The powder concentration module employs the Suspension balance model (SBM) to predict the powder segregation effect.
In this model the particle normal stress gradient is believed to be the driving force for particle migration. As a result, both shear induced powder segregation and the convection of powder concentration from upstream to downstream can be considered.
The SBM models the fluid and particle as two phases, but the full Navier-Stokes equations are only solved on the fluid and particle mixture, or suspension. One extra particle-phase mass balance equation is used, which is similar to a transport equation.
In Moldflow, the SBM model is defined by the following four governing equations:
Conservation of mass for a fluid
[1]
Where
is the suspension density
is time
is the velocity vector
Conservation of momentum
[2]
Where
is pressure
is the viscous stress tensor
is the gravitational acceleration vector
Conservation of energy
[3]
Where
is the thermal conductivity
is the specific heat capacity
is the expansivity which is defined as follows
Particle-phase mass balance
[4]
Where
is the particle volume fraction
-
is the particle migration flux, relative to the bulk motion defined in [5]
[5]
Where
is the sedimentation hindrance function
is the suspension fluid viscosity
is the particle radius
is the particle normal stress, which is defined in [6]
[6]
Where
is the particle normal stress viscosity, defined in [7]
- Tensor
defines the anisotropy of the normal stress, defined in [8]
is shear rate, defined in [9]
[7]
[8]
[9]