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NASA Technical Reports Server (NTRS) 20040110387: A Study of the Effects of Blade Shape on Rotor Noise PDF

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Preview NASA Technical Reports Server (NTRS) 20040110387: A Study of the Effects of Blade Shape on Rotor Noise

A STUDY OF THE EFFECTS OF BLADE SHAPE ON ROTOR NOISE Henry E. Jones U.S. Army Joint Research Program Office/AFDD Casey L. Burley NASA Langley Research Center Abstract c rotor aerodynamic reference blade chord A new rotor noise prediction system called the Til- c rotor blade chord at tip tip trotor Aeroacoustic Code (TRAC) has been developed under the Short Haul (Civil Tiltrotor) program T between NASA, the Army, and the U.S. helicopter C rotor thrust coefficient, ------------------------------ industry. This system couples the comprehensive T rp W ( R)2R2 rotorcraft code CAMRAD.Mod1 with either the high resolution sectional loads code HIRES or the full r spanwise coordinate along blade potential CFD code FPRBVI to predict unsteady blade DNW Duits-Nederslandse Windtunnel loads, which are then input to the noise prediction program WOPWOP. In this paper, HIRES will be used FW-H Ffowcs Williams-Hawkings equation to predict the blade-vortex interaction (BVI) noise Y spanwise location of vorticity, measured trends associated with blade shape. The baseline BAR from tip shape selected was a 17% scale model of a contempo- rary design 4 bladed rotor. Measurements for this BPF rotor blade passage frequency; 96.17 Hz rotor were acquired in the Duits-Nederslandse Wind- BVISPL sound pressure level obtained by tunnel (DNW). The code is used to predict noise for integrating from the 7th through 30th the base configuration and the results are compared to harmonics of the BPF (nominally 673 the measured data. This provides a firm foundation Hz to 2885 Hz), dB for investigating the BVI noise trends associated with blade shape. The shapes selected for study are based l blade sweep angle, deg on variation of sweep and taper which reflect plausi- b ’ observer elevation angle, deg ble “passive” design concepts. Comparisons of power required, integrated noise, and aerodynamics are Y ’ observer azimuthal angle, deg made and important trends are noted. p pressure variable in WOPWOP model max Nomenclature N force, newtons a freestream sound speed, m/sec m meters 0 V freestream velocity, m/sec Background b number of blades Impulsive rotor noise is caused by rapid c blade mean chord, m changes in the local aerodynamic environment of the R rotor radius, m/sec blade. Until recently, computing these effects has been beyond the state of the art, and hence experimental r air density, kg/m3 studies were used to investigate the relevant phenom- W rotational speed, rpm ena. Brooks1 provides an excellent review of much of this work. Recently, a new rotor noise prediction sys- s blade solidity ratio, bc/p R tem called the Tiltrotor Aeroacoustic Code (TRAC) m rotor advance ratio, V/W R has been developed under the Short Haul (Civil Tiltro- tor) program between NASA, the Army, and the U.S. helicopter industry. The code system has, to date, been successfully demonstrated on a model tiltrotor configuration by Burley2; furthermore, subsets of the Presented at the AHS Technical Specialists’ Meeting for system have also been presented by Brooks3, Rotorcraft Acoustics and Aerodynamics; Williamsburg, Visintainer4, and Brentner5. The current effort contin- VA, October 28-30 1997 ues the exploration of the application of this new sys- tem. Here, for the first time, the system as a whole is 1 used to exploreconventional rotors within the context essential methodology of the original model is of a geometric parameter sweep. The goal is to test the retained; however, a number of key enhancements ability of TRAC, with all of its modeling assumptions, and modifications have been made, including to predict noise trends for a family of rotors. A com- increased azimuthal resolution, swept planform plete study of all the issues associated with the solu- effects, indicial aerodynamic blade response model- tion of this problem would be beyond the scope of this ing, and vortex roll-up modeling. The resulting paper, hence we will restrict the discussion to wake method is much more suited to the prediction of noise. modeling, rotor loads, and blade-vortex interaction (BVI) noise. The emphasis will be on the use of TRAC Computational results from CAMRAD.Mod1 pro- and the predicted results and not on the relative mer- vide the spanwise blade section loading, performance, its of a particular design. and trim solution for the rotor. Additional processing is required to produce the high resolution solution of The paper is divided into three sections: an intro- the rotor wake, blade motion, and sectional loading duction to the system of codes, application of the solution which is necessary for noise prediction. method to a single configuration and a brief correla- tion with experimental data, and the blade geometry Compact Section Loading study. HIRES is an extension to the CAMRAD.Mod1 The Tiltrotor Acoustics Code System: TRAC which is executed following the trim calculation. HIRES is typically used to compute blade loads at .5 TRAC consists of a set of computational tools degrees azimuthal step and at 100 radial stations. which, taken together, provide a prediction method These high temporal and spanwise resolution loads for the complex multi-disciplinary problem of rotor are obtained by recomputing the wake velocity influ- acoustics. Figure 1 depicts the flow of data between ence coefficients for recalculated blade motion and the various codes within the system. For the current interpolated wake geometries at each azimuth step. effort, the CAMRAD.Mod1-HIRES-WOPWOP The aerodynamic calculations in HIRES are accom- method is employed. plished in a post-processing program which uses the high-resolution definition of the induced velocity over High Resolution Acoustics the rotor disc. The resulting high resolution lift and Low Resolution Blade Loads drag are then available for use with the acoustic pre- Harmonic, Impulsive, diction code. Broadband Noise and FPRBVI propagation Acoustics CFD Full Surface After the TRAC modules have produced the high Loading Rotorcraft CAMRAD.Mod1 WOPWOP resolution airloads, the acoustics propagation model Operating Performance WOPWOP+ WOPWOP7,8 is employed to predict the noise level at Condition Trim/Wake Code specified microphone locations. WOPWOP is the cod- KIRCHHOFF ing of acoustic formulation 1A of Farassat7, which is a HIRES BARC time domain solution to the FW-H equation, exclud- Non−CFD RNM ing the volume source or “quadrupole” term. It was Compact ROTONET Section developed as a method to predict the discrete fre- Loading quency noise of helicopter rotors, and is valid for arbi- trary blade motion, geometry, and observer location. FIGURE 1. TRAC flowchart. The HIRES option of TRAC provides high-resolution section blade loads which are converted into equiva- Rotorcraft Trim lent “compact” pressures acting at a specified chord location (usually the local quarter chord). The CAMRAD.Mod1 computer code is capable of predicting the dynamics, aerodynamics, loads, and Test Data performance of a trimmed rotorcraft system in a wind tunnel or in flight. The basic method makes use of A limited correlation with test data will be lifting line theory coupled with airfoil section force conducted in order to provide a firm foundation for and moment data tables to compute the load on the the planform study. The data will be compared to blade. The method is described in some detail by acoustic data from the 1989 aeroacoustic test con- Brooks.3 Basically, CAMRAD.Mod1 is a highly modi- ducted in the DNW.9 The test was part of the U.S. fied version of the original CAMRAD6 model. The Army Aerodynamic and Acoustic Testing of Model 2 Rotors (AATMR) Program and involved U.S. Govern- and 1500, in contrast to the smoother changes which ment agencies and United Technologies Corporation occur on the retreating side of the disc. The secondary (UTC). vortex features much more rapid variations in Y bar and is not present on the retreating side. It will later be Application of the Method shown that the primary BVI for this configuration occurs near the azimuth angle of about 750, just before In this section, a set of results for a base configura- the sharp change in Y for both vortices. The source tion will be used to establish formats, to introduce the bar of the vortex is at aboutY = 1200. Another interesting use of the system, and for a limited correlation. Predic- issue related to the rotor wake is the loading distribu- tions will fall into three categories: (1) wake geometry; tion during the actual BVI which is presented in figure (2) rotor airloads, and (3) rotor acoustics. 3. Note especially, the multiple loading peaks for this The CAMRAD.Mod1 model provides the user condition, most probably a result of predicted multi- with a rich choice of options for use in predicting rotor ple interactions. It should be noted that the actual BVI performance, loads, and acoustics. These models was not measured or observed during the test but include extensive treatments of the rotor structural measured blade loads indicate similar trends. and aerodynamic environments. Before proceeding, it is, therefore, important to establish the modeling options to be used. This will provide a frame of refer- TipVortexShedding&Rollup ence within which comparisons can be made. The fol- 1 lowing assumptions are employed for the study: 1. an isolated main rotor in a wind tunnel 0.9 a. R = 1.428 m )R TipVortex b. a0 = 338.19 m/sec -yBA SecondVortex 1 c. r = 1.226 kg/m3 n,( 0.8 o d. W = 1442.5rev/min ati c o e. V = 215.7 m/sec L 0.7 TIP al f. l = 200 (at r=.94 for base adi R configuration) 0.6 2. shaft axes at 5.150 (modeling descent) 3. C /s = 0.0714 T 0.5 0 60 120 180 240 300 360 4. m =.151 AzimuthalLocationofShedding 5. constant blade area for each configuration FIGURE 2. Predicted spanwise emission locations 6. linear blade twist of -120 (except for baseline) for both the tip and secondary vortices 8. The full free-wake model (3 iterations) Rotor Airloads with multiple vortex trailers and a multi-core (9) vortex model Rotor airloads will be presented as contours of loading (in N/m) over the rotor disc of the blade as in 9. The blade structural response will be modeled figure 4 below. Of particular interest in this figure are with six bending modes and 1 torsion mode. the regions of dense “bands” which indicate high tem- poral gradients. When these bands are near parallel to Rotor Wake the rotating blade, BVI impulsive noise results. It is Performance and wake data are presented to sup- seen that this occurs in the first quadrant between azi- port the acoustic results. Of particular interest here is muth angles of 600 and 900 and on the retreating side the vortex roll-up behavior. Figure 2 is a plot of the between about 2900 and 3100. predicted tip and secondary vortex spanwise emission locations as a function of azimuth. Note the presence of the secondary vortex which is deposited into the wake beginning at 300 azimuth and existing until about 1900. Also note the sharp decrease in Y at800 bar 3 loads, the input WOPWOP subroutines were adapted to utilize such a loading description. SpanwiseLoading CAMRAD-Mod In WOPWOP the pressure on the lower surface is 800 Y =700 assumed to be zero and the upper surface pressure is given by: 0 (x/c) <.2 600 p = 20((x/c) -.2)p .2< (x/c) <.25 max 20((x/c) -.3)p (x/c) >.3 max N d, 400 a where p is set such that the total section lift is the o max L same as that produced by the distributed load. The WOPWOP blade motion is specified using the pre- dicted results from CAMRAD.MOD1. The first and 200 second harmonics of rigid blade flap, lead-lag and 1st torsion are considered. VortexHits Figure 5 compares the measured and predicted 0 noise time history at a microphone location 250 below 0 0.2 0.4 0.6 0.8 1 RadialStation the advancing side. The figure shows that the TRAC system is capable of computing the BVI noise ampli- FIGURE 3. Spanwise blade load during vortex tude including important blade passage features and encounter, Baseline configuration (HIRES) BVI events, but that many of the details, such as blade to blade variations of the waveform are still beyond the ability of the system to capture. BaselineBlade ShaftAngle=5.15 CT/S=.0714 400 600 AcousticWaveform 600 600 600 640000 25 PREDICTED 20 MEASURED 800 600 400 200 400 15 600 600800400600 400 204006000 800800600 600600 240006000 600400400 tot-pa 1050 400 800 600 600400 -5 -10 FIGURE 4. Contour of blade loading for base configuration. (HIRES) -15 0.25 0.5 0.75 1 TIME Rotor Acoustics FIGURE 5. Sound pressure level for base Acoustic Signal configuration at a specified microphone location compared with test data. (HIRES) As stated above, the WOPWOP code predicts the noise time histories and sound pressure level (SPL) Noise Directivity generated by the blade at a user specified microphone location. In the WOPWOP code, the loading must be It has long been recognized that the impulsive given as a force distribution over the blade surface. loading of the BVI generates a highly directional Since CAMRAD.Mod1/HIRES computes sectional acoustic field. It follows that a large number of 4 observer locations must be computed to capture this effect. To study this characteristic, Brentner5 proposed HIRES MODEL BaseBlade that the sound be predicted on a sphere of 1.5 rotor NoTorsion-Rollup ShaftAngle=5.15 7th-30thHarmonics dltYohi’cae aa mrtneiedogtneibosr’n sla i -erc6e ea0 ntt0h t 1e<e5r e0aY dzini ’m co<rnu e6 tm0ht0h e aeann ntdsrdo o et3nol0e r0tv h a<hetu i sobbpn’. h <aTen-rh2ege1 l s0euo0s,br sfwsahecohrevwe irenner 300 83 897185999133 8995 95 97 919389 111000975 99 103 in figure 6. -30 101 99 ObserverLocationson 101 99 95 97 Y / -60 95 ComputatinalSphere 95 93 hi-90 97 97 9819 p 93 95 87 85 Z -120 101 99 887319 X Y -150110031 105 9973 95 7775 -180 95101 9997 9591 89 89 b / -210 103 -60 -30 0 30 60 psip FIGURE 7. Directivity pattern for predicted mid- range noise of baseline blade. (HIRES) Blade Planform Study The remainder of the paper will deal with the blade planform study. The shapes selected for study are based on variation of sweep and taper which FIGURE 6. Geometric distribution of observers in a reflect plausible “passive” designs of a family of con- “bowl” around the rotor. ventional single main rotor configurations. Figure 8 The noise predictions are presented as contours of provides a tabular and visual summary of the configu- the midrange noise metric which is the sum of the 7th rations. Each configuration is assumed to have the through 30th harmonic of the blade passage frequency same mass and stiffness distributions. Furthermore, of the overall sound pressure level (OASPL) on theY- airfoil section shape and distribution are held constant b plane. Figure 7 gives this result for the baseline as is the sweep angle of 200. Chord and sweep location rotor. are the only variables. Chord is changed via a tapering of the blade and by moving the location of the taper The figure shows two regions of focused high initiation point. The sweep initiation point is also var- noise: a large region centered around (Y,b) = 200,-600 ied. For each of the configurations, the root chord has at about 101 dB.; and a smaller but more intense been modified in order to maintain a constant blade region centered at (Y,b) = (-450,-1500) at about 105 dB. area. Twist is held constant at -120, except for the base- Both these regions can be related to the high loading line which has a highly non-linear twist distribution. gradients seen in figure 4. Finally, a five bladed version of the last swept-tapered configuration is examined. The configurations can be viewed as being “grouped” with the LinTwt, Lamda1, and Lamda2 group representing taper changes, and LamdaSwp1, LamdaSwp2, and LamdaSwp3 repre- senting sweep changes. The Base and LinTwt configu- rations show the effect of twist and the LamdaSwp3 and Blds configurations show the effect of number of blades. 5 etry (miss distance), and vortex strength during the interaction. The issue here is how the blade loading BaseBlade LamdaSwp1Blade BladePlanformVariations changes with shape, and how this affects the vortex Name Taper Sweep Taper rollup. Table 1 gives a summary of the key (closest) Starts Starts BVI events for each blade. The major interaction for Base1 1. .94 .94 most of the configurations is in the first quadrant Lintwt2 1. .94 .94 between 65 and 75 degrees azimuth; the first swept- LinTwtBlade LamdaSwp2Blade Lamda1 .75 .94 .94 tapered blade is an unexplained exception. Another feature of these interactions is that it would seem that Lamda2 .50 .94 .94 each blade has at least several encounters at the same LamdaSwp1.50 .94 .94 location. The source of these vortices all seem to be located in the second quadrant at about 1200azimuth. Lamda1Blade LamdaSwp3Blade LamdaSwp2.50 .87 .87 LamdaSwp3.50 .87 .75 SpanwiseLoading Blds3 .50 .87 .75 CAMRAD-Mod 2000 1Non-LinearTwist Lamda2Blade BldsBlade Base 2LinearTwist 1800 LinTwt Lamda1 35Blades Lamda2 1600 LamdaSwp1 LamdaSwp2 AMSiearcfsotsiiol&SneSCct.tifiGofnn.e&DssAisP.trCriob.puAetidrotjnuies&steCSdohfnaosprteSanwCteoenpstant 1400 LBaldmsdaSwp3 FIGURE 8. Planform views of blade shapes. 1200 N d,1000 Rotor Performance and Wake a o L 800 600 15 TotalRotorPowerRequired 400 200 VortexHits 0 0 0.2 0.4 0.6 0.8 1 p 10 RadialStation h r, e RotorPow 5 Baseline LinTwt Lamda1 Lamda2 LamdaSwp1 LamdaSwp2 LamdaSwp3 5Blds FFIilgGoucUraReti Eo10 n1 0pfo.r rBe selaeadnctehs r ctaohdnei fiaslgp luaornaawdtiiionsneg ; baHlta ItdRheEe Slmo maadjooidnr egBl V.foIr each configuration at the location of the principal BVI. Please note that the “zero” for each configuration is shifted by 200 N in order to separate the curves for easy viewing. With the exception of the baseline rotor, which has exceptionally large variations (or response), 0 0 1 2 3 4 5 6 7 8 9 the remaining blades show a similar loading curve, Configuration with the geometric changes appearing as variations in the location of the peaks. Note that a general trend of FIGURE 9. Rotor power required at test point. shifting load inboard follows the location of the taper/ Figure 9 is a summary chart of the predicted rotor sweep initiation point. Also note the small variation at power required for the test condition. The figure the location of sweep initiation. shows a clear trend in power with shape/geometry Figure 11 gives the vortex centroid locations, that change. HIRES is executed following the trim compu- is the final rolled-up position, for the various configu- tation, and it is from its results that the details neces- rations. Note that except for the baseline configura- sary to predict the rotor BVI phenomena are obtained. tion, the vortex rollup follows a smooth pattern. The Rotor BVI effects are influenced by four wake roll-up behavior seems to “group” with geometry, related factors: blade loading at the time the vortex is that is, LinTwt-Lamda1-Lamda2 all have similar generated, blade loading during the BVI, wake geom- 6 behavior as does the LamdaSwp1-LamdaSwp2- LamdaSwp3 group. BaselineBlade ShaftAngle=5.15 CT/S=.0714 TipVortexShedding&Rollup 400 1 600 600 0.975 600 600 640000 0.95 800 600 400 200 n 400 ortexLocatio0.902.95 bLLaiansmTedwtiapt1loc 600800400600 400 204000 600 606000600 400600 600400400 TipV0.875 LLLaaammmdddaaa2SSwwpp13 600 800800 200 Blds 400 0.85 800 600 600400 0.825 0.8 0 30 60 90 120 150 180 210 240 270 300 330 360 FIGURE 12. Contour of blade loading for base configuration. (HIRES) AzimuthalLocationofShedding FIGURE 11. Tip vortex roll-up characteristics. LinTwtBlade ShaftAngle=5.15 CT/S=.0714 Airloads ratioAnisr laoraed p rceosnetnotuerd pinlo ftisg uforre sr e1p2-r1e7s.entative configu- 600800 460000 600 600420600000 Figures 12, and 13 present the effect of twist change on the loading: note here, the increase in load- 800 400 200 600 iecnoxgnte fniggtr uaordfai teain oBtn V.i nIA intsh iemn cosrereecao sanepd pi naq rutehanedt rnfaoonrit s.te h Teah sle ia n serpaearsn utwwlt iisoseft 600 600600 400606000 600600 400 the increased lateral coherence is expected and shown 400 200 200 ionf ttahpee nr:e txhte s cehctainogne. sF higeurere asr e1 3m aonsdtl y1 4in s dheotwai ltsh we iethff encot 400 400 600 640080000 600 400 major impact. Figures 14 and 15 show the effect of 200 800 sweep change: here there is a noticeable reduction in loading gradient especially in the first quadrant. Fig- 600 806000400 200 ures 16 and 17 show the change with blade number. There is a definite reduction in the intensity of the gra- dients on the disc. FIGURE 13. Contour of blade loading for linear twist configuration. (HIRES) 7 Lamda2Blade LamdaSwp3Blade ShaftAngle=5.15 ShaftAngle=5.15 CT/S=.0714 CT/S=.0714 600 400 400 400 600 200 600 600 600 200600 400 600 800 400 600 600 400 400600800804000400 606000440000 200200 800 240408000060000 600600606000400602000400 660004000600 400 400400 200 600800 600200400 600600 600200600400 200 200 600 400 600 804000 800400 400 880000 600 FIGURE 14. Contour of blade loading for second FIGURE 16. Contour of blade loading for third tapered configuration. (HIRES) swept-tapered configuration. (HIRES) LamdaSwp1Blade BldsBlade ShaftAngle=5.15 ShaftAngle=5.15 CT/S=.0714 CT/S=.0714 600 804000 200 300 604050000 200 604000600402006800000 400400460000 260000 200 400 200 604600060000606000660000400460000600 400200 400350300000500200434000500500000 404030400000500550000602100003000302005000 704000502060000300545000000 400505000345005000000300400320000200 400600800 800600 2000 300 600 650300000 200 FIGURE 15. Contour of blade loading for first FIGURE 17. Contour of blade loading for five swept-tapered configuration. (HIRES) bladed configuration. (HIRES) 8 Acoustic Predictions Figure 31 gives the change in noise with shaft angle. Here, the “noise slope” for each configuration is Signal Characteristics seen to “group” with geometry - the LinTwt-Lamda1- Lamda2 all have slopes of about 3dB/deg while the The loading predictions are utilized to predict LamdaSwp1-LamdaSwp2-LamdaSwp3 are at about the noise for the various configurations. Figures 18-21 2.8~2.9dB/deg. The Base slope is ~2dB/deg while the give the comparison of the noise signal at a single five-bladed configuration is ~2.2dB/deg. These differ- microphone location (corresponding to the “hot” spot ences may be due to the strength of the vortex encoun- noted in figure 10) for the key geometric changes. tered. Note from table 1 that LinTwt-Lamda1-Lamda2 Figure 18 shows the effect of changing twist from all have “hits” from the tip (i.e. stronger) vortex, linear to non-linear; note here the shift in phase and whereas all others have at least on hit from a second- the reduction in some of the peak pressures. Figure 19 ary vortex. gives the effect of taper, which appears to have little or Figure 32 is taken from reference 1 and represents no effect. Figure 20 gives the effect of sweep location, the only source of data which can be used to assess the which appears to be mostly a phase change. Finally, validity of figure 31. These data were taken for a vari- figure 21 gives the effect of number of blades; shown ety of blades and are operating at different conditions. here is the obvious change in peak location due to the Also the data-base was sparse. In spite of this, the gen- shift in blade-passage frequency, but also a general eral comparison between these figures, qualitatively reduction in the amplitude. shows similar trends. Noise Directivity Comments and Observations Noise directivity contour results are shown in fig- Rotor noise prediction is a complex problem. In ures 22 to 29. The acoustic results using the HIRES order to meet this challenge, the TRAC system has blade loading show a noise ‘hot’ spot on both the evolved from a number of different disciplines advancing and retreating sides, with the most intense (dynamics, aerodynamics, and acoustics) into an inte- region on the retreating side. The blade loading con- grated tool. tours (figures 12-17) for these conditions, indicate high loading levels and strong gradients on the retreating The following observations can be made: side. The wake geometry results predict a single 1. TRAC is capable of predicting the basic strong tip vortex, with a small miss distance for this noise level of a conventional rotor even with geometri- region, whereas on the advancing side there is typi- cally complex features such as non-linear twist and cally two vortices of lesser intensity. In general the sweep. advancing side ‘hot’ spot consistently was at a level of 101 dB for all the blade configurations, except for the 2. Noise can be affected using “passive” blade 5-bladed rotor, where the level decreased significantly designs. by 5 dB. This is expected since the load is distributed 3. Noise effects seem to “group” within Archi- among 5 blades rather than 4, and the resulting tip tectures (i.e. shape, twist, or number of blades). vortices should be weaker. 4. Architectural changes, especially step Several changes in the noise directivity and level changes, have a greater effect on noise than do para- as a function of twist and sweep are of note. The linear metric changes (i.e. taper). twist results compared to the baseline (and all others) shows a much larger advancing side ‘hot’ spot. The 5. The trends predicted for overall noise as a HIRES airloads produce a considerable reduction in function of shaft angle are similar to those obtained the size of the advancing side ‘hot’ spot for a change in from experimental studies. the sweep location. Issues which remain for future study include: Integrated Acoustics 1. Addition of a surface loading model to the CAMRAD.Mod1 system. Figure 30 gives the integrated noise result in bar chart format. Note here especially the drop in noise 2. Improved wake modeling within CAM- between the linear and non-linear configurations RAD.Mod1, Base-LinTwt. Also note the sharp drop for the five- 3. Continued investigation using the FPRBVI bladed configuration. The other configurations show a CFD post processor. steady drop in noise with taper and sweep location which parallels the trend seen in power. 9 15 15 Base Lamda2 LinTwt LamdaSwp2 10 10 a a p 5 p 5 e, e, r r u u s s s s e e r 0 r 0 P P -5 -5 -10 -10 0 0.05 0.1 0.15 0.2 0.25 0 0.05 0.1 0.15 0.2 0.25 TIME TIME FIGURE 18. Effects of non-linear twist on noise FIGURE 20. Effects of sweep location on noise signal. signal. 15 15 LinTwt LamdaSwp3 Lamda2 Blds 10 10 a a p 5 p 5 e, e, r r u u s s s s e e r 0 r 0 P P -5 -5 -10 -10 0 0.05 0.1 0.15 0.2 0.25 0 0.05 0.1 0.15 0.2 0.25 TIME TIME FIGURE 19. Effects of taper on noise signal. FIGURE 21. Effects of blade number on noise signal 10

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