How much thrust per unit of propellant does a combination deliver? Rocket Nozzle Performance answers the classic NASA CEA question with Cantera: it finds the equilibrium products in the combustion chamber, computes the characteristic velocity c*, and expands the gas through a quasi-1-D nozzle to give specific impulse, thrust coefficient and exit conditions over a map of area or pressure ratios. On published CEA cases (H2/O2, CH4/O2 and LH2/LOX at 1000 psia) c* and Isp agree with CEA to better than 0.1 %. It runs on CPU.
How it works
- Chamber. Fuel and oxidizer streams mix by mass at your O/F ratio (or an equivalence ratio). By default the chamber is adiabatic: the products are equilibrated at the propellants' enthalpy and the chamber pressure. You can fix the chamber temperature instead. The chamber is treated as an infinite-area combustor, so its state is the stagnation state of the expansion.
- Expansion. Along the nozzle the entropy and total enthalpy stay at their chamber values. Frozen expansion keeps the chamber composition; shifting equilibrium re-equilibrates at every pressure. Real nozzles fall between the two, so both are reported, each with its own sound speed and effective γ: the spread between them is the honest uncertainty of a one-number Isp.
- Throat and exit. The throat is where the flow speed equals the sound speed; c* is the chamber pressure divided by the throat mass flux. Each exit point, given as an area ratio A/A* or a pressure ratio p_c/p_e, yields vacuum Isp, ambient Isp at your back pressure, thrust coefficients and exit Mach.
- Finite rate (optional). With a mechanism that has reactions, the supersonic section can also be integrated with finite-rate chemistry along the nozzle contour. It starts from the equilibrium state just past the throat, so the result lands between the frozen and equilibrium values.
- Checks. Every row carries its element-balance error, the area ratio is solved to a 10⁻⁶ residual, and equilibrium Isp is checked against frozen. Where graphite would be thermodynamically stable (fuel-rich carbon propellants), the job flags it; it does not form solid carbon.
Inputs
- Thermochemistry: built-in
h2o2orgri30(mechanism_id), or your own Cantera YAML or single CHEMKIN file, uploaded or from an artifact. Extra species thermo, for example custom propellant species from NASA / Cantera Species Builder, can be added asspecies_thermo. - Propellants: fuel and oxidizer compositions (mole amounts, such as
CH4:1), each with a temperature and, for cryogenic liquids, an assigned enthalpy (about −4470 kJ/kg for liquid hydrogen and −405.6 kJ/kg for liquid oxygen at their boiling points). Then an O/F mass ratio or an equivalence ratio. - Chamber and exit: chamber pressure, adiabatic or fixed temperature, the back pressure (0 for vacuum), and the exit area and pressure ratios to map.
- Nozzle contour: a conical nozzle (half-angles, contraction ratio, exit area ratio, number of stations) or your own table of axial position and A/A*. The contour sets the profile stations and the finite-rate path.
- Efficiencies: an optional c* efficiency and divergence factor. Delivered values apply them; ideal values are always reported alongside.
Outputs
| File | Contents |
|---|---|
performance.csv | Per mode and exit point: area and pressure ratio, exit T / p / Mach / velocity, γ (isentropic and frozen), c*, thrust coefficients, vacuum / ambient / exit Isp, delivered values, and a flow-separation flag |
profiles.csv | Per mode and contour station: x, A/A*, pressure, temperature, density, velocity, Mach, γ, element-balance error, graphite activity and mole fractions |
isp_map.png, profiles.png | Vacuum Isp against area ratio; temperature and Mach along the nozzle |
summary.json | Chamber and throat states, contour, efficiencies, invariant checks, warnings and model limits |
Not covered
- Boundary layers, two-phase flow, heat transfer and plume modeling: ambient Isp is a back-pressure correction that assumes attached flow.
- Finite-area combustion chambers and condensed products.
- 2-D nozzle flow, bell-contour design and air-breathing cycles.
Related tools
Build species thermo with NASA / Cantera Species Builder, generate or reduce mechanisms with RMG Mechanism Generator and Mechanism Reduction, and run single equilibrium or flame calculations in Cantera.