For non-rotating particles, Ansys Fluent provides a model that accounts for the energy loss due to inelastic collision with the wall. The particle rebounds off the boundary in question with a change in its momentum as defined by the coefficient of restitution. (See Figure 12.2: Particle Reflection at Wall.)

Figure 12.2: Particle Reflection at Wall

The normal coefficient of restitution defines the amount of momentum in the direction normal to the wall that is retained by the particle after the collision with the boundary  [642]:

(12–193)

where is the particle velocity normal to the wall and the subscripts 1 and 2 refer to before and after collision, respectively. Similarly, the tangential coefficient of restitution, , defines the amount of momentum in the direction tangential to the wall that is retained by the particle.

For rotating particles, Ansys Fluent provides a model for estimating a particle velocity after rebounding from a wall, as proposed by Tsuji et al. [660]. The model is based on classical mechanics (see Figure 12.3: Particle-Wall Collision Forces) and accounts for energy loss due to inelastic collision and friction.

Figure 12.3: Particle-Wall Collision Forces

In this model, the time during which the particle and the wall are in contact is divided into two periods; namely, compression and recovery. The system of equations is defined according to whether or not the particle stops sliding within the compression period.

Adhesive Impact

If the particle stops sliding within the compression period, the following condition holds:

(12–194)

The limiting case of equality in Equation 12–194 corresponds to the Coulomb friction law (Equation 12–505), where the tangential force is directly proportional to the normal force , and the proportionality factor is the friction coefficient .

The momentum equations for the particle motion before and after the collision with the wall are as follows:

(12–195)

The coefficient of restitution is defined as the ratio of the momenta in the normal direction before and after the collision. If the particle mass remains constant during rebounding off the wall, the coefficient of restitution can be simply defined as the ratio of the particle normal velocities before and after the collision:

(12–196)

The angular momentum in the wall normal direction is not affected by the collision, that is . This results in static (unchanging) particle angular velocity:

(12–197)

For adhesive impact, the following boundary condition for the particle velocity at the point of contact with the wall can be defined:

(12–198)

where the superscript refers to the particle velocity at the contact point during collision (see Figure 12.3: Particle-Wall Collision Forces).

For a given boundary condition, the post-collision velocities, and , can be computed by solving Equation 12–195.

Sliding Impact

If the tangential force exceeds the frictional force (that is, the inequality in Equation 12–194 is not fulfilled), the particle does not stop sliding within the compression period. The particle linear and angular velocities are not correlated kinematically, and post-collision velocities can be estimated directly from the respective momentum equations. Equation 12–196 and Equation 12–197 are still valid. The change in the tangential momentum can be defined using Equation 12–194 as follows:

(12–199)

where,

(12–200)

where is the sign function that returns +1 for positive values and –1 for negative values.

See Particle Rotation in the Fluent User's Guide for information about how to use the particle rotation model.