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OpenFOAM 1.5 User Guide © 2000-2008 OpenCFD Ltd

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  \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 7.1.

Equation of State -- equationOfState


perfectGas

Perfect gas equation of state

Basic thermophysical properties -- thermo


hConstThermo

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

janafThermo

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

Derived thermophysical properties -- specieThermo


specieThermo

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

Transport properties -- transport


constTransport

Constant 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  \special {t4ht=

inhomogeneousMixture

Combustion mixture based on b  \special {t4ht= and total fuel mass fraction ft  \special {t4ht=

veryInhomogeneousMixture

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

dieselMixture

Combustion mixture based on ft  \special {t4ht= and fu  \special {t4ht=

multiComponentMixture

Combustion mixture based on multiple components [**]

chemkinMixture

Combustion mixture using CHEMKIN thermodynamics and reaction schemes database files

Thermophysical model -- thermoModel


hThermo

General thermophysical model calculation based on enthalpy h  \special {t4ht=

hMixtureThermo

Calculates enthalpy for combustion mixture

hhuMixtureThermo

Calculates enthalpy for unburnt gas and combustion mixture

Table 7.1: Layers of thermophysical modelling.

The thermoType entry takes the form:


    thermoModel<mixture<transport<specieThermo<thermo<equationOfState>>>>>
so that the following is an example entry for thermoType:


    hThermo<pureMixture<constTransport<specieThermo<hConstThermo<perfectGas>>>>>

7.1.1 Thermophysical property data

The basic thermophysical properties are specified for each species from input data. The data is specified using a compound entry with the following format for a specie accessed through the keyword mixture:


    mixture <specieCoeffs> <thermoCoeffs> <transportCoeffs>
The specie coefficients <specieCoeffs> contains the entries listed in 7.2 in the order that they are specified in input.


Description Entry


String name e.g.mixture
Number of moles of this specie nmoles  \special {t4ht=
Molecular weight W  (kg/kmol)  \special {t4ht=



Table 7.2: Specie coefficients.

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

hConstThermo
assumes a constant c
 p  \special {t4ht= and a heat of fusion H
  f  \special {t4ht= which is simply specified by a two values cp Hf  \special {t4ht= following the <specieCoeffs>.
janafThermo
calculates cp  \special {t4ht= as a function of temperature T  \special {t4ht= from a set of coefficients taken from JANAF tables of thermodynamics. The ordered list of coefficients is given in 7.3. The function is valid between a lower and upper limit in temperature T
 l  \special {t4ht= and T
 h  \special {t4ht= respectively. Two sets of coefficients are specified, the first set for temperatures above a common temperature Tc  \special {t4ht= (and below Th  \special {t4ht=, the second for temperatures below Tc  \special {t4ht= (and above Tl  \special {t4ht=). The function relating cp  \special {t4ht= to temperature is:
c =  R((((a T + a )T +  a )T + a )T + a )
 p         4      3      2      1       0
      \special {t4ht=
(7.1)

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


Description Entry


Lower temperature limit Tl (K)  \special {t4ht=
Upper temperature limit Th (K)  \special {t4ht=
Common temperature Tc (K)  \special {t4ht=
High temperature coefficients a0...a4   \special {t4ht=
High temperature enthalpy offset a5   \special {t4ht=
High temperature entropy offset a6   \special {t4ht=
Low temperature coefficients a0...a4   \special {t4ht=
Low temperature enthalpy offset a5   \special {t4ht=
Low temperature entropy offset a6   \special {t4ht=



Table 7.3: JANAF thermodynamics coefficients.

The transport coefficients <transportCoeffs> are used to to evaluate dynamic viscosity m  \special {t4ht=, thermal conductivity k  \special {t4ht= and laminar thermal conductivity (for enthalpy equation) a  \special {t4ht=. The current transport models are described as follows:

constTransport
assumes a constant m  \special {t4ht= and Prandtl number Pr = cpm/k  \special {t4ht= which is simply specified by a two values m P r  \special {t4ht= following the <thermoCoeffs>.
sutherlandTransport
calculates m  \special {t4ht= as a function of temperature T  \special {t4ht= from a Sutherland coefficient A
 s  \special {t4ht= and Sutherland temperature T
 s  \special {t4ht=, specified by values following the <thermoCoeffs>; m  \special {t4ht= is calculated according to:
         V~ --
m = --As--T--
    1 + Ts/T
      \special {t4ht=
(7.2)

The following is an example entry for a specie named fuel modelled using sutherlandTransport and janafThermo, with comments to explain the entries:


    fuel                                          // keyword
    fuel 1 44.0962                                // specie
    200 5000 1000                                 // -- janafThermo --
    7.53414 0.0188722 -6.27185e-06 9.14756e-10 -4.78381e-14
    -16467.5 -17.8923
    0.933554 0.0264246 6.10597e-06 -2.19775e-08 9.51493e-12
    -13958.5 19.2017                              // -----------------
    1.67212e-06 170.672;                          // sutherlandTransport
The following is an example entry for a specie named air modelled using constTransport and hConstThermo, with comments to explain the entries:


    mixture                                       // keyword
    air 1 28.9                                    // specie
    1000 2.544e+06                                // hConstThermo
    1.8e-05 0.7;                                  // constTransport