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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 pressure-temperature 
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 pre-compiled 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:
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
The most general solvers that use thermophysical modelling construct a fluidThermo model that allows the user to specify the thermophysical model through the type entry (described below) at run-time. These solvers include rhoSimpleFoam, rhoPorousSimpleFoam and rhoPimpleFoam.
Each solver that uses thermophysical modelling constructs an object of a specific 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 rhoCentralFoam, uncoupledKinematicParcelFoam and
coldEngineFoam.
- rhoThermo
- Thermophysical model for fixed composition, based on density
. The solvers that construct rhoThermo include
the buoyantSimpleFoam, buoyantPimpleFoam, 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, engineFoam, fireFoam and
reactingFoam, and some lagrangian solvers, e.g. coalChemistryFoam.
- psiuReactionThermo
- Thermophysical model for combustion, based on
compressibility of unburnt gas
. The solvers that construct
psiuReactionThermo include combustion solvers that model combustion
based on laminar flame speed and regress variable, e.g.XiFoam,
XiEngineFoam, PDRFoam.
- rhoReactionThermo
- Thermophysical model for reacting
mixture, based on
. The solvers that construct rhoReactionThermo
include chtMultiRegionFoam, some combustion solvers, e.g.chemFoam,
rhoReactingFoam, rhoReactingBuoyantFoam, and some lagrangian
solvers, e.g. reactingParcelFoam and simpleReactingParcelFoam.
- multiphaseMixtureThermo
- Thermophysical models for multiple phases. The solvers that construct multiphaseMixtureThermo include compressible multiphase interface-capturing 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 sub-dictionary 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 sub-dictionaries 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) - logPolynomial
- calculates
and 
as a function of 
from a
polynomial of any order 
; from which 
, 
are calculated by taking
the exponential, e.g.: ![N∑- 1
ln(μ) = ai[ln(T )]i.
i=0
\relax \special {t4ht=](img/user462x.png)
(7.3)
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:
In addition, there are constants of integration,
(7.4) 
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 
: 
(7.5) - ePolynomial
- calculates
as a function of temperature by a polynomial of any
order 
: 
(7.6) - hPower
- calculates
as a power of temperature according to: 
(7.7) - ePower
- calculates
as a power of temperature according to: 
(7.8) - hTabulated
- calculates
by interpolating tabulated data of 
value pairs,
e.g.:
Cp ( (200 1005) (400 1020) );
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:
(7.9) - perfectGas
- Perfect gas:
(7.10) - icoTabulated
- Tabulated data for an incompressible fluid using
value pairs,
e.g.
rho ( (200 1010) (400 980) ); - incompressiblePerfectGas
- Perfect gas for an incompressible fluid:
where
(7.11) 
is a reference pressure.
- perfectFluid
- Perfect fluid:
where
(7.12) 
is the density at 
.
- linear
- Linear equation of state:
where
(7.13) 
is compressibility (not necessarily 
).
- adiabaticPerfectFluid
- Adiabatic perfect fluid:
where
(7.14) 
are reference density and pressure respectively, and 
is a
model constant.
- Boussinesq
- Boussinesq approximation
where![ρ = ρ0[1 - β (T - T0)]
\relax \special {t4ht=](img/user519x.png)
(7.15) 
is the coeffient of volumetric expansion and 
is the reference
density at reference temperature 
.
- PengRobinsonGas
- Peng Robinson equation of state:
where the complex function
(7.16) 
can be referenced in the source code in
PengRobinsonGasI.H, in the $FOAM_SRC/thermophysicalModels/specie/equationOfState/
directory.
- icoPolynomial
- Incompressible, polynomial equation of state:
where
(7.17) 
are polynomial coefficients of any order 
.
- rPolynomial
- Reciprocal polynomial equation of state for liquids and solids:
where
(7.18) 
are coefficients.
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
 | (7.19) |
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 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;
- 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:
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;
}
}
air
{
specie
{
nMoles 1;
molWeight 28.96;
}
thermodynamics
{
Cp 1004.5;
Hf 2.544e+06;
}
transport
{
mu 1.8e-05;
Pr 0.7;
}
}
