Stability of quasi-one-dimensional isentropic flows

The stability of complex fluid systems is often estimated to the first order using one-dimensional models, illustrated by Dowling, who describes several model problems related to the prediction of combustion instabilities in gas turbines and rocket engines. The numerical method using a frequency-domain approach similar to that of the recent development of Prasad and Feng to study the stability of spatially varying one-dimensional flows. The magnitudes of the acoustic reflection coefficients at the inlet and exit boundaries influence the stability of the flow, whereas the phases of these coefficients have a bearing on the natural frequencies of the system eigenmodes. The frequencies obtained by the two methods are in very good agreement, although the damping rates exhibit some differences at small mode orders.