A novel particle-resolved direct numerical simulations (PR-DNS) method for non-spherical particles is developed and validated in the open-source MFiX (Multi-phase Flow with Interphase eXchanges) code for simulating the suspension of non-spherical particles and fluidisation. The model is implemented by coupling superquadric Discrete Element Method-Computational Fluid Dynamics (DEM-CFD) with the immersed boundary method. The model was first validated by applying it to analyse fluid dynamic coefficients ($C_{\!D} , C_{\!L} , C_{\!T}$) of superellipsoids and cylinders at different Reynolds numbers, and the PR-DNS results closely matched those of previous methods, demonstrating the reliability of the current PR-DNS approach. Then, the model was applied to the simulation of the fluidisation of spheres and cylinders. The PR-DNS results were compared with both particle-unresolved superquadric DEM-CFD simulation and experimental data. The pressure drop, height distribution and orientation distribution of particles were analysed. The results show that the PR-DNS method provides a reliable method for reproducing fluidisation experimental results of non-spherical particles. In addition, the comparison of the drag correction coefficients predicted by existing models with that obtained from PR-DNS results indicates the need for a new drag model for particle-unresolved simulation of non-spherical particles.

The effects of the external intermittent behaviour on the Kolmogorov constants $C_{k1}$ and $C_2$ in spectral and the physical spaces are investigated using high-resolution direct numerical simulations of a turbulent plane jet. Well-defined $- 5/3$ energy spectrum and $2/3$ structure function can be found in the intermittent flows without large-scale vortex shedding. For different cross-wise positions, the profiles of conditional energy spectra and conditional structure functions exhibit self-similarity at small and intermediate scales when normalised by the conditional Kolmogorov scale of the turbulent region. The conditional Kolmogorov constants are close to those of the fully turbulent flow. The constants $C_{k1}$ and $C_2$ are found to have a power-law dependence on the intermittency factor $\gamma$, that is, $C_{k1}\sim \gamma ^{1/3}$ and $C_{2}\sim \gamma ^{1/3}$, except for the scaling of the structure function in the highly intermittent region with $\gamma =0.25$. In the highly intermittent region, e.g. $\gamma =0.25$, the scaling in the conditional structure function can be considerably influenced by the blocking/sheltering mechanisms of the turbulent/non-turbulent interface (TNTI), leading to slight deviations from self-similarity. We further confirm that the conditional structure function recovers self-similarity after excluding a turbulent region at an average distance of approximately $20$ Kolmogorov length scales from the outer edge of the TNTI, which is comparable to the mean thickness of the TNTI. These findings contribute to the modelling of the edge of a turbulent region.

The inertial migration of hydrogel particles suspended in a Newtonian fluid flowing through a square channel is studied both experimentally and numerically. Experimental results demonstrate significant differences in the focusing positions of the deformable and rigid particles, highlighting the role of particle deformability in inertial migration. At low Reynolds numbers (${Re}$), hydrogel particles migrate towards the centre of the channel cross-section, whereas the rigid spheres exhibit negligible lateral motion. At finite ${Re}$, they focus at four points along the diagonals in the downstream cross-section, in contrast to the rigid particles which focus near the centre of the channel face at similar ${Re}$. Numerical simulations using viscous hyperelastic particles as a model for hydrogel particles reproduced the experimental results for the particle distribution with an appropriate Young’s modulus of the hyperelastic particles. Further numerical simulations over a broader range of ${Re}$ and the capillary number ($Ca$) reveal various focusing patterns of the particles in the channel cross-section. The phase transitions between them are discussed in terms of the inertial lift and the lift due to particle deformation, which would act in the direction towards lower shear. The stability of the channel centre is analysed using an asymptotic expansion approach to the migration force at low ${Re}$ and $Ca$. The theoretical analysis predicts the critical condition for the transition, which is consistent with the direct numerical simulation. These experimental, numerical and theoretical results contribute to a deeper understanding of inertial migration of deformable particles.

Rotor–stator interactions in turbomachines are characterised by a complex interplay of hydrodynamic instabilities, acoustic pressure waves and receptivity mechanisms, as well as the collision of coherent structures with the blade geometry. An unsteady dual analysis of self-excited instabilities and flow interactions, exemplified by a simple model compressor stage under subsonic conditions, is proposed and presented. Using a low-dissipation sliding-plane implementation, instability-resolving nonlinear-adjoint looping simulations provide detailed sensitivity information that allows for the dissection of the full flow into sub-components linked to distinct flow phenomena. This sensitivity information further links observed flow behaviour to its hydrodynamic or acoustic origin, thereby laying the foundation for a cause-and-effect analysis and for flow control.

To study the physics of small-scale properties of homogeneous isotropic turbulence at increasingly high Reynolds numbers, direct numerical simulation results have been obtained for forced isotropic turbulence at Taylor-scale Reynolds number $R_\lambda =2500$ on a $32\,768^3$ three-dimensional periodic domain using a GPU pseudo-spectral code on a 1.1 exaflop GPU supercomputer (Frontier). These simulations employ the multi-resolution independent simulation (MRIS) technique (Yeung & Ravikumar 2020, Phys. Rev. Fluids, vol. 5, 110517) where ensemble averaging is performed over multiple short segments initiated from velocity fields at modest resolution, and subsequently taken to higher resolution in both space and time. Reynolds numbers are increased by reducing the viscosity with the large-scale forcing parameters unchanged. Although MRIS segments at the highest resolution for each Reynolds number last for only a few Kolmogorov time scales, small-scale physics in the dissipation range is well captured – for instance, in the probability density functions and higher moments of the dissipation rate and enstrophy density, which appear to show monotonic trends persisting well beyond the Reynolds number range in prior works in the literature. Attainment of range of length and time scales consistent with classical scaling also reinforces the potential utility of the present high-resolution data for studies of short-time-scale turbulence physics at high Reynolds numbers where full-length simulations spanning many large-eddy time scales are still not accessible. A single snapshot of the $32\,768^3$ data is publicly available for further analyses via the Johns Hopkins Turbulence Database.

The study of the shape of droplets on surfaces is an important problem in the physics of fluids and has applications in multiple industries, from agrichemical spraying to microfluidic devices. Motivated by these real-world applications, computational predictions for droplet shapes on complex substrates – rough and chemically heterogeneous surfaces – are desired. Grid-based discretisations in axisymmetric coordinates form the basis of well-established numerical solution methods in this area, but when the problem is not axisymmetric, the shape of the contact line and the distribution of the contact angle around it are unknown. Recently, particle methods, such as pairwise-force smoothed particle hydrodynamics (PF-SPH), have been used to conveniently forego explicit enforcement of the contact angle. The pairwise-force model, however, is far from mature, and there is no consensus in the literature on the choice of pairwise-force profile. We propose a new pair of polynomial force profiles with a simple motivation and validate the PF-SPH model in both static and dynamic tests. We demonstrate its capabilities by computing droplet shapes on a physically structured surface, a surface with a hydrophilic stripe and a virtual wheat leaf with both micro-scale roughness and variable wettability. We anticipate that this model can be extended to dynamic scenarios, such as droplet spreading or impaction, in the future.

Wall-based active and passive flow control for drag reduction in low-Reynolds-number (${\textit{Re}}$) turbulent flows can lead to three typical phenomena: (i) attenuation or (ii) amplification of the near-wall cycle, and (iii) generation of spanwise rollers. The present study conducts direct numerical simulations of a low ${\textit{Re}}$ turbulent channel flow and demonstrates that each flow response can be generated with a wall transpiration at two sets of spatial scales, termed streak and roller scales. The effect of the transpiration is controlled by its relative phase to the background flow, which can be parametrised by the wall pressure. Streak scales (i) attenuate the near-wall cycle if transpiration and wall pressure are approximately in-phase or (ii) amplify it otherwise, and (iii) roller scales energise spanwise rollers when transpiration and wall pressure are out-of-phase. Conditions for establishing these robust phase relations are derived from the analytical solution to the pressure Poisson equation and rely on splitting the pressure into its fast, slow and Stokes component. The importance of each condition depends on the relative magnitude of the pressure components, which is significantly altered by the transpiration. The analogy in flow response suggests that transpiration with the two scale families and their phase relations to the wall pressure represent fundamental building blocks for flows over tailored surfaces including riblets, porous and permeable walls.

A discrete Markov model is proposed to study the interscale dynamics of high Reynolds number wall turbulence. The amplitude modulation of the small turbulent scales due to the interaction with large turbulent scales is investigated for three experimental turbulent boundary layers. Through an appropriate discretisation of the turbulence signals, recently proved universal thermodynamic bounds for discrete-state stochastic systems are shown to apply to continuous-state systems like turbulence, regardless of the distance from the wall and the Reynolds number. Adopting Schnakenberg’s network theory for stochastic processes, we provide evidence for a direct proportionality relation between the mean cycle affinity-based entropy production rate (a stochastic thermodynamic quantity) and a mean entropy production rate associated with the net large-to-small-scale turbulent kinetic energy production. Finally, new insights into the relative arrangement (lag/lead) between large and small scales are provided.

The moulting of birds creates different trailing-edge gaps in their wings, which inspires the handling of damaged wings in micro-air vehicles. The effects of the moult gap on aerodynamic performance are investigated by employing a bird-inspired flapping wing model. The aerodynamic performance is evaluated by numerically solving the Navier–Stokes equations for incompressible flows. Moult-gapped wings with different gap widths and positions are compared with the original intact wing in terms of aerodynamic forces and vortex structures. It is found that the decrease in the average lift is slower than that expected from the classical aerodynamic model. The moult gap results in three-dimensional gap vortices, which interact with leading-edge vortices and tip vortices. The interaction generates a pair of parallelly arranged vortex loops on each wing. The downwash momentum associated with this pair of vortex loops is enhanced by the gap vortices. The gap-vortices-enhanced downwash compensates for the loss in the lifting surface, increasing the aerodynamic force per unit area. A composite actuator disk model is proposed based on the vortex loops. The proposed model accounts for not only the finite-span wing effects but also the vortex compensation effects, while the previous quasi-steady model only accounts for the finite-span wing effects.