Combustion Chamber Design

Combustion Chamber Design (propulsion/rocket/combustion-chamber-design)

Use when the task is rocket combustion chamber design: the characteristic velocity, the throat area, the thrust coefficient, the contraction ratio, the chamber volume from L-star, and the vacuum specific impulse of the chamber upstream of the nozzle throat.

Domain quick reference

• Characteristic velocity (defining relation): c-star = Pc * At / mdot with Pc the chamber pressure in Pa, At the throat area in m^2, and mdot the propellant mass flow in kg/s; c-star has units of m/s and measures the combustion quality of the chamber. Worked: LOX/RP-1 at 7.0 MPa, throat area 0.02 m^2, and 80 kg/s gives c-star = 7e6 * 0.02 / 80 = 1750 m/s, a typical delivered value.
• Theoretical c-star from gas properties: c-star = sqrt(gamma * R * Tc) / (gamma * sqrt((2 / (gamma + 1))^((gamma + 1) / (gamma - 1)))) with R = 8314 / Mw the gas constant from the molecular weight Mw in kg/kmol and Tc the chamber temperature in K. Worked: LOX/RP-1 at Tc = 3670 K, Mw = 23, gamma = 1.20 gives about 1776 m/s. The ratio of delivered to theoretical c-star is the c-star efficiency, 0.92 to 0.98; 1750 / 1776 = 0.985 in the worked case.
• Throat area from the propellant flow: At = mdot * c-star / Pc. Worked: 80 * 1750 / 7e6 = 0.02 m^2, closing the loop with the defining relation.
• Thrust coefficient: Cf = F / (Pc * At) with F the thrust in N; Cf is about 1.4 to 1.6 at sea level and 1.8 to 2.0 in vacuum depending on the expansion. Worked: 252 kN over 7.0 MPa and 0.02 m^2 gives Cf = 252000 / 140000 = 1.8, a vacuum-class value. Thrust from the coefficient: F = Cf * Pc * At.
• Vacuum specific impulse: Isp = F / (mdot * g0) with g0 = 9.80665 m/s^2. Worked: 252000 / (80 * 9.80665) = 321.2 s, consistent with LOX/RP-1 vacuum performance.
• Contraction ratio: epsilon_c = Ac / At with Ac the chamber cross section area, typically 2 to 5 for liquid engines. Worked: Ac = 0.07 m^2 over At = 0.02 m^2 gives epsilon_c = 3.5.
• Chamber volume from L-star: Vc = L-star * At with L-star the characteristic chamber length in m, typically 0.5 to 1.5 m for liquid propellants; L-star sets the residence time for complete combustion. Worked: L-star = 0.9 m gives Vc = 0.018 m^3.
• Throat radius: for a circular throat, r = sqrt(At / pi). Worked: At = 0.02 m^2 gives r = 0.0798 m, about 80 mm.
• Theoretical c-star depends only on the gas (Tc, Mw, gamma), not on the chamber pressure; raising Pc raises the achievable thrust at fixed throat area but not the ideal c-star.

Workflow

1. Fix the design point: chamber pressure Pc, propellant mass flow mdot, and the propellant gas properties Tc, Mw, gamma.
2. Compute the theoretical c-star with theoretical_cstar and the delivered c-star with characteristic_velocity once the throat area is known; the ratio gives the c-star efficiency.
3. Size the throat area with throat_area_from_flow(mdot, c-star, Pc); this At is the interface to the nozzle downstream.
4. Compute the thrust coefficient with thrust_coefficient, or the thrust with thrust_from_cf, and the vacuum specific impulse with vacuum_specific_impulse.
5. Select the chamber cross section and compute the contraction ratio with contraction_ratio and the chamber volume with chamber_volume(L-star, At).
6. Check the throat radius with nozzle_throat_radius for the mechanical layout, then pass At, Pc, and the gas properties to the nozzle-design leaf for the expansion downstream of the throat.

Pitfalls

• Routing the nozzle downstream of the throat here: area ratio, exit Mach, expansion, and the diverging section belong to the nozzle-design leaf; this leaf stops at the throat and hands over At.
• Routing propellant choice here: mixture ratio, density impulse, and storability belong to propellant-selection; this leaf consumes the chosen propellant's Tc, Mw, and gamma.
• Routing the rocket equation here: delta-v, mass ratio, and staging belong to rocket-sizing and rocket-staging; the Isp from this leaf feeds those leaves.
• Routing gas turbine combustor questions here: stoichiometric fuel-air-ratio and adiabatic flame temperature for continuous-flow jet engine combustors belong to combustor-design; a rocket chamber is a different device with c-star bookkeeping.
• Confusing the two c-star values: c-star = Pc * At / mdot is the measured defining value; the gas-property formula is the ideal ceiling, and their ratio is the c-star efficiency, 0.92 to 0.98.
• Using psi instead of Pa or bar: c-star, Cf, and At sizing are only consistent in Pa, m^2, kg/s, and N; a pressure in bar silently shifts every result by 1e5.
• Forgetting g0 in the specific impulse: Isp = F / (mdot * g0), so a 252000 N thrust at 80 kg/s gives 321 s, not 3150 s.
• Accepting a contraction ratio at or below 1: the chamber must converge into the throat, so Ac must exceed At and contraction_ratio raises ValueError otherwise.
• Sizing the volume without L-star: Vc = L-star * At, so a small throat at fixed L-star gives a small chamber and a short residence time, which lowers the c-star efficiency.

Behavior contract (gate 3)

The combustion chamber sizing logic is exercised by the gate 3 contract test: scripts/test_combustion_chamber_design.py against scripts/combustion_chamber_design_logic.py (stdlib unittest, offline). Run: python3 scripts/test_combustion_chamber_design.py

Compliance

• ECSS is cited as reference only for the space systems propulsion context; the characteristic velocity, thrust coefficient, L-star, and contraction ratio relations are standard rocket propulsion methodology, paraphrased here. No proprietary or copyrighted text is reproduced.
• compliance: STANDARDS-REF, gated: false.