Gas Models

flow_state provides three gas models with increasing complexity for different temperature regimes. See Gas Properties for definitions of \(R\), \(\gamma\), \(c_p\), \(c_v\).

Overview

Model	Class	Valid Range	Real-Gas Effects
Perfect Gas	PerfectGas	All	None (constant γ, R)
Park	ParkGas	~800–2500 K	Vibrational excitation
Equilibrium Air	EquilibriumAir	300–15000 K	Vibration, dissociation, ionization

Perfect Gas

Constant \(\gamma\) and \(R\). Uses the ideal gas law \(p = \rho R T\).

Use when temperatures are below ~800 K or when real-gas effects are negligible.

Park

Harmonic oscillator model that captures the decrease in \(\gamma\) as vibrational modes become excited:

\[ c_v = c_{v,\text{trans}} + c_{v,\text{rot}} + c_{v,\text{vib}}(T) \]

The vibrational contribution uses characteristic temperatures:

• \(\theta_{\text{vib,N}_2} = 3395\) K
• \(\theta_{\text{vib,O}_2} = 2239\) K

\[ c_{v,\text{vib}} = R \left( \frac{\theta_{\text{vib}}}{T} \right)^2 \frac{e^{\theta_{\text{vib}}/T}}{(e^{\theta_{\text{vib}}/T} - 1)^2} \]

Use for moderate high-temperature flows (~800–2500 K) where vibrational excitation matters but dissociation has not yet begun.

Equilibrium Air

Tannehill curve fits for air in chemical equilibrium, accounting for:

• Vibrational excitation of N₂, O₂
• Dissociation: O₂ ↔ 2O (starts ~2500 K), N₂ ↔ 2N (starts ~4000 K)
• NO formation
• Ionization (>9000 K)

The effective gas constant increases with dissociation (lower average molecular weight):

\[ R_{\text{eff}}(T, p) = Z(T, p) \cdot R_{\text{cold}} \]

where \(Z\) is the compressibility factor from curve fits.

Valid range: 300 K < T < 15000 K, 10⁻⁴ atm < p < 100 atm.

Use for high-enthalpy flows where dissociation and ionization are significant.