13.3. Particle/Particle and Particle/Wall Collisions

Ansys Fluent provides a hard sphere collision algorithm (billiard ball model) to account for particle-particle and particle-wall collisions. All collisions are assumed to be binary and quasi-instantaneous, and with contact occurring at a single point. The algorithm considers impulse forces and momentum experienced by particles during collision and it also accounts for energy dissipation.

The motions of two particles at the time of the collision are expressed as:

(13–5)

where,

 
 

and subscripts refer to particles participating in the collision

 

is the particle mass

 

is the particle moment of inertia

 

and are the linear and angular particle velocities, respectively

 

superscript refers to particle velocities before the collision

 

is the particle radius

 

is the impulse force

 

is the unit vector in the normal direction

The impulse force in the normal direction is expressed by:

(13–6)

The impulse force in the tangential direction for sticking collision is expressed as:

(13–7)

The impulse force in the tangential direction for sliding collision is expressed as:

(13–8)

In the above equations:

 

and are the normal and tangential coefficients of restitution, respectively

 

is the friction coefficient

 

is the unit vector in the tangential direction

 

 

is the relative surface velocity (rotational and translational) of the two particles