Fan Noise: A Challenge to CAA

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2002-2560, 8th AIAA/CEAS Aeroacoustics Conference, Brecken- ridge, Colorado. Envia, E. (2002) “Application of a Linearized Euler Analysis to Fan Noise.
International Journal of Computational Fluid Dynamics, August 2004 Vol. 18 (6), pp. 471–480

Fan Noise: A Challenge to CAA EDMANE ENVIAa,*, ALEXANDER G. WILSONb,† and DENNIS L. HUFFc,‡ a

Acoustics Branch, Mail Stop 54-3, NASA Glenn Research Center, 21000 Brookpark Road, Cleveland, OH 44135, USA; bMailcode SinA-76, P.O. Box 31, Rolls-Royce plc, Derby DE24 8BJ, UK; cStructures and Acoustics Division, Mail Stop 49-6, NASA Glenn Research Center, 21000 Brookpark Road, Cleveland, OH 44135, USA

The objective of this paper is to expose the computational aeroacoustics (CAA) community to the current unresolved issues in modeling and predicting fan noise. The paper includes a description of the sources of fan noise and a discussion of the current status of the fan noise prediction methods and their shortcomings. The discussion is focused on the issues and includes sufficient details to help outline the scope of the fan noise problem and define the level of fidelity required for meaningful CAA simulations. Keywords: Fan noise; Computational aeroacoustics; Broadband noise; Rotor-stator interaction noise; Multiple pure tones; Self-noise

INTRODUCTION Increasingly, computational aeroacoustics or CAA{, is viewed as a viable tool for analysis of engineering problems in which noise plays a significant role. In fact, CAA has already been used to study fundamental aspects of noise generation and propagation in a number of model problems of technological interest like jets, cavity flows, and duct radiation (Freund et al., 1998; Shieh and Morris, 1999; ¨ zyo¨ru¨k and Long, 1999). The promise of CAA lies in its O ability to simulate accurately the physical processes involved in the generation and propagation of sound and thus it offers insights that can complement the knowledge gained from analytical and experimental methods. In this sense CAA may be used in tackling some outstanding issues in fan noise modeling that, owing to their complexity, have not yet been fully resolved. The motivation for understanding and predicting fan noise derives from its significance as a major contributor to the total noise output of a modern aeroengine and the need to mitigate noise emissions from aircraft for environmental reasons. To devise effective means of reducing fan noise, a detailed understanding of its mechanisms and characteristics is needed. Yet many, but by no means all, of the current theoretical models used in fan noise prediction rely on simplified descriptions of the hardware and flow conditions that prevail inside the engine. As a result, such models do not have the required level of fidelity to describe all of the relevant

aspects of the physical mechanisms involved in the generation of fan noise and thus are of limited use for developing effective noise mitigation methods. Experimental approaches have also seen only limited success in tackling the fan noise problem due to the overlapping nature of its sources which often mask the contribution from a specific source under consideration. Another complicating factor is that the strengths of various sources of fan noise depend on the fan rotational speed and thus they can vary significantly with the engine power setting. In view of these difficulties, it is hoped that CAA can provide much-needed help in resolving the outstanding issues in fan noise modeling. Depending on the particular problem, this help could be in the form of fundamental theoretical studies to elucidate, and perhaps even uncover, mechanisms involved in noise generation. The help could also be in the form of improvements to (or replacement of ) current prediction capabilities for practical design and analysis purposes. To that end, the objective of this paper is to describe “the fan noise problem” and identify opportunities for CAA to make an impact. The paper includes a description of the sources of fan noise and a discussion of the current status of the fan noise prediction methods and their shortcomings. The discussion is focused on the issues and not on a review of all current prediction efforts. The paper includes sufficient details to outline the scope of the fan noise problem and to help define the level of fidelity required for meaningful CAA simulations.

*Corresponding author. Tel.: þ 1-216-433-8956. Fax: þ 1-216-433-3918. E-mail: [email protected] † E-mail: [email protected] ‡ E-mail: [email protected] { As the name suggests, CAA is a computational approach for solving the unsteady flow equations with special emphasis on resolving acoustic perturbations normally ignored in CFD. Informative reviews of CAA may be found in the articles by Tam (1995), Lele (1997) and Wells and Renaut (1997). ISSN 1061-8562 print/ISSN 1029-0257 online q 2004 Taylor & Francis Ltd DOI: 10.1080/10618560410001673489

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FIGURE 1 Sources of fan noise in a high bypass ratio turbofan engine. Sketch adopted from Tam and Hardin (1997).

FAN NOISE Fan noise is a generic term that refers to the noise associated with the fan stage of a turbofan aeroengine and, as indicated in Fig. 1, is produced by a number of different sources (Smith, 1989; Groeneweg et al., 1991). Most of the sources involve the interaction of small unsteady flow perturbations – principally vortical and acoustic –with the fan (rotor) and stationary guide vane (stator) blade rows within the stage. These include the interaction of inflow distortions and the inlet boundary layer with the fan and the interaction of fan flow perturbations (blade viscous wakes, tip clearance flow, etc) with the bypass and core stators. The interaction can also be self-generated (often called self-noise) as in the case of the noise produced by scattering of blade boundary layer turbulence at the blade trailing edge, or noise due to local separation of the flow on the airfoil, or noise associated with vortex shedding at the trailing edge. Depending on the nature of the unsteady perturbations involved, the interaction sources generate discrete frequency tones or broadband noise or, in most cases, both. There are also other sources that are associated with the steady part of the flow within the fan stage. These include the interaction of the fan with the steady potential (i.e. pressure) field of the engine struts§ and the multiple pure tones (MPT) of the fan (also called buzz-saw noise) that are produced as a result of spatial non-uniformities in the rotor-locked pressure field. The fan-strut interaction produces discrete tones at the harmonics of the blade passing frequency, while buzz-saw is produced at the multiples of fan shaft rotational frequency. It has been suggested by Morfey (1971), Mani (1971) and, more recently, by Mani et al. (1997) that the fluctuating Reynolds stress, or the so-called volume quadrupole, of the turbulent flow within the fan stage is also an important source of fan noise at high frequencies and fan loading

conditions. As indicated earlier, the strengths of fan noise sources depend on the fan tip (rotational) speed. As an example, the MPT noise is only significant when the fan tip speed is supersonic. At subsonic tip speeds the rotorlocked pressure field is evanescent and contributes very little to the total noise signature of the fan. As the fan tip speed varies across the operating regime of the engine, the proportions of the contributions from various sources change (see, for example, Woodward et al., 2002). Measurements of fan noise from scale model rigs and fullscale engines have provided indications of the relative importance of some of the fan noise sources as a function of the fan tip speed, but owing to the overlapping nature of the sources it is not always possible to differentiate between them (Joppa, 1999). The noise produced by the fan stage must propagate fore and aft along the fan duct through a non-uniform flow and in most cases through the fan and stator blade rows to reach the duct terminations before radiating to the far field. It is known that the acoustic pressure waves will be strongly affected by the non-uniform flow and particularly by the swirl in the region between the fan and stator (Sofrin and Cicon, 1987a,b; Atassi, 1997). The acoustic waves passing through the blade rows are also subject to transmission and reflection as well as frequency scatteringk. The fan duct itself is typically lined with acoustic treatment (see Fig. 1), varies in cross-sectional area and in some cases is even non-axisymmetric, all of which can influence the noise within the fan duct in significant ways (Rienstra, 1998; Cooper and Peake, 2001). Finally, in addition to the blade rows and struts, it might be necessary to take into account other noise obstacles in the fan duct such as engine struts, pylons, pressure and temperature probes, bleed holes and service access points (see, for example, Scharpf, 1998). Noise reaching the inlet plane is diffracted around the intake lip and that reaching the exhaust plane is scattered by the developing nozzle lip shear layer before radiating to the far field as sketched in Fig. 2. The inlet field could also be dramatically modified if the engine inlet is scarfed for the purpose of providing noise shielding on the ground (Clark et al., 1997). Due to the variety and complexity of the mechanisms involved in the generation and propagation of fan noise, the problem is often tackled by dividing it into more manageable parts. The obvious way for splitting the fan noise problem is to divide it into a source (i.e. noise generation) problem and a propagation problem as shown schematically in Fig. 3. This split has the advantage that the source problem is now an internal one requiring no far field radiation prediction and the propagation problem does not require source prediction. It should be noted that in this scheme, the propagation of

§ The fan-stator potential field interaction is weaker than the fan-strut potential field interaction, since the stator vane count is typically higher and its chord smaller than those of a strut assembly. In fact, due to the large axial spacing between the fan and stator in a modern high bypass ratio aeroengine, the fan-stator potential field interaction is often quite weak. k While transmission and reflection occur at both the fan and stator, only the fan causes frequency scattering.

FAN NOISE: A CHALLENGE TO CAA

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Source Modeling

FIGURE 2 Schematics of the bypass section of a fan stage. Transmission and reflection of acoustics waves occur at both the fan and stator. Acoustic waves are also scattered by the fan.

noise within the fan stage (say, between the fan and stator) is considered part of the source problem and only the noise propagating upstream of the fan and downstream of the bypass stator is included in the propagation problem. Once the solutions for the source and propagation problems are obtained, they can be coupled in a judicious manner to produce a complete solution for the fan noise problem. Examples of this type of approach may be found in the work by Topol (1997) and Rumsey et al. (1998).

In principle, the source problem must account for all of the noise mechanisms described earlier as well as the coupling between the fan and stator blade rows. For modeling purposes, if it can be assumed that the noise within the fan stage does not influence the noise generation mechanisms in any significant way, then the source contribution of each blade row can be considered separately as indicated on the bottom of Fig. 3. The coupling between the blade rows can then be thought of as ‘acoustic’ only and enforced in a manner similar to that proposed by Hanson (1997) and, independently, by Silkowski et al. (1997). Take, for example, the case of the rotor-stator interaction noise that is produced when the viscous wakes of the fan impinge on the stator. If it is assumed that the interaction noise generated at the stator and propagating upstream does not alter the nonlinear viscous processes that generate the fan wakes in the first place, then the blade rows can be considered to be only acoustically coupled in the sense described above. There is some justification for this assumption from Navier-Stokes-based aerodynamic calculations of flow through multi-blade-row turbomachines, such as those made by Adamczyk et al. (1990) and Hall (1997), in which the acoustic effects between the blade rows are eliminated as a result of averaging. The viscous fan wakes produced from such calculations are in good agreement with the experimentally measured wakes that include the acoustic effects (see for example, Gliebe et al., 2000 and Nallasamy et al., 2002). It should be noted that these favorable comparisons involve the time-averaged wakes and so, strictly speaking, the assumption is only validated for tone noise mechanisms. Its validity for broadband noise remains an open question. Nevertheless, the tremendous modeling simplifications offered by the acoustic coupling assumption has made it the cornerstone of many fan noise modeling efforts (for a brief review, see Huff, 1998). In the next few paragraphs, a summary of the current status of fan noise source modeling is given and the outstanding issues are discussed. No attempt is made to be thorough in covering all contributions in a particular area. Instead, the focus is on describing the current best state of practice using representative examples and on identifying shortcomings and opportunities for CAA to make a contribution.

Tone Sources

FIGURE 3 Simplification of the fan noise problem. As one moves down the sketch, the simplification is gained at the expense of fidelity.

Rotor-stator Interaction Noise This is a major source of fan tone noise, especially for high bypass ratio aeroengines, and has received much attention and is furthest along in the level of fidelity of models designed to predict it. The state-of-the-art models for predicting this noise source include three-dimensional real blade as well as nonlinear mean flow effects. The modeling of this problem typically relies on two separate calculations. First, a Reynolds averaged Navier-Stokes (RANS) calculation is carried out to compute the timeaveraged viscous wakes of the rotor. Then, the wake

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information is fed as an unsteady vortical input disturbance to a separate calculation for the acoustic response of the stator (see, for example, Berge et al., 1998). If reliable wake data are available, the first calculation may be unnecessary. Owing to the inherently inviscid processes that generate the tonal acoustic response of the stator, the second calculation can be performed in a linearized Euler sense as suggested by Montgomery and Verdon (1997) where the acoustic response is computed, in the frequency domain, as a linear perturbation to a nonlinear inviscid background flow through the stator. This approach was used by Verdon (2001) and Envia (2002) to compute rotor-stator interaction tone noise generated by 22-inch model fan stages that were tested in a NASA wind tunnel. Both measured and calculated wake inputs were used in these simulations. The computed wakes required RANS simulations with slightly more than 106 grid points while the acoustic response calculations required approximately 1:8 £ 104 grid points to resolve reduced frequencies (based on stator chord) of up to four. Since the RANS simulations were steady and the acoustic calculations were performed in the frequency domain, both sets of calculations required only one passage of their respective blade rows to be modeled, which reduced the computational requirements substantially. Comparisons, on acoustic power level basis, of the predicted and measured first and second harmonics of the blade passing frequency tone for the fan rigs studied show very good agreement downstream of the stator where the effect of rotor-stator acoustic coupling should be negligible. The good agreement is both for the total tone power levels (typically within 3 dB) as well as the power distribution within the modal content# of the tones. It should be noted that attempts to extend these calculations to higher reduced frequencies (say, six corresponding to the third harmonic of the blade passing frequency) have not been entirely successful (Verdon, 2001). The problem seems to be primarily one of insufficient grid resolution in both the RANS and acoustic calculations to adequately capture the higher harmonic content of the wake and noise. Naturally, increasing the grid density will come at the cost of increasing computational effort which is undesirable for design and development purposes. Where the acoustic coupling between the rotor and stator should be important (i.e. in the region between the fan and guide vanes) the data-theory comparisons are not possible since noise measurements in the inlet are only made upstream of the fan. Nonetheless, the importance of rotor-stator acoustic coupling can be gauged by comparing the computed tone levels upstream of the stator with the measured fan inlet levels. When this is done, the computed levels typically overpredict the measured levels substantially (e.g. 17 dB in the case considered by Envia, 2002). The poor comparison

clearly demonstrates the need for including the acoustic coupling between the blade rows to account for acoustic transmission loss through the fan. To do this, the acoustic response of the fan to incident acoustic waves must be calculated first. This will involve the calculation of reflection, transmission and scattering of the incident acoustic waves. Then using a procedure similar to that proposed by Hanson (1997), the blade rows can be coupled in the acoustic sense. In this context, the coupling is defined as accounting for all types of small amplitude unsteady disturbances (i.e. acoustic, vortical and entropic) that may exist between the two blade rows and which may be reflected, transmitted and scattered by each blade row infinitely many times. Naturally, in practice, the number of multiple reflections, transmissions and scatterings taken into account is finite and commensurate with the level of accuracy needed for the computation, since the amplitudes of waves tend to diminish through each successive cycle of reflection, transmission and scattering. In Hanson’s procedure, which relies on a modal description in the frequency domain, the reflection, transmission and scattering characteristics of each blade row are built one mode at a time resulting in a transfer matrix for each blade row. A system of linear algebraic equations is then set up that relates the unknown modal amplitudes of all the waves within the coupled system via these transfer properties to the known source (i.e. fan wake) amplitudes that drive the system. The solution of the resulting matrix equation is the desired unsteady coupling between the blade rows. The problem is that Hanson’s theory was derived for uniform background flows for which the three wave types are fully decoupled, form complete basis systems and can be described analytically. For swirling background flows, the waves are partially coupled, do not form a complete basis system for all wave types, and they must be constructed numerically (see, for example, Kousen, 1995). Therefore, the implementation of this type of unsteady coupling for realistic cases must await an extension of Hanson’s theory that addresses these concerns. In view of the technical challenges associated with using the acoustic coupling approach in real flows, it might seem advantageous to consider solving for the response of the blade rows as a fully coupled system from the onset. This approach to rotor-stator interaction noise calculation was attempted in a landmark simulation by Rumsey et al. (1998) for a 12-inch model scale fan stage. Using a time-accurate nonlinear viscous flow code, the wakes of the fan, the acoustic response of the stator to these wakes, and the acoustic coupling of the two blade rows were captured in a single calculation. A sliding-zone interface was employed to pass information between the fan and stator rows. The computed pressure field associated with the blade passing frequency tone was then propagated from upstream of the fan to the far field using a combination of a duct propagation code

# Fan tones are usually expressed in terms of their modal structure (Goldstein, 1976). The mode description is an expansion in a suitable set of basis functions that is appropriate to the local fan duct geometry and mean flow.

FAN NOISE: A CHALLENGE TO CAA

(Parrett and Eversman, 1986) and a version Kirchhoff formula due to Spence (1997) and compared with the measured far field levels. The comparison, done on the basis of directivity of sound pressure level, shows agreement to within 10 dB over a narrow range of directivity angles. This rather poor data-theory agreement notwithstanding, the conceptual simplicity of the coupled blade row approach is attractive. In addition to requiring only a single calculation that encompasses all relevant features of the problem, this approach also requires simpler inflow and outflow boundary conditions. That is because the flow upstream and downstream of the fan stage is effectively axial. In contrast, the single blade row calculations discussed earlier require swirling flow type inflow (or outflow) boundary conditions (Ali et al., 2001; Verdon, 2001) which are computationally more intensive to implement than the axial flow conditions. There is, however, one major drawback to a coupled calculation; its sheer size. Despite the fortuitous blade/vane count ratio for the fan stage considered by Rumsey et al. (1998), which required only a quarter of the annulus to be considered, the grid requirements were still substantial at about 2.4 £ 106 grid points. The target of the calculation, the blade passing frequency tone, has a reduced frequency of two which is rather modest considering the realistic frequencies of engineering interest. A more representative case, say at a reduced frequency of eight and without rotational symmetry, would require over 1.5 £ 108 grid points making the fully coupled approach too large for routine use even with today’s computational resources. It should be noted here that there are more efficient alternatives to a full annulus description when blade count ratios require it. For example, Giles (1988) used the concept of “timeinclined planes” to enable approximate matching of rotor and stator sectors to be modeled in a single calculation. A more recent treatment of the problem is given by Gerolymos et al. (2002) in their application of the “chorochronic periodicity” method. Generally such methods require somewhat longer convergence times than single passage calculations, but they should provide significant savings over the full annulus calculations. CAA-based approaches to the fan tone noise problem would likely require the use of high-order algorithms such as those described in Goodrich (1997) and Hixon and Turkel (1998) with their promise of superior computational efficiency. Naturally, like the second-order methods described in Verdon (2001) and Rumsey et al. (1998), high-order CAA methods must be able to handle complex three-dimensional blade row geometries and non-linear background flows (viscous or inviscid), and still resolve the acoustic waves accurately. Complex geometries, in particular, have traditionally been a challenge for high-order methods, but lately progress is being made (see, for example, Delfs, 2001). Ultimately, widespread use of CAA methods for solving the fan tone noise problem would largely depend on their ability to be more cost effective than the conventional unsteady CFD

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approaches, or, if that is not the case, on their ability to produce superior quality results compared with the standard CFD.

Multiple Pure Tones (Buzz-saw Noise) This is another important source of fan tone noise, but only when the fan tip speed is supersonic. It arises from the rotor-locked steady pressure field of the fan which at subsonic tip speeds is evanescent and decays before it reaches the fan duct inlet. But when the tip speed becomes supersonic a rotating shock system (locked to the fan) is formed at the fan blade leading edges. Due to small imperfections in the blade geometry (created during manufacturing) and spacing (created during installation) perturbations are formed in the rotating shock system. These perturbations are further exaggerated by the nonlinear mechanisms involved in the propagation of shock waves resulting in a rotating pressure pattern that, to a stationary observer, is periodic in the fan shaft rotational frequency instead of the blade passing frequency. Owing to the preponderance of the frequencies produced, MPT noise has a raspy quality and hence is often called buzzsaw noise. With identical blades, and in the absence of distortions to the background flow, the rotor-locked shock systems have for a number of years been effectively modeled for aerodynamic analysis purposes using conventional single passage steady CFD calculations. By extending the grid upstream it is possible, in the same calculation, to predict the propagation of the blade passing tone noise along the inlet duct, with or without an intake liner (Breard et al., 2001; Wilson, 2001). However, the key for calculating MPT noise lies in accounting for the variations in blade geometry and spacing around the wheel which lead to the imperfections in the shock system. In a novel approach, Gliebe et al. (2000) developed an approximation method based on the superposition principle to calculate the MPT noise from CFD results. They recognized that the amplitudes of the pure tones change linearly with blade shape and spacing variations. Taking advantage of this fact, they developed a prediction method that can estimate MPT noise from a single multipassage transonic steady CFD solution where only one blade is modified. The MPT spectrum for a real fan, where every blade is slightly different, is constructed by using superposition from the canonical solution. Owing to the observed linear dependence of MPT amplitudes on blade variations, the same CFD solution can be used to calculate spectra for different prescribed variations of non-uniformity around the wheel, thus obviating the need to do a new CFD simulation for each new case. The CFD calculations reported in the work by Gliebe et al. (2000) typically required 2.5 £ 106 mesh points with half of the annulus modeled. Data-theory comparisons indicate that this method can predict spectral shapes and amplitudes reasonably well (usually within 5 dB of the measured levels). While improvement in the fidelity of these calculations is desirable, it would come at the cost of

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increased grids resolution and increased computational resource requirements. It is not entirely clear how CAA might be used for MPT noise calculation given the nature of the source mechanism involved. The main difficulty presented by the supersonic fan noise problem is its nonlinearity. The pressure gradients steepen into high-amplitude discrete shocks, which decay nonlinearly with upstream distance (Morfey and Fisher, 1970). The steep gradients in the shock pose a difficult problem for high-order codes, since high curvatures in the steep regions of the shock profile are not conducive to high-order modeling and spurious oscillations in the solution are frequently observed in these regions. These oscillations can be damped by switching on low-order numerical smoothing (typically second order) in the vicinity of steep pressure gradients, but care has to be exercised to avoid artificially increasing the dissipation rate of the shock itself which would influence the MPT amplitudes. Naturally, the smoothing reduces the order of accuracy of the code requiring a commensurate increase in grid density near the shock to retain accuracy. Broadband Sources Rotor-stator Interaction Noise ** A major source of fan broadband noise, it is produced as a result of the impingement of fan stream (i.e. wake and tip clearance flow) turbulence on the stator. While, in principle, the computational tools developed for predicting rotor-stator tone noise are applicable to the rotor-stator broadband noise prediction, in practice, the random nature of the incident disturbances makes the use of such approaches prohibitively expensive. That is because, in the time domain a large number of noise calculations (i.e. realizations), each corresponding to a randomly selected set of input disturbance amplitudes, are needed to construct a statistically meaningful ensemble average. In the frequency domain, on the other hand, a large number of constituent frequencies are needed to accurately represent the spectrum of incident disturbances, which also requires a large number of noise calculations. In either case, highly resolved grids are needed to capture the fine details corresponding to the high frequency content making such calculations extremely CPU intensive even on a large computer. For this reason, the bulk of the modeling work in rotor-stator interaction broadband noise is statistically based. Furthermore, due to the complexity of the problem, the models are analytical in nature and based on simplified descriptions of the background flow and blade geometry. Both single blade row models (Ventres et al., 1982; Hanson, 1998; Gliebe et al., 2000) and acoustically coupled blade row models (Gliebe et al., 2000; Hanson, 2001), which take into account multiple reflections, transmissions and frequency

scatterings have been developed. Formulated in the frequency domain, these models assume a uniform background flow and a flat plate idealization of the blade sections to make the problem tractable. These models describe the sound spectral density in terms of the spectral density of incident turbulent velocity fluctuations. The incident velocity spectrum, often assumed to be locally homogeneous, is sometimes expressed in terms of known frequency-wavenumber spectra (say, von Ka´rma´n or Liepmann) which require the specification of only two parameters; a root mean square intensity level and an appropriate integral length scale. The response of the blade row to the incident fluctuations is computed on a perfrequency and per-duct-mode basis using flat plate cascade response models of the type ultimately traceable to those developed by Smith (1972) and Whitehead (1972). The turbulence input parameters (intensity and length scale) are supplied from experimental measurements (Ganz et al., 1998; Podboy et al., 2002) or from RANS calculations of the fan flowfield (Gliebe et al., 2000; Nallasamy et al., 2002). The noise spectrum calculations typically require a very large number of duct modes over the range of frequencies of interest (see Nallasamy et al., 2002) making these calculations unwieldy. An efficient alternative to the Fourier-based approach, especially when the inhomogeneity of fan stream turbulence must be taken into account, has been suggested by Glegg and Devenport (2001). This approach, which relies on the so-called proper orthogonal decomposition, or POD (Lumley, 1967), describes in a compact fashion the structure of turbulent flow downstream of the fan using a relatively small set of “proper” structures or modes. These modes are obtained from the two-point space-time correlation of the turbulence behind the fan which itself is constructed using a method suggested by Devenport and Glegg (2001). Generally speaking, the analytical models of broadband noise predict the basic spectral characteristics (such as shape of the narrowband and third octave spectra) and the trends with blade geometry (such as count and sweep) correctly, but fall short of predicting the absolute spectral levels accurately except at low tip fan speed conditions (Morin, 1999; Nallasamy et al., 2002). This is not surprising since the flat plate blade row response models are too simplified to capture accurately the details of the flow around the realistic blade profiles, the distortion of incident turbulence by the blade and the three-dimensionality of the background flow. Alternative, CAA-based approaches are therefore needed that retain higher levels of fidelity for both flow and blade row geometry. Ideally, the source (i.e. incident turbulence) spectrum should also be calculated from first principles, since turbulence data may not always be available to construct a POD description. If linearized noise prediction methods are to be used, an independent unsteady RANS, or large eddy simulation (LES), or even a direct numerical

** Fan-inlet turbulence interaction noise, produced as a result of interaction of inflow and inlet boundary layer turbulence with the fan, is fundamentally similar in nature to rotor-stator interaction broadband noise and is modeled in a similar fashion. For examples of models developed to predict it see de Gouville (1998), Glegg and Walker (1999) and Joseph and Parry (2001).

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simulation (DNS) calculation is needed to compute the spectrum of incident turbulence†† that will be used as input to the noise calculations. The noise calculation itself must resolve the wide range of frequencies present in typical fan broadband noise spectra. In view of the tone calculation examples discussed earlier, even a modest frequency resolution requirement would quickly exhaust computer storage and CPU time requirements if all frequencies of interest in the spectrum are to be resolved for a threedimensional problem. Clearly, alternative approaches are needed. An attractive frequency domain approach, suggested by Elhadidi and Atassi (2002), involves the use of high-frequency asymptotics in conjunction with a linearized Euler method to reduce the computational cost. A nonlinear (viscous) time domain approach in which both the incident turbulence and broadband noise are computed simultaneously has the advantage of solving for all relevant mechanisms in a single calculation, but such a calculation would require at least LES-type fidelity and incur an enormous computational cost. Fan Self-noise Self-generated interactions involving scattering of blade boundary layer turbulence at the fan trailing edge, local separation of the flow on the blade, and vortex shedding at the blade trailing edge are all thought to be sources of fan self-noise. Compared to rotor-stator interaction noise, much less work has been done on self-noise modeling and most of that has been focused on the turbulent boundary layer interacting with the blade trailing edge. Recent modeling work (Glegg, 1996) has been based on the pioneering experimental studies of Brooks and Marcolini (1983) and Brooks et al. (1989), although earlier work by Sharland (1964), Morfey (1971) and Mugridge (1973) has also been used by Gliebe et al. (2000) in their development of a fan self-noise model. Self-noise models use flat plate response theories and experimental correlations to define a connection between the boundary layer turbulence spectrum near the trailing edge and the radiated noise. Like the rotor-stator interaction broadband noise models, the self-noise models tend to produce reasonable qualitative agreements but quantitatively they are off (by as much as 10 dB). It is the lack of detailed knowledge about the structure of turbulence that is largely to blame and improved prediction tools are needed to help develop accurate descriptions of turbulence in the vicinity of the blade trailing edge. Some steps have already been taken in this direction as exemplified by the work of Devenport and Spitz (2003) who propose to use Reynolds stress and length scale information to construct the two-point space-time correlation of turbulent vorticity near the trailing edge that will be used as the source of trailing edge noise. There have also

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been attempts to compute the trailing edge noise directly such as the calculation carried out by Wang and Moin (2000) who used LES to compute the flow and radiated noise near the trailing edge. These types of calculations require huge computer resources and cannot be used for routine prediction work, but they can be used to provide numerical benchmarks against which theoretical models such as the one being developed by Devenport and Spitz (2003) can be tested. Propagation Modeling Since the target of noise computation is the far field, a complete noise prediction strategy has to address issues not only of noise generation, but also of noise propagation along the intake and bypass ducts and then of radiation to the far field. In a conventional bypass aeroengine the mean flow in both the intake and bypass ducts is largely axial. In the intake it is also largely irrotational. Furthermore, wall geometries are generally smooth and frequently axisymmetric. These features lend themselves to analytic approximation and many duct calculations have been performed with analytic or semi-analytic methods, such as the Wiener-Hopf-based method of Savkar and Edelfelt (1975), the cutoff ratio‡‡-based method of Rice (1978), the boundary integral method of Dunn et al. (1996), and the multiple scales method of Rienstra and Eversman (1999). Most of these models rely on highly idealized representations of the duct (usually a thin cylindrical shell) and background flow (usually uniform). These types of calculations provide a good first approximation but do not include the realistic nacelle geometry and flow effects necessary for a high fidelity simulation. Some of these effects are included in the more advanced numerical codes such as those developed by Eversman and Danda (1993) and Eversman (1998). In these codes the acoustic propagation is handled as a linearization about a potential background flow using finite element discretization of the flowfield in the interior and exterior of the nacelle. These codes propagate the input information, usually specified using a classical mode description upstream of the fan or downstream of the stator, through the duct accounting for acoustic energy loss and scattering at the acoustically treated sections and diffraction around the intake lip and shear layer downstream of fan nozzle. These calculations have been shown to provide good agreement with measured data for low tip speed fans and when the input acoustic pressure levels are accurately specified (Heidelberg et al., 1996). Alternative radiation methods based on Kirchhoff formulation have also been developed (Spence, 1997) which propagate the near field data to the far field while accurately preserving the phase information.

†† Numerical turbulence prediction is a large and complex field and beyond the scope of this paper. An up-to-date summary of the state of the art can be found in a series of articles in a book edited by Launder and Sandham (2002). ‡‡ Cutoff ratio is a measure of how close a duct mode is to being evanescent (i.e. cutoff). A plane wave has a cutoff ratio of infinity and a mode with a cutoff ratio of unity is just on the verge of propagation. A cutoff ratio below unity implies a decaying mode.

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All of these codes are restricted to axisymmetric geometries and cannot be used for prediction of radiated noise when struts or pylons have to be taken into account. The influence of these geometric features can be assessed using other methods such as those developed by Dougherty (1996; 1997; 1999). Using (high-frequency) ray tracing in three dimensions, these methods can be used to address flow nonuniformities, acoustic treatment and non-axisymmetric duct features. In recent years, fully CAA-based approaches to fan duct radiation have been investigated, by among others, ¨ zyo¨ru¨k et al. (2001; 2002); Li et al. (2002) who have O demonstrated the feasibility of these types of calculations in both time and frequency domains for realistic nacelle geometries. All of the duct radiation models discussed above are either restricted to, or have only been applied to, the tone noise radiation problem. In fact, very few attempts have been made to develop practical broadband noise radiation models. One exception is the approximate model developed by Rice (1999) which is essentially an extension of his tone-based model (Rice, 1978) to the broadband noise radiation problem. It uses the mode cutoff ratio to calculate the directivity pattern (i.e. location of the principal lobe of radiation in the far field) for each mode separately and then combines them to obtain the broadband directivity. Another notable exception is the application of ray theory to broadband noise radiation by Kempton (1981; 1983). Of course, these models do not have the fidelity of numerical codes, but they provide reasonable first approximations. Application and extension of the advanced numerical techniques to broadband noise radiation is the next obvious step.

CONCLUSIONS The previous section provided a brief overview of some of the current activities in fan noise modeling. It might be helpful to summarize the outstanding issues and spell out the challenges that must be addressed in their resolution. To begin with, it seems that partitioning of the fan noise problem into source and radiation parts is likely to remain a sensible approach for the foreseeable future given the complexity of the fan noise problem. This split will, of course, continue to encourage the development of separate models for source prediction and propagation/radiation prediction. The review in the last section should make it clear that there are many more unresolved issues in source modeling than there are in radiation modeling. Furthermore, over the past several years significant strides have been made in the development of high-fidelity radiation codes. As such, it is desirable to have a greater proportion of CAA modeling efforts invested in resolving the issues in the source problem. The single most important issue in fan noise source modeling is turbulence and its wide-ranging impact on fan broadband noise generation. Clearly, a complete resolution of the turbulence problem is a daunting challenge unlikely to be solved in the near future. However, for the purposes of practical fan broadband noise calculations, it

may be sufficient to rely on reduced order modeling of turbulence. This could be in the form of steady or unsteady RANS predictions for inlet boundary layer or rotor wake turbulence which will then be used as input for fan broadband noise calculations. For the less understood broadband noise sources like self-noise, LES could be used to improve our understanding of the physics of the noise generation process, thereby providing clues for improved reduced order noise prediction models. Aside from capturing the source details correctly, CAA must also be capable of accurate and efficient handling of the wide spectrum of acoustic frequencies involved. This is likely to require substantial computational resources. Consider, for example, that the bypass section of a large modern aeroengine has a volume on the order of 12 m3. To account for frequencies up to 5 kHz (full scale) in the presence of flow, wavelengths on the order of 4 cm must be resolved. Assuming seven points per wavelength resolution, 64 million grid points would thus be needed to compute the acoustic field within the bypass duct. While 1 million grid point calculations are now fairly routine, 64 million grid point calculations are practical only as research tasks. Therefore, either high-order CAA algorithms or some form of highfrequency asymptotics, or both, are needed to reduce the computational requirements. Naturally, tone calculations will also benefit from such improvements as higher harmonics of the blade passing frequency could be reliably resolved. As for the question of time domain or frequency domain, the answer is not entirely clear. For tone calculations, evidence suggests that frequency domain approaches provide adequate solutions for modest frequencies. However, for broadband noise calculations, it remains to be seen which approach is best suited for the task. Another factor impacting this choice is whether an acoustically coupled blade row or a fully coupled blade row strategy is to be used to tackle the fan noise problem. The published results from a handful of cases indicate that the acoustically coupled blade row approach provides sufficient fidelity at substantially lower computational cost, especially if the problem of acoustic coupling between the blade rows can be rigorously solved for three-dimensional configurations with real flow effects. However, the fully coupled blade row approach cannot be entirely dismissed, especially if the acoustic coupling theories cannot be extended to the realistic geometry and flow conditions. The choice between linear and nonlinear approaches is clearer in that there are some sources of fan noise that are thought to be controlled by linear processes (like rotor-stator interaction) and yet others (like MPT noise) that definitely require the nonlinear effects. Ideally, if both methods could be used, their comparison would provide insights not available when only linear models are used. There are also some additional considerations not covered here that must be given equal attention since they can have an enormous impact on the robustness, efficiency and accuracy of the simulations. These include the issues of grid generation (structured and unstructured), boundary conditions (non-reflecting inflow/outflow conditions),

FAN NOISE: A CHALLENGE TO CAA

multi-block/multi-time-stepping, and parallelization. These issues have been expertly covered in the CAA literature and are excluded here in the interest of brevity. Finally, it should be noted that there have been many workshops and conferences dedicated to showcasing the progress and achievements of CAA. A particularly good series for source material is the CAA Workshops on Benchmark Problems of which there have so far been four (Hardin et al., 1995; Tam and Hardin, 1997; Dahl, 2001; proceedings for the fourth to be published in 2004) with a fourth one scheduled for October of 2003. A series of progressively more sophisticated turbomachinery related benchmark problems have been defined and solved in these workshops. These problems serve as benchmarks against which to test new CAA algorithms and codes.

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