Hybrid Prediction of Fan Tonal Noise

Transcription

1 Hybrid Prediction of Fan Tonal Noise Sheryl M. Grace and Douglas L. Sondak Boston University Boston, MA 2215 Walter Eversman Missouri University of Science and Technology, Rolla, MO 6541 Michael J. Cannamela Boston University Boston, MA 2215 A hybrid method is used to simulate the downstream rotor-vane interaction tonal noise associated 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 unsteady surface pressure on the exit guide vanes (EGVs). The resulting downstream duct acoustics are then computed using two methods. The first is an analytical Green s function method approximation for an infinite, fixed duct geometry. The second is a finite element model for a realistic duct geometry. One case from the SDT matrix is the main focus of this paper: approach condition for 22 rotor blades and 54 vanes. The configuration was designed for cut-off at the first blade-passing frequency. Comparison of the exhaust power level results for the 22x54 case reveal that the nonuniformity of the duct does not significantly influence the overall power level but it does cut-off the fifth radial mode and redistributes the energy between the other modes. The current acoustic simulation which models only the vane-wake interaction predicts an exhaust power approximately 13 db lower than the experimental exhaust power. Nomenclature β = 1 M 2 compressibility parameter ω radial frequency of disturbance Φ nm annulus eigenfunction c mean speed of sound I acoustic intensity k = ωr t /c nondimensional acoustic wave number k nm ± axial wave number (± upstream/downstream) M Mach number m radial mode number n circumferential mode number p, p nm pressure, complex amplitude of pressure for mode (n,m) r h, r t, r radial location of rotor hub, tip, radial coordinate u acoustic velocity in the axial direction x 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. 1 of 12

2 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 of the exit guide vanes to an acoustic duct calculation. The cascade calculations have varied from semianalytical approaches valid for two-dimensional, unloaded, flat-plate cascades, 1 to flat-plate cascades used in conjunction with a strip theory, 2, 3 to computational and asymptotic solutions of the linearized Euler equations for two-dimensional cascades with a real blade section geometry. 4 8 The acoustic calculations have been based on Green s method 4, 9 11 and other semi-analytical methods. 12, 13 In these simulations, the wake flow has been canonically modeled (e.g., [4, 5, 8]), empirically derived (e.g., [9]), and predicted using CFD simulations (e.g., [7]). Some of these methods were used to study tonal noise (e.g., [4, 11]) and others broadband noise (e.g., [7, 1]). Recently, researchers have integrated computational fluids simulations more fully into turbofan noise prediction by calculating the exit guide vane and/or duct sources via CFD The results from the studies that integrate CFD simulations in order to generate the wake flow or compute directly 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 both study fan noise directly and to provide validation data for simulations Data from NASA s Source Diagnostic Test are used to validate the current simulations. Others who have validated their method against the SDT data include Nallasamy and Envia 7 who studied broadband noise created by vane-wake interaction. In many ways, their simulation was the catalyst for this work, albeit only tonal noise is addressed in 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 coupled turbomachinery flow field as compared to using the average passage computational method. Second, the unsteady EGV pressure computed via the CFD is used as input to a duct acoustic calculation. Both the classical Green s function method and a finite element method that can account for geometry variation are used. This paper focuses mainly on the simulation of one case from the SDT matrix. The fan configuration has 22 rotor blades and 54 EGVs and it is run at the approach condition. At this speed, the blade passing frequency is cut off. A second, cut-on, configuration with 26 exit guide vanes (EGVs) is currently being analyzed 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 provide the acoustic predictions. Then acoustic results from the case are presented. The sensitivity of the simulations to inclusion of real duct effects are discussed. Finally, the preliminary results for the case are presented. Here the focus is mainly on the comparison between the simulated vane unsteady surface pressure and the experimental data. II. CFD Method The flow field simulation has been performed using Phantom, a time-dependent, three-dimensional 26, 27 Reynolds-averaged Navier-Stokes solver for turbomachinery. It uses an implicit, time-marching, finite difference scheme that is third-order accurate in space and second-order accurate in time. The inviscid fluxes are 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. One may think of this as decomposing the scales as shown in Eq. (1) φ = φ + ˆφ + φ (1) where φ represents a time-varying quantity, φ is it s ensemble average at a fixed phase of the blade-passing frequency, ˆφ is deviation from φ 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 elliptic equation solution procedure. They give good resolution at the leading and trailing edges of the blades, and make it easy to apply the turbulence model. O-grids are also used in the tip-clearance region. Algebraically 2 of 12

3 generated H-grids are used to discretize the remainder of the flow field. Further details on the numerical procedure can be found in Ref. [26]. At the inlet, the total pressure, total temperature and the circumferential and radial flow angles are specified, and the upstream-running Riemann invariant is extrapolated from the interior of the computational domain. At the exit, the circumferential and radial velocity components, entropy, and the downstreamrunning Reimann invariant are extrapolated from the interior of the computational domain. The static pressure is specified at the mid-span of the exit of the domain, and the pressure values at all other radial locations are obtained by integrating the radial equilibrium equation. Periodicity is enforced along the outer boundaries of the H-grids in the circumferential direction. No-slip boundary conditions are enforced at the hub and tip end walls and along the airfoil surfaces. It is assumed that the normal derivative of the pressure is zero at the solid wall surfaces, and that the walls are adiabatic. The flow variables at zonal boundaries are 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 While prior comparisons of simulations using this turbomachinery code have all shown excellent agreement with experiment, 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 approximated as an infinite annular cylinder with uniform axial flow and the acoustic propagation is computed via Green s method as described in Ref. [1]. The application of this semi-analytic method to the current simulation is described in more detail in Ref. [32]. This is referred to as the uniform duct case. Second, the variation in the duct cross-sectional area is modeled and the acoustic propagation is computed using an axisymmetric frequency domain finite element model (FEM). 33 This is referred to as the nonuniform duct case. The input for the FEM simulation is obtained by using the semi-analytic method to propagate the vane surface pressure to duct modal amplitudes just downstream of the vane. Both methods are performed in the frequency domain and model the acoustic pressure at the source as an eigenfunction expansion such that p(x, r, θ, t) = p nm Φ nm (r)e i(kt nθ k± nm x) (2) n= m= The FEM models the non-uniform duct geometry and mean flow field and currently treats the termination as non-reflecting. The termination is described as non-reflecting because the duct is extended past the nominal termination as a uniform duct and the process of radiation to the far field and the resulting termination 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 are represented by a mean flow potential and acoustic particle velocity potential. A separate FEM code generates the mean flow using a weak formulation. For the propagation code the mean flow field is compressible and an iterative process is used in which a succession of incompressible calculations converge to the compressible solution. The acoustic solution is based on a weak form of the method of weighted residuals in which the acoustic continuity equation is cast in a potential formulation. Acoustic pressure is obtained by postprocessing the acoustic potential solution using the acoustic momentum equation. In the present case the duct 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 the source plane the acoustic field is expanded in terms of a finite number of incident modes with specified amplitudes plus an equal number of reflected modes with amplitudes determined by the solution of the problem. The termination is represented by a like number of transmitted modes in a short uniform duct extension of the geometry. No reflected modes are present providing the reflection free boundary condition. IV. Results for the case. The off-design operating point simulated for the geometry matched the approach condition in the SDT. This will be called Case 1. The flow conditions were provided in the form of a solution file from a similar simulation performed by NASA Glenn using APNASA. A corrected fan speed of 788 RPM was used with a corrected mass flow of 58.1 lbm/s. 3 of 12

4 axial velocity, ft/s axial velocity, ft/s axial velocity, ft/s experiment current simulation APNASA simulation passage fraction (a) 1% span 3 28 experiment current simulation APNASA simulation passage fraction (b) 5 % span 3 28 experiment current simulation APNASA simulation passage fraction (c) 9 % 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 rotor blades and 54 EGVs with the EGV geometry scaled by 54/55 to maintain the correct blockage. The actual tip 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 are given in the appendix and also in Ref. [32]. The computations were first validated via comparison with available LDV velocity measurements. There are 11 grid points in the circumferential direction, resulting in approximately 14 grid points resolving the rotor wake mid-way between the rotor trailing edge and vane leading edge. The axial wake profiles inches from the rotor trailing edge (1/5th the distance between the rotor trailing edge and vane leading edge) at 1%, 5%, and 9% span are shown in figure 1. The plots compare the current simulation with both the experimental data and the APNASA simulation. The two simulations tend to over-predict or under-predict the wake deficit in different locations and both seem quite reasonable BPF BPF time, s (a) pressure vs. time frequency, Hz (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 acoustic simulation, 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 3 blade passings of the surface pressure on the representative vane for a point located at mid-span on the suction surface near the leading edge. The pressure is normalized by the upstream static pressure, p s. 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.334. The acoustic simulation was set to match the experimental system and has 54 EGVs. The circumferential interaction mode of interest is thus n = 1. The real part of the nondimensional surface pressure at 4 of 12

5 the first and second blade passing frequencies is shown in figure 3. The real and imaginary parts of the nondimensional unsteady pressure along the midspan at 1BPF and 2BPF are shown in figure 4. The (a) 1 BPF Figure 3. (b) 2 BPF Real part of the nondimensional unsteady pressure on the EGV. x Real:pres surf Imag:pres surf Real:suc surf Imag:suc surf 5 x Real:pres surf Imag:pres surf Real:suc surf Imag:suc surf x/a (a) 1 BPF x/a (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 6 blade passings in the FFT from much earlier in the CFD simulation when transients waves were large. For the results reported in this paper 3 blade passing events have been used to obtain the pressure spectrum and the transient has greatly decayed. First the semianalytical Green s method was employed to simulate the downstream acoustics produced by the vane-wake interaction. A uniform duct, as depicted in figure 5 with hub-to-tip radius of.4814 (matching the duct dimensions at the leading edge of the EGV) was used. For this cross-section geometry, the associated nondimensional acoustic wave number is k = When the duct area is not changing, the power in each mode at every cross-section is identical. Table 2 shows the resulting power in each radial mode as well as the total power for the n = 1 circumferential mode. 5 of 12

6 1 When the FEM is used to compute the downstream acoustics, the input modal amplitudes are specified from the.8 semianalytical method at the location in the duct just downstream of the trailing edge of the EGV where the hub-to-tip.6.4 radius is The modal amplitudes are listed in Table 1 and are normalized such that the associated radial eigenfunction has a maximum of 1.. At the input location for the.2 FEM, the outer radius differs from that used in the semianalytic duct calculation. Therefore, the reduced frequency is.2 renormalized to for the FEM simulations. However,.4 there is still a slight mismatch between the geometry used to compute the input modal amplitudes and the geometry at the FEM input location. Figure 5. Flowpath of the experimental rig Table 2 summarizes the acoustic power computed by the with uniform flowpath for the semianalytical method (dashed line) superposed. FEM for both the uniform (assuming a slightly smaller annulus than used in the semianalytic calculation) and the nonuniform ducts. For the nonuniform duct, power in the incident reflected, and transmitted modes are reported. The total power is also shown in each category. Table 1. Modal amplitudes for first 5 radial modes at n = -1. The modal amplitudes are unscaled and have dimensions consistent with pressure (lb f /ft 2 ). Mode 1st mode 2nd mode 3rd mode 4th mode 5th mode Amplitude e e-2 i e e-2 i 8.624e e-2 i e e-3 i 6.3e e-3 i Visualizations of the acoustic field in the uniform and nonuniform ducts are shown in figure 6. The plots depict contours of equal SPL scaled so that the highest level on the source plane in terms of acoustic pressure magnitude is set at 1 db. Levels on the figure are therefore only relative and not consistent with the acoustic power reported in Table 2. Due to constructive and destructive interference of the five input modes, the acoustic pressure field is not highly organized and in fact the highest SPL levels are not on the source plane. For the uniform duct, the acoustic results from the semianalytical and FEM simulations are in good agreement with differences arising from the difference in duct geometry between the two simulations. When one compares the results for the uniform and nonuniform simulations, the most notable difference is that the 5th radial mode is almost completely reflected by the nonuniform 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 incident modes. It is also clear that the acoustic power at the source is affected very little by the duct. This indicates that it is not necessary to account for the interaction of reflections due to duct nonuniformity with the vanes in this case. Table 2. Modal power for first 5 radial modes at n = BPF. Power (lb f ft/s) Mode Semianalytic FEM uniform Input FEM Reflected FEM Transmitted FEM 1st mode 8.816e e e e e-4 2nd mode e e e e e-5 3rd mode e e e e e-6 4th mode e e e e e-6 5th mode e e e e e-26 Total at exhaust 9.625e e e e e-4 As part of the SDT, exhaust power levels were measured. 25 A rotating rake gave an overall exhaust power level for the n = 1 mode of almost 115 db (reference 1 12 Watts). The exhaust power level reconstructed from far-field measurements (that filtered out sound emanating from the inlet) was 15 db. 22 More faith is placed in the power levels obtained from the field measurements because of complexities in 6 of 12

7 (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 the annulus. The simulated exhaust power level varied from 9.6 to 93.4 db when the simulation was run with variations in the inputparameters and input data. For instance, we analyzed the effect of variation in the unsteady surface pressure due to the number of blade passings used to obtain the values at 2BPF, of slight errors in Mach number and reduced frequency, of the geometry mismatch at the input source location, and of uniform and nonuniform duct geometry. The estimated power is lower than the experimental value which is expected because many noise sources have not been modeled here including rotor related noise and duct self noise. However, it is unclear which neglected physical phenomena are most important and if the simulation has 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 methods 16, 18 in that the acoustic propagation is computed using a linearized Euler solver. It is of interest, however, to determine the extent to which the CFD simulation itself resolves the acoustic pressure downstream of the EGV. At this point, only a preliminary analysis of the CFD data has been completed. Time correlation of the computed pressure at two axial locations in the duct does indicate correlation at a propagation speed of u+c where u is the mean axial speed and c is the speed of sound. Visualization of the nondimensional pressure at 1BPF and 2BPF in figure 7 on an axial cut through the duct annulus indicates that 1BPF contains only hydrodynamic information. In addition, while the remnants of the rotor wakes are clearly visible in a snapshot of pressure at 2BPF, radial variation of the type depicted in figure 6 can also be seen. Further modal decomposition will hopefully allow for better assessment of the CFD capabilities. 7 of 12

8 (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.2.4 V. Preliminary results for the case. Preliminary results for a second SDT configuration are reported in this section. The case (Case 2) differs from Case 1 in two important ways. First, the configuration gives rise to a propagating mode at 1 BPF. Second, experimental measurements of the unsteady vane surface pressure are available. For this simulation the exact blade count was used, with 11 rotor blades and 13 vanes. The grid size for.6 this case is shown in the Appendix. The CFD simulations were run at a corrected wheel speed of 788 rpm..4 Currently in the simulation, the mass flow rate is lbm/s. 39 blade passings have been simulated thus far. For performance calculations, and even for turbine clocking studies, often 1.5 rotor revolutions has been sufficient to obtain good results. 29 For this simulation, however, blade passings Figure 8. CFD generated pressure trace near suction side leading edge at midspan. Dashed: actual unsteady pressure trace for 15 blade passings. Solid: highpass filtered result. the transients are just beginning to die away at 1.5 rotor revolutions. In order to compare the experimentally measured vane pressure to the numerically simulated data, the experimental data must be lowpass filtered in order to eliminate the noise as shown in figure 9. Early in the CFD simulation, when transients are still present, highpass filtering the computational data, as shown in figure 8 aids the comparison. Some of the energy can be lost when the data are filtered, but the filter allows one to get an indication if the simulation models the experimental flow field well. The EGV pressure data were obtained experimentally using untaped and taped configurations. 24 The untaped configuration measured p across the blade and the taped configuration measured pressure on the pressure side of the vane. Comparison between the experimental and computational EGV pressure results for p is shown in figure 1 for the 1%, 3%, 5% and 7% chord locations at 6% span. The figures show the CFD results from the last 15 blade passings computed. The agreement between the latest data from the CFD simulation and the experiment indicates that the computation, once settled, will predict the vane pressure very well. 8 of 12

9 blade passings Figure 9. Experimental pressure trace on suction side at 1% chord and 6% span for 2 blade passings. Dotted: actual unsteady pressure trace. Solid: lowpass filtered result blade passings (a) 1% chord blade passings (b) 3% chord blade passings (c) 5% chord blade passings (d) 7% chord Figure 1. Thin line: computational highpass filtered, Thick line: experimental lowpass filtered, unsteady pressure on EGV at 6% span for 15 blade passings. 9 of 12

10 VI. Conclusions and Future Work A 3-D, unsteady, Reynolds-averaged Navier-Stokes CFD code was used to predict the fully coupled turbomachinery flow field and vane surface pressures for two geometries consistent with the NASA 22 inch fan rig. The vane unsteady surface pressures were then used in conjunction with both a semi-analytical duct acoustic 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 the overall power, however, the distribution of power between circumferential modes is modified as compared to the uniform duct case. The simulated power at the exhaust for the 22x54 case is much lower than that measured in the SDT. At least part of the difference is due to the lack of inclusion of all sources (rotor self-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 be performed into the dependence of the vane surface pressure on the number of blade passings included in the FFT. Our analyses have shown that using 1, 2, or 3 blade passings from our data set can affect the final power 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 that the simulation is capturing the vane pressures reasonably well. The simulation will be continued in order to eliminate the effect of transients. As the computed 22x26 data become available, futher comparisons with the vane measurements, both taped and untaped, will be completed. The duct propagation at 1 and 2 BPF will be simulated using both the semianalytical method and the FEM. In addition, the FEM will be used to compute the far field acoustics and these will be compared to the measurements. The simulation will take advantage of the ability of the FEM code to represent the non-uniform duct geometry, the interior mean flow field, the extended center body, and the exterior flow field including the shear layer between the fan exhaust 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 and an H grid were used for each EGV. Tables 3 and 4 show the grid densities for the two configurations described in this paper. The H-grid dimensions are given as axial, circumferential, and spanwise respectively, and the O-grid and clearance-grid dimensions are given as around-the-blade, normal-to-the-blade, and spanwise.the grid spacing at the airfoil surface normalized by chord is approximately Table 3. GRID DIMENSIONS, CASE 1 grid type no. dimensions pts. per grid total pts. duct h 2 37x51x46 69, ,564 rotor h 2 124x51x46 29,94 581,88 rotor o 2 351x41x46 661,986 1,323,972 rotor cl 2 351x12x5 21,6 42,12 EGV h 5 122x21x46 117, ,26 EGV o 5 351x31x46 5,526 2,52,63 total 5,179,35 Acknowledgments The authors would like to thank Dr. E. Envia of NASA Glenn for providing the relevant experimental test specifications and data and discussing the testing and related simulation work. We thank Dan Dorney for his contributions to the running of the 22x26 CFD simulations. BU undergraduate Angelina Giammalvo s reduction of the experimental data is also acknowledged. 1 of 12

11 Table 4. GRID DIMENSIONS, CASE 2 grid type no. dimensions pts. per grid total pts. duct h 5 37x53x46 9,26 451,3 rotor h x53x46 32,312 3,325,432 rotor o x31x46 5,526 5,55,786 rotor cl x12x5 21,6 231,66 EGV h x45x46 252,54 3,283,2 EGV o x31x46 5,526 5,55,786 total 18,32,784 References 1 Goldstein, M. E., Aeroacoustics, McGraw-Hill International Book Co., New York, etc., Namba, M., Three-dimensional analysis of blade force and sound generation for an annual cascade in distorted flows, Journal of sound and vibration, Vol. 5, No. 4, 1977, pp Ventres, C., Theobald, M. A., and Mark, W. D., Turbofan Noise Generation Volume 1: Analysis, Tech. Rep. CR , NASA, July Hall, K. C. and Verdon, J. M., Gust Response Analysis for Cascades Operating in Nonuniform Mean Flows, AIAA Journal, Vol. 29, No. 9, 1991, pp Fang, 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 Majumdar, S. J. and Peake, N., Three-dimensional effects in cascade-gust interaction, Wave Motion, Vol. 23, No. 4, 1996, pp Nallasamy, M. and Envia, E., Computation of rotor wake turbulence noise, Journal of Sound and Vibration, Vol. 282, 25, pp Atassi, H. and Vinogradov, I. V., A model for fan broadband interaction noise in nonuniform flow, AIAA Paper No , 25, 11th AIAA/CEAS Aeroacoustics Conference. 9 Hanson, D. B., Influence of Lean and Sweep on Noise of Cascades with Turbluent Inflow, AIAA Paper No , 1999, 5th AIAA/CEAS Aeroacoustics Conference. 1 Ganz, U., Glegg, S., and Joppa, P., Measurement and prediction of broadband fan noise, AIAA Paper No , June , 4th AIAA/CEAS Aeroacoustics Conference. 11 Atassi, 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 Peake, 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, 24, pp Peake, 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 Schnell, 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 24, Vol. 5B, 24, pp Tsuchiya, 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 24, Vol. 5B, 24, pp Sipatov, A., Avgustinovich, V., Usanin, M., and Chuhlantseva, N., Computational analysis of tonal noise generated high-bypass ratio fan stage, Proceedings of ASME Turbo Expo 25, Vol. 6B, 25, pp Prasad, A. and Prasad, D., Unsteady Aerodynamics and Aeroacoustics of a High-Bypass Ratio Fan Stage, Transactions of the ASME, Vol. 127, 25, pp Polacsek, C., Burguburu, S., Redonnet, S., and Terracol, M., Numerical Simulations of Fan Interaction Noise Using a Hybrid Approach, AIAA Paper No , 25, 11th AIAA/CEAS Aeroacoustics Conference. 19 Sutlif, D., Curtis, A., Heidelberg, L., and Remington, P. J., Performance of Active Noise Control System for Fan Tones Using Vane Actuators, AIAA Paper No , 2, 6th AIAA/CEAS Aeroacoustics Conference. 2 Ganz, U. W., Joppa, P. D., Patten, T. J., and Scharpf, D. F., Boeing 18-Inch Fan Rig Broadband Noise Test, Tech. Rep. CR , NASA, September Podboy, G. G. and Helland, S. M., Fan Noise Source Diagnostic Test-Two-Point Hot-Wire Results, AIAA Paper No , 22, 8th AIAA/CEAS Aeroacoustics Conference. 22 Woodward, R. P., Fan Noise Source Diagnostic Test-Farfield Acoustic Results, AIAA Paper No , 22, 8th AIAA/CEAS Aeroacoustics Conference. 23 Premo, J., Fan Noise Source Diagnostic Test-Circumferential Mode Measurements. AIAA Paper No , 22, 8th AIAA/CEAS Aeroacoustics Conference. 24 Envia, E., Fan Noise Source Diagnostic Test-Vane Unsteady Pressure Results. AIAA Paper No , 22, 8th AIAA/CEAS Aeroacoustics Conference. 11 of 12

12 25 Heidelberg, L. J., Fan Noise Source Diagnostic Test-Tone Modal Structure Results, AIAA Paper No , 22, 8th AIAA/CEAS Aeroacoustics Conference. 26 Dorney, D. J. and Davis, R. L., Navier-Stokes Analysis of Turbine Blade Heat Transfer and Performance, ASME Journal of Turbomachinery, Vol. 114, No. 4, 1992, pp Sondak, D. L. and Dorney, D. J., General Equation Set Solver for Compressible and Incompressible Turbomachinery Flows, AIAA , 23, 39th AIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit. 28 Roe, P. L., Approximate Riemann Solvers, Parameter Vectors and Difference Schemes, Journal of Computational Physics, Vol. 43, 1981, pp Saren, V. E., Savin, N. M., Dorney, D. J., and Sondak, D. L., Experimental and Numerical Investigation of Airfoil Clocking and Inter-Blade-Row Gap Effects on Axial Compressor Performance, International Journal of Turbo and Jet Engines, Vol. 15, 1998, pp Dorney, D. J. and Sondak, D. L., Three-Dimensional Simulations of Airfoil Clocking in a 1-1/2 Stage Turbine, AIAA Paper , 2, 36th AIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit. 31 Dorney, D. J. and Sondak, D. L., Effects of Tip Clearance on Hot Streak Migration in a High-Subsonic Single-Stage Turbine, ASME Journal of Turbomachinery, Vol. 122, 2, pp Grace, S. M., Sondak, D. L., Dorney, D. J., and Logue, M., CFD Computation of Fan Interaction Noise, Proceedings of ASME IMECE, Vol. IMECE , Seattle, WA, Listerud, E. and Eversman, W., Finite Element Modeling of Acoustics Using Higher Order Elements. Part I: Nonuniform Duct Propagation, Journal of Computational Acoustics, Vol. 12, No. 3, 24, pp Listerud, E. and Eversman, W., Finite Element Modeling of Acoustics Using Higher Order Elements. Part II: Turbofan Acoustic Radiation, Journal of Computational Acoustics, Vol. 12, No. 3, 24, pp of 12