二维圆柱对旋转单极子点源的声散射  

Sound Scattering of a Two-dimensional Cylinder due to a Rotating Monopole Point Source

作　　者：薛丝丹 钱振昊 何嘉华 刘秋洪[1,2] XUE Sidan;QIAN Zhenhao;HE Jiahua;LIU Qiuhong(National Key Laboratory of Science and Technology on Aerodynamic Design and Research,Northwestern Polytechnical University,Xi′an 710072,China;Key Laboratory of Aerodynamic Noise Control,China Aerodynamic Research and Development Center,Mianyang 621000,Sichuan,China)

机构地区：[1]西北工业大学翼型叶栅空气动力学重点实验室,西安710072 [2]中国空气动力研究与发展中心气动噪声控制重点实验室,四川绵阳621000

出　　处：《噪声与振动控制》2022年第5期60-65,共6页Noise and Vibration Control

基　　金：中国空气动力研究与发展中心气动噪声控制重点实验室开放课题资助项目(ANCL20200303);翼型、叶栅空气动力学重点实验室基金资助项目(JZX7Y202001SY002101-614220120030101)。

摘　　要：采用理论分析和数值计算方法研究二维刚性圆柱对旋转单极子点源入射声波的散射效应。齐次Helmholtz方程基本解在极坐标系内用自由空间格林函数的级数展开式表示。对任意形状的刚性散射边界,通过求解线性声学波动方程建立声场边界积分表达式。数值解可在频域下采用边界元方法获取。进一步利用贝塞尔函数的加法定理,分别推导点源与圆柱同轴、异轴旋转状态下的声场理论解析表达式。边界元方法的数值解与理论解析解吻合一致。点源向外辐射声波的频率由点源谐振频率、旋转频率和谐波阶次共同决定。点源与圆柱同轴旋转时,谐波阶次为0的声波以同心圆状向外辐射,不为0的声波则以螺旋状向外辐射,螺旋瓣的数量由谐波阶次的绝对值相同。点源与圆柱异轴旋转时,圆柱的声散射呈现显著的偶极子特征,且声场的指向性复杂。The sound scattering from a two-dimensional rigid cylinder due to a rotating monopole point source is studied numerically and theoretically. The fundamental solution of the homogeneous Helmholtz equation is expressed in terms of a series expansion of the free-space Green ′ s function in a polar coordinate system. An integral expression for the sound field is established by solving the linear acoustic wave equation with the acoustic hard boundary condition on the scattering surface of arbitrary shape. The numerical solution is then obtained in the frequency domain by means of boundary element method. Incorporating the free space Green ′ s function and the addition theorem of the Bessel function, the analytical solution is derived for the sound scattering due to a point monopole rotating coaxially and off-axially with the acoustic hard cylinder, respectively. The numerical solutions by the boundary element method agree well with the analytical results for all observer angles and frequencies. The frequencies of the acoustic wave radiating form the rotating source are dependent on the source frequency, the rotation frequency and the harmonic order. For the case of the point source rotating coaxially with the cylinder, the acoustic harmonic wave of order 0 radiates outwards in the form of concentric circles, while those of non-zero orders radiate outwards in a spiral form, with the number of spiral flaps being equal to the harmonic order. When the point source is in off-axis rotation with the cylinder, the acoustic scattering from the cylinder presents obvious dipole characteristics and the directivity of the acoustic field becomes complicated.

关 键 词：声学 边界元方法 刚性圆柱 理论分析 声散射 旋转单极子点源 

分 类 号：O42[理学—声学]