Utilities for the Fluid Properties Module

Newton method solver

The fluid properties module includes a 1D and a 2D Newton method solver.

Brent's method solver

Brent's method may be used to find roots of a general function. It was adapted from Numerical Recipes in C++.

More information may be found here.

NASA 7-coefficient polynomials

The NASA7 utilities, as used in NASA7IdealGasFluidProperties, evaluate the standard-state thermodynamic properties of ideal-gas species from NASA 7-coefficient polynomials (McBride et al., 1993). Each species has two sets of coefficients , one for temperatures and one for :

where , , and are the molar isobaric heat capacity, enthalpy, and entropy at the reference pressure of the data, and is the universal gas constant. The enthalpy includes the enthalpy of formation, so the enthalpies of different species share a common reference and reaction enthalpies follow from their differences. The entropy is the absolute (third-law) entropy. The utilities return these dimensionless forms, so they do not depend on the value of , and they accept automatic differentiation types.

The built-in species are H, O, HO, CH, CO, CO, and N, with the GRI-Mech 3.0 data (Smith et al., 1999) as distributed with Cantera 3.2.0 (Goodwin et al., 2025) in gri30.yaml. The reference pressure is 101325 Pa, and K. The fits cover 200 K to 3500 K, except for N, which covers 300 K to 5000 K. The utilities do not check these ranges. The molar masses are those Cantera computes from its atomic weights.

At the low-temperature polynomial applies, as in Cantera. The two polynomials of a species do not match exactly at : for the built-in species, the mismatch is below relative in , J/mol in , and J/(mol K) in .

Gas transport properties

The GasTransportUtils functions, as used in NASA7IdealGasFluidProperties and IdealGasMixtureFluidProperties, evaluate transport properties of dilute gases from kinetic theory (Poling et al., 2001). The Chapman-Enskog viscosity of a species and binary diffusion coefficient of a pair of species and are

where is the molecular mass, is the reduced mass of the pair, is the Boltzmann constant, is the collision diameter, is the reduced temperature with the depth of the Lennard-Jones potential, and the pair parameters follow the combining rules and . The reduced collision integrals and of the Lennard-Jones (12-6) potential follow the fits of Neufeld et al. (1972), valid for .

The Lennard-Jones parameters of the built-in species, H, O, HO, CH, CO, CO, and N, are those of GRI-Mech 3.0 (Smith et al., 1999) as distributed with Cantera 3.2.0 (Goodwin et al., 2025), the same source as the NASA 7-coefficient data. Their reduced temperatures remain within the range of the fits over the temperature ranges of the NASA 7-coefficient data. The viscosities of the species other than HO agree with those of Cantera within 0.5%. The GRI-Mech parameters of HO assume a correction for its dipole moment, which is not applied here, so the binary diffusion coefficients of pairs with HO differ from those of Cantera by up to 4%.

The thermal conductivity of a nonpolar gas follows from its viscosity and molar heat capacity with the modified Eucken correlation (Poling et al., 2001),

where is the specific gas constant and the universal gas constant.

The viscosity of steam in the limit of zero density follows the formulation of IAPWS (2008), as in Water97FluidProperties, and its thermal conductivity in the limit of zero density that of IAPWS (2011). Water97FluidProperties uses the formulation of IAPS (1985) for the thermal conductivity, whose zero-density term agrees within 2% below 1500 K but decreases above about 2200 K and becomes negative near 3300 K. Both formulations are fitted up to about 1173 K.

References