Experimental verification of the minimum entropy production principle in thermoacoustic systems

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The Newton's calculation of the sound speed in free space became the first step in showing the importance of thermodynamics in sound. The study of sound in hollow tubes also has a long history ; notably Kirchhoff did some theoretical work on this topic, in which sound exhibits a rich variety of visco-thermal effects through interactions with the solid walls of the tubes. In particular, thermo-acoustic phenomena such as self-sustained gas oscillations and heat pumping, which are typical examples of the dissipative structure appeared in non-equilibrium systems, are produced in a tube with strong temperature gradients. The phenomena observed in thermo-acoustic system might be related to the minimum entropy production principle.The propagation of sound in a circular tube is indeed a fundamental theme common to many areas of classical acoustics. Surprisingly, however, full experimental verification of Kirchhoff's theory has not been forthcoming despite the numerous works undertaken since that early research. First we measured the phase velocity and attenuation coefficient in the narrow regions of tubes, where the sound undergoes anomalous dispersion, such as light passing through an optical prism, and is seen to slow down remarkably to the extent that a runner can pass ahead of it. Kirchhoff's theory can be verified by experiment over a wide range of thermodynamical cycle from isentropic to isothermal. Secondary, experiments are performed to test the applicability of the minimum entropy production principle, using traveling a wave thermoacoustic engine in a looped tube. We obtained experimental evidence that acoustic fields around the tube, pressure and velocity distribution including phase difference between them, are observed to follow the principle.