19840008075 - nasa · the free-streamspeed of sound, w refers to the blade radial station. the...

NASA Technical Memorandum 85872

NASA-TM-85872 19840008075

rHOT to BE TAKEN fUOM nUB RooM?

Comparison of Calculated and.Measured Pressures on Straightand Swept-Tip Model RotorBladesMichael E. Tauber, I-Chung Chang, David A. Caugheyand Jean-Jacques Philippe

December 1983

FFR 6 1984

LANGLEY RESEARCH CENTERLIBRARY, NASA

HAjI"lU>.TOI'II, VIRGINIA

NI\S/\National Aeronautics andSpace Administration

https://ntrs.nasa.gov/search.jsp?R=19840008075 2020-04-17T21:44:29+00:00Z

3 1176 00517 7812

NASA Technical Memorandum 85872

Comparison of Ca~culated andMeasured Pressures on Straightand Swept-Tip Model RQtorBladesMichael E. Tauber,I-Chung Chang, Ames Research Center, Moffett Field, CaliforniaDavid A. Caughey, Cornell University, Ithaca, New YorkJean-Jacques Philippe, ONE RA, Chatillon, France

NI\SI\National Aeronautics andSpace Administration

Ames Research CenterMoffett Field, California 94035

COMPARISON OF CALCULATED AND MEASURED PRESSURES ON STRAIGHT- ANDSWEPT-TIP MODEL ROTOR BLADES

Michael E. Tauber, I-Chung Chang, David A. Caughey,*and Jean-Jacques Philippet

Ames Research Center

SUMMARY

Using the quasi-steady, full potential code, ROT22 , pressures were calculatedon straight- and'swept-tip model helicopter rotor blades at advance ratios of 0.40and 0.45, and into the transonic tip speed range. The calculated pressures werecompared with values measured in the tip regions of the model blades. Good agreementwas found over a wide range of azimuth angles when the shocks on the blade Were nottoo strong. However, strong shocks persisted longer than predicted by ROT22 when theblade was in the second quadrant. Since the unsteady flow effects present at highadvance ratios primarily affect shock waves, the underprediction of shock strengthsis attributed to the simplifying, quasi-steady, assumption made in ROT22.

INTRODUCTION

The emphasis on increasing helicopter flight speed has resulted in higher rotoradvance ratios and tip Mach numbers. However, it is essential that desired performance improvements not be made at the expense of increasing noise. The formation ofshock waves in the transonic flow on the advancing blade is a major source of highpower requirement and high-speed noise. Therefore, it is essential to understandand to calculate this three-dimensional, unsteady, transonic flow field.

The first three-dimensional, transonic calculations for flow over rotor bladeswere performed by Caradonna and Isom (ref. 1), using small disturbance theory. Thecalculations were made for a non1ifting rotor in hover such that the tip speed wasrepresentative of forward flight. Subsequently, this steady formulation was extendedto the unsteady, forward flight case (ref. 2); however, the spanwise free-streamvelocity component due to rotation was assumed to be small and thus ignored. Grant(ref. 3) included all free-stream velocity components in his solution of the transonic small disturbance equation for non1ifting forward flight, but assumed quasisteady flow.

~ In contrast to the difficulties encountered in calculating the rotary wing flowfield, computer codes for solving the three-dimensional transonic flow over liftingfixed wings have been available for some time. A widely used one is the full poten·tial code, FL022 , developed by Jameson and Caughey (ref. 4). The FL022 code solvesthe nonconservative, inviscid, full potential equation using exact surface tangencyboundary conditions. The ROT22 code (refs. 5 and 6) was developed by reformulatingFL022 to calculate the flow about a lifting rotor blade in forward flight. Althoughthe full potential equation is solved, the formulation is quasi-steady in that thetime derivatives of the perturbation potentials were neglected in the interest of

*Cornell University, Ithaca, ' New York.tONERA, Chatillon, France.

greatly speed~ng the computation. Since the unsteadiness of the flow increases withadvance ratio, it is important to determine the effect of the quasi-steady assump~

tion on the flow field calculation at high advance ratios. Also in high-speed forward flight, it was proven advantageous to sweep the blade tips to delay shock formation. The objective of the present computation/experiment comparison is to .determine the ability of the ROT22 code to predict pressure distributions on nonlifting straight- and swept-tip blades at high rotor speeds and high advance ratios.

TEST CONDITIONS AND MODEL CONFIGURATIONS

The pressure measurements used were made by ONERA (refs. 7 and 8) on modifiedA10uette helicopter tail rotor models having non1ifting, sYmmetrical, airfoil sections. The test was conducted using a rotor on a stand in a wind tunnel; rotor speedand tunnel velocities were varied to achieve desired advance ratios. Two differentrotor blade configurations were tested. One had a nearly straight leading edge anda 75-cm radius from the center of rotation (fig. 1); the second configuration (whichhad a radius of 83.5 cm) had 30 0 of leading edge sweep on the outer 15% (fig. 2).Both types of blades had sYmmetric NACA four-digit airfoils, varying in thicknessto-chord ratio from 17% at the widest chord station to 9% at the tip.

Instrumentation on both blades consisted of three chordwise rows of Ku1ite LDQLpressure transducers, nominally at the 85%, 90%, and 95% radial stations. To achievethe desired instrumentation density, two tips were built for each configuration. Thestraight tips were nearly identical. However, the swept tips differed slightly, thusintroducing some scatter in the data, notably at the middle, most densely instrumented, stations. The measured data were transmitted via an electro-pneumatic switchand slip rings to amplifiers. Mean instantaneous pressures were computer averaged;values were measured at 256 blade azimuthal positions. On the straight blade, thethickness-to-chord ratios at the instrumented stations were,in the direction of thetip, 13.1%, 12.15%, and 10.6%; while for the swept-tip blade the ratios were 13.5%,12%, and 10.5%.

COMPUTATIONS

The ROT22 code, described in references 5 and 6, with the correction of reference 9, was used to calculate the pressure distributions on the blades. ROT22 solvesa quasi-steady approximation to the three-dimensional, full potential equation in ablade-attached coordinate system. The quasi-steady approximation greatly reducescomputation time, since the true time-dependent history of the solution need not becomputed. A computational grid of 120 points chordwise, 16 vertically, and 24 spanwise, was used for the straight blade; resolution was more critical for the swept-tipblade,and the number of spanwise stations was increased to 32. About two-thirds ofthe spanwise computational stations were on the blade; the remainder were in thefield inboard and outboard of the blade tip. Using an efficient, fully vectorizedversion of the code on a CRAY IS computer, computation times of 20-30 sec per casefor the straight blade, and 40-50 sec for the swept-tip configuration were obtained.

2

RESULTS AND DISCUSSION

The results of the ROT22 computations were compared with the ONERA measurementsat blade azimuth angles of 30°, 60°, 90°, 120°, 150°, 180°, and 270° for advanceratios of 0.40 and 0.45 (see table 1). For the straight blade, the spanwise meshspacing was adjusted so that a computational plane was located at the middle instru-·mented station (0.892) while for the swept-tip blade, the crank in the tip (0.857station) was matched. The pressure coefficients were linearly interpolated betweenthe nearest computational stations for the other two radial stations. The pressurecoefficient was defined as

Cp

= 1 1:2.-. _ ]\o•7M~ \Poo ')

where the section Mach number was

(1)

(2)

Here Voo was the forward flight speed, aooblade rotation rate, and the subscript s

the free-stream speed of sound, wrefers to the blade radial station.

the

Theory and experiment compared well for the straight blade at an advance ratioof 0.4 at all azimuth angles except 270°1 (see figs. 3(a)-3(g». At the important90° position (fig. 3(c», the tip Mach number was 0.84, resulting in a sizable regionof supersonic flow. However, at 120° the flow was entirely subsonic. At the higheradvance ratio of 0.45, and a maximum tip Mach number of 0.87, agreement with the datawas again good (figs. 3(h)-3(n». The exception was at 120° where a pocket of supersonic flow was present near the leading edge, and the subsequent shock persistedlonger than was calculated; this caused the peak expansion pressures to be somewhatunderpredicted.

The swept-tip blade represents a more complex geometry than the straight, andexperienced higher tip Mach numbers since the tip speed was increased from 200 m/secto 210 m/sec. At the advance ratio of 0.40, the maximum tip Mach number was 0.88,and at 0.45 it was 0.91. In general, the agreement was not as good as for thestraight blade; however, there was also more scatter in the data for the swept-tipcases. Still, agreement at both advance ratios (figs. 4(a)-4(n» was good in thefirst quadrant to about 60° and in the second quadrant beyond 120°. At 90° (figs. 4(c)and 4(j», at the station where the crank in the p1anform occurs, the pressure expansion rate near the leading edge is somewhat overpredicted; however, it is possiblethat viscous effects were responsible due to the abrupt change in leading edge sweep.At 120° (figs. 4(d) and 4(k», the tendency of the supersonic region and its terminating shock to persist longer and be stronger (the shock was farther aft) than predicted by the quasi-steady calculation is noticeable. The combination of the 30° tipsweep angle and the 120° azimuth angle resulted in peak Mach numbers on the blade

1At 270° there was much scatter in the data for all cases since the pressureswere below the sensitivity range of the gauges. While ROT22 does not treat thereverse flow, inboard region, of the blade accurately, the calculation of the flowon the outboard part of the blade should not be strongly affected by the inaccuraciesin the reverse flow region.

3

surface which were almost as high as those at 90° azimuth. Therefore, the region ofsupersonic flow persisted farther into the second quadrant when the tip was sweptback, as was previously discussed in reference 8.

CONCLUSIONS

Calculations from the ROT22 quasi-steady full potential rotor flow field codewere compared with pressure distributions measured by ONERA on straight- and swepttip model rotors at advance ratios of 0.40 and 0.45.

For the straight blade at an advance ratio of 0.4 (corresponding to a tip Machnumber of 0.84 at 90° azimuth), the calculated and measured pressures agreed well.At the higher advance ratio of 0.45 (corresponding to a peak tip Mach number of 0.87),agreement was still good, except at 120° where the supersonic region and the shockpersisted longer than predicted by the quasi-steady calculation. The importance ofthe unsteady effects for this case was also shown in reference 10 using time-dependentsmall disturbance theory.

For the swept-tip blade at the 0.4 advance ratio, the tip Mach number was 0.88at 90° azimuth and for the 0.45 advance ratio it was 0.91. For both advance ratios,agreement was good to azimuth angles of about 60° and beyond 120°. At 90°, the pressures were somewhat overpredicted, especially near the crank in the tip. At 120°,the shock strength and locations were underpredicted by the quasi-steady code.

In summary, the unsteadiness of the flow affected shock waves and their positionmost in the second quadrant, beyond 90° azimuth. When the combination of tip Machnumber, advance ratio, and airfoil thickness ratio produced relatively weak shocks,the ROT22 code gave good results. However, when the shocks were strong, they persisted longer on the blade than predicted by the quasi-steady calculation; this wasespecially noticeable at the 120° blade position.

4

REFERENCES

1. Caradonna, F. X.; and 1som, M. P.: Subsonic and Transonic Potential Flow overHelicopter Rotor Blades. AIAA Journal, vol. 10, no. 12, Dec. 1972,pp. 1606-1612.

2. Caradonna, F. X.; and Isom, M. P.: Numerical Calculation of Unsteady TransonicPotential Flow over Helicopter Rotor Blades. A1AA Journal, vol. 14, no. 4,Apr. 1976.

3. Grant, J.: Calculation of the Supercritica1 Flow over the Tip Region of a Non-Lifting Rotor Blade at Arbitrary Azimuth. Royal Aircraft EstablishmentTechnical Report 77180, Dec. 1977.

4. Jameson, A.; and Caughey, D. A.: Numerical Calculation of the Transonic FlowPast a Swept Wing. Courant Institute of Mathematical Sciences, COO-3077-140,New York University, N.Y., June 1977.

5. Arie1i, R.; and Tauber, M. E.: Computation of Subsonic and Transonic Flow aboutLifting Rotor Blades. AIAA Paper 79-1667, Aug. 1979.

6. Arie1i, R.; and Tauber, M. E.: Anaa1ysis of the Quasi-Steady Flow about anIsolated Lifting Helicopter Rotor Blade. Joint Institute for Aeronauticsand Acoustics TR-24, Stanford University, Aug. 1979.

7. Caradonna, F. X.; and Philippe, J. J.: The Flow over a Helicopter Blade Tip inthe Transonic Regime. Vertica, vol. 2, 1978, pp. 43-60.

8. Monnerie, B.; and Philippe, J. J.: Aerodynamic Problems of Helicopter BladeTips. Vertica, vol. 2, 1979, pp. 217-231.

9. Chang, I. C.; and Tauber, M. E.:tia1 Flow Past a Cranked Wing.

Numerical Calculation of the Transonic Poten-·NASA TM-84391, 1983.

10. Chattot, J. J.; and Philippe, J. J.: Pressure Distribution Computation on aNonlifting Symmetrical Helicopter Blade in Forward Flight. La RechercheAerospatia1e (English version), no. 1980-5, pp. 19-33.

5

TABLE 1. - TABLE OF FIGURES

1\ Tip configuration

$\. Straight Swept0.4 0.45 0.4 0.45

30° 3a 3h 4a 4hI

60° 3b 3i 4b 4i90° 3c 3j 4c 4j

120° 3d 3k 4d 4k150° 3e 31 4e 41180° 3f 3m 4f 4m270° 3g 3n 4g 4n

6

p-Mo.:tN

1

- N (If)

<i. <i. <i.~

~ ~CI) CI)

J"'=/ .:r -

II~f--- IIi ------ ----------------- I- - ----

~ III ~ Lt)...cC(l)...

-VI -.co.....:::-

~

RAD. =750 mmR = 0.855 0.892 0.946 -

+

Figurel.- ONERA straight blade geometry.

«ICI)

-~f- - -- - -+--i-::

co

---1-- - -- - -- - _

Ifa~-1

R = 0.857 0.9080.955· I~------------------RAD. = 835 mm--------------------..

+

Figure 2.- ONERA swept-tip blade geometry.

Ms =0.686C *p

STATION 3

Ms =0.654C *p

STATION 2

Ms = 0.631

STATION 1-1.0...---------------.-----------------..--------------.

-.8

-.6

-.4

-.2

o .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0X/C

-------------_._---:.>-----

1.01.2 L....::::::t=.....L.--L---l~d==:::t::::::I.:__L___..JL__L..::::::::h=_1..__.JL__..!.....===!=::::::i:::::::I=_L_..l.__L..:::::::±=_'L_...L_.J__=b=::t::::::::r::::.:::::...t.__L___.J

o .1 .2 .3 .4 .5 .6 .7 .8 .9 0 .1 .2 .3 .4 .5 .6 .7 .8 .9X~ X~

oCp .2

.4

.6

.8

Figure 3.- Theoretical and experimental pressure comparison for straight blades.

•

Ms =0.783

•

STATION 3

Ms = 0.751

•

~. ~.. .c* •p •

STATION 2

•

Ms =0.729

•

c*p•

.1 .2 .3 .4 .5 .6 .7 .8 .9 1.0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0 .1 .2 .3 .4 .5 .6 .7 .8.9 1.0X/C X/C X/C

o.2

.4

.6

.8

1.01.2 l:::::::l::==.L-...L--..I...-..=d===±::::::c:::r=:.....t---L:::::::I::::......L-L---I..-=:=b~::::::I::::::I~_I~b.....L_L_.l..._.J=:±:::::::t:::::::c:::L..._l

o

STATION 1-1.0,...---------------r---------------,-----------------,

-.8

-.6

-.4

-.2

f-'o

(b) II = 0.4, 1Ji= 60 0•

Figure 3.- Continued.

STATION 2 STATION 3

IVls =0.751 Ms =0.773 Ms =0.806

c* •• • c*p• • p •

• ••

STATION 1-1.0...--------------...------------'-----r---------------,

-.8

-.6

-.4

-.2

o.2

.4

.6

.8

1.01.2 L::::::±:=.""---..L-......L-='===i:::=:c=c~__l:::::::::::i:=_IL.::....-.L_i_.=J::=:±::::::::i::::::c:L___l:::::::::±:=_1____l___l_I==:t=::=:c::::c==:L.J

o .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0X/C X/C X/C

(c) p = 0.4, W= 90°.


STATION 1 STATION 2 STATION 3-1.0

-.8 c* Ms =0.719 Ms =0.741 Ms =0.774

-.6• P

• c*• •-.4 • P

• •

-.2

I-' cp0

N.2

.4

.6

.8

1.0

1.20 .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0

X/C X/C X/C

Cd) ~ = 0.4, ~ = 120°.


c* Ms = 0.686P

STATION 3

•• •

STATION 2

.1 .2 .3 .4 .5 .6 .7 .8 .9 1.0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0 .1 .2 .3 .4 .5.6 .7 .8 .9 1.0~c X~ X~

STATION 1-1.0 r--.........,..-----------r-~----------___,._------------__,

c*-.8 Ms =0.631 P Ms =0.654

-.6 •

-.4

-.2

o.2

.4

.6

.8

1.0,1.2 t:::::1::::=.J---l.---J..-=b~::::::r::=L~i:::::l:=_L_.......L.-...J.....d:=:::t:::::::::r::::::::::cc.~b_i___.l____l_!=:d::::::!::::::I:::I~

o

(e) ~ = 0.4, ~ = 150°.


Ms =0.566

A

STATIQN 3

A

Ms =0.534

A A A

A

STATION 2

A

.4 .5 .6 .7 .8 .9 1.0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0X/C X/C X/C

Ms =0.512

STATION 1-1.0

-.8

-.6A

-.4

-.2

I-'Cp

0.po

.2

.4

.6,

.8

1.0

1.20 .1 .2 .3

(f) ~ = 0.4, ~ = 180°.


Ms = 0.327

STATION 3

Ms =0.295

STATION 2STATION 1-1.0 r--------------,....--------------r--------------,-.8 Ms =0.272

-.6

-.4

-.2

o.2

• •• •

.6

.8

1.01.2 t:::::i::=-I............JL......J--d~=::::::I::::::I=:i:=_t:::::::±::::_L..__L~_=I::::=:t::::::c:::::c:~_.t::::::t==_l.____I____L_....I=:::::t=::~::c::::L::l

o .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0.1 .2 .3 .4 .5 .6 .7.8 .9 1.0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0X/C X/C X!C

(g) ~ = 0.4, ~ = 270°.


STATION 1 STATION 2 STATION 3-1.0 c*p Ms =0.646 c* Ms = 0.669 Ms =0.701-.8 p c*-.6

P~

'"'"-.4 '" '"

-.2 '"'"

0f-" cp0'\ .2

.4

.6

.8 -----1.0

1.20 .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0

X/C X/C X/C

(h) p = 0.45, ~ = 30°.


.7 .8 .9 1.0

..

Ms =0.811

STATION 3

..

Ms = 0.779

STATION 2

....

Ms =0.757

STATION 1-1.0.--------------r--------------,...----------------,

-.8

-.6

-.4

-.2

o.2

.4

.6

.8

1.0

1.2 0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0 .1 .2 .3 .4 .5 .6X!C X!C

(i) ~ = 0.45, ~ = 60°.


STATION 3

Ms = 0.836

•

Ms =0.803

•

•

.1 .2 .3 .4 .5 .6 .7 .8 .9 1.0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0.1 .2 .3 .4 .5 .6 .7 .8 .9 1.0X/C X/C X/C

o.2

.4

.6

.8

1.0,

1.20

I-'00



-.8&

Ms =0.745& &

Ms =0.767 Ms =0.800

-.6&

c* /

P c* .c*---P-.4 & • P ••

&

-.2

I-' cp 0\D

.2

.4

.6

.8

1.0 ---

1.20 .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0 .~ .2 .3 .4 .5 .6 .7 .8 .9 1.0

X!C X!C X!C

(k) 1.I = 0.45, IjJ = 120°.


STATION 1 STATION 2 STATION 3-1.0 c*p Ms =0.646 c* Ms =0.669 Ms =0.701-.8 p c*

-.6P..

-.4 •

-.2 ! ..N cp

0,0

.2

.4

.6

.8

1.0

1.20 .1 .2 .3 .4 .5. .6 .7 .8 .9 1.0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0 .1· .2 .3 .4 .5 .6 .7 .8 .9 1.0

X!C X/C: X/C

(1) p = 0.45, ~ = 150°.


Ms =0.566

STATION 3

Ms =0.534

• • •

STATION 2

Ms =0.5'2

STATION'

o.2

.4

.6

.S

'.0'.2Ob::±.'=-.2L.-..L3 ---1.4-=.5:b=.::t:6:::::::J.7C.:iS=:l.g=-,.tO::::::±.,=-'.2L.-•..L3----J.4---=.5:b==t.6:::::.7C.::lS:::i.gL::..,.t.O=::::::::i.,==-.2J---L.3--1.41-..1=:5==t.6===.7:C::::I.S==.gU,.0

X1C .X/C 'X/C

-'.0-.S

-.6

-.4

(m) ~ = 0.45, W= 180°.


Ms =0.297

..

STATION 3

..Ms =0.265

..

STATION 2

.. ..

Ms = 0.242

....

STATION 1-1.0 .....--------------.---------------....--------------,

-.8

-.6

-.4

-.2

Cp 0

.2

.4

.6

.8

1.01.2 L:::::::!:=..L..-L-J.,........,:b=::t=:::::r:.=C::L.--t::::::b...L.-..l..-.....L.-.d=:±:::::c::::c:L.._t:::::::6--L-L-l--=b=i=:::::::t:::::::c=I=:J

o .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0~C ~C X~

NN

(n) II = 0.45, 1jJ = 270 0•

Figure 3.- Concluded.

STATION 3STATION 2STATION 1-1.0 r---------------,---------------......---------------,

Ms =0.726

C*p

Ms =0.696

..

C*p

.7 .8 .9 1.0.1 .2 .3 .4 .5 .6 .7 .8 .9 1.0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0X!C X!C

Ms =0.664c*p-.8

-.6

-.4

-.2

Cp 0

.2

.4

.6

.8

1.0 L:::::::t=....L.....-....L-....l.-.d=~:=:r::::L.__L'_l::=:::::t=-l_L_J.......b=:±::::::::c::::::c~_t:::::::::b=_oL___l---JI........_.ib=±=:::c::::c::::...t.__.J

o .1 .2 .3 .4 .5 .6X!C

NW

Figure 4.- Theoretical and experimental pressure comparison for swept-tip blades.

STATION 1-1.0

-.8Ms =0.756

-.6 c*p-.4 • • •

•-.2 •

N cp 0.j::-o

.2

STATION 2

Ms =0.788

c*p ••• •

STATION 3

•

Ms =0.818

.7 .8 .9 1.0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0X/C X/C

.4

.6

.8

1.0 L:::::::i::::::.-~L......1...-=:b=::t:::=I:::::CLl::::::::l=..l......-..l.-...l....-d.=:±::=:::r::::::c::=L.....t::::::i::=-I...---l.......--l...-b:=±:::::::::t:::::::c::L:Jo .1 .2 .3 .4 .5 .6

X/C

(b) 1.1 = 0.4, 1/1 = 60 0•



-.8Ms =0.790 Ms =0.822 Ms =0.852

-.6 ~c* • • • •

-.4 P • c*• • p c*-.2 P

N •V1 cp 0

.2

.4

.6

.8

1.00 .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0

X/C X/C X/C

(c) 1..l = 0.4, ljJ = 90°.



-.8Ms =0.756 Ms =0.788 Ms =0.818

•• •-.6 c* • • •p.

c*-.4 P•• •-.2 • •

•N Cp 00\

.2

.4

.6

.81

1.00 .1 .2 .3 .4 ..5 .6 .7 .8 .9 1.0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0

X!C XlC X!C

Cd) V = 0.4, ~ = 120°.


STATION 1-1.0

C* Ms =0.664-.8 P

-.6o.

o. o.I

-.4 o.

-.2o.

N Cp 0-....J

.2

STATION 2

C*Po.

o. o.o.

Ms =0.696

o.o.

o.o.

STATION 3

o.

C*p

Ms = 0.726

o.

o.

.4

.6

.8

1.0 0 2.1 . .3 .4 .5 .6 .7 .8 .9 1.0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0.1 .2 .3 .4 .5 .6 .7 .8 .9 1.0

X/C X/C X/C·

(e) ~ = 0.4, W= 150°.


Ms =0.600

STATION 3

• •

Ms = 0.571

•.•

STATION 2

•

Ms =0.539

• •

•

STATION 1-1.0 ,...--------------..,---------------.----------------,

-.8

-.6

-.4

-.2

Cp 0

.2

.4

.6

.8

1.0 L:::::±=".J.....-.l..--..1.-=d::=:::c:::::L:.:Ll--L:::::::i::==..L..-...l..-...l...-d=:::±::::::::r:::::::c:::=:L..-i:::::::±=-J.......---L-----L-....d==±=::::I:::I::=L=.Jo .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0

X!C X!C X!C

N00

(f) ~ = 0.4, ~ = 180°.


STATION 1-1.0

-.8

-.6

-.4 ..-.2

N\.0 Cp 0

.2

.4

Ms =0.287

STATION 2

Ms =0.319

STATION 3

Ms =0.349

.6

.8

1.0 L:::::.::±=...l.....-..L-.....L-,.d=::::::±::::::I:::::::i.---L--l~=-l-.JL-L.....k=±=:::r::::x:::..L-L:::::::::b~---l.---l~b=±:=::::t:=:J::=..L-.J

o .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0X/C X/C X/C

(g) l.l = 0.4, 1/J = 270°.


STATION 3STATION 2STATION 1-1.0 r-------------'----~------------__.__------------.....,

Ms = 0.742Ms =0.712

C*p

Ms = 0.680·C*p-.8

-.4

-.2

Cpt 0

.2

.4

wo

.7 .8 .9 1.0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0XlC' X/C

.6

.81.0 t::::::i=-.l..-...JL.....J--=oI==::l::::::::r:::.:::L~__l::::::.±:__l....__L___l_...d:=±:::::::c::c:=L=t:::~_L___L____l._...b==:l=:::r:::::c:=CJ

o .1 .2 .3 .4 .5 .6X/C'

(h) II = 0.45, 1/J = 30°.


.)

Ms =0.845

c*p

STATION 3

Ms =0.816

C*· .p •

STATION 2

Ms =0.784

c*• p.

STATION 1-1.0 .....-------------- -------------r---------------,

-.8

-.6

-.4

-.2

cp a.2

.4

.6,

.8

1.0 L::::::l:=..JL..-JL.-....J-=::I==t:=:::I::::L==:L_t::::::::±:=:...I...-L--l--=:b:;=±::==:c:::::c:=L:=.t::::::b-L--l---J-...bd:::::::C::::C::cJa .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0.1 .2 .3 .4 .5 .6 .7 .8 .9 1.0

X!C X!C X!C

(i) p = 0.45, $ = 60°.


Ms =0.883

STATION 3

Ms =0.854

STATION 2

Ms =0.822

STATION 1-1.0 r--------------;r--------------.----------------,

-.8

WN

•• ••• •

C*p

.6

.8

1·°0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0X/C ' I X/C X/C

(j) p = 0.45, $ = 90°.


Ms = 0.845•

c*p

STATION 3

• •

Ms =.0.816

c*p

STATION 2

Ms = 0.784

.4

.6

.8

1.00 .1 .2 .3 .4 .5 .6 .7 .8 .9 0 .1 .2 .3 .4 .5 .6 .7 .8 .9 0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0X/C X/C X/C

STATION 1-1.0 .-----...,------------.----------------...,...,----------------,

-.8• •

-.6 r-.4 p•

-.2

Cp 0

.2

(k) p = 0.45, ~ = 120°.



Ms =0.680 • Ms =0.712 Ms =0.742-.8 c* . .

p •. .c* •-.6 • • P

-.4 •• • •• •

-.2 • •w cp.p-

O

.2

.4

.6

.8

1.00 .1 .2 .3 .4 .5 .6- .7 .8 .9 0 .1 .2 .3 .4 .5 .6 .7 .8 .9 0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0

X/C X/C X/C

(1) ~ = 0.45~ W= 150°.


.,

• •

•

STATION 3

Ms =0.571•

STATION 2

Ms = 0.539

STATION 1-1.0r---------------,---------------.--------------,

-.8

••

••

• •• •

.6

.8

1.0 0 .1 .2 .3 .4 .5 .6 .7 .8 .9 0 .1 .2 .3 .4 .5 .6 .7 .8 .9 0 .1 .2 .3 .4 .5 ·.6 .7 .8 .9-1.0X/C X/C X/C

-.6• •

-.4• •

-.2w Cp\Jl 0

.2

.4

(m) p = 0.45, ~ = 180°.


Ms =0.317

STATION 3

Ms =0.288

STATION 2

Ms =0.256

STATION 1-1.0,-------------,..--------------r-r---------------,

-.8

-.6• •-.4 • __• •

-.2

Cp 0

.2

.4

.6

.8

1.00 .1 .2 .3 .4 .5 .6 .7 .8 .9 0 .1 .2 .3 .4 .5 .6 .7 .8 .9 0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0X/C X/C X/C

(n) ~ = 0.45, ~ = 270°.

Figure 4.- Concluded.

-.,

(

1. Report No. 2. Government Accession No. 3. Recipient's Catalog No.

NASA TM- 858724. Title and Subtitle 6. Report Date

COMPARISON OF CALCULATED AND MEASURED PRESSURES ONDecember 1983

6. Performing Organization CodeSTRAIGHT- AND SWEPT-TIP MODEL ROTOR BLADES ATP

7. Author(s) 8. Performing Organization Report No.

Michael E. Tauber, I-Chung Chang, David A. A-9584Caughev.* and Jean-Jacques Philippe t 10. Work Unit No.

9. Performing Organization Name and Address T-3414YAmes Research Center, Moffett Field, Calif . 94035

11. Contract or Grant No.*Corne11 University, Ithaca, N.Y.t ONERA,Chati11on, France

13. Type of Report and Period Covered12. Sponsoring Agency Name and Address Technical Memorandum

National Aeronautics and Space Administration 14. Sponsoring Agency Code

Washington, D.C. 20546 505-42-1115. Supplementary Notes

Point of Contact: Michael Tauber, Ames Research Center, MS 227-8, -MoffettField, Calif . 94035. (415) 965-5656 or FTS 448-5656

16. Abstract

Using the quasi-steady, full potential code, ROT22, pressures werecalculated on straight- and swept-tip model helicopter rotor blades atadvance ratios of 0.40 and 0.45, and into the transonic tip speed range.The calculated pressures were compared with values measured in the tipregions of the model blades. Good agreement was found over a wide rangeof azimuth angles when the shocks on the blade were not too strong. However,strong shocks persisted longer than predicted by ROT22 when the blade was inthe second quadrant. Since the unsteady flow effects present at highadvance ratios primarily affect shock waves, the underprediction of shockstrengths is attributed to the simplifying, quasi-steady, assumption madein ROT22.

17. Key Words (Suggested by Author(s)) 18. Distribution Statement

Helicopter rotor aerodynamics Unlimited

Subject Category - 02

19. Security Classif. (of this reportl 20. Security Classif. (of this page) 21. No. of Pages 22. Price"

Unclassified Unclassified 39 A03

"For sale by the National Technical Information Service, Springfield, Virginia 22161

III1I111111 ~~rllllll~ Ilrll[r~ll~11 m~ll~11111111111 i

3 1176 00517 7812-- -- --- ------------------

19840008075 - nasa · the free-streamspeed of sound, w refers to the blade radial station. the...

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