Reynolds number swarm

The rise velocity, Uo, in general depends on the bubble size, or the bubble Reynolds number but as bubble size increases, as in two-phase upflow, Ua approaches an asymptotic value that is independent of Reynolds number. The following expressions have been accepted for a single bubble rising in an infinite medium, and for one rising in a swarm of surrounding bubbles, respectively (Duckler and Taitel, 1991b) ... 

This result can also be applied directly to coarse particle swarms. For fine particle systems, the suspending fluid properties are assumed to be modified by the fines in suspension, which necessitates modifying the fluid properties in the definitions of the Reynolds and Archimedes numbers accordingly. Furthermore, because the particle drag is a direct function of the local relative velocity between the fluid and the solid (the interstitial relative velocity, Fr), it is this velocity that must be used in the drag equations (e.g., the modified Dallavalle equation). Since Vr = Vs/(1 — Reynolds number and drag coefficient for the suspension (e.g., the particle swarm ) are (after Barnea and Mizrahi, 1973) ... 

For the swarm of bubbles, it is necessary to modify this equation to account for the interaction between bubbles and bubble wakes. Measurements by Tsuji et al. (1984) for two spheres in the Reynolds number range 100 to 200 can be expressed as... 

Fig. 5.4 shows the effect of the dynamic viscosity /z upon Although the state of flow in the tank is turbulent, the viscosity of the medium is important, because it affects the sinking velocity of the particle swarm iVss. The particle Reynolds number Rep formulated with Wss and dp ties in the laminar to transition ranges. 

Le Clair, B. P. and Hamielec, A. E., Viscous flow through particle assemblies at intermediate Reynolds numbers. A cell model for transport in bubble swarms, Can. J. Chem. Eng., Vol. 49, No. 6, pp. 713-720, 1971. 

The exponent m depends on the Reynolds number of the particles as shown in Fig. 6.4-3. An evaluation of (6.4-3) reveals that small drops (laminar flow) can be retarded up to a factor of 80 (Fig. 3.6-9). In turbulent flow the swarm effect is much lower, e.g., as low as a factor of 10. A simpler formulation of the swarm effect is possible when the influence of swarm concentration is accounted for in the friction factor instead as in the velocities ... 

Hence, the swarm effect itself does not depend on Reynolds number at all. It is the same in laminar as well as in turbulent flow. Just the friction factor depends on Re. However, this dependency on Reynolds number is well known. 

Roghair I, Lau YM, Deen NG, et al On the drag force ofbubbles in bubble swarms at intermediate and high Reynolds numbers, Chem Eng Sci 66 3204—3211, 2011. 

The particle swarm optimization (PSO) imitates the flocking behavior of birds or fish. The algorithm is based on the work of Reynolds (Reynolds 1987), where a model of decentralized behavior of herds and flocks is presented. The swarm is set up by a large number of particles, which represent the solutions. Every solution, meaning each particle, can choose its path by itself and follows three basic rales ... 

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