Skip to content

Chamber acoustics#

High-frequency combustion instability grows when heat release couples to an acoustic mode of the chamber. EnSim finds the modes. Whether a mode will grow depends on the injector and the flame, which no geometry-only model can predict, so EnSim only says stable or unstable when you supply the driving and damping rates.

Modes of a cylinder#

The chamber is a closed cylinder of length \(L\) and diameter \(D\) filled with gas at the chamber sound speed

\[ a=\sqrt{\gamma_f\,\frac{R}{M}\,T_c}. \]

Longitudinal modes are those of a pipe closed at both ends,

\[ f_{nL}=\frac{n\,a}{2L}, \]

and transverse (tangential and radial) modes follow from the zeros of the Bessel derivative \(J_m'\):

\[ f_{mn}=\frac{\alpha_{mn}\,a}{\pi D},\qquad \alpha_{10}=1.8412\ (1T),\ \alpha_{20}=3.0542\ (2T),\ \alpha_{01}=3.8317\ (1R). \]

For the 366 kN methalox engine on the Python API page, the contour chamber is 0.331 m long and 0.319 m across, the sound speed is 1282 m/s, and the lowest modes are 1L at 1936 Hz and 1T at 2354 Hz. The first tangential mode is the one that has destroyed the most engines, and it is the one baffles and acoustic cavities are tuned against.

Growth#

When you supply a driving rate \(\alpha_d\) and a damping rate \(\alpha_\delta\) for a mode (from test data or a separate model, in 1/s), EnSim reports

\[ \alpha_\text{net}=\alpha_d-\alpha_\delta. \]

A positive value means the mode grows in that linear model, a negative one that it decays. Without the rates the result stays not assessed. EnSim does not derive a threshold from chamber pressure, L* or injector count.

Chugging#

Low-frequency chug couples the feed system to the chamber. A lumped inertance–compliance estimate gives its frequency:

\[ f_\text{chug}=\frac{1}{2\pi}\sqrt{\frac{A}{\rho\,L\,C}} \]

with feed-line area \(A\), length \(L\), propellant density \(\rho\) and the combined compliance \(C\) of feed system and chamber in m³/Pa. Treat it as a screening number for where to look in test data.

Not modelled#

Injector admittance and time lag, the flame's response function, nozzle damping, baffles and acoustic liners, non-linear limit cycles, and the entropy and vorticity waves that matter for low-frequency coupling.

Sources#

  • D. T. Harrje and F. H. Reardon (eds.), Liquid Propellant Rocket Combustion Instability, NASA SP-194, 1972.
  • F. E. C. Culick, "Combustion Instabilities in Liquid-Fueled Propulsion Systems", AGARD CP-450, 1988.