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.     

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.     

Time- and frequency-domain computations of broadband noise due to interaction between incident turbulence and rectilinear cascade of flat plates

Time-domain computational aeroacoustic (CAA) techniques are developed to investigate the broadband noise resulting from the interaction of a rectilinear cascade of flat plates with incident homogeneous, isotropic turbulence. The investigation is carried out by comparing the prediction results obtained by employing the time-domain CAA method with those using existing frequency-domain methods. A semi-analytic model (Wei & Cheong, 2010) and a full three-dimensional rectilinear cascade model (Lloyd & Peake, 2008; Lloyd, 2009) are adopted for the frequency-domain computations. By comparing these computation results, the three-dimensional characteristics of inflow turbulence noise are investigated; in particular, the effects of the wavenumber components of ingested turbulence in the spanwise direction are taken into consideration in the investigation. First, CAA results are compared with those from the semi-analytic model. The results for the acoustic modes of relatively low spanwise wavenumbers obtained using both methods show good agreement, but as the spanwise wavenumber increases, the results obtained by the two methods become increasingly different. To investigate in detail the reason for these differences, mode-decomposition analysis is performed by adopting a hybrid method as well as by employing the CAA and the semi-analytic method. The hybrid method involves the following two sequential computations: (i) the upwash velocities on the flat plate airfoils of the rectilinear cascade are first predicted using the frequency-domain method, and (ii) the acoustic wave propagation is subsequently analyzed using time-domain CAA techniques, with these upwash velocities applied as the boundary conditions on the flat plate. It is seen that the results of the time-domain CAA technique and the hybrid method show good agreement, irrespective of the wavenumber and frequency. However, comparisons of the acoustic solutions from three computations reveal that the prediction results of the semi-analytic model deviate more from the other two predictions as the spanwise wavenumber of the acoustic wave increases and the frequency decreases. On a basis of this observation, a formulation is derived for the error in the pressure jump across the flat-plate predicted by using the semi-analytic method. This formulation shows that the error is approximately inversely proportional to the sound speed in the spanwise direction of the concerned acoustic modes. This result quantitatively clarifies the limitations of applying the frequency-domain method of Wei & Cheong (2010) to the three-dimensional turbulence-cascade interaction problems. Secondly, the prediction results using the time-domain CAA method are compared with those from the full three-dimensional rectilinear model that is believed to be exact model for the cascade geometry considered in this paper. This comparison shows the good agreements between two predictions, which support the above arguments for the error and the successful application of the time-domain CAA methods. It is expected that these methods can be extended to the broadband noise problem in an annular cascade, including the nonlinear interaction of the real-airfoil cascade with the incident nonhomogeneous gust.     

The application of a semi-actuator disk model to sound transmission calculations in turbomachinery,part I: The single blade row

The work described in this paper generalizes the semi-actuator disk model of a blade row of Kaji and Okazaki [1, 2] to include a three-dimensional incident sound field. This field is equivalent, for example, to a radially fluctuating spinning mode in an annular compressor duct. The dependence of the earlier model upon the wavelength of the incident sound field is removed by adopting an average frequency approach. In this model, the acoustic energy entering the cascade of blades across one interface and leaving it across the other interface is summed over an infinite series of reflections within the cascade. This is equivalent, in effect, to the assumption of an incident delta function of pressure and thus gives an average frequency result. The validity of the model is demonstrated in a series of comparisons with data obtained from earlier models. The model is subsequently extended to include the effects of introducing cambered blades. In a companion paper (Part II), the model is applied to multiple blade rows.     

Aerodynamics and interaction noise of streamlined bodies in nonuniform flows

The unsteady aerodynamics and interaction noise of streamlined bodies are modeled in terms of the Euler equations linearized about a nonuniform flow. The validity of the inviscid approach is supported by recent LES simulations of an airfoil in a gust indicating that for not-too-small impinging excitations, the interaction process is dominated by inertia forces. Results in the present paper are focused on the aerodynamics and interaction noise of a turbofan modeled as an annular cascade. The model accounts for the inflow-fan-duct coupling and the high frequency of the interaction process. Two high-order numerical algorithms are developed with body-fitted coordinate system. One algorithm uses a primitive variable formulation, the other uses an efficient velocity splitting algorithm and is suitable for broadband computations. Analytical and numerical analysis of disturbances in rotational flows is developed and exact inflow/outflow boundary conditions are derived, yielding directly the radiated acoustics. The upstream disturbances evolve in rotational flows and as a result the aerodynamic-aeroacoustic response of the annular cascade depends on the initial conditions location. Computational results show that the three-dimensional geometry of the annular cascade, the mean flow swirl, and the blade geometry have strong influence on the blade sectional lift and the radiated sound. These results also show the inadequacy of using the popular linear cascade model particularly for realistic fan geometry and inflow conditions.     

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。      

不同叶轮形式下离心泵噪声特性对比研究

针对具有无短叶片和有短叶片两种叶轮形式的离心泵,对设计状态下离心泵内部流场进行了全三维、非定常数值模拟,对比分析了其非定常流场特性和噪声辐射特性。流场分析表明:叶轮叶片和蜗舌的相互作用造成了叶片表面强烈的压力脉动,对长短叶片的叶轮形式,在局部增加长叶片表面压力脉动的同时,短叶片表面的压力脉动保持较低水平;同时能够有效降低泵体进口压力脉动,但出口压力脉动有所增强。以叶轮叶片表面作为声源辐射面,对比分析了两种叶轮的偶极子噪声辐射特性,结果表明:长短叶片结构通过改变声能在频域上的分布,从而能有效降低总声压级。      

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.     

Prediction of propeller non-cavitation noise by superimposing shifted sound signal from an isolated blade

The time-cost of the propeller non-cavitation noise prediction can be greatly reduced by the isolated blade method,which is validated via hybrid URANS and acoustic analogy,followed by the acoustic characteristics of propeller in time domain are analyzed.Firstly,we predicted the sound of the E779 A propeller operating in uniform inflow and found a typical periodic characteristic of the sound pressure distribution on propeller blade as well as the sound signal of the receiver,and the result by the superimposing shifted sound signal from an isolated blade(isolated blade method) agreed well with the result by the integration on total blades,which validated the credibility of the isolated blade method in uniform inflow.Finally,we predicted the sound of a propeller running in the wake of submarine by the isolated blade method,and the result also agreed well with the result by the integration on total blades,which further indicated that the isolated blade method was also applicable for the non-cavitation noise prediction of the propeller running in non-uniform inflow.The noise prediction of the counter-rotating propeller,the pump-jet can also benefit from this method.     

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.     

The prediction of broadband noise from wind turbines

This paper describes a broadband noise prediction scheme for wind turbines. The source mechanisms included in the method are unsteady lift noise, unsteady thickness noise, trailing edge noise and the noise from separated flow. Special methods have been developed to model the inflow turbulence from the atmospheric boundary layer and acoustic radiation to the geometric near field of the rotor. Predictions are compared with measurements on 20 m and 80 m diameter wind turbines. The results show that the turbulence length scale in the atmospheric boundary layer is too large to give the measured noise levels. Very good agreement is obtained between predictions and measurements if the turbulence length scale is taken to be equal to the blade chord.     

Simulation and modelling of the waves transmission and generation in a stator blade row in a combustion-noise framework

The combustion noise in aero-engines is known to have two different origins. First, the direct combustion noise is directly generated by the flame itself. Second, the indirect combustion noise is caused by the acceleration in the turbine stages of entropy spots generated by the combustion. In both cases, the turbo-machinery is involved in the combustion-noise transmission and generation. Numerical simulations are performed in the present study to assess the global noise for a real aeronautical configuration. On the one hand, the acoustic and entropy transfer functions of an isolated blade row are obtained using two-dimensional unsteady simulations. The transfer functions of the blade row are compared with the model of Cumpsty and Marble that assumes an axially compact configuration. On the other hand, the acoustic and entropy sources coming from a combustion chamber are calculated from a three-dimensional Large Eddy Simulation (LES). This allows an evaluation of the error introduced by the model for the present combustion chamber using the previous numerical simulations. A significant error is found for the indirect combustion noise, whereas it stays reasonable for the direct one.     

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。      

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.     

Experiments on the unsteady flow field and noise generation in a centrifugal pump impeller

This paper reports on an experimental investigation of large-scale flowfield instabilities in a pump rotor and the process of noise generation by these instabilities. Measurements of the fluctuating components of velocity and surface pressure were made with hot-wire probes and surface mounted pressure transducers on a seven bladed back swept centrifugal water pump impeller operating with air as the working fluid. The impeller was operated without a volute or scroll diffuser, thereby eliminating any sound generation from pressure fluctuations on the volute cutoff. Thus the study focused on flow field and noise components other than the blade passage frequency (and its harmonics). The primary goal of the study was to provide fundamental information on the unsteady flow processes, particularly those associated with the noise generation in the device. It was further anticipated that detailed flow measurements would be useful for the validation of future computational simulations.The measured data at the discharge show a jet-wake type of flow pattern which results in a strong vorticity field. The flow with high velocity found on the pressure side of the impeller tends to move to the low-pressure region present at the suction side of the passage as a form of roll-up around the blade trailing edge. This motion causes an unsteady flow separation at the suction side of the blade and consequently disturbs the flow in the adjacent passage. By interacting with the impeller blades near the trailing edges, this instability flow causes a periodic pressure fluctuation on the blade surface and generates noise by a trailing edge generation mechanism. The spectrum of surface pressure measured at the trailing edge of each blade reveals a cluster of peaks which were identified with azimuthal mode numbers. The correlation between the acoustic farfield pressure and the surface pressure on the impeller blade has proven that the azimuthal modes synchronized with the number of impeller blades generate noise much more efficiently than the other modes. The paper also clarifies the correlation between unsteady flowfield measurements, in both impeller and laboratory co-ordinates, with the radiated noise properties. Thus some light is shed on the noise generation mechanisms of this particular device.     

Passive control of discrete-frequency tones generated by coupled detuned cascades

Discrete-frequency tones generated by rotor-stator interactions are of particular concern in the design of fans and compressors. Classical theory considers an isolated flat-plate cascade of identical uniformly spaced airfoils. The current analysis extends this tuned isolated cascade theory to consider coupled aerodynamically detuned cascades where aerodynamic detuning is accomplished by changing the chord of alternate rotor blades and stator vanes. In a coupled cascade analysis, the configuration of the rotor influences the downstream acoustic response of the stator, and the stator configuration influences the upstream acoustic response of the rotor. This coupled detuned cascade unsteady aerodynamic model is first applied to a baseline tuned stage. This baseline stage is then aerodynamically detuned by replacing alternate rotor blades and stator vanes with decreased chord airfoils. The nominal aerodynamically detuned stage configuration is then optimized, with the stage acoustic response decreased 13 dB upstream and 1 dB downstream at the design operating condition. A reduction in the acoustic response of the optimized aerodynamically detuned stage is then demonstrated over a range of operating conditions.     

Comparison of sound power radiation from isolated airfoils and cascades in a turbulent flow

An analytical model of the sound power radiated from a flat plate airfoil of infinite span in a 2D turbulent flow is presented. The effects of stagger angle on the radiated sound power are included so that the sound power radiated upstream and downstream relative to the fan axis can be predicted. Closed-form asymptotic expressions, valid at low and high frequencies, are provided for the upstream, downstream, and total sound power. A study of the effects of chord length on the total sound power at all reduced frequencies is presented. Excellent agreement for frequencies above a critical frequency is shown between the fast analytical isolated airfoil model presented in this paper and an existing, computationally demanding, cascade model, in which the unsteady loading of the cascade is computed numerically. Reasonable agreement is also observed at low frequencies for low solidity cascade configurations.     

弯扭静子叶片的环形叶栅试验

弯扭静子叶片的环形叶栅试验徐文远，于清，杨弘，王仲奇（哈尔滨工业大学动力工程系哈尔滨１５０００１）关键词：弯扭叶片，环形叶栅，试验随着弯扭叶片理论的发展，它在国内外叶轮机械中的应用日益广泛。在国外，弯扭叶片已应用于新一代航空发动机中，如Ｖ２５００、Ｐ...     

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.     

Analytical and numerical prediction of harmonic sound power in the inlet of aero-engines with emphasis on transonic rotation speeds

Tone noise radiated through the inlet of a turbofan is mainly due to rotor-stator interactions at subsonic regimes (approach flight), and to the shock waves attached to each blade at supersonic helical tip speeds (takeoff). The axial compressor of a helicopter turboshaft engine is transonic as well and can be studied like turbofans at takeoff. The objective of the paper is to predict the sound power at the inlet radiating into the free field, with a focus on transonic conditions because sound levels are much higher. Direct numerical computation of tone acoustic power is based on a RANS (Reynolds averaged Navier–Stokes) solver followed by an integration of acoustic intensity over specified inlet cross-sections, derived from Cantrell and Hart equations (valid in irrotational flows). In transonic regimes, sound power decreases along the intake because of nonlinear propagation, which must be discriminated from numerical dissipation. This is one of the reasons why an analytical approach is also suggested. It is based on three steps: (i) appraisal of the initial pressure jump of the shock waves; (ii) 2D nonlinear propagation model of Morfey and Fisher; (iii) calculation of the sound power of the 3D ducted acoustic field. In this model, all the blades are assumed to be identical such that only the blade passing frequency and its harmonics are predicted (like in the present numerical simulations). However, transfer from blade passing frequency to multiple pure tones can be evaluated in a fourth step through a statistical analysis of irregularities between blades. Interest of the analytical method is to provide a good estimate of nonlinear acoustic propagation in the upstream duct while being easy and fast to compute. The various methods are applied to two turbofan models, respectively in approach (subsonic) and takeoff (transonic) conditions, and to a Turbomeca turboshaft engine (transonic case). The analytical method in transonic appears to be quite reliable by comparison with the numerical solution and with available experimental data.