One-dimensional model describing eigenmode frequency shift during transverse excitation

Abstract

A shift in transverse eigenmode frequency was observed in an experimental combustion chamber when exposed to large amplitude acoustic oscillations during oxygen–hydrogen combustion tests. A shift in eigenmode frequency under acoustic conditions representative of combustion conditions is of critical importance when tuning acoustic absorbers or investigating injection coupled combustion instabilities. The experimentally observed frequency shift was observed both in the frequency domain and as an asymmetric amplitude response to a linear frequency ramp of an external excitation system in the time domain. The frequency shift was found to be dependent on amplitude and operating condition. A hypothesis is presented for the frequency shift based on change in speed-of-sound distributions due to flame contraction when exposed to high amplitude pressure oscillations. A one-dimensional (1D) model was created to test the hypothesis. Model parameters were based on relationships observed in experimental data. The model was found to accurately recreate the frequency shifting asymmetric response observed in test data as well as its amplitude dependence. Further development is required to investigate the influence of operating conditions and chamber design on the quantitative modeling of the frequency shift.

Wall Heat Loads in a Cryogenic Rocket Thrust Chamber During Thermoacoustic Instabilities

“…A similar effect of shifting eigenmode frequency has also been observed in the research combustor model H (BKH) under acoustic forcing [32,33]. A siren is used to force resonance of the 1T mode of the combustion chamber, and the response of the five clustered igniter tube injector faceplate Fig.…”

Selection Rules for Resonant Longitudinal Injector-Coupling in Experimental Rocket Combustors

“…Otherwise, the flame shape and subsequently, the speed of sound field, would be modified such that coupling is not possible anymore. Previous work [26,29] on longitudinal-transverse mode coupling reported a shift in eigenmode frequencies when the excitation frequency was close to an eigenfrequency of the chamber. This effect seems to be reduced for longitudinal mode coupling, but might still be strong enough to prevent higher mode coupling in other cases.…”

“…Resonant mode coupling between a closed injector and a closed-closed combustion chamber shows a slightly different behavior, as indicated by the dispersion relation in Figure 6. One can now apply a similar analysis as before assuming that the injector's fundamental mode shape corresponds to a closed-open pipe mode whose frequency is given by Equation (29). For the combustion chamber, it is once again assume that it is acoustically closed on both ends.…”