Abstract:

In typical conditions the time scale for the development of the thermoacoustic instability in a tube is slow compared with the acoustic period. It is therefore possible to solve the problem by the method of multiple time scales. In this way a time-domain description of the process is obtained. The perturbation results are compared with the exact solution of the linear problem and their range of validity is discussed. It is found that they are accurate only when the spacing of the plates in the stack is sufficiently large. The ``short-stack approximation'' is also introduced and evaluated with comparable results, provided the effective wave number is chosen appropriately. [Work supported by the Office of Naval Research.]