In dense flows, particle-particle interactions may impact the erosion rates due to the shielding effects of a dense near-wall layer of solid particles. In addition, solid particles that move nearly parallel to the wall may lead to an abrasive erosion. In Ansys Fluent, the total erosion rate in dense systems is computed as follows:

(12–340)

where is the abrasive erosion rate calculated as described in Abrasive Erosion Caused by Solid Particles, and is the impact erosion rate calculated as described in Wall Shielding Effect in Dense Flow Regimes.

The abrasive erosion and shielding are computed under the following conditions:

In many cases with wall erosion, particles tend to concentrate in streaks in the near-wall regions. This very strongly violates the basic (and essential) DPM assumption of dispersed flow regime. To simulate densely packed particles using the Lagrange approach, particle-particle interactions as well as the volume displacement of the particles must be considered. This can be done using the DEM model in the densely packed regions, but at immense computational costs. To avoid this expense, ANSYS Fluent uses a dispersed Euler phase, which accounts for the volume displacement and any interphase interactions. The dispersed Euler phase is assumed to adequately represent the particle behavior close to the wall. The erosion is to a large extent calculated from Euler phase quantities (such as wall shear erosion). The classical impact-based erosion is reduced by blending via the shielding function.

 

12.10.5.1. Abrasive Erosion Caused by Solid Particles

The abrasive erosion of the solid phase in the near-wall region is modelled as a function of the solid phase wall shear stress and the solid phase near-wall velocity:

(12–341)

where
	= empirical constant
	= solid phase velocity
	= velocity exponent
	= wall shear stress of the solid phase
	= solid phase volume fraction
	= packing limit (~0.63 for spherical particles)

For multiphase flows with N granular phases, the erosion rate due to wall shear stress is the accumulated erosion rate of all granular phases:

(12–342)

 

12.10.5.2. Wall Shielding Effect in Dense Flow Regimes

In the dense flow regime, particles approaching the wall may be slowed down or reflected by other solid particles that move nearly parallel to the wall in its vicinity. This shielding effect will lower the erosion rates caused by the particles impacting the solid wall surface.

To account for this effect, the following shielding function is used in Ansys Fluent:

(12–343)

where
	= volume fraction of the solid phase
	= packing limit (~0.63 for spherical particles)

When calculating the impact erosion rate , the shielding function is used to scale the impact erosion rate for the single phase :

(12–344)

If the local solid phase volume fraction approaches the packing limit , then the wall surface will be shielded from any impacting particles, that is, the impact erosion rate will be zero.

For flows with N granular phases, the shielding function is computed from the sum of the individual Eulerian volume fractions:

(12–345)