# Modélisation et calcul numérique des collisions de gouttes en écoulements laminaires et turbulents

Abstract : This thesis is devoted to the calculation of drop collisions in laminar and turbulent flows. Using the low Reynolds number approximation, Stokes equations are solved exactly in a bispherical coordinate system and the hydrodynamic forces between two drops are derived. Calculations of trajectories in the cases of a simple shear flow and a pure straining motion then provide the collision cross section and collision rate. The collision efficiency increases with the inertia of drops. Using an expression analogous to that used in the kinetic theory of gases, the collision rate in isotropic homogeneous turbulence is expressed in term of drop pair probability. Collision rates are calculated without and with gravity. The size evolution of a drop cloud is described by Smoluchowski kinetic equation which is then solved with a new numeric method. Two cases are considered. For small drops in isotropic homogeneous turbulent flow, the hydrodynamic interactions tend to delay the broadening of the drops spectrum. For large drops, the formation by collision of drops larger than $200$ $\mu m$ depends strongly on turbulence, gravity being taken into account. These results corroborate in situ observations in stratus clouds.
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Theses

Cited literature [149 references]

https://tel.archives-ouvertes.fr/tel-00433421
Contributor : Franck Pigeonneau <>
Submitted on : Thursday, November 19, 2009 - 12:03:03 PM
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• HAL Id : tel-00433421, version 1

### Citation

Franck Pigeonneau. Modélisation et calcul numérique des collisions de gouttes en écoulements laminaires et turbulents. Dynamique des Fluides [physics.flu-dyn]. Université Pierre et Marie Curie - Paris VI, 1998. Français. ⟨tel-00433421⟩

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