three primary coupling mechanisms are identified: (i) advection of the particle concentrations by the bulk velocity, (ii) feedback of the particle-size and/or frictional properties on the bulk flow field and (iii) influence of the shear rate, pressure, gravity, particle size and particle-size ratio on the locally evolving segregation and diffusion rates. The numerical method is extensively tested in one-way coupled computations, before the fully coupled model is compared with the discrete element method simulations of Tripathi & Khakhar (Phys. Fluids, vol. 23, 2011, 113302) and used to compute the petal-like segregation pattern that spontaneously develops in a square rotating drum.

The unsteady behaviour of a rarefied gas caused by a sudden change of the angular velocity of a sphere, placed in an otherwise quiescent gas, is investigated based on the linearized Bhatnagar–Gross–Krook model of the Boltzmann equation and the diffuse reflection boundary condition. The initial and boundary value problem is solved numerically by the method of characteristics, which is capable of tracking the discontinuity of the velocity distribution function moving in the phase space. The transient behaviour of the macroscopic quantities, such as the circumferential flow velocity and shear stress as well as the heat flow around the sphere, is clarified for a wide range of the Knudsen number. Furthermore, the long-time behaviour of the macroscopic quantities is elucidated, that is, they approach terminal values with a rate $t^{-3/2}$ for $t\gg 1$, with $t$ being a time variable. The analytical expression for the free molecular gas as well as for the slip flow is obtained. It is found that the circumferential heat flow reverses its direction as time proceeds when the Knudsen number is finite. More precisely, the direction is the same as that of the circumferential velocity of the sphere in the initial stage and opposite in the final stage, being reversed at some point of time depending on the distance from the sphere. This makes a clear contrast with the case of a free molecular gas, for which the heat flow is always in the direction of the sphere rotation in finite time and vanishes in the long-time limit.

A new lattice Boltzmann model for multicomponent ideal gas mixtures is presented. The model development consists of two parts. First, a new kinetic model for Stefan–Maxwell diffusion amongst the species is proposed and realized as a lattice Boltzmann equation on the standard discrete velocity set. Second, a compressible lattice Boltzmann model for the momentum and energy of the mixture is established. Both parts are consistently coupled through mixture composition, momentum, pressure, energy and enthalpy whereby a passive scalar advection–diffusion coupling is obviated, unlike in previous approaches. The proposed model is realized on the standard three-dimensional lattices and is validated with a set of benchmarks highlighting various physical aspects of compressible mixtures. Stefan–Maxwell diffusion is tested against experiment and theory of uphill diffusion of argon and methane in a ternary mixture with hydrogen. The speed of sound is measured in various binary and ternary compositions. We further validate the Stefan–Maxwell diffusion coupling with hydrodynamics by simulating diffusion in opposed jets and the three-dimensional Kelvin–Helmholtz instability of shear layers in a two-component mixture. Apart from the multicomponent compressible mixture, the proposed lattice Boltzmann model also provides an extension of the lattice Boltzmann equation to the compressible flow regime on the standard three-dimensional lattice.

We present a new data reconstruction method with supervised machine learning techniques inspired by super resolution and inbetweening to recover high-resolution turbulent flows from grossly coarse flow data in space and time. For the present machine-learning-based data reconstruction, we use the downsampled skip-connection/multiscale model based on a convolutional neural network, incorporating the multiscale nature of fluid flows into its network structure. As an initial example, the model is applied to the two-dimensional cylinder wake at $Re_D = 100$. The reconstructed flow fields by the present method show great agreement with the reference data obtained by direct numerical simulation. Next, we apply the current model to a two-dimensional decaying homogeneous isotropic turbulence. The machine-learned model is able to track the decaying evolution from spatial and temporal coarse input data. The proposed concept is further applied to a complex turbulent channel flow over a three-dimensional domain at $Re_{\tau }=180$. The present model reconstructs high-resolved turbulent flows from very coarse input data in space, and also reproduces the temporal evolution for appropriately chosen time interval. The dependence on the number of training snapshots and duration between the first and last frames based on a temporal two-point correlation coefficient are also assessed to reveal the capability and robustness of spatio-temporal super resolution reconstruction. These results suggest that the present method can perform a range of flow reconstructions in support of computational and experimental efforts.

Several studies concerning the turbulent pipe flow of generalized Newtonian (GN) fluids may be found in the literature, but not for channel flow, although that has been extensively studied for other types of non-Newtonian fluids, such as those with viscoelastic effects. Direct numerical simulations corresponding to statistically converged turbulent channel flow of GN fluids at a low frictional Reynolds number have been performed. The shear-dependent viscosity is introduced through the Carreau fluid model, and results corresponding to the Newtonian fluid case are compared to those of moderate shear-thickening and shear-thinning fluid behaviour. The different statistics studied reveal that shear-dependent fluid rheology appears mainly to affect the flow within the inner layer region and with shear-thinning behaviour; suppressing near-wall structures such as quasi-streamwise vortices and low-speed streaks, inhibiting turbulence generating events and leading to different drag reduction features. These include: enhancement of streamwise turbulence intensity and suppression of the other cross-sectional intensities, decrease of the Reynolds shear stress (leading to a lessening in turbulent production), decrease in energy redistribution between individual components of the Reynolds stress tensor through the velocity–pressure gradient term and overall increase in turbulence anisotropy at both small and large scales. In particular, it is noted that at the channel centre ‘rod-like’ turbulence states, a known low-Reynolds-number behaviour, are more clearly seen with shear-thinning fluid rheology.

Saturated film boiling over an elliptical heater is investigated in the mixed regime considering both aiding and orthogonal liquid flow configurations relative to gravity. A computational framework developed for phase change problems on unstructured grids based on a coupled level set and volume of fluid interface capturing method is used to characterize interface evolution and vapour wake dynamics alongside quantifying heat transfer at low values of the Froude number (Fr). The influence of hydrodynamic and thermal conditions along with cross-flow direction for a fixed heater geometry manifests in the form of varied wake profiles with the quasi-steady nature of film boiling lost as Fr increases. Additionally, while the heater aspect ratio affects the rate of vapour infusion into the wake, the heater orientation significantly affects the film boiling behaviour. With horizontal cross-flow, higher angles of incidence entail a lower influence of flow inertia while augmenting buoyancy-driven vapour removal leading to enhanced heat transfer compared to aiding flow under certain cases, and adding a further dimension to the interplay between buoyancy and inertia. Similarly an anomalous impairment of heat transfer with an increase in cross-flow velocity arises from a competing influence of buoyancy and drag as an artefact of heater and cross-flow configurations. The mutual coupling of liquid and vapour wakes is also discussed in detail under such conditions. Finally, a shape factor $(\psi )$ is proposed to comprehensively predict the heat transfer in conjunction with correlations for a circular heater, and determined based on the effect of the elliptical geometry in the mixed regime.

The influence of miscibility and liquid wettability during droplet impact onto thin wall films is investigated experimentally. Despite similar liquid properties and impact conditions, differences in the splashing limit, in the crown extension and in the duration of the ascending phase are observed. These differences are related to the interfacial tension of the droplet/wall-film liquid pairs, which is linked to their miscibility and wettability. More precisely, by calculating the crown surface energy, we show that the energy stored in the interface between droplet and wall film (if any) is not negligible and leads to smaller crown extensions and tendentially the need for more kinetic energy to initiate splashing. Similarly, by calculating a modified capillary time taking into account all surface and interfacial tensions, we show that the interfacial tension acts as a non-negligible recoiling force, which reduces the duration of the ascending phase. The dynamics of this ascending phase is well captured for different wall-film thicknesses if accounting for the variations of the liquid masses in movement. Overall, droplet/wall-film interactions can be seen as inertio-capillary systems where the interfacial tension between droplet and wall film plays a significant role in the storage of energy and in the crown kinetics during the impact process. In addition, this analysis highlights that viscous losses have already a significant effect during the crown extension phase, by dissipating almost half of the initial energies for droplet impact onto thin wall films, and most likely by influencing the capillary time scale through damping.