No Arabic abstract
We study the effect of particle shape on the turbulence in suspensions of spheroidal particles at volume fraction $phi = 10%$ and show how the near-wall particle dynamics deeply changes with the particle aspect ratio and how this affects the global suspension behavior. The turbulence reduces with the aspect ratio of oblate particles, leading to drag reduction with respect to the single phase flow for particles with aspect ratio $mathcal{AR}leq1/3$, when the significant reduction in Reynolds shear stress is more than the compensation by the additional stresses, induced by the solid phase. Oblate particles are found to avoid the region close to the wall, travelling parallel to it with small angular velocities, while preferentially sampling high-speed fluid in the wall region. Prolate particles, also tend to orient parallel to the wall and avoid its vicinity. Their reluctancy to rotate around spanwise axis reduce the wall-normal velocity fluctuation of the flow and therefore the turbulence Reynolds stress similar to oblates; however, they undergo rotations in wall-parallel planes which increases the additional solid stresses due to their relatively larger angular velocities compared to the oblates. These larger additional stresses compensates for the reduction in turbulence activity and leads to a wall-drag similar to that of single-phase flows. Spheres on the other hand, form a layer close to the wall with large angular velocities in spanwise direction, which increases the turbulence activity in addition to exerting the largest solid stresses on the suspension, in comparison to the other studied shapes. Spherical particles therefore increase the wall-drag with respect to the single-phase flow.
We investigate experimentally the spatial distributions of heavy and neutrally buoyant particles of finite size in a fully turbulent flow. As their Stokes number (i.e. ratio of the particle viscous relaxation time to a typical flow time scale) is close to 1, one may expect both classes of particles to aggregate in specific flow regions. This is not observed. Using a Voronoi analysis we show that neutrally buoyant particles sample turbulence homogeneously, whereas heavy particles do cluster. One implication for the understanding and modeling of particle laden flows, is that the Stokes number cannot be the sole key parameter as soon as the dynamics of finite-size objects is considered.
We study single-phase and particulate turbulent channel flows, bounded by two incompressible hyper-elastic walls. Different wall elasticities are considered with and without a 10% volume fraction of finite-size rigid spherical particles, while elastic walls are modelled as a neo-Hookean material. We report a significant drag increase and an enhancement of the turbulence activity with growing wall elasticity for both single-phase and particulate cases in comparison with the single-phase flow over rigid walls. A drag reduction and a turbulence attenuation is obtained for the particulate cases with highly elastic walls, albeit with respect to the single-phase flow of the same wall elasticity; whereas, an opposite effect of the particles is observed on the flow of the less elastic walls. This is explained by investigating the near-wall turbulence of highly elastic walls, where the strong asymmetry in the magnitude of wall-normal velocity fluctuations (favouring the positive), is found to push the particles towards the channel centre. The particle layer close to the wall is shown to contribute to the turbulence production by increasing the wall-normal velocity fluctuations, while in the absence of this layer, smaller wall deformation and in turn a turbulence attenuation is observed. We further address the effect of the volume fraction at a moderate wall elasticity, by increasing the particle volume fraction up to 20%. Migration of the particles from the interface region is found to be the cause of a further turbulence attenuation, in comparison to the same volume fraction in the case of rigid walls. However, the particle induced stress compensates for the loss of the Reynolds shear stress, thus, resulting in a higher overall drag for the case with elastic walls. The effect of wall-elasticity on the drag is reported to reduce significantly with increasing volume fraction of particles.
The features of turbulence modulation produced by a heavy loaded suspension of small solid particles or liquid droplets are discussed by using a physically-based regularisation of particle-fluid interactions. The approach allows a robust description of the small scale properties of the system exploiting the convergence of the statistics with respect to the regularisation parameter. It is shown that sub-Kolmogorov particles/droplets modify the energy spectrum leading to a scaling law, $E(k)propto k^{-4}$, that emerges at small scales where the particle forcing balances the viscous dissipation. This regime is confirmed by Direct Numerical Simulation data of a particle-laden statistically steady homogeneous shear flow, demonstrating the ability of the regularised model to capture the relevant small-scale physics. The energy budget in spectral space, extended to account for the inter-phase momentum exchange, highlights how the particle provide an energy sink in the production range that turns into a source at small scales. Overall, the dissipative fluid-particle interaction is found to stall the energy cascade processes typical of Newtonian turbulent flows. In terms of particle statistics, clustering at small scale is depleted, with potential consequences for collision models.
At finite Reynolds numbers, Re, particles migrate across laminar flow streamlines to their equilibrium positions in microchannels. This migration is attributed to a lift force, and the balance between this lift and gravity determines the location of particles in channels. Here we demonstrate that velocity of finite-size particles located near a channel wall differs significantly from that of an undisturbed flow, and that their equilibrium position depends on this, referred to as slip velocity, difference. We then present theoretical arguments, which allow us to generalize expressions for a lift force, originally suggested for some limiting cases and Re<<1, to finite-size particles in a channel flow at Re < 20. Our theoretical model, validated by lattice Boltzmann simulations, provides considerable insight into inertial migration of finite-size particles in microchannel and suggests some novel microfluidic approaches to separate them by size or density at a moderate Re.
Direct simulations of two-dimensional channel flow of a viscoelastic fluid have revealed the existence of a family of Tollmien-Schlichting (TS) attractors that is nonlinearly self-sustained by viscoelasticity [Shekar et al., J.Fluid Mech. 893, A3 (2020)]. Here, we describe the evolution of this branch in parameter space and its connections to the Newtonian TS attractor and to elastoinertial turbulence (EIT). At Reynolds number $Re=3000$, there is a solution branch with TS-wave structure but which is not connected to the Newtonian solution branch. At fixed Weissenberg number, $Wi$ and increasing Reynolds number from 3000-10000, this attractor goes from displaying a striation of weak polymer stretch localized at the critical layer to an extended sheet of very large polymer stretch. We show that this transition is directly tied to the strength of the TS critical layer fluctuations and can be attributed to a coil-stretch transition when the local Weissenberg number at the hyperbolic stagnation point of the Kelvin cats eye structure of the TS wave exceeds $frac{1}{2}$. At $Re=10000$, unlike $3000$, the Newtonian TS attractor evolves continuously into the EIT state as $Wi$ is increased from zero to about $13$. We describe how the structure of the flow and stress fields changes, highlighting in particular a sheet-shedding process by which the individual sheets associated with the critical layer structure break up to form the layered multisheet structure characteristic of EIT.