Some recent results for nonlinear acoustics in combustion chambers

Conditions of high energy densities and low losses in combustion chambers encourage the excitation and of organized unsteady motions generically called combustion instabilities. The fluctuations, common in propulsion systems, often reach sufficient amplitudes to cause excessive rates of heat transfer to exposed and unacceptable structural vibrations, causing failure in extreme cases. In many cases, to avoid the of instabilities, combustion chambers are operated below their maximum performance. Considerable effort has been spent, for more than four decades, on experimental and analytical programs devoted to solving problems of combustion instabilities. Much of the work has been required to measure quantities which, because of the complex processes involved, cannot be predicted accurately from first principles. Analytical work has been concerned largely with linear behavior, the chief purpose being to predict stability of small disturbances in combustion chambers. Many useful results have been obtained, serving in practice to help design experiments, correlate data, and predict the stability of new systems. However, linear behavior is only a small part of the general problem. A combustion chamber is an isolated system so far as its stability is concerned, and unstable disturbances evolve as 'self-excited' motions. Hence their amplitudes will grow indefinitely unless nonlinear processes are effective. Complete understanding of observed behavior will therefore be reached only by treating nonlinear behavior. In the recent past, increased attention has been paid to nonlinear combustion instabilities. It is particularly important for practical purposes to explain the existence of limit cycles and the occurrence of unstable motions in linearly stable systems exposed to large initial disturbances. These matters are far from closed, and although substantial progress has been accomplished, little impact has been made on the development of new systems. The chief purpose of this paper is to provide a brief review of work on nonlinear combustion instabilities, largely in the framework of an approximate analysis. Some connections will be made with the modern theory of nonlinear dynamical systems, including very recent and incomplete attempts by others to assess the possible chaotic behavior observed in laboratory tests.