ABSTRACT: An approximate time-domain description of the development of the thermoacoustic
instability in gas-filled tubes is developed by exploiting the difference between the
instability time scale and the period of standing waves. The perturbation results compare
very favorably with the exact frequency-domain theory of Rott. The perturbation results
are further simplified by introducing a short-stack approximation which is numerically
much simpler and only slightly less accurate. An approximate expression for the critical
temperature gradient accounting for viscous effects and other design features is also
derived. In addition to the fundamental mode of a tube closed at both ends, the theory
includes higher modes as well as open-end boundary conditions.
J. Acoust. Soc. Am. 103, 3309-3317, 1998
Andrea Prosperetti's Homepage | Publications