4.4.2. Cantera Material Properties

For more complicated simulations, particularly those involving multi-species gas mixtures, Fuego supports using Cantera XML files to define the fluid properties. To use Cantera, your material property block should specify a Cantera XML file:

# At the sierra-block level
Begin Property Specification for Fuego Material air

    CANTERA XML FILE = helium.xml

    REFERENCE PRESSURE = 1.0             $ atmosphere
    REFERENCE TEMPERATURE = 298.         $ Kelvin
    REFERENCE MASS_FRACTION N2 = 0.767
    REFERENCE MASS_FRACTION HE = 0.00
    REFERENCE MASS_FRACTION O2 = 0.233

    SCHMIDT_NUMBER = 0.9
End

The XML file should include a <phase> block, which defines the elements and species present and what mixture models to use, and a <speciesData> block which defines thermodynamic and transport models for each species.

<?xml version="1.0"?>
<ctml>
  <!-- phase gas     -->
  <phase dim="3" id="gas">
    <elementArray>He  O  N</elementArray>
    <speciesArray datasrc="#species_data">HE  O2  N2 </speciesArray>
    <thermo model="IdealGas"/>
    <transport model="Mix"/>
  </phase>

  <!-- species definitions     -->
  <speciesData id="species_data">
    <!-- ...  -->
  </speciesData>
</ctml>

Note

The order the species are listed in the Cantera XML file is the order used throughout Fuego. The last species listed (N2 here) will be the “fracbal” species that is not solved for, but whose mass fraction is set to achieve a unity mass fraction sum.

Note

Older versions of the Cantera XML file may have referenced an elements.xml file in the <elementArray> tag, which would have required a separate elements.xml file defining valid elements and their molecular weights. This is no longer required unless you are using custom elements not in the periodic table. Simply removing that attribute from the <elementArray> will use the default periodic table.

Aside from changing the list of elements and species, one generally should not change any other parts of the <phase> block. Within the <speciesData> block, there should be an entry for each species, including <thermo> and <transport> sub-blocks.

<!-- species HE    -->
<species name="HE">
  <atomArray>He:1 </atomArray>
  <thermo>
    <NASA Tmax="1000.0" Tmin="300.0" P0="100000.0">
       <floatArray name="coeffs" size="7">
         2.500000000E+00,   0.000000000E+00,   0.000000000E+00,   0.000000000E+00,
         0.000000000E+00,  -7.453750000E+02,   9.153488000E-01</floatArray>
    </NASA>
    <NASA Tmax="5000.0" Tmin="1000.0" P0="100000.0">
       <floatArray name="coeffs" size="7">
         2.500000000E+00,   0.000000000E+00,   0.000000000E+00,   0.000000000E+00,
         0.000000000E+00,  -7.453750000E+02,   9.153489000E-01</floatArray>
    </NASA>
  </thermo>
  <transport model="gas_transport">
    <string title="geometry">atom</string>
    <LJ_welldepth units="K">10.200</LJ_welldepth>
    <LJ_diameter units="A">2.580</LJ_diameter>
    <dipoleMoment units="Debye">0.000</dipoleMoment>
    <polarizability units="A3">0.000</polarizability>
    <rotRelax>0.000</rotRelax>
  </transport>
</species>

4.4.2.1. Thermodynamic Properties

The <thermo> section specifies standard thermodynamic polynomials for the different species over different temperature ranges. The common types of polynomials are described below.

4.4.2.1.1. NASA7

The NASA7 polynomial takes 7 coefficients (a_0-a_6) and expects one or two temperature ranges, as shown below.

<thermo>
  <NASA Tmax="1000.0" Tmin="300.0" P0="100000.0">
      <floatArray name="coeffs" size="7">
        2.500000000E+00,   0.000000000E+00,   0.000000000E+00,   0.000000000E+00,
        0.000000000E+00,  -7.453750000E+02,   9.153488000E-01</floatArray>
  </NASA>
  <NASA Tmax="5000.0" Tmin="1000.0" P0="100000.0">
      <floatArray name="coeffs" size="7">
        2.500000000E+00,   0.000000000E+00,   0.000000000E+00,   0.000000000E+00,
        0.000000000E+00,  -7.453750000E+02,   9.153489000E-01</floatArray>
  </NASA>
</thermo>

These coefficients define the following properties:

(4.1)\frac{C_p(T)}{R} = a_0 + a_1 T + a_2 T^2 + a_3 T^3 + a_4 T^4

(4.2)\frac{h(T)}{R} = a_0 T + \frac{a_1}{2} T^2 + \frac{a_2}{3} T^3 + \frac{a_3}{4} T^4 + \frac{a_4}{5} T^5 + a_5

(4.3)\frac{s(T)}{R} = a_0 \ln(T) + a_1 T + \frac{a_2}{2} T^2 + \frac{a_3}{3} T^3 + \frac{a_4}{4} T^4 + a_6

4.4.2.1.2. NASA9

The NASA9 polynomial takes 9 coefficients (a_0-a_8) and can use an arbitrary number of temperature ranges, as shown below.

<thermo>
  <NASA9 Pref="1 bar" Tmax="1000.00" Tmin="200.00">
    <floatArray size="9">
      4.943650540e+04, -6.264116010e+02,  5.301725240e+00,  2.503813816e-03,
      -2.127308728e-07, -7.689988780e-10,  2.849677801e-13, -4.528198460e+04,
      -7.048279440e+00
    </floatArray>
  </NASA9>
  <NASA9 Pref="1 bar" Tmax="6000.00" Tmin="1000.00">
    <floatArray size="9">
      1.176962419e+05, -1.788791477e+03,  8.291523190e+00, -9.223156780e-05,
      4.863676880e-09, -1.891053312e-12,  6.330036590e-16, -3.908350590e+04,
      -2.652669281e+01
    </floatArray>
  </NASA9>
  <NASA9 Pref="1 bar" Tmax="20000.00" Tmin="6000.00">
    <floatArray size="9">
      -1.544423287e+09,  1.016847056e+06, -2.561405230e+02,  3.369401080e-02,
      -2.181184337e-06,  6.991420840e-11, -8.842351500e-16, -8.043214510e+06,
      2.254177493e+03
    </floatArray>
  </NASA9>
</thermo>

These coefficients define the following properties:

(4.4)\frac{C_p(T)}{R} = a_0 T^{-2} + a_1 T^{-1} + a_2 + a_3 T + a_4 T^2 + a_5 T^3 + a_6 T^4

(4.5)\frac{h(T)}{R} = -a_0 T^{-1} + a_1 \ln(T) + a_2 T + \frac{a_3}{2} T^2 + \frac{a_4}{3} T^3 + \frac{a_5}{4} T^4 + \frac{a_6}{5} T^5 + a_7

(4.6)\frac{s(T)}{R} = -\frac{a_0}{2} T^{-2} - a_1 T^{-1} + a_2 \ln(T) + a_3 T + \frac{a_4}{2} T^2 + \frac{a_5}{3} T^3 + \frac{a_6}{4} T^4 + a_8

4.4.2.1.3. Shomate

The Shomate polynomial takes 7 coefficients (A-G) and expects one or two temperature ranges, as shown below.

<thermo>
  <Shomate Pref="1 bar" Tmax="1400.0" Tmin="298">
    <floatArray size="7">
        72.3870,    8.8501,    0.0007,         0,
        -1.1428, -197.3525,  131.4492
    </floatArray>
  </Shomate>
</thermo>

Unlike the NASA polynomials, the Shomate polynomials are not normalized by the ideal gas constant. The expected units of C_p, h, and s are J/mol-K, kJ/mol, and J/mol-K, respectively. These coefficients define the following properties, using a scaled temperature t:

(4.7)t = \frac{T}{1000}

(4.8)C_p(T) = A + B t + C t^2 + D t^3 + \frac{E}{t^2}

(4.9)h(T) = A t + \frac{B}{2} t^2 + \frac{C}{3} t^3 + \frac{D}{4} t^4 - \frac{E}{t} + F

(4.10)s(T) = A \ln(t) + B t + \frac{C}{2} t^2 + \frac{D}{3} t^3 - \frac{E}{2 t^2} + G

4.4.2.2. Transport Properties

The <transport> block in the Cantera file requires 6 entries:

  • Geometry - One of atom (for monatomic species like He), linear (for diatomic species like N2), or nonlinear (for all others)

  • Lennerd Jones Well Depth - Value in Kelvin for the species interaction potential depth.

  • Lennerd Jones Diameter - Value in angstroms for the species interaction diameter.

  • Dipole moment - Value in Debye determined from the molecular structure.

  • Polarizability - Vale un Angstroms cubed which affects interactions between charged and un-charged species.

  • Rotational Relaxation - Value that affects only thermal conductivity (not typically used in Fuego).

These values are typically tabulated in standard transport data sets from NIST or NASA. For un-common species, methods for estimating L-J parameters from other properties like critical point and boiling point properties can be found in Estimated Viscosities and Thermal Conductivities of Gases at High Temperatures, Svehla, 1962.

<transport model="gas_transport">
  <string title="geometry">atom</string>
  <LJ_welldepth units="K">10.200</LJ_welldepth>
  <LJ_diameter units="A">2.580</LJ_diameter>
  <dipoleMoment units="Debye">0.000</dipoleMoment>
  <polarizability units="A3">0.000</polarizability>
  <rotRelax>0.000</rotRelax>
</transport>

4.4.2.3. Resources

The following web resources and SAND reports can provide useful information for constructing Cantera files.