Compute properties of materials

Compute local properties of materials (density, viscosity, etc.) from geometry, equation of state and reference properties of materials. More...

Namespaces
module	mod_linearized_enthalpy_functions
	Temperature-Enthalpy functions for the Linearized Enthalpy method.
module	mod_material_properties_boundary_conditions
	Boundary conditions related routines for materials.
module	fields_material_properties
	Local properties of material defined on cells or faces.
module	mod_temperature_enthalpy_functions
	Temperature-Enthalpy functions for the Apparent Heat Capacity method.
module	variables_material_properties
	Declaration of local properties of the materials involved in the simulation (density, conductivity, viscosity, etc.)

Classes
type	type_material_reference_properties::material_reference_properties
	Definition of the reference properties of a material. More...

Enumerations
enum	{ type_material_reference_properties::rheology_fluid , type_material_reference_properties::rheology_solid , type_material_reference_properties::rheology_porous_medium }
	Enumaration associated to the rheology of a material. More...
enum	{   type_material_reference_properties::eos_constant , type_material_reference_properties::eos_perfect_gas , type_material_reference_properties::eos_stiffened_gas , type_material_reference_properties::eos_isentropic ,   type_material_reference_properties::eos_peng_robinson , type_material_reference_properties::eos_linear_acoustic , type_material_reference_properties::eos_linear_temperature , type_material_reference_properties::eos_linear_concentration ,   type_material_reference_properties::eos_linear_temperature_concentration , type_material_reference_properties::eos_coolprop }
	Enumaration associated to the equation of stage. More...

Functions
subroutine, public	mod_compute_material_properties::compute_material_properties ()
	Compute local material properties.
subroutine	mod_compute_material_properties::compute_property_sutherland_law (temperature, material_law, local_field)
	Compute a material property \( X \) according to a sutherland law of the temperature :
subroutine	mod_compute_material_properties::compute_property_polynomial_temperature_nist_law (temperature, material_law, local_field)
	Compute a material property \( X \) according to a polynomial law of the temperature proposed by refprop NIST:
subroutine	mod_compute_material_properties::compute_property_polynomial_temperature_law (temperature, material_law, local_field)
	Compute a material property \( X \) according to a polynomial law of the temperature :
subroutine	mod_compute_material_properties::compute_property_neural_network (pressure, temperature, material_law, reference_pressure, local_field)
	Compute a material property \( X \) according to a neural_network function of the pressure and the temperature :
subroutine	mod_predict_material_properties::predict_material_properties ()
	Compute time extrapolation of material properties.

Detailed Description

Compute local properties of materials (density, viscosity, etc.) from geometry, equation of state and reference properties of materials.

Introduction

Compute local properties of materials (density, viscosity, etc.) from geometry, equation of state and reference properties of materials.

                         ┌───────────────┐
                         │  Temperature  │
                         │ Concentration │
                         │      etc.     │
                         └───────────────┘
                                 ↓
┌───────────────┐         ┏━━━━━━━━━━━━━┓          ┌──────────────┐
│   Reference   │         ┃ Equation of ┃          │   Geometry   │
│ properties of │ ───────>┃    state    ┃ <─────── │ (e.g. volume │
│   materials   │         ┃    (EoS)    ┃          │   faction)   │
└───────────────┘         ┗━━━━━━━━━━━━━┛          └──────────────┘
                                 ↓
                         ┌───────────────┐
                         │     Local     │
                         │ properties of │
                         │   materials   │
                         └───────────────┘

Non-exhaustive list of reference properties:

• Density \( \rho_0 \)
• Viscosity \( \mu \)
• Thermal expansion \( \beta_{T} \)
• Specific heat capacity \( C_{p} \)

1-fluid model

When multiple materials are involved in the simulation, the properties ( \( \rho, \mu, C_{p}, \lambda, etc.) \) are locally computed from the volume fraction of materials \( f_i \) (possibly smoothed) according to the following formula:

\[ \phi = \sum_{i=1}^{n} \phi_{i} f_{i} \]

where \( \phi_{i} \) denotes any property of material \( i \) such as density or conductivity.

Depending on the modeling, density may vary linearly with temperature and species concentration \( C_i \):

\[ \rho = \rho_0(1 - \beta_T(T - T_0) + \sum_{i=1}^{m} \beta_{C_i} (C_i - C_{i_0})) \]

When driving pressure is considered (defined as \( \nabla p^* = \nabla p - \rho_0 \bf{g} \)), previous equation reads:

\[ \rho = \rho_0(- \beta_T(T - T_0) + \sum_{i=1}^{m} \beta_{C_i} (C_i - C_{i_0})) \]

Enumeration Type Documentation

anonymous enum

anonymous enum

Enumaration associated to the rheology of a material.

Enumerator
rheology_fluid	The material is a fluid.
rheology_solid	The material is a solid.
rheology_porous_medium	The material is a porous medium.

anonymous enum

anonymous enum

Enumaration associated to the equation of stage.

Enumerator
eos_constant	Thermodynamic variables are constant.
eos_perfect_gas	Perfect gas.
eos_stiffened_gas	Stiffened gas.
eos_isentropic	Isentropic.
eos_peng_robinson	Peng-Robinson.
eos_linear_acoustic	Linear acoustic.
eos_linear_temperature	Linear temperature (Boussinesq)
eos_linear_concentration	Linear concentration (Boussinesq)
eos_linear_temperature_concentration	Linear temperature concentration (Boussinesq)
eos_coolprop	Coolprop.

Function Documentation

compute_property_neural_network()

subroutine mod_compute_material_properties::compute_property_neural_network ( double precision, dimension(:,:,:), intent(in), allocatable pressure, double precision, dimension(:,:,:), intent(in), allocatable temperature, type(t_material_law), intent(in) material_law, double precision, intent(in) reference_pressure, double precision, dimension(:,:,:), intent(inout), allocatable local_field )

private

Compute a material property \( X \) according to a neural_network function of the pressure and the temperature :

\[ X^{*,n+1}(p^*,T^*) =\alpha(w^n \cdot X^{*,n} + b^n) \]

with \( \alpha \) the activation function (could be sigmoid or tanh), \( X^*, p^*,T^* \) respectively the dimensional computed field, pressure and temperature, \( w^n, X^{*,n}, b^n \) the weights, dimensionless field and bias at neural network layer \( n \).

compute_property_polynomial_temperature_law()

subroutine mod_compute_material_properties::compute_property_polynomial_temperature_law ( double precision, dimension(:,:,:), intent(in), allocatable temperature, type(t_material_law), intent(in) material_law, double precision, dimension(:,:,:), intent(inout), allocatable local_field )

private

Compute a material property \( X \) according to a polynomial law of the temperature :

\[ X(T) =\sum_{i=0}^{4} a_i T^i + a_5 T^5 \]

with \( p \) the degree of the polynom and \( T \) the temperature field.

compute_property_polynomial_temperature_nist_law()

subroutine mod_compute_material_properties::compute_property_polynomial_temperature_nist_law ( double precision, dimension(:,:,:), intent(in), allocatable temperature, type(t_material_law), intent(in) material_law, double precision, dimension(:,:,:), intent(inout), allocatable local_field )

private

Compute a material property \( X \) according to a polynomial law of the temperature proposed by refprop NIST:

\[ X(T) =\sum_{i=0}^{p-2} a_i (T/1000)^i + a_{p-1} (T/1000)^{-2} \]

with \( p \) the degree of the polynom and \( T \) the temperature field.

compute_property_sutherland_law()

subroutine mod_compute_material_properties::compute_property_sutherland_law ( double precision, dimension(:,:,:), intent(in), allocatable temperature, type(t_material_law), intent(in) material_law, double precision, dimension(:,:,:), intent(inout), allocatable local_field )

private

Compute a material property \( X \) according to a sutherland law of the temperature :

\[ X(T) = X^* \Big( \frac{T}{T^*} \Big)^{3/2} \frac{T^* + S}{T + S} \]

with \( X^* \), \( T^* \), \( S \), the coefficients of the law material_lawcoef = [ \( X^* \), \( T^* \), \( S \)]