Turbulent Transport of Material Particles: An Experimental Study of Finite Size Effects

Abstract

We use an acoustic Lagrangian tracking technique, particularly adapted to measurements in open flows, and a versatile material particles generator (in the form of soap bubbles with adjustable size and density) to characterize Lagrangian statistics of finite sized, neutrally bouyant, particles transported in an isotropic turbulent flow of air. We vary the size of the particles in a range corresponding to turbulent inertial scales and explore how the turbulent forcing experienced by the particles depends on their size. We show that, while the global shape of the intermittent acceleration probability density function does not depend significantly on particle size, the acceleration variance of the particles decreases as they become larger in agreement with the classical k −7/3 scaling for the spectrum of Eulerian pressure fluctuations in the carrier flow.

Transport of Finite-Sized Particles in Chaotic Flow

“…Even with this loading density, we calculate that interactions between the tracer particles are generally negligible. As mentioned above, our flow is not turbulent, even though the carrier flows studied both in simulation [8,13,14] and experiment [9][10][11]15] are typically turbulent. In previous work, the particle size is typically assumed to be smaller than the Kolmogorov length scale.…”

“…For particles with St > 0:1, previous studies have found that the acceleration statistics of inertial particles differ from those of fluid elements, for both heavy [8,9] and large particles [7,10]. In each case, the acceleration variance decreased as the Stokes number increased; for the heavy particles, the acceleration probability density function (PDF) also became narrower for higher St.…”

“…Instead, they behave as if they have inertia relative to the carrier flow, responding to changes in the underlying flow field only over a finite time. This lagging effect is evident, for example, in the reduction of the acceleration variance for such inertial particles in turbulence [7][8][9][10]. Inertial particles have also been shown to accumulate in particular regions of the flow: particles denser than their carrier flow, for example, are ejected from vortices and therefore congregate in regions of high strain [11][12][13][14][15].…”

“…If they have a density different from the carrier flow, they take a finite time to respond to flow accelerations. Even if they are neutrally buoyant, however, particles of finite size can behave inertially since the flow stresses are averaged over the particle surface [10,16,17]. The latter case has implications for flow measurements: simply choosing particles of the same density as the fluid does not imply that the particles will faithfully follow the flow.…”

“…Though the Stokes numbers of our inertial particles are relatively small, we observe measurable inertial effects, particularly for timeresolved statistics. Particles whose inertia comes purely from finite-size effects are less well studied than their heavy counterparts [10,16,17]. In numerical simulations, for example, it is simpler to study a pointlike, heavy particle than to simulate a large particle accurately, which would require solving the Navier-Stokes equations along the particle surface.…”