Frequency-domain method for discrete frequency noise prediction of rotors in arbitrary steady motion

A novel frequency-domain formulation for the prediction of the tonal noise emitted by rotors in arbitrary steady motion is presented. It is derived from Farassat's ‘Formulation 1A’, that is a time-domain boundary integral representation for the solution of the Ffowcs-Williams and Hawkings equation, and represents noise as harmonic response to body kinematics and aerodynamic loads via frequency-response-function matrices. The proposed frequency-domain solver is applicable to rotor configurations for which sound pressure levels of discrete tones are much higher than those of broadband noise. The numerical investigation concerns the analysis of noise produced by an advancing helicopter rotor in blade–vortex interaction conditions, as well as the examination of pressure disturbances radiated by the interaction of a marine propeller with a non-uniform inflow.     

On the use of a uniformly valid analytical cascade response function for fan broadband noise predictions

The present paper extends an existing analytical model of the aeroacoustic response of a rectilinear cascade of flat-plate blades to three-dimensional incident vortical gusts, to the prediction of the noise generated by a three-dimensional annular blade-row. The extended formulation is meant to be implemented in a fan broadband noise prediction tool. The intended applications include the modern turbofan engines, for which analytical modelling is believed to be a good alternative to more expensive numerical techniques. The prediction noise model resorts to a strip theory approach based on a three-dimensional rectilinear cascade model. The latter is based on the Wiener-Hopf technique, and yields the pressure field in the blade passage and the unsteady blade loading. The analytical pressure solution is derived by making an extensive use of the residue theorem. The obtained unsteady blade loading distribution over the blades is then used as a dipole source distribution in an acoustic analogy applied in the annular rigid duct with uniform mean flow. The new achievements are then tested on three-dimensional annular-benchmark configurations and compared with three-dimensional lifting-surface models and three-dimensional Euler linearized codes available in the literature. The accuracy of the model is shown for high hub-to-tip ratio cases. When used as such in a true rectilinear-cascade configuration, it also reproduces the exact radiated field that can be derived directly. For low hub-to-tip ratio configurations, the model departs from three-dimensional computations, both regarding the blade loading and the acoustic radiation. A correction is proposed to account for the actual annular dispersion relation in the rectilinear-cascade response function. The results suggest that the proposed correction is necessary to get closer to the underlying physics of the annular-space wave equation, but that it is yet not sufficient to fully reproduce three-dimensional results.     

Sound radiation from inflow turbulence in axial flow fans

The sound radiated when inflow turbulence is present in axial flow fans has been investigated. Theoretically, two noise radiating mechanisms can be identified: (i) interaction of turbulence with the rotor potential field results in a quadrupole-type volume source distribution, producing “flow-interaction” noise; (ii) impingement of turbulence on the blades results in a dipole-type (fluctuating force) surface source distribution, producing “fluctuating lift” noise. A theoretical expression for the flow interaction sound power in the upstream radiation field has been developed, in terms of parameters that can be experimentally determined by near field flow measurements involving spatial cross-correlations of the fluctuating axial velocity, with respect to both radial and circumferential position. Both these measurements and radiated sound pressure measurements have been made for eight- and ten-bladed rotors of relatively low tip Mach number (< 0·3). The sound pressure measurements revealed the occurrence of band-spreading of discrete tones at the blade passing frequency and its harmonics, as would be theoretically predicted for quadrupole-type sources here. The theoretical predictions and the measurements, respectively, of the sound power radiated upstream were compared. The results indicated that, for the fans tested, the “fluctuating lift” noise strongly predominated over the “flow-interaction” noise. The observed sound power levels were consistent with levels estimated from the theory.     

Three-dimensional analysis of blade force and sound generation for an annular cascade in distorted flows

An unsteady lifting-surface theory for a rotating subsonic annular cascade has been developed to predict the unsteady blade forces and the acoustic power generation caused by interaction of blades with inlet distortions or wakes. Disturbance pressure and velocity fields induced by the rotor blades with fluctuating blade force are expressed in terms of the blade force distribution and kernel functions. The spanwise distribution of the blade force is given as a sum of blade force modes, and the kernel functions are resolved into the corresponding modal components. The sound pressure and intensity are expressed as a sum of acoustic modes, the modal components of which are given in terms of the blade force mode components.Numerical computations have been conducted .for interaction with the external disturbance flows that are sinusoidal in the circumferential direction, but possess a phase skewing in the radial direction. Correlations among the acoustic modes, the blade force modes and the flow patterns of the external disturbance have been investigated. When the predominant acoustic mode is subresonant, the blade force amplitude is reduced by the three-dimensional effect, which is lessened as the frequency increases. At deeply superresonant states, however, the three-dimensional effect upon the spanwise average of the blade force amplitude is small. The generated sound power is effectively reduced by increasing the radial non-uniformity of the external disturbance.     

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 the nature of idling noise of circular saw blades

An experimental investigation of the effects of important saw blade geometric and kinematic parameters on idling circular saw noise was conducted. Blade tip speed was determined t0 be the dominant factor in the noise production. The sound power generated was found to vary approximately as the 5·3 power of the tip velocity. Variations in blade geometry, which included the number of teeth, the blade thickness, and the tooth-gullet shape, produce effects in the radiated sound of the order of 6 dB for the blades tested. It is shown that slotted disks may be used to provide a closely controlled simulation of the saw blade noise produced aerodynamically. Results suggest that the sources are likely to be compact and are dominated by the unsteady forces acting on the tooth surfaces resulting from the interaction 0f the tooth and the incident unsteady flow in the wake of the preceding tooth.     

On vortex–airfoil interaction noise including span-end effects,with application to open-rotor aeroacoustics

A linear analytical model is developed for the chopping of a cylindrical vortex by a flat-plate airfoil, with or without a span-end effect. The major interest is the contribution of the tip–vortex produced by an upstream rotating blade in the rotor–rotor interaction noise mechanism of counter-rotating open rotors. Therefore the interaction is primarily addressed in an annular strip of limited spanwise extent bounding the impinged blade segment, and the unwrapped strip is described in Cartesian coordinates. The study also addresses the interaction of a propeller wake with a downstream wing or empennage. Cylindrical vortices are considered, for which the velocity field is expanded in two-dimensional gusts in the reference frame of the airfoil. For each gust the response of the airfoil is derived, first ignoring the effect of the span end, assimilating the airfoil to a rigid flat plate, with or without sweep. The corresponding unsteady lift acts as a distribution of acoustic dipoles, and the radiated sound is obtained from a radiation integral over the actual extent of the airfoil. In the case of tip–vortex interaction noise in CRORs the acoustic signature is determined for vortex trajectories passing beyond, exactly at and below the tip radius of the impinged blade segment, in a reference frame attached to the segment. In a second step the same problem is readdressed accounting for the effect of span end on the aerodynamic response of a blade tip. This is achieved through a composite two-directional Schwarzschild's technique. The modifications of the distributed unsteady lift and of the radiated sound are discussed. The chained source and radiation models provide physical insight into the mechanism of vortex chopping by a blade tip in free field. They allow assessing the acoustic benefit of clipping the rear rotor in a counter-rotating open-rotor architecture.     

环形压气机叶栅内部分离流结构分析 第一部分:近壁区分离流

1前言随着对叶轮机械研究的深入,叶轮机械内部的真实复杂流动已成为重要的研究课题。认识扩压叶栅内的流动分离和旋涡的发生、发展及相互作用,对于揭示压气机内部流动机制,改善流动结构,提高其喘振裕度,以及发展喘振控制技术都具有重要意义山。尽管人们已进行了许多研究,但尚未完整充分地认识这一复杂现象的物理现象和物理模型。对处在严重流动分离状态下的环形叶栅内部流动的研究就更为少见。本文应用油膜法显示了从约零度到二十几度多个来流攻角下,一大展弦比叶片低稠度环形压气机叶棚的表面流场。进口气流马赫数约为0．1。叶片进…     

Fan interaction noise reduction using a wake generator: experiments and computational aeroacoustics

A control grid (wake generator) aimed at reducing rotor-stator interaction modes in fan engines when mounted upstream of the rotor has been studied here. This device complements other active noise control systems currently proposed. The compressor model of the instrumented ONERA CERF-rig is used to simulate suitable conditions. The design of the grid is drafted out using semi-empirical models for wake and potential flow, and experimentally achieved. Cylindrical rods are able to generate a spinning mode of the same order and similar level as the interaction mode. Mounting the rods on a rotating ring allows for adjusting the phase of the control mode so that an 8 dB sound pressure level (SPL) reduction at the blade passing frequency is achieved when the two modes are out of phase. Experimental results are assessed by a numerical approach using computational fluid dynamics (CFD). A Reynolds averaged Navier-Stokes 2-D solver, developed at ONERA, is used to provide the unsteady force components on blades and vanes required for acoustics. The loading noise source term of the Ffowcs Williams and Hawkings equation is used to model the interaction noise between the sources, and an original coupling to a boundary element method (BEM) code is realized to take account of the inlet geometry effects on acoustic in-duct propagation. Calculations using the classical analytical the Green function of an infinite annular duct are also addressed. Simple formulations written in the frequency domain and expanded into modes are addressed and used to compute an in-duct interaction mode and to compare with the noise reduction obtained during the tests. A fairly good agreement between predicted and measured SPL is found when the inlet geometry effects are part of the solution (by coupling with the BEM). Furthermore, computed aerodynamic penalties due to the rods are found to be negligible. These results partly validate the computation chain and highlight the potential of the wake generator system proposed.     

Panel methods for airfoils in turbulent flow

This paper describes how panel methods can be used to calculate the unsteady loading and radiated noise from airfoils in incompressible turbulent flow, while completely accounting for the mean flow distortion of the turbulence in the vicinity of the blade. Formulations based on the velocity and on the stagnation enthalpy are discussed. In three-dimensional flows, care must be taken with the velocity-based formulation to avoid singular behavior associated with vortex stretching by the mean flow. The velocity-based method is implemented in two dimensions to illustrate application of these methods, and is validated against Amiet's theory. Calculations showing the effect of blade thickness and angle of attack on the unsteady loading spectra are given. It is concluded that airfoil angle of attack has only a small effect on the unsteady loading, but that blade thickness reduces the spectral levels at high frequencies.     

Surface pressure characteristics of a highly loaded turbine blade at design and off-design conditions; a CFD methodology

The flow field passing through a highly loaded low pressure (LP) turbine cascade is numerically investigated at design and off-design conditions. The Field Operation And Manipulation (OpenFOAM) platform is used as the computational Fluid Dynamics (CFD) tool. In this regard, the influences of grid resolution on the results of k-ε, k-ω, and large-eddy simulation (LES) turbulence models are investigated and compared with those of experimental measurements. A numerical pressure undershoot is appeared near the end of blade pressure surface which is sensitive to grid resolution and flow turbulence modeling. The LES model is able to resolve separation on both coarse and fine grid resolutions. In addition, the off-design flow condition is modeled by negative and positive inflow incidence angles. The numerical experiments show that a separation bubble generated on blade pressure side is predicted by LES. The total pressure drop has also been calculated at incidence angles between -20° and +8°. The minimum total pressure drop is obtained by k-ω and LES at design point.     

Broadband noise prediction of fan outlet guide vane using a cascade response function

An analytical model of the broadband noise produced by both the interaction of ingested turbulence with a fan rotor blades and the rotor-wake impingement on downstream stator vanes is proposed and detailed. The noise prediction methodology is a strip-theory approach based on a previously published formulation of the three-dimensional unsteady blade loading for a rectilinear cascade. This three-dimensional cascade response applied in each strip combined with an acoustic analogy in an annular duct have been chosen to account for the main three-dimensional effects. To further improve some of the identified limitations of this approach, a correction is added to mitigate the effects of the non-coincidence of the cut-on frequencies of the annular duct modes and of the modes of the rectilinear cascade. A correction of the unsteady blade loading formulation, previously developed in a tonal configuration, is also introduced to account for the dispersion relation of annular duct modes in the rectilinear-cascade model. The model is compared with experimental results of the 22-in source diagnostic test (SDT) fan rig of the NASA Glenn Research Center. A numerical assessment of the simplifications proposed in the model and of the convergence of the truncated sums in spanwise wavenumbers and azimuthal orders of the incident perturbation is carried out. The subcritical gusts are shown to have a crucial effect at low frequencies, whereas they become negligible at higher frequencies. Furthermore, alternative high-frequency formulations lead to a satisfactory accuracy above a Helmholtz number based on the duct radius of 20. The strong reduction in computational time associated with these formulations could justify their use for parametric studies in industrial context. The effect of the turbulence model is also investigated showing the relevance of Liepmann's isotropic model in the SDT case, and a possible strong effect of anisotropy in static tests. Finally, the model is compared with NASA's experimental results for two outlet guide vanes at approach condition, showing a very good agreement upstream, whereas an underestimate of 3-5 dB is observed downstream in the middle frequency range.     

Characteristic correlation between propellers cavitating wake and cavitation noise

The characteristic correlation between the propellers cavitating wake and their cavitation noise has been studied. Based on the viscous multiphase flow theory, the Navier–Stokes equations, a turbulence model and a cavitation model were applied to predict numerically the vapor volume fraction and the pressure in the wake. Compared with experimental results, the numerical predictions of the sheet cavitation and the tip vortex cavitation are in agreement with the corresponding experimental data, which indicates the numerical method in present paper is feasible. The characteristic of the low line spectra of the numerical pressure fluctuation signals and the measured noise signals for uniform inflow and wake flow is analyzed, and the characteristic correlation of the two line spectra is also validated. Therefore, it can be concluded that due to the wake and the radiated noise both modulated by the revolving propeller blades, the features of the low line spectra for noise signals and the pressure signals in the wake are close to each other.     

Frequency-domain acoustic pressure formulation for rotating source in uniform subsonic inflow with arbitrary direction

This paper presents a frequency-domain formulation for predicting noise radiated from the rotating thickness and loading sources in uniform subsonic inflow with arbitrary direction. The proposed frequency-domain formulation is an extension of the recently published frequency-domain formulation for the stationary medium. It avoids the singular integral and numerical interpolation problems encountered in the time-domain numerical method. Three test cases, i.e., noise radiation from the rotating monopole and dipole point sources and the Isom thickness noise of a transonic rotor in the subsonic uniform flow, have been carried out to validate the proposed formulation. Both the acoustic pressure spectrum and directivity pattern computed with the present frequency-domain method are in good agreement with those obtained from the time-domain method, thus validating the correctness of the present formulation. Furthermore, the numerical results indicate that the frequency-domain formulation is suitable for tonal noise prediction, while it is inefficient for broadband noise prediction.     

大小叶片贯流风机内流特性分析与实验研究

为降低空调用贯流风机的噪声,改善音质,通过采用直叶片贯流风轮达到斜扭叶片贯流风轮的音质和低噪声特性,从而降低贯流风轮的制造成本,本文设计了大小叶片交错组合的新型非等距贯流风机,并采用滑动网格对其内流特性进行了非定常数值模拟,同时对其气动噪声特性进行了实验研究.大小叶片贯流风机的偏心涡基本稳定在叶轮中心与蜗舌相连的切线上,位于叶轮内圆周附近.风轮非定常运转时,偏心涡的涡核位置在直径为2mm的圆所围成的区域内变化.大小叶片交错组合的贯流风轮改变了叶轮与蜗舌的间距,有效地降低叶片通过频率噪声并改善了音质.采用大小叶片交错组合的贯流风轮能够达到斜扭叶片贯流风机的降噪效果.     

亚音速轴流风扇后掠叶片定子与湍流互作用宽频辐射噪声预报

针对亚音速轴流风扇后掠叶片定子的宽频辐射噪声问题,介绍并推导了叶栅宽频辐射声功率计算公式,通过该公式计算后掠叶片定子的宽频辐射声功率级,并从湍流入流和叶栅响应的角度揭示后掠角对定子辐射噪声的影响机理。在此基础上,考虑到实际风扇定子工作在转子尾流中的情况,采用Gauss尾流模型模拟转子尾流,建立转子尾流湍流波数谱模型,推导得到定子叶片与转子尾流互作用的宽频辐射声功率计算公式。通过与NASA风扇试验模型对比得到,考虑转子尾流的定子叶栅宽频辐射声功率计算公式能够较好的预报后掠定子宽频辐射声功率。最后,针对试验风扇模型,分析叶片安装角、叶片弦长对后掠叶片定子辐射噪声的影响。      

弯曲时片压气机时栅内二次流的数值研究

本文应用Ｂｅａｍ－Ｗａｒｍｉｎｇ近似隐式因子分解格式以及ＭＭＬ代数湍流模型,采用拟压缩性方法求解雷诺平均拟压缩Ｎ－Ｓ方程组,对弯曲叶片压气机叶栅内的三维粘性流场进行了数值研究．结果表明,正弯曲叶栅内通道涡较直叶栅强,其诱导产生的壁面涡较弱且位于吸力面与壁端的角区内,与壁角涡接近．在正弯曲叶栅出口处,通道涡开始处于破裂前期,叶栅总损失增加。反弯曲叶栅通道涡较弱,其诱导的壁面涡很强,位于通道涡左上方,壁面涡和通道涡的有利作用,使通道涡更稳定,叶栅总损失比直叶栅和正弯曲叶栅要小．     

A numerical investigation of the noise radiated by a turbulent flow over a cavity

The tonal noise radiated by a two-dimensional cavity submerged in a low-speed turbulent flow has been investigated computationally using a hybrid scheme that couples numerical flow computations with an implementation of the Ffowcs Williams-Hawkings equation. The turbulent near field is computed by solving the short-time-averaged, thin-layer approximation of the Navier-Stokes equations, with turbulence modelled by the Wilcox k-ω model. Second order spatial and temporal discretization schemes with fine grids in the immediate region of the cavity and a small time step were used to capture the unsteady flow physics. Along all external boundaries, a buffer zone is implemented to absorb propagating disturbances and prevent spurious numerical reflections. Comparisons with experimental data demonstrate good agreement in both the frequency and amplitude of the oscillations within the cavity. The unsteady characteristics of the cavity flow are discussed, together with the mechanisms for cavity noise generation. The influence of freestream flow velocity and boundary layer thickness on the frequency and amplitude of the oscillations within the cavity and the nature of the noise radiated to the far field are also investigated. Results indicate that both the frequency and amplitude of oscillation are sensitively dependent on the characteristics of the shear layer spanning the mouth of the cavity.     

A numerical study on the flow and sound fields of centrifugal impeller located near a wedge

Centrifugal fans are widely used and the noise generated by these machines causes one of the serious problems. In general, the centrifugal fan noise is often dominated by tones at blade passage frequency and its higher harmonics. This is a consequence of the strong interaction between the flow discharged from the impeller and the cut-off in the casing. However, only a few researches have been carried out on predicting the noise because of the difficulty in obtaining detailed information about the flow field and considering the scattering effect of the casing. The objective of this study is to understand the generation mechanism of sound and to develop a prediction method for the unsteady flow field and the acoustic pressure field of the centrifugal impeller. A discrete vortex method is used to model the centrifugal impeller and a wedge and to calculate the flow field. The force of each element on the blade is calculated by the unsteady Bernoulli equation. Lowson's method is used to predict the acoustic source. In order to consider the scattering and diffraction effects of the casing, Kirchhoff-Helmholtz boundary element method (BEM) is developed. The source of Kirchhoff-Helmholtz BEM is newly developed, so the sound field of the centrifugal fan can be obtained. A centrifugal impeller and wedge are used in the numerical calculation and the results are compared with the experimental data. Reasonable results are obtained not only for the peak frequencies but also for the amplitudes of the tonal sound. The radiated acoustic field shows the diffraction and scattering effect of the wedge.     

汽轮机次、末两级弯扭静叶的工程设计与实验研究

本文的主要目的是讨论弯扭叶片在大功率汽轮机低压缸末级和次东级的工程应用问题。具有弯扭叶片的通流设计方法采用基于求解欧拉方程的Ｓ２流面正问题计算，静叶栅的实验是在环形叶栅实验风洞上进行的，通过对计算结果和实验结果的分析，本文讨论了弯扭叶片在次、末两级中对改善流场的作用。