分布稳态热源声传播与熵产的理论分析
Theoretical analysis of sound propagation and entropy generation across a distributed steady heat source
摘要：
声波和熵波相互作用的管道与稳定的热源和平均流进行了分析，使用渐近展开（AE）的低频。通过利用流动不变量和应用多步策略获得解析AE解。所提出的解决方案提供了一阶修正的紧凑模式的平均流量变量的积分的形式。然后建立了一个特征值系统来预测含有分布式热源或热沉的管道的热声模态。从AE解决方案的预测同意以及与线性化的欧拉方程的数值结果的频率和增长率，只要满足低频条件。AE解决方案能够准确地重建声波和熵波，并纠正与紧凑模型相关的预测熵波中的重大错误。分析表明，热声系统需要考虑的熵波所产生的相互作用的声波和分布的稳定热源，特别是当密度或熵依赖的边界条件规定在管道端部。此外，AE方法和修改的WKB近似方法的组合进行了讨论的冷却情况。AE解决方案弥补了WKB解决方案在低频和极低频域的缺点，并促进非均匀管道流场中的声传播和熵产生的全频理论分析。
英文摘要：
Acoustic and entropy waves interacting in a duct with a steady heat source and mean flow are analysed using an asymptotic expansion (AE) for low frequencies. The analytical AE solutions are obtained by taking advantage of flow invariants and applying a multi-step strategy. The proposed solutions provide first-order corrections to the compact model in the form of integrals of mean flow variables. An eigenvalue system is then built to predict the thermoacoustic modes of a duct containing a distributed heat source or sink. Predictions from the AE solutions agree well with the numerical results of the linearised Euler equations for both frequencies and growth rates, as long as the low-frequency condition is satisfied. The AE solutions are able to accurately reconstruct the acoustic and entropy waves and correct the significant errors in the predicted entropy wave associated with the compact model. The analysis illustrates that the thermoacoustic system needs to account for the entropy wave generated by the interaction of acoustic wave and the distributed steady heat source, especially when density- or entropy-dependent boundary conditions are prescribed at the duct ends. Furthermore, a combination of the AE method and the modified WKB approximation method is discussed for a cooling case. The AE solutions remedy the disadvantage of the WKB solution in the low and very low-frequency domain and facilitate full-frequency theoretical analyses of sound propagation and entropy generation in inhomogeneous duct flow fields.
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