Document
Computation of Helicopter Rotor Acoustics
in Forward Flight
Roger Strawn Rupak Biswas The Research Institute of Advanced Computer Science is operated by Universities Space Research Association, The American City Building, Suite 212, Columbia, MD 21044, (410) 730-2656 Work reported herein was supported by NASA via Contract NAS 2-13721 between NASA and the Universities Space Research Association (USRA). Work was performed at the Research Institute for Advanced Computer Science (R1ACS), NASA Ames Research Center, Moffett Field, CA 94035-1000.
COMPUTATION OF HELICOPTER ROTOR ACOUSTICS IN FORWARD FLIGHT Roger C. Strawn Rupak Biswas US Army AFDD, ATCOM, MS 258-1 RIACS, MS T27A-I NASA Ames Research Center Moffett Field, CA 94035-1000 Abstract iams and Hawkings equation [1]. This approach contains terms that model three different compo- This paper presents a new method for comput- nents of rotor noise. The first two components are ing acoustic signals from helicopter rotors in for- thickness noise and loading noise. These are com- ward flight, The aerodynamic and acoustic puted from the linear superpositioa of integrated monopole and dipole sources over the surface of solutions in the near field are computed with a finite-difference solver for the Euler equations. A the blade. The third term is a nonlinear quadru- nonrotating cylindrical Kirchhoff surface is then pole integral that is much more difficult to evalu- placed around the entire rotor system. This Kirch- ate and typically neglected. Examples of this type hoff surface moves subsonically with the rotor in of acoustics model are given in Refs. [2-3].
forward flight. The finite-difference solution is The difficulty in modeling the nonlinear qua- interpolated onto this cylindrical surface at each drupole term is the main drawback with acoustics models that are based on the Ffowcs Williams and time step and a Kirchhoff integration is used to carry the acoustic signal to the far field. Com- Hawkings equation. Without this term, the acous- puted values for high-speed impulsive noise show tic signals in the far field are typically underpre- dicted as shown in Ref. [4].
excellent agreement with model-rotor and flight- test experimental data. Results from the new Improved accuracy has been obtained with alternate methods that are based on nonlinear method offer high accuracy with reasonable com- puter resource requirements. computational fluid dynamics (CFD). For exam- ple, Baeder [4] solved the Euler equations to Introduction model the acoustics of rotor blades both in hover and in forward flight. Acoustic solutions were obtained at distances of up to 3.5 radii from the In addition to the desire for high aerodynamic rotor hub. The problem with this approach is that performance, modern helicopter designs also aim the demand for computer resources increases for low rotor noise. This is particularly important exponentially as the solution domain is extended for civilian helicopters that operate near heavily beyond the rotor blade. It is not currently practi- populated areas.
cal to propagate helicopter acoustic waves much There are two main types of noise that cause beyond 3 rotor radii without excessive numerical problems for helicopters. The first type is noise dissipation.
that is due to the interaction of the rotor blades A third approach to rotor acoustic prediction with their vortical wake systems. This type of uses the combination ofa CFD method close to the noise is called blade-vortex interaction, or BVI, rotor blade and a linear Kirchhoff integral for- noise. The second type of noise is called high- mula to carry the acoustic solution to the far field.
speed impulsive, or HSI, noise. It is characterized The Kirchhoff integral approach, such as that in by a strong acoustic disturbance that occurs over Ref. [5], integrates a known pressure field over a a very short period of time. Impulsive noise is gen- prescribed surface and then propagates this sig- erally associated with high tip speeds and advanc- nal to arbitrary distances from the rotor blade.
ing tip Mach numbers greater that 0.9.
The CFD method accurately captures the tran- Accurate prediction of rotor noise is essential sonic flow nonlinearities close to the blade, while for its control. The most commonly used noise pre- the Kirchhoff integral scheme is computationally diction techniques are based on the Ffowcs Will- more efficient over large distances.
Two types of hybrid CFD/Kirchhoff methods *Presented at the 19th Army Science Confer- have been demonstrated for rotary-wing applica- ence, 20-24 June, 1994, Orlando, Florida.
tions. The two methods differ as to whether or not **This paper is declared the work of the US the Kirchhoff surface rotates with the blade.
Government and is not subject to copyright pro- Lyrintzis et al. [6-8] use a Kirchhoff surface that tection in the United States.
rotates with the blade. Pressure data on the for the unsteady flowfield. The purpose of the cur- Kirchhoff surface are computed from a numerical rent work is to develop a new CFD/Kirchhoff solution of the fu_l-potential equations. The Kirch- scheme for predicting helicopter acoustics in for- hoff integral for the moving surface is computed ward flight. The new formulation uses a nonrotat- with the formulation given in Ref. [5]. This ing Kirchhoffsurface that moves subsonicaUy with approach has the advantage that the Kirchhoff the rotor hub. The Kirehhoff integral is evaluated integral uses the same computational mesh as the with the formulation given in Ref. [5]. Develop- CFD calculation. Also, the Kirchhoff surface can ment of appropriate data structures and efficient be positioned to minimize numerical dissipation in interpolation schemes are the primary tasks in the CFD solution.
this effort.
However, this rotating-surface Kirchhoff formu- This is the first time that a nonrotating Kirch- lation has one major problen_ The Kirchhoff inte- heftsurfacehas been used to compute the acous- gral in Refs. [5-8] assumes that the Kirchhoff tics from rotors in forward flight_ Resultsfrom the surface moves subsonically. Evaluation of the inte- method are compared to experimental data for gral for a surface that moves supersonically is HSI noise.Solution accuracy is addressed and much more difficult and has not been successfully computed solutions exhibit minimal numericaldis- applied to a helicopter problem.
sipation. The overall computationalefficiency of Restriction ofthe Kirchhoff integral to subsonic the method is also discussed.
surfacemotion can be a major problem forhigh- speed rotary-wing applications. This isbecausethe Near-Field CFD Solution rotating velocity increases as _2r, where .o is the blade angular velocity and r isthe distance in the The structured-grid Euler/Navier-Stokes solver plane of the rotorfrom the hub to a pointon the called TURNS [10,11] is used to compute the aero- Kirchhoff surface.For the high-speed test case dynamic field close to the helicopter rotor.
computed laterin thispaper, a rotating Kirchhoff CFD code solves the Navier-Stokes equations surfacemust be located lessthan 1.4 chords from about rotating helicopter blades. Since viscous the tip of the blade in order to ensure subsonic effects are minimal for the test cases considered in motion.This location may be too close for accurate this paper, the TURNS code is run in an inviscid acoustic predictions because the strong aerody- mode.
namic shock on the blade surface creates nonlin- The two computed cases in this paper were earities near the tip.
experimentally tested by Schmitz et al. [12]. They The acoustic prediction methods in Refs. [3,9] do consist of a 1/7 scale research model of a US Army not have this problem with supersonic motion of AH-1 helicopter with a blade aspect ratio of 9.22.
the Kirchhoffsurface. This isbecause the integral Both cases have the same hover-tip Mach number evaluations take placeon a nonrotating surface. A of 0.665, with advance ratios of 0.258 and 0.348, coordinate transformationis used to interpolate the near-field CFD solutiononto a nonrotating, respectively.
Identical computational grids for the TURNS cylindrical Kirchhoffsurface. The challenge with code have been constructed for both test cases.
thismethod iswhether the CFD solution can carry They consist of a series of 50 C-meshes that are the acoustic signalout to the Kirchhoff cylinder stacked in the spanwise direction, with 20 located with low numerical dissipation. However, there is on the blade surface. Because the computed cases no constraint on the radiallocation of the surface are nonlifl2ng, the problem is symmetric about the as longas it completelyencloses therotor blades.
plane of the rotor. This means that the solution Baeder et al. [3] have used a structured-grid need onlybe computed overhalfthe computational Euler CFD solver and the nonrotatingKirchhoff domain. Each C-mesh is locatedalong a constant formulationto compute HSI noise for a hovering radiallinefrom the hub of the rotor and contains rotor. Strewn et al. [9] have used a similar scheme, 68 pointsin the cherdwise direction with 48 points but their Euler solver used unstructured, solution- on the lower surface of each airfoil section. 35 adaptive grids to improve the resolution of the points are located in the direction normal to the near-field acoustic signals.Both methods have blade surface.
shown excellentagreement with experimental A view ofthe CFD mesh in theplane of therotor data forHSI noisefrom hoveringrotors.
is shown in Fig. 1. Note that the computational Both the Baeder et al. [3] and Strawn et al.[9] domain extends out to 2 rotorradii from thehub in Kirchhoff integration schemes were limitedtohov- the plane of the rotor. The outer boundary of the ering rotors. Rotors in forward flight are signifi- grid below the rotor blade is set at 1.5 radii.
cantly more difficult because the CFD solutions Between the blade tip and the outer spanwise must be computed and stored at many time steps boundary, the clustered region of the mesh is surface. Pressure values that are located on the swept backwards_m an effort to capture the acous- Kirchhoff surface are written out to a file at inter- tic signal with minimal numerical dissipatio_ vals of one degree of azimuthal angle. This time- Similar solutions for these cases were computed dependent data base is later used to evaluate the on similar grids by Baeder [4], who also used the Kirc hhoff integral.
TURNS code. In that study, however, the acoustic field was computed directly with the CFD code and Kirchhoff Surface Method the Kirchhoff surface approach was not used.
Because of this, Baeder's CFD solutions covered a It is not practical to continue the CFD solution much larger computational domain in the span- to large distances in the spanwise direction. Large wise direction than in the current work. In spite of numbers of mesh points are required and the cal- these differences, the acoustic solutions near the culation rapidly becomes too large for existing blade tip in this paper are virtually identical to computers. An alternate approach is to place a those computed by Baeder.
nonrotating cylindrical Kirchhoff surface around The TURNS code is first run in the quasi-steady the rotor blades as shown in Fig. 2. Strictly speak- mode to determine a starting solution at zero hag, the Kirchhoff surface should completely degrees azimuth angle. This requires approxi- enclose the rotor blades, but the top and bottom mately 1800 iterations corresponding to 24 CPU surfaces are neglected for these computations.
minutes on a Cray C-90 computer. The unsteady They are located so far above and below the rotor time marching is then started with each time step plane that their contributions to the far-field corresponding to 0.25 degrees of blade azimuth acoustics are typically very small. Most of the rotor angle. Approximately one hour of C-90 CPU time noise is produced in the plane of the rotor.
is required to complete a full 360 ° of rotor motion.
The Kirchhoff surface translates with the rotor The TURNS code has been modified so that the hub when the helicopter is in forward flight. The acoustic pressure, p, as well as its normal and acoustic pressure, p, at a fixed observer location, temporal derivatives, p,, and Pt, are computed at k, and observer time, t, can be evaluated by per- forming the following integration on the cylindri- each time step. Note that the Pt derivative must be cal surface: computed in a nonrotating reference frame so that it is compatible with the nonrotating Kirchhoff Portio11 of / Kirchhoff .. / x Observer Figure 1: View of the 3-D CFD grid in the plane of Figure 2: Schematic for the Kirch_hoff surface the rotor.
integration.
sion for E2in Eq. (3)has been modified from the orig- p(_, t) = + --- dS (1) inal Farassat and Meyers" [5]formula by using the r(1-Mr) r2(l -Mr) x simplified expression found in Ref. [13].
In the above equations, M n and M r are the com- This formulation is taken from Ref. [5]. It ponents of M along h and _- in Fig. 2. Mt isthe veloc- assumes that the Kirchhoff surface is moving with ity vector tangent to the Kirchhoff surface, and Vp Mach number M. The distance between a point on is the gradient of the pressure on the Kirchhoff sur- the Kirchhoff surface and the observer is given by face.The freestream speed of sound is assumed to be [_1, as shown in Fig. 2. Also note that the entire uniform at a_, and the angle, 0, is defined in Fig. 2.
integral in Eq. (1) is evaluated at the time of emis- sion for the acoustic signal, x.
Evaluation of the integral in Eq. (1) at the emis- sion time requires a seriesof coordinate transforma- The expressions for E 1 and E 2 are given as: tions to properly access the CFD database on the Kirchhoff surface. These transforms can be described with the aid of Fig. 3. Fig. 3a shows the rotor blade and Kirchhoff surface at the time the
Laooj
sound reaches the observer. However, Eq. (1) (2) requires that the pressures on the Kirchheff surface
[ /cosO - M) p,]
be evaluated at the time they were emitted. At the
-L J
time of emission, both the Kirchhoff surface and the rotorblade were in differentlocations.
In order to findthese locations,the delay between (3) the observer time, t, and the emission time, x, must (1 _Mr)2 (COS0-Mn) first be computed. This can be determined from Fig.
3b by noting that the time ittakes the acoustic sig- These expressions assume that the surface is mov- nal to travel from the Kirehhoff surface to the ing with steady translational motion. Addi_onal observer is equal to the time it takes the translating terms that are required to account for unsteady or Kirchhoff surface to move the distance, d. These rotational motion are given in Ref. [5]. The expres- Observer q, (_, t) Observer,, (_, t)
.......... [-
Kirchhoff SUl-lacc surface ................ (_',x) CFD grid Kkchhoff surface (a) (b) (c) Figure 3: Two successive coordinate transformations are applied to evaluate the pressure data on the Kirch- hoff surface.
a complicated task and is not the focus of this times are given as I;'l/aoo , and dao/l_l[ , respec- paper.
tively. This leads to a quadratic equation for the The justification for neglecting the rotor thrust required time delay. One of the roots is nonphysi- is that HSI pressure signals in the plane of the cal and can be discarded. The locations of the rotor are generally insensitive to thrust. This has Kirchhoff surface and the rotor blade at the emis- been experimentally documented by Schmitz et al.
sion time can then be computed.
[12,14]. The nonlLedng assumption in the analysis Once the geometry is established at the emis- has little effect on the computed results as long as sion time, the acoustic pressures and their deriva- acoustic comparisons are restricted to the plane of tives on the Kirchhoff surface are interpolated the rotor. Acoustic predictions that are out of the from the stored CFD database (see Fig. 3c). The rotor tip path plane will require realistic rotor CFD solutions are stored at discrete time steps on wake models in the CFD solutions. This is particu- the Kirchhoff surface as two-dimensional quadri- larly true for cases with blade-vortex interactions.
lateral meshes. The required acoustic data are The Kirchhoff surface is located at 1.39 rotor determined by linear interpolation in time and radii for both computations. This location is far space.
enough from the blade tip that nonlinear transonic This procedure must be performed for every dis- effects are small, but close enough so that numeri- crete integration point on the Kirchhoff surface.
cal dissipation does not degrade the CFD solution.
Typical grid sizes for this integral evaluation are Both Baeder et al. [3] and Strawn et al. [9] have 1440 points in the azimuthal direction and 100 investigated the choice of Kirchhoff surface loca- points normal to the plane of the rotor. The azi- tions for high-speed hovering rotors. Their results muthal points are equally spaced to enclose both show grid independence for Kirchhoff surfaces at rotor blades. The vertical extent of the Kirchhoff 1.4 radii.
surface is + 1.5 rotor radii, the same as that for the If comparisons to experiment are restricted to CFD grid. The point spacings in this direction are the plane of the rotor, then the Kirchhoff integra- exponentially stretched from the plane of the rotor tion is symmetric about this plane. This means to the outer boundaries.
that the integral in Eq. (1) need only be computed over half of the Kirchhoff surface. The resulting Results pressure can then be doubled to account for the remainder of the integration. As such, the numeri- cal integration on the Kirchhoffsurface consists of The new hybrid CFD/Kirchhoff method has 1440 equally-spaced points around the azimuth been used to predict the acoustic signals from two model-rotor wind-tunnel cases described in Ref. and 50 unequally-spaced points in the lower half- plane of the rotor blade.
[12]. These experiments recorded acoustic signals With this grid, the Kirchhoff integration in Eq.
from a 1/7 scale model of the Army's AH-1 helicop- (1) requires about 30 CPU seconds on the Cray C- ter main rotor. Microphones were placed at several 90 for each evaluation of the observer pressure.
fixed locations around the rotor system. Scaled Most of this time is spent performing interpola- acoustic data from flight tests is also reported in tions in the CFD database. There is a potential for Ref. [12].
significant speedup if these interpolations can be The two computed test cases both a have hover- performed more efficiently.
tip Mach number, Mtip, equal to 0.665. The Typical acoustic pressure signals in this paper advance ratios, _, for the low-speed and high- consist of approximately 24 evaluations of the speed cases are 0.258 and 0.348, respectively. The observer pressure. This requires a total CPU time rotor thrust coefficient is the same for both cases of 12 minutes to obtain the complete acoustic sig- and is equal to 0.0054. These rotor blades have nal at each observer location. At large distances symmetric airfoil sections with a thickness-to- from the rotor blade, this is orders of magnitude chord ratio of 0.0971 and an aspect ratio of 9.22.
less than the time that would be required to com- The primary noise-generation mechanism in both pute a pure CFD solution for the same location.
cases is high-speed impulsive (HSI) noise.
Figure 4 compares the computed and experi- In spite of the fact that the model rotor experi- mental results for the low-speed case. This case ments have a significant amount of thrust, the has an advancing-tip Math number, Mat , of 0.837 computations in this paper are for nonlifting rotors and the computations show significant transonic with the collective pitch set to zero. This simplifies flow at the blade tip. This transonic flow is limited the analysis since the rotor wake does not have to to the blade and does not connect to the far-field be modeled in the CFD solution. In general, this is region of supersonic flow relative to the blade. The
o
,-"-; 0 °° ......... i -°°°" ........
Computation -20 _-4o ........................ Model-Scale Exp.
-60 -80 "30 40 _ _ 70
@ .......... • @
®
20, oO°°°°,.Oo..
,.o*.o., O -20 ,;,° a., -40 .60 ¸ 200 2i0 220 230 240 250" -gO 250 24o250 2_ 2702_ 260 2_0 280 200 300" Blade azimuth angle (deg) Blade izlmuth angle (deg) Blade azimuth angle (deg) °-" _/ °° "'" "" rlR-6.88 "" " fiR-3.44 Figure 4: Acoustic pressure comparisons for Mat = 0.837.
phone 3).
experimental pressures in Fig.4 were obtained by Results for the high-speed case are shown in Fig.
manually digitizing the published data in Ref. [12].
5. The advancing-tip Math number has been As a resul_ the acoustic signal plots may deviate increased to 0.896, and the amplitudes of the acous- slightly from the original experimental data.
tic disturbances axe much higher than those in Fig.
Because this ease is a windtunnel experiment, the 4. The computed results show reasonably good observer location is fixed with respect to the rotor agreement with the experimental data but the peak hub. The equivalent numerical simulation requires negative pressures are underpredieted uniformly that the observer moves with the rotor hub in for- by about 20 percent. Note that the maximum ward flight.
acoustic amplitude is now directed straight ahead Excellent agreement is seen between experiment (microphone 2). This is seen in both the experimen- and computation for all of the microphone locations tal and computed results.
in Fig. 4. The first three microphones are located at 3.44 rotor radii while a fourth is located at 6.88 A possible reason for this underprediction of peak negative pressures is shown in Fig. 6. This fig- radii. The computed peak negative pressures and ure shows computed Mach contours relative to the wave shapes are very close to their experimental rotor blade in the tip path plane. The blade is counterparts. The directivity of the acoustic signal is located on the advancing side at 105 ° azimuth also computed accurately. The loudest noise radiates toward the advancing side of the rotor disk (micro- Computation 0 ...... " °' "" .........
................. Model-Scale Exp.
o o o o Full-Scale Exp.
_.2oo ": "3001 -400 6o Yo 8o 9o l_
O
0 ..... '_" °'" ......
_-200 :.i
V
"30 7 -400 260 270 28o 29o 36o 316 '250 2_ 2#0 280 29o' 220 230 240 250 260 270 Blade azimuth angle (deg) Bhde azimuth angle (deg) Blade azimuth angle {deg) "'"'"'"'"'"'"" ....... __ ........... "'"'"'"'"'"'"" r/R-6.88 r/R- 3, 44 Figure 5: Acoustic pressure comparisons for Mat = 0.896.
angle, where the surface shock at the blade tip is 6. ffthese effects caused the flowfield to delocalize, the strongest.The Mach-one lines are drawn darker then the predicted peak negative pressures would than the other contours. Note that the supersonic be larger, and thereby show better agreement with region on the blade surface almost connects with the experimental results.
the supersonic region in the far field. When this Experimental data from the flight test are also phenomenon occurs, it is referred to as delocaliza- shown for microphone 2 in Fig. 5. This flight-test tion and the surface shock is free to propagate to data shows excellent agreement with the computer the far feld with very little dissipation.The acous- predictions but not with the model-scale results.
tic amplitude increases dramatically at the onset of The reasons for the discrepancies between model- delocalization.
scale and flight test are not known. Perhaps it is The delocalizationphenomena is highly depen- related to the sensitivity of the far-field acoustic dent on nonlinear transonic effectsthat occur near pressures when the flowfield at the rotor tip is very the blade tip.Fig. 6 shows that the flowfieldis not close to delocalization.
quite delocalized,but it should be noted that this In spite of these differences, the computed CFD solution was computed for a nonlffi_g rotor. If results in Fig. 5 are significantly better than those the cyclic pitch and wake effects were included in shown by other researchers. Baeder [4] computed the computation, it is reasonable to assume that this case with a pure CFD approach and obtained a these might have some effecton the picture in Fig.
peak negative pressure of 270 Pa for microphone This means that the surface must be located far enough from the rotor blade to completely enclose all nonlinear transonic effects. We can check M>I whether this condition has been met for the com- puted results shown in Figs. 4 and 5 by performing a new computation with a different Kirchhoff sur- face location. If the predicted acoustic pressures differ, then there may be some nonlinear effects that are not completely inside the surface.
Figure 7 shows computed pressure signals for the high-speed test case at microphone location 2.
The results differ in the positions of the Kirchhoff surfaces, s/R. The first prediction has a surface located at 1.39 radii and the second at 1.28. The two computed results are virtually identical, which indicates that the nonlinear effects are completely contained inside the Kirchhoffsurface.
Figure 7 also provides evidence of grid indepen- dence of the CFD solution. If numerical dissipation played a role in the CFD solution, then the far- field acoustic pressures would be affected by the Figure 6: Math contours at 105 ° for Mat = 0.896. location of the Kirchhoff surface.
A final question involves the numerical resolu- location 2. It is likely that part of this underpredic- tion of the Kirchhoffintegral in Eq. (1). The calcu- tion is caused by numerical dissipation in the lations in Figs. 4 and 5 used a 1440 x 50 mesh on numerical solution at 3.44 radii. The CFD mesh the lower half of the Kirchhoff surface. This corre- did not include the 6.88 radii location in that sponds to a constant azimuthal resolution of 0.25 ° , study. Baeder also mentions that linear methods and a minimum vertical resolution of 0.01 chords based on the Ffowcs Williams and Hawkings equa- at the plane of the rotor. Figure 8 compares the tion predict a peak negative pressure of only 210 original results for the high-speed case at micro- Pa for the same location. The current computation phone location 2 with those from a finer Kirchhoff gives a peak negative pressure of 312 Pa compared to the experimental result of 397 Pa.
Discussion The accuracy of the calculationscan be addressed by examining both the fundamental , approximations in the Kirchhoff formulation and the mesh independence of the computed results.
The first assumption in the Kirchhoff formulation isthattheKirchhoffsurface moves through undis- -100- turbed air. This isnot entirely truefor a helicopter because lifl2ng rotorblades generate aerodynamic d_ -200- disturbancesin theirwake systems.The interac- tion of the acoustic signalswith the rotor wake outsidethe Kirchhoff surfaceis not considered in the presentmethod..The effect of this approxima- -300- tion should be small however. This is because a • s/R ffi 1.28 rotor in forward flight propagates most of its acoustic disturbances ahead of it while the wake -400 system is left behind.Thus there is little interac-
2go 290 280 296
tion between the forward-radiating acoustic sig- Blade azimuth angle (deg) nals and the rotor wake.
Another basic assumption is that the speed of Figure 7: Comparison of results for microphone sound is constant outside the Kirchhoffsurface.
location 2 using two different Kirchhoff surfaces.
applicable to cases with blade-vortex interactions.
The primary challenge for such computations will 100" be the accurate modeling of the rotor wake system in the CFD solver.
References ,-, 0"
?--
[11 Ffowcs Williams, J. E., and Hawkings, D. L.,
g
"Sound Generated by Turbulence and Sur- _ -100" faces in Arbitrary Motion," Philosophical Transactions of the Royal Society, Vol. A264, May 1969, pp. 321-342.
d: -2oo- [2] Brentner, K. S., "Prediction of Helicopter Rotor Discrete Frequency Noise - A Computer Program Incorporating Realistic Blade -300- Motion and Advanced Acoustic Formula- m 1440 x 50 grid • 2880 x 80 grid tion," NASA TM-87721, Oct. 1986.
[3] Baeder, J. D., GaUman, J. M., and Yu, Y. H., -4O0 "A Computational Study of the Aeroacoustics '250 2(_0 2+0 280 290' of Rotors in Hover," presented at the AHS Blade azimuth angle (deg) 49th Annual Forum, St. Louis, MO, May 1993.
Figure 8: Comparison of results with two different [4] Baeder, J. D., "Euler Solutions to Nonlinear mesh resolutions on the Kirchhoff surface.
Acoustics of Nonlifl2ng Rotor Blades," pre- mesh. This finer mesh has a resolution of 2880 x sented at the International Technical Special- ..
ists Meeting on Rotoreraft and Rotor Fluid 80, where the minimum vertical spacing at the Dynamics, Philadelphia, PA, Oct. 1991.
plane of the rotor has been decreased to 0.005 [5] Farassat, F., and Myers, M. K., "Extension of chords. The two results are virtually identical, Kirchhotrs Formula to Radiation from Mov- indicating that the computed values from the orig- inal Kirchhoff integration are mesh independent. hag Surfaces," Journal of Sound and Vibra- tion, Vol. 123, No. 3, 1988, pp. 451-460.
Summary 16] Lyrintzis, A. S., "The Use of KirchhoffMethod in Aeroacoustics," in Computational Aero and This paper presents a new method for comput- Hydro-Acoustics, FED Vol. 147, 1993, pp. 53- ing far-field acoustics from helicopter rotor blades 61.
in forward flight. A solution to the Euler equations [7] Xue, Y., and Lyrintzis, A. S., "The Use of a accurately models the nonlinear effects near the Rotating KirchJaoffFormulation for 3-D Tran- blade surface and a Kirchhoff integration propa- sonic BVI Noise," presented at the AHS 49th gates the near-field acoustic signals to the far field Annual Forum, St. Louis, MO, May 1993.
in a computationally-efficient manner. The key to [8] Lyrintzis, A. S., Xue, Y., and Kilaras, M. S., the Kirchhoff formulation is the use of a nonrotat- "The Use of a Rotating Kirchhoff Formulation ing surface which ensures that its motion is for High-Speed Impulsive Noise," AIAA paper always subsonic.
94-0463, Jan. 1994.
Close to the blade tip, computed results with the [9] Strawn, R. C., Gareeau, M., and Biswas, R., new method compare favorably with experimental "Unstructured Adaptive Mesh Computations results and predictions from pure CFD methods.
of Rotorcraft High-Speed Impulsive Noise," However, the major advantage of the new method AIAA paper 93-4359, Oct. 1993.
over its pure CFD counterparts occurs for far-field [10] Srinivasan, G. R., Baeder, J. D., Obayashi, S., calculations. CFD computations are generally lim- and McCroskey, W. J., "Flowfield of a Lifting ited to computational domains of less than 3 or 4 rotor radii. The combined CFD/Kirchhoff method Rotor in Hover: A Navier-Stokes Simulation," can compute acoustic signals at arbitrary observer AIAA Journal, Vol. 30, No. 10, Oct. 1992, pp.
2371-2378.
locations with minimal numerical dissipation.
Although the method is demonstrated for cases with high-speed impulsive noise, it should also be [ 11] Srinivasan, G. R., and Baeder, J. D., "Turns: A Free-Wake Euler/Navier-Stokes Numerical Method for Helicopter Rotors," AIAA Journal, Vol. 31, No. 5, May 1993, pp. 959-962.
[12] Schmitz, F. H., Boxwell, D. A., Splettstoesser, W. R., and Schultz, K. J., "Model-Rotor High- Speed Impulsive Noise: Full-Scale Compari- sons and Parametric Variations," Vertica, Vol.
8, No. 4, 1984, pp. 395-422.
[13] Meyers, M. K., and Hausmann, J. S., "Compu- tation of Acoustic Scattering from a Moving Rigid Surface," Journal of Acoustical Society of America, Vol. 91, No. 5, 1992, pp. 2594- 2605.
[14] Schmitz, F. H., BoxweU, D. A., and Vause, C.
R., "High-Speed Helicopter Impulsive Noise," Journal of the American Helicopter Society, Oct. 1977, pp. 28-36.