离心风机气动声学分析的一个理论模型和计算方法

Theoretical Model for Aeroacoustics Analysis of Centrifugal Fans

通过求解具有延迟时间、包含三维流速影响的非齐次波动方程,得到了离心叶轮气动声学的基本方程.对气动声源的分析表明,在离心风机的气动噪声中,起主要影响作用的是偶极子和四极子声源,而流动过程中产生的涡是最主要的四极子源.提出了一种用于分析离心风机气动噪声的声学模型,即忽略蜗壳进、出口声学软边界的影响,将蜗壳简化为一个封闭的声学硬边界柱壳,并推出了柱壳腔体内的格林函数.利用该函数对离心风机内部由旋转叶轮产生的气动声场进行了时域求解并给出了理论解方程.在计算出离心风机内部的三维非稳定流场之后,利用本文模型和理论解方程就可求出与该流场相对应的气动声场.

The fundamental aeroacoustic equation of the centrifugal impeller was established by solving the inhomogeneous, uniformly moving medium wave equation. Then, the Lighthill's acoustic analogy theory and Powell-Howe's vortex sound theory were applied to the analyses of the aeroacoustic sources of a centrifugal fan. It is shown that the dipole and quadrupole sources are the key factors for the fan's aerodynamic sound, and the vortexes inside the fan flow field are the uppermost quadrupole sources. For aeroacoustics analysis of a centrifugal fan, we proposed a theoretical model, i.e. neglecting the influence of sound-soft boundary at the inlet and outlet of a centrifugal fan. The volute was simplified to be a cylindrical cavity with sound hard wall. Finally, Green function in the cylindrical cavity space was presented, and the aeroacoustic solution in the centrifugal fan was deduced in time-domain by using the Green function. According to the calculated results of the three-dimensional unsteady flow in a centrifugal fan, the corresponding sound field may be obtained.