Turbulent plane-Couette flow suspended with finite-size spheroidal particles is studied using fully particle-resolved direct numerical simulations. The effects of particle aspect ratio on turbulent arguments and particle statistics are explored, leading to the same conclusions as the previous experimental findings (Wang et al., J. Fluid Mech., vol. 937, 2022, A15). By performing stress analysis, we find that the presence of particles introduces extra stresses to the system and accounts for the global drag increases. The particle-laden flow cases exhibit spectra that are consistent with the scalings $k^{-5/3}$ and $k^{-3}$ in the large and small scales, respectively. While the $k^{-3}$ scaling observed in the particle-laden flow is reminiscent of bubbly flow, an examination of the particle Reynolds number suggests that the mechanism responsible may not be attributable to the pseudo-turbulence induced by particles as in the case of bubbles. In the view of particle statistics, we observe that spherical and non-spherical particles cluster preferentially in the near-wall and the bulk region, respectively, and that the orientations of non-spherical particles are affected by their aspect ratios, especially in the near-wall region. The present numerical results, combined with previous experimental findings in Wang et al. (J. Fluid Mech., vol. 937, 2022, A15), provide in-depth information on both the fluid and the particle phase, contributing to a better understanding of particle suspension in shear flows.

We present novel numerical simulations investigating the bag breakup of liquid droplets. We first examine the viscous effect on the early-time drop deformation, comparing with theory and experiment. Next, a bag film forms at late time and is susceptible to spurious mesh-induced breakup in numerical simulations, which has prevented previous studies from reaching grid convergence of fragment statistics. We therefore adopt the manifold death (MD) algorithm which artificially perforates thin films once they reach a prescribed critical thickness independent of the grid size, controlled by a numerical parameter $L_{sig}$. We show grid convergence of fragment statistics when utilising the MD algorithm, and analyse the fragment behaviour and bag film disintegration mechanisms including ligament breakup, node detachment and rim destabilisation. Our choice of the critical thickness parameter $L_{sig}$ is limited by numerical constraints and thus has not been matched to experiment or theory; consequently, the current simulations yield critical bag film perforation thicknesses larger than experimentally observed. The influence of the MD algorithm configuration on the bag breakup phenomena and statistics will be investigated in future work. We also study the effects of moderate liquid Ohnesorge number ($0.005 \leqslant Oh \leqslant 0.05$) on the bag breakup process and fragment statistics, where a non-monotonic dependency of the average diameter of bag film fragments on $Oh$ is found. These results highlight the utility of the MD algorithm in multiphase simulations involving topological changes, and pave the way for physics-based numerical investigations into spume generation at the air–sea interface.

This study presents the results of a numerical simulation of two horizontal flows of miscible magnetic and non-magnetic fluids at low Reynolds numbers in a vertical uniform magnetic field. The problem is solved by taking into account the dependence of the viscosity and magnetization of the fluid on the concentration of the magnetic phase, and the dependence of the magnetic field on the concentration. Four flow modes are found: the diffusion mixing mode with a flat diffusion front, the wave mode and two different plug flow modes. In the first of them, the growing wave instability forms the plugs, whereas in the second, the growing magnetostatic instability does. A combination of dimensionless criteria is found that determines the transition from one mode to another. The dependences of the phase velocity of the waves on the diffusion front and the period of the oscillations of the front near the point of the confluence of the two flows on dimensionless criteria are found.

Green hydrogen is expected to have a key role in the transition towards a carbon-neutral society, particularly in the transportation sector. Exploration of novel solutions for the direct injection of hydrogen in internal combustion engines (ICEs) is a main topic for both academia and industry. Here, the authors explore the gas-dynamic and mixing features of hydrogen under-expanded jets exiting from non-axisymmetric cross-sections, with the aim to provide guidelines for designing novel generations of ICE hydrogen injectors. Triangular and star shapes have been compared with elliptical and rectangular sections with different aspect ratios. Differences in the shock wave systems are reported, and explanations of the gas-dynamic mechanisms developed by each section are proposed. Non-uniformity in the radial expansion of the jet boundary has been noticed in all of the non-axisymmetric sections, leading to an axis switching of the jet in some cases. Differences in the radial mixing and axial jet penetration have been reported too, and a robust correlation with the vorticity distribution along the jet boundary has been observed.

This paper proposes a low-divergence method to generate inhomogeneous and anisotropic turbulence. Based on the idea of correlation reconstruction, the proposed method uses the Cholesky decomposition matrix to re-establish turbulence correlation functions. This is in contrast with the time-consuming procedure used in conventional methods to solve eigenvalues and eigenvectors in each location required by coordinate transformation, thereby reducing the computational complexity and improving the efficiency of synthetic turbulence generation. The proposed method is based on the classical spectrum-based method that is widely used to generate homogeneous and isotropic turbulence. By adjusting the generation strategy of specific random vectors, inhomogeneous and anisotropic turbulence with a relatively low divergence level can be obtained in practice, with almost no additional computational burden. Two versions of the proposed method are presented: the inverter and shifter versions. Both the versions are highly efficient, easy to implement, and compatible with high-performance computing. This method is also suitable for providing high-quality initial or boundary conditions for scale-resolving turbulence simulations with large grid numbers (such as direct numerical simulations or large eddy simulations); it can be rapidly implemented using various open-source computational fluid dynamics codes or common commercial software.

The logarithmic law of the wall does not capture the mean flow when a boundary layer is subjected to a strong pressure gradient. In such a boundary layer, the mean flow is affected by the spatio-temporal history of the imposed pressure gradient; and accounting for history effects remains a challenge. This work aims to develop a universal mean flow scaling for boundary layers subjected to arbitrary adverse or/and favourable pressure gradients. We derive from the Navier–Stokes equation a velocity transformation that accounts for the history effects and maps the mean flow to the canonical law of the wall. The transformation is tested against channel flows with a suddenly imposed adverse or favourable pressure gradient, boundary layer flows subjected to an adverse pressure gradient, and Couette–Poiseuille flows with a streamwise pressure gradient. It is found that the transformed velocity profiles follow closely the equilibrium law of the wall.

A mathematical model for the effect of the spatial variation of the local evaporative flux on the evaporation of and deposition from a thin pinned particle-laden sessile droplet is formulated and solved. We then analyse the behaviour for a one-parameter family of local evaporative fluxes with the free parameter $n \, (>-1)$ that exhibits qualitatively different behaviours mimicking those that can be obtained by, for example, surrounding the droplet with a bath of fluid or using a mask with one or more holes in it to achieve a desired pattern of evaporation enhancement and/or suppression. We show that when $-1< n<1$ (including the special cases $n=-1/2$ of diffusion-limited evaporation into an unbounded atmosphere and $n=0$ of spatially uniform evaporation), all of the particles are eventually advected to the contact line, and so the final deposit is a ring deposit at the contact line, whereas when $n>1$ all of the particles are eventually advected to the centre of the droplet, and so the final deposit is at the centre of the droplet. In particular, the present work demonstrates that a singular (or even a non-zero) evaporative flux at the contact line is not an essential requirement for the formation of a ring deposit. In addition, we calculate the paths of the particles when diffusion is slower than both axial and radial advection, and show that in this regime all of the particles are captured by the descending free surface before eventually being deposited onto the substrate.

We consider the dynamics of a gravity current of viscous liquid propagating above a dense granular medium that obeys a $\mu (I)$-rheology. Initially, the pool of liquid depresses the granular layer to form levees at its edges. Next, these levees are pushed outwards by the gravity-driven slumping of the liquid, but the levees are not surmounted. In the third stage, the top of the levee is pushed out beyond the rest of the levee. This segregates the liquid into a pond trapped by the remnant of the original levees, and a slowly spreading thin film ahead of the levees. The trapped fraction of liquid depends on the extent of the early granular erosion, which in turn is controlled by the initial shape of the deposit and the yield criterion of the granular layer. The key physical ingredients that lead to such dynamics are inertia-less flow and a lower layer with a yield criterion. The latter gives rise to the all-important levees, which lead to the eventual trapping.

We investigate the hydrodynamics of a spherical and dumbbell-shaped swimmer in a viscoelastic fluid, modelled by the Giesekus constitutive equation. The ‘squirmer’, a model of a micro-swimmer with tangential surface waves at its boundaries, is simulated utilizing a direct-forcing fictitious domain method. We consider the competitive effects of the fluid inertia and elasticity on the locomotion of the swimmers. For the neutral squirmer, its speed increases monotonically with increasing Reynolds number in the Giesekus fluid, in contrast to holding a constant speed in a Newtonian one. Meanwhile, the speed of the finite inertial squirmer increases monotonically with fluid elasticity, as measured by the Weissenberg number. Regarding the dumbbell-shaped swimmers in the Giesekus fluid, we find the pusher–puller (the puller is in front of the pusher) dumbbell swimming to be significantly faster than other dumbbells, providing practical guidance in assembling the complex micro-swimming devices. We further consider the squirmer's (or the dumbbell-shaped squirmer's) energy expenditure and hydrodynamic efficiency, finding that swimming in viscoelastic fluids expends less energy than its Newtonian counterpart, and the neutral squirmer expends more energy than a pusher or puller. The energy expenditure and hydrodynamic efficiency are relevant to steady swimming speeds, in which a faster counterpart squirmer (dumbbell-shaped squirmer) expends less energy but has higher hydrodynamic efficiency.

The flow-induced snap-through dynamics of a buckled flexible filament was explored using the penalty immersed boundary method. The effects of the filament length, bending rigidity and Reynolds number on the mode transition were systematically examined. Three different modes were observed when the aforementioned parameters were varied: an equilibrium mode, a streamwise oscillation mode and a snap-through oscillation mode. Two mode transitions occurred when the bending rigidity was lowered and the length and Reynolds number were increased: a direct transition from the equilibrium mode to the snap-through oscillation mode and the successive appearance of the three modes. An increase in transverse fluid force induced the snap-through oscillation mode. A vortex-induced vibration and a self-excited vibration occurred in the streamwise oscillation mode and the snap-through oscillation mode, respectively. A wake pattern of 2S appeared in the streamwise oscillation mode, and a pattern of 2S + 2P appeared in the snap-through oscillation mode. A hysteresis was observed near the critical Reynolds number. The hysteresis loop increased in magnitude with increasing bending rigidity. The greater energy harvesting was achieved by the larger deflection and the higher strain energy. We found that most of the strain energy was concentrated in the last half of the filament.