CP-ROT: [CP pressure coefficient measurement on the rotating blade] :

NINETEENTH EUROPEAN ROTORCRAFT FORUM

Paper

n'

C22

-

CP-ROT-First Results from Pressure Instrumented

B0105 Hingeless Model Rotor Tests

by

Berend G, van der Wall

Institute for Flight Mechanics, DLR Braunschweig, Germany

September 14-16, 1993

CERNOBBIO (COMO)

ITALY

ASSOCIAZIONE INDUSTRIE AEROSPAZIALI

Abstract

CP-ROT (CP pressure coefficient. measurement on the ROTating blade) is a common project of several inst.itllt.es of DLR. Its purpose is t.o get insight int.o rotor aeromechanics and unst.cady aerodynamics via measurement of the pressure distribution on the upper and lower rotor blade surface. Additionally, the blade bending moment.

distribution is measured via strain gages along the radius in flap, lead-lag and torsion. ln DPcember 1992 a highly

instrumented model rotor (40% scaled BOJ05 hingeless rotor system, rectangular blades, l\ACA 23012 mod. airfoil) was tested in the German-Dutch Windtunnel (Dl\W) within the BR.ITE/EURAM project HELINOlSE [1]. The rotor was equipped with 124 absolute pressure sensors and 32 strain gages (all on one blade) for high frequency measurement of the surface pressures and blade deformations. A specially made data acquisition system allowed the simultaneous measurement of all these sensors with a sampling rate of about 36kHz (2048 samples per revolution). The data match the analyses requirements of unsteady aerodynamics and aeroacoustics as well. With this equipment, the pressure distribution along the leading edge of the blade (3% chord on upper and lower side) at radial positions from 60% up to 99% and at three radial positions along chord (x

=

0.75, 0.87 and 0.97) could be evaluated experimentally. (This instrumentation corresponds to CP-ROT phase I; an even larger number of pressure sensors is planned in future phases of CP-ROT.) The test matrix included hover as well as forward flight configurations up to advance ratios of f.l

=

0.352. Of special interest were a large number of blade-vortex interaction (BY!) cases in the range of f.l

=

0.089 to f.l

==

0.314.

This paper investigates a low speed BY! case at f.l

==

0.149 with a shaft angle of

os

==

+5.05' (tilted backwards) at a thrust coefficient of Cr/"

==

0.058, representing a 6' descent flight condition. Also, a high speed BY! case at f.l

==

0.314, cxs

==

-0.94 and

C1'/"

as before is investigated. With the low speed configuration, two tests were conducted on different days in order to evaluate the repeateability which was found to be excellenL From the time history of the leading edge pressure sensors, the BY! locations can be clearly identified. The vortex core radii can also be identified to first order accuracy from these signals. The aerodynamic lift. at three radial positions is related direcly to the leading edge pressure while t.he aerodynamic moment. is found to act with a small time delay.

The BY! effects at the high speed case are also interesting. The vortex pattern shows pairs of votices on the advancing side, rotating in opposite directions. An investigation of the aerodynamic lift distribution shows negative lift on the outer 20% of the blade from 1/J

==

85'

to 175°. Thus, at the tip a vortex of negative circulation is created and more inboard, a vortex of positive circulation is forming because of another significant radial-gradient in the blade's circulation.

The vortex core radii found in the high speed case correlate well to those found at the low speed and a core radius widening formula was extracted. The results show that the core radius grows about 20% chord per 300° azimuthal vortex age and the core radii of the ))youngest" vortices found is in the range of 20% chord. This is a commonly used value in rotor simulation codes. The associat.ed reduced frequencies, k, are in the rangr· between 1.8 and 3.4. Thus, for simulation purposes quasisteady aerodynamic theory is not applicable for correct aerodynamic loading calculations during BY!.

Due to the reproduction technique, the originally colored graphs on Fig. 2, 6, 7, 9, 12, 13 are printed only in blackfwhite1

Nomenclature

a

e

C1

=

L/(qc)

Cm

=

M/(qc2) Cr

==

Tf(prrR2_\~2₎ k,

=

c/(2R) k==k,V,/V L M Pu,Pl

pitch axis location wrt.

mid-chord, pos. aft, in halfchords airfoil chord [m]

section lift coefficient section moment coefficient thrust coefficient.

reduced frequency of blade tip in hover

local reduced frequency section lift [N /m]

section moment [Nm/m]

air pressure on upper and lower side of the airfoil [N/m2

] q==pV2/2

r,R

r, t T V

==

V, (

x

+

f.l sin 1j;) V, diR Vr

x

==

r/

R

1_{The colored originals are available on request from the author in limited number.}

local dynamic pressure [ N

/m'J

radial coordinate, radius

[m]

vortex core radius (m.]

time

[s]

rotor thrust

[NJ

local velocity

[m/ s]

tip speed in hover [m/ s] wind tunnel velocity [m/ s] radial coordinate

airfoil vertical coordinate of up-per and lower side [m]

shaft angle of attack

angle bet\veen vortex axis and blade leading edge

rotor azimuth) azimuth of a BVI event

p

=

VT cos nsfV, p

!J.?j; peak-to-peak azimuthal distance of a BVI event

1

Introduction

advanee rat.lo air density

[kgfm"J

rotor rotational speed

[rad/s]

A lot of rotor testing has been done in the past but only a few tests have been conducted with instrumented model rotor blades for high frequency pressure signals [2, 3, 4]. This is due to the complexity of the experimental setup

and to the limitations of the data acquisition system. To achieve good insight into rotor unsteady aerodynam·cs,

a lot of pressure sensors have to be installed on one blade. Additionally, the data measurement rate must be high

to get also acoustically relevant pressure flue. tions and all sensor signals have to be recorded simultaneously.

This is especially true when the blades an· .tic and can be expected to behave slightly different during each revolution. Therefore, the decision was de in the HELINOISE program

[1]

to have one blade highly instrumented with all 124 pressure sensors anu, in addition, with all 32 strain gages mounted in flap, lead-lag and torsional directions. All of the sensor signals were stored simultaneously for 60 revolutions at a rate of 2048 data points per revolution [5]. For data analysis, one single revolution time history and the average of all 60 cycles were stored after postprocessing. The objective was to analyse the BY! locations, the BY! impact on aerody> ·nic lift and moment beh<>viour during BY!, and to compute the blade response from the strain gage

signals addition to the rotor instrumentation, the HELINOISE program used a microphone rig below the

rotor tc· .nalyse the noise radiation. Noise results are presented in [6]. Thjs paper, however, is confined to the

aerodynamic analysis of the pressure data.

2

Methodology of Analyses

2.1

Identifying BVI Events

To analyse BY! effects most clearly, a very sensitive position of the blades must be selected. This is the leading edge of the airfoil because the pressure gradients are very large due to the highspeed flow around the airfoil nose radius. Thus, the time history of the sensors at 3% chord (upper side of the airfoil) gives the best information about the airflow the airfoil is entering. For the low speed test case the time histories at radial positions from

x

=

0.6, 0.7, 0.75, 0.8, 0.87, 0.9, 0.94, 0.97 and 0.99 are given in Fig. I. The more inboard sections on the advancing side show BY! pressure peaks are stronger than on the retreating side. Since the Mach numbers are relatively small on bot b sides, this means the vortices are either closer to the airfoil on the advancing side or they are stronger in circulation. At the outer positions the retreating side BY! appears to be much stronger. This effect is mostly due to the larger Mach numbers on the advancing side where the airfoil is operating with

a small supersonic regime on the upper surface.

From each of the time histories, the azimuthal and radial position of BY! can be identified as follows,

assuming a positive sense of rotation of the vortices encountered. First, from Fig. 1 it can be seen that the BVI

induced pressure signals are of high frequency nature (they extend only over a small azimuthal range) while the total signal has a large low frequcnc~· '<'Intent (one to three harmonics) in addition. Thus, it eases the further analyses, when subtracting the first . .1armonics from each time history; the result is shown for the radial position x

=

0.99 in Fig. 1 below. Also, the same filtering procedure is applied to the average signal obtained from 60 revolutions and plotted below. As can be seen, the sequence and intensity of BY! is very stable since

the differences between average and single revolution are very small.

On the advancing side, the blade first encounters a downwash from the vortex. This leads to a reduction of the effective angle of attack at the airfoils' leading edge and thus increases tk pressure at the sensor until the maximum of the down wash is reached. Basically, the pressure is following the compressible Bernoulli-law known from airfoil theory. When the interaction is very dose, say within the vortex' core radius, then the change of downwash to upwash and with it a change to lower pressure at the sensor position happens very quickly, causing a steep opposite gradient in pressure until the maximum upwash is reached. The peaks are very sharp in contour and the peak-to-peak level is the largest in a sequence of BY! events. In cases where the vortices are farther away when interacting with the airfoil, the peak-to-peak amplitudes are smaller and the distance between the peaks is larger. This is easy to explain with the Biot·Savart law for the induced velocity field of a vortex. On

the retreating side the sequence of the pressure peaks is opposite because first an upwash is encountered and

then f,he down wash. A verY close blad<>-Vort.ex encounter can be found at :r

=

O.IJ9 and t··m· 1

=

29f)o. In all of the BVI. events, the vortex. center can be localised in t.bt" middle between th<' two (orresponding; peaks.

2.2

BVI Locations

\Vith this information, a contour plot of the 10/rev filtered signals in polar coordinates directly gives the vortex patterns and the BVI intensity in the rotor plane, see Fig. 2. In addition, the BVI locations a..<; identified from

Fig. 1 are marked here. The vortex positions can beo graphically obtained b,y plotting the gradients of each

time history (the positive ones on the advandng side and the negative ones on t.be retreating side). Also, in

Fig. 2 the calculated BY! locations using the Beddoes' model [7] are shown together with the experimentally evaluated locations. It. can be seen that in general the prediction is good but at the front of the disk the vortices actually seem to travel backwards faster than predicted. From the intensity of BY!, the areas where the vortices are passing the rotor plane can be identified to be usually where the blade is almost parallel to the vortex encountered making the noise emission very significant, known as BVI noise or blade slap.

2.3

Vortex Core Radius Analyses

The time history of these sensors also gives information about the vortex' core radius. Assuming the blade-vortex miss distance to be within or very close to the core radius, rc, the azimuthal distance 6..1/-' between the

two corresponding peaks of a BVI event (see Fig. 1) is a nondimensional measure for the vortex core diametcL This is defined as the geometrical length between the maximum upwash velocity before the vortex' center and the maximum down wash behind it. From Fig. 3 (top graph), that is an enlargement of Fig. I. one can find this distance to be /:l'f/;

=

1.9°. This includes the convection velocity of the vortex during the interaction that can

be assumed to be I'· The azimuth of the BY! location is found to be 1/JBVI

=

295.5'. Next, using

,.,

R

!:J.,P !:J.!);

- " " - (x

+

iJ.Sin V'BVI)-cos/3 = -cos;3

c c 2 4k

where j3 is the angle with which the vortex is interacted

({3

=

0 when the blade leading edge and the vortex are parallel). Note that the angle between the BY! location traces in Fig. 2 and a blades leading edge line are not identically with j3 except where the interaction is parallel. This is because the vortices are moving with a certain convection velocity relative to the blade. To find (3, the vortex system has to be plotted for every azimuthal position separately as is done in Fig. 4 with increments in 1/J of 15'. The result is as follows: at certain BVI locations the instantaneous vortex traces are plotted around this BVI location and it is clearly to

be seen that there are differences between

f3

and the angle of the BVI location traces with the blades. Tlw da1 •1

are calculated using the experimentally identified vortex locations as input for the vortex modeling. Tllf'JI. th1

graph below (containing the BVI locations during one revolution) is cornplet.f'd with the inst.ant.a.neous WHlr'.\

positions at various BY! locations in order to identify the angle {3.

In the example mentioned before, !3 can be identified to be::::::::: 22° from Fig. 4. ~·m·₁ i~ tht-' rotor aziiJH!\h

(Jr

the BVI event. under consideration and, in combination with J..l, accounts for t-hf' velocity of t.he vort.f'X reL·\tl\·,.

to the blade. With the ratio of radius to chord being R/c

=

16.53 for this model rotor. the core radius of tlw vortex is approximately 22% chord. This is well within common assumptions about. the tip vortex core radii used in rotor analysis of about 20% chord. However, it has to be kept in mind that this vortex is already :\:!0"

old and originated at

7/J""

245° from the blade that is currently at 1/J

=

205°. Thus, some diffusion effects lllight already be in progress, widening the originally smaller vortex core.

2.4

Aerodynamic Lift and Moment

Three sections at x = 0.75, 0.87, 0.97 were instrumented along chord to obtain the chord wise pressure distribu-tion. The time history of these signals will show the BVl effect along chord and therefore its effect on lift and moment after proper integration. Fig. 5 shows typical pressure distributions for the 3 sections at the azimuth

1/J

=

90' and 270' (data from the high speed case). The pressure distributions represent the raw data, averaged over 60 cycles. A lot of these signals do have a steady offset that will affect the calculation of the steady com-ponent of the aerodynamic lift and especially the moment. For a better estimation of these steady comcom-ponents. the various offsets have to be corrected manually which is a cumbersome job that needs some experience. It must be noted, that the dynamic. part of lift and moment is not affected by this correction procedure. In Fig. 4 at 1/.• = 90' the outer sections clearly show supersonic regions on the airfoils' upper surface. The Mach number is about 0.84 for the section at x

= 0.99,

0.76 at x

=

0.87 and 0.68 at x

=

0.75. The reason that these supersonic areas are not larger is due to the relatively small angles of attack. On the retreating side, no supersoniC areas are to be found and thus typical sub critical pressure distributions are present. The Mach numbers are 0.43, 0.36

and 0.28 at the radial positions J'

=

0.99, 0.87, 0.75, respectively. Large pressure peaks at t.be leading edge on

the upper side indicate large angles of attack that. are necessary to balance the rotor.

The integration of tlw pressurf' is done at ever;·· data point during the revolution. For tlw lift. here defined as the aerodynamic force normal to the airfoils' chord, the local pressure is taken as constant. along a line bet.weeJl

the middle of two neighbouring pairs of sensors. The resulting local force is acting normal to the local surface that is inclined with respect to the airfoils' center line. Thus, with a: being here the chord wise coordinate and zu l z₁ the contour coordinat.e of upper and lower surface, the aerodynamic lift L and rnoment. about quarter

chord M_{0 .25} are evaluated via the following formula. Results are presented in the following sections. L

=

Mo.2s

=

3

Low Speed BVI

The low speed flight condition repr <ents a

6'

descent flight, that is known to produce large BVI-induced noise. Thus, the BVI-induced pressure fluctuations are large, especially in areas, where the vortices are almost parallel to the blades. In this case, the noise sources can be located in Fig. 2 between 1/J

=

45' and 65' on the ad,ancing side and between

1/>

=

290' and 305' on the retreating side. The figure shows the peak-to-peak differences in pressure to be very large. The advancing side shows smaller pressure differences t.han the retreating side, even though the blade-vortex distance must be about. the same. This is partly due to the larger Mach number on the advancing blade as explained before.

3.1

Vortex Locations

The vortex locations for this test case are shown in Fig. 2, where the traces of BVI are clearly visible. This is where the vortices are relatively close to the blade and where the angle (3 is not too large. It must be noted that (3 is large (almost 90') in the front region of the disk which would induce only low frequency fluctuations in the pressure at a constant radius. These were filtered out by the procedure described above and are not visible here. Additionally, in this region the vortices are positioned significantly above the rotor plane and thus are not inducing pressure changes with locally large gradients.

On the advancing side at 1/J "" 60' some irregularities can be found in Fig. 2. This might be due to some roll-up processes of the oncoming vortices in the vicinity of the blade. At the rear of the disk between ,P

=

340'

and 1/J

=

10' some disturbances appear. They are due to the rotor hub wake, distorting the rotors' vortex wake system. Additionally, the tip vortices are quickly travelling below the rotor and thus are not able to induce any significant local pressure gradients in the rotor plane.

3.2

Vortex Core Radius

The method to measure the vortex core radius was discussed in section 2.3. This method is useful only where the vortices are very close to the blade (otherwise the apparent core radii will appear too large) and where the angle (3, with which the vortices are interacted, is smaller than about 40°. However, there are enough BVI events available to satisfy the objectives. The problem mainly is in a correct identification of the angle (3 from Fig. 4 and all the D.l/J from the time history of each radial section. Where the vortices are not close to the blades

D.l/J is difficult to obtain. On the other hand, the effective

tl1/>

indicates the vertical distance between the blade and a vortex following the Biot-Savart law.

Two more BVI events on the advancing side are investigated here, see Fig. 3 (bottom graph). At radial position

x

=

0.6, a close encounter can be found at 1/JBVI

=

32.3', Fig. 2, where

tll/•

=

5.4° and (3"" 35'

from Fig. 4. The result here is

7',/c"'

0.44. Here the vortex was generated at about ,P

=

160' from the blade currently being at ,P

=

112.3' and the vortex age is 680'. Thus, although the vortex is very close to the rotor disk, its core radius is much larger than in the example before. A third example: at x

=

0.94 and V'BVI

=

fi7.7',

Fig. 2, we find D.¢= 2.1' from Fig. 3 (middle graph) and (3 "'45° from Fig. 4. This gives

r,jc"'

0.23. Here the vortex was created at 1/J

=

120' by the same blade and is 308' old. Thus, its age and size fit well to the first example and additionally, the widening of the core radius with time can be assumed to be about 0.2 chord per

300' of vortex age. Of course, for validation of this assumption much more BVI events have to be investigated. This analyses is useful only at those events which show a very close blade-vortex distance, visible by the largest pressure peak-to-peak amplitudes. There are usually only few of these available. For other BVI locations, the results are given in Table 1.

3.3

Reduced Frequencies

\Yit.h the approximation of the induced velocity Held of a BVl event to \w close to sinusoidal for the airfoil. 1 ben the wave length is t.wicc the distance between the two corresponding pressure peaks. ~l"- Thus, the freqn(~\lcy

of a BV! event is'"= 2rrD/(2~~"l· With this. the reduced frequency of a IlVl ev·ent is

we 1r c/(2R) -rrk;

k

= - = - --'·

-';-~-

=

-;-:-;---~-~

2V ~~' x

+

11 sin "'m' r ~~·(x

+

f1 sin t.·Jw I)

As an example, for the model rotor the reduced frequency of the tip in hover, k1 = 0.03025, is not very large and justifies quasisteady assumptions. Now, t;~J usually is very small and x• is smaller than one. Using the BV!

envent mentioned in section 2.3 with x =.: 0.99, ?i!BVI :::::: 295.5° and /J:.1p

=

1.9°, the local reduced frequency

is about k

=

3.4. No quasisteady assumptions can be used for simulation purposes. I\ote that t.his BVI event primarily is a sine wave that is only 2.6.1/lr/c:::: 1.08 chords long, so at some instances of time both pressure peaks· are present on the airfoil with a distance of 0.54 chords. The corresponding results for the other two examples mentioned before (section 3.2) are: at ?fsvJ = 67.7°,X = 0.94 the reduced frequency is k

=

2.4 and the wavelength is 1.13 chords long. At lfsvi

=

32.3',x = 0.6, we find k

=

1.5 and a wavelength of about 1.9 chords.

3.4 Blade Loading

Following the integration procedure described in section 2.4, the aerodynamic lift and mornent. about the quarter chord can be calculated at the three radial sections x = 0. 75, 0.87, 0.97. It should be noted that the steady part includes some uncertainties because of the manual correction of the offsets of most of the sensor signals, however the dynamic parts are not affected. Fig. 6 (top) shows the lift distribution without filtering, below the first 10 harmonics are subt.racted to compare with the leading edge pressure data of Fig. 2.

The total lift in the top graph shows a small region of negative lift at the blades' tip between V'

=

150" and 180'. Additionally, the radial gradient of lift is not large, so the tip vortex will form more inboard than at the tip which might be a reason for the discrepancies in the prediction of the BVI trajectories and experiment as shown in Fig. 2. The prediction assumes the tip vortex always to form at the tip and not inboard.

The graph at the bottom of Fig. 6 shows very clearly the BVI induced lift fluctuations, and the vortex trajectories from Fig. 2 again are exactly in the middle between two corresponding peaks as has been in the leading edge pressure distribution. Thus, the lift is directly proportional to the leading edge pressure without a time lag. This is to be expected since the lift results mainly from the pressure difference in the first half of t.he airfoil.

Fig. 7 gives insight into the aerodynamic moment (about quarter chord) development during one revolution: on top, the unfiltered data and below the first !0 harmonics are subtracted. From the unfiltered data the effect of transonic Mach numbers can be seen at the tip around 1jJ

==

90°, where the moment is negative. There dw center of pressure is moving aft. of the quarter chord point. producing a nose-down moment. Below, the filtered data again show very clearly the various BVI induced loadings. However, there is a certain time delay between the vortex trajectories as identified from the leading edge pressure and the resulting aerodynamic moment development.. This can be explained by the fact that the pressure data are multiplied with (>:- 0.25) and thus the effects of large pressure differences at the leading edge are reduced while small pressure differences at the trailing edge are amplified. So it takes some time for the changes in pressure to produce a change in the aerodynamic moment about quarter chord.

4

High Speed BVI

This test condition is characterised by an advance ratio of fl = 0.3!4,

as

=

-0.94" and CT/0' = 0.058. This flight condition is interesting since there are strong BVI effects found at azimuth angles from 90' to 150" and from 270' to 300'. Fig. 8 shows the pressure at 3% upper chord in analogy to Fig. I. In the upper part, a large !/rev variation in the pressure signals can be seen due to the large fluctuation in the local Mach number. The tip Mach number varies from 0.87 at 1/>

=

90° to 0.46 at 270'. Strong BVI effects can be found in the regions mentioned above with peak-to-peak amplitudes very similar to those found in Fig. I. The number of BVI events in the lower part of Fig. 8 are less than can be found in Fig. l since the wake is convected by twice the velocity of the low speed case. Again, the average time history is very close to the single revolution except in the rear of

4.1

Vortex Locations

From the pressure sensor signals at. :3% upper chord the BVl locations can he clearly seen. when subtracting the first 6 harmonics . .see Fig. 8 (lo\ve~ part). Surprisingly, the BVI locations t.o be t~X]Wcted show an opposit<' time history c the advancing side, c.>mpared to the low speed BVI case. First an upwash is encountered, than a downwash, indicating a vortex having a negative circulation. Also, there are more vortex interactions bet\\'Cen these locations with an opposite tirne history. as if there are secondary vortices with positive circulation. obviously created at a more inboard station than at the tip. All of these BVl locations can be clearly ~;een in

Fig. 9, where again the first 6 harmonics are subtracted from the time history. The BVI locations on the

advancing side, where the circulation is positive, are marked by a da...••;hed line, They are inbetwecn the tip vortex locations and have been identified by a pressure time history to be first down, then up (as they were in

the low speed BVI case, see Fig. 1). Also, the results from the wake program [7] already used for the prediction in Fig. 2 are given. The BVJ locations at this large advance ratio are predicted almost exactly. Additionally, the region of negative lift (as evaluated in a later section) is marked by the shaded area. It can be seen that the strongest BVI on the advancing side takes place where the lift is almost zero.

4.2

Vortex Core Radius

Based on the BVI induced pressure fluctuations in Fig. 9, the smallest blade-vortex distance was found to be at x == 0.9, 1/JBvi

==

93.6° and D.7j>

=

2.5', (the time history is given in Fig. 10). To evaluate {3., the instantaneous

vortex positions at the various azimuth must be knovm. For this, Fig. 11 shows these vortex trajectories at different azimuth (top graphs) and an overview of the BVI locations with the various vortex trajectories at

the BVI location. The value of [3 is about 70° from Fig. II and is rather large. The result is a core radius of about 15% chord that is surprisingly well within the earlier evaluated data. It has to be noted that this vortex is relatively young. It was created at

1•

== !17° from th blade being currently at 183.6° and thus the vortex is only 67' old. Another example: at x

=

0.99, 1/JBv 1

=

291.2° the value of /:;.7j> is 3.8° from Fig. 10. The angle [3 is

about 40° from Fig. II and thus a vortex core radius of 28% chord can be calculated. This vortex was created at 1/;

=

248' from the blade being at 1/;

=

21.2° and its age is 133°. Again the result agrees well with those obtained from the low speed case.

As mentioned before, on the advancing side double vortex systems can be found. One of these at

x

= 0.8 around 1/;

=

38° is shown in Fig. 10 (top graph). The tip vortex with negative circulation is indicated with the

index '2' and the secondary, more inboard created vortex with positive circulation is indicated with '1 '. For

event '2' we find 1/JBvi

=

40.6', D.l/;

=

1.6° and fj"" 1.6° so a core radius of 23% chord is the result. The vortex was created at 1}; == !50' from the same blade's tip and is 250.6° old. The other event, 'I', has the following data: 1/JBVI

= ..

5.6°, A:.

=

2' and [3"' 12°. A core radius of 28% is the result. Again. this vortex is created

from the same blade, but at a more inboard station of x:::::::: 0.9 at the same azimuth and thus the vortex age is about the same as for event '2'.

4.3

Reduced Frequencies

As in the low speed BVI case, the reduced frequencies of the various BVI events can be calculated. For the examples just given, the local reduced frequencies are at x

=

0.9, 1i'BI'l

=

93.6': k

=

1.8; at x

=

0.99. 1/.•avi

=

291.2°: k

=

2.1. On the advancing side for event '2': k

=

3.4 and for event'!': k

=

2.77. Again, these values are about the same as in the low speed BVI case.

4.4

Blade Loading

After having corrected the static offset in the pressure signals manually, the integration over chord gives the

aerodynamic lift and the aerodynamic moment. about quarter chord. The total lift distribution is presented in Fig. 12. A large negative lift area can be found between 1jJ

==

85° and 178' with the peak negative lift at 1/;

=

140°. All of the outer 25% radius has negative lift and thus it is clear that the tip vortex will have negative

circulation. Also, a secondary vortex will form here at x:::::::: 0.75 with positive circulation since the radial gradient

of the blade loading is large. Because of the large !/rev and 2/rev lift amplitudes in the total lift, BVI induced lift fluctuations are hardly visible here. Thus, the first 6 harmonics are subtracted and the result is given below in Fig. 12. All of the vortex induced loadings are dearly "isible now and the peak-to-peak lift fluctuations are very comparable to those of the low speed BVI case, Fig. 6. The BVI locations obtained from Fig. 9 are added to the figure and it is to be seen that there are no phase lags between BVI location and lift development.

Fig. 13 gives an impression of the aerodynamic moment. The total aerodynamic moment about quarter chord is shown on top. Although the low freque: v amplitudes are larger than :; the low speed case (see Fig. 7), the

BVI impact. on the moment is clearly visible. In the first quadrant- at the tip strong negative rnoment~ appear, mostly due to transonic effects moving the center of presstlrf' aft of the quart-<>r chord point. This area is ended with the interaction of the vort.ex from thf' blade before. Since this vortex. first indue<':-; an upwash, tlw nt:gat.ivl' moment extends to more inboard regions ('1,::'

=

85° to 1200). Then. t.he lift. changes to JJegatiV<' lift (s<:(' Fig. lL)

so the transonic effects produ<"J:: positive moments from then on.

The BVI impact on the moment is more visible when subtracting the first 6 harmonics frolll the data. This is done in Fig. 13, lower graph. Strong negative moments appear at the upwash side of t.he BVI events. followed by a positive moment. In addition to the moment, the BVI locations obtained from the leading edge sensors are indicated. A small time delay bet.\vecn the BVI location and t.hc response of the aerodynamic moment. can be

found while the lift does not show a time delay as mentioned before.

5

Summary and Conclusions

A hingeless BOI05 40% Mach-scaled model rotor was instrumented with 124 pressure transducers and 32 strain gages on one blade. Experiments were made in the German~ Dutch \Vindtunnel in 1992, concentrating especially on BVI configurations. Two of the test runs are presented and analysed in this paper; a low speed BVI case at fJ.

=

0.149 and a high speed BVI case at fJ.

=

0.314. both representing descent flight conditions with a high noise level. From the pressure data at 3% upper chord the BVI locations are identified and the intensity of BVI induced pressure oscillations indicates the proximity of the vortex to the blade. From these data, the vortex core radii have been evaluated to a certain degree of accuracy and are found to be in the range of 20% chord, giowing with the vortex age. The reduced frequencies of the BVI locations under investigation were found to be between k

=

1.8 and k

=

3.4> therefore no quasisteady assumptions can be made for puposes of simulation of these effects.

The ]ow speed BVI is characterised by very strong BVI at the blade tip, 1j;

=

295° azimuth (retreating side) and on the advancing side between 'lj.;

=

35° and 65° over all radial positions. This results in an extreme noise producing state, known as blade slap. The vortices in the front of the disk have a larger distance to the disk and do not strongly affect the pressure distribution. Since the lift is positive almost everywhere on the disk, the

tip vortices always have positive circulation. In contrast to this, the high speed BVI case shows a large negative lift area between 'ljJ

=

85° and 1800, producing a tip vortex in this area with negative circulation. Thus, the time history of pressure on the advancing side is opposite than what was found in the !ow speed BVI case. In addition, the radial gradient from negative lift to positive lift more inboard is strong enough to produce a second vortex with positive circulation at a. more inboard location. This vortex also produces BVI effects on the advancing side that are clearly visible in the pressure time histories.

The tift development is found to have no time delay with respect to the leading edge pressure time history at

3%

chord, while the aerodynamic moment time history shows a time delay of up to 2° azimuth. This is because for the aerodynamic moment about quarter chord the leading edge pressure is not that important while pressure changes at the trailing edge are. Thus, the aerodynamic moment is changing while the vortex induced pressures reach the trailing edge.

A simulation of the BVI locations shows good agreement in t.he high speed case but in the low speed case. the simulated BVI locations are generally predicted to be too far in the front. of the disk. One explanation may be found in the lift distribution: in the front of the disk the total lift is dose to zero and the radial gradients are not large. This may lead to a tip vortex forming not at the tip but more inboard. shifting the BVI locations in downstream direction.

References

[I] W.R. Splettster, K.J. Schultz, B. Junker, W. Wagner, B. Weitemeier, "The HELINOISE Aeroacoust.ic Rotor Test in the DNW," DLR-Mitt. 93-09, Braunschweig. 1993

[2] D.A. Boxwell, F.H. Schmitz, W. Spletster, K.J. Schultz, "Model Helicopter Rotor High Speed Impulsive Noise: Measured Acoustic and Blade Pressures," 9th European Rotorcraft Forum, Stresa, Italy, 1983 [3] Y.H.Yu, A.J. Landgrebe, S.R. Liu, P.F. Lorber, M.J. Pollack, R.M. Martin, D.E. Jordan, "Aerodynamic

and Acoustik Test of a United Technologies Model Scale Rotor at DNW," 46th Annual Forum of the American Helicopter Society, Washington, D.C., 1990

[4) M.K. Lal, S.G. Liou, G.A. Pierce, M.M. Komerath, "Measurements of Unsteady Pressure on a Pitching Rotor Blade," 49th Annual Forum of the Amertcan Helicopter SoCJety, St. Louis, Missouri, 1993

[5] B. Gelhaar, B. Junker. W. Wagner, "DLR- Rotoc Teststand Measures Unsteady Rotor Aerodynalllic Data." 19th European Rotorcraft Forum, Como, Italy, 199~1

[6] W.R. Splettster, G. Niesl. D.G. Papanikas. F. Cenedese, F. !\itti, "Experimental Results of the European Helinoise Aeroacoustik Rotor Test in the D!\W." 19th European Rotorcraft Forum, Como, lt.aly, l\JV3

[7]

T.S. Beddoes, "A Wake Model for High Resolution Airloads," International Conference on Rotorcmft Basic Research, Research Triangle Park, NC, !985

psi_BVI Del_psi (deg) (deg) r/R = 0.60: 32.3 48.0 63.6 77.0 5.4 4.3 2.8 9.2 289.2 313.5 10.5 9.0 r/R = 0.70: 35.2 48.3 62.4 5.0 3.5 2.3 74.4 6.0 264.0 10.0 286.4 8.0 306.0 7.0 r/R

=

0.80: 36.5 5.0 47.8 4.5 60.7 3.5 71.5 3.8 271.8 289.0 303.5 r/R

=

0.90: 7.5 6.0 4.4 24.7 2.5 37.0 7.0 47.2 4.5 55.8 68.2 292.5 303.0 r/R

=

0.99: 2.0 3.0 3.3 4.5 37.6 2.7 46.6 3.3 53.4 1.6 62.8 2.0 66.5 77.9 295.5 304.5 316.7 2.8 3.1 1.9 4.0 5.8 beta (deg) 34.0 6.0 9.0 31.0 4.0 29.0 27.0 0.0 16.0 35.0 30.0 6.0 20.0 25.0 1.0 25.0 35.0 28.0 13.0 13.0 38.0 15.0 6.0 14.0 39.0 16.0 6.0 12.0 9.0 21.0 32.0 39.0 63.0 22.0 2.0 18.0 r_c/c (-) 0.44 0.44 0.29 0.85 0.69 0.56 0.50 0.41 0.27 0.60 0.69 0.64 0.55 0.58 0.59 0.43 0.42 0.62 0.56 0.42 0.27 0.97 0.65 0.~9 0.35 0.35 0.50 0.41 0.52 0.24 0.27 0.35 0.23 0.22 0.50 0.71 psi_BVI Del_psi (c ) (deg) r/1-. = 0.60 33.6 39.6 57.0 75.4 95.5 269.7 r/R

=

0.70 35.3 40.1 72.0 4.0 2.5 2.0 2.2 3.5 8.0 3.5 2.2 2.5 87.1 2.8 90.5 1.6 276.4 5.5 r/R

=

0.80 35.6 2. 0 40.6 1.6 52.8 2.0 61.3 2.5 68.6 1.6 79.9 110.8 281.8 r/R

=

0.90 3.1 3.5 3.5 35.6 2. 2 50.9 2.2 64.5 2.5 72.4 78.5 93.6 287.0 r/R

=

0.99 2.3 2.0 2.5 4.2 25.0 5. 2 35.3 2.4 39.6 1.0 48.6 2.4 56.0 62.0 66.5 80 j 291.2 1.2 1.3 2.3 3.5 3.8 beta (deg) 25.0 17.0 3.0 25.0 56.0 19.0 17.0 13.0 32.0 51.0 55.0 19.0 12.0 8.0 11.0 23.0 35.0 48.0 78.0 24.0 10.0 14.0 35.0 49.0 55.0 70.0 27.0 40.0 7.0 5.0 15.0 29.0 37.0 48.0 67.0 42.0 r_c/c (-) 0.40 0.28 0.25 0.26 0.26 0.31 0.43 0.28 0.31 0.26 0.13 0.29 0.28 0.23 0.30 0.36 0.21 0.33 0.11 0.23 0.34 0.35 0.35 0.26 0.20 0.15 0.32 0.65 0.40 0. 17 0.41 0.19 0.19 0.29 0.26 0.28

Table 1: BVI core radius evaluation. J1

=

0.149, o:s

=

+5.05' (left table) and J1

=

0.314, o:s

=

-0.9°

(right table).

Cr/u

= 0.058

in both cases.

1

-

c:; c:.... ..!<

-

c:....

I

20

15

10

5

0

-5

-10

0.(/

'·

"·

...

.,

____

.---·-'·

' '

·,,

'

______ ... ;i

l

6.---,

-lj

r/R

=

0.99, single revolution, 0-10/rev subtracted

~ 2J

'

~

0

~'---~~~---~-/

-2

6.---,

-l

r /R

=

0.99, average of 60 revolutions, 0-1 0/rev subtroct]e

j

2

'l'

0 .

Figure 1: Leading edge pressure time history at r/R. = 0.6, 0.7, 0.75, 0.8, 0.87, 0.9, 0.94, 0.97, 0.99. Sensor position: 3%. chord, upper side. 11 = 0.149, o:s

= +5.05",

Cr/<r = 0.058.

-P at 3% upper chord, 80105, ,u=0.149, a

₅

=+5.05°

1.0 .6 .6 .4 .2

-

I

-~

.0 -.2 -.4 -.6 -.6 -1.0 -1.0 Yrunnel

-

t:xperiment

t

t

Prediction

-.5 \

'

'

.0

r/R (-)

,

I

I

I

I I 1.0

--

1111 IIlli !ill]

m

llfll Ill

-lillll IE 11m c:l c:l c:l ll!!!l

-

--

-

---P (kPa)

4.50. max 4.25 • 4.50 4.00 • 4.25 3.75 • 4.00 3.50 • 3.75 3.25 • 3.50 3.00 • 3.25 2.75 • 3.00 2.50 • 2.75 2.25 • 2.50 2.00 • 2.26 1.75 • 2.00 1.50 • 1.75 1.25 • 1.50 1.00 • 1.25 .75 • 1.00 .50 • .75 .25 • .50 .00 • .25 -.25. .00 -.50. -.25 -.75. -.50 -1.00. -.75 -1.25. -1.00 -1.50. -1.25 -1.75. -1.50 -2.00. -1.75 -2.25 • -2.00 -2.50 • -2.25 -2.75 • -2.50 -3.00 • -2.75 -3.25 • -3.00 -3.50 • -3.25 mln. -3.50

Figure 2: Leading edge pressure distribution (first 10 harmonics subtracted) and BVI locations in the rotor disk. Sensor position: 3% chord, upper side. Comparison of theory (Beddoes' wake model) and experiment below. p.

=

0.149, o:s

=

+5.05°, Cru

=

0.058.

r/R

=

0.99

₌

_1.9'

4 _fBVI

₌

_295.5'

~

.. 22'

-;;

2 p.,

c

p., 0 I -2 -4 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303

"'

(•) 2

r/R = 0.94

6.'if;=2.

fBVI ::

67. 7'

~

.. 45'

-;;

1 p.,

"'

~ p., I 0 -1 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75

"'

(') 1.0

r/R :: 0.6

ffNI

=

32.3'

6.'f=5.4'

.5 ~

.. 35'

-;;

.0 ~ ~ p., -.5 I -1.0 -1.5 25 26 27 26 29 30 31 32 33 34 35 36 37 38 39 40

"'

(')

Figure 3: Leading edge pressure time history at selected locations for vortex core radius evaluation. Sensor

'if; -

0,90,180,270°

'if;

=

15,105,195,285°

'if; -

45, 135,225,315°

'if; -

60,150,240,330°

Yrunnel

\

\

'

I

I

~=0'

'if;

=

30,120,210,300°

'if;

=

75,165,255,345°

Figure 4: Wake geometry and instantaneous vortex positions at various BVI locations for identification

of the angle (3. I'= 0.149,

cxs

=

+5.05°,

Cr/"

=

0.058.

'"'1 Q;i'

"

Azimuth 90.0'" Az:tmuth 270.()'1'

.,

"'

""

60

15 (}

40

rfR

=

0.97

~

r/R = 0.97

""

10 0 ~ ~

zo

""'

""

_{~ <>.}

_"

_"

5 <>. :;;· _-"'

₀

_-"' 0

---~-"

~ ~

-""""""

"'

<>. a_ -5

r

~ _{1 -20} I

"

M

"'

-40

-10

"'

~

"

""

-60

- 15 ,_,... ---r-···~·-.---. ~· ~

.0

.1

.2

.3

.4

.5

.6

.7

.8

.9

1.0

.0

.1

.2

.3

.4

.5

.6

.7

.8 .9

1.0

~

x/c (-)

x/c (-)

0.:

"

~

c;·

60

15 t:l

"'

"'

40

J:

~

r/R

=

0.87 10 r/R

=

0.87 ~ n

"'

~ ~ N

_"'

"

20

"

N

"

<>.

v

~ !l. 5 I n

"'

0

-"'

~--

"

~ ~

""

""

a.. 0..

0'

· +

-"'

1 -20

I

..

N

a·

-40 -5

"

-

:;,- -60 -10.

"'

.0 .1

.2

.3 .4 xfc (-)

.5

.6

.7

.8

.9 1.0

.0

.1

.2 .3 .4 xfc (-)

.5

.6

.7

.8 .9 1.0 0

""

-

40 1 5 r "

..

.

,.

1

c

r/R

=

0.75 r/R = 0.75

"'

_II ~

zo

~ 10

"

"

I !l. (L 0

"'

0

"'

5 io ~

_.

c _a.. 0..

.?

I

-20

I 0

_il

--~~-~---...

_q -40 .f.-.-.-,.

-5

II 0 .0

.1

.2 .3 .4

.5

.6

.7

.8

.9

1.0

.0

• 1

.2

.3

.4

.5 .6

.7

.8 .9

1.0

0

_{x/c (-)}

_{x/c (-)}

"'

00

Lift distribution,

80105, ,u=0.149, as=+5.05°

L (N/m)

1.0

•

600 , max

•

580 • 600

•

560 • 580 .8 !l!!l 540 • 560 l!llll 520 ' 540 !lll 500 ,520 .6 !l!l _l!llll 480 • 500 _{460 ,480} ll!ill 440 • 460 1111!1 420 • 440 .4 1111 400 ,420 IIIII 380 ,400 ll!ll 360 ,380 .2 !lll 340 ,360 !lll 320 ,340 ~ CJ 300 ,320 I ~

"""

r::J 280 ,300

"'

.0 Vrunnel r::J 260 ,280 ~ llll 240 ,260 I I 220 ,240 -.2

•

200 • 220

•

180 ,200

•

160 • 180 -.4

•

140 • 160

•

120 '140

•

100 • 120 -.6

•

•

80 • 100 _{60 ' 80}

•

40 ' 60

•

20 ' 40 -.8

•

0 20

•

-20: 0

•

-40 '-20 -1.0

•

min, -40 -1.0 -.5 1.0 r/R (-) 1.0

•

_{180 • max}

•

170 ' 180

•

160 ' 170 • 8 I I 150 ' 160 I I 140 • 150 Ill! 130 • 140 .6

•

120 • 130 1111 110 • 120

..

100 • 110 1111 90 100 .4

•

80 90 I I 70 80 11!!1 60 70 .2 !lll 50 60 !lll 40 50 ~ I ~

.o

"'

~ CJ 30 40 CJ 20 30 r::J 10 20 !lll 0 10

..

-10 : 0 Vrunnel -.2

•

-20. -10

•

-30. -20

•

-40. -30 -.4

•

-so,

-40

•

-60. -50

•

-70' -60 -.6

•

•

-so,

_{-90. -80} -70

•

-100 • -90

•

-110,-100 -.8

•

-120.-110

•

-130,-120

•

-140,-130 -1.0

•

min, -140 -1.0 -.5 .5 1.0 r/R (-)

Figure 6: Aerodynamic lift distribution, unfiltered (top) and the first 10 harmonics subtracted (below).

I'=

0.149, <>s

= +5.05°,

CT/"

= 0.058.

1.0

.a

.6 .4 .2 .0 -.2 -.4 -.6 -.8 -.5 1.0

. a

.6 .4 .2 ~ I ~

.o

"'

';::--.2 -.4 -.6

j.-.

~

.

...

.. -.8

§~,·

-1.0 -1.0 -.5 r/R ( -) Yrunnel

.o

r/R (-) .5 1.0 1.0

Mo.zs (Nm/m)

• 2.0 mox • 1.a 2.0 • 1.6 1.8 ll!fj 1.4 1.6 ll!fj 1.2 • 1.4 CJ 1.0 • 1.2

ra

.a

1.0

ra

.6 ,

.a

l!l!l .4 • .6 111!1 .2 . .4

m

.o,

.2

m

-.2,

.o

l!!il -.4. -.2 l!:!!l -.6. -.4 l'3J -.8 • -.6 CJ -1.0. -.8 Cl -1.2,-1.0 Cl -1.4. -1.2 IE:! -1.6. -1.4

m

-1.8,-1.6 • -2.0. -1.8 • -2.2. -2.0 • -2.4. -2.2 • -2.6. -2.4 • -2.8. -2.6 • -3.0. -2.8 • -3.2. -3.0 • -3.4. -3.2 • -3.6. -3.4 • -3.8. -3.6 • -4.0. -3.8 • -4.2. -4.0 • -4.4, -4.2 • min, -4.4

•

•

•

Ill ll!fj l!!ll Ill!! lll!i 1!111 lll!i 1111 11!1 l!!ll Gl G:l CJ CJ CJ 1!:!3 Ill

•

•

•

•

•

•

•

_•

•

_•

•

•

•

•

1.7 , max 1.6 • 1.7 1.5 • 1.6 1.4 • 1.5 1.3 • 1.4 1.2 • 1.3 1. 1 • 1.2 1.0 1. 1 .9 1.0 .8 .9 .7 .8 .6 .7 .5 .6 .4 .5 .3 .4 .2 .3 .1 .2

.o

.1 -.1 .0 -.2. -.1 -.3. -.2 -.4. -.3 -.5. -.4 -.6. -.5 -.7. -.6 -.8. -.7 -.9. -.8 -1.0. -.9 -1.1 ,-1.0 -1.2,-1.1 -1.3. -1.2 -1.4, -1.3 -1.5. -1.4 min, -1.5

Figure 7: Aerodynamic moment distribution about

c/4,

unfiltered (top) and the first 10 harmonics sub-tracted (below).

I'=

0.149,

as=

+5.05°,

Crfu =

0.058.

30

25

20

i

10

15

-

.,

₅

~ ..::.::

0

-

~ I

_-5

-10

-15

-20

O.o

_

..

,

. - - - · - · - · ,! ·...., " ' ·

-·-.-·

_____

...

-·--·- i '·,,

---·-·

'·

.-...

---·-·-·-·-·-·-Figure 8: Leading edge pressure time history at rfR

=

0.6, 0.7, 0.75, 0.8, 0.87, 0.9, 0.94, 0.97, 0.99. Sensor position: 3% chord, upper side. p.

=

0.314, as= -0.9', Crfcr

=

0.058.

-P

at

3% upper chord, 80105, J.L=0.314, as=-0.94°

-P (kPa)

-.6 -.6

Vrunnel

Experiment

-Prediction

+

+

• 4.50 , max • 4.25 • 4.50 - 4.00. 4.25 liil 3.75 • 4.00 llill 3.50 ' 3. 75 llill 3.25 • 3.50 151 3.00 • 3.25 llill 2.7{> • 3.00 1111 2.00 • 2. 7ll IIIII 2.25 , 2.50 Ill 2.00 • 2.25 1111 1.75 • 2.00 51 L.50 , 1. 75 llill 1.25 • 1.50 1:;::} 1.00 • 1. 25 Cl .75 • 1.00 Cl .50 • .75 Cl .25 • .50

m

.oo .

.25 11!11 -.25 • .00 • -.50. -.25 - -.75. -.50 • -1.00. -.75 - -1.25. -1.00 - -1.50. -1.25 • -1.75. -1.50 • -2.00.-1.75 • -2.25 • -2.00 • -2.50 • -2.25 • -2.75. -2.50 - -3.00 • -2.75 • -3.25 • -3.00 • -3.50 '-3.25 =-~--=='r----..,...__j

•

mJn • -3.50

Figure 9: Leading edge pressure distribution (first 6 harmonies subtracted) and BV!locations in the rotor disk. Sensor position: 3% chord, upper side. Comparison of theory (Beddoes' wake model) and experiment below. p.

= 0.314,

as=

-0.9°,

Crfu

=

0.058.

7

"'

c.

..

I

~

-

_"'

_I 1.0 .5 .0

r/R a

0.800

b.'f1=z.o·

/

l

ll1f

₂

=

1.6"

frM.1 = 35.6"

p, ..

12°

\_

frM,2 = 40.6°

I

Pz'"

so

_~

-.~ -1.0

1~/

v

I

30 31 32 33 3~ 35 36 37 38 39 ~ .1 42 43 44 45

"'

(') -2 85 4 2 0 -2 280

r/R

= 0.900

'1/irM

=

93.6°

p ..

70°

""

'

..

87 88

r/R •

0.990

YrM = 291.2°

p ..

42"

281 282 28:i 89 284 285 91 286

!!."{1=2.5°

92 93

"'

(') 287 288

"'

(') I . 94 289 95 97 99 100

ll"f=3.8"

290 291 292

Figure 10: Leading edge pressure time history at selected locations for vortex core radius evaluation. Sensor

position: 3% chord, upper side. p.

= 0.314,

as= -0.9', Cr/<r

= 0.058.

1f; -

0,90,180,270°

1f;

=

45, 135,225,315°

Vrunnel

1f;

=

15,105, 195,285"

1f;

=

60,150,240,330°

\

'

_'

'

\

1f;

=

30,120,210,300°

,

1f;

=

75,165,255,345°

Figure 11: Wake geometry and instantaneous vortex positions at various BV!locations for identification of the angle

fl.

/1

= 0.314,

as=

-0.9°,

Cr/tr

=

0.058.

.8 .6 .4 .2 ~ I :::;.-~

"'

.o

Yrunnel ';:--.2 -.4 -.6 -.8 -1.0 -1.0 -.5 1.0 1.0 . 8 .6 .4 .2 ~ I ~

.o

"'

';:- Yrunnel -.2 -.4 -.6 -.8 -1.0 -1.0 -.5 .5 1.0 r/R

H

• 1000, max • 950 '1000 • 900 ' 950 111.!1 850 ' 900 11!!1 800 ' 850 mll 750 ' 800 1:!!1 700 ' 750 lllll 650 ' 700 Ill! 600 ' 650 1111 550 ' 600 ill! 500 ' 550 IIIII 450 , 500 111.!1 400 ' 450 l:!i 350 ' 400 IE!:! 300 ' 350

•

•

•

•

111!1 1:!!1 IIIII 111!1 Ill IIIII 1111 1111 IIIII lllll lllll El El Cl lllll

..

_•

•

•

_•

•

•

_•

•

•

_•

•

•

_•

•

250 ' 300 200 ' 250 150' 200 100 ' 150 50 ' 100 0 ' 50 -50' 0 -100, -50 -150' -100 -200' -150 -250' -200 -300' -250 -350' -300 -400' -350 -450' -400 -500' -450 -550' -500 -600' -550 mtn, -600 180' max 170 ' 180 160' 170 150 ' 160 140 ' 150 130' 140 120 ' 130 110 ' 120 100 ' 110 90 100 80 90 70 80 60 70 50 60 40 50 30 40 20 30 10 : 20 0 10 -10 : 0 -20. -10 -30. -20

-•o.

-30

-so.

-40 -60' -50 -70' -60 -80' -70 -90. -80 -100' -90 -110' -100 -120' -110 -130' -120 -140,-130 min,-140

L {N/m)

Figure 12: Aerodynamic lift distribution, unfiltered (top) and the first 6 harmonics subtracted (below).

p

=

0.314,

as=

-0.9°,

Cr/u

=

0.058.

Moment distribution,

1.0 .8 .6 -.8 -l.0+---~----~----~---1 -1.0 -.5 1.0 _lili!

m

lili! .8 Ell Ell Ell .6 li!l

_m

m

.4

_m

Ell !l!l Ell .2 [2! 0 ~ 0 I

-

.o

_Vrunnel

c:J

"'

El ~

m

8 -.2 lim lim

m

-.4 lili! 1m lim -.6 lili! _lili!

m

1m -.8 lllll lili! ll!lll -1.0 Iii -1.0 r/R (-)

M

_0.25

(Nm/m)

3.6 1 mcx 3.3 ' 3.6

:;.o ,

3.3 2.7 • 3.0 :2.4 ~ 2.7 2.1 • 2.4 1.8 • 2.1 1.5 • 1.8 1.2 • 1.5 .9 • 1.2

.s .

.9 .3 • .6 .0 • .3 -.3.

.o

-.6. -~3 -.9 ~ -.6 -1.2, -.9 -1.5. -1.2 -1.8. -1.5 -2.1 , -1.S -2.4. -2.1 -2.7. -2.4 -3.0. -2.7 -3.3. -3.0 -3.6. -3.3 -3.9. -3.6 -4.2. -3.9 -4.5. -4.2 -4.8 f -4.5 -5.1. -4.8 -5.4. -5.1 -5.7. -5.4 -6.0. -5.7 mtn, -6.0 2.55

_•

max 2.40

_•

2.55 2.25 2.40 2.10 : 2.25 1.95

.

2.10 1.80 1.95 1.65 : 1.80 1.50 , 1.65 1.35

_•

1.50 1.20 J 1.35 1.05

_•

1.20 • 90

_•

1.05 . 75

_•

.90 • 50 , .75 .45

_•

.60 .30 , .45 .15

_•

.30 • 00

_•

.15 -. 1!5 • .00 -.30 t -.15 -.45. -.30 -.60 l -.45 -.75, -.60 -.90. -.75 -1.05. -.90 -1.20.-1.05 -1.35.-1.20 -1.50,-1.35 -1.65 , -1.50 -1.80 • -1.65 -1.95.-1.80 -2.10.-1.95 -2.25.-2.10 min, -2.25

Figure 13: Aerodynamic moment distribution about cf4, unfiltered (top) and the first 10 harmonics sub-tracted (below). J.1

=

0.314,

os

=

-0.9°, Cr/tr

= 0.058.