有限长号筒中非线性声传播的数值模拟研究

研究了大振幅活塞声源经有限长号筒向外辐射声波的非线性声学问题。采用具有频散保持特性的高精度计算格式求解了适用于变截面管道的一维非线性声场模型,并考虑到声波的非线性畸变及管口处的声反射,加入了宽频时域声阻抗边界条件。宽频阻抗模型的共轭复数系数采用优化拟合方法近似求解,并采用递推卷积算法快速求解出时域声阻抗。在弱非线性条件下模拟指数形号筒中的声传播取得了与已有实验相一致的结果,表明模型能够描述声波非线性畸变带来的宽频特性。进而采用本模型数值模拟了大振幅活塞声源在双曲形、锥形、指数形和正弦形号筒中的非线性声传播问题,结果表明号筒出口声压级受活塞振动速度、频率以及号筒形状的影响,并分析讨论了波形畸变与号筒几何形状之间的关系。 

Numerical simulation of nonlinear propagation of sound waves in a finite horn

Nonlinear acoustic propagation generated by a vibrating piston in a finite horn is numerically studied. A quasi-one-dimensional nonlinear model with varying cross-section uses high-order low-dispersion numerical schemes to solve the governing equation. Considering the nonlinear wave distortion and reflected sound waves at the mouth, broadband time-domain impedance boundary conditions are employed. The impedance approximation can be optimized to identify the complex-conjugate pole-residue pairs of the impedance functions, which can be calculated by fast and efficient recursive convolution. The numerical results agree very well with experimental data in the situations of weak nonlinear wave propagation in an exponential horn, it is shown that the model can describe the broadband characteristics caused by nonlinear distortion. Moreover, finite-amplitude acoustic propagation of a piston source in types of horns is simulated, including hyperbolic, conical, exponential and sinusoidal horns, it is found that the sound pressure level at the horn mouth are strongly affected by the driving velocity and frequency of the piston and the horn profiles, and the interplay between the waveform distortion and the horn geometry is discussed.