We obtain linearized, BiGlobal thermoacoustic solutions in a pulse tube driven via an imposed mean temperature gradient. Here, the pulse tube is treated as a key unit of a thermoacoustic heat engine, in which the conversion of thermal energy to useful acoustic fluctuations occurs. A primary goal of this work is to understand the hydrodynamic efficiency of the energy conversion process and how it depends upon some of the important operating parameters, including the geometry of the device which in the limit of long length-to-diameter ratio approaches the so-called narrow tube approximation. As this limit is frequently imposed in the wave propagation analyses of thermoacoustic devices, it is critical to investigate the physical connections of such a model to more realistic finite-length pulse tube configurations, which we do here. The mean flow is quiescent with an analytic mean temperature profile that still models the necessary physical details of the hot heat exchanger and regenerator. The computed thermoacoustic oscillations are found to be globally stable, approaching neutral stability conditions at the narrow tube limit. In finite-length tubes, three distinct types of modes are identified and analyzed. Here, within a linear framework, radial modes do appear to act as key enablers for longitudinal modes to be the primary carriers of acoustic energy from the pulse tube section, while the identified boundary modes, essentially numerical constructs, are ignored in the analysis. Further, a disturbance energy-based efficiency metric is constructed that provides mechanistic understanding of some of the key parameters in pulse tube operation. For finite-length tubes, it shows oscillations of the first asymmetric mode to be the most efficient, while the axisymmetric perturbations dominate for longer tubes that eventually lead to the idealized plane wave propagation.

中文翻译：

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热驱动脉冲管中的全局热声振荡

我们在通过施加的平均温度梯度驱动的脉冲管中获得线性化的 BiGlobal 热声解。在这里，脉管被视为热声热机的关键单元，其中发生热能向有用的声波波动的转换。这项工作的主要目标是了解能量转换过程的流体动力学效率以及它如何依赖于一些重要的操作参数，包括在长长径比的限制下接近如此的装置的几何形状。 -称为窄管近似。由于在热声设备的波传播分析中经常施加此限制，因此研究此类模型与更现实的有限长度脉冲管配置的物理连接至关重要，我们在此进行。平均流量是静止的，具有解析平均温度曲线，该曲线仍对热换热器和再生器的必要物理细节进行建模。计算出的热声振荡被发现是全局稳定的，在窄管极限处接近中性稳定条件。在有限长度的管中，识别和分析了三种不同类型的模式。在这里，在线性框架内，径向模式似乎确实是纵向模式的关键促成因素，纵向模式是来自脉管部分的声能的主要载体，而识别出的边界模式，本质上是数值结构，在分析中被忽略。此外，构建了一个基于干扰能量的效率度量，它提供了对脉管操作中一些关键参数的机械理解。对于有限长度的管子，