# POROSITY_MODEL

Specifies a porosity model for the flow equation.

## Type

AcuSolve Command

## Syntax

POROSITY_MODEL("name") {parameters...}

## Qualifier

User-given name.

## Parameters

- type (enumerated) [=none]
- Type of the porosity model.
- none
- No porosity.
- constant or const
- Darcy-Forchheimer porosity model. Requires permeability, darcy_coefficient, forchheimer_coefficient and permeability_direction.

- porosity (real) >0 <=1 [=1]
- Porosity value.
- permeability_type (enumerated) [=cartesian]
- Permeability type.
- cartesian
- Use Cartesian coordinate system to specify permeabilities and directions.
- cylindrical
- Use cylindrical coordinate system to specify permeabilities and directions.
- spherical
- Use spherical coordinate system to specify permeabilities and directions.

- direction_1_permeability (real) [=1]
- direction_2_permeability (real) [=1]
- direction_3_permeability (real) [=1]
- Permeability of the porous media in each of the three orthogonal principal axes. Used with constant type. These commands are valid only when permeability_type=cartesian. Also, these commands are equivalent to the previously used permeability array [={1,1,1}], which has been deprecated. AcuSolve will automatically map the permeability_array to the appropriate direction_1_permeability, direction_2_permeability, and direction_3_permeability parameters when reading an input file that uses the deprecated syntax. Note that if both parameters are specified, this mapping will cause the permeability to take precedence over the values that are specified for direction_1_permeability, direction_2_permeability and direction_3_permeability.
- cartesian_permeability_directions (array) [={1,0,0;0,1,0;0,0,1}]
- Orthogonal principal axes of the permeability values. The vectors are ortho-normalized prior to use. Used with constant type. This command is equivalent to the previously used permeability_direction [={1,0,0;0.1.0;0,0,1}]. Note that if both are specified in the input file, the one that appears last will be used for the computation.
- direction_1_permeability_multiplier_function (string) [=none]
- direction_2_permeability_multiplier_function (string) [=none]
- direction_3_permeability_multiplier_function (string) [=none]
- User-given name of the multiplier function for scaling the permeabilities. If none, no scaling is performed. These commands are valid only when permeability_type = cartesian.
- radial_permeability (real) [=1]
- Radial permeability of the porous media in cylindrical and spherical coordinate systems. This command is valid only when permeability_type = cylindrical or spherical.
- axial_permeability (real) [=1]
- Axial permeability of the porous media in cylindrical coordinate system. This command is valid only when permeability_type = cylindrical.
- tangential_permeability (real) [=1]
- Tangential permeability of the porous media in cylindrical and spherical coordinate systems. This command is valid only when permeability_type = cylindrical or spherical.
- cylindrical_permeability_axis (array) [={0,0.0;1,0,0}]
- Principal axis of the axial permeability value. Other two principal axes in cylindrical coordinate are computed internally and ortho-normalized prior to use.
- radial_permeability_multiplier_function (string) [=none]
- User-given name of the multiplier function for scaling the permeabilities. If none, no scaling is performed. This command is valid only when permeability_type = cylindrical or spherical.
- axial_permeability_multiplier_function (string) [=none]
- User-given name of the multiplier function for scaling the permeabilities. If none, no scaling is performed. This command is valid only when permeability_type = cylindrical.
- tangential_permeability_multiplier_function (string) [=none]
- User-given name of the multiplier function for scaling the permeabilities. If none, no scaling is performed. This command is valid only when permeability_type = cylindrical or spherical.
- spherical_permeability_center (array) [={0,0,0}]
- Spherical center of permeability values. This command is valid only when permeability_type = spherical.
- darcy_coefficient (real) [=0]
- Coefficient of Darcy's (linear) term. Used with constant type.
- forchheimer_coefficient (real) [=0]
- Coefficient of Forchheimer's (quadratic) term. Used with constant type.
- darcy_multiplier_function (string) [=none]
- User-given name of the multiplier function for scaling the Darcy coefficient. If none, no scaling is performed.
- forchheimer_multiplier_function (string) [=none]
- User-given name of the multiplier function for scaling the Forchheimer coefficient. If none, no scaling is performed.
- effectiveness (real) [=1]
- Effectiveness of the flow resistance exerted by the porous medium.This command is valid only when effectiveness_type = constant.
- effectiveness_type (enumerated) [=none]
- Type of the effectiveness of the porous model.
- effectiveness_curve_fit_variable (enumerated) [=temperature]
- Independent variable of the curve fit for effectiveness. Used with piecewise_linear and cubic_spline types.
- effectiveness_curve_fit_values (array) [={0,0}]
- A two-column array of independent-variable/effectiveness data values. Used with piecewise_linear and cubic_spline effectiveness types.

## Description

This command specifies a porosity model for the flow (momentum) equations. This model is only applicable to fluid element sets.

```
POROSITY_MODEL( "my porous media" ) {
type = constant
direction_1_permeability = 1.e-6
direction_2_permeability = 1.e-2
direction_3_permeability = 1.e-6
cartesian_permeability_directions = { 1, 0, 0 ;
0, 1, 0 ;
0, 0, 1 ; }
darcy_coefficient = 0
forchheimer_coefficient = 0.5
}
MATERIAL_MODEL( "my material model" ) {
porosity_model = "my porous media"
...
}
ELEMENT_SET( "fluid elements" ) {
material_model = "my material model"
...
}
```

- Superficial Velocity
- Physical Velocity

where ${C}_{Darcy}$ is the Darcy coefficient, ${C}_{Forch}$ is the Forchheimer coefficient, and $k$ is the permeability.

```
POROSITY_MODEL( "ramped Darcy coefficient" ) {
type = constant
permeability_type = cartesian
direction_1_permeability = 1.e-6
direction_2_permeability = 1.e-2
direction_3_permeability = 1.e-6
cartesian_permeability_directions = { 1, 0, 0 ; 0, 1, 0 ; 0, 0, 1 ; }
darcy_coefficient = 1
forchheimer_coefficient = 0.5
darcy_multiplier_function = "ramped"
}
MULTIPLIER_FUNCTION( "ramped" ) {
type = piecewise_linear
curve_fit_vales = { 1, 0 ; 10, 0.5 }
curve_fit_variable = time_step
}
```

```
POROSITY_MODEL( "ramped Forchheimer coefficient" ) {
type = constant
direction_1_permeability = 1.e-6
direction_2_permeability = 1.e-2
direction_3_permeability = 1.e-6
cartesian_permeability_direction = { 1, 0, 0 ; 0, 1, 0 ; 0, 0, 1 ; }
darcy_coefficient = 0.5
forchheimer_coefficient = 1
forchheimer_multiplier_function = "ramped"
}
```

```
POROSITY_MODEL( "my porous media" ) {
type = constant
permeability_type = cylindrical
radial_permeability = 1.e-6
axial_permeability = 1.e-2
tangential_permeability = 1.e-6
cylindrical_permeability_axis = {0, 0, 0 ; 1, 0, 0 ; }
darcy_coefficient = 1
forchheimer_coefficient = 0.5
}
```

```
POROSITY_MODEL( "my porous media" ) {
type = constant
permeability_type = spherical
radial_permeability = 1.e-2
tangential_permeability = 1.e-6
spherical_permeability_axis = {0, 0, 0 ;
darcy_coefficient = 1
forchheimer_coefficient = 0.5
}
```

The effectiveness parameter may be used to define a multiplicative constant applied to the force f in equations (Equation 4) and (Equation 7). This parameter controls the effectiveness of the porous medium at providing a resistance to the flow. By setting a value of 1, the porous medium fully exerts its resistance to the flow, while by setting a value of 0, no resistance to the flow is applied.

```
POROSITY_MODEL( "ModelforMelting" ) {
type = constant
direction_1_permeability = 1.0
direction_2_permeability = 1.0
direction_3_permeability = 1.0
cartesian_permeability_direction = { 1, 0, 0 ; 0, 1, 0 ; 0, 0, 1}
darcy_coefficient = 5e+8
forchheimer_coefficient = 0
effectiveness_type = piecewise_linear
effectiveness_curve_fit_values = { 0, 1 ; 261.15, 1; 263.15, 0; 1000, 0 }
effectiveness_curve_fit_variable = temperature
```