Modeling particle collision processes in high Reynolds number flow

• We model the collision frequency function applicable to particulate compressible flow.
• The model agrees well with prior incompressible formulation.
• We examine changes in the collision frequency due to the compressibility.
• Contraction of fluid element will increase the collision frequency significantly.
• Dilatation of fluid element will decrease the collision frequency.

Shearing and inertial collision frequency functions are derived for spherical particles with motivation to high-speed flows where compressibility effects are present. Orthokinetic collision is considered under laminar flow where the radial component of relative velocity between two colliding particles is a source of collision. For a general laminar movement of flow, contraction and dilatation effects in compressible flow on shearing collision are assessed. The newly derived shearing collision frequency function consists of compressible and incompressible parts and is obtained from first principles using the local strain-rate tensor. It is shown that the contraction and dilatation of a fluid element significantly effects shearing collisions. The new shearing collision frequency function is compared with inertial collision frequency under laminar flow and the laminar total collision frequency is compared with the total collision frequency function for turbulent flow.