LINEAR AND NONLINEAR ACOUSTICS WITH NONUNIFORM ENTROPY IN COMBUSTION CHAMBERS

A one-dimensional analytical model is presented for calculating the longitudinal acoustic modes of idealized "dump-type" ramjet engines. A plane flame has been studied and incorporated into the combustor model where the flame is allowed to move or oscillate in the combustor. This provides three mechanisms of interaction at the flame sheet: change in mean temperature in the combustor, energy conversion at the sheet due to upstream fluctuations, and fluctuating heat release. A supersonic inlet upstream contains a shock wave in its diffuser section while the downstream exit is terminated by a choked nozzle. The linear coupling of the acoustic and entropy waves at the inlet shock, flame sheet, and exit nozzle along with acoustic admittances at the inlet and exit are combined to determine the stability of the system as well as the acoustic modes.; In the linear case, the entropy and acoustics are decoupled in the flow field. All linear coupling occurs at the boundary conditions. For cases where the entropy fluctuations are of the same order of magnitude as the pressure oscillations and the coupling is of comparable order, the linear stability of the acoustic field is strongly dependent upon the entropy fluctuations. The linear acoustics are predominantly governed by the boundary conditions; thus it is imperative that the entire system of inlet, combustor, and exit be considered together to determine the characteristic eigenvalues (resonant frequencies) and eigenfunctions (mode shapes).; The energy in the acoustics of this model is controlled by the energy loss (gain) at the boundaries balances with the energy gain (loss) at the flame front. Acoustic energy is typically lost at both the inlet and exit, but fluctuating entropy waves convecting with the mean flow velocity that impinge upon a choked nozzle generate acoustic waves that can, under the proper conditions, feed acoustic energy into the system. The plane flame mechanism also contributes to the acoustic energy from the interaction of entropy and acoustic waves at a flame sheet. This allows a systematic study of the influence of entropy-acoustic wave interactions on the linear stability and modes of this combustor system. (Abstract shortened with permission of author.)...