T. Lieuwen et Bt. Zinn, Application of multipole expansions to sound generation from ducted unsteady combustion processes, J SOUND VIB, 235(3), 2000, pp. 405-414
Predicting and controlling the behavior of oscillatory combustion systems r
equires an understanding of the interactions between the periodic combustio
n and acoustic processes. Due to the complexity of these interactions, a nu
mber of past analyses of these problems have assumed a "concentrated", infi
nitely thin, combustion region. Although such treatments of the combustion
process as a lumped element are attractive because of their simplicity, thi
s paper shows that they may produce significant errors. It is further shown
that such errors can be minimized by use of multipole expansion techniques
similar to those used in acoustic radiation problems. Specifically, this p
aper develops a formalism for describing the combustion region as a series
of lumped parameters whose magnitudes are proportional to ascending powers
of the ratio L/lambda, where L and lambda are the length of the combustion
region and the acoustic wavelength respectively. In the limit as L/lambda g
oes to zero, only the first term of this expansion is significant and the "
concentrated" combustion approximation is recovered. As L/lambda, increases
, additional parameters (e.g., higher order terms) are needed to accurately
describe the effect of the combustion process on the acoustic oscillations
and must be included in the analysis. The paper closes with example calcul
ations showing that accuracy in modelling combustion-acoustics interactions
can be significantly increased by implementation of the developed techniqu
e. (C) 2000 Academic Press.