We develop a model for the interaction of a fluid flowing above an otherwise static particle bed, with generally the particles being entrained or detrained into the fluid from the upper surface of the particle bed, and thereby forming a fully two phase fluidized cloud above the particle bed. The flow in this large-scale fluidized region is treated as a two-phase flow, whilst the key processes of entrainment and detrainment from the particle bed are treated by examining the local dynamical force balances on the particles in a thin transition layer at the interface between the fully fluidized region and the static particle bed. This detailed consideration leads to the formation of an additional macroscopic boundary condition at this interface, which closes the two-phase flow problem in the bulk fluidized region above. We then introduce an elementary model of the well-known helicopter brownout problem, and use the theory developed in the first part of the paper to fully analyse this model, both analytically and numerically.

A hydrodynamic theory of premixed flame propagation within closed vessels is developed assuming the flame is much thinner than all other fluid dynamic lengths. In this limit, the flame is confined to a surface separating the unburned mixture from burned combustion products, and propagates at a speed determined from the analysis of its internal structure. Unlike freely propagating flames that propagate under nearly isobaric conditions, combustion in a closed vessel results in continuous increases in pressure, burning rate and flame temperature, and a progressive decrease in flame thickness. The flame speed is shown to depend on the voluminal stretch rate, which measures the deformation of a volume element of the flame zone, and on the rate of pressure rise. Both effects are modulated by pressure-dependent Markstein numbers that depend on heat release and mixture properties while capturing the effects of temperature-dependent transport and stoichiometry. The model applies to flames of arbitrary shape propagating in general flows, laminar or turbulent, within vessels of general configurations. The main limitation of hydrodynamic flame theories is the assumption that variations inside the flame zone due to chemistry or turbulence, which could potentially alter its internal structure, are physically unresolved. Nonetheless, the theory, deduced from physical first principles, identifies the various mechanisms involved in the combustion process as demonstrated in detailed discussions of planar flames propagating in rectangular channels and spherically expanding flames in spherical vessels. It also enables the construction of instructive models to numerically simulate the evolution of multi-dimensional and corrugated flames under confinement.

We study liquid plugs in the pulmonary airways based on the two-phase axisymmetric weighted residual integral boundary-layer model of Dietze et al. (J. Fluid Mech., vol. 894, 2020, A17), which was originally developed to study liquid films coating the inner surface of a cylindrical tube in interaction with a core gas flow. The augmented form of this model, which was never applied beyond a proof of concept, allows for the representation of liquid pseudo-plugs. Here, we demonstrate its predictive power vs experiments and direct numerical simulations, in terms of the dynamics of plug formation and the characteristics of developed liquid plugs, such as their shape, flow field, speed and length, as well as the associated wall stresses and their spatial derivatives. In particular, we show that the augmented model allows us to establish a direct continuation path from travelling-wave solutions (TWS) to travelling-plug solutions (TPS). We then apply the model to predict mucus plugs in the conducting zone of the tracheobronchial tree, based on the lung architecture model of Weibel. We proceed by numerical continuation of travelling-state solutions in terms of the airway generation, whereby we impose the wavelength of the linearly most-amplified convective instability (CI) mode or that of the absolute instability (AI) mode. We identify the critical airway generation for liquid-plug formation (TWS/TPS transition), maximum potential for wall-stress-induced epithelial cell damage and CI/AI transition, and investigate how these phenomena are affected by the main control parameters, i.e. airway orientation vs gravity, air flow rate, mucus properties and airway size.

Shock refraction in a gas–liquid interface is ubiquitous in nature and engineering. This study investigates the shock refraction phenomena in air–water interfaces for various inclination angles. The interface inclination angles are achieved using a tiltable vertical shock tube. The time-resolved schlieren images are compared with numerical simulations performed using the BlastFoam solver in the OpenFOAM software. The stiffened gas equation of state is used to model water in the simulations. The shock polar analysis using modified shock relations for a stiffened gas is used to elucidate the refraction patterns. A regular refraction pattern with a reflected shock wave and a bound precursor refraction with a regular reflection are observed experimentally for the first time in an air–water system. Further, a new free precursor refraction pattern with a Mach reflection is observed. The transition criteria and the corresponding boundaries for each refraction pattern are demarcated in the ($M_S, \theta _w^c$)-plane. The refraction sequence and the range for various incident shock strength regimes are also identified.

Interface-resolved direct numerical simulations (DNS) of clustered settling suspensions in a periodic domain are performed to study the filtered drag force for clustered particle-laden flows. Our results show that, for the homogeneous system, the filtered drag is independent of the filter size, whereas for the clustered particle-laden flows, the averaged drag becomes smaller than the homogeneous drag at the filter size above 4 particle diameters. The drag reduction saturates at the filter size being comparable to the cluster size in the horizontal direction in our simulations. A new correlation is proposed to account for the mesoscale effect on the filtered drag force by using drift velocity and variance of the solid volume fraction, based on the modification of existing subgrid drag models for the inhomogeneous system. The existing models for the drift velocity and the variance of the solid volume fraction are assessed using our DNS data. A new model for the drift velocity and the variance of the solid volume fraction is proposed, based on the combination and modification of the previous models. All mesoscale models considered can predict well the filtered drag with comparable accuracy, and are superior to the homogeneous drag model for the clustered system. Our models with the same parameter values obtained from the large-scale system can also predict well the filtered drag for smaller computational domain sizes.

In the generalized quasilinear approximation (GQLA) (Marston et al., Phys. Rev. Lett., vol. 116, 2016, 214501), a threshold wavenumber ($k_0$) in the direction of translational symmetry segregates the total into large- ($l$) and small-scale ($h$) fields. While the governing equation for the large-scale field is fully nonlinear, that for the small scales is linearized with respect to the large-scale field. In addition, some nonlinear triad interactions are omitted in the GQLA. Herein, the GQLA is applied to two-dimensional planar Rayleigh–Bénard convection (RBC). A scale separation between the large-scale convection rolls and small-scale turbulent fluctuations is typical in RBC. The present work explores the efficacy of GQLA in capturing the scale-by-scale energy transfer processes in RBC. The initial condition for the GQLA simulations was either the statistically stationary state obtained in direct numerical simulation (DNS) or random fluctuations superimposed on the linear conductive temperature profile and $\boldsymbol {u}=0$. The GQLA simulations can capture the convection rolls for $k_0$ larger than or equal to the dominant wavenumber for thermal driving of the flow ($k_0 \ge k_{\hat {Q}}$). Additionally, the GQLA emulates the fully nonlinear dynamics for $k_0$ larger than or equal to the first harmonic of the convection-roll wavenumber ($k_0 \ge 2k_{roll}$). In the intermediate regime with $2k_{roll} > k_0 \ge k_{\hat {Q}}$, the dynamics captured in GQLA simulations is different from the DNS. In DNS, two primary energy transfer processes dominate: (i) the energy transfer to/from the convection rolls and (ii) the scale-by-scale inverse kinetic energy and forward thermal energy cascades mediated by the convection rolls. The fully nonlinear dynamics is emulated by GQLA when these energy transfer processes are faithfully reproduced. Utilizing the framework of altering the triad interactions in GQLA, an additional intrusive calculation, including target triad interactions, is performed here to study their influence. This intrusive calculation shows that the convection rolls are not captured in GQLA for $k_0 < k_{\hat {Q}}$ because of the exclusion of the $h \to l \to l$ and $l \to h \to h$ triad interactions in GQLA. The inclusion of these triad interactions in the intrusive calculation yields the convection rolls, and the reproduced dynamics is similar to that of the intermediate GQLA regime with $2k_{roll} > k_0 \ge k_{\hat {Q}}$.

This work experimentally investigates the flow structure around a rectangular cylinder with an aspect ratio of 2 under varying incidence angles to examine how acoustic perturbations modify and modulate the unsteady flow instabilities. In the absence of acoustic excitation, the angle of incidence is found to markedly influence the flow topology and the natural shedding pattern altering the vortex formation length and wake dynamics. With acoustic perturbations, it is observed that for incidence angles $\alpha = 0^{\circ }$ and $\alpha = 5^{\circ }$, the masked impinging leading-edge vortex (ILEV)/trailing-edge vortex shedding (TEVS) instability modes of $n= 1$ and $n= 2$ become evident when their frequencies coincide with the frequencies of the acoustic perturbations (i.e. resonant condition). Both trailing-edge and leading-edge vortices were found to be modulated by the acoustic pressure cycle. These instability modes, which are naturally present under non-resonant conditions for significantly higher aspect ratios, highlight the role of incidence angle and self-excited acoustic resonance in virtually augmenting the streamwise length of the cylinder, thereby facilitating the emergence and sustenance of the ILEV/TEVS shedding pattern.

Shear-induced self-diffusion is a fundamental mode of transport in granular flows. Yet its critical behaviour and dependence on the particle solid fraction are still unclear. Here, we rationalize these dependencies by performing two-dimensional pressure-imposed numerical simulations of dense non-Brownian frictional suspensions. Our results, combined with existing numerical data on inertial granular flows, show that the shear-induced diffusion coefficients of both systems can be captured by a single function of the distance to jamming. They further show that the grain diffusive behaviour is underpinned by a specific random walk process, having a constant elementary step length driven at a frequency that increases with the solid fraction. The proposed scaling laws pave the way for a better understanding of mixing processes in granular media.

Flying insects exhibit remarkable capabilities in coordinating their olfactory sensory system and flapping wings during odour plume-tracking flights. While observations have indicated that their flapping wing motion can ‘sniff’ up the incoming plumes for better odour sampling range, how flapping motion impacts the odour concentration field around the antennae is unknown. Here, we reconstruct the body and wing kinematics of a forwards-flying butterfly based on high-speed images. Using an in-house computational fluid dynamics solver, we simulate the unsteady flow field and odourant transport process by solving the Navier–Stokes and odourant advection-diffusion equations. Our results show that, during flapping flight, the interaction between wing leading-edge vortices and antenna vortices strengthens the circulation of antenna vortices by over two-fold compared with cases without flapping motion, leading to a significant increase in odour intensity fluctuation along the antennae. Specifically, the interaction between the wings and antennae amplifies odour intensity fluctuations on the antennae by up to 8.4 fold. This enhancement is critical in preventing odour fatigue during odour-tracking flights. Further analysis reveals that this interaction is influenced by the inter-antennal angle. Adjusting this angle allows insects to balance between resistance to odour fatigue and the breadth of odour sampling. Narrower inter-antennal angles enhance fatigue resistance, while wider angles extend the sampling range but reduce resistance. Additionally, our findings suggest that while the flexibility of the wings and the thorax's pitching motion in butterflies do influence odour fluctuation, their impact is relatively secondary to that of the wing–antenna interaction.

The spatio-temporal scales, as well as a comprehensive self-sustained mechanism of the reattachment unsteadiness in shock wave/boundary layer interaction, are investigated in this study. Direct numerical simulations reveal that the reattachment unsteadiness of a Mach 7.7 laminar inflow causes over $26\,\%$ variation in wall friction and up to $20\,\%$ fluctuation in heat flux at the reattachment of the separation bubble. A statistical approach, based on the local reattachment upstream movement, is proposed to identify the spanwise and temporal scales of reattachment unsteadiness. It is found that two different types, i.e. self-induced and random processes, dominate different regions of reattachment. A self-sustained mechanism is proposed to comprehend the reattachment unsteadiness in the self-induced region. The intrinsic instability of the separation bubble transports vorticity downstream, resulting in an inhomogeneous reattachment line, which gives rise to baroclinic production of quasi-streamwise vortices. The pairing of these vortices initiates high-speed streaks and shifts the reattachment line upstream. Ultimately, viscosity dissipates the vortices, triggering instability and a new cycle of reattachment unsteadiness. The temporal scale and maximum vorticity are estimated with the self-sustained mechanism via order-of-magnitude analysis of the enstrophy. The advection speed of friction, derived from the assumption of coherent structures advecting with a Blasius-type boundary layer, aligns with the numerical findings.