# 5.2 Thermophysical models

Thermophysical models are used to describe cases where the thermal energy, compressibility or mass transfer is important.

OpenFOAM allows thermophysical properties to be constant, or functions of temperature, pressure and composition. Thermal energy can be described in form of enthalpy or internal energy. The relation can be described with various equations of state or as isobaric system.

The thermophysicalProperties dictionary is read by any solver that uses the thermophysical model library. A thermophysical model is constructed in OpenFOAM as a pressure-temperature system from which other properties are computed. There is one compulsory dictionary entry called thermoType which specifies the complete thermophysical model that is used in the simulation. The thermophysical modelling starts with a layer that defines the basic equation of state and then adds further layers for the thermodynamic, transport and mixture modelling, as listed in Table 5.1.

 Equation of State — equationOfState icoPolynomial Incompressible polynomial equation of state, e.g. for liquids perfectGas Perfect gas equation of state Basic thermophysical properties — thermo eConstThermo Constant specific heat model with evaluation of internal energy and entropy hConstThermo Constant specific heat model with evaluation of enthalpy and entropy hPolynomialThermo evaluated by a function with coefficients from polynomials, from which , are evaluated janafThermo evaluated by a function with coefficients from JANAF thermodynamic tables, from which , are evaluated Derived thermophysical properties — specieThermo specieThermo Thermophysical properties of species, derived from , and/or Transport properties — transport constTransport Constant transport properties polynomialTransport Polynomial based temperature-dependent transport properties sutherlandTransport Sutherland’s formula for temperature-dependent transport properties Mixture properties — mixture pureMixture General thermophysical model calculation for passive gas mixtures homogeneousMixture Combustion mixture based on normalised fuel mass fraction inhomogeneousMixture Combustion mixture based on and total fuel mass fraction veryInhomogeneousMixture Combustion mixture based on , and unburnt fuel mass fraction dieselMixture Combustion mixture based on and basicMultiComponentMixture Basic mixture based on multiple components multiComponentMixture Derived mixture based on multiple components reactingMixture Combustion mixture using thermodynamics and reaction schemes egrMixture Exhaust gas recirculation mixture Thermophysical model — thermoModel hePsiThermo General thermophysical model calculation based on enthalpy or internal energy , and compressibility heRhoThermo General thermophysical model calculation based on enthalpy or internal energy , and density hePsiMixtureThermo Calculates enthalpy for combustion mixture based on enthalpy or internal energy , and heRhoMixtureThermo Calculates enthalpy for combustion mixture based on enthalpy or internal energy , and heheuMixtureThermo Calculates enthalpy or internal energy for unburnt gas and combustion mixture Table 5.1: Layers of thermophysical modelling.

Various combinations are available as ‘packages’, specified using, e.g.

17
18thermoType
19{
20    type            heRhoThermo;
21    mixture         pureMixture;
22    transport       const;
23    thermo          hConst;
24    equationOfState perfectGas;
25    specie          specie;
26    energy          sensibleEnthalpy;
27}
28
29mixture
30{
31    specie
32    {
33        molWeight       28.96;
34    }
35    thermodynamics
36    {
37        Cp              1004.4;
38        Hf              0;
39    }
40    transport
41    {
42        mu              1.831e-05;
43        Pr              0.705;
44    }
45}
46
47
48// ************************************************************************* //

Only certain combinations are predefined. One method to identify the possible combinations from Table 5.1 is to use a nonexistent setting for one of the entries, e.g.banana and execute the solver. OpenFOAM will issue an error message and list all possible combinations to the terminal.

### 5.2.1 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 sub-dictionaries of coefficients, including:

specie
containing i.e. number of moles, nMoles, of the specie, and molecular weight, molWeight in units of g/mol;
thermo
containing coefficients for the chosen thermodynamic model (see below);
transport
containing coefficients for the chosen transport model (see below).

The thermodynamic coefficients are ostensibly concerned with evaluating the specific heat from which other properties are derived. The current thermo models are described as follows:

hConstThermo
assumes a constant and a heat of fusion which is simply specified by a two values , given by keywords Cp and Hf.
eConstThermo
assumes a constant and a heat of fusion which is simply specified by a two values , given by keywords Cv and Hf.
janafThermo
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 5.2. 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: (5.1)

In addition, there are constants of integration, and , both at high and low temperature, used to evaluating and respectively.

hPolynomialThermo
calculates as a function of temperature by a polynomial of any order. The following case provides an example of its use: \$FOAM_TUTORIALS/lagrangian/porousExplicitSourceReactingParcelFoam/filter

 Description Entry Keyword Lower temperature limit Tlow Upper temperature limit Thigh Common temperature Tcommon High temperature coefficients highCpCoeffs (a0 a1 a2 a3 a4... High temperature enthalpy offset a5... High temperature entropy offset a6) Low temperature coefficients lowCpCoeffs (a0 a1 a2 a3 a4... Low temperature enthalpy offset a5... Low temperature entropy offset a6)

Table 5.2: JANAF thermodynamics coefficients.

The transport coefficients are used to to evaluate dynamic viscosity , thermal conductivity and laminar thermal conductivity (for enthalpy equation) . The current transport models are described as follows:

constTransport
assumes a constant and Prandtl number which is simply specified by a two keywords, mu and Pr, respectively.
sutherlandTransport
calculates as a function of temperature from a Sutherland coefficient and Sutherland temperature , specified by keywords As and Ts; is calculated according to: (5.2)

polynomialTransport
calculates and as a function of temperature from a polynomial of any order.

The following is an example entry for a specie named fuel modelled using sutherlandTransport and janafThermo:

fuel
{
specie
{
nMoles       1;
molWeight    16.0428;
}
thermodynamics
{
Tlow         200;
Thigh        6000;
Tcommon      1000;
highCpCoeffs (1.63543 0.0100844 -3.36924e-06 5.34973e-10
-3.15528e-14 -10005.6 9.9937);
lowCpCoeffs  (5.14988 -0.013671 4.91801e-05 -4.84744e-08
1.66694e-11 -10246.6 -4.64132);
}
transport
{
As           1.67212e-06;
Ts           170.672;
}
}
The following is an example entry for a specie named air modelled using constTransport and hConstThermo:

air
{
specie
{
nMoles          1;
molWeight       28.96;
}
thermodynamics
{
Cp              1004.5;
Hf              2.544e+06;
}
transport
{
mu              1.8e-05;
Pr              0.7;
}
}