Experimental verification of the minimum entropy production principle in thermoacoustic systems

牛顿对自由空间中声速的计算，成为证明热力学在声音中的重要性的第一步。对空心管中声音的研究也有很长的历史;特别是基尔霍夫在这方面做了一些理论工作，其中声音通过与管的固体壁的相互作用表现出丰富的粘热效应。特别是，热声现象，如自持气体振荡和热泵，这是典型的例子出现在非平衡系统中的耗散结构，产生在一个强的温度梯度管。在热声系统中观察到的现象可能与最小熵产生原理有关，声在圆管中的传播确实是经典声学许多领域的共同基本主题。然而，令人惊讶的是，基尔霍夫理论的全面实验验证并没有出现，尽管自早期研究以来进行了许多工作。首先，我们测量了管道狭窄区域的相速度和衰减系数，在狭窄区域中，声音会发生反常的色散，比如光通过光学棱镜，并且可以看到明显的减速，以至于一个跑步者可以在它前面通过。Kirchhoff的理论可以在从等熵到等温的很宽的循环范围内得到实验的验证。其次，以行波热声发动机为例，对最小熵产生原理的适用性进行了实验验证。实验结果表明，管内声场分布、压力分布和速度分布（包括相位差）均遵循这一规律。

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.