非紧致气动噪声传播的理论模型与数值预测方法

The propagation of non-compact aerodynamic noise in an inhomogeneous medium is a hotspot and difficulty problem in aeroacoustics. To predict the acoustic propagation by the traditional acoustic analogy methods, the medium is supposed to be homogeneous and the solid bodies are assumed to be acoustically compact and hard, and therefor the noise scattering from the non-compact impedance boundaries and the noise refraction from the inhomogeneous medium are excluded in the prediction results. To overcome these shortcomings, the FW-H equation is solved by introducing a tailored Green’s function, which includes the scattering from the bodies and the refraction from the medium. A theoretical model of the tailored Green’s function is constructed to account for the scattering from the non-compact impedance bodies. An adjoint Green’s function including the refraction from the inhomogeneous flow is used to solve the theoretical model. Moreover, an imaged observer method is proposed to extend the theoretical model to analysis the noise propagation in half-space. The tailored Green’s function is evaluated numerically by the Boundary Element Method (BEM), and is applied to solve the FW-H equation to simulate the noise propagation. The theoretical and numerical methods developed in this project contribute significantly in revealing the propagation mechanisms of the non-compact noise, improving the numerical accuracy of the noise propagation prediction, and be valuable for noise control.

非均匀介质中非紧致气动噪声的传播问题是气动声学研究的热点与难点问题之一。传统声模拟理论在假设声传播介质均匀的同时将固体边界看作声学紧致硬边界，难以考虑非均匀介质的声折射和非紧致阻抗边界的声散射。本项目采用精确格林函数求解FW-H方程，将非均匀介质的声折射和非紧致阻抗边界的声散射计入精确格林函数。借助理论分析建立非紧致阻抗边界声散射的精确格林函数模型，利用伴随格林函数求解模型方程来考虑非均匀介质的声折射。在此基础上，提出一种镜像观察点方法拓展精确格林函数模型，使之能分析半空间内气动噪声的传播。采用边界元方法数值计算精确格林函数，积分求解FW-H方程模拟非紧致气动噪声从近场到远场的传播。本项目研究成果有助于更正确地认识非紧致气动噪声的传播机制，提高气动噪声传播数值预测的精度，从而为气动噪声的控制提供理论基础和指导原则。

非紧致气动噪声的传播问题是气动声学研究的热点与难点问题之一。传统声比拟理论在假设声传播介质均匀的同时将声源视为声学紧致，难以考虑非紧致边界的声散射和非均匀运动介质的声折射。本项目将声传播介质的非均匀性计入格林函数，采用精确格林函数求解声比拟方程。对均匀运动介质中非紧致噪声传播，利用边界元方法获得精确格林函数的数值解，建立一种非紧致阻抗边界声散射理论模型。二维圆柱算例结果显示，传统声比拟方程中的四极子源是具有物理意义的唯一声源，偶极子源和单极子源仅是固体边界对四极子源的散射效应。对半空间中的气动噪声传播，提出了一种复等效观察点方法以考虑半空间边界的阻抗特性。二维圆柱绕流算例显示半空间边界强化了声源的声辐射能力，小于0.2马赫的介质运动对声传播的影响可以忽略。对非均匀运动介质中非紧致噪声传播，基于等熵和无黏假设，通过线化N-S方程得到一个广义的声比拟方程。将非均匀运动介质的声折射化为伴随平均流的声散射，利用伴随格林函数作为基本解去求解广义声比拟方程，形成一个非均匀运动介质散射气动噪声的理论模型。三维圆柱-NACA0012翼型和三段翼绕流算例显示，广义声比拟方法相比传统声比拟方程能更准确预测远场气动噪声，与实验测试结果的误差在2dB范围内。广义声比拟方法在频域下考虑气动噪声的传播，具有计算效率高的优势。广义声比拟方程的源项与涡紧密关联，有益于分析气动噪声的产生机理。由于广义声比拟方法考虑了非紧致边界的声散射和非均匀运动介质的声折射，是对传统声比拟方法的一种补充和完善。