SpectraSim Documentation
Parameter · 04 Material

Heat capacity model

material.compressible.cp_model Step 04 · Material

Chooses between a heat capacity that varies with temperature (polynomials of the selected gas, the solver's janaf thermodynamics) and the constant cpc_p and molar mass typed below (the solver's hConst).

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Theory

The specific heat capacity of air rises from 1005 J/(kg K) at room temperature to about 1136 J/(kg K) at 700 °C; that of exhaust gas rises more (water vapour and CO₂). With a hot gas and heat transfer, a constant cpc_p therefore misstates the enthalpy carried by the flow and the ratio γ\gamma that sets the speed of sound.

With "temperature":

  • The molar heat capacity of the gas is the 7-coefficient polynomial of equation (1), with one set of coefficients below and one above the common temperature 1000 K.
  • The mixture coefficients are the mole-fraction-weighted sums of the species coefficients of N₂, O₂, Ar, CO₂ and H₂O (exact for an ideal-gas mixture of fixed composition). The program writes them into the solver's thermophysicalProperties together with the mixture molar mass.
  • The molar mass and cpc_p boxes show the mixture's values and are locked.
  • Enthalpy differences (heat balance) are integrals of the same polynomial, equation (2).

With "constant", Specific heat capacity cp and Molar mass are used as typed, for any fluid.

The model also serves incompressible and acoustics-only cases: the density uses the molar mass, and the acoustics the ratio γ(T)\gamma(T).

Equations

cp(T) MR=a1+a2T+a3T2+a4T3+a5T4\frac{c_p(T)\,M}{\mathcal{R}} = a_1 + a_2 T + a_3 T^2 + a_4 T^3 + a_5 T^4
(1)
hs(T)=RM(a1T+a22T2+a33T3+a44T4+a55T5+a6)−h(298.15 K)h_s(T) = \frac{\mathcal{R}}{M}\left(a_1 T + \frac{a_2}{2}T^2 + \frac{a_3}{3}T^3 + \frac{a_4}{4}T^4 + \frac{a_5}{5}T^5 + a_6\right) - h(298.15\,\mathrm{K})
(2)
γ(T)=cp(T)cp(T)−R/M\gamma(T) = \frac{c_p(T)}{c_p(T) - \mathcal{R}/M}
(3)
wheremeaningunit
cpc_pSpecific heat capacity at constant pressureJ/(kg K)
MMMolar mass of the mixturekg/kmol
R\mathcal{R}Universal gas constant, 8314.47J/(kmol K)
a1…a6a_1 \ldots a_6Mixture polynomial coefficients (low or high set)-
hsh_sSensible enthalpy relative to 298.15 KJ/kg
γ\gammaRatio of heat capacities-

Default and rule

Default
temperature (cp(T) of the selected gas)
Rule

Temperature. A saved case without this setting is read as "constant" when its molar mass or cpc_p differ from the defaults (28.9644 kg/kmol, 1006 J/(kg K)), so typed values are kept; otherwise as "temperature".

Source

The species data are the NASA Glenn 9-term polynomials (McBride et al., 2002). The program fits the 7-term form of equation (1) to them once per species:

  • least squares on cpc_p over 200-1000 K and 1000-3000 K;
  • cpc_p continuous at 1000 K and exact at 298.15 K;
  • enthalpy and entropy constants matched at 298.15 K.

The fit stays within 0.11 % of the NASA cpc_p from 250 to 1500 K (0.34 % worst over 200-3000 K). The resulting cpc_p of air agrees with standard heat-transfer textbook tables within ±0.5 %. The coefficients are written to the solver's constant/thermophysicalProperties with janaf thermodynamics.

Valid range temperature | constant

Verified

Checked on real runs (2026-11-11): the solver selects the janaf package; a heat-transfer muffler run with it closed its energy balance to 0.7 %, with cp 1034 J/(kg K) at 523 K.

Data not readable

When the program's species data cannot be read, the gas falls back to the constant cpc_p and molar mass with a warning; the program never substitutes estimated values.

Validity

The fitted polynomials are valid from 200 to 3000 K. The composition is frozen (no dissociation or reaction).

References 1

  1. McBride, B. J., Zehe, M. J. and Gordon, S. (2002). NASA Glenn coefficients for calculating thermodynamic properties of individual species. NASA/TP-2002-211556, NASA Glenn Research Center. Web page