开口/封闭薄壳体声辐射和散射的统一边界积分方程解法

推导了在二维和三维空间下开口和封闭薄壳体在任意阻抗边界条件下声辐射和散射的统一边界积分方程.相对于以前的求解方法,该方程求解声辐射和散射问题具有相同的影响矩阵,能够同时求解薄壳体气动和振动噪声的辐射和散射现象,以及分析壳体声阻抗对声波传播的影响.推导的方程可以应用于叶轮机械、管道等噪声和消声器消声性能的预测等方面.在此方程基础上,可以进一步考虑运动边界和运动介质对声辐射和散射的影响. 关键词： 薄壳体 声阻抗 积分方程 边界元方法     

矢量气动声学的理论研究进展及应用

气动声学的声比拟理论以密度、声压等标量为波动算子变量,建立非齐次波动方程,描述流体运动及与边界作用诱发声音的辐射,但标量无法直接描述声能量的传播过程和途径.在流体力学研究中,标量用于描述当前当地的物质状态,而矢量用于描述质量和能量的传输.借鉴上述思想,开展了矢量气动声学的研究,概述矢量气动声学的理论研究进展及应用,主要包括:（1）以声粒子速度为变量,采用声比拟理论的思想直接从Navier-Stokes方程出发推导建立了气动声学的矢量波动方程及两种频域解;（2）综合利用声压和声粒子速度的积分解,直接求解声源周围的瞬时和有功声强矢量场,直观显示声能量的传播途径,应用于旋转声源辐射声能量的传播分析,揭示了亚音速旋转声源辐射声能量的3种传播模式:螺旋模式、声学黑洞模式和R-A模式;（3）采用球谐级数展开方法建立旋转点/紧凑声源辐射噪声的声压和声粒子速度的频域解析解,在此基础上推导了声功率谱的频域解析解,建立了识别旋转叶片声源在空间域和频域分布特征的方法;（4）综合利用矢量气动声学方法和等效源方法,显示声源和散射边界周围声强矢量场的分布特征和能量传播途径,直接揭示了阻抗边界主要的吸声位置以及直接计算得到阻抗边界的吸收声功率.      

声场作用下两空化泡相互作用的研究

建立了声场作用下两空化泡泡壁的运动方程,得出了双空化泡的共振频率,振动半径及空化噪声声压．由频率方程,振动半径和声压方程可以看出两气泡的运动情况与单气泡的运动情况有着明显的不同．共振频率,共振振幅及声压与两气泡之间的间距有关．在一定的简化条件下,运用MATLAB语言对共振频率,共振振幅及空化噪声声压进行了数值求解,发现共振频率和共振振幅随空泡间距的增大而增大,空化噪声声压随距离增大先增大后减小． 关键词： 超声 空化 频率 声压     

标量波传播问题的双互易精细积分法

为避免使用计算多种特征频率下的声场响应，采用双互易方法将边界积分方程中时间二次导数项的域积分转化为边界积分.首先，将计算场点配置在边界上并考虑边界条件，可以获得由内部节点上声压量线性表示的边界节点上的物理量；其次，将计算场点配置于域内离散节点上，将所得边界积分方程组中关于边界物理量用内部节点的声压量线性表示，获得关于声压量的二阶常微分方程组；第三，引入声压变化速度作为未知量，将二阶常微分方程组转化为一阶常微分方程组；最后，采用精细积分法精确求解常微分方程组.数值算例验证了双互易精细积分法的正确性和稳定性.     

三维串列双圆柱绕流气动流场及声场模拟

数值模拟三维串列双圆柱在不同间距比下湍流流态及其辐射声场.采用大涡模拟(LES)求解非定常不可压缩Navier-Stokes方程得到瞬时流场数据,从而得到声源相关数据,求解基于FW-H积分方程的Farassat-1A方程计算载荷噪声得到相应声场分布.通过对不同间距比下相应的声场及观测点的声压频谱图进行比较可以发现:随着间距的变化,流场呈现出3种不同的流态,其声场也呈现不同的特点,在临界间距比下,总噪声值最大.     

共轴双旋翼悬停状态气动噪声特性分析

结合CFD(Computational fluid dynamics)方法和FW-H(Ffowcs Williams-Hawkings)方程,建立了一套适合于悬停状态下共轴刚性双旋翼气动噪声特性计算方法。为了准确模拟共轴旋翼流场的涡干扰现象和非定常特性,基于运动嵌套网格技术与双时间推进方法,采用积分形式的可压雷诺平均Navier-Stokes(RANS)方程作为双旋翼非定常流场求解控制方程,湍流模型选用Baldwin-Lomax模型。通过Farassat 1A公式计算双旋翼气动噪声特性,每个声源微面的位置和载荷信息直接从桨叶表面网格中获取。然后,对水平面内和竖直面内观测点处共轴双旋翼厚度噪声、载荷噪声和总噪声的声压时间历程和频谱特性做了细致对比。模拟结果表明:上旋翼和下旋翼反向旋转的特点对声压时间历程影响显著,不同方向观察点的声压波形峰值对应的相位不同;共轴旋翼流场中存在的文丘里效应、桨-涡干扰现象以及下洗流的作用使得桨叶气动载荷呈现明显的非定常特征,导致共轴双旋翼的载荷噪声辐射强度较大;在低频段,总噪声受厚度噪声主导,而在高频段则受载荷噪声主导。      

势问题的径向基函数——局部边界积分方程方法

将基于径向基函数构造的具有插值特性的近似函数和局部边界积分方程方法相结合，建立了求解势问题的径向基函数——局部边界积分方程方法，推导了相应离散方程.与其他边界积分方程的无网格方法相比，本文方法具有数值实现过程简单、计算量小、精度高的优点，并可直接施加边界条件.最后通过算例说明了该方法的有效性. 关键词： 径向基函数 无网格方法 局部边界积分方程 势问题     

包含动边界的非定常流场动网格数值模拟

发展建立了用于多体分离等包含动边界的非定常流场数值模拟方法,建立了笛卡尔坐标系下边界以任意速度运动的控制体上的流动控制方程,结合几何守恒律确定网格速度,发展了基于结构网格的动网格方法,网格移动量采用加权插值方法得到.通过数值模拟二维翼型及三维机翼的强迫振荡非定常流场,表明该方法可以数值模拟包含动边界的非定常流场.     

一种新的计算叶轮机械内流场的方法——涡-速度方程组在数值求解叶轮机械内流场的应用研究

本文以涡-速度形式N-S方程为基础,提出了对惯性与非惯性坐标系均适用的叶轮机械内流场的计算方法,推导了非惯性坐标系下的涡-速度方程组及其在任意非正交曲线坐标系下的展开式,上述方程组与惯性坐标系下的方程组具有相同的形式,证明了该形式的非惯性效应仅表现在初、边值条件的实现上,本方法在很大程度上简化了具有复杂几何域的叶轮机械内流流场的数值求解。     

单叶片桨噪声相移叠加法预报多叶片船舶螺旋桨非空化低频噪声

单个桨叶噪声预报螺旋桨非空化噪声可显著降低计算耗时,本文联合URANS和声类比方程对该方法进行验证,并对螺旋桨噪声的时域特征进行分析。首先计算均匀流中E779A螺旋桨的声辐射,揭示了桨叶上声压分布及测点声压信号的典型周期特征,采用单个叶片噪声相移叠加(简称"单叶片方法")预报螺旋桨噪声的结果,与对螺旋桨所有叶片积分的计算结果吻合良好,验证了均匀流中单叶片方法的可行性。将该方法应用于潜艇伴流场中无侧斜和大侧斜螺旋桨噪声辐射计算,预报结果与所有叶片积分的结果吻合较好,验证了非均匀流场中单叶片方法的可行性,说明单叶片相移叠加法预报螺旋桨普遍进流条件下的辐射噪声是可行的。研究结论也可为对转桨、泵喷等噪声预报提供参考。      

PREDICTION OF NON-CAVITATING UNDERWATER PROPELLER NOISE

Non-cavitation noise of underwater propeller is numerically investigated. The main purpose is to analyze non-cavitation noise in various operating conditions with different configurations. The noise is predicted using time-domain acoustic analogy and boundary element method. The flow field is analyzed with potential-based panel method, and then the time-dependent pressure data are used as the input for Ffowcs Williams-Hawkings formulation to predict the farfield acoustics. Boundary integral equation method is also considered to investigate the effect of ducted propeller. Sound deflection and scattering effect on the duct is considered with the BEM. The governing equations are based on the assumption that all acoustic pressure is linear. A scattering approach is applied in which the acoustic pressure field is split into the known incident component and the unknown scattered component. Noise prediction results are presented for single propeller and ducted propeller in non-uniform flow conditions similar to real situation. The investigation reveals that the effect of a duct on the acoustic performance propeller is small in the far field under non-cavitating situations since the noise directivities of single and ducted propellers are almost the same. Only the high order BPFs are influenced by the existence of the duct.     

Energy flow model considering near field energy for predictions of acoustic energy in low damping medium

The Acoustic Energy Flow Boundary Element Method (AEFBEM) is developed to predict the acoustic energy density and intensity of an engineering system. Up to now, the acoustic energy flow model has been used only for analysis of high frequencies or radiation noise because of plane wave and far-field assumptions. In this research, a new energy flow governing equation that can consider the near field acoustic energy term and spherical wave characteristics is derived successfully to predict the acoustic energy density and intensity of a system in the medium-to-high frequency range. A near field term of acoustic energy in spherical coordinate is added to the relationship between energy density and energy flow. But with the far-field assumption, this term vanishes, so the relationship between energy density and energy flow becomes the same as that of the plane wave. By considering the near field energy term without far-field assumption, the energy density at medium frequencies can be estimated. However, the governing equation has to be numerically manipulated for use in the analysis of complex structures; therefore, the Boundary Element Method (BEM) is implemented. AEFBEM is a numerical analysis method formulated by applying the boundary element method to an acoustic energy flow governing equation. It is very powerful in predicting the acoustic energy density and intensity of complex structures in medium-to-high frequency ranges, and can analyze interior noise and radiating sound. To verify its validity, several numerical results are provided. BEM and AEFBEM were compared with respect to energy density, and the results from both methods were similar.     

Numerical analysis of immersed finite cylindrical shells using a coupled BEM/FEM and spatial spectrum approach

This study numerically analyzes submerged cylindrical shells using a coupled boundary element method (BEM) with finite element method (FEM) in conjunction with the wave number theory, in which the spatial Fourier transform of surface velocity for cylinders is directly related to pressure in a far field. The acoustic loading is formulated using a symmetric complex matrix derived from a boundary integral equation where the symmetry is based on an acoustic reciprocal principle for surface acoustics. In this formulation the acoustic loading matrix is a large acoustic element whose degree of freedom is connected to the normal displacement of the vibrating structures. The coupled BEM/FEM equation is a banded, symmetric matrix, and thus its bandwidth can be minimized using a proper algorithm. This formulation significantly increases numerical efficiency. The computed normal velocity is thus transformed to wave number representation to examine acoustic radiation. A finite plane cylindrical shell, without attached stiffeners, and a shell with internal ring stiffeners are chosen to demonstrate the present analysis procedure. The far field pressure computed directly from the integral equation and predicted by wave number theory correlates closely with increasing vibrating frequency. Meanwhile, the influences of the internal ring structures on acoustic radiation are examined using the wave number theory, which helps in understanding how internal structures influence radiated noise.     

A finite element approach for predicting nozzle admittances

A finite element method is used to predict the admittances of axisymmetric nozzles. It is assumed that the flow in the nozzle is isentropic and irrotational, and the disturbances are small so that linear analyses apply. An approximate, two dimensional compressible model is used to describe the steady flow in the nozzle. The propagation of acoustic disturbances is governed by the complete linear wave equation. The differential form of the acoustic equation is transformed to an integral equation by using Galerkin's method, and Green's theorem is applied so that the acoustic boundary conditions can be introduced through the boundary residuals. The boundary conditions are described for both straight and curved sonic lines. A two dimensional FEM with linear elements is used to solve the acoustic equation. A one dimensional FEM is also used to solve the reduced equation of Crocco, and the solution verifies the sufficiency of the boundary residual formulation. Comparison between computed admittances and experimental data is shown to be quite good.     

Analytic formulation and numerical implementation of an acoustic pressure gradient prediction

Two new analytical formulations of the acoustic pressure gradient have been developed and implemented in the PSU-WOPWOP rotor noise prediction code. The pressure gradient can be used to solve the boundary condition for scattering problems and it is a key aspect to solve acoustic scattering problems. The first formulation is derived from the gradient of the Ffowcs Williams–Hawkings (FW–H) equation. This formulation has a form involving the observer time differentiation outside the integrals. In the second formulation, the time differentiation is taken inside the integrals analytically. This formulation avoids the numerical time differentiation with respect to the observer time, which is computationally more efficient. The acoustic pressure gradient predicted by these new formulations is validated through comparison with available exact solutions for a stationary and moving monopole sources. The agreement between the predictions and exact solutions is excellent. The formulations are applied to the rotor noise problems for two model rotors. A purely numerical approach is compared with the analytical formulations. The agreement between the analytical formulations and the numerical method is excellent for both stationary and moving observer cases.     

On combustion noise related to chemical reactions

An inhomogeneous pressure wave equation has been derived for chemically reacting multicomponent gas mixtures to predict the acoustic field associated with combustion. Out of three source terms for the generation of combustion noise—namely, fluctuations in the heat release rate, in the momentum flow rate and in the viscous and diffusive working—the first is examined to relate this acoustic source strength to the concentration and temperature fluctuations through the chemical kinetics of reaction processes. The relationships between the spectral features of combustion noise and the statistical aspects of these fluctuations are obtained. The essential feature that combustion noise has substantial low-frequency components is explained by the dependence of the contribution of reaction fluctuations on the integral of the time correlation with respect to the correlation time.     

Surface impedance design with ground corrugation for mitigation of large-calibre gun blast noise

The surface impedance design approach is proposed for mitigating large-calibre gun blast noise. Surrounding the blast noise, we employ a group of concentric trenches with critical depths to dampen the propagation of the acoustic wave. These trenches behave like quarter-wavelength resonators and produce acoustic soft surfaces at their openings. The sound pressure is then mitigated over these soft surfaces by destructive interference and the wave attenuates rapidly along the ground surface. To evaluate the overall acoustic performance of such a design, we develop an efficient numerical solver by treating the geometry as a body of revolution (BOR). The symmetry of the structure in the revolution direction allows the 3D boundary integral equation (BIE) for acoustic wave scattering to be reduced to a 2D integral equation by the use of Fourier series expansions. Numerical experiments show that this model can effectively suppress the acoustic wave propagation horizontally and the reduction can reach about 15 dB for large-calibre gun noise with very low-frequency components.     

进一步改进边界元方法以克服振动声辐射计算中解的非唯一性

章利用基于三次B样条插值的边界元方法，对振动体外部声辐射问题进行了研究，对CHIEF法及其改进方法作了进一步的改进，提出在加权余量意义下，通过把内部Helmholtz积分方程与其对内点坐标取导后的方程式作线性叠加，在域外构作的一个小体积块上进行积分以形成补充方程，经与表面Helmholtz积分方程相结合，来求解任意频率下的声辐射问题，并以脉动球和摆动球作为算例，说明本提出的方法能够有效地克服在特殊频率处解的非唯一性问题。