Wake attenuation in large Reynolds number dispersed two-phase flows

Abstract

The dynamics of high Reynolds number-dispersed two-phase flow strongly depends on the wakes generated behind the moving bodies that constitute the dispersed phase. The length of these wakes is considerably reduced compared with those developing behind isolated bodies. In this paper, this wake attenuation is studied from several complementary experimental investigations with the aim of determining how it depends on the body Reynolds number and the volume fraction a. It is first shown that the wakes inside a homogeneous swarm of rising bubbles decay exponentially with a characteristic length that scales as the ratio of the bubble diameter d to the drag coefficient C d , and surprisingly does not depend on a for 10 K2 %a%10 K1 . The attenuation of the wakes in a fixed array of spheres randomly distributed in space (aZ2!10 K2 ) is observed to be stronger than that of the wake of an isolated sphere in a turbulent incident flow, but similar to that of bubbles within a homogeneous swarm. It thus appears that the wakes in dispersed two-phase flows are controlled by multi-body interactions, which cause a much faster decay than turbulent fluctuations having the same energy and integral length scale. Decomposition of velocity fluctuations into a contribution related to temporal variations and that associated to the random character of the body positions is proposed as a perspective for studying the mechanisms responsible for multi-body interactions.

Velocity fluctuations generated by the flow through a random array of spheres: a model of bubble-induced agitation

“…At this stage, it is important to recall that the wake of a sphere surrounded by many spheres is strongly attenuated compared to that of an isolated sphere, as is the case for a bubble in a swarm of bubbles (Risso & Ellingsen 2002;Roig & Larue de Tournemine 2007). Risso et al (2008) have shown that both the wake of a sphere or the wake of a bubble exponentially decay with the distance, and have almost vanished before 3 diameters. Spatial fluctuations are therefore dominant at scales comparable or larger than d ≈ Λ.…”

“…This is illustrated by the fact that, at the same Reynolds number, the drag coefficient of a bubble is much smaller than that of a solid sphere. Nonetheless, the wake of a bubble in a swarm of bubbles and that of a solid sphere in a swarm of spheres both exponentially decrease with the distance, and differ from each other only by their length of decay (Risso et al 2008). At same α and Re, the fluctuations generated by an array of spheres will have different magnitudes and length scales than those of a swarm of bubbles.…”

“…The second quantity is the integral length scale Λ of the fluctuations, which has been found to be independent of the gas volume fraction and thus does not scale with the average distance between the bubbles. It is also not proportional to the diameter of bubble, but rather corresponds to the length of the bubble wake (Risso et al 2008). There is, however, no consensus on its exact expression (Mendez-Diaz et al 2013).…”

“…However, even if it clearly appears that bubble wakes and their interactions play a major role, the physical mechanisms responsible for all the observed specific properties were still obscure. As pointed out by Risso et al (2008), a major difficulty in the understanding of bubble-induced agitation lies in the fact that it combines two contributions of different natures, which have no reason to share the same properties. The first, which is called spatial fluctuation, is the result of the strong spatial heterogeneity of the flow around each bubble and within the wakes.…”

“…A relevant configuration to isolate the bubble-induced agitation from the other sources of fluctuations is the homogeneous swarm of rising bubbles. In recent years, several works have carried out experimental investigations of this configuration in order to characterize the properties of the bubble-induced agitation (Martinez-Mercado, Palacios-Morales & Zenit 2007;Roig & Larue de Tournemine 2007;Risso et al 2008;Martinez-Mercado et al 2010;Riboux, Risso & Legendre 2010;Mendez-Diaz et al 2013;Colombet et al 2015).…”