Experimental verification of the minimum entropy production principle in thermoacoustic systems

牛顿对自由空间声速的计算成为表明热力学在声音中的重要性的第一步。中空管声的研究也有很长的历史；值得注意的是，基尔霍夫在这个问题上做了一些理论工作，其中通过与管子的固体壁相互作用，声显示了丰富的各种粘热效应。特别是，非平衡系统中出现的耗散结构的典型例子，如自持气体振荡和热泵等热声现象，都是在具有强烈温度梯度的管内产生的。在热声系统中观察到的现象可能与最小熵产生原理有关。声音在圆管中的传播确实是许多经典声学领域共同的基本主题。然而，令人惊讶的是，尽管自早期研究以来进行了大量的工作，但基尔霍夫的理论并没有得到充分的实验验证。首先，我们测量了管子狭窄区域的相速度和衰减系数，在管子的狭窄区域，声音经历了反常的色散，例如光穿过光学棱镜，可以看到声音显著减慢到跑步者可以超过它的程度。Kirchhoff的理论可以在从等熵到等温的大范围热力学循环中得到实验验证。其次，利用环形管内行波热声发动机对最小熵产生原理的适用性进行了实验验证。我们得到的实验证据表明，管子周围的声场，包括压力和速度分布，包括它们之间的相位差，都遵循这一原理。

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.