12 Thermochemistry and Mixture Properties

12.1 Thermally perfect species

For a thermally perfect ideal-gas species , the specific heat depends on temperature while the ideal-gas relation is retained. With species gas constant where is the universal gas constant and is molecular weight,

The species enthalpy relative to a reference temperature is (12.1) and the internal energy is (12.2) If contains the standard formation enthalpy, Eq. (12.1) naturally includes both formation and sensible contributions.

12.2 NASA seven-coefficient form

NeuralFlow supports the common NASA polynomial representation used by equilibrium and thermochemistry databases (Gordon and McBride 1971). Within one temperature interval, (12.3) (12.4) and (12.5) The appropriate low- or high-temperature coefficient set is selected for the current temperature range.

A convenient standard reference is . The sensible enthalpy relative to that state is which is identically zero at .

12.3 Mixture thermodynamics

For mass fractions satisfying , mass-specific mixture properties are (12.6) For an ideal-gas mixture, For the constant-density incompressible regime, that equation of state is not used to update carrier density; the material must provide the validated constant physical density required by Chapter 4.

12.4 Derivatives in the coupled Jacobian

Because temperature and independent species mass fractions are primitive columns, thermodynamic functions evaluated with AD contribute derivatives such as to the active residual where the equation of state requires them. In the constant-density incompressible carrier path, and are not used as physical density couplings.

12.5 Transport-property qualification

Thermodynamic mixture properties such as and can depend on temperature and composition. Do not assume that every transport property automatically uses the same mixture dependence. For cases sensitive to viscosity, conductivity or molecular diffusion, verify the selected material-property method and its valid temperature/composition range in the Materials GUI.

12.6 Current fluid EOS families

The current carrier material formulation supports ideal-gas, stiffened-gas and constant-density incompressible closures. The pressure-temperature density laws are

where the stiffened-gas effective gas constant is

The stiffened-gas internal-energy pressure relation and sound speed are

The corresponding ideal-gas expressions are recovered with when the caloric model is compatible. The constant-density closure has and is coupled through artificial compressibility rather than a physical acoustic EOS.

A complete NeuralFlow derivation, including thermodynamic derivatives, total-state relations, caloric formulas and homogeneous-VOF embedding, is given in Equations of State and Caloric Models.

12.7 Transport-property closures

Available transport-property choices include constant and piecewise-polynomial forms, a Sutherland-type viscosity relation, high-temperature fitted viscosity/conductivity relations and kinetic-theory-style conductivity where selectable. Their equations, valid ranges and extrapolation behavior are documented in Transport Properties and Material Closures.