ALBERT

Beschreibung: We present a series of experiments to explore the dynamics of particle-laden fountains rising through a stratified environment with zero buoyancy flux at the source. We find that the ratio $U$ between the particle sedimentation speed $V_s$ and the characteristic fountain velocity $(M_0N^{2})^{1/4}$ , where $M_0$ is the initial momentum flux and $N$ the frequency of the ambient stratification, has a profound effect on the structure of the fountain and the dispersal of the particles. In a mono-disperse particle fountain, when the settling speed of the particles is small in comparison to the characteristic fountain speed ( $Ull 1$ ) the flow initially behaves in an analogous fashion to a single-phase fountain, forming an intrusion at a height of approximately 0.5 of the maximum fountain height. As the fluid–particle mixture spreads out, the particles gradually sediment to the tank floor. The intruding fluid subsequently rises and forms a new intrusion at its neutral buoyancy height. Some of the particles are carried up from the original intrusion with the rising fluid. This leads to the formation of a sedimenting column of particles with a characteristic radius. We observe a transition in the behaviour of the particle fountains in the vicinity of $Usim 0.1$ , with the particles now separating from the fluid near the top of the fountain. The separation of the particles leads to a reduction in the steady-state height of the particle-laden fountain, while the fluid in the fountain continues upwards until reaching its neutral buoyancy height and forming an intrusion above the fountain top. We compare the experimental data with two models of turbulent fountains to help rationalise the trends observed as a function of the dimensionless fall speed $U$ . We briefly consider the dynamics of poly-disperse particle fountains and relate their dynamics to the regimes observed in their mono-disperse counterparts. We discuss the implications of this work for the dispersal of different sized particles from submarine volcanic eruptions.

Beschreibung: Starting from the Boltzmann–Enskog kinetic equations, the charge transport equation for bidisperse granular flows with contact electrification is derived with separate mean velocities, total kinetic energies, charges and charge variances for each solid phase. To close locally averaged transport equations, a Maxwellian distribution is presumed for both particle velocity and charge. The hydrodynamic equations for bidisperse solid mixtures are first revisited and the resulting model consisting of the transport equations of mass, momentum, total kinetic energy, which is the sum of the granular temperature and the trace of fluctuating kinetic tensor, and charge is then presented. The charge transfer between phases and the charge build-up within a phase are modelled with local charge and effective work function differences between phases and the local electric field. The revisited hydrodynamic equations and the derived charge transport equation with constitutive relations are assessed through hard-sphere simulations of three-dimensional spatially homogeneous, quasi-one-dimensional spatially inhomogeneous bidisperse granular gases and a three-dimensional segregating bidisperse granular flow with conducting walls.

Beschreibung: Direct numerical simulations (DNS) of oscillatory flow around a cylinder show that the Stokes–Wang (S–W) solution agrees exceptionally well with DNS results over a much larger parameter space than the constraints of $ eta K^2ll 1$ and $ eta gg 1$ specified by the S–W solution, where $K$ is the Keulegan–Carpenter number and $ eta$ is the Stokes number. The ratio of drag coefficients predicted by DNS and the S–W solution, $varLambda _K$ , mapped out in the $Kext {--} eta$ space, shows that $varLambda _K 〈 1.05$ for $Kleq {sim }0.8$ and $1 leq eta leq 10^6$ , which contradicts its counterpart based on experimental results. The large $varLambda _K$ values are primarily induced by the flow separation on the cylinder surface, rather than the development of three-dimensional (Honji) instabilities. The difference between two-dimensional and three-dimensional DNS results is less than 2 % for $K$ smaller than the corresponding $K$ values on the iso-line of $varLambda _K = 1.1$ with $ eta = 200ext {--}20,950$ . The flow separation actually occurs over the parameter space where $varLambda _Kapprox 1.0$ . It is the spatio-temporal extent of flow separation rather than separation itself that causes large $varLambda _K$ values. The proposed measure for the spatio-temporal extent, which is more sensitive to $K$ than $ eta$ , correlates extremely well with $varLambda _K$ . The conventional Morison equation with a quadratic drag component is fundamentally incorrect at small $K$ where the drag component is linearly proportional to the incoming velocity with a phase difference of ${ m pi} /4$ . A general form of the Morison equation is proposed by considering both viscous and form drag components and demonstrated to be superior to the conventional equation for $K 〈 {sim }2.0$ .

Beschreibung: The effect of turbulence on snow precipitation is not incorporated into present weather forecasting models. Here we show evidence that turbulence is in fact a key influence on both fall speed and spatial distribution of settling snow. We consider three snowfall events under vastly different levels of atmospheric turbulence. We characterize the size and morphology of the snow particles, and we simultaneously image their velocity, acceleration and relative concentration over vertical planes approximately $30 extrm {m}^2$ in area. We find that turbulence-driven settling enhancement explains otherwise contradictory trends between the particle size and velocity. The estimates of the Stokes number and the correlation between vertical velocity and local concentration are consistent with the view that the enhanced settling is rooted in the preferential sweeping mechanism. When the snow vertical velocity is large compared to the characteristic turbulence velocity, the crossing trajectories effect results in strong accelerations. When the conditions of preferential sweeping are met, the concentration field is highly non-uniform and clustering appears over a wide range of scales. These clusters, identified for the first time in a naturally occurring flow, display the signature features seen in canonical settings: power-law size distribution, fractal-like shape, vertical elongation and large fall speed that increases with the cluster size. These findings demonstrate that the fundamental phenomenology of particle-laden turbulence can be leveraged towards a better predictive understanding of snow precipitation and ground snow accumulation. They also demonstrate how environmental flows can be used to investigate dispersed multiphase flows at Reynolds numbers not accessible in laboratory experiments or numerical simulations.

Beschreibung: We investigate the effect of helicity on the scale-similar structures of homogeneous isotropic and non-mirror-symmetric turbulence based on the Lagrangian renormalised approximation (LRA), which is a self-consistent closure theory proposed by Kaneda (J. Fluid Mech., vol. 107, 1981, pp. 131–145). In this study, we focus on the time scale representing the scale-similar range. For the LRA, the Lagrangian two-time velocity correlation and response function determine the representative time scale. The LRA predicts that both the Lagrangian two-time velocity correlation and response function equation do not explicitly depend on helicity. We assume the extended scale-similar spectra and time scale by considering the helicity dissipation rate. Considering the small-scale structures, the requirements for the energy and helicity fluxes and response function equation to be scale similar, yield the conventional inertial-range power laws and provide the energy and helicity spectra $propto k^{-5/3}$ and the time scale $propto varepsilon ^{-1/3} k^{-2/3}$ , where $varepsilon$ and $k$ denote the energy dissipation rate and wavenumber, respectively. Notably, energy flux can be scale similar only when $k^H /k ll 1$ , where $k^H = varepsilon ^H/varepsilon$ and $varepsilon ^H$ denotes the helicity dissipation rate. This condition makes the energy cascade process in the scale-similar range completely independent of helicity. We also investigate the localness of the interscale interaction in the energy and helicity cascades for the LRA. We demonstrate that the helicity cascade is slightly non-local in scales compared with the energy cascade. This study provides a foundation on the modelling of non-mirror-symmetric turbulent flows.

Beschreibung: Particle–wall interactions have broad biological and technological applications. In particular, some artificial microswimmers capitalize on their translation–rotation coupling near a wall to generate directed propulsion. Emerging biomedical applications of these microswimmers in complex biological fluids prompt questions on the impact of non-Newtonian rheology on their propulsion. In this work, we report some intriguing effects of shear-thinning rheology, a ubiquitous non-Newtonian behaviour of biological fluids, on the translation–rotation coupling of a particle near a wall. One particularly interesting feature revealed here is that the wall-induced translation by rotation can occur in a direction opposite to what might be intuitively expected for an object rolling on a solid substrate. We elucidate the underlying physical mechanism and discuss its implications on the design of micromachines and bacterial motion near walls in complex fluids.

Beschreibung: We study the reactive displacement of two miscible fluids in channel flows and establish a quantitative link between fluid stretching and chemical reactivity. At the mixing interface, the two fluids react according to the instantaneous irreversible bimolecular reaction $A + B ightarrow C$ . We simulate the advection–diffusion–reaction problem using a random walk based reactive particle method that is free of numerical dispersion. The relative contributions of stretching and diffusion to mixing-limited reaction is controlled by changing the Péclet number, and the channel roughness is also systematically varied. We observe optimal ranges of fluid stretching that maximize reactivity, which are captured by a Lagrangian stretching measure based on an effective time period that honours the stretching history. We show that the optimality originates from the competition between the enhanced mixing by fluid stretching and the mass depletion of the reactants. We analytically derive the spatial distribution of reaction products using a lamellar formulation and successfully predict the optimal ranges of fluid stretching, which are consistent across different levels of channel roughness. These findings provide a mechanistic understanding of how the interplay between fluid stretching, diffusion and channel roughness controls mixing-limited reactions in rough channel flows, and show how reaction hot spots can be predicted from the concept of optimal fluid stretching.

Beschreibung: The modelling of natural convection in porous media is receiving increased interest due to its significance in environmental and engineering problems. State-of-the-art simulations are based on the classic macroscopic Darcy–Oberbeck–Boussinesq (DOB) equations, which are widely accepted to capture the underlying physics of convection in porous media provided the Darcy number, $Da$ , is small. In this paper we analyse and extend the recent pore-resolved direct numerical simulations (DNS) of Gasow et al. (J. Fluid Mech, vol. 891, 2020, p. A25) and show that the macroscopic diffusion, which is neglected in DOB, is of the same order (with respect to $Da$ ) as the buoyancy force and the Darcy drag. Consequently, the macroscopic diffusion must be modelled even if the value of $Da$ is small. We propose a ‘two-length-scale diffusion’ model, in which the effect of the pore scale on the momentum transport is approximated with a macroscopic diffusion term. This term is determined by both the macroscopic length scale and the pore scale. It includes a transport coefficient that solely depends on the pore-scale geometry. Simulations of our model render a more accurate Sherwood number, root mean square (r.m.s.) of the mass concentration and r.m.s. of the velocity than simulations that employ the DOB equations. In particular, we find that the Sherwood number $Sh$ increases with decreasing porosity and with increasing Schmidt number $(Sc)$ . In addition, for high values of $Ra$ and high porosities, $Sh$ scales nonlinearly. These trends agree with the DNS, but are not captured in the DOB simulations.