承受平均流量和平均温度梯度的光滑变截面管道中的声吸收和声产生
Acoustic absorption and generation in ducts of smoothly varying area sustaining a mean flow and a mean temperature gradient
摘要：
在具有变化的横截面积和维持亚音速非等熵平均流的管道中，轴向变化的流动条件影响系统的声能平衡。这对于理解和控制热声现象，特别是燃烧室中的热声现象具有重要意义。这项工作的目的是量化的声能变化，在这样的配置，使用的吸声系数，$Δ$。管道的声学响应，以声强迫确定使用的分析模型，忽略熵波动的影响声场，随后，$Δ$估计。$Δ$的模型预测使用线性化欧拉方程（LEEs）求解器进行验证。结果表明，只要满足解析解设定的频率下限，该模型在低于$0.25$的马赫数下是准确的。对于具有线性平均温度梯度的圆锥形变面积管道，观察到$Δ$对频率的依赖性很小，并且当上游边界为消声而非非消声时，$Δ$的绝对值趋于最大化。更重要的是，还观察到$Δ$对平均温度梯度的依赖性比对这种配置的面积梯度变化的依赖性更强。对$Δ$的进一步参数和优化研究揭示了一个重要发现，即正平均温度梯度（代表加热管道）引起声能吸收。类似地，负平均温度梯度，表示冷却管道引起的声能产生-该分析的关键结果。这种行为被证明是符合一个简化的分析的声能平衡。基于这一发现，通过改变平均温度梯度，实现了声能产生的线性比例减少。
英文摘要：
In ducts with varying cross-sectional area and sustaining a subsonic non-isentropic mean flow, the axially varying flow conditions affect the acoustic energy balance of the system. This is significant in understanding and controlling thermo-acoustic phenomena, particularly in combustors. This work aims at quantifying the acoustic energy change in such configurations, using the acoustic absorption coefficient, $Δ$. The acoustic response of the duct to acoustic forcing is determined using an analytical model, neglecting the effect of entropy fluctuations on the acoustic field, and subsequently, $Δ$ is estimated. The model predictions of $Δ$ are validated using a linearised Euler equations (LEEs) solver. The model was found to be accurate for Mach numbers below $0.25$, provided the lower frequency limit set by the analytical solution is satisfied. For conically varying area ducts with linear mean temperature gradient, it was observed that $Δ$ showed very little dependence on frequency, and that the absolute value of $Δ$ tended to be maximised when the upstream boundary was anechoic rather than non-anechoic. More importantly, $Δ$ was also observed to show stronger dependence on the mean temperature gradient than area gradient variation for such configurations. Further parametric and optimisation studies for $Δ$ revealed a crucial finding that a positive mean temperature gradient, representing a heated duct caused acoustic energy absorption. Similarly, a negative mean temperature gradient, representing a cooled duct caused acoustic energy generation -- a key result of this analysis. This behaviour was shown to be consistent with a simplified analysis of the acoustic energy balance. Based on this finding, a linearly proportional reduction in acoustic energy generation was achieved by changing the mean temperature gradient.
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