Hybrid Prediction of Fan Tonal Noise

Sheryl M. Grace ∗ and Douglas L. Sondak †

Boston University Boston, MA 02215

Walter Eversman ‡

Missouri University of Science and Technology, Rolla, MO 65401

Michael J. Cannamela §

Boston University Boston, MA 02215

A hybrid method is used to simulate the downstream rotor-vane interaction tonal noiseassociated with the NASA Source Diagnostic Test (SDT) 22-in fan rig. A 3-D, unsteady,Reynolds-averaged Navier-Stokes (URANS) CFD simulation is used to predict the un-steady surface pressure on the exit guide vanes (EGVs). The resulting downstream ductacoustics are then computed using two methods. The first is an analytical Green’s functionmethod approximation for an infinite, fixed duct geometry. The second is a finite elementmodel for a realistic duct geometry. One case from the SDT matrix is the main focusof this paper: approach condition for 22 rotor blades and 54 vanes. The configurationwas designed for cut-off at the first blade-passing frequency. Comparison of the exhaustpower level results for the 22x54 case reveal that the nonuniformity of the duct does notsignificantly influence the overall power level but it does cut-off the fifth radial mode andredistributes the energy between the other modes. The current acoustic simulation whichmodels only the vane-wake interaction predicts an exhaust power approximately 13 dBlower than the experimental exhaust power.

Nomenclature

β =√

1−M2 compressibility parameterω radial frequency of disturbanceΦnm annulus’ eigenfunctionc mean speed of soundI acoustic intensityk = ωrt/c nondimensional acoustic wave numberk±nm axial wave number (± upstream/downstream)M Mach numberm radial mode numbern circumferential mode numberp, pnm pressure, complex amplitude of pressure for mode (n,m)rh, rt, r radial location of rotor hub, tip, radial coordinateu acoustic velocity in the axial directionx axial coordinate

∗Assoc. Prof., Dept. of Aero. and Mech. Eng., Associate Fellow, AIAA†Scientific Computing and Visualization, member AIAA‡Curators’ Professor, Mechanical and Aerospace Engineering Department. Associate Fellow AIAA§Graduate student, Dept. of Aero. and Mech. Eng.

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I. Introduction

One source of fan noise is the interaction of rotor wake flow with downstream exit guide vanes (EGV).Many previous studies of fan noise have coupled cascade models that provide the unsteady response ofthe exit guide vanes to an acoustic duct calculation. The cascade calculations have varied from semi-analytical approaches valid for two-dimensional, unloaded, flat-plate cascades,1 to flat-plate cascades usedin conjunction with a strip theory,2,3 to computational and asymptotic solutions of the linearized Eulerequations for two-dimensional cascades with a real blade section geometry.4–8 The acoustic calculationshave been based on Green’s method4,9–11 and other semi-analytical methods.12,13 In these simulations, thewake flow has been canonically modeled (e.g., [4, 5, 8]), empirically derived (e.g., [9]), and predicted usingCFD simulations (e.g., [7]). Some of these methods were used to study tonal noise (e.g., [4, 11]) and othersbroadband noise (e.g., [7, 10]). Recently, researchers have integrated computational fluids simulations morefully into turbofan noise prediction by calculating the exit guide vane and/or duct sources via CFD.14–18

The results from the studies that integrate CFD simulations in order to generate the wake flow or computedirectly the exit guide vane or duct noise sources show great promise.

In addition to the development of turbofan noise simulations, experiments have been constructed to bothstudy fan noise directly and to provide validation data for simulations.19–25 Data from NASA’s SourceDiagnostic Test21–25 are used to validate the current simulations. Others who have validated their methodagainst the SDT data include Nallasamy and Envia7 who studied broadband noise created by vane-wakeinteraction. In many ways, their simulation was the catalyst for this work, albeit only tonal noise is addressedin this research. The current simulation method extends Nallasamy and Envia’s method in three ways.First, a 3-D, unsteady, Reynolds-averaged Navier-Stokes CFD code is used to predict the fully coupledturbomachinery flow field as compared to using the average passage computational method. Second, theunsteady EGV pressure computed via the CFD is used as input to a duct acoustic calculation. Both theclassical Green’s function method and a finite element method that can account for geometry variation areused.

This paper focuses mainly on the simulation of one case from the SDT matrix. The fan configurationhas 22 rotor blades and 54 EGVs and it is run at the approach condition. At this speed, the blade passingfrequency is cut off. A second, cut-on, configuration with 26 exit guide vanes (EGVs) is currently beinganalyzed and some preliminary CFD results are included in this paper.

The first section of the paper will describe briefly the computational methods that combine to providethe acoustic predictions. Then acoustic results from the 22 × 54 case are presented. The sensitivity of thesimulations to inclusion of real duct effects are discussed. Finally, the preliminary results for the 22 × 26case are presented. Here the focus is mainly on the comparison between the simulated vane unsteady surfacepressure and the experimental data.

II. CFD Method

The flow field simulation has been performed using Phantom, a time-dependent, three-dimensionalReynolds-averaged Navier-Stokes solver for turbomachinery.26,27 It uses an implicit, time-marching, finitedifference scheme that is third-order accurate in space and second-order accurate in time. The inviscid fluxesare discretized using Roe’s scheme,28 and the viscous fluxes are calculated using standard central differences.Approximate-factorization is used along with dual time-stepping, which minimizes factorization errors.

Large-scale unsteady phenomena such as tip vortices and wake interactions are resolved in the simulation,and small-scale turbulent structures are modeled using the Baldwin-Lomax algebraic turbulence model. Onemay think of this as decomposing the scales as shown in Eq. (1)

φ = φ̃+ φ̂+ φ′ (1)

where φ represents a time-varying quantity, φ̃ is it’s ensemble average at a fixed phase of the blade-passingfrequency, φ̂ is deviation from φ̃ due to large-scale, non-random fluctuations such as vortex shedding, and φ′

is the random fluctuation.The solver uses O and H-type zonal grids to discretize the flow field and facilitate relative motion of the

blades and vanes. The O-grids are body fitted to the surfaces of the blades and generated using an ellipticequation solution procedure. They give good resolution at the leading and trailing edges of the blades, andmake it easy to apply the turbulence model. O-grids are also used in the tip-clearance region. Algebraically

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generated H-grids are used to discretize the remainder of the flow field. Further details on the numericalprocedure can be found in Ref. [26].

At the inlet, the total pressure, total temperature and the circumferential and radial flow angles arespecified, and the upstream-running Riemann invariant is extrapolated from the interior of the computationaldomain. At the exit, the circumferential and radial velocity components, entropy, and the downstream-running Reimann invariant are extrapolated from the interior of the computational domain. The staticpressure is specified at the mid-span of the exit of the domain, and the pressure values at all other radiallocations are obtained by integrating the radial equilibrium equation. Periodicity is enforced along the outerboundaries of the H-grids in the circumferential direction. No-slip boundary conditions are enforced at thehub and tip end walls and along the airfoil surfaces. It is assumed that the normal derivative of the pressureis zero at the solid wall surfaces, and that the walls are adiabatic. The flow variables at zonal boundariesare explicitly updated after each time step by interpolating values from adjacent grids.

Phantom has been extensively validated in the past on a wide variety of configurations.29–31 Whileprior comparisons of simulations using this turbomachinery code have all shown excellent agreement withexperiment, this is the first time it is being used as part of an aeroacoustic simulation.

III. Acoustic Method

Two acoustic propagation methods are used and the results are compared. First, the duct is approximatedas an infinite annular cylinder with uniform axial flow and the acoustic propagation is computed via Green’smethod as described in Ref. [1]. The application of this semi-analytic method to the current simulation isdescribed in more detail in Ref. [32]. This is referred to as the uniform duct case. Second, the variation inthe duct cross-sectional area is modeled and the acoustic propagation is computed using an axisymmetricfrequency domain finite element model (FEM).33 This is referred to as the nonuniform duct case. The inputfor the FEM simulation is obtained by using the semi-analytic method to propagate the vane surface pressureto duct modal amplitudes just downstream of the vane.

Both methods are performed in the frequency domain and model the acoustic pressure at the source asan eigenfunction expansion such that

p(x, r, θ, t) =∞∑

n=−∞

∞∑m=−∞

pnmΦnm(r)e−i(kt−nθ−k±nmx) (2)

The FEM models the non-uniform duct geometry and mean flow field and currently treats the termi-nation as non-reflecting. The termination is described as non-reflecting because the duct is extended pastthe nominal termination as a uniform duct and the process of radiation to the far field and the resultingtermination impedance is not modeled. Reflections that occur due to duct non-uniformities are included.

An irrotational formulation is used in which mean flow and acoustic particle velocity perturbations arerepresented by a mean flow potential and acoustic particle velocity potential. A separate FEM code generatesthe mean flow using a weak formulation. For the propagation code the mean flow field is compressible andan iterative process is used in which a succession of incompressible calculations converge to the compressiblesolution. The acoustic solution is based on a weak form of the method of weighted residuals in whichthe acoustic continuity equation is cast in a potential formulation. Acoustic pressure is obtained by post-processing the acoustic potential solution using the acoustic momentum equation. In the present case theduct walls are acoustically hard so that only the natural boundary condition is required.

The acoustic source is modeled at a nominally uniform section of duct in terms of duct modes. On thesource plane the acoustic field is expanded in terms of a finite number of incident modes with specifiedamplitudes plus an equal number of reflected modes with amplitudes determined by the solution of theproblem. The termination is represented by a like number of transmitted modes in a short uniform ductextension of the geometry. No reflected modes are present providing the reflection free boundary condition.

IV. Results for the 22 × 54 case.

The off-design operating point simulated for the 22 × 54 geometry matched the approach condition inthe SDT. This will be called Case 1. The flow conditions were provided in the form of a solution file froma similar simulation performed by NASA Glenn using APNASA. A corrected fan speed of 7808 RPM wasused with a corrected mass flow of 58.01 lbm/s.

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0 0.2 0.4 0.6 0.8 1260

280

300

320

340

360

380

400

420

passage fraction

axia

l vel

ocity

, ft/s

experiment current simulationAPNASA simulation

(a) 10% span

0 0.2 0.4 0.6 0.8 1260

280

300

320

340

360

380

400

420

passage fraction

axia

l vel

ocity

, ft/s

experiment current simulationAPNASA simulation

(b) 50 % span

0 0.2 0.4 0.6 0.8 1260

280

300

320

340

360

380

400

420

passage fraction

axia

l vel

ocity

, ft/s

experiment current simulationAPNASA simulation

(c) 90 % span

Figure 1. Axial wake profile 1/2 rotor chord downstream of rotor trailing edge.

To increase the computational speed, a 2 on 5 scaling was used as an approximation to the 22 rotorblades and 54 EGVs with the EGV geometry scaled by 54/55 to maintain the correct blockage. The actualtip clearance from the experiment was not available, so a value of 1% span was assumed.

Details of the grid which consists of O- and H-grids for the rotor and EGVs and moving rotor grids aregiven in the appendix and also in Ref. [32].

The computations were first validated via comparison with available LDV velocity measurements. Thereare 101 grid points in the circumferential direction, resulting in approximately 14 grid points resolving therotor wake mid-way between the rotor trailing edge and vane leading edge. The axial wake profiles 3.125inches from the rotor trailing edge (1/5th the distance between the rotor trailing edge and vane leading edge)at 10%, 50%, and 90% span are shown in figure 1. The plots compare the current simulation with both theexperimental data and the APNASA simulation. The two simulations tend to over-predict or under-predictthe wake deficit in different locations and both seem quite reasonable.

0 0.002 0.004 0.006 0.008 0.01 0.0121

1.02

1.04

1.06

1.08

1.1

1.12

time, s

p/p s

(a) pressure vs. time

0 1000 2000 3000 4000 5000 60000

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

0.045

0.05

p/p s

frequency, Hz

BPF

2 BPF

(b) pressure vs. frequency

Figure 2. Nondimensional pressure at a point near the suction side leading edge of the EGV midspan.

The surface pressure on one of the five EGVs has been recorded from the CFD solution. For the acousticsimulation, it is assumed that all of the EGVs have the same pressure adjusted by the inter-vane phase angle.Figure 2 shows the time trace over 30 blade passings of the surface pressure on the representative vane for apoint located at mid-span on the suction surface near the leading edge. The pressure is normalized by theupstream static pressure, ps. The corresponding FFT is also shown in figure 2.

For Case 1, the blade passing frequency of 2863 Hz is cut off in the duct and 2 BPF, 5726 Hz, is cut-on.The average Mach number of the flow downstream of the EGV calculated by the CFD simulation is 0.334.The acoustic simulation was set to match the experimental system and has 54 EGVs. The circumferentialinteraction mode of interest is thus n = −10. The real part of the nondimensional surface pressure at

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the first and second blade passing frequencies is shown in figure 3. The real and imaginary parts of thenondimensional unsteady pressure along the midspan at 1BPF and 2BPF are shown in figure 4. The

(a) 1 BPF (b) 2 BPF

Figure 3. Real part of the nondimensional unsteady pressure on the EGV.

0.68 0.7 0.72 0.74 0.76 0.78 0.8

−8

−6

−4

−2

0

2

4

6

8

x 10−3

x/a

p/p s

Real:pres surfImag:pres surfReal:suc surfImag:suc surf

(a) 1 BPF

0.68 0.7 0.72 0.74 0.76 0.78 0.8−5

−4

−3

−2

−1

0

1

2

3

4

5x 10

−3

x/a

p/p s

Real:pres surfImag:pres surfReal:suc surfImag:suc surf

(b) 2 BPF

Figure 4. Nondimensional unsteady pressure along the midspan of the EGV.

surface pressures shown here differ from the results reported in Ref. [32] which were obtained using only 6blade passings in the FFT from much earlier in the CFD simulation when transients waves were large. Forthe results reported in this paper 30 blade passing events have been used to obtain the pressure spectrumand the transient has greatly decayed.

First the semianalytical Green’s method was employed to simulate the downstream acoustics producedby the vane-wake interaction. A uniform duct, as depicted in figure 5 with hub-to-tip radius of 0.4814(matching the duct dimensions at the leading edge of the EGV) was used. For this cross-section ge-ometry, the associated nondimensional acoustic wave number is k = 29.4. When the duct area is notchanging, the power in each mode at every cross-section is identical. Table 2 shows the resulting powerin each radial mode as well as the total power for the n = −10 circumferential mode.

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−0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 1 1.2

−0.4

−0.2

0

0.2

0.4

0.6

0.8

1

Figure 5. Flowpath of the experimental rigwith uniform flowpath for the semianalyticalmethod (dashed line) superposed.

When the FEM is used to compute the downstreamacoustics, the input modal amplitudes are specified from thesemianalytical method at the location in the duct just down-stream of the trailing edge of the EGV where the hub-to-tipradius is 0.5274. The modal amplitudes are listed in Table1 and are normalized such that the associated radial eigen-function has a maximum of 1.0. At the input location for theFEM, the outer radius differs from that used in the semian-alytic duct calculation. Therefore, the reduced frequency isrenormalized to 29.049 for the FEM simulations. However,there is still a slight mismatch between the geometry usedto compute the input modal amplitudes and the geometryat the FEM input location.

Table 2 summarizes the acoustic power computed by theFEM for both the uniform (assuming a slightly smaller an-nulus than used in the semianalytic calculation) and thenonuniform ducts. For the nonuniform duct, power in the incident reflected, and transmitted modes arereported. The total power is also shown in each category.

Table 1. Modal amplitudes for first 5 ra-dial modes at n = -10. The modal am-plitudes are unscaled and have dimensionsconsistent with pressure (lbf /ft2).

Mode Amplitude1st mode 2.9461e-02 + 5.5917e-02 i2nd mode -4.5807e-03− 1.8956e-02 i3rd mode 8.624e-03 − 1.6624e-02 i4th mode 1.2784e-02 − 8.4086e-03 i5th mode 6.0003e-03 − 9.7450e-03 i

Visualizations of the acoustic field in the uniform andnonuniform ducts are shown in figure 6. The plots depictcontours of equal SPL scaled so that the highest level onthe source plane in terms of acoustic pressure magnitudeis set at 100 dB. Levels on the figure are therefore onlyrelative and not consistent with the acoustic power re-ported in Table 2. Due to constructive and destructiveinterference of the five input modes, the acoustic pres-sure field is not highly organized and in fact the highestSPL levels are not on the source plane.

For the uniform duct, the acoustic results from thesemianalytical and FEM simulations are in good agree-ment with differences arising from the difference in duct

geometry between the two simulations. When one compares the results for the uniform and nonuniformsimulations, the most notable difference is that the 5th radial mode is almost completely reflected by thenonuniform duct. Power is also scattered into the 1st radial mode at the expense of the 2nd and 3rd modes.However, the net transmitted power at the termination is only slightly less than the power in the incidentmodes. It is also clear that the acoustic power at the source is affected very little by the duct. This indicatesthat it is not necessary to account for the interaction of reflections due to duct nonuniformity with the vanesin this case.

Table 2. Modal power for first 5 radial modes at n = -10. 2 BPF.

Power (lbf ft/s)Mode Semianalytic FEM uniform Input FEM Reflected FEM Transmitted FEM

1st mode 8.0816e-04 8.0526e-04 8.0526e-04 -3.0685e-08 9.0033e-042nd mode 8.1885e-05 8.3627e-05 8.3627e-05 -1.9926e-08 2.8532e-053rd mode 4.8143e-05 3.8554e-05 3.8554e-05 -7.3669e-08 9.3533e-064th mode 1.8121e-05 1.7335e-05 1.7335e-05 -1.5832e-07 5.0751e-065th mode 5.7432e-06 2.8417e-06 2.8417e-06 -2.8289e-06 1.7793e-26

Total at exhaust 9.6205e-04 9.4761e-04 9.4761e-04 -4.1114e-06 9.4329e-04

As part of the SDT, exhaust power levels were measured.25 A rotating rake gave an overall exhaustpower level for the n = −10 mode of almost 115 dB (reference 10−12 Watts). The exhaust power levelreconstructed from far-field measurements (that filtered out sound emanating from the inlet) was 105 dB.22

More faith is placed in the power levels obtained from the field measurements because of complexities in

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(a) Uniform duct. (b) Nonuniform duct.

Figure 6. Sound pressure level on cut through annular duct from source plane to exhaust plane.

resolving modal information from the rakes which are affected by the mean flow velocity gradient in theannulus. The simulated exhaust power level varied from 90.6 to 93.4 dB when the simulation was run withvariations in the inputparameters and input data. For instance, we analyzed the effect of variation in theunsteady surface pressure due to the number of blade passings used to obtain the values at 2BPF, of slighterrors in Mach number and reduced frequency, of the geometry mismatch at the input source location, and ofuniform and nonuniform duct geometry. The estimated power is lower than the experimental value which isexpected because many noise sources have not been modeled here including rotor related noise and duct selfnoise. However, it is unclear which neglected physical phenomena are most important and if the simulationhas done a good job of producing the interaction noise duct source term.

A. CFD Duct results

The hybrid method used in this research to simulate fan noise is similar to other methods16,18 in that theacoustic propagation is computed using a linearized Euler solver. It is of interest, however, to determine theextent to which the CFD simulation itself resolves the acoustic pressure downstream of the EGV. At thispoint, only a preliminary analysis of the CFD data has been completed. Time correlation of the computedpressure at two axial locations in the duct does indicate correlation at a propagation speed of u+c where u isthe mean axial speed and c is the speed of sound. Visualization of the nondimensional pressure at 1BPF and2BPF in figure 7 on an axial cut through the duct annulus indicates that 1BPF contains only hydrodynamicinformation. In addition, while the remnants of the rotor wakes are clearly visible in a snapshot of pressureat 2BPF, radial variation of the type depicted in figure 6 can also be seen. Further modal decompositionwill hopefully allow for better assessment of the CFD capabilities.

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(a) 1 BPF from CFD (b) 2 BPF from CFD

Figure 7. Nondimensional pressure at axial location 4.35 chord lengths downstream of the EGV

V. Preliminary results for the 22 × 26 case.

Preliminary results for a second SDT configuration are reported in this section. The 22 × 26 case (Case2) differs from Case 1 in two important ways. First, the configuration gives rise to a propagating mode at 1BPF. Second, experimental measurements of the unsteady vane surface pressure are available.

0 2 4 6 8 10 12 14 16−0.06

−0.04

−0.02

0

0.02

0.04

0.06

p/p s

blade passings

Figure 8. CFD generated pressure trace near suc-tion side leading edge at midspan. Dashed: ac-tual unsteady pressure trace for 15 blade passings.Solid: highpass filtered result.

For this simulation the exact blade count was used,with 11 rotor blades and 13 vanes. The grid size forthis case is shown in the Appendix. The CFD simula-tions were run at a corrected wheel speed of 7808 rpm.Currently in the simulation, the mass flow rate is 55.75lbm/s. 39 blade passings have been simulated thus far.For performance calculations, and even for turbine clock-ing studies, often 1.5 rotor revolutions has been sufficientto obtain good results.29 For this simulation, however,the transients are just beginning to die away at 1.5 rotorrevolutions.

In order to compare the experimentally measuredvane pressure to the numerically simulated data, theexperimental data must be lowpass filtered in order toeliminate the noise as shown in figure 9. Early in theCFD simulation, when transients are still present, high-pass filtering the computational data, as shown in figure8 aids the comparison. Some of the energy can be lostwhen the data are filtered, but the filter allows one to getan indication if the simulation models the experimentalflow field well.

The EGV pressure data were obtained experimentally using untaped and taped configurations.24 Theuntaped configuration measured ∆p across the blade and the taped configuration measured pressure on thepressure side of the vane. Comparison between the experimental and computational EGV pressure resultsfor ∆p is shown in figure 10 for the 10%, 30%, 50% and 70% chord locations at 60% span. The figures showthe CFD results from the last 15 blade passings computed.

The agreement between the latest data from the CFD simulation and the experiment indicates that thecomputation, once settled, will predict the vane pressure very well.

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0 5 10 15 20−0.015

−0.01

−0.005

0

0.005

0.01

0.015

p/p s

blade passings

Figure 9. Experimental pressure trace on suction side at 10% chord and 60% span for 20 blade passings.Dotted: actual unsteady pressure trace. Solid: lowpass filtered result.

0 5 10 15−0.01

−0.008

−0.006

−0.004

−0.002

0

0.002

0.004

0.006

0.008

0.01

p/p s

blade passings

(a) 10% chord

0 5 10 15−0.01

−0.008

−0.006

−0.004

−0.002

0

0.002

0.004

0.006

0.008

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p/p s

blade passings

(b) 30% chord

0 5 10 15−0.01

−0.008

−0.006

−0.004

−0.002

0

0.002

0.004

0.006

0.008

0.01

p/p s

blade passings

(c) 50% chord

0 5 10 15−0.01

−0.008

−0.006

−0.004

−0.002

0

0.002

0.004

0.006

0.008

0.01

p/p s

blade passings

(d) 70% chord

Figure 10. Thin line: computational highpass filtered, Thick line: experimental lowpass filtered, unsteadypressure on EGV at 60% span for 15 blade passings.

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VI. Conclusions and Future Work

A 3-D, unsteady, Reynolds-averaged Navier-Stokes CFD code was used to predict the fully coupledturbomachinery flow field and vane surface pressures for two geometries consistent with the NASA 22 inchfan rig. The vane unsteady surface pressures were then used in conjunction with both a semi-analytical ductacoustic model and an finite element model to predict the tonal sound power level at the exhaust plane.

The results show that for the 22x54 case, the changing cross-section in the duct area does not affect theoverall power, however, the distribution of power between circumferential modes is modified as comparedto the uniform duct case. The simulated power at the exhaust for the 22x54 case is much lower than thatmeasured in the SDT. At least part of the difference is due to the lack of inclusion of all sources (rotorself-noise, duct noise, etc.) in the simulation, but the magnitude of these effects is not presently known.

The computations for the 22x54 case will be continued so that a more detailed investigation can beperformed into the dependence of the vane surface pressure on the number of blade passings included in theFFT. Our analyses have shown that using 10, 20, or 30 blade passings from our data set can affect the finalpower level by more than 2 dB. A better understanding of this effect will help guide future CFD simulations.

The preliminary results for the 22x26 case for which there are experimental vane pressure data show thatthe simulation is capturing the vane pressures reasonably well. The simulation will be continued in order toeliminate the effect of transients. As the computed 22x26 data become available, futher comparisons withthe vane measurements, both taped and untaped, will be completed. The duct propagation at 1 and 2 BPFwill be simulated using both the semianalytical method and the FEM. In addition, the FEM will be used tocompute the far field acoustics and these will be compared to the measurements. The simulation will takeadvantage of the ability of the FEM code to represent the non-uniform duct geometry, the interior meanflow field, the extended center body, and the exterior flow field including the shear layer between the fanexhaust jet and the exterior mean flow field.34

Appendix

A total of 18 grids were used in the Case 1 simulation and 64 in the Case 2 simulation. For both cases,H-grids were used for the inlet duct, an O, H, and clearance grid were used for each rotor blade, and an O andan H grid were used for each EGV. Tables 3 and 4 show the grid densities for the two configurations describedin this paper. The H-grid dimensions are given as axial, circumferential, and spanwise respectively, and theO-grid and clearance-grid dimensions are given as around-the-blade, normal-to-the-blade, and spanwise.Thegrid spacing at the airfoil surface normalized by chord is approximately 2.5× 10−4.

Table 3. GRID DIMENSIONS, CASE 1

grid type no. dimensions pts. per grid total pts.duct h 2 37x51x46 69,782 139,564rotor h 2 124x51x46 290,904 581,808rotor o 2 351x41x46 661,986 1,323,972rotor cl 2 351x12x5 21,060 42,120EGV h 5 122x21x46 117,852 589,260EGV o 5 351x31x46 500,526 2,502,630total 5,179,305

Acknowledgments

The authors would like to thank Dr. E. Envia of NASA Glenn for providing the relevant experimentaltest specifications and data and discussing the testing and related simulation work. We thank Dan Dorneyfor his contributions to the running of the 22x26 CFD simulations. BU undergraduate Angelina Giammalvo’sreduction of the experimental data is also acknowledged.

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Table 4. GRID DIMENSIONS, CASE 2

grid type no. dimensions pts. per grid total pts.duct h 5 37x53x46 90,206 451,030rotor h 11 124x53x46 302,312 3,325,432rotor o 11 351x31x46 500,526 5,505,786rotor cl 11 351x12x5 21,060 231,660EGV h 13 122x45x46 252,540 3,283,020EGV o 13 351x31x46 500,526 5,505,786total 18,302,784

References

1Goldstein, M. E., Aeroacoustics, McGraw-Hill International Book Co., New York, etc., 1976.2Namba, M., “Three-dimensional analysis of blade force and sound generation for an annual cascade in distorted flows,”

Journal of sound and vibration, Vol. 50, No. 4, 1977, pp. 479–508.3Ventres, C., Theobald, M. A., and Mark, W. D., “Turbofan Noise Generation Volume 1: Analysis,” Tech. Rep. CR-167952,

NASA, July 1982.4Hall, K. C. and Verdon, J. M., “Gust Response Analysis for Cascades Operating in Nonuniform Mean Flows,” AIAA

Journal , Vol. 29, No. 9, 1991, pp. 1463–1471.5Fang, J. and Atassi, H., “Direct calculation of sound radiated from a loaded cascade of loaded airfoils,” Proceedings of

Computational Aero- and Hydro-Acoustics, ASME FED , Vol. 147, 1993, pp. 111–116.6Majumdar, S. J. and Peake, N., “Three-dimensional effects in cascade-gust interaction,” Wave Motion, Vol. 23, No. 4,

1996, pp. 321–337.7Nallasamy, M. and Envia, E., “Computation of rotor wake turbulence noise,” Journal of Sound and Vibration, Vol. 282,

2005, pp. 649–678.8Atassi, H. and Vinogradov, I. V., “A model for fan broadband interaction noise in nonuniform flow,” AIAA Paper No.

2005-2880 , 2005, 11th AIAA/CEAS Aeroacoustics Conference.9Hanson, D. B., “Influence of Lean and Sweep on Noise of Cascades with Turbluent Inflow,” AIAA Paper No. 99-1863 ,

1999, 5th AIAA/CEAS Aeroacoustics Conference.10Ganz, U., Glegg, S., and Joppa, P., “Measurement and prediction of broadband fan noise,” AIAA Paper No. 98-2316 ,

June 2-4 1998, 4th AIAA/CEAS Aeroacoustics Conference.11Atassi, H. M., Fang, J., and Patrick, S. M., “Direct Calculation of Sound Radiated from Bodies in Nonuniform Flows,”

Journal of Fluids Engineering, Vol. 115, December 1993, pp. 573–579.12Peake, N. and Kerschen, E. J., “Influence of mean loading on noise generated by the interaction of gusts with a cascade:

downstream radiation,” Journal of Fluid Mechanics, Vol. 515, 2004, pp. 99–133.13Peake, N. and Kerschen, E. J., “Influence of mean loading on noise generated by the interaction of gusts with a cascade:

upstream radiation,” Journal of Fluid Mechanics, Vol. 347, 1997, pp. 315–346.14Schnell, R., “Investigation of the tonal acoustic field of a transonic fanstage by time-domain cfd-calculations with arbitrary

blade counts,” Proceedings of ASME Turbo Expo 2004 , Vol. 5B, 2004, pp. 1763–1773.15Tsuchiya, N., Nakamura, Y., Goto, S., Kodama, H., Noazaki, O., Nishizawa, T., and Yamamoto, K., “Low noise FEGV

designed by numerical method based on CFD,” Proceedings of ASME Turbo Expo 2004 , Vol. 5B, 2004, pp. 1691–1698.16Sipatov, A., Avgustinovich, V., Usanin, M., and Chuhlantseva, N., “Computational analysis of tonal noise generated

high-bypass ratio fan stage,” Proceedings of ASME Turbo Expo 2005 , Vol. 6B, 2005, pp. 1265–1274.17Prasad, A. and Prasad, D., “Unsteady Aerodynamics and Aeroacoustics of a High-Bypass Ratio Fan Stage,” Transactions

of the ASME , Vol. 127, 2005, pp. 64–75.18Polacsek, C., Burguburu, S., Redonnet, S., and Terracol, M., “Numerical Simulations of Fan Interaction Noise Using a

Hybrid Approach,” AIAA Paper No. 2005-2014 , 2005, 11th AIAA/CEAS Aeroacoustics Conference.19Sutlif, D., Curtis, A., Heidelberg, L., and Remington, P. J., “Performance of Active Noise Control System for Fan Tones

Using Vane Actuators,” AIAA Paper No. 2000-1906 , 2000, 6th AIAA/CEAS Aeroacoustics Conference.20Ganz, U. W., Joppa, P. D., Patten, T. J., and Scharpf, D. F., “Boeing 18-Inch Fan Rig Broadband Noise Test,” Tech.

Rep. CR-1998-208704, NASA, September 1998.21Podboy, G. G. and Helland, S. M., “Fan Noise Source Diagnostic Test-Two-Point Hot-Wire Results,” AIAA Paper No.

2002-2431 , 2002, 8th AIAA/CEAS Aeroacoustics Conference.22Woodward, R. P., “Fan Noise Source Diagnostic Test-Farfield Acoustic Results,” AIAA Paper No. 2002-2427 , 2002, 8th

AIAA/CEAS Aeroacoustics Conference.23Premo, J., “Fan Noise Source Diagnostic Test-Circumferential Mode Measurements.” AIAA Paper No. 2002-2429 , 2002,

8th AIAA/CEAS Aeroacoustics Conference.24Envia, E., “Fan Noise Source Diagnostic Test-Vane Unsteady Pressure Results.” AIAA Paper No. 2002-2430 , 2002, 8th

AIAA/CEAS Aeroacoustics Conference.

11 of 12

American Institute of Aeronautics and Astronautics

25Heidelberg, L. J., “Fan Noise Source Diagnostic Test-Tone Modal Structure Results,” AIAA Paper No. 2002-2428 , 2002,8th AIAA/CEAS Aeroacoustics Conference.

26Dorney, D. J. and Davis, R. L., “Navier-Stokes Analysis of Turbine Blade Heat Transfer and Performance,” ASMEJournal of Turbomachinery, Vol. 114, No. 4, 1992, pp. 795–806.

27Sondak, D. L. and Dorney, D. J., “General Equation Set Solver for Compressible and Incompressible TurbomachineryFlows,” AIAA 2003-4420 , 2003, 39th AIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit.

28Roe, P. L., “Approximate Riemann Solvers, Parameter Vectors and Difference Schemes,” Journal of ComputationalPhysics, Vol. 43, 1981, pp. 357–372.

29Saren, V. E., Savin, N. M., Dorney, D. J., and Sondak, D. L., “Experimental and Numerical Investigation of AirfoilClocking and Inter-Blade-Row Gap Effects on Axial Compressor Performance,” International Journal of Turbo and Jet Engines,Vol. 15, 1998, pp. 235–252.

30Dorney, D. J. and Sondak, D. L., “Three-Dimensional Simulations of Airfoil Clocking in a 1-1/2 Stage Turbine,” AIAAPaper 2000-3359 , 2000, 36th AIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit.

31Dorney, D. J. and Sondak, D. L., “Effects of Tip Clearance on Hot Streak Migration in a High-Subsonic Single-StageTurbine,” ASME Journal of Turbomachinery, Vol. 122, 2000, pp. 613–620.

32Grace, S. M., Sondak, D. L., Dorney, D. J., and Logue, M., “CFD Computation of Fan Interaction Noise,” Proceedingsof ASME IMECE , Vol. IMECE2007-43779, Seattle, WA, 2007.

33Listerud, E. and Eversman, W., “Finite Element Modeling of Acoustics Using Higher Order Elements. Part I: NonuniformDuct Propagation,” Journal of Computational Acoustics, Vol. 12, No. 3, 2004, pp. 397–429.

34Listerud, E. and Eversman, W., “Finite Element Modeling of Acoustics Using Higher Order Elements. Part II: TurbofanAcoustic Radiation,” Journal of Computational Acoustics, Vol. 12, No. 3, 2004, pp. 431–446.

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