Input reference

The input is a YAML file (or, from Python, a dictionary) with the sections below. Quantities are SI numbers or strings with units:

Dimension	Units
pressure	Pa, kPa, MPa, bar, atm, psi, psia
force	N, kN, MN, lbf
length	m, cm, mm, in, ft
temperature	K
angle	deg

A number without a unit is SI (angles in degrees). A unit of the wrong dimension is an error.

Complete example

propellants:
  fuel: RP-1
  oxidizer: O2(L)
  # fuel_temperature: 298.15 K       # optional; CEA reference temperature otherwise
  # oxidizer_temperature: 90.17 K
chamber:
  pressure: 500 psi
  mixture_ratio: 2.4
design:
  thrust: 500 lbf
  altitude: 0 ft                     # or ambient_pressure and ambient_temperature
  sizing: frozen                     # frozen | equilibrium | constant-gamma
geometry:
  characteristic_length: 40 in
  convergent_half_angle: 30 deg
  divergent_half_angle: 15 deg
  contraction_ratio: auto
  throat_upstream_radius: 1.5        # times the throat radius
  throat_downstream_radius: 1.5
  chamber_fillet_radius: 1.0
mesh:
  radial_cells: 40
  cell_aspect: 1.0
  scale: 1.0
  wedge_angle: 5.0
  growth: 1.05
  include_cylinder: false
  plume_length: 0
  plume_radius: 3
solver:
  model: kOmegaSST
  iterations: 20000
  write_interval: 2000
  max_co: 0.2
  n_procs: 1

Every key except propellants (or gas), chamber and design.thrust has the default shown.

propellants

Key	Default	Meaning
fuel	required	CEA species name, e.g. RP-1, CH4(L), H2(L), CH6N2(L)
oxidizer	required	CEA species name, e.g. O2(L), N2O4(L), O2
fuel_temperature	CEA reference	inlet temperature of the fuel
oxidizer_temperature	CEA reference	inlet temperature of the oxidizer

Liquid propellants enter at the reference temperature of their condensed phase in the CEA library (90.17 K for O2(L), 111.643 K for CH4(L), 20.27 K for H2(L), 298.15 K for RP-1), since CEA assigns their enthalpy at that temperature.

gas instead of propellants

For cold-flow cases (validation against air nozzles, for instance) a gas of fixed composition replaces the propellants, and the chamber temperature is given:

gas:
  composition: {N2: 0.78084, O2: 0.20946, AR: 0.00934}   # mole fractions
  mechanism: air.yaml                                     # Cantera input file
chamber:
  pressure: 100 psi
  temperature: 294 K

chamber

Key	Default	Meaning
pressure	required	chamber (stagnation) pressure \(p_c\)
mixture_ratio	required with propellants	oxidizer-to-fuel mass ratio O/F
temperature	required with gas	chamber temperature \(T_c\)

design

Key	Default	Meaning
thrust	required for a sized geometry	design thrust \(F_d\) at matched expansion
altitude	0	ambient state from the NASA Glenn Earth atmosphere model
ambient_pressure, ambient_temperature	—	ambient state given directly (temperature default 288.15 K)
sizing	frozen	sizing model, see below
gamma	gammas	constant-gamma model only: gammas (CEA equilibrium \(\gamma_s\) of the chamber), frozen (frozen \(\gamma\) at \(T_c\)) or a number
molecular_weight	chamber	constant-gamma model only: chamber, station-average (mean of the CEA chamber, throat and exit values) or a number [kg/kmol]

The sizing models are described on the Method page:

• frozen sizes the nozzle along the isentrope of the frozen chamber mixture with temperature-dependent \(c_p\). It is consistent with the simulation and is the recommended model.
• equilibrium takes \(I_{sp}\), \(c^*\) and the area ratio of CEA's shifting-equilibrium solution.
• constant-gamma uses the calorically perfect gas relations.

The last two are kept for comparison. In a frozen-flow simulation they give nozzles that over-expand the gas (see Verification and validation).

geometry

The thrust chamber is sized from the design point unless throat_radius is given.

Key	Default	Meaning
characteristic_length	40 in	\(L^*\); the chamber volume up to the throat is \(L^* A_t\)
convergent_half_angle	30 deg	\(\theta_c\)
divergent_half_angle	15 deg	\(\theta_d\)
contraction_ratio	auto	\(A_c/A_t\); auto uses \(8.0\,D_t^{-0.6} + 1.25\), \(D_t\) in cm (Humble et al., 1995)
throat_upstream_radius	1.5	radius of curvature upstream of the throat, in throat radii
throat_downstream_radius	1.5	radius of curvature downstream of the throat, in throat radii
chamber_fillet_radius	1.0	fillet between cylinder and convergent cone, in throat radii

Explicit geometry

To reproduce a given nozzle, give its dimensions instead of sizing it:

Key	Meaning
throat_radius	\(r_t\)
area_ratio	\(A_e/A_t\)
contraction_ratio	\(A_c/A_t\) (a number)
chamber_length	optional length of the cylinder; otherwise \(L^*\) sets the volume

The arc radii and cone angles above apply as well. The mass flow rate of the one-dimensional frozen flow through this throat is then the reference for the discharge coefficient.

mesh

Key	Default	Meaning
radial_cells	40	cells between the axis and the wall, at every axial station
cell_aspect	1.0	axial over radial cell size
scale	1.0	multiplies every cell count (mesh studies)
wedge_angle	5.0	total angle of the wedge [deg]
growth	1.05	growth ratio of the cells in the plume region, from the exit-plane cell size
include_cylinder	false	mesh the cylindrical chamber as well
plume_length	0	length of a plume region behind the exit, in exit diameters; 0 ends the domain at the exit
plume_radius	3	radius of the plume region, in exit radii

The cell counts scale with the throat radius, so the same settings give the same resolution for a 500 lbf engine and for a 1.5 Mlbf engine.

solver

Key	Default	Meaning
model	kOmegaSST	inviscid (slip walls), laminar or kOmegaSST (wall functions)
iterations	20000	iterations of local time stepping (one time unit each)
write_interval	2000	iterations between written fields
max_co	0.2	Courant number of the local time step
limiter	vanLeer	limiter of the reconstruction of \(\rho\), \(U\) and \(T\)
lts_smoothing	0.02	rDeltaTSmoothingCoeff
turbulence_intensity	0.05	at the inlet
mixing_length	0.07	at the inlet, in chamber diameters
n_procs	1	processors; above 1 Allrun decomposes and runs in parallel
inlet_velocity_bc	zeroGradient	or pressureInletOutletVelocity

Thermodynamic data

Key	Default	Meaning
mechanism (top level)	gri30_highT.yaml	Cantera data set in which the frozen chamber composition is evaluated

Product species that the data set does not contain are dropped and the remaining mole fractions renormalised. The dropped fraction is printed and recorded in ceatofoam.json; for RP-1, CH₄ and H₂ with LOX at 500 and 1500 psia it does not exceed 20 ppm.