THERMOACOUSTICS - TRANSIENT REGIMES AND SINGULAR TEMPERATURE PROFILES

The stationary, periodic solution to the problem of oscillating flow o f a conducting fluid, in a duct closed at one end and with periodical mass flow rate at the other end, is known to exhibit a singularity in the mean temperature at the closed end when transverse conduction in t he fluid and the duct wall is taken into account, but longitudinal con duction is neglected. For instance, a solution of that type was origin ally suggested by Gifford and Longsworth as a prototype for pulse-tube refrigeration. Whether these stationary singular solutions are physic al or mere theoretical curiosities depend upon the existence of a scen ario leading to such a Limit cycle. To address that question, a transi ent theory is formulated, using the narrow duct approximation. The res ults show that at least for constant fluid thermal conductivity, all s ingular profiles generated by the mechanism under study are linearly s table. For round tubes, the temperature profile is shown to evolve, fr om an arbitrary initial value, toward an equilibrium profile which res ults in balanced energy fluxes. (C) 1998 American Institute of Physics .