Usage

ceaToFoam is used through the ceatofoam command:

Command	What it does
ceatofoam design INPUT	Print the CEA results, the frozen mixture and the design point
ceatofoam case INPUT CASE_DIR	Write the OpenFOAM case and its record ceatofoam.json
ceatofoam post CASE_DIR [--window 0.25]	Average the last part of the run and write results.json
ceatofoam sweep --fuel F --oxidizer O --pressure P	Run CEA over a range of O/F
ceatofoam interactive CASE_DIR	Ask for the inputs on the console, then write the case

INPUT is a YAML file; see Input reference.

Walkthrough: an RP-1/LOX thrust chamber

The example examples/rp1-lox-500psi.yaml describes a 500 lbf RP-1/LOX engine at 500 psi and O/F 2.4, at sea level:

propellants:
  fuel: RP-1
  oxidizer: O2(L)
chamber:
  pressure: 500 psi
  mixture_ratio: 2.4
design:
  thrust: 500 lbf
  altitude: 0 ft
  sizing: frozen
geometry:
  characteristic_length: 40 in
  convergent_half_angle: 30 deg
  divergent_half_angle: 15 deg
mesh:
  radial_cells: 40
solver:
  model: kOmegaSST
  iterations: 20000

1. The design point

$ ceatofoam design examples/rp1-lox-500psi.yaml
Chamber: pc = 34.47 bar, Tc = 3526.5 K
Ambient: p = 101400.9 Pa, T = 288.19 K
CEA equilibrium: Isp =  278.00 s, c* =  1792.5 m/s, gamma_s(c) = 1.1389, M(c) = 22.549
CEA frozen     : Isp =  265.02 s, c* =  1748.5 m/s, gamma_s(c) = 1.2173, M(c) = 22.549
Frozen mixture: M = 22.5487 kg/kmol, gamma(Tc) = 1.2173, dropped species {'COOH': 1e-05}
Design (frozen):
  thrust       2224.11
  pc           3.44738e+06
  tc           3526.5
  p_amb        101401
  pe           101401
  te           1831
  mach_e       2.83779
  ve           2600.04
  mdot         0.855414
  cstar        1748.52
  area_ratio   5.04889
  at           0.000433869
  ae           0.00219056
  gamma_c      1.2173
  gamma_e      1.24337
  mw           22.5487
  rt           0.0117518
  re           0.026406
  isp          265.13
Contour:
  cylinder length 0.148708 m, throat at x = 0.186253 m, exit at x = 0.243264 m
  contraction ratio 6.041, area ratio 5.049

The design point is in SI units. The frozen sizing reproduces CEA's own frozen solution: \(I_{sp}\) = 265.13 s against 265.02 s, \(c^*\) = 1748.5 m/s in both. Species that the thermodynamic data set does not contain are dropped and reported (here 10 ppm of COOH).

2. The case

$ ceatofoam case examples/rp1-lox-500psi.yaml cases/rp1
Wrote cases/rp1: 8720 cells, design thrust 2224.11 N, mdot 0.855414 kg/s. Run ./Allrun in the case.

The case is described on The OpenFOAM case. Its file ceatofoam.json records the input, the CEA results, the frozen mixture, the fit errors, the design point, the contour, the mesh and the versions of every component, including the source revision of ceaToFoam, so that a case can always be traced back to how it was made.

3. Running it

cd cases/rp1
./Allrun        # blockMesh, checkMesh, topoSet, setFields, rhoCentralFoam

With the default 20 000 iterations, one core takes about 5 min (inviscid) to 8 min (k-ω SST) for the 8720 cells of this case. Set solver.n_procs to run in parallel.

4. Evaluating it

ceatofoam post .

post averages the function-object output over the last quarter of the iterations (--window) and writes results.json. For the k-ω SST run of the same engine at 2250 lbf it contains, among others:

{
  "mdot_exit": 3.8203,
  "mdot_balance": -0.00036,
  "thrust_exit": 9741.4,
  "thrust_wall_budget": 9737.8,
  "momentum_closure": -0.00037,
  "isp": 260.02,
  "pe_mean": 105142.5,
  "te_mean": 1863.2,
  "mach_e_mean": 2.779,
  "iterative_std_mdot": 0.0020,
  "iterative_std_thrust": 0.0028,
  "discharge_coefficient": 0.9921,
  "design": {"model": "frozen", "thrust": 10008.5, "mdot": 3.8494, "pe": 101400.9, "...": "..."},
  "thrust_error": -0.0267,
  "mdot_error": -0.0076,
  "pe_error": 0.0369
}

Key	Meaning
mdot_inlet, mdot_throat, mdot_exit	mass flow rate through the inlet, the throat plane and the exit plane [kg/s]
mdot_balance	relative difference of the exit and inlet mass flow rates; judge convergence by it (accept within 0.5 %)
thrust_exit	thrust from the exit-plane momentum and pressure integrals [N]
thrust_wall_budget	the same thrust from the inlet fluxes and the wall force; momentum_closure is the relative difference
pe_mean, te_mean, mach_e_mean	area-averaged exit pressure, temperature and Mach number
iterative_std_*	relative standard deviation over the averaging window
discharge_coefficient	\(\dot m / \dot m_{1D}\), the one-dimensional frozen mass flow through the throat area of the contour
t_min_window, t_max_window, janaf_t_low	temperature extremes of the window and the lower limit of the janaf fit
design	the design point the case was sized for
thrust_error, mdot_error, pe_error	relative deviation of the simulation from the design point

The thrust deficit of −2.7 % in this example is the divergence loss of the 15° cone (1.7 %), the two-dimensional transonic flow (0.3 %) and the turbulent boundary layer (0.7 %); see Verification and validation.

Mixture-ratio sweep

sweep runs CEA alone over a range of mixture ratios, which helps to choose the operating point:

$ ceatofoam sweep --fuel RP-1 --oxidizer "O2(L)" --pressure "500 psi" --plot of.png
O/F      Tc [K]     Isp [s]
 1.35     2139.6     233.10
 ...
Peak chamber temperature 3593.4 K at O/F = 2.95
Peak Isp 278.05 s at O/F = 2.45

Options: --of-min, --of-max, --of-step (default 1.0 to 5.0 in steps of 0.05), --altitude (default sea level) and --analysis equilibrium|frozen.

Interactive input

ceatofoam interactive CASE_DIR asks for the propellants, the chamber pressure, the mixture ratio, the thrust, the altitude, the sizing model and the main geometry parameters on the console, with defaults, and writes the case. It is a shortcut for a first case; for repeatable work, keep the input in a YAML file.