考虑体粘滞效应的超声驻波热声发动机的高保真模拟
High-fidelity simulation of an ultrasonic standing-wave thermoacoustic engine with bulk viscosity effects
摘要：
本文对超声驻波热声发动机（TAE）模型进行了边界层解析、非结构化全可压缩Navier-Stokes数值模拟。该模型被构造为四分之一波长发动机，尺寸约为4 mm × 4 mm，工作频率为25 kHz，包括一个热声堆栈和一个硬币形腔体，这一设计灵感来自Flitcroft和Symko（2013）。解决了热和粘性边界层（10 $\mathrmμ$ m的顺序）。振动和旋转分子松弛建模与有效的体积粘度系数修改的粘性应力张量。根据理论衰减曲线和半经验衰减曲线的差异，估算了有效体积粘度系数。对有效体积粘度系数的贡献可以被确定为来自振动和旋转分子弛豫。系数的包含捕获从次声（$\sim$ 10 Hz）到超声（$\sim$ 100 kHz）频率的声吸收。体积粘度的值取决于压力、温度和频率，以及工作流体的相对湿度。模拟的TAE进行的极限环，与增长率和极限环的振幅随体积粘度的大小非单调变化，达到最大值的相对湿度水平为5%。开发了相应的线性模型，具有较小的损失，线性模型过度预测瞬态增长率，但给出了一个准确的估计极限环的行为。基于高保真度计算框架的超声状态下的热声能量转换的更好理解将有助于进一步提高小型热声发动机的功率密度优势。
英文摘要：
We have carried out boundary-layer-resolved, unstructured fully-compressible Navier--Stokes simulations of an ultrasonic standing-wave thermoacoustic engine (TAE) model. The model is constructed as a quarter-wavelength engine, approximately 4 mm by 4 mm in size and operating at 25 kHz, and comprises a thermoacoustic stack and a coin-shaped cavity, a design inspired by Flitcroft and Symko (2013). Thermal and viscous boundary layers (order of 10 $\mathrmμ$m) are resolved. Vibrational and rotational molecular relaxation are modeled with an effective bulk viscosity coefficient modifying the viscous stress tensor. The effective bulk viscosity coefficient is estimated from the difference between theoretical and semi-empirical attenuation curves. Contributions to the effective bulk viscosity coefficient can be identified as from vibrational and rotational molecular relaxation. The inclusion of the coefficient captures acoustic absorption from infrasonic ($\sim$10 Hz) to ultrasonic ($\sim$100 kHz) frequencies. The value of bulk viscosity depends on pressure, temperature, and frequency, as well as the relative humidity of the working fluid. Simulations of the TAE are carried out to the limit cycle, with growth rates and limit-cycle amplitudes varying non-monotonically with the magnitude of bulk viscosity, reaching a maximum for a relative humidity level of 5%. A corresponding linear model with minor losses was developed; the linear model overpredicts transient growth rate but gives an accurate estimate of limit cycle behavior. An improved understanding of thermoacoustic energy conversion in the ultrasonic regime based on a high-fidelity computational framework will help to further improve the power density advantages of small-scale thermoacoustic engines.
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