克希荷夫旋转声场预估方法  

Kirchhoff rotation sound field estimation method

作　　者：李建华 刘志红[1,2] 孙琪 张开业 徐希鑫[1,2] LI Jianhua;LIU Zhihong;SUN Qi;ZHANG Kaiye;XU Xixin(School of Mechanical and Automotive Engineering,Qingdao University of Technology,Qingdao 266520,Shandong,China;Key Laboratory of Industrial Fluid Energy Conservation and Pollution Control(Qingdao University of Technology),Ministry of Education,Qingdao 266520,Shandong,China)

机构地区：[1]青岛理工大学机械与汽车工程学院,山东青岛266520 [2]工业流体节能与污染控制教育部重点实验室(青岛理工大学),山东青岛266520

出　　处：《哈尔滨工业大学学报》2024年第8期103-111,123,共10页Journal of Harbin Institute of Technology

基　　金：国家自然科学基金(61871447);山东省自然科学基金(ZR2023MF018)。

摘　　要：为精确预估旋转声场的声辐射,提出了一种克希荷夫旋转声场预估方法。以旋转点声源的声辐射为基础,利用球谐波、勒让德函数和偶极子几何关系,构建了旋转横向和纵向两种偶极子源的声辐射频域解析式,量化了横向和纵向偶极子源对旋转声场声辐射的贡献;引入克希荷夫积分,融合旋转点源及偶极子源,构造了旋转克希荷夫源,推导了旋转克希荷夫源的声辐射预估数学模型及其声压解析式,确定了解析无限项谐波阶次截断的关键影响因素及其截断门限值。经数值仿真,探讨了旋转马赫数Ma<1时,基频、旋转频率和旋转半径对旋转声场的影响,给出了旋转声场的声压空间分布、多普勒和指向性特征,并经声场等价性验证,空间任意点声压值相对误差为0.05,进一步证明了旋转克希荷夫源的有效性。在半消声室对旋转声场进行实验测试,结果表明:与仿真一致,验证了克希荷夫积分方法的有效性和精确性;该方法通过构建的旋转克希荷夫源代替传统点源叠加,有效提高了旋转声辐射预估精确性。To accurately predict the acoustic radiation of rotating sound field,a prediction method of Kirchhoff rotating sound field is proposed.Based on the acoustic radiation of rotating point sound source,using spherical harmonics,Legendre function and dipole geometry,the frequency domain analytical expressions of acoustic radiation of rotating transverse and longitudinal dipole sources are constructed.The contributions of transverse and longitudinal dipole sources to acoustic radiation of rotating sound field are quantified.By introducing Kirchhoff integral and combining rotating point source with dipole source,the rotating Kirchhoff source is constructed.The mathematical model of acoustic radiation prediction of rotating Kirchhoff source and its analytical expression of sound pressure are derived.The key factors influencing its cutoff threshold for analyzing infinite harmonic order truncation are determined.Through numerical simulation,the effects of fundamental frequency,rotation frequency and rotation radius on the rotating sound field are discussed when Ma<1.The spatial distribution of sound pressure,Doppler and directivity characteristics of the rotating sound field are analyzed.The validity of the rotated Kirchhoff source is verified by the equivalence verification of the sound field,with a relative error of the sound pressure value at any arbitrary point being within 0.05,which further demonstrates the effectiveness of the rotating Kirchhoff source.The results obtained from experimental testing in a semi-anechoic chamber confirm the effectiveness and accuracy of the Kirchhoff integral method,consistent with the simulations.This method effectively improves the prediction accuracy of the rotating sound radiation by replacing the traditional point source superposition with the constructed rotating Kirchhoff source.These research findings hold significant theoretical reference value and significance for the control of rotating machinery radiation noise and the design of low-noise rotation structures.

关 键 词：声辐射 偶极子源 截断误差 克希荷夫积分方程 克希荷夫源 

分 类 号：TB52[理学—物理]