The effect of finger spreading on drag of the hand in human swimming.

The effect of finger spread on overall drag on a swimmer's hand is relatively small, but could be relevant for elite swimmers. There are many sensitivities in measuring this effect. A comparison between numerical simulations, experiments and theory is urgently required to observe whether the effect is significant. In this study, the beneficial effect of a small finger spread in swimming is confirmed using three different but complementary methods. For the first time numerical simulations and laboratory experiments are conducted on the exact same 3D model of the hand with attached forearm. The virtual version of the hand with forearm was implemented in a numerical code by means of an immersed boundary method and the 3D printed physical version was studied in a wind tunnel experiment. An enhancement of the drag coefficient of 2% and 5% compared to the case with closed fingers was found for the numerical simulation and experiment, respectively. A 5% and 8% favorable effect on the (dimensionless) force moment at an optimal finger spreading of 10° was found, which indicates that the difference is more outspoken in the force moment. Moreover, an analytical model is proposed, using scaling arguments similar to the Betz actuator disk model, to explain the drag coefficient as a function of finger spacing.

Universal Scaling Laws for Dense Particle Suspensions in Turbulent Wall-Bounded Flows.

The macroscopic behavior of dense suspensions of neutrally buoyant spheres in turbulent plane channel flow is examined. We show that particles larger than the smallest turbulence scales cause the suspension to deviate from the continuum limit in which its dynamics is well described by an effective suspension viscosity. This deviation is caused by the formation of a particle layer close to the wall with significant slip velocity. By assuming two distinct transport mechanisms in the near-wall layer and the turbulence in the bulk, we define an effective wall location such that the flow in the bulk can still be accurately described by an effective suspension viscosity. We thus propose scaling laws for the mean velocity profile of the suspension flow, together with a master equation able to predict the increase in drag as a function of the particle size and volume fraction.

Collision model for fully resolved simulations of flows laden with finite-size particles.

We present a collision model for particle-particle and particle-wall interactions in interface-resolved simulations of particle-laden flows. Three types of interparticle interactions are taken into account: (1) long- and (2) short-range hydrodynamic interactions, and (3) solid-solid contact. Long-range interactions are incorporated through an efficient and second-order-accurate immersed boundary method (IBM). Short-range interactions are also partly reproduced by the IBM. However, since the IBM uses a fixed grid, a lubrication model is needed for an interparticle gap width smaller than the grid spacing. The lubrication model is based on asymptotic expansions of analytical solutions for canonical lubrication interactions between spheres in the Stokes regime. Roughness effects are incorporated by making the lubrication correction independent of the gap width for gap widths smaller than ∼1% of the particle radius. This correction is applied until the particles reach solid-solid contact. To model solid-solid contact we use a variant of a linear soft-sphere collision model capable of stretching the collision time. This choice is computationally attractive because it allows us to reduce the number of time steps required for integrating the collision force accurately and is physically realistic, provided that the prescribed collision time is much smaller than the characteristic time scale of particle motion. We verified the numerical implementation of our collision model and validated it against several benchmark cases for immersed head-on particle-wall and particle-particle collisions, and oblique particle-wall collisions. The results show good agreement with experimental data.

Laminar, turbulent, and inertial shear-thickening regimes in channel flow of neutrally buoyant particle suspensions.

The aim of this Letter is to characterize the flow regimes of suspensions of finite-size rigid particles in a viscous fluid at finite inertia. We explore the system behavior as a function of the particle volume fraction and the Reynolds number (the ratio of flow and particle inertia to viscous forces). Unlike single-phase flows, where a clear distinction exists between the laminar and the turbulent states, three different regimes can be identified in the presence of a particulate phase, with smooth transitions between them. At low volume fractions, the flow becomes turbulent when increasing the Reynolds number, transitioning from the laminar regime dominated by viscous forces to the turbulent regime characterized by enhanced momentum transport by turbulent eddies. At larger volume fractions, we identify a new regime characterized by an even larger increase of the wall friction. The wall friction increases with the Reynolds number (inertial effects) while the turbulent transport is weakly affected, as in a state of intense inertial shear thickening. This state may prevent the transition to a fully turbulent regime at arbitrary high speed of the flow.

Shear thickening in non-Brownian suspensions: an excluded volume effect.

Shear thickening appears as an increase of the viscosity of a dense suspension with the shear rate, sometimes sudden and violent at high volume fraction. Its origin for noncolloidal suspension with non-negligible inertial effects is still debated. Here we consider a simple shear flow and demonstrate that fluid inertia causes a strong microstructure anisotropy that results in the formation of a shadow region with no relative flux of particles. We show that shear thickening at finite inertia can be explained as an increase of the effective volume fraction when considering the dynamically excluded volume due to these shadow regions.