Solids model

Specifying the solids types and their properties. Every type uses the solids model set by solids.model (see particle options); the model inputs are described in DEM model and PIC model.

	Description	Type	Default
solids	Specified name(s) of the solids types or None to disable the solids solver. The user-defined names are used to specify the type inputs, such as restitution coefficients.	Strings	None
solids.species	Specify which species can constitute the solids phase. Defined species must be a subset of the species defined in species.	Strings	None

Specific heat

The following inputs are defined with the prefix [solid_name].specific_heat:

	Description	Type	Default
model	Specify which specific heat model to use for solids. A specific heat model is required if advecting enthalpy. Furthermore, the model must be mixture if species equations are solved. Options: constant - constant solid specific heat NASA7-poly the solid specific heat is defined by NASA-7 polynomials. NASA7 polynomial format: \(c_p(T)/R = \sum_{i=0}^4 a_{i}T^{i}\) Additional information on NASA-7 polynomials is provided in species specific heats. mixture - a mixture specific heat is computed from species specific heats and local species mass fractions. \(c_{p,\mathrm{mixture}} = \sum_n X_n c_{p,n}\)	String	constant
constant	Constant solids specific heat value. A value is required for constant specific heat model.	Real	0
NASA7.a[i]	Specific heat polynomial coefficients. Polynomial coefficients are required if the fluid specific heat model is NASA7-poly. Additional information on NASA-7 polynomials is provided in species specific heats.	Reals	None
NASA7.Tsplit	Defines the transition temperature between NASA-7 polynomials. If there are N sets of coefficients for N temperature ranges, then N-1 transition temperatures must be specified. In the standard case of two temperature ranges, a transition temperature of 1000K is assumed if Tsplit is not provided.	Reals	1000
ignore_discontinuities	Ignore discontinuities in NASA-7 polynomials at transition temperatures (Tsplit). More information is provided in species specific heats.	Int	0

The following inputs are defined with the prefix [solid_name]:

	Description	Type	Default
molecular_weight	Value of constant solid molecular weight.	Real	0
enthalpy_of_formation	Enthalpy of formation of solids. Only used when the solids specific heat model is constant.	Real	0
reference_temperature	Reference temperature used to compute solids specific enthalpy when using constant solids specific heat model or mixture model with constant model for species.	Real	298.0

Thermal conductivity

The following inputs are defined using the prefix [solid_name].thermal_conductivity.

	Description	Type	Default
model	Specify the thermal conductivity model. Options: constant - constant thermal conductivity Sutherland [Sut93] - \(\displaystyle\kappa(T) = \kappa_{ref}\left(\frac{T}{T_{ref}}\right)^{3/2}\times\frac{(T_{ref}+S)}{(T+S)}\) power_law : Power law formulation \(\displaystyle\kappa(T) = \left(\frac{T}{T_{ref}}\right)^n\) A thermal conductivity model is required if advecting enthalpy.	String	None
constant	Value of constant thermal conductivity.	Real	None
Sutherland.T_ref	Sutherland model reference temperature.	Real	None
Sutherland.k_ref	Sutherland model reference conductivity at T_ref.	Real	None
Sutherland.S	Sutherland model temperature.	Real	None
power_law.T_ref	Power law model reference temperature.	Real	None
power_law.exponent	Power law model exponent \(n\)	Real	None

The following inputs are defined with the prefix solids:

	Description	Type	Default
min_conduction_dist	The surface roughness separating two touching particles. This value is used to remove the singularity that the particle-fluid-particle conduction model develops at the contact interface.	Real	2.e-8
flpc	The fluid lens proportionality constant (flpc) is used to calculate the radius of the fluid lens surrounding the particle for particle-fluid-particle conduction.	Real	0.4

Radiation

The following inputs are defined using the prefix [solid_name].radiation.

	Description	Type	Default
scattering_factor	Particle scattering factor.	Real	None
emissivity.model	Specify which radiation emissivity coefficient model to use for the solid. Options: gray-poly - Emissivity is defined by a temperature-dependent polynomial (0-5th order). Piecewise polynomials are defined by specifying temperature ranges. An emissivity model is required if radiation is enabled.	String	None

Gray polynomial

The following inputs are defined using the prefix [solid_name].radiation.emissivity.

	Description	Type	Default
form	Specifies the polynomial form used to represent the absorption coefficient as a function of temperature. Options: 0 - Absorption coefficient is defined as a polynomial in temperature. \(\displaystyle a(T) = a_0 + a_1 T + a_2 T^2 + \ldots\) 1 - Absorption coefficient is defined as a polynomial in the inverse of temperature. \(\displaystyle a(T) = a_0 + a_1 / T + a_2 / T^2 + \ldots\)	Int	0
T_range	Valid temperature range for the polynomial. If no temperature is provided, then the polynomial is assumed valid for all temperatures. Piecewise polynomials are defined by specify multiple ranges. For example, two piecewise polynomials can be specified by providing three temperatures: low, mid and high.	Reals	None
polynomial_coeffs	Polynomial coefficient. Polynomials can be up to 5-th order, and a set of polynomial coefficients must be defined for each temperature range.	Reals	None

Example: Constant valued emissivity

A constant value is used over the entire valid temperature range.:

solid0.radiation.absorption.model = gray-poly
solid0.radiation.absorption.polynomial_coeffs = 0.9

Density

The following inputs are defined with the prefix solids:

	Description	Type	Default
density	Specify which density model to use for solids. Options (case-insensitive): None - solids density specified through initial and boundary conditions; Mixture - solids density computed as a weighted average of the solid phase species densities. It requires constant species densities to be defined by the user.	String	None

Newton solver

The following inputs are defined with the prefix solids:

	Description	Type	Default
newton_solver.absolute_tol	Define absolute tolerance for damped Newton solver.	Real	1.e-6
newton_solver.relative_tol	Define relative tolerance for damped Newton solver.	Real	1.e-6
newton_solver.max_iterations	Define max number of iterations for damped Newton solver.	Int	100