Effect of cutter geometric configuration on aerodynamic noise generation in face milling cutters

Aerodynamic noise spectrum of rotary face milling cutters consists of a broad range of high frequencies and discrete tones. This paper aims to develop a method to calculate the aerodynamic noise generation and propagation by rotary face milling cutters. The effects of milling cutter geometry on the generation of aerodynamic noise are analyzed. Based on the computational fluid dynamics (CFD) method, the Ffowcs Williams–Hawkings (FW–H) equation is used to predict the sound pressure level (SPL) of aerodynamic noise in face milling cutters. The accurate calculation of time-varying flow variables along with the rotation of cutter is very important for the prediction of aerodynamic noise. In this case, the Navier–Stokes (N–S) equation is employed to evaluate the pressure and velocity fields around the milling cutters, first in a steady mode with the Multiple Reference Frames (MRF) model, and then in an unsteady mode with sliding mesh technique (SMT) by introducing the steady flow variables as its initial fields. It is found that both the overall aerodynamic noise due to the entire cutter and the aerodynamic noise only due to the cutter gullet regions are significantly affected by the number of cutter teeth/gullet regions. Moreover, six representative milling cutters with different tooth numbers and geometries of gullet regions are chosen to study the effects of gullet configuration on aerodynamic noise generation, and the characteristics of noise spectra generated by the cutters are analyzed. The aerodynamic noise generated only by the cutter gullet regions is found to be strongly dependent on the gullet design-volume and shape. The results also reveal that the gullet design advantage of Cutter C in reducing noise generation among the eight-tooth designs, and the gullet design advantage of Cutter A in reducing noise generation among the five and seven-tooth designs in this investigation.     

除垢超声波传播影响因素的理论研究

从一维平面波理论入手分析了超声波声压分布特性。依据多普勒频移原理,在声场的运动方程,连续性方程,波动方程的基础上,建立一个超声波在流动的液体中传播的控制方程。根据轴对称模型的实际特点,简化了所得方程,并求出解析解。结果表明流动液体可以产生声波的衰减。液体的黏滞性是产生超声波衰减的重要原因。超声波的频率较高,液体的黏滞性对超声波衰减影响明显。依据黏滞力与速度梯度的关系,建立一个超声波在黏滞液体传播的控制方程,并依据边界条件求出解析解,反映了媒质黏滞性对超声波传播尤其是衰减特性的影响。     

Influence of viscosity on aerodynamic sound emission in free space

The theory of aerodynamic sound is reformulated with account taken of the influence of viscosity in the source flow on the sound emission in free space. This is based on the Ffowcs Williams form of the Lighthill equation. The source flow is assumed to be determined by a localized vorticity field and characterized by low Mach numbers and high Reynolds numbers. It is found that the acoustic pressure emitted by the viscous vortex motion is composed of a quadrupole and two kinds of monopole. The Reynolds stress in the source flow is decomposed into isotropic and non-isotropic parts. The non-isotropic part leads to the quadrupole wave derived by Möhring, while the isotropic part is related to one of the monopole-like waves radiated when the total kinetic energy changes. The other monopole wave is associated with entropy production by viscous dissipation of the kinetic energy. All three components are influenced by viscosity.     

弹性拍翼悬停时的流固耦合效应

自然界中的昆虫和鸟类大都采用拍翼飞行的策略，其优越的气动表现使拍动飞行方式备受关注.值得注意的是，拍动飞行昆虫和鸟类在实现高机动性的同时，产生的噪音并不十分显著.因此，对拍翼飞行的流固声耦合问题进行研究，揭示其飞行动力学和声学特性，对于应用这类飞行技术具有重要的指导意义.文章采用一种浸入边界法对拍翼悬停时的流固声耦合问题进行数值模拟研究.具体针对刚性拍翼和不同刚度、质量比的柔性拍翼进行了数值模拟，分析了拍翼刚度和质量比对拍翼悬停时的升力和声学特性的影响.结果表明拍翼的转动能有效增加升力，提高效率并降低拍翼运动产生的声音；同时悬停拍翼的近场声受涡的影响明显，尤其是在较大的转动角度时；引入适当的弹性可有效提高拍翼在悬停时的气动表现，包括提高升力系数和效率；综合考虑气动和声学表现，可以看出当无量纲拍动频率在0.3~0.4时，低质量的拍翼（拍翼-流体质量比为1.0）产生的声音较小，同时又具备较高的效率.      

Slat noise modeling and prediction

This paper presents a model for aircraft slat noise prediction, based on the theory of aerodynamic sound generation and the first principles of source flow physics. Starting from the theory of acoustic analogy, the noise from the high Reynolds number and low Mach number flows in the slat cove region is formulated as a general solution by the method of dimensional analysis, far-field asymptotic expansion and statistical modeling. The solution relates the far-field noise spectrum to the surface pressure statistics, the characteristic length and time scales in the surface pressure statistics and Green's function that accounts for the sound-flow coupling and propagation effects. The general solution is then used to extract scaling laws and correlation models for the individual functional dependences between the far-field noise and various parameters, including the slat noise spectral shape, its Mach number dependence and its far-field directivity. The simple scaling laws and correlation models are validated by test data and serve as building blocks to construct a slat noise prediction model.     

流体通过涡激振动机翼的声辐射研究

为了有效地降低涡激噪声,研究了粘性流体通过涡激振动机翼的声辐射。采用Navier-Stokes方程描述二维机翼的流固耦合运动,用弹簧系统代替实际固体变形产生的回复力和力矩,翼型的运动是两个自由度,即垂直于来流的振荡和转动振荡;为了模拟涡激振动,机翼的初始攻角取得比较大,以便产生周期性的旋涡脱落及周期性的流体动力,后者与弹簧系统相耦合,引起振动,用Lighthill声比拟方法研究了由此引起的声辐射。计算结果表明:当涡脱频率和机翼的固有的振动频率一致时,发生锁定的现象,此时的声辐射达到最大。     

Sound generation and transmission in flow ducts with axial temperature gradients

This article describes a one-dimensional, linearized, analysis of fundamental mode sound generation and propagation in rigid-walled flow ducts with axial temperature variation. An acoustic wave equation, including damping effects and volume sources, is derived and its solution (in the absence of sources) by a numerical technique and an approximate analytical method is discussed. The “forced” wave equation is then solved (the existence of an oscillating solution to the “unforced” equation being assumed) for sound generation by a side-branch volume source in an infinite duct, and the results are applied to a duct of finite length. Reasonably good agreement is obtained between measurements and predictions of the sound pressure field in a flow duct, away from the source region.     

A numerical study of the effects of design parameters on the acoustics noise of a high efficiency propeller

A numerical study of a high efficiency propeller in the aerodynamic noise generation is carried out. Based on RANS, three-dimensional numerical simulation is performed to obtain the aerodynamic performance of the propeller. The result of the aerodynamic analysis is given as input of the acoustic calculation. The sound is calculated using the Farassat 1A, which is derived from Ffowcs Williams–Hawkings equation, and compared with the data of wind tunnel. The propeller is modified for noise reduction by changing its geometrical parameters such as diameter, chord width and pitch angle. The trend of variation between aerodynamic analysis data and acoustic calculation result are compared and discussed for different modification tasks. Meaningful conclusions are drawn on the noise reduction of propeller.     

机翼颤振的有源声控制

借助于己推导出的声激励下绕三维薄翼的非定常位势流的精确解，本文进一步分析了限于弱扰动的声激励消除颤振的机理，讨论了声源参数对颤振边界的影响，并通过声一涡耦合的理论计算，解释了原有的风洞实验。结果表明，对于不同位置的声源，声致气动载荷的无环量和有环量部分起着不同的作用，而且，在声控制颤振的过程中，系统的各种参数存在一定的关系，必须合理地选取最佳参数。本文的研究为声控制技术在气动领域中的实际应用提供了理论基础。     

钝锥再入飞行器黏性干扰效应建模

针对典型的钝锥外形, 采用统一气体动理学格式(UGKS)模拟了高度70~110 km下不同Mach数和攻角的流场, 进行了流场特性的分析, 并基于黏性干扰的理论成果, 将气动力特性与第3黏性干扰参数、攻角和Mach数等参数进行关联, 建立了气动力系数的黏性干扰模型, 给出了模型预测结果的相关性分析和准确性评估。经初步测试, 该模型预测结果与UGKS直接模拟结果具有良好的一致性, 对工程应用快速获取高空气动特性具有重要意义。      

On the simple-source theory of sound from statistical turbulence

A theory for the generation of aerodynamic sound, stated in terms of convected simple sources and dipoles, is presented. The sources are found to depend upon convective derivatives of the hydrodynamic pressure within the turbulent source region. The results are similar to earlier efforts involving simple sources, sometimes called dilatational sources. The results are modified for effects involving measurements on moving flows. The theory shows explicitly the refractive effects of shear flow within the source region, as well as of temperature changes (if any) within the source region. The oscillating cylinder problem is discussed and the results of the present theory are found to agree with those obtained by Lauvstad using a matched asymptotic expansion for the same problem. The theory is used to predict the temperature dependence of sound power for hot jets.Consultant for Bolt Beranek and Newman, Inc.     

气动/几何约束条件下翼型优化设计的最优控制理论方法

基于最优控制理论原理和Navier-Stokes方程,研究了气动/几何约束条件下多设计变量的翼型气动优化设计问题.根据给定的目标函数表达形式,在计算坐标下详细推导了相应的共轭方程及边界条件,以及梯度方程的具体数学形式.通过合理数学变换,得到了物理空间上适应于CFD数值求解的共轭方程直观表达形式,并发展了有效数值求解目的.通过将流动方程、共轭方程、目标函数敏感性导数和优化算法相结合,发展了一种新的气动优化设计目的.相关设计算例表明该目的在设计理论、适用性以及时间费用等方面具有显著特色和优点,且设计结果更为可靠.     

Effect of blade wrap angle on efficiency and noise of small radial fan impellers—A computational and experimental study

Radial impellers have several technical applications. Regarding their aerodynamic performance, they are well optimized nowadays, but this is in general not true regarding acoustics. This work was therefore concerned with analyzing the flow structures inside isolated radial impellers together with the far-field sound radiated from them in order to optimize the aerodynamic and acoustic performance. Both numerical and experimental techniques were applied in order to study the effect of varying wrap angle and otherwise identical geometric configuration on aerodynamics and acoustics of the radial impellers. The results give a detailed insight into the processes leading to sound generation in radial impellers. Measurements were performed using laser Doppler anemometry for the flow field and microphone measurements to analyze the radiated noise. In addition, unsteady aerodynamic simulations were carried out to calculate the compressible flow field. An acoustic analogy was employed to compute far-field noise. Finally, the phenomena responsible for tonal noise and the role of the wrap angle could be identified. Using this knowledge, design guidelines are given to optimize the impeller with respect to the radiated noise. This work shows that improved aerodynamic efficiency for isolated impellers does not automatically lead to a smaller flow-induced sound radiation.     

On acoustic radiation by a rigid object in a fluid flow

A problem of sound radiation by an absolutely rigid object, moving with respect to the surrounding fluid, is considered on the basis of the Lighthill's equation for aerodynamic sound. An integral representation of the radiated acoustic field is utilized, where the field is characterized as the sum of three fields, generated by a volume distribution of monopoles and by distributions of monopoles and dipoles on the surface of the rigid object. It is shown that, due to a discontinuity of Lighthill's stress tensor on the rigid boundary, a layer of surface divergence of hydrodynamic stresses on the boundary must be taken into account when evaluating the volume integral over Lighthill's quadrupole sources. When the contribution of the surface divergence is included in the solution of Lighthill's equation, amplitudes of the monopole and dipole sound radiated by the rigid object are shown to depend on the potential components of the normal velocity and the pressure on the rigid surface. The obtained solution is compared with Curle's solution for this problem, which establishes that the sound radiation by a rigid object is determined by the force exerted by the object upon the fluid. Both solutions are applied to two known problems of sound scattering and radiation by a rigid sphere in variable pressure and velocity fields. It is shown that predictions based on the obtained solution are equivalent to the results known from literature, whereas Curle's solution gives predictions contradicting the known results. It is also shown that the Ffowcs Williams and Hawkings equation, which coincides with Curle's equation for an immoveable rigid object, does not lead to the correct predictions as well.     

环境风对高速列车气动噪声特性的影响分析

气动噪声随着列车运行速度的提高急剧增加,是高速列车噪声的重要组成部分。本文使用缩比为1:20的三车编组模型,通过三维瞬态延迟分离涡模型求解高速列车的外流场,分析了环境风对流场结构与声源特性的影响;之后使用FW-H方程进行噪声传播计算,分析了不同速度的环境风对高速列车气动声学行为特性的影响。结果表明：高速列车主要的噪声源分布在转向架附近,在环境风的影响下,列车背风侧声源强度高于迎风侧,列车底部声源强度增幅较大。10 m/s以内的环境风会改变高速列车在尾流区域的声学指向性,并使气动噪声增加2.1~8.7 dB。相关结论可以为高速列车气动声学设计等研究提供参考。     

Vortex sound under the influence of a piecewise porous material on an infinite rigid plane

The vortex dynamics and the sound generation by an inviscid vortex in the presence of a finite length porous material on an otherwise rigid plane are studied numerically in the present study in an attempt to understand the sound generation near the surface of a wall lining in a lined duct. The combined effects of the effective fluid density and flow resistance inside the porous material, and the length and thickness of the porous material on the sound generation process are examined in detail. Results obtained demonstrate the sound pressure is longitudinal dipole and show how seriously the above-mentioned parameters are affecting the vortex sound pressure under the influence of the porous material.     

Numerical simulation of parametric sound generation and its application to length-limited sound beam

In this study we propose a simulation model for predicting the nonlinear sound propagation of ultrasound beams over a distance of a few hundred wavelengths, and we estimate the beam profile of a parametric array. Using the finite-difference time-domain method based on the Yee algorithm with operator splitting, axisymmetric nonlinear propagation was simulated on the basis of equations for a compressible viscous fluid. The simulation of harmonic generation agreed with the solutions of the Khokhlov–Zabolotskaya–Kuznetsov equation around the sound axis except near the sound source. As an application of the model, we estimated the profiles of length-limited parametric sound beams, which are generated by a pair of parametric sound sources with controlled amplitudes and phases. The simulation indicated a sound beam with a narrow truncated array length and a width of about one-quarter to half that of regular a parametric beam. This result confirms that the control of sound source conditions changes the shape of a parametric beam and can be used to form a torch like low-frequency sound beam.     

Nonlinear Modeling Study of Aerodynamic Characteristics of an X38-like Vehicle at Strong Viscous Interaction Regions

Strong viscous interaction and multiple flow regimes exist when vehicles fly at high altitude and high Mach number conditions. The Navier–Stokes(NS) solver is no longer applicable in the above situation. Instead, the direct simulation Monte Carlo (DSMC) method or Boltzmann model equation solvers are usually needed. However, they are computationally more expensive than the NS solver. Therefore, it is of great engineering value to establish the aerodynamic prediction model of vehicles at high altitude and high Mach number conditions. In this paper, the hypersonic aerodynamic characteristics of an X38-like vehicle in typical conditions from 70 km to 110 km are simulated using the unified gas kinetic scheme (UGKS), which is applicable for all flow regimes. The contributions of pressure and viscous stress on the force coefficients are analyzed. The viscous interaction parameters, Mach number, and angle of attack are used as independent variables, and the difference between the force coefficients calculated by UGKS and the Euler solver is used as a dependent variable to establish a nonlinear viscous interaction model between them in the range of 70–110 km. The evaluation of the model is completed using the correlation coefficient and the relative orthogonal distance. The conventional viscous interaction effect and rarefied effect are both taken into account in the model. The model can be used to quickly obtain the hypersonic aerodynamic characteristics of X38-like vehicle in a wide range, which is meaningful for engineering design.     

Evaluation of sound absorption capacity of asphalt mixtures

Noise generation is an environmental problem that affects human beings, animals and even plants. Several serious diseases have their development associated to the exposure of human beings to high levels of noise pressure, such as arterial hypertension, gastrointestinal changes, alterations in blood glucose and high heart rate, among others. Vehicle traffic is part of a group of noise-generating factors. Various mechanisms govern the generation and propagation of vehicle noises, which are produced mainly by motor vibration at speeds below 50 km/h and by the tire-pavement contact at speeds above 50 km/h. The noise generated by tire-pavement contact is the result of two components: aerodynamic noise (mainly related to the coating porosity), and mechanical noise (related to the coating texture). The noise generation according to these two components may be mitigated by using special asphalt mixtures. This work evaluates the sound absorption of four different types of asphalt mixtures (common dense-graded asphalt mixture, dense-graded rubberized asphalt mixture, rubberized porous coat with void volumes varying from 22% to 27%, and rubberized open-graded friction course) and the effect of granulometry and void volume of each mixture on the sound absorption coefficient. Mixture slabs were molded in a slab compactor developed by LCPC (Laboratoire Central des Ponts et Chaussées) and specimens were extracted from each one for assessing the sound absorption capacity in the laboratory. The acoustic behavior was evaluated according to standard ISO 10534-2, using impedance tubes. Results showed that sound absorption is strongly influenced by void percentage, interconnected void percentage and layer thickness.