| 气动声学Lighthill方程的Kirchhoff积分解分析 |
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| 引用本文： | 蔡建程,刘志宏,曾向阳. 气动声学Lighthill方程的Kirchhoff积分解分析[J]. 声学技术, 2014, 33(2): 99-103 |
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| 作者姓名： | 蔡建程 刘志宏 曾向阳 |
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| 作者单位： | [1]浙江师范大学工学院,浙江金华321004; [2]西北工业大学航海学院,陕西西安710072 |
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| 基金项目： | 国家自然科学基金（51306163）、浙江省自然科学基金（LQ13E06000）资助项目. |
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| 摘 要： | Lighthill的声类比(acoustic analogy)是目前气动声定量预测中应用最为广泛的一种方法。使用非齐次波动方程的Kirchhoff积分公式对Ligthhill方程进行求解。Kirchhoff公式中的延迟时间表示不同位置点声源对场点声压叠加时的相位作用,推导时强调延迟时间函数的导数运算。基于Kirchhoff积分公式对于有物体存在于流场中的情况,详细推导了Curle解,并对Curle公式中的各声源项进行了分析。文章有助于气动声学初学者正确地认识声类比理论,加深对Curle公式的理解。
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| 关 键 词： | 气动声学 声类比 Lighthill方程 Kirchhoff积分公式 Curle公式 |
| 收稿时间： | 2013-11-05 |
| 修稿时间： | 2014-02-01 |
An analysis of the Kirchhoff integral approach to the Lighthill equation in aeroacoustics |
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| CAI Jian-cheng,LIU Zhi-hong and ZENG Xiang-yang. An analysis of the Kirchhoff integral approach to the Lighthill equation in aeroacoustics[J]. Technical Acoustics, 2014, 33(2): 99-103 |
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| Authors: | CAI Jian-cheng LIU Zhi-hong ZENG Xiang-yang |
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| Affiliation: | CAI Jian-cheng,LIU Zhi-hong,ZENG Xiang-yang(College of Engineering, Zhejiang Normal University, Jinhua 321004, Zhejiang, China;College of Marine Engineering, Northwestern Polytechnical University, Xi＇an 710072, Shaanxi, China) |
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| Abstract: | Lighthill＇s acoustic analogy is used extensively in predicting aerodynamic sound.In this paper,the Kirchhoff integral solution to the inhomogeneous wave equation is employed to solve the Lighthill equation.The retarded time in Kirchhoff＇s formula accounts for the phase interactions from different sources.Special attention is paid to the derivadves of functions with retarded times.Based on Kirchhoff＇s solution,the Curle formula which takes into account the effect of rigid surface boundary on aerodynamic sound emission is derived,and the sound sources are discussed.This paper can help practicing acousticians and young researchers better understand the acoustic analogy theory and Curle＇s equation. |
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| Keywords: | aeroacoustics acoustic analogy Lighthill＇s equation Kirchhoff＇s integral formula Curle＇s formula |
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