Mushy Zone Permeability Model Reference

When the solid volume fraction increases above a critical solid volume fraction, a mushy zone permeated with dendrites is formed. The flow resistance in a mushy zone is modeled as an isotropic porous medium.

Table 1. Mushy Zone Permeability Model Reference
Theory	See Mushy Zone Permeability Model.
Provided By	[phase name] > Models > Optional Models
Example Node Path	[phase name] > Models > Mushy Zone Permeability
Requires	The Melting-Solidification model activated in the Eulerian phase.
Properties	None.
Activates	Physics Models	Average Mushy Zone Permeability (in the physics continuum) See Average Mushy Zone Permeability Properties.
	Materials	Mushy Zone Permeability See Material Properties.
	Field Functions	See Field Functions.

Average Mushy Zone Permeability Properties

When the Mushy Zone Permeability model is activated in a phase, the Average Mushy Zone Permeability model node appears in the parent physics continuum. The contributions to flow resistance from each phase where melting and solidification occur are volume-weighted for the computed cell. These contributions are then added to the flow resistance source term of the momentum equation.

Use Forchheimer’s Term: Adds the contribution of the Forchheimer’s term to the flow resistance of the Carman-Kozeny mushy zone model.
See Eqn. (2718) in Mushy Zone Permeability Model.
Ergun Coefficient: Sets the Ergun coefficient in Eqn. (2718). The default value is 0.55.
Max. Porous Viscous Resistance: Sets a maximum level of resistance. This setting applies only to the cells with a solid volume fraction greater than zero, in all regions to which the respective physics continuum is assigned.
Mushy Zone Permeability Under-Relaxation Factor: Governs the extent to which the newly computed solution supplants the old solution at each iteration. The default value is 0.7.

Material Properties

The phase has the following material property:

Mushy Zone Permeability

The available methods are Field Function and Carman-Kozeny.

See Mushy Zone Permeability Model.

The Carman-Kozeny method has the following properties:

Use Switching Function
Use the switching function for the combined use of the Metzner slurry viscosity model and the Carman-Kozeny mushy zone model.

See Switching Function for Metzner Slurry Viscosity and Carman-Kozeny Mushy Zone Permeability Model.
Switching Function: Critical Solid Fraction
The critical solid volume fraction ${α *}_{c r}$ (see Eqn. (2720)). The default value is 0.27 (for Aluminum alloy A201).
Secondary Dendrite Arm Spacing
The secondary dendrite arm spacing is used for the calculation of the Carman-Kozeny Shape Factor.
Switching Function: Constant s
The non-dimensional constant $s$ (see Eqn. (2720)). The default value is 100 because the shape is rather insensitive for values from 80 through 120.
Carman-Kozeny Shape Factor c
The shape factor $c_{s}$ is a function of the dendrite dimension (typically secondary dendrite arm spacing $d$ ) and a shape constant $c$ (see Eqn. (2715)). The default value for $c$ is 180.

The mixture has the following material property:

Mushy Zone Permeability: For simulations with different phases, the mushy zone permeability for one cell is taken as a volume-weighted average for the whole mixture.

Field Functions

Average Mushy Zone Permeability: The volume-weighted mushy zone permeability of a mixture, which is calculated from the mushy zone permeability of the component phases.
Average Mushy Zone Porous Viscous Resistance: The dynamic viscosity of the mixture divided by Average Mushy Zone Permeability. This field function is provided because the effect of a resistance on the flow is easier to understand than the effect of a permeability.
Mushy Zone Permeability of [phase]: The permeability due to obstruction of the flow by a dendritic mesh resulting from partial solidification of the specific phase. The effect of the dendritic mesh is modeled as a porous medium with spatially varying properties.
Mushy Zone Velocity: The momentum source terms of the Mushy Zone Permeability model enforce a flow velocity equal to the Mushy Zone Velocity.