On acoustic damping of a cylindrical chamber in resonant modes

Acoustic damping of a cylindrical chamber with open and closed ends in resonant modes is analytically and numerically investigated to understand the low damping characteristic of the chamber without chocked nozzle. First, on the basis of the analytic solution of resonant acoustic modes inside a cylinder, the damping by radiation from the open end is calculated analytically using simple acoustic source modeling for velocity fluctuation. The effect of viscosity is also considered as an attenuation mechanism. The values of acoustic damping calculated for the first longitudinal and tangential modes are in good agreement with the corresponding values obtained using numerical simulation. The damping is also investigated for a configuration of the chamber with an injector installed off-center. Finally, we numerically and semi-analytically investigate the acoustic damping for a configuration that includes a hot-gas injection. The obtained mode is found to be a spinning tangential mode and the radiated wave also has a spinning feature. The damping for the spinning tangential mode is found to be larger than that for the symmetric dipole-like radiation under a uniform standing condition, but much smaller than the chamber with a chocked nozzle. Therefore, the chamber with an open end has the low damping characteristic suitable for intentionally generating oscillatory combustion.