Hava Laboratory Tools

Compressible Flow Calculator

Interactive gas-dynamics relations for course work and preliminary analysis. This version includes perfect-gas relations, reacting-air equilibrium, and finite-rate Park chemistry for high-temperature estimates.

Isentropic Flow Relations

Perfect gas

Gamma, γ Input Mach number T/T₀ p/p₀ ρ/ρ₀ A/A* subsonic A/A* supersonic Mach angle, deg. Prandtl-Meyer angle, deg. Value

Speed of Sound

a = sqrt(γRT)

Gas Air CO₂ Argon N₂ O₂ Helium Custom Gamma, γ R, J/(kg K) MW, kg/kmol T, K

Normal Shock Relations

Perfect gas

Non Dimensional Analysis

Gamma, γ Input M₁ M₂ p₂/p₁ ρ₂/ρ₁ T₂/T₁ p₀₂/p₀₁ p₁/p₀₂ Value

Dimensional Analysis

M₁ Gamma, γ p₁, Pa T₁, K

Reacting Normal Shock

Hansen equilibrium

M₁ T₁, K p₁, Pa N₂ (X) O₂(X)

Oblique Shock Relations

Perfect gas θ-β-M

Non Dimensional Analysis

Gamma, γ M₁ θ (turn angle), deg.

Dimensional Analysis

Gamma, γ M₁ p₁, Pa T₁, K θ (turn angle), deg.

Conical Shock Relations

Perfect gas Taylor-Maccoll

Gamma, γ M₁ Cone half-angle, deg.

Reacting Oblique Shock

Hansen equilibrium

M₁ T₁, K p₁, Pa θ (turn angle), deg. N₂ (X) O₂(X)

Reacting Cone Shock

Hansen equilibrium Taylor-Maccoll

M₁ T₁, K p₁, Pa Cone half-angle, deg. N₂ (X) O₂(X)

Reacting Air Species

Equilibrium and finite-rate models

Model Hansen equilibrium Park 5-species finite-rate Park 11-species finite-rate QK 5-species finite-rate MMT 5-species finite-rate Initial T, K Initial Tv, K Initial p, Pa End time, s Knab V-V coupling

Hansen returns an equilibrium state. Park 5, QK 5, Park 11, and MMT integrate finite-rate two-temperature models from the supplied initial state.
Species are reported as mole fraction (X), mass fraction (Y), and concentration (mol/m³).

Special thanks to Prof. William Devenport and the VT Compressible Aerodynamics Calculator for serving as a source of inspiration for this calculator and for Ozgur Tumuklu’s personal and classroom use over the years in perfect-gas calculations.

References

• Standard air calculations: Anderson, J. D., Jr., Modern Compressible Flow: With Historical Perspective, 3rd ed., McGraw-Hill, 2003.
• Hansen model: Hansen, C. F., “Approximations for the Thermodynamic and Transport Properties of High-Temperature Air,” NASA Technical Report R-50, 1959.
• Hansen model: Dunn, A., Ranstead, J., and Ölçmen, S., “Reconstruction of Hansen’s High-Temperature Air Model,” Axioms, Vol. 15, No. 4, Article 283, 2026, doi:10.3390/axioms15040283.
• Park model: Park, C., “Two-temperature interpretation of dissociation rate data,” AIAA Journal, Vol. 29, No. 2, 1991.
• Park model: Park, C., “A review of reaction rates in high-temperature air,” AIAA Journal, Vol. 32, No. 3, 1994.
• QK model: Scanlon, T. J., White, C., Borg, M. K., Palharini, R. C., Farbar, E., Boyd, I. D., Reese, J. M., and Brown, R. E., “Open source Direct Simulation Monte Carlo chemistry modelling for hypersonic flows,” AIAA Journal, Vol. 53, No. 6, 2015.
• MMT model: Torres, J. P., Gross, M., Candler, G. V., and Schwartzentruber, T. E., “Modified Marrone-Treanor Model: Parameterization and Benchmarking for Five-Species Air,” arXiv:2506.20521, 2025.