Thermophysical models

7.1 Thermophysical models

Thermophysical models are concerned with the 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 p - T  \relax \special {t4ht= 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 more layers of modelling that derive properties from the previous layer(s). The naming of the thermoType reflects these multiple layers of modelling as listed in Table 7.1.

Equation of State equationOfState


adiabaticPerfectFluid

Adiabatic perfect gas equation of state

icoPolynomial

Incompressible polynomial equation of state, e.g. for liquids

perfectFluid

Perfect gas equation of state

incompressiblePerfectGas

Incompressible gas equation of state using a constant reference pressure. Density only varies with temperature and composition

rhoConst

Constant density equation of state

Basic thermophysical properties thermo


eConstThermo

Constant specific heat cp  \relax \special {t4ht= model with evaluation of internal energy e  \relax \special {t4ht= and entropy s  \relax \special {t4ht=

hConstThermo

Constant specific heat cp  \relax \special {t4ht= model with evaluation of enthalpy h  \relax \special {t4ht= and entropy s  \relax \special {t4ht=

hPolynomialThermo

cp  \relax \special {t4ht= evaluated by a function with coefficients from polynomials, from which h  \relax \special {t4ht=, s  \relax \special {t4ht= are evaluated

janafThermo

cp  \relax \special {t4ht= evaluated by a function with coefficients from JANAF thermodynamic tables, from which h  \relax \special {t4ht=, s  \relax \special {t4ht= are evaluated

Derived thermophysical properties specieThermo


specieThermo

Thermophysical properties of species, derived from c
 p  \relax \special {t4ht=, h  \relax \special {t4ht= and/or s  \relax \special {t4ht=

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 b  \relax \special {t4ht=

inhomogeneousMixture

Combustion mixture based on b  \relax \special {t4ht= and total fuel mass fraction f
 t  \relax \special {t4ht=

veryInhomogeneousMixture

Combustion mixture based on b  \relax \special {t4ht=, ft  \relax \special {t4ht= and unburnt fuel mass fraction fu  \relax \special {t4ht=

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

singleStepReactingMixture

Single step reacting mixture

Thermophysical model thermoModel


hePsiThermo

General thermophysical model calculation based on compressibility ψ  \relax \special {t4ht=

heRhoThermo

General thermophysical model calculation based on density ρ  \relax \special {t4ht=

psiReactionThermo

Calculates enthalpy for combustion mixture based on ψ  \relax \special {t4ht=

psiuReactionThermo

Calculates enthalpy for combustion mixture based on ψu  \relax \special {t4ht=

rhoReactionThermo

Calculates enthalpy for combustion mixture based on ρ  \relax \special {t4ht=

heheupsiReactionThermo

Calculates enthalpy for unburnt gas and combustion mixture

Table 7.1: Layers of thermophysical modelling.

The following 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 energy can be internal energy or enthalpy and in forms that include the heat of formation Δhf  \relax \special {t4ht= or not. We refer to absolute energy where heat of formation is included, and sensible energy where it is not. For example absolute enthalpy h  \relax \special {t4ht= is related to sensible enthalpy hs  \relax \special {t4ht= by
         ∑
h = hs +     ciΔhi
          i      f
\relax \special {t4ht=
(7.1)

where ci  \relax \special {t4ht= and hif  \relax \special {t4ht= are the molar fraction and heat of formation, respectively, of specie i  \relax \special {t4ht=. 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.

7.1.1 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;
thermodynamics
containing coefficients for the chosen thermodynamic model (see below);
transport
containing coefficients for the chosen tranpsort model (see below).

The thermodynamic coefficients are ostensibly concerned with evaluating the specific heat cp  \relax \special {t4ht= from which other properties are derived. The current thermo models are described as follows:

hConstThermo
assumes a constant cp  \relax \special {t4ht= and a heat of fusion Hf  \relax \special {t4ht= which is simply specified by a two values cp Hf  \relax \special {t4ht=, given by keywords Cp and Hf.
eConstThermo
assumes a constant cv  \relax \special {t4ht= and a heat of fusion Hf  \relax \special {t4ht= which is simply specified by a two values cv Hf  \relax \special {t4ht=, given by keywords Cv and Hf.
janafThermo
calculates cp  \relax \special {t4ht= as a function of temperature T  \relax \special {t4ht= from a set of coefficients taken from JANAF tables of thermodynamics. The ordered list of coefficients is given in Table 7.2. The function is valid between a lower and upper limit in temperature Tl  \relax \special {t4ht= and Th  \relax \special {t4ht= respectively. Two sets of coefficients are specified, the first set for temperatures above a common temperature Tc  \relax \special {t4ht= (and below Th  \relax \special {t4ht=, the second for temperatures below Tc  \relax \special {t4ht= (and above Tl  \relax \special {t4ht=). The function relating cp  \relax \special {t4ht= to temperature is:
cp = R((((a4T + a3)T +  a2)T + a1)T + a0)
      \relax \special {t4ht=
(7.2)

In addition, there are constants of integration, a5   \relax \special {t4ht= and a6   \relax \special {t4ht=, both at high and low temperature, used to evaluating h  \relax \special {t4ht= and s  \relax \special {t4ht= respectively.

hPolynomialThermo
calculates C
  p  \relax \special {t4ht= 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 T  (K )
 l  \relax \special {t4ht= Tlow
Upper temperature limit T  (K )
 h  \relax \special {t4ht= Thigh
Common temperature T  (K)
 c  \relax \special {t4ht= Tcommon
High temperature coefficients a ...a
 0    4   \relax \special {t4ht= highCpCoeffs (a0 a1 a2 a3 a4...
High temperature enthalpy offset a5   \relax \special {t4ht= a5...
High temperature entropy offset a6   \relax \special {t4ht= a6)
Low temperature coefficients a0...a4   \relax \special {t4ht= lowCpCoeffs (a0 a1 a2 a3 a4...
Low temperature enthalpy offset a5   \relax \special {t4ht= a5...
Low temperature entropy offset a6   \relax \special {t4ht= a6)




Table 7.2: JANAF thermodynamics coefficients.

The transport coefficients are used to to evaluate dynamic viscosity μ  \relax \special {t4ht=, thermal conductivity κ  \relax \special {t4ht= and laminar thermal conductivity (for enthalpy equation) α  \relax \special {t4ht=. The current transport models are described as follows:

constTransport
assumes a constant μ  \relax \special {t4ht= and Prandtl number Pr = c μ ∕κ
      p  \relax \special {t4ht= which is simply specified by a two keywords, mu and Pr, respectively.
sutherlandTransport
calculates μ  \relax \special {t4ht= as a function of temperature T  \relax \special {t4ht= from a Sutherland coefficient As  \relax \special {t4ht= and Sutherland temperature Ts  \relax \special {t4ht=, specified by keywords As and Ts; μ  \relax \special {t4ht= is calculated according to:
      A √T--
μ = ---s-----
    1 + Ts∕T
      \relax \special {t4ht=
(7.3)

polynomialTransport
calculates μ  \relax \special {t4ht= and κ  \relax \special {t4ht= as a function of temperature T  \relax \special {t4ht= 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;
    }
}

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