7.1 Thermophysical models
Thermophysical models are concerned with energy, heat and physical properties. The thermophysicalProperties dictionary is read by any solver that uses the thermophysical model library. A thermophysical model is constructed in OpenFOAM as a pressuretemperature system from which other properties are computed. There is one compulsory dictionary entry called thermoType which specifies the package of thermophysical modelling that is used in the simulation. OpenFOAM includes a large set of precompiled combinations of modelling, built within the code using C++ templates. This coding approach assembles thermophysical modelling packages beginning with the equation of state and then adding more layers of thermophysical modelling that derive properties from the previous layer(s). The keyword entries in thermoType reflects the multiple layers of modelling and the underlying framework in which they combined. Below is an example entry for thermoType:
{
type hePsiThermo;
mixture pureMixture;
transport const;
thermo hConst;
equationOfState perfectGas;
specie specie;
energy sensibleEnthalpy;
}
The keyword entries specify the choice of thermophysical models, e.g. constant transport (constant viscosity, thermal diffusion), Perfect Gas equationOfState, etc. In addition there is a keyword entry named energy that allows the user to specify the form of energy to be used in the solution and thermodynamics. The following sections explains the entries and options in the thermoType package.
7.1.1 Thermophysical and mixture models
Each solver that uses thermophysical modelling constructs an object of a particular thermophysical model class. The model classes are listed below.
 psiThermo
 Thermophysical model for fixed composition, based on compressibility , where is Gas Constant and is temperature. The solvers that construct psiThermo include the compressible family of solvers (sonicFoam, simpleFoam, etc. , excluding rhoPorousSimpleFoam) and uncoupledKinematicParcelFoam and coldEngineFoam.
 rhoThermo
 Thermophysical model for fixed composition, based on density . The solvers that construct rhoThermo include the heatTransfer family of solvers (buoyantSimpleFoam, CHT solvers, etc. , excluding Boussinesq solvers) and rhoPorousSimpleFoam, twoPhaseEulerFoam and thermoFoam.
 psiReactionThermo
 Thermophysical model for reacting mixture, based on . The solvers that construct psiReactionThermo include many of the combustion solvers, e.g. sprayFoam, chemFoam, fireFoam and reactingFoam, and some lagrangian solvers, e.g. coalChemistryFoam and reactingParcelFilmFoam.
 psiuReactionThermo
 Thermophysical model for combustion, based on compressibility of unburnt gas . The solvers that construct rhoReactionThermo include some combustion solvers, e.g. rhoReactingFoam, rhoReactingBuoyantFoam, and some lagrangian solvers, e.g. reactingParcelFoam and simpleReactingParcelFoam.
 rhoReactionThermo
 Thermophysical model for reacting mixture, based on . The solvers that construct psiuReactionThermo include combustion solvers that model combustion based on laminar flame speed and regress variable, e.g. XiFoam, PDRFoam and engineFoam.
 multiphaseMixtureThermo
 Thermophysical models for multiple phases. The solvers that construct multiphaseMixtureThermo include compressible multiphase interfacecapturing solvers, e.g. compressibleInterFoam, and compressibleMultiphaseInterFoam.
The type keyword specifies the underlying thermophysical model. Options are listed below.
 hePsiThermo: for solvers that construct psiThermo and psiReactionThermo.
 heRhoThermo: for solvers that construct rhoThermo, rhoReactionThermo and multiphaseMixtureThermo.
 heheuPsiThermo: for solvers that construct psiuReactionThermo.
The mixture specifies the mixture composition. The option typically used for thermophysical models without reactions is pureMixture, which represents a mixture with fixed composition. When pureMixture is specified, the thermophysical models coefficients are specified within a subdictionary called mixture.
For mixtures with variable composition, required by thermophysical models with reactions, the reactingMixture option is used. Species and reactions are listed in a chemistry file, specified by the foamChemistryFile keyword. The reactingMixture model then requires the thermophysical models coefficients to be specified for each specie within subdictionaries named after each specie, e.g. O2, N2.
For combustion based on laminar flame speed and regress variables, constituents are a set of mixtures, such as fuel, oxidant and burntProducts. The available mixture models for this combustion modelling are homogeneousMixture, inhomogeneousMixture and veryInhomogeneousMixture.
Other models for variable composition are egrMixture, multiComponentMixture and singleStepReactingMixture.
7.1.2 Transport model
The transport modelling concerns evaluating dynamic viscosity , thermal conductivity and thermal diffusivity (for internal energy and enthalpy equations). The current transport models are as follows:
 const
 assumes a constant and Prandtl number which is simply specified by a two keywords, mu and Pr, respectively.
 sutherland
 calculates as a function of temperature from a Sutherland coefficient and Sutherland temperature , specified by keywords As and Ts; is calculated according to:
(7.1)  polynomial
 calculates and as a function of temperature from a polynomial of any order , e.g. :
(7.2)
7.1.3 Thermodynamic models
The thermodynamic models are concerned with evaluating the specific heat from which other properties are derived. The current thermo models are as follows:
 hConst
 assumes a constant and a heat of fusion which is simply specified by a two values , given by keywords Cp and Hf.
 eConst
 assumes a constant and a heat of fusion which is simply specified by a two values , given by keywords Cv and Hf.
 janaf
 calculates as a function of temperature from a set of coefficients taken from JANAF tables of thermodynamics. The ordered list of coefficients is given in Table 7.1. The function is valid between a lower and upper limit in temperature and respectively. Two sets of coefficients are specified, the first set for temperatures above a common temperature (and below , the second for temperatures below (and above ). The function relating to temperature is:
(7.3) In addition, there are constants of integration, and , both at high and low temperature, used to evaluating and respectively.
 hPolynomial
 calculates as a function of temperature by a polynomial of any order :
(7.4) The following case provides an example of its use: $FOAM_TUTORIALS/lagrangian/porousExplicitSourceReactingParcelFoam/filter
7.1.4 Composition of each constituent
There is currently only one option for the specie model which specifies the composition of each constituent. That model is itself named specie, which is specified by the following entries.
 nMoles: number of moles of component. This entry is only used for combustion modelling based on regress variable with a homogeneous mixture of reactants; otherwise it is set to 1.
 molWeight in grams per mole of specie.
7.1.5 Equation of state
The following equations of state are available in the thermophysical modelling library.
 rhoConst
 Constant density:
(7.5)  perfectGas
 Perfect gas:
(7.6)  incompressiblePerfectGas
 Perfect gas for an incompressible fluid:
(7.7) where is a reference pressure.
 perfectFluid
 Perfect fluid:
(7.8) where is the density at .
 linear
 Linear equation of state:
(7.9) where is compressibility (not necessarily ).
 adiabaticPerfectFluid
 Adiabatic perfect fluid:
(7.10) where are reference density and pressure respectively, and is a model constant.
 PengRobinsonGas
 Peng Robinson equation of state:
(7.11) where the complex function can be referenced in the source code in PengRobinsonGasI.H, in the $FOAM_SRC/thermophysicalModels/specie/equationOfState/ directory.
 icoPolynomial
 Incompressible, polynomial equation of state:
(7.12) where are polynomial coefficients of any order .
7.1.6 Selection of energy variable
The user must specify the form of energy to be used in the solution, either internal energy and enthalpy , and in forms that include the heat of formation or not. This choice is specified through the energy keyword.
We refer to absolute energy where heat of formation is included, and sensible energy where it is not. For example absolute enthalpy is related to sensible enthalpy by

(7.13) 
where and are the molar fraction and heat of formation, respectively, of specie . In most cases, we use the sensible form of energy, for which it is easier to account for energy change due to reactions. Keyword entries for energy therefore include e.g. sensibleEnthalpy, sensibleInternalEnergy and absoluteEnthalpy.
7.1.7 Thermophysical property data
The basic thermophysical properties are specified for each species from input data. Data entries must contain the name of the specie as the keyword, e.g. O2, H2O, mixture, followed by subdictionaries of coefficients, including:
 specie
 containing i.e. number of moles, nMoles, of the specie, and molecular weight, molWeight in units of g/mol;
 thermodynamics
 containing coefficients for the chosen thermodynamic model (see below);
 transport
 containing coefficients for the chosen tranpsort model (see below).
The following is an example entry for a specie named fuel modelled using sutherland transport and janaf thermodynamics:
{
specie
{
nMoles 1;
molWeight 16.0428;
}
thermodynamics
{
Tlow 200;
Thigh 6000;
Tcommon 1000;
highCpCoeffs (1.63543 0.0100844 3.36924e06 5.34973e10
3.15528e14 10005.6 9.9937);
lowCpCoeffs (5.14988 0.013671 4.91801e05 4.84744e08
1.66694e11 10246.6 4.64132);
}
transport
{
As 1.67212e06;
Ts 170.672;
}
}
The following is an example entry for a specie named air modelled using const transport and hConst thermodynamics:
{
specie
{
nMoles 1;
molWeight 28.96;
}
thermodynamics
{
Cp 1004.5;
Hf 2.544e+06;
}
transport
{
mu 1.8e05;
Pr 0.7;
}
}