Procedure for determining the acoustic characteristics of combustion chambers of a rocket engine for solid fuel

Many developers of new high-thrust solid-propellant rocket engines are faced with the problem of acoustic instability of combustion. The phenomenon of resonant combustion of solid fuel is associated with a number of specific features. The cavities of the combustion chambers of such engines have complex geometric shapes. The gas channel is long enough. Its length usually exceeds five or more calibers. The thickness of the flame front is measured in micrometers and the combustion zone is localized over the open fuel surface. The flame front often turns out to be capable of amplifying pressure perturbations at the frequency of one of the acoustic eigenmodes if the wave antinode falls on a thin combustion zone. The oscillatory process can be regular or sporadic. Resonances of the longitudinal acoustic mode are most often observed. However, there were cases of simultaneous oscillation of two modes. In some cases, during the operation of the engine, the amplitude of the resulting oscillations began to decrease and the combustion process became almost quasi-stationary. Self-oscillatory processes in the combustion chambers of solid propellants have a threshold sensitivity to pressure overshoots. The vibration amplitudes can be several tens of percent, sometimes reaching the nominal working pressure in the chamber. The amplitude-frequency characteristics of the oscillations are sensitive to the composition of the fuel, responding to changes in the chemical composition, as well as to the mechanical properties of the fuel. The regions of unstable regimes are definitely related to the geometry of the gas cavity. Together with pressure fluctuations, the combustion process is influenced by gas-dynamic factors, significant non-uniformity of the gas flow parameters along the length of the channel, its turbulence, and other factors. When designing solid rocket motors, it is necessary to estimate the frequencies of the natural acoustic resonances of the combustion chambers. The article discusses a technique for determining the frequencies of natural resonances of the first and second tone of the longitudinal mode of acoustic vibrations in the combustion chambers of solid propellant rocket engines. The gas path of the combustion chamber is divided into homogeneous sections, for which the solutions of the wave equation are presented. To determine the natural frequencies and distribution of vibrational pressures and velocities, the method of "stitching" acoustic fields at the boundaries of the cavities was used.