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Collisions of Small Drops in a Turbulent Flow. Part I: Collision Efficiency. Problem Formulation and Preliminary Results

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  • 1 Institute of the Earth Science, The Hebrew University of Jerusalem, Jerusalem, Israel
  • | 2 Faculty of Mechanical Engineering, Technion—Israel Institute of Technology, Haifa, Israel
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Abstract

A mathematical approach to the calculation of the collision efficiency between droplets within a turbulent flow is suggested. The problem of drops’ hydrodynamic interaction is reconsidered taking into account additional inertia-induced relative velocities between droplets of different sizes moving within a turbulent flow. The relative velocities are determined at different points of a turbulent flow using a model of homogeneous and isotropic turbulent flow.

The collision efficiencies of Stokesian droplets are calculated using the superposition method. Two important results have been obtained: 1) the droplet collision efficiencies in a turbulent flow are usually greater than those in calm atmosphere and 2) in a turbulent flow the collision efficiency between droplets is a random value with significant dispersion. The maximum values of the collision efficiency can be several times as much as the mean values.

Variation of the collision efficiency in a turbulent flow is attributed to the variations of drop–drop relative velocities and the angles of drop approach. The velocities stem from the differential response of droplets of different inertia to flow velocity shears and flow accelerations. Specific features of drop approach geometry in a turbulent flow can also contribute to the increase of the collision efficiency.

Corresponding author address: Prof. Alexander P. Khain, Institute of the Earth Science, The Hebrew University of Jerusalem, Givat Ram, Jerusalem 91904, Israel.

Email: khain@vms.huji.ac.il

Abstract

A mathematical approach to the calculation of the collision efficiency between droplets within a turbulent flow is suggested. The problem of drops’ hydrodynamic interaction is reconsidered taking into account additional inertia-induced relative velocities between droplets of different sizes moving within a turbulent flow. The relative velocities are determined at different points of a turbulent flow using a model of homogeneous and isotropic turbulent flow.

The collision efficiencies of Stokesian droplets are calculated using the superposition method. Two important results have been obtained: 1) the droplet collision efficiencies in a turbulent flow are usually greater than those in calm atmosphere and 2) in a turbulent flow the collision efficiency between droplets is a random value with significant dispersion. The maximum values of the collision efficiency can be several times as much as the mean values.

Variation of the collision efficiency in a turbulent flow is attributed to the variations of drop–drop relative velocities and the angles of drop approach. The velocities stem from the differential response of droplets of different inertia to flow velocity shears and flow accelerations. Specific features of drop approach geometry in a turbulent flow can also contribute to the increase of the collision efficiency.

Corresponding author address: Prof. Alexander P. Khain, Institute of the Earth Science, The Hebrew University of Jerusalem, Givat Ram, Jerusalem 91904, Israel.

Email: khain@vms.huji.ac.il

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