In standard Lagrangian-Eulerian predictions, particles are assumed to be mass points and, therefore, do not displace the carrier phase. The volume fraction of the carrier phase is assumed to be unity throughout the entire domain, regardless of the actual particle concentration. Physically, the assumption of particles sharing the same physical space with the carrier phases only holds true if the volume fraction of the Lagrangian phase is negligible. In many technically relevant simulations, the volume fraction of the local particle phase may not be small, and the blocking effect of the particulate phase on the carrier phase may need to be taken into account.

The blocking effect impact requires the flow around the particles to be incorporated into transport equations. Any transported variable belonging to a carrier phase is represented by:

(12–520)

where

= carrier phase density

= kinematic combined (laminar + turbulent) diffusivity

= velocity of the carrier phase

= optional source per unit volume

The blocking effect changes the transport equation to:

(12–521)

where is the carrier phase volume fraction.

The carrier phase volume fraction is computed from the particle phase volume fraction as:

(12–522)

where is a user-specified value. This value is clipped between 0 and 1.

The DPM blocking model modifies the single-phase equations to incorporate the effect of blocking due to the appearance of the carrier phase volume fraction in the transient, convection, diffusion, and source terms of the corresponding transport equation. Note that particle source terms in the carrier phase are still computed using the “mass-point” assumption, that is, no scaling of the particle source terms is performed based on the volume fraction of the carrier phase.