Unsteady rotor aerodynamics and acoustics

r

(

(

UNSTEADY ROTOR AERODYNAMICS AND ACOUSTICS

i\I.

Kuntz. R. Heinrich. K. Pahlke .

.J.

Raddatz

DLR. Institute of Design Aerodynamics

Lilienthalplatz

I,

:38108 Braunschweig, Germany

Absttact

:\n at'roacoustic method for noise prediction of heli-copter rotors in forward flight is presented. The un-stf'ady aerodynamic flow field is computed using an

Euler :-;olver for arbit.rary moving coordinate systen1s and flexible grids taking into account the prescribed rigid blade motion. l'sing the computed pressure da-ta as input. two acoustic methods are applied, on one side t.he linear part of the acoustic analogy method and on the other side the Kirchhoff method.

rirBt for t.he 4-bladed ONERA/ECF 7 AD rotor in high-speed forward flight (p

=

0.4) the blade pressure duta computed wit.h the present method is compared wit.h experitnental data and numerical results of other authors using e.g. Chimera method. A good overall agreement can be statet.

For the same ONERA/ECT 7 AD rotor test

conditi-ons defined in the HELISHAPE project are applied

(/' =

o.:l:l). The comparison of computed pressure da-ta with t.he experimental data is less satisfactory than for tlw first test ca.'Se.

The acoust.ic evaluation for t.he second test case de-monstrates. that for in-plane microphones the nega-tive peak pressure is ahnost. independent on the rotor r.!nust. For microphones out of the rotor plane, a more accurate noise predict.ion is obtained with lifting flow conditions by prescribing the correct blade motion at

tlw aerodynamic computation instead of non-lifting

fton· conditions.

The overall differences to the experimental data are cansecl by t.he following facts. Applying the Kirchhoff \llf't hod wit.h a rotating integration surface. for the pr,~senr. conditions at moderate high-speed forward flight not all non-linear effects can be included inside the Kirchhoff surface. The Kirchhoff method with a non-rotating integration surface requires sufficiently accuratt:> aerodynamic data. which cannot be obtai-JH"d on t.he grid used due to nnsufficient clustering of ).!;rid points.

Pn·~f"nted at- r.he :l3rd European Rotorcraft. Forum. Dresden. ( ;,•nnany. lt.l-18 Sept.ember 1997

Introduction

The aim of helicopter noise reduction requires the de-velopment of advanced computational methods. An-noying noise of helicopter has impulsive character and is either high-speed impulsive (HSI) noise or blade-vortex interaction (BVI) noise. The present paper concentrates on the numerical simulation of HSI noi-se. Most of the simulation methods are split in two parts, on one side aerodynamic

codes

for the compu-t.ation of the acoustic sources generated by the rotor blades and on the other side acoustic codes for the prediction of noise propagation to the farfield. Especially for the aerodynamic flow field computati-on the methods differ by the computaticomputati-onal effort. ac-curacy and flexibility. For unsteady computations of rotors in forward flight, wake capturing methods like Chimera or overset grid methods (Pahlke and Rad-datz [1]. Ahmad and Duque [2]) or the moving grid approach (Boniface et al. [:3]. Boniface and Pahlke [4]) have been developed.

Experimental studies have shown that for HSl noi-se predictions for microphones located in the plane of the rotor the maximum peak pressure value is in-dependent on the rotor thrust (Schmitz et. al. [5]). Therefore. most of the aeroacoustic computations of high-speed impulsive noise from lifting helicopter ro-t.ors in forward flight are carried out bv simulatina • 0

non-lifting conditions. No wake capturing algorithm or wake models are included in this case (Stra\'.-·n et al. [6]). ror microphones not located in the rotor pla-ne, non-symmetric blade loadings have to be conside-red by applying wake capturing methods or aerody-namic methods coupled to a wake-model.

The acoustic methods applied are on one side linear methods (monopole and dipole term of the acoustic analogy method) and the Kirchhoff method. which al-lows to include non-linear effects. For test cases in the transonic regime studies comparing these methods were carried out (Kuntz [7], Brentner et al. [8]). Both methods agree well for conditions below the delocali-zation Nlach number, but accurate noise predictions at higher Mach numbers require the use of the

Kirch-hoff met. hod.

Ont> t>xample for a cmnbined aerodynamic and acou-st ir mdhod using the overset grid techniq~e is pu-hli;hed hy Ahmad et al. [9]. The purpose of the pre-sPilt work is to sho\\1. the feasibility of a combined cwroacoust.ic method including an Euler solver using fif"'Xihl~~ grids. This paper contains first results of com-pur at ions on coarse grids. For a high-speed forward Oight test case (J.l

=

0.4) d•fined by ONERA for the 0\iER.A/ECF 1 AD rotor comparisons of

aerodyna-tlli<: blade pressure data with experiments (Beaumier et. al. [lO]l and Euler results computed by other au-t.hor::; using different methods (e.g. Chimera) are car~ ricd out.

Ful't he·rmore this paper shows comparisons of aero-acoustic con1putations \Vith experimental data for the 0'\ERA./ECF lAD rotor measured in the DNW in the framework of the HELISHA.PE program (Schultz Pt al.[ll]). For this moderat.e high-speed forward flight te:•H case with J1

==

0.:3:3 aerodynamic and acoustic rornparisons are done.

Aerodynamic Nlethods

Th ... DLR aerodynamic code FLOWer is applied for the computation of t.he present test cases. FLOWer is a rinite-volume solver for t.he solution of the Navier-Stokef:' f>quat.ions on arbitrary moving coordinate

sy-"'''lllS

and flexible grids (Kroll et al.[l2j). In the fra-lllt:'\\·ork of the ptesent work only inviscid computati-OilS ;n·e carried out. The integral form of the three-dimensional Euler equations in a moving ('artesian

~·n{)rdinate system can be written as:

with

!!__ ;·

~~·,w

ill .

,.

+

.!

'F" .

i'idS'

+.!

GdF

=

0 &F F = [ p ]. ptt pt•

~;

=

[

p(if-</1,)

l

""(if-f,) +pf... p1· (if-0,)

+

p €₉ pw (if-f,)

+

pe, pE (

</-

r/1,)

+

prJ [ p

(:ox

<Tlr

l

p (.v X if)₉ p(2x<J), 0 ( 1)

(2)

t~V is the vector of conservative quantities with p,

f

and E denoting the density, absolute velocity vector refered to the blade fixed coordinate system and spe-cific total energy, respectively. V denotes an arbitrary

deforming control volume with boundary

av

and the

outer normal ii. A source term

G

has to he added, in-cluding the time derivatives of the unit base vectors of

the coordinate system rotating with the angular velo-rity

W.

The gas is assumed to behave like a calorically perfect gas with constant specific heats.

='

For the calculation of the convective flux tensor F

the boundary ve!ocit:· 0, has to be introduced. This vector is defined in the moving frame and contains three components induced through translation, rota-tion of the coordinate system and the deformarota-tion of t.he mesh (compare figure 1):

(3)

y' Inertial-system

r_

x' z'

Figure 1: Moving coordinate system

The translational velocity is determined by the ad-vance direction of the rotor and the t.ilt of the rotor

plane according to the tip path plane angle aypp and {

is obtain~d by the free stream velocity in the intertial system iitra.n$ by:

= - 1 ' rhrrm.s

==

D iftran,(

The rotational velocity is defined by: ~ot

==

W

X 17

with the angular velocity:

~

₍

cos ,d . cos,)

)

w

=

-cos J ·sin

V

sin 3

J(

sin l}

)+tl(n

+

cos 1) 0

(4)

(6)

(

(

(

(

(

1 ·• J and tl are the azimut.ha.l angle, flapping angle

and pitching angle. respectively. Finally the defor-ming; grid velocity is given by the local velocity for

~·a('h ~rid point:

(7)

Tlu· t.ransfonnation between moving frame,-:- and the

ilwrtial frame F'1 is described by:

(8)

IJ is the tensor including the rotation around three axis. For the present. application of helicopter rotors in tOrward flight the pitching and flappi11g angle are

periodic functions of the azimuthal angle:

J

.J. .•

+ J,.

cos

u·

+ Js

sin li' (9)

The approximation of the governing equations

fol-\uw::: the method of lines, which decouples the dis-nNizat.ion of space and time (Jameson et al. [13]).

The spatial discretization is based on a finite volu-llH? mPt.hod which subdivides the flow field into a set of 11011-overlapping hexahedral cells. The cell-vertex Npproarh is realized, in which the flow variables are '""oci;,ted \\'it.h the vertices of the cell. The spatial disc-r1?tization leads to a system of ordinary differenti-al equations for the rate of change of the conservative

flo\\- \·;uiables in each grid point. The t.in1e

integrati-ou is realized using t.he Dual-Ti1ue-Stepping method according to .Jameson [14] implemented in FLOWer. This methoJ has been already applied to other un-steady test cases (Heinrich et al. [15]).

Ttw 110-normal flow condition is imposed on a bo-dy. The far field boundary is treated following the roncept. of chatacteristic variables for non reflecting boundary conditions (Kroll [16]). Auxiliary cells are u:;,~d t.o st.ore t.he neig11bour flow values in order to mt\tch the solution across inner cut.s. In order to have

~t->cond order spatial accuracy at inner cuts two layers

or

auxiliary cetls are used.

Tlw mult.ihladed rotor is computed by simulating all blades together without introducing special bounda-ry conditions to take into account the influence of the

ot lwr blades. Body conforming single block computa~

t iona.l ~rids of an OH topology with a. wraparound 0

in chonlwise direction a-nd t.he H-type in spa.nwise di~ rP('tlon are generated around each blade. These gtids ar~' tnuu;formed in a cylindrical shape with an

azimu-thal f'Xtension of the segment of 2rr/:V {N =number

of hlades). Finally the blotks of all blades are connec-H··d for('ing an t:>quivalent point. distribution at the

connection planes. For each block. the /-index runs in the wraparound direction, the ./~index in the bla-de normal direction and the K-inbla-dex in the span wise direction.

To take into account the relative motion of the blades. the technique of flexible grids is applied. The overall grid system is defined with zero pitching and flap-ping angles. the angular velocity vector according to eq. (6) is

w

=

~·e,. While the outer part (farfield) of each block is fixed in the rotating system, the inner part including the rotor blade is moving according to eq. (9) dependent on the actual azimuthal location. The outer boundary of this inner part is typica!!y a few chord length away from the rotor blade and is gi-ven by the location of the Kirchhoff surface (compare description of the acoustic methods). lnbetween the grid is distorted linearly. Consequently, the velocity is split ted according to eq. (3) in a translational part, a rotational part without pitching and flapping (which is the same for all blades) and a deforming grid ve-locity dependent on the actual location of each grid point.

For the application of the acoustic methods an inter-face is defined. This interinter-face allows to extract pres-sure data (prespres-sure and prespres-sure gradient) from the aerodynamic solution on planes of the aerodynamic grid (also the blade surface itself). Furthermore data can be computed on cylindrical surfaces in the flow field (including top and bottom), whereby the values at the nodes of the cylinder are obtained by a triline-ar interpolation of the flow solution at the nodes of the aerodynamic grid. The pressure data is written to special files at the end of each physical time step.

Acoustic Met.hods

The acoustic program system used for the present computations is called APSIM (Acoustic Prediction System based on Integral Methods). It is in principle an acoustic postprocessor for the aerodynamic solu-tion and gives results in the form of acoustic signa-tures. sound pressure levels or spectra. The methods included are the linear acoustic analogy method (mo-nopole and dipole term according to Farassat formu-lation l and !A) and the Kirchhoff method including the formalism with rotating and non-rotating inte-gration surface. Parallel t.o these methods a routine is implemented to e:dract directly pressure data from the flowfield solution to allow the acoustic evaluati-on for microphevaluati-ones located inside the computatievaluati-onal domain.

The code is based on the results of former code de-velopments of DLR on the field of acoustic integral methods and is the basis for further code improve-ments. In the present code version results of the work

(

or Lohmann [II], Schultz et. al. [18]. Kuntz et al. [19] <l!ld Kuntz [I] is included.

f 11 t lw· framework of the present paper information is

~h-•'n focttssed on code adaptions and extensions for tlw applicat.ion in combination with an aerodynamic

11wthod u~ing flexible grids. further det.ails about the

acou:<;tic codes is given by Kuntz [IJ.

Tlw lineat acoust.ic analogy method uses the rotating blade as integration surface. The formula for

mono-pole ,nd dimono-pole are ( Farassat and Succi [20].

Brent-""'" [11] ):

f'.tr( .1'. I)

+ _l_

I

[q~a~.\1.,

(J.J,.-

JI')]

dS ~;r. r'(1- .\!")3 8 T (10) (ll)

The Kirchhoff method included in APSIM is using the

formulas according to Farassat (Farassat and Myers

[11].

Lyrintzis [23]): _ l ;· [• £1 _E,P

l ,

P(.r.l) = -

+ "

de, ~". r(l-M") 1'·(1-J[,.)" r:,

₌

+

+

s .... .U,l · J/.,J/ · \ P- i'i · \ P- - P a ':'X:

(/;,.- .li,-

i>.u)P+(n" -JI.,)P

ax(l-.\1") JJ,.(n,.- .\I.,)P a , ( l - .\!,.)'

(12)

( 1:3) E'.! == (1-M') (n"-

M.,)

(1-Mr)' ( 14)

The Kirchhoff method evaluating the integral in the

rotating frame has in general a subsonically moving

integration surface a few chord length away from the

rotor blade. The part of the grid between the rotor blade and the Kirchhoff surface is rigidly connected with the bladed and the grid adjustment to the far field is done in the outer part outside the Kirchhoff

surface. Therefore, the laws for location and

veloci-ty are the same for the rotor blade and the rotating Kirchhoff surface using the actual values for ~·.!3, iJ

(eqs. (8), (3)). The acceleration of the integration sur-face is just the derivative of the rotational boundary velocity vector (compare eq. (:3)).

(15)

For the Kirchhoff method with the non-rotating

inte-gration surface the combination with an aerodynamic

code using flexible grids requires no further code ad-aptions, because the integration surface is defined in

the wind tunnel system. The velocity is equal to the

translational velocity and all acceleration terms are zero.

The acoustic integrals are computed using wind tun-nel conditions. All vectors are transformed in the sy-stem of the integration surface. which is depending on

the method either directly connected with the blade

or non-rotating. The evaluation time level can be eit-her the emission time or the reception time

(Brent-ner [24]). For the application of helicopter rotors in

forward flight. it is advantageous to use the

emission-time-based formalism. because the pressure data has to be stored only for one time level. Furthermore the

computation of the reception time for a glven emis-sion time is faster than vice versa. because at least for a rotating integration surface the movement of ( t.he microphone is simpler than the one of the

acou-stic sources. The acouacou-stic pl'essure at a fixed observer

time is obtained by a temporal interpolation of the acoustic reception time signals.

ONERA/ECF lAD Rotor (51)

The I AD rotor was tested in the ON ERA 51 wind

tunnel at the Modane test center and results were

published by Beaumier et. al. [10]. Further details about the rotor are also given in

[I

OJ.

The rotor has

an aspect ratio of 15 and experimental data are given as pressute coefficients at the span wise location of 0 .. 5.

0. 7. 0.82. 0.92 and 0.98 rotor radii. The test caBe

cho-sen corresponds to a rotational tip Mach number of

.ffwR

=

0.611 with an advance ratio of 11

=

OA and a

(

( (

fr<'e >tream Mach number of J[00

=

0.2468. The

w-1 or shaft. angle is equal to -11.8 degree. The following fl.:tpping and pitching motions of the blades are used for the computations (see Boniface and Pahlke [4]):

\o hinge offset was considered for t.he computat.ions. Fot· this test. case no experimental acoustic data is available, therefore:- no acoust.ic computations are car-ried out.

Af·todynamic Results

ThE~ gl'id used for the pre:sent computation has 4 OH-hlork'3 with 07 grid points in chordwise direction, 25 grid point-s in blade IlOtmal direction and 37 grid poiut.s in spanwise direction and 57 x 28 points on t.he hlade. therefore 2!0 900 points in total. Figure :3 ~haws t.he t.ot.al block structure. To show t.he effect or grid distortion. :lD views are shown for grid

pla-tH~s wir.h span wise locations of about r/R=0.9 and 4 azimuthal positions in figure 4.

The Dual-Time-Stepping method is used with 512 phy::dcal time steps per p(:'riod and :30-.!50 subitera-t.ion..;,; ;Jt. Pach step. The C'Pl' time for one period is

ahout. tOh ou a ~EC SX4 vector computer.

A <·omparison of numerical and experimental resUlts fot· t lw normal force coefficient at -l radial position is

pn~:-:PnlPd in figure .j, The results of the current fie-xihlP ~rid nwthod are given by the solid line, while the dotted and the dashed line show results which

haw heen published by Boniface and Pahlke [4] of " DLR chimera computat-ion and an ONERA defor-ming grid computation. The experimental data is gi-Vf'll hy the symbols. In figure 6 the pressure coefficient at r/R=O.il2 for 6 azimuthal positions is presented. The overall agreement of the prediction Inethods is quite good. The DLR chimera and the DLR flexible ,g,ri(l computations agree \veil with each other, where-a:S the ON ERA deforrr{ing grid solution predicts

hig-!wr ~'11 .\12-valw~s. The agreement of all three

nume-ric;'~! pre-dictions with the experimental data is fair. .·Uiut<,r hods underpredict the c,.\1°-values for r/R

=

o.:,

anc! v

=

l 10°. The authors believe that the high PXPt'rimental normal force coefficients at this radial

pn~ition are due to the fact. that the rotor support induces velorities which increase the effective pitch an.de at. the hlade (see Schwarz [25]). For r/R

=

0.92 and ~'/ R.

=

0.!18 all mtnlel'ical methods predict. nor-nnd Force coPtficiems with a phase shift compared to tlu· I'XJwrimental dat.a. The reason for this phase shift and \'or the overprediction of the normal force coeffi-eit·Ht i:-: tlw rigid hlaJe assumption in the numerical ;-;it~tulations which is not. fully valid in the t.ip region

of the advancing blade of this high-speed rotor.

ONERA/ECF TAD Rotor (DNW)

The measurements were carried out. in the DNVV

wi-tchin the HELlS HAP E project, the test procedure is described hy Schultz et. al. [11]. Pressure data is mea-sured at radial stations of 0.5. 0.7, 0.82, 0.92 and 0.98 rotor radii. For this test case acoustic data is availa-ble for microphones on a traverse perpendicular to the advance direction. This traverse is located about 2.5 rotor radii in front of the rotor and one 1·ot.or radius under the rotor plane. The microphones are equallv spaced from -1.25 to 1.25 rotor radii along the tr;-verse. For the present investigation only microphone l. 6 and additionally an in-plane microphone located above microphone 6 is considered (see figure 2). The

y

Figure 2: DNVV microphone arrangement

computation was conducted using the blade motion measured at the blade root in the experiment. Test run 142 of the DNW measurement series is cho-sen. which corresponds to the flight conditions .~I .... R

=

0.6604. I'

=

0.3276 and ;\1[00

=

0.2164. Pitching and tip path plane angles are typical for a test case with moderate high-speed level flight flow conuitions. The rotor was trimmed with zero flapping.

Aerodynamic Results

The aetodynamic computations are carried out on the same grid described already for the first test case. Fi-gures 7 and 8 show the comparison of predicted and measured norn1al force coefficient and pressure

coef-ficients respectively. The agreement between r;he si-mulation and the experiment is less favourable than for t.he Sl test case. The numerical simulation uuder-ptedicts a.t aU radial positions the normal force coeffi-cient in the range of 60° t.o 260°. The reason for these deviations bet.ween theory and experirnent is not un-derst.ood up to now. The best. agreement. is achieved for r/R=0.98.

Additionally non-lifting test. conditions with zero pit-ching and flapping angles are applied for this rotor to (•xamine the influence of t.he aerodynan1ic input. data

ou tlw acoustic results. No aerodynamic results are sho\\'n. because they are intentional different to the ('XIwrimental data.

Di !l"Pt'f>Jlt acoustic methods are applied to compare 1H~':'3Sll rP signatures at the location of the micropho-Hes. Results of st.udies are shown comparing the acou-:;;t ic nnalogy method (in the figures denoted as Far! A

=

farassat formulation !A) and the Kirchhoff method

(in tlw figures denot.ed as KirchRot (rotating surface) aud KirchNonrot. (non-rotating surface)). The fimv conditions of the present. t.est case with an advancing t.ip \lach number of about. 0.88 are suitable to

ap-ply both Kirchhoff formalisms. Furthermore

compu-tat-ion:-:: using lifting or non-lifting aerodynamic input data are performed t.o show the influence for in-plane and out.-plane microphones.

The discretization of an integration surface is deter-mined hy t.he aerodynamic grid in case of the rota-ting integration surface. The blade itself has 1596 grid points and a typical Kirchhoff surface has about 2394 points. The non-rotating cylindrical surface has 51.3

x '21 grid points with a clustering of points near the rotor plane. An \·iew of the integration surfaces (t,vo hladP surfaces. t.wo rot.ating Kirchhoff surfaces and a pa.l't of the non-rotating cylindrical surface) is shown in tig-ure !:1. The CPF t.ime required for t.he acoustic computation of one microphone is in the order of a few :=-Pconds. therefore negligible compared to the ef-fort tOr t,he aerodynamic computation.

In fig.un;- !0 the acoustic slgnatures for monopole and dipolf' contribution for microphone 1 (advancing side) and () (centerline) are compared using the follmving conditions. Firstlv aerodvnamic data of t.he lifting ro-tor is t.aken and the

aco~stic

computation is evalua-t·.Pd using the same blade locations and velocity as for tlw aerodmamic computation (Euler lift/Far!A lift). The

set~nd

curve (denoted as Euler lift/Far!A nonlift) uses the same input data. but neglects t.he pitching and flapping angles for the acoustic evalua-tion. The change for the acoustic pressure is quite :=-;mall. Finallv the aerodvnamic solution of the non-!ift.ing rotor

is

used as

i~put

data and zero pitching and flapping is forced for the acoustics yielding a dif-ference in the acoustic signature (Euler nonlift/Far!A nonlift). A better agreement in peak value and tem-pol'al peak locat.ion is obtained for the aerodynamic d(lta using the correct blade motion. The differences to tlw PXpedment.al data are partly due to neglecting 110n-line·ar effects. but t.he BVI-like pressure fluctua-1 ioll~ lOHml for mlcrophone ()are not. expected for the

pw~t ... nt. mode!'ate high-speed level flight. flow

condit.i-ons.

Before executing the same studies for the Kirchhoff method with rotating surface, the effect of different locations of the Kirchhoff surface is investigated. The results are shown in figure 11. The distance to the rotor is varied using l, 2 or :3 chord lengths. A good agreement of the numerical results with each other and with the experimental data is found for the lo-cations not. so close to the rotor blade. In figure 12 a comparison with different aerodynamic input using t.he Kirchhoff method wit.h rotating integration sur-face is shown. The same conclusion as for the acoustic analogy method can be drawn. The difference to the experimental data can be explained as follows. For an advancing tip Mach number of about 0.88 it is not possible to include all transonic effects inside a Kirchhoff surface, which has to be restricted to the subsonic flow regime corresponding to 1.1 rotor ra-dii. Therefore the same discrepancies as for the linear acoustic analogy method are observed.

For the Kirchhoff method with non-rotating surface the location of the Kirchhoff surface is varied in order to find the correct location of the integration surface (Figure 13). In all cases the vertical extension of the Kirchhoff surface is 0.5 rotor radii and top and bot-tom part of the cylinder are included. for both mi-crophone locations, almost identical results for both inner surface locations are obtained. For the surface far away from the rotor the peak value of the signa-ture is decreasing and also the temporal peak locati-on is changed. This leads to the clocati-onclusilocati-on, that t.he acoustic wave is not computed accurately up to the location of the Kirchhoff surface, because the aero-dynamic grid is too coarse in this region. The study of the influence of liftingfnon-lift.ing input data (fi-gure 14) show the same tendency as for the other acoustic methods.

A summarizing result of the studies sho\v·n up to now can be seen in figure 15. The discrepancies to the experimental data have been already explained be-fore. A further comparison of lifting and non-lifting input data is performed for an in-plane microphone using t.he linear acoustic analogy method. This mi-crophone is located at the centerline in front of the rotor, one rotor radius above microphone 6. Figure 16

shows an almost constant peak pressure value. This confirms the experimental result. of Schmitz et al. [.5], who stated a peak pressure value independent on ro-tor thrust. An equivalent tendency is found applying t.he Kirchhoff method.

The next comparison is carried out. for micropho-ne 1 between t.he limicropho-near acoustic analogy method. the Kirchhoff method with a rotating surface and the ex-perimental data. Figure 17 (left) indicates, t.hat ap-proximately up to the 6t.h harmonic t.he sound

pressu-c

(

I

rP \'ctlues are computed \Vell by the numerical method.

Au on~ra.ll comparison for all microphones along the tra\·erse for t.he 1st and ()t.h harmonic is shown in

figu-n· l T (right). The sound pressure levels are computed

lwt tr•r 011 the advancing side ( t•

<

180°) than on the

n'l r1'<1fing side.

Conclusions

.-\n cwroacoustic method which is a combination of t!ll :wrodynamic mt:-thod based on the flexible grid approach with acoustic integral methods for the pre~ dicr ion of HSI noise of helicopt.er rotors in forward flight is presPnt.ecl. The method is applied to t.\Vo test

Th<o' lirst test. case is the ONERA/ECF 'i AD rotor in high-speed forward flight. as it \Vas measured in the S l .\Iodane wind tunnel. Comparisons of aerodynamic blade pressure data show a good correlation with the nw;,:t-::ured pressure. Additionally a good agreement to !H!l11Prical results of other authors is achieved.

'[he same rotor with different test conditions defined in the HELISHAPE project is used for aerodynamic and acoustic comparisons of the present method with ~'XJWrimental data measured in the DN\V. The

corre-l<~t.ion of the blade pressure is less satisfactory com-pat·t•d to the first t.t:>st ca-::e.

BasPd on t.he aerodynamic flowfield data of t.he se-coml tPst. case acoustic integral met.ods ate applied to pn-·diet. the pressure disturbance at the farfield. Ad-ditionally aerodynamic data of a non-lifting compu-t <:Hion is used as input. For off-plane microphones a

lwt tP!' agreement \Yith experin1ental data is obtained hy 1 a king into account. the correct blade loadings ba-:-;,_,d on t-he prescribed blade motion. In contrast to

1 his. a negat.ive peak value independent on the rotor thrust is found for in-plane microphones ..

Th1" OVf'rali differences to t.he experimental data are r<uiSt"d by different reasons. Applying the linear

acou-:--t k rmalogy method neglects non-linear effects in the 1\mrfield. The Kirchhoff method with a rotating in-t c·.~rat..ion surface is connected with the restriction of a :=-uh~onic integration surface .. Therefore. the present conditions at moderate high-speed forward flight does not allo\\' to include all transonic effect.s inside the l{irehhoff surface. The Kirchhoff method with a non-rot<.Jting int.egrat.ion surface requires accurate aerody-namic data. at. t.he Kirchhoff surface. which can not. lw obtained with t.he present coarse grid. Grid refine-!ut>nrs promise t.o improve the results.

Acknowledgment

The expel'imental aerodynamic and acoustic data of

t.he ONERA/ECF 7 AD rotor used for t.he compa-rative st.udies of the second t.est case \Vas measured in the framewot·k of the HELISHAPE project

fun-ded by t-he European Community under the

BRI-TE/EURAM Program. For the first t.est case expe-rimental data was kindly provided by ON ERA .

References

[1] K. Pahlke and .J. Raddatz. Flexibility Enhance-ment of Euler Codes for Rotor Flows by Chimera Techlliques. Paper No .. JS, 20th European

Rotor-craft Forum .. 4msterdam. 1994.

[2] .). Ahmad and E.P.N. Duque. Helicopter

Ro-tor Blade Computation in Unsteady Flows using

Moving Embedded Grids.

AIAA

94-1922. 1994.

[3] .J.-C. Boniface, B. Mialon, and J. Sides. Nume-rical Simulation of Unsteady Euler Flow Around Multibladed Rotor in Forward Flight Using a

Moving Grid Approach. 51th Annual Forum

of the American Helicopter Society, Fort Worth, TX. May 9-11, 1995.

[4] .J.-C. Boniface and K. Pahlke. Calculations of Multi bladed Rotors in Forward Flight Using 3-D

Euler Methods of DLR and ONERA. Paper No.

-58. 22nd European. Rotorcraft Forum. Brighton.

Ult, 1996.

[5] F.H. Schmitz, D.A. Boxwell, W.R. Splettstosser, and W. Schultz. Model Rotor High-Speed Impul-sive Noise: Full-Scale Comparisons and Parame-tric Variations. Vertica. \iol.8. No.4. pp.J95-422. 1984.

[6] R.C. Strawn. R. Biswas, and A.S. Lyrintzis. He-licopter Noise Predictions using Kirchhoff :V!e-t.hods . .jJth Annual Forum of the American Heli-copter Society. Fort Worth. TX . .lfa.if 9-11. 1995. [I] :VI. Kuntz. Rotor Noise Predictions in Hover and Forward Flight Using Different Aeroacoustic Me-thods. AIAA 96-1695. 1996.

[8] K. Brentner. A.S. Lyrintzis. and E.K.

Koutsav-dis. A Comparison of Computational Aeroacou~

stic Prediction Methods for Transonic Rotor Noi-se . .52th A .. nnual Forum of the American

Helico-pter Society. Washington, 1996.

[9] .). Ahmad, E.P.N. Duque, and R.C. Strawn.

Computations of Rotorcraft Aeroacoustics

with a Navier-Stokes/Kirchhoff Method.

Pa-per .Vo.SJ, !!2nd European Rotorcraft Forum. Brighton. Ult. 1996.

[I OJ

1'. Beaumier. M. Costes. and R. Gaveriaux. C'om-pat·ison between FP3D Full Potential Calculati-nns and S1 Modane Wind Tunnel Test Results

011 Advanced Fully Intrumented Rotors. Paper

.\"o. CI.:!. 19th European Rotorcrafi Forum. C'o-11/0, Hl93.

[II]

K.-.J. Schultz, W. Splettstosser. B . . Junker.

1r. Wagner. E. Schoell. E. ~!errker, K. PengeL (; .. .\.rnaud. and D. Fertis. A Parametric Wind

Tunnel Test on Rotorcraft Aerodynamics and

Aeroaroustics (HELISHAPE)- Test Procedures

and Representative Results. Paper No. S2. J!Jnd

Furopcan Rotorcraft Forltm. Brighton. UI\, 1996.

[12] \. KrolL R. Radespiel. and

C'.-C'.

Rossow. Ac-rllt·at.e and Efficient Flow Solver for :lD

Appli-nu.ions on Structured Meshes. Lect.ure Series

/99.J. Computational Fluid Dynamics. Von

A"ar-1111!11 !nslit!ttr of Fl~tid Dynamics. 1994.

[!:\) A . .Jameson. W. Schmidt. and E. Turkel. Nu-nwrical Solutions of the Euler Equations by

Fi-ll itt:> Volume .Nlethods Using Runge-Kutta

Time-Skpping Schemes. ALU 81-JJ-59. 1981.

[ l-1] .\ .. ! ameson. Time Dependent Calculation using .\lultigrid. with . .\.pplications t.o Unsteady Flows past. Airfoils and Wings. AIAA 91-1.596, 1991.

[l:i] IL Heinrich. K. Pahlke. and H. Bleecke. A Three Dimensional Dual-Time St-epping Method for the Solution of the Unsteady Navier-Stokes

Equati-on. Cnsteady Aerodynamics. Royal Aeronautical

,<.,'ocidy. London. 1996.

[IIi] :\.

Kroll. Berechnung der Str6mungsfeldgr6Ben

tun Propeller und Rotoren im Schwebeflug durch die Losung der Euler-Gleichungen. DLR FB

89-!7. 1989.

[II] D. Lohmann. Prediction of Ducted Radiator Fan

:\t>roacoustics VVith a Lifting Surface Method .

. \HA-9:!-02-098. 11th Aeroaco~tstic Conference . .\'o.J. pp.-576-606. Aachen . . lfay, 1992.

[l~] K . .J. Schultz. D. ·Lohmann. J.A. Lieser, and K. Pahlke. Aeroacoustic Calculations of Heli-··opter Rotors at. DLR. Paper No. 29 .. 4GARD

:-;lfllljlosium on Aerodynamics and A.eroacoust.ics

of Rotorcraft. Berlin. Oct.J0-11. 1994.

[19] \1. Kuntz. D. Lohmann . . J.A. Lieser. and

K. Pahlke. Comparisons of Rotor Noise

Pte-dictions obtained by a Lifting Surface Method

;llld Euler Solutions using Kirchhoff Equation.

IEAS/AIAA 9.j-/.J6. 1995.

[:!0] F. Farassa.t and G.P. Succi. The Prediction of

\[Piicopter Rotor Discrete Frequency Noise. \-~er­

llr". l of. 7 . .\'o .. {. pp . .J09-:J:!O. 198-3.

[21] K.S. Brentner. Prediction of Helicopter Rotor

Discrete Frequency Noise. NASA Technical

A!e-morandum 87721, 1986.

[22] F. Farassat and M.K. Myers. Extension of Kirch-hoffs Formula to Radiation from Moving Surfa-. ces . .Journal of So11nd and Vibration. Vo/.12.1(:3). pp. 451-160. 1988.

[23] A.S. Lyrintzis. The Use of Kirchhoff Method in Computational Aeroacoustics . .4SME Io!!rnal of Fluids Engineering, Dec. 1994.

[24] K. Brentner. Numerical Algotithms for Acoustic Integrals - The Devil is in the Details. AIAA 96-1706, 1996.

[25] T. Schwarz. Berechnung der Umstromung einer Hubschrauber- Rotor- Rumpf- Konifguration auf Basis der Euler-Gleichungen mit cler Chimiiren-Technik. Shtdienarbeit, DLR Braunschweig,

1997.

I"

(

(

I

Figures

Figure :): ONERA/ECF 7 AD rotor, view of 4-block grid system (rotor plane and blade)

'¥ =0"

'¥ = 180~ '¥ = 270"

Experiment 0.30 Rex.Grid (present) 0.30 CnMl _Chimera 0.20

/\,---

Flex.Grid (ONERA)

r~

0.10 0.00 _0.00 -0.10 -Q.10 r/R=O.S riR=0.7 ·0.200 60 120 180 240 300 '!' 360 -o.2o0 60 120 180 240 300'1' 360 0.30 0.30 CnMz 0.20

-~~

'·

.

,.

':

'.

0.00

_'

.

_'

'

.

.

v

.

-0.10 -0.10

\./"

r/R=0.92 r!R=0.98 .0.200 60 120 180 240 300 'I' 360 -0.200 60 120 180 240 300 '!' 360

Figure.): ONERA/ECF 7 AD rotor comparison of Cnlvi' (Sl test case, MwR = 0.617, J1. = 0.4)

c, Exp. Lower

·4.0 Exp. Upper Rex. Grid (present)

·3.0 _Chimera Aex.Grid (ONEAA)

..

1.0 '!':()" 0.0 02 0.4 0.6 0.8 Jdct.O c, -4.0 -3.0 -2.0 !.0 '1'=180" 0.0 0.2 0.4 0.6 0.8 Jdcl.O c, -4.0 -3.0 ·2.0 1.0 _'Y=W" 0.0 0.2 0.4 0.6 c, -4.0 0.8 xJcl.O c, -4.0 ·3.0 -2.0 -1.0 0.0 [)::'·

-~----1.0 '+'=!20" 0.0 0.2 0.4 0.6 0.8 xlc1.0 c, -4.0 ·3.0 '+'=300" 0.0 0.2 0.4 0.6 0.8 xJcl.O

F'i~un• (j: ONERA/ECF lAD rotor. comparison of pressure coefficient at r/R=0.92 (Sl test case, ,'vfwR = O.fi 17. J1

=

OA)

c

(

·0.10 Experiment Flex. Grid r/R=O.S ·0·20o.\--.-,s'-'o,...,1-;;2,-o...,1*a"o-""2,;.40,...,30*'o'""'I'-,;360 ·0.10 r/A=0.92 ·0·20o.\--""'s'-o--,1*2o,...,1*ao"""""""""2""4o,...-"-"3oo""""'l'-3"'so 0.30 -0.10 r/A=0.7 0.30 r/R=0.98 ·0_·20_{o~-..,s;;o-....,.,12;,0,.-....,.,1a;,o,.-.._,24;-,o,.--3:;;o"'o'""'l'"""""'3,i,so}

Fi~ure 1: ONERA/ECF I AD rotor, comparison of Cnlv/2 (DNW test case, MwR

=

0.6604, J1.

=

0.3276)

c, Exp. Upper c, c, ·4.0 Exp. Lower -4.0 -4.0 Rex. Grid -3.0 -3.0 -3.0 ·2.0 ·2.0 1.0 '1':0" r/A=0.92 1.0 '1'::60" r/A=0.92 1.0 '1'=120" r/R=0.92 0.0 0.2 0.4 0.6 0.8 'dc1.0 0.0 0.2 0.4 0.6 0.8 x/c1.0 0.0 0.2 0.4 0.6 0.8 x/c1.0 c, c,

c,

-4.0 -4.0 -4.0 -3.0 ·3.0 ·2.0 ·2.0 -1.0

..

0.0

1.0 '1'=180" r/A=0.92 1.0 '+'=240° r/A=0.92 1.0 'f'=JOOu r/R=0.92

0.0 0.2 0.4 0.6 0.8 x/c1.0 0.0 0.2 0.4 0.6 0.8 x/c1.0 0.0 0.2 0.4 0.6 0.8 x/c1.0

Figure 8: 0 NERA/ECF 7 AD rotor, comparison of pressure coefficient at r/R=0.92 (DNW test case. :vfwR

IJ.<ifiO~.I'

=

0.:32/G)

(

(

Non-rotating Kirchhoff surface

Figure 9: ONERA/ECF 7 AD rotor, view of blade surfaces and Kirchhoff grids

0NEA.6JECF7AD rotor P [Pa] Mo>ll"' 0.6604. ll= 0.3276 40 Mic 1 ltl ONW 20 --·--·-'-

...

0 ... -· -20 \ -40 -60 -800 10 20 30 40 - - - Experiment - - - - • Eulerlift/Far1Aiift ---·-·-·· Euler llft/FartA nonlift

Euler nonlift I FarfA nonllft

j j

I

50 60 70 80 _"'90

ONERAIECF 7AD rotor P [PaJ MO>tl"' 0.6604, 11= 0.3276

Mic6inDNW

20

- - - Experiment

Euler lilt/ Far1A lift Euler lift I Far1A nonlift

Euler non lift I Far1A non lift

Figure 10: ONERA/ECF I AD rotor. influence of lifting/non-lifting aerodynamic data on pressure signature for linPar acoustic analogy method (DNW test case, lvfwR

=

0.6604, Jl

=

0.3276),

40 --80

' '

_'

'

' '

E:xper1ment EuleriKirchRot(xlc: 1) EuleriKirchAot(xle=2) Eu!eriKirchRot(xfe=3)

---..,,_

/ ' ! ' ! '

'

'

"120_{lo~--:;, o,--,;,o,.._...,,.,.o-"•"'o---;s!=o--,60:0-..,7t:o--,a,;;o,-.,--!so} P[Pa] 80 ONERNECF 7 AD rotor Mto~~ = 0.6604, 11"' 0.3276 Mic61nONW 40 -0 .. , ... , ... ______ ... ...!""'·"-.· ... _{,._}

'

~0 -80

'

'

_'

'

E)(penment Euler/KirchRot(x/e= 1 ) EuleriKirchRot(xlc=2) Euler/KirchAot(xlc=3)

'

'

---fig;ur<' ll: O'iERA/ECF lAD rotor. Kirchhoff surface location variations for rotating Kirchhoff formalism (DNW l>-'>f case . . \f~R

=

0.6604.p

=

0.:3216).

c

(

I'

(

ONERA'ECF 7AO rotor P {PaJ M-"' Q.6604. ~= 0.3276 40 Mic 1 in ONW 20 ·20 ·40 ·60 Exponment

Euler nlt/KlrchAot fift Euler lift tKirchRot non lift Euler ncmlift I KirchRot non lift

.aoot~_.,o_.-"2o~~ao"---,~o---s~o---6~o---,~o---a~o--o/""oo

ONEANECF 7AO rotor

P (Pa] M""' = 0.6604. ~= 0.3276

Mic6in ONW

20

·20

- - - Experiment

- - - - • Euler lilt I KirchAol lilt

-·---·-·· Euler lift I Kirch Rot non!ilt

Euler nonllft I Kirch Rot non lilt

figure 12: ONERA/ECf TAD rotor. influence of lifting/non-lifting aerodynamic data on pressure signature for rotating Kirchhoff method (DNW test case. i'vfwR = 0.6604, I'= 0.3276),

ONERNECF 7AD rotor

P {Pa] M.,.. = 0.13604, ~= 0.3276 40 Mic 1 tn ONW 20 0 ·20 ·40 ·60 Experiment Euler/KirchNonrot (rJA:::1.1) Euler/KirchNonrot (r/A=l.2) Euler/Kirci'INonrot (rJR=1.4) ·•oo!-~-",o--:2o,._...,,.,.o--"'•"'o--"'s"'o--.,6"o--"''"o-"'a"o,....o/--=oo

ONEANECF 7AD rotor P (Pa] M...n = 0.6604, ll'"' 0.3276 Mic6in ONW 20 Experiment Euler/KirchNonrot {r.,IR=1.1) Euler/KirchNonrot (rJR=1.2) Euklr/KirchNonrot (rJA=1.4)

figure 1:3: ONERA/ECF TAD rotor, Kirchhoff surface location variations for non-rotating Kirchhoff formalism ( DNW test case. MwR = 0.6604, I'= 0.3276),

ONERNECF 7 AD rotor - - - Expenment P {Pa] M,,,.. = 0.6604. J..l"' 0.3276 Euler I KirchNonrot lift

40 Mic 1 in DNW · • • · · · · • Euler I KirchNonrot nonlitt

20

ONERA/ECF 7AD rotor

P [Pa] M""' = 0.6604. j.!= 0.3276

Mic6 in ONW

20

- - - Experim&flt Euler I KirchNonrot lift

· · · • • · • Euler I KirchNonrot nonlift

Figure l-1: ONERA/ECF TAD rotor. influence of lifting/non-lifting aerodynamic data on pressure signature for non-rotating Kirchhoff method (DNW test case, MwR = 0.6604, I'= 0.3276),

(

( ONERIVECF7AD rotor P [Pa) M""~ "'0.6604. Jl"' 0.3276 40 Mic 1 10 DNW 20 Experimonl Euler/FartA Euler I K!rchRot Euler I KirchNonrot P[Pa] 20 ·20 ONERAIECF7AD rotor M..,."' 0.6604, J1"" 0.3276 Mic6in0NW

'

,

. _.. \'· . \ \."

'

'

Experiment Euler/FartA Euler I Kirch Rot

Euler I KirchNonrot

figure 15: ONERA/ECF TAD rotor, comparison of pressure signatures for different acoustic methods (DNW test. case. M •. R

=

0.6604. Jl

=

0.3276),

ONERAIECF 7AD rotor

P [Pa) M..n = 0.6604, 11"' 0.3276

Mic in rotor plane

20

·20

·40

Euleflilt/Far1Aiift Euler lift/ FactA non lift Euler non lift I Far! A non lilt

Figure 16: ONERA/ECF TAD rotor. influence of lifting/non-lifting aerodynamic data on pressure signature at in-plane microphone for linear acoustic analogy method (DNW test case, MwR = 0.6604, Jl = 0.3276),

SPL{dB) "0 100 80 60 0 ONERNECF 7 AD rotor M,,. = 0.6604. p= 0.3276 Mic1 inDNW

...

··

...

_.

_.

.

_{. .}

_...

10 20

.. ..

_..

_.

..

30 Experiment Euler I Far! A Euler I KirchRot

...

_.

·

...

40 N 50

ONERA'ECF 7AD rotor SPL !dB] M0011 = 0.6604. ~t= 0.3276 140 120 100

•

_•

80 60 150.0 160.0 170.0

•

Experiment t.BPF .a.. Experiment6.BPF e Experiment 11.BPF - - - Euler I Far1A Euler I KirchRot

•

180.0 190.0 200.0 'i'210.0

figure l /: ONERA/ECF TAD rotor. comparison of sound pressure level (DNW test case, lvfwR

=

0.6604, Jl

=

0.:11/ri).

''

c