Abstract
This paper attempts to simulate thermoacoustic oscillations in an air-filled, looped tube with a so-called stack inserted and subjected to a temperature gradient. The boundary-layer theory is applied, focusing on initial processes in instability. While the theory can describe the emergence of self-excited Taconis oscillations in a helium-filled, quarter-wavelength tube, it is open whether or not the theory is applicable to the case of the looped tube because the stack consisting of many narrow tubes is usually employed. Marginal conditions of instability are obtained by solving an initial-value problem for evolution of a small disturbance of velocity. It is found that the marginal conditions for the temperature ratios agree qualitatively with the experimental results by Ueda & Kato. It is unveiled that, as the porosity of the stack decrease, the traveling waves tend to appear in the course of time.
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