Validations#

A set of the results obtained using Combustion Toolbox, NASA’s CEA [Gordon and McBride, 1994], Cantera [Goodwin et al., 2021], Caltech’s SD-Toolbox [Browne et al., 2008, Browne et al., 2008], and TEA [Blecic et al., 2016].

Note

Caltech’s SD-Toolbox uses the Cantera software package as kernel for the thermochemical calculations.

For the sake of clarity, we only show a reduced set of species in the validation of the mole fractions. To run all the validations contrasted with CEA at once, at the prompt type:

run_validations_CEA

Validation TP 1#

  • Contrasted with: NASA’s Chemical Equilibrium with Applications software

  • Problem type: Equilibrium composition at defined temperature and pressure

  • Temperature [K] = 2500

  • Pressure [bar] = 1

  • Initial mixture [moles]: \(\text{C}_6\text{H}_6 + \frac{7.5}{\phi}\left(3.76 \text{N}_2 + \text{O}_2\right)\), with equivalence ratio \(\phi \in [0.5, 4]\)

  • List of species considered = list_species('Soot formation Extended')

  • URL Folder Results CEA: ./validations/cea/data/tp

To repeat the results, run:

run_validation_TP_CEA_1.m

Validation TP 2#

  • Contrasted with: NASA’s Chemical Equilibrium with Applications software

  • Problem type: Equilibrium composition at defined temperature and pressure

  • Temperature [K] = 2500

  • Pressure [bar] = 1

  • Initial mixture [moles]: \(\text{C}_6\text{H}_6 + \frac{7.5}{\phi} \text{O}_2\), with equivalence ratio \(\phi \in [0.5, 4]\)

  • List of species considered = list_species('Soot formation Extended')

  • URL Folder Results CEA: ./validations/cea/data/tp

To repeat the results, run:

run_validation_TP_CEA_2.m

Validation TP 3#

  • Contrasted with: NASA’s Chemical Equilibrium with Applications software

  • Problem type: Equilibrium composition at defined temperature and pressure

  • Temperature [K] = 2500

  • Pressure [bar] = 1

  • Initial mixture [moles]: \(\text{C}\text{H}_3\text{OH} + \frac{1.5}{\phi}\left(3.76 \text{N}_2 + \text{O}_2\right)\), with equivalence ratio \(\phi \in [0.5, 4]\)

  • List of species considered = list_species('Soot formation Extended')

  • URL Folder Results CEA: ./validations/cea/data/tp

To repeat the results, run:

run_validation_TP_CEA_3.m

Validation TP 4#

  • Contrasted with: NASA’s Chemical Equilibrium with Applications software

  • Problem type: Equilibrium composition at defined temperature and pressure

  • Temperature [K] = 2500

  • Pressure [bar] = 1

  • Initial mixture [moles]: \(\text{C}\text{H}_3\text{OH} + \frac{1.5}{\phi}\text{O}_2\), with equivalence ratio \(\phi \in [0.5, 4]\)

  • List of species considered = list_species('Soot formation Extended')

  • URL Folder Results CEA: ./validations/cea/data/tp

To repeat the results, run:

run_validation_TP_CEA_4.m

Validation HP 1#

  • Contrasted with: NASA’s Chemical Equilibrium with Applications software

  • Problem type: Adiabatic temperature and composition at constant pressure

  • Temperature [K] = 300

  • Pressure [bar] = 1

  • Initial mixture [moles]: \(\text{C}_2\text{H}_2\text{acetylene} + \frac{2.5}{\phi}\left(3.76 \text{N}_2 + \text{O}_2\right)\), with equivalence ratio \(\phi \in [0.5, 4]\)

  • List of species considered = list_species('Soot formation Extended')

  • URL Folder Results CEA: ./validations/cea/data/hp

To repeat the results, run:

run_validation_HP_CEA_1.m

Validation HP 2#

  • Contrasted with: NASA’s Chemical Equilibrium with Applications software

  • Problem type: Adiabatic temperature and composition at constant pressure

  • Temperature [K] = 300

  • Pressure [bar] = 1

  • Initial mixture [moles]: \(\text{C}_2\text{H}_2\text{acetylene} + \frac{2.5}{\phi}\text{O}_2\), with equivalence ratio \(\phi \in [0.5, 4]\)

  • List of species considered = list_species('Soot formation Extended')

  • URL Folder Results CEA: ./validations/cea/data/hp

To repeat the results, run:

run_validation_HP_CEA_2.m

Validation HP 3#

  • Contrasted with: NASA’s Chemical Equilibrium with Applications software

  • Problem type: Adiabatic temperature and composition at constant pressure

  • Temperature [K] = 300

  • Pressure [bar] = 1

  • Initial mixture [moles]: \(\text{C}\text{H}_4 + \frac{2}{\phi}\left(3.76 \text{N}_2 + \text{O}_2\right)\), with equivalence ratio \(\phi \in [0.5, 4]\)

  • List of species considered = list_species('Soot formation Extended')

  • URL Folder Results CEA: ./validations/cea/data/hp

To repeat the results, run:

run_validation_HP_CEA_3.m

Validation HP 4#

  • Contrasted with: NASA’s Chemical Equilibrium with Applications software

  • Problem type: Adiabatic temperature and composition at constant pressure

  • Temperature [K] = 300

  • Pressure [bar] = 1

  • Initial mixture [moles]: \(\text{C}\text{H}_4 + \frac{2}{\phi}\text{O}_2\), with equivalence ratio \(\phi \in [0.5, 4]\)

  • List of species considered = list_species('Soot formation Extended')

  • URL Folder Results CEA: ./validations/cea/data/hp

To repeat the results, run:

run_validation_HP_CEA_4.m

Validation TV 1#

  • Contrasted with: NASA’s Chemical Equilibrium with Applications software

  • Problem type: Equilibrium composition at defined temperature and volume

  • Temperature [K] = 3000

  • Pressure [bar] = 1.0132

  • Initial mixture [moles]: \(\text{C}\text{H}_4 + \frac{2}{\phi}\left(3.73 \text{N}_2 + \text{O}_2 + 0.0447\text{Ar} + 0.00152 \text{CO}_2\right)\), with equivalence ratio \(\phi \in [0.5, 4]\)

  • List of species considered = list_species('Soot formation Extended')

  • URL Folder Results CEA: ./validations/cea/data/tv

To repeat the results, run:

run_validation_TV_CEA_1.m

Validation EV 1#

  • Contrasted with: NASA’s Chemical Equilibrium with Applications software

  • Problem type: Adiabatic temperature and composition at constant volume

  • Temperature [K] = 300

  • Pressure [bar] = 1.0132

  • Initial mixture [moles]: \(\text{C}\text{H}_4 + \frac{2}{\phi}\left(3.73 \text{N}_2 + \text{O}_2 + 0.0447\text{Ar} + 0.00152 \text{CO}_2\right)\), with equivalence ratio \(\phi \in [0.5, 4]\)

  • List of species considered = list_species('Soot formation Extended')

  • URL Folder Results CEA: ./validations/cea/data/ev

To repeat the results, run:

run_validation_EV_CEA_1.m

Validation DET 1#

  • Contrasted with: NASA’s Chemical Equilibrium with Applications software

  • Problem type: Chapman-Jouguet detonation

  • Temperature [K] = 300

  • Pressure [bar] = 1

  • Initial mixture [moles]: \(\text{C}_2\text{H}_2\text{acetylene} + \frac{2.5}{\phi}\left(3.76 \text{N}_2 + \text{O}_2\right)\), with equivalence ratio \(\phi \in [0.5, 4]\)

  • List of species considered = list_species('Soot formation Extended')

  • URL Folder Results CEA: ./validations/cea/data/hp

To repeat the results, run:

run_validation_DET_CEA_1.m

Validation DET 2#

  • Contrasted with: NASA’s Chemical Equilibrium with Applications software

  • Problem type: Chapman-Jouguet detonation

  • Temperature [K] = 300

  • Pressure [bar] = 1

  • Initial mixture [moles]: \(\text{C}_2\text{H}_2\text{acetylene} + \frac{2.5}{\phi}\text{O}_2\), with equivalence ratio \(\phi \in [0.5, 4]\)

  • List of species considered = list_species('Soot formation Extended')

  • URL Folder Results CEA: ./validations/cea/data/det

To repeat the results, run:

run_validation_DET_CEA_2.m

Validation DET 3#

  • Contrasted with: NASA’s Chemical Equilibrium with Applications software

  • Problem type: Chapman-Jouguet detonation

  • Temperature [K] = 300

  • Pressure [bar] = 1

  • Initial mixture [moles]: \(\text{C}\text{H}_4 + \frac{2}{\phi}\left(3.76 \text{N}_2 + \text{O}_2\right)\), with equivalence ratio \(\phi \in [0.5, 4]\)

  • List of species considered = list_species('Soot formation Extended')

  • URL Folder Results CEA: ./validations/cea/data/det

To repeat the results, run:

run_validation_DET_CEA_3.m

Validation DET 4#

  • Contrasted with: NASA’s Chemical Equilibrium with Applications software

  • Problem type: Chapman-Jouguet detonation

  • Temperature [K] = 300

  • Pressure [bar] = 1

  • Initial mixture [moles]: \(\text{C}\text{H}_4 + \frac{2}{\phi}\text{O}_2\), with equivalence ratio \(\phi \in [0.5, 4]\)

  • List of species considered = list_species('Soot formation Extended')

  • URL Folder Results CEA: ./validations/cea/data/det

To repeat the results, run:

run_validation_DET_CEA_4.m

Validation SHOCK IONIZATION 1#

  • Contrasted with: NASA’s Chemical Equilibrium with Applications software

  • Problem type: Planar shock wave

  • Temperature [K] = 300

  • Pressure [bar] = 1

  • Initial mixture [moles]: \(3.7276 \text{N}_2 + \text{O}_2 + 0.0447\text{Ar} + 0.00152 \text{CO}_2\)

  • List of species considered = list_species(‘Air_ions’)

  • URL Folder Results CEA: ./validations/cea/data/shocks

To repeat the results, run:

run_validation_SHOCK_IONIZATION_CEA_1.m

Validation SHOCK REFLECTED IONIZATION 1#

  • Contrasted with: NASA’s Chemical Equilibrium with Applications software

  • Problem type: Normal reflection of a planar shock wave from a parallel rigid wall

  • Temperature [K] = 300

  • Pressure [bar] = 1

  • Initial mixture [moles]: \(3.7276 \text{N}_2 + \text{O}_2 + 0.0447\text{Ar} + 0.00152 \text{CO}_2\)

  • List of species considered = list_species('Air_ions')

  • URL Folder Results CEA: ./validations/cea/data/shocks

To repeat the results, run:

run_validation_SHOCK_R_IONIZATION_CEA_1.m

Validation SHOCK POLAR 1#

  • Contrasted with: Caltech’s SD Toolbox within Cantera

  • Problem type: Shock polar diagrams

  • Temperature [K] = 300

  • Pressure [bar] = 1.01325

  • Initial mixture [moles]: \(3.7619 \text{N}_2 + \text{O}_2\)

  • List of species considered = Frozen

  • URL Folder Results SDToolbox: ./validations/sdtoolbox/data

To repeat the results, run:

run_validation_SHOCK_POLAR_SDToolbox_1.m

Validation ROCKET 1#

  • Contrasted with: NASA’s Chemical Equilibrium with Applications software

  • Problem type: ROCKET

  • Description: Equilibrium composition at exit of the rocket nozzle

  • Temperature Fuel [K] = 298.15

  • Temperature Oxid [K] = 90.17

  • Chamber pressure [bar] = 22

  • Finite-Area-Chamber model (FAC)

  • Area ratio \(A_{\rm chamber} / A_{\rm throat}\) = 2

  • Area ratio \(A_{\rm exit} / A_{\rm throat}\) = [1:2.6]

  • Initial mixture [moles]: \(\text{RP1} + \frac{0.6723}{\phi}\text{LOX}\)

  • List of species considered = HC/O2/N2 PROPELLANTS

  • URL Folder Results CEA: ./validations/cea/rocket

To repeat the results, run:

run_validation_ROCKET_CEA_1.m
run_validation_ROCKET_CEA_16.m

Validation ROCKET 2#

  • Contrasted with: NASA’s Chemical Equilibrium with Applications software

  • Problem type: ROCKET

  • Description: Equilibrium composition and performance parameters at exit of the rocket nozzle

  • Temperature Fuel [K] = 20.27

  • Temperature Oxid [K] = 90.17

  • Chamber pressure [bar] = 22

  • Infinite-Area-Chamber model (IAC)

  • Area ratio \(A_{\rm exit} / A_{\rm throat}\) = 3

  • Initial mixture [moles]: \(\text{LH2} + \frac{0.5}{\phi}\text{LOX}\)

  • List of species considered = HYDROGEN_L

  • URL Folder Results CEA: ./validations/cea/rocket

To repeat the results, run:

run_validation_ROCKET_CEA_17.m

Validation ROCKET 3#

  • Contrasted with: NASA’s Chemical Equilibrium with Applications software

  • Problem type: ROCKET

  • Description: Equilibrium composition and performance parameters at exit of the rocket nozzle

  • Temperature Fuel [K] = 20.27

  • Temperature Oxid [K] = 90.17

  • Chamber pressure [bar] = 22

  • Finite-Area-Chamber model (FAC)

  • Area ratio \(A_{\rm chamber} / A_{\rm throat}\) = 2

  • Area ratio \(A_{\rm exit} / A_{\rm throat}\) = 3

  • Initial mixture [moles]: \(\text{LH2} + \frac{0.5}{\phi}\text{LOX}\)

  • List of species considered = HYDROGEN_L

  • URL Folder Results CEA: ./validations/cea/rocket

To repeat the results, run:

run_validation_ROCKET_CEA_18.m

Validation TEA 1#

  • Contrasted with: Thermochemical Equilibrium Abundances of chemical species software

  • Problem type: Equilibrium composition at defined temperature and pressure

  • Temperature [K] = linspace(500, 5000)

  • Pressure [bar] = logspace(-5, 2)

  • Initial mixture [moles]:

    • H = 1.0000000000e+00

    • He = 8.5113803820e-02

    • C = 2.6915348039e-04

    • N = 6.7608297539e-05

    • O = 4.8977881937e-04

  • List of species considered = {‘C’, ‘CH4’, ‘CO2’, ‘CO’, ‘H2’, ‘H’, ‘H2O’, ‘He’, ‘N2’, ‘N’, ‘NH3’, ‘O’}

  • URL Results TEA: https://github.com/dzesmin/TEA/blob/master/doc/examples/quick_example/results/quick_example.tea

To repeat the results, run:

run_validation_TP_TEA_1.m

Validation TEA 2#

  • Contrasted with: Thermochemical Equilibrium Abundances of chemical species software

  • Problem type: Equilibrium composition at defined temperature and pressure

  • Description: Thermochemical equilibrium vertical distribution of WASP-43b with a metallicity \(\zeta = 1\) assumming a T-P profile

  • Temperature [K] = [958.36, 1811.89]

  • Pressure [bar] = [2.3988e-06, 31.6230]

  • Initial mixture: Computed from solar abundances assuming a metallicity zeta = 1

  • List of species considered = {‘C2H2_acetylene’, ‘C2H4’, ‘C’, ‘CH4’, ‘CO2’, ‘CO’, ‘H2’, ‘H2O’, ‘H2S’, ‘H’, ‘HCN’, ‘He’, ‘SH’, ‘N2’, ‘N’, ‘NH3’, ‘O’, ‘S’}

  • URL Results TEA: https://github.com/dzesmin/RRC-BlecicEtal-2015a-ApJS-TEA/tree/master/Fig6/WASP43b-solar

To repeat the results, run:

run_validation_TP_TEA_2.m

Validation TEA 3#

  • Contrasted with: Thermochemical Equilibrium Abundances of chemical species software

  • Problem type: Equilibrium composition at defined temperature and pressure

  • Description: Thermochemical equilibrium vertical distribution of WASP-43b with a metallicity \(\zeta = 10\) assumming a T-P profile

  • Temperature [K] = [958.36, 1811.89]

  • Pressure [bar] = [2.3988e-06, 31.6230]

  • Initial mixture: Computed from solar abundances assuming a metallicity zeta = 10

  • List of species considered = {‘C2H2_acetylene’, ‘C2H4’, ‘C’, ‘CH4’, ‘CO2’, ‘CO’, ‘H2’, ‘H2O’, ‘H2S’, ‘H’, ‘HCN’, ‘He’, ‘SH’, ‘N2’, ‘N’, ‘NH3’, ‘O’, ‘S’}

  • URL Results TEA: https://github.com/dzesmin/RRC-BlecicEtal-2015a-ApJS-TEA/tree/master/Fig6/WASP43b-10xsolar

To repeat the results, run:

run_validation_TP_TEA_3.m

Validation TEA 4#

  • Contrasted with: Thermochemical Equilibrium Abundances of chemical species software

  • Problem type: Equilibrium composition at defined temperature and pressure

  • Description: Thermochemical equilibrium vertical distribution of WASP-43b with a metallicity \(\zeta = 50\) assumming a T-P profile

  • Temperature [K] = [958.36, 1811.89]

  • Pressure [bar] = [2.3988e-06, 31.6230]

  • Initial mixture: Computed from solar abundances assuming a metallicity zeta = 50

  • List of species considered = {‘C2H2_acetylene’, ‘C2H4’, ‘C’, ‘CH4’, ‘CO2’, ‘CO’, ‘H2’, ‘H2O’, ‘H2S’, ‘H’, ‘HCN’, ‘He’, ‘SH’, ‘N2’, ‘N’, ‘NH3’, ‘O’, ‘S’}

  • URL Results TEA: https://github.com/dzesmin/RRC-BlecicEtal-2015a-ApJS-TEA/tree/master/Fig6/WASP43b-50xsolar

To repeat the results, run:

run_validation_TP_TEA_4.m