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NASA CONTRACTOR REPORT 177507 USAVSCOM TR-88-A-008

Wake Model for Helicopter Rotors in High Speed Flight

Wayne R. Johnson I!

Johnson Aeronautics .)

(IiASA-C€i-l775C7) U A K E UODBL €OB HELXCOPTEE 889-17573 b C T O E S Ili 81Gb SFEED FLIGEIB (Johnson Aeronautics) 3C5 p CSCL O l A

Onclaz G3/02 0 I9 174 1

Prepared for Ames Research Center under Contract NAS2-12767

November 1988

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NASA National Aeronautlcs and Space Administration

US ARM AVlATlO SYSTEMS COMMAND

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AVIATION RESEARCH AND TECHNOLOGY ACTIVIW

https://ntrs.nasa.gov/search.jsp?R=19890008206 2020-07-25T19:56:06+00:00Z

NASA CONTRACTOR REPORT 177507 USAVSCOM TR-88-A-008

Wake Model f o r Helicopter R o t o r s in High Speed F l i g h t

I _ Wayne R. Johnson

I CONTRACT NAS2-12767 I

November 1988

National Aeronautics and Space Administration

Ames Research Center Moffett Field, California 94035

us AR AVlAT SYSTEMS COMMAND

AVIATION RESEARCH AND TECHNOLOGY ACTIVITY MOFFElT FIELD. CA 943051099

TABLE OF CONTENTS

Page

I ..

SYMBOLS AND ABBREVIATIONS ...................................................................... v

SUMMARY .................................................................................................... 1

1 . INTRODUCTION ....................................................................................... 3 1.1 Background ......................................................................................... 3 1.2 Objectives ........................................................................................... 4 1.3 Approach ............................................................................................ 4

2 . HIGH SPEED WAKE MODEL ....................................................................... 7 2.1 Rotor blade loading ................................................................................ 7 2.2 Far wake model .................................................................................... 8 2.3 Geometry ........................................................................................... 10 2.4 Induced velocity calculation ...................................................................... 11

3 . SECOND ORDER LIFTING-LINE THEORY ..................................................... 13 3.1 Objective ........................................................................................... 13 3.2 Outline of second order lifting-line theory ..................................................... 14 3.3 Summary of wake and wing model ............................................................. 21 3.4 Near wake model .................................................................................. 21

4 . LIFIWG-SURFACE THEORY CORRECTION .................................................. 25 4.1 Objective ........................................................................................... 25 4.2 Lifting-surface theory expression ............................................................... 25 4.3 Lifting-line theory expression ................................................................... 27 4.4 Revised lifting-line theory expression .......................................................... 28

5 . OUTLINE OF CALCULATIONS AND CORRELATIONS ...................................... 31 5.1 CAMRAD modifications ......................................................................... 31 5.2 Rotors analyzed ................................................................................... 31 5.3 Format of data presentation ...................................................................... 33

6 . HOVERING ROTOR CIRCULATION DISTRIBUTION ........................................ 35

7 . LATERAL FLAPPING WIND TUNNEL TEST ................................................... 37

8 . SA349f2 HELICOPTER FLIGHT TEST ............................................................ 39

9 . SWEPTTIP CALCULATIONS ...................................................................... 43

10 . BOEING MODEL 360 SCALE ROTOR TEST ..................................................... 45

11 . H-34 ROTOR WIND TUNNEL TEST .............................................................. 51

12 . AH-1G HELICOPTER FLIGHT TEST ............................................................. 55

... 111

PRECEDING PAGE BLANK NOT flLMED

13 . H-34 HELICOPTER FLIGHT TEST ................................................................ 59 I 14 . UH-60A ROTOR CALCULATIONS ................................................................ 61

15 . HARMONIC CONTENT OF AIRLOADS DATA ................................................. 63

......................................... 16 . REVIEW OF MEASURED ROTOR AIRLOADS DATA 65

17 . CONCLUSIONS AND RECOMMENDATIONS .................................................. 67 17.1 Conclusions ..................................................................................... 67 17.2 Recommendations: lift measurement at high Mach number ............................... 69 17.3 Recommendations: wake geometry and rollup ............................................. 69 17.4 Recommendations: airloads measurements and correlation ............................... 70 17.5 Recommendations: future airloads tests ..................................................... 71

APPENDIX A . CAMRAD PROGRAM MODIFICATIONS .......................................... 73 New and revised input ......................................................................... 73

A.2 New and revised common blocks ............................................................. 74 I A.3 Revised subroutines ............................................................................ 75

I A . 1

I REFERENCES ............................................................................................... 77 I ~ FIGURES ..................................................................................................... 81

.

iv

SYMBOLS AND ABBREVIATIONS

b wing or blade semichord

C

R C

C m

Cmt/u

C P

C S

=T

=X d

d (CT/u) /dr

h

k

L

M

Mat

Mt

'tip

N

R

r C

wing or blade chord

section lift coefficient, ~/(pU'c)

section moment coefficient, M/(pU cA); or blade mean chord

dimensionless torsion moment, Mt/(@(fiR) R cm)

pressure coefficient, p/(;i.pU 1

speed of sound

rotor thrust coefficient, T/(p(nR) nR2)

rotor drag force coefficient, X/p(nRI2nR2)

1 3

1 2 3

2 2

1 2 A

2

radial resolution of trailed vorticity in d i scret i zed wake

blade section lift, L / ( D ( ~ R ) ~ C ~ ) = (c/2cm)uTcR 2

vertical separation between vortex and wing

reduced frequency, &/U

wing or blade section lift (force per unit span)

wing or blade section moment (moment per unit span); or Mach number, U/cs

advancing tip Mach number, {l+rr)Mtip

blade structural torsion moment

rotor tip Mach number, nR/cS

number of blades

blade surface pressure

1 2 dynamic pressure,

blade radial station, measured from center of rotati on

ZP"

blade radius

tip vortex core radius (defined by maximum ci rcumf erent i a1 vel oci ty 1

', V

T

U

T U

V

X

X

Y

U S

U tPP

#lC

r

c1

P

U

8

Y

w

n

rotor thrust

wing or blade section velocity

blade tangential velocity, r/R+usin*

flight speed

blade chordwise position, measured from leading edge

rotor drag force

wing spanwise coordinate

rotor shaft angle of attack, positive aft

rotor tip-path-plane angle of attack, positive aft

rotor longitudinal tip-path-plane tilt relative shaft, positive forward

rotor lateral tip-path-plane tilt relative shaft, positive toward retreating side

wing or blade bound circulation; or line vortex strength

rotor advance ratio, V / ( n R 1

air density; or blade radial station

rotor solidity, Ncm/nR

velocity potential; or rotor wake age

rotor azimuth angle, measured from downstream, in direction of rotor rotation

frequency of wing or loading oscillation

rotor rotational speed

spanwise derivative

! vi

WAKE MODEL FOR HELICOPTER ROTORS IN HIGH SPEED FLIGHT

SUMMARY

An improved rotor wake model for helicopter rotors is developed, and applied to airloads data from several tests, including the Boeinq model 360 scale rotor test. The emphasis is on wake effects (including blade-vortex interaction) in high speed flight, considering in particular cases with negative loading on the blade advancing tip. The capability is developed to model the wake created by dual-peak span loading (inboard and outboard circulation peaks, of opposite sign), optionally with multiple rollup of the trailed vorticity. Two alternative approaches for blade-vortex interaction are considered: second order lifting-line theory, and a lifting-surface theory correction. The common approach of using a larger vortex core radius to account for lifting-surface effects is quantified. The second order lifting-line theory also improves the modeling of yawed flow, swept tips, and low aspect-ratio blades. Calculated rotor airloads are compared with measured data from tests of the model 360, S A 3 4 9 4 H-34, and AH-1G rotors. The correlation illustrates the features and effects of the wake model, provides an assessment of the importance of the wake to high speed rotor airloading, and shows the capability to calculate the airloading. In addition, the requirements for future airloads measurements are defined.

1

1 . I NTRODUCTI ON

1 . 1 Background

The vortex wake of the rotor is a factor in most problems of helicopters, including blade loads, vibration, noise, and even performance (Johnson, 1980a). The wake, particularly the discrete tip vortices, are a principal source of the higher harmonic loading on the blades. Hooper (1984) provides a summary of rotor airloads measurements in forward flight, including tests of the H-34, UH-1, NH-3A, XH-SlA, CH-53A, and AH-1G rotors. The H-34 rotor tests in flight (Scheiman, 1964) and the wind tunnel (Rabbott, Lizak, and Paglino, 1966a) have been particularly fruitful, exhibiting several phenomena that are unusual, and as yet not fully explained.

Hooper (1984) observed relatively consistent behavior in all the data sets examined. At transition speeds, there was impulsive loading of the blade tip, on both the advancing and retreating sides of the rotor disk. Considering the locus of the tip vortex from the preceding blade, this loading was attributed in certain cases to blade-vortex interaction. At high speed, there was an impulsive (up-down) loading on the tip of the advancing blade. The locus of the tip vortex was similar to the locus of the peak loading, but the impulse was the opposite sign from the low speed case. This suggested that significant negative vorticity was being produced by the negative lift region on the advancing tip at high speed. Miller (1985) discussed the implications of the negative loading on the advancing tip. The trailing wake may be expected to roll up into two vortices of opposite sign: a negative tip vortex; and a stronger, positive inboard vortex. A simple three-trailer model of the wake was developed and applied by Miller and Ellis (1986).

Johnson (1971a) observed in the H-34 low speed flight test data that the vortex-induced loads on the advancing side are generally high when the blade first encounters the vortex from the preceding blade, but decrease inboard as the blade sweeps over the vortex. Evidently there is some phenomenon limiting the loads. Several possibilities have been proposed: local distortion of the vortex geometry; bursting of the vortex core, induced by the blade (Scully, 1975); vortex interaction with the trailed wake it induces behind the blade, with the effect of diffusing the circulation in the vortex; and local flow separation produced by the high radial pressure gradients on the blade (Ham, 1975) . The exact physical mechanism involved remains speculative. The phenomena (or at least their e+fect on the blade airloads) can be modelled by increasing the vortex core size as the blade-vortex interaction progresses.

The computer code "Comprehensive Analytical Model of Rotorcraft Aerodynamics and Dynamics" (CAMRAD) introduced a new wake model for helicopter rotor airloads calculations (Johnson, 1986a). This model has been applied with considerable success in calculations of important rotor phenomena, i ncl udi nq:

PRECEDING PAGE BLANK rJoP FILMED

correlation with flight test measurements of blade loads and airloading (Yamauchi, Heffernan, and Gaubert, 1988); lateral flapping as influenced by the wake geometry (Johnson, 1981); and hover loading calculations using prescribed wake geometry (Johnson, 1986a). A major advance was the coupling of the CAMRAD wake analysis with finite-difference calculations for advancing blade tip transonic flow (Tung, Caradonna, and Johnson, 1986). These various applications have established the capabilities and limitations of the CAMRAD models.

The Aerof lightdynamics Directorate of the U.S. Army Aviation Research and Technology Activity has recently acquired a n e w set of blade pressure data, from a wind tunnel test of a Boeing model 360 scaled rotor. This data set is notable for the use of modern instrumentation; the inclusion of scaled blade dynamics in the model rotor; and the advanced design of the rotor system, intended for high speed operation. The next step in the model 360 scale rotor project must be to apply analyses to the rotor system, and compare the results with the measured data.

1.2 Objectives

The objectives o+ the present investigation were to develop an improved rotor wake analysis capability for helicopter rotors, and to apply the analysis in particular to the data from the model 360 scale rotor test, The emphasis was on wake effects (including blade-vortex interaction) in high speed flight. Much of the existing rotor airloads data from high speed tests was examined. The product of the investigation is an advanced and demonstrated wake and aerodynamics model for the calculation of rotor airloads.

1.3 Approach

Rotor blade airloads are considered in the present investigation, since they provide the most detailed information available about the aerodynamic phenomena involved. Wake geometry measurements would be very useful, but are seldom available. Blade structural bending and torsion loads are of interest, but provide only an indirect picture of the aerodynamics. Performance data are of interest themselves, and because errors in performance prediction will produce errors in blade loads predictions also. Moreover, as has been remarked for the lateral flapping problem (Johnson, 19811, if the mean and l / rev airloading can not be predicted, it is unreasonable to claim to know much about the higher harmonic loading.

The starting point for the investigation was the existing code CAMRAD (Johnson, 1986a). This code is applicable to a wide range of rotorcraft configurations and rotor types. It has had numerous successful applications to rotorcraft aerodynamics and dynamics problems. The code can calculate performance, airloads, response, loads, and stability. It has a highly developed rotor

4

aerodynamic model, and a wake model wi th many unique features. The present work extends th is aerodynamic and wake model t o improve the predic t ion o f airloads, blade loads, and performance-

Key aspects of the aerodynamics and wake models i n CAMRAD are as follows. The r o t o r aerodynamic model i s based on l i f t i n g l i n e theory, using steady two-dimensional a i r f o i l charac ter is t i cs and a vortex wake. The model includes a correct ion f o r c lose blade-vortex passage loading using a l inear l i f t i n g - s u d a c e theory solut ion; an empir ical dynamic s t a l l model; a yawed f low correction; and unsteady aerodynamic forces from th in a i r f o i l theory. The aerodynamic model i s appl icable t o a x i a l and nonaxial f l i g h t , w i t h h igh in f low and large angles. The induced ve loc i t y i s obtained from momentum theory or a vortex wake model.

The CAMRAD r o t o r wake model i 5 based on a vortex l a t t i c e ( s t ra igh t l i n e segment) approximation f o r the wake. A small viscous core rad ius i s used f o r the t i p vort ices. CS l a rge core s ine i s used f o r the inboard wake elements, not as a representation of a physical e f fect , but t o produce an approximation f o r sheet elements. Sheet elements are avai lab le i n CAMRAD f o r the inboard wake, but have not proved necessary i n appl icat ions so far . The wake inf luence coe f f i c i en ts are ca lcu lated f o r incompressible flow. A model o f t he wake r o l l u p process i s included. Eventual ly the t i p vortex has s t rength equal t o the maximum bound c i r cu la t i on of the azimuth where the wake element was t ra i led . A number of parameters a l low the t i p vortex t o have only a f r a c t i o n of t h i s maximum st rength when i t encounters the fo l lowing blade, wi th the remainder o f the v o r t i c i t y s t i l l i n the inboard wake. The r a d i a l loca t ion of the t i p vortex formation a t the generating blade i s a lso prescribed i n the model. Close blade-vortex passage loading i s calculated using a small viscous core rad ius f o r the vortex and a l i f t i n g - surface theory correct ion f o r the induced loads. I n addi t ion, i t i s possible t o increase the core radius a f t e r t he f i r s t encounter w i t h a blade, i n order to model the phenomena l i m i t i n g vortex- induced loads on a rotor blade.

The CAMRAD wake geometry models include simple undistorted geometry; hover prescribed wake models based on experimental measurements; and a calculated f ree wake. The free-wake analysis (Scully, 1975) calcu lates the d is tor ted t i p vortex geometry fo r a s ing le r o t o r i n forward f l i g h t , using modelling features consistent wi th the CAMRAD wake anal ys i s.

The present invest igat ion developed and implemented several major improvements i n the wake model. The focus on h igh speed f l i g h t requires consideration of cases w i t h negative loading on t h e blade advancing t i p . Hence the capab i l i t y was introduced to model the wake created by dual-peak span loading, perhaps wi th mu l t i p le r o l l u p of the t r a i l e d v o r t i c i t y . I f the wake e f fec ts are important, i t fo l lows tha t the blade-vortex i n te rac t i on load5 m u s t be proper ly calculated. Two approaches f o r blade-vortex i n te rac t i on were considered. For the f i r s t approach, t he capab i l i t y t o use a second order l i f t i n g - l i n e theory was

5

introduced, For the second approach, a lifting-surface theory correction was implemented. The second order lifting-line theory is also applicable to swept tips, and improves the calculation of t h e loading in yawed flow and for low aspect-ratio blades.

The airloading calculated using the improved wake model was compared with measured data from the model 360 scale rotor test, as well as with data from other wind tunnel and flight tests. This correlation illustrates the features and effects of the wake model, provides an assessment of the importance of the wake to high speed rotor airloading, and shows the capability to calculate the airloading. In addition, the requirements for future airloads measurements are defined.

6

2. HIGH SPEED WAKE MODEL

2.1 Rotor Blade Loading

On a lifting rotor in hover or low speed flight, the bound circulation is positive along the entire blade length. In such flight conditions there may be local minima and maxima of the circulation, such a5 produced by blade-vortex interaction or blade twist, but generally the circulation monotonically increases to a maximum value at a radial station near the tip.

It is common for helicopter rotors in high speed forward flight to encounter negative lift on the advancing tip, particularly in the second quadrant of the rotor disk. With a flapping rotor, the net pitch and roll moment acting on the rotor hub must be small (zero for an articulated rotor with no flap hinge offset). In forward flight, the lifting capability of the retreating side is limited by the combination of low dynamic pressure and stall of the blade airfoil. Consequently the lift on the advancing side must be small also, in order to maintain roll moment balance. At sufficiently high speed, the lift on the advancing tip can become negative. Large twist, either built-in or elastic, will increase the negative loading. In such cases, the bound circulation is still positive along the entire blade length for most of the rotor disk, but in the second quadrant there is a negative maximum near the tip and a positive maximum inboard. Hence in this region the tip vortex rolls up with negative strength (i-e., opposite sign from normal rollup), with a region of positive vorticity trailed between the positive and negative circulation peaks. This positive vorticity might also rollup somewhat, but normally the peaks are widely separated, so the circulation gradient is not large and the rollup will not be a5 strong as for the tip vortex.

Figures 2-1 to 2-3 illustrate the phenomenon. The radial d i s t ibution of the blade bound circulation (dimensionless, r/nR 1 is shown for azimuth angles around the rotor disk, These are calculated results, for several cases that are considered in detail later. Figure 2-1 is a typical low speed case. The bound circulation is always positive, and generally concentrated at the tip, implying strong rollup of the tip vortex. Note the blade- vortex interaction on the advancing and retreating tips. Figure 2-2 and 2-3 are typical high speed cases. For azimuth angles between 90 and 135 degrees, the tip loading is negative. In this region, the positive circulation peak occurs well inboard on the blade. The objective is to develop a wake model that encompasses the rollup implied by such loading distributions.

5

Other cases with major positive and negative circulation peaks can be encountered. For example, a tiltrotor has a large twist that is far from optimum for most of its flight conditions. For a tiltrotor in cruise the twist is generally smaller than optimum, hence the blade circulation is negative inboard and positive outboard. For a tiltrotor in helicopter mode the twist

7

is larger than optimum, hence the blade circulation is negative on the advancing tip, even for relatively low speed flight. The loading distribution of a helicopter rotor will also exhibit local minima and maxima, such as from blade-vortex interaction and the reverse flow region.

For the present wake analysis, the rollup process is modelled rather than calculated. The rollup is determined by the spanwise distribution of the bound circulation where the wake is created, and by certain input parameters. Regarding the basic configuration of the circulation distribution, r ( r ) at a given t, only two major cases are considered:

a) r the same sign all along the length of the blade (single- peak model);

b) r with one positive region and one negative region (dual-peak model 1 .

More complicated circulation distributions ( m o r e than one zero- crossing, or local minima and maxima) imply more complicated rollup processes. which will likely require detailed calculation.

2.2 Far Wake Model

The wake model of CAMRAD is described by Johnson (1980b). CAMRAD assumes a single peak of the bound circulation. The radial maximum of the blade bound circulation is r (F). The vorticity distribution of the rolled up wake is described entirely by r tip vortex, wf?& is represented by discrete line segments. The corresponding negative trailed vorticity (of total strength - 1 is in an inboard sheet. Since the rollup process is not being calculated, there is no information on the distribution of vorticity in this sheet. Hence it is assumed that the trailed vorticity has constant strength spanwise (at each 9). This wake configuration can be viewed as arising from a circulation

the tip. The equivalent circulation distribution and I-esulpzng wake segment models for the CAMRAD far wake are shown in figure 2-4, (The equivalent circulation distribution is not the actual blade loading, but rather it is a way to represent the rollup process. 1

max

. It is assumed that all of rmax rolls up into a

rmax

distribution that is linear from r = 0 at the root to r = I- ax at

CAMRAD also includes a rollinq-up wake model, defined by r at radial station oRU, and frmax at the tip (figure 2-41. ssXparameters oRU and f vary from rRU and f at the blade, to 1

(the wake age of the rollup process).RUThe values of r at 'RU and 0 are input parameters. The resulting wake model ' RU, consists aqua tip vortex line and two inboard sheet segments. Note that the strength of this wake model is still described sol el y by rmax.

RU'

8

This CAMRAD model assumes that r has the same sign (positive or negative) along the entire blade length. Consider the application of this model to a case where r ( r ) changes sign (figure 2-51. The maximum bound circulation r is obtained from the peak (positive or negative) with maximum magnitude. If

h be correct. weak outboard and of wrong sign inboard. Getting the correct sign for the tip vortex might be sufficient though. The more common circumstance is that r is the inboard peak (for example, small negative circu!!%ion at the tip and large positive circulation inboard). Then the CAMRAD model will produce a tip vortex of the wrong sign and too large magnitude- Such a result 1s not acceptable.

max

is the most outboard peak, then the sign of the tip vortex However, the single trailed sheet will be too

To accommodate more complex loadings, consider a representation of the bound circulation distribution by two peaks of opposite sign (negative and positive peaks of r (r) 1 . The outboard peak (positive or negative) is r and the inboard peak 0 is rI , at reo and r respectively. Figure 2-5 illustrates the I following possibiliFes for the wake model:

a) A single-peak model, using rmax. This is the CAMRAD model described above.

b) A single-peak model, using ro- This model gives the correct sign and magnitude for the tip vortex, which is usually the first priority.

c)

d) A dual-peak model, with a rolled-up inboard trailed

A dual-peak model, using both ro and rI-

wake. Whether or not such rollup occurs, and its extent (core size), are defined by input parameters, not calculated.

It is a s s u m e d that r(r) ha5 at most one zero crossing between the root and tip. The in+luence of. two or m o r e zero crossings, or local peaks produced by blade-vortex interaction, is not dealt with. Such complexities require detailed calculations.

In summary, two wake configurations are now possible for the far wake and rolling up wake: single-peak or dual-peak. For the single-peak model, either r influence coefficients) . d P X t h e dual-peak model , the inboard trailed vorticity can be rolled up or not.

or ro can be used (with the same

The equivalent circulation distributions for the dual-peak wake model are shown in figure 2-6. The rolling up wake has a line tip vortex, and three inboard sheet element (from radial

The far wake has a line tip vortex, and t w o inboari'sheet e ements (from radial station pGI) . stations p

the slope from rI to r is small, so strong rollup of the inbaord trailed wake is unlikeyy. option for rollup of the trailed sheet from p G I t o the tip, which

Typically

Still, the analysis includes the

3

will then be a line segment in the middle of the panel, with an appropriate core radius (input). The shed wake for this panel is still a sheet (a trailed line implies that the shed vorticity has a stepped rather than linear strength variation radially). Note that vortex lines (with large cores) are commonly used as approximations for the sheet panels. Here however, the vortex line in the inboard wake model is intended to represent an actual physical configuration.

The radial station pGI in the dual-peak model is a wake geometry parameter. It can be input, or the analysis can use the calculated location rGI of the inboard circulation peak, from the latest wake iteration. It will be important that pGI in the wake geometry (and hence influence coefficients) be consistent with r of the current circulation solution. This consistency must be checked (by the user, not the computer). It may be necessary to iterate on the influence coefficient calculation in order to achieve consistency (see Johnson, 1980b, section 5.3.91. Such iteration is required when the wake geometry varies significantly with the loading solution. Generally the wake geometry is influenced by parameters such as the rotor thrust and tip-path- plane incidence, which are constrained by the rotor trim. With the dual-peak model the wake geometry is also influenced by nGI, which will be dif+erent +or t h e uni+orm inflow and nonuniform in+low sol uti ons,

GI

The analysis must also consider the case where the inboard peak exists in either the wake geometry or the circulation distribution, but not the other. If the inboard peak is absent in the wake geometry (input p not available, or no peak in the last circulation solution), t h the influence coefficients will be calculated as for a single-peak model, and r I will be ignored in calculating the inflow. If the inboard peak is absent in the circulation distribution, then rI will be the circulation at P obtained by interpolating between 0 and ro, so the dual-peak w%e model will give the single-peak result.

2.3 Geometry

The description of the wake geometry follows the CAMRCID documentation (Johnson, 1980b1, which defines the parameters in the equations below. The dual-peak model requires r be obtained from one of two sources:

which may GI’

a) input (including the possibility that the inboard peak does not exist 1 ;

b) the position of rI f r o m the latest calculation.

Then for each wake panel, pGI is the average of the leading edge and trai 1 ing edge values:

’GI

10

-L For the wake geometry, rw a t the i ns ide and outs ide edges i s in terpolated t o p G I (Johnson, 1980b, sect ion 3-1-31 .

the r o l l i n g up wake: It w i l l a l so be required t h a t oRU be greater than pGI for

+.05 s P~~ Q 1 ROOT single-peak model r

dual -peak model +.05(1-~~.) S PRU 5 1 'GI For the rol led-up inboard t r a i l e d wake, the l i n e vortex w i l l be placed midway between the panel edges:

By using the l i n e aproximation f o r a sheet (Johnson, 1980b, section 3.1-81, th is i s automatical ly accomplished.

2.4 Induced Veloc i ty Calculat ion

The evaluat ion of the induced v e l o c i t y f o l l ows the CAMRAD documentation (Johnson, 1980b1, which de+ines the parameters i n the equations below. The c i r cu la t i on peaks are located by searching r ( r ) a t each e- The search i s conducted between r Fmax (an input l i m i t ) and r ( the loca t ion of t he t i p vortex r o l up a t the blade). The search i s r e s t r i c t e d t o inboard of r since TU otherwise a small negative c i r c u l a t i o n a t the t i p might be considered an outboard peak. The p o s i t i v e and negative peaks, and t h e i r corresponding r a d i a l s ta t ions are i den t i f i ed . Then the p o s i t i v e and negative peaks are assigned t o t h e inboard and outboard peaks as appropriate. F ina l l y , rmax is the pos i t i ve or negative peak w i t h maximum absolute value.

TU

I f an inboard peak i s not found but D~~ e x i s t s (i.e. the inboard peak was used i n the wake geometry, for the dual-peak model) then the inboard peak value is, obtained by in terpolat ion:

)/(1 - rROOT) ROOT r I = ro (pGI - r so the dual-peak wake geometry gives near ly the single-peak r e s u l t .

The induced ve loc i t y i s obtained from t h e blade bound c i r c u l a t i o n and the inf luence coe+f ic ien ts as fol lows:

J J Q

j=l j=l j-a-K,, is1

Tho fo l low ing th ree options are considered:

a) fo r the single-peak model using rmax, the second term i 5

I1

absent and rmax replaces ro i n the f i r s t term;

for the single-peak model using ro, the second term i s absent;

b)

c) for the dual-peak model, a l l three terms are used.

The wake geometry, e i t h e r prescribed (section 3.1.3) or f r e e (sect ion 3.2), is based on rmax for opt ion (a) or on r opt ions (b) and (c) - 5-1-12) i s based on rmax for opt ion (a); on ro for opt ion (b); or on both ro and r I for opt ion (c)-

for The c i r c u l a t i o n convergence testo(sect ion

.

3. SECOND ORDER LIFTING-LINE THEORY

3.1 Objective

With the focus of this investigation on improving the rotor wake model, it is important that the analysis accurately calculate the airloading produced by blade-vortex interaction. With the CAMRCID model it has been necessary to use an unrealistically large vortex core radius in order to obtain good correlation between measured and calculated rotor airloads (Johnson, 1986a). Such an empirical approach has limitations that are unacceptable in the long term, such as not being able to select the correct core size until after the data has been measured, and not being able to account for other effects such as swept or yawed flow. The long term goal must be to improve the wing and wake models to the point where the vortex core in the analysis simply represents the actual physical core and nothing else.

The present investigation introduces two alternative methods for improving the wing model for blade-vortex interaction: second order lifting-line theory, and a lifting-surface theory correction (the latter developed in the next chapter). The intent is to improve the calculation of the airloads without actually resorting to methods such as lifting-surface theory, which require more computation and still need some development for rotary wing applications. Several investigations have shown that second order lifting-line theory gives nearly the same result as lifting-surface theory, including the lift produced in close blade-vortex interactions (Johnson, 1986b) . In addition, second order lifting-line theory should improve the loads calculated for swept tips, yawed flow, and low aspect-ratio blades.

Formal lifting-line theory is the solution of the three- dimensional wing loading problem using the method of matched asymptotic expansions. Based on the assumption of: large wing aspect-ratio, the problem is split into separate outer (wake) and inner (wing) problems, which are solved individually and then combined through a matching procedure. For a rotor in forward flight it is also necessary to consider a swept and yawed planform, and unsteady, compressible, and viscous flow. The lowest order fixed wing solution is Prandtl’s theory (steady and no sweep). The development of higher order lifting line theories originated with Weissinger for intuitive methods, and with Van Dyke for singular perturbation methods.

The lifting-line theories generally found in the literature, even including unsteady, transonic, and swept flow, are analytical methods, i.e. they obtain analytical solutions for both the inner and outer problems. For the rotary wing however, it is necessary to include stall (high angle-of-attack) in the inner solution, and the helical, distorted, rolled-up wake geometry in the outer solution. Hence for the rotor problem the

13

objective is to obtain from lifting-line theory a separate formulation of the inner (wing) and outer (wake) problems, with numerical not analytical solutions, and a matching procedure that will be the basis for an iterative solution.

Lifting-line theory contains so many approximations and assumptions that ultimately it must be replaced by a more accurate method; but that is in the future. Now lifting-line theory is still the only practical method for including viscous effects in the analysis, allowing two-dimensional experimental data containing information on stall and compressibility to be combined with three-dimensional theory. So it is important to develop the best possible lifting-line theory for the rotor. Higher order perturbation methods are not directly applicable, since they involve analytical solutions and quadrature rather than integral form. The objective is t o define a practical method, one that gives the best accuracy without convergence problems or singularities, For this purpose the perturbation solutions provide a guide and a sound mathematical foundation for the approach.

3.2 Outline of Second Order Lifting-Line Theory

This section summarizes the development and results of higher order lifting-line theory. Johnson (1986b) provides a more detailed description, and cites the sources responsible for developing various aspects of the theory. The intent here is to concentrate on presenting the basis for the analysis to be implemented (i.e. a practical version of higher order lifting- line theory), with enough information to justify its use.

The method of matched asymptotic expansions for this problem is based on the small parameter E = c /R = l/(aspect-ratio). The inner (wing) and outer (wake) solutions are expanded as series, with each term order E smaller than its predecessor. Then the n-term/m-order inner solution is matched to the m-term/n-order outer solution. At each level, the matching provides boundary conditions for the next term in the inner or outer expansion, from the solution at previous levels, For the high aspect-ratio wing, the inner problem has simpler geometry (two-dimensional 1 but complex flow (Navier-Stokes equations). In the outer limit, the inner solution can be considered irrotational. The outer problem has complex geometry (the vortex wake), but irrotational flow. In the inner limit, the outer solution has simple geometry. In the matching domain, there is both simple geometry and irrotational flow. Hence it is appropriate to represent the order-n inner or outer solution by @I ; 9 can be considered the velocity potential, or just a symbolric representation of the solution.

3.2.1 Steady, Unswept, Incompressible Fixed Wing

The method of matched asymptotic expansions produces the following results for a fixed wing at speed U. The steady, unswept, incompressible case is considered first.

a) Inner a : two-dimensional airfoil with thickness, camber, and the geometric angle of attack (boundary conditions on the surface), in free stream U (boundary conditions at infinity).

0

0' b) Outer al: i.e. a lifting line,

line of dipoles from inner bound circulation r

c) Inner 8 two-dimensional airfoil with zero boundary 1' conditions on the surface; in a uniform flow at infinity that i 5 the induced velocity v. produced by the outer Ol; v. regular part, i .e. excludes the bound vortex contrihution.

is the

d) Outer a2: note that a2 is more singular than @ this is a singular perturbation.

dipole line from r1 and quadrupole line from rO; in the inner limit, hence 1

e) Inner a2: inhomogeneous equation with a particular solution produced by second spanwise derivatives of the inner a ; zero boundary conditions on surface; boundary conditions at infinity from outer to r") and a regular term (a linear variation of induced 0 velocity); note that a2 is more singular than a1 in the outer limit.

0

and a2, consisting of a singular term (proportional

The outer 0' Consider the outer a- quadrupole line from r limit of the inner a solfition is unchanged if the quadrupole line has zero streng?h and instead the dipole line (bound vortex) is offset. For a thin airfoil the bound vortex must be at the quarter-chord. (Camber introduces an additional chordwise shift, and thickness a vertical shift, but these are not proportional to r , so the position of the bound vortex would depend on the lift. These effects will be neglected.) With the bound vortex at the quarter-chord, only a dipole line solution is needed in the w t e r problem, i.e. a wake of vortex sheets.

Consider the inner a2 boundary condition at infinity that corresponds to an induced velocity that varies linearly in space. For a thin airfoil, the same lift will be obtained with a boundary condition at infinity that is a uniform induced velocity, if the value at the three-quarter-chord is used. However, a linear induced velocity variation (chordwise) produces a section moment about the quarter chord, while the uniform induced velocity does not, Also, the inner has a particular solution, as well as other terms in the boundgry conditions.

Consider the remainder problem, consisting of the inner U J ~ solution after accounting for the induced velocity at the three- quarter-chord. This remainder problems has been solved by Van Dyke for constant geometric angle of attack (spanwise), and by

15

Van Holten f o r constant chord. I n pract ice t h i s p a r t o f the second order theory i s neglected, so such so lut ions provide an error estimate. Generally the l i f t error i s small (second order) ; and the moment e r ro r i s also small, except perhaps f o r t he term tha t would be produced by the l i n e a r l y varying induced ve loc i ty .

The perturbat ion so lu t ion a l ternates between the inner and outer problems, using only the so lut ion up t o the previous order. Combining the inner problems and combining the outer problems, t o so lve a t a l l orders simultaneously, i s an a l te rna t i ve t h a t i s equivalent i n t e r m s of the perturbat ion expansions. For the inner problem, the a i r f o i l (ao) and wake-induced v e l o c i t y ( @ 1 1 boundary condit ions are combined. T h i s i s l og i ca l and easy, s ince the boundary condi t ion i s just an angle o f a t tack increment from the wake-induced veloci ty. For the outer problem, the wake strength i s obtained from the t o t a l bound c i rcu la t ion , r +rl ra ther than ro. tge so lut ion from d i r e c t quadrature t o an i n teg ra l equation, i.e. Prandt l ’s formulation. It i s found that the so lu t ion o f the i n t e q r a l equation i s ac tua l l y bet ter behaved: the d i r e c t so lu t ion i s s ingular a t the t i p s for normal wing planforms.

Using the t o t a l bound c i r c u l a t i o n changes

I n general, the i n teg ra l formulation o-f l i f t i n g - l i n e theory w i l l be used here. Another general feature w i l l be the neglect o f the so lut ion of the remainder problem, as described above. T h i s i s j u s t i f i e d by the f a c t that an ana ly t i ca l inner so lu t ion w i l l not be used, and i s consistent wi th other approximations t h a t are made. Experience shows tha t the r e s u l t i n g three- dimensional wing theory i s second order accurate f o r l i f t , but l e s s accurate f o r moments.

Hence a prac t ica l second order l i f t i n g - l i n e theory has f o r t he inner problem a two-dimensional a i r f o i l i n a uni form flow, consis t ing of the f ree stream U and the wake induced ve loc i ty . The outer problem i s a vortex wake from the bound vortex a t the quarter-chord, w i t h d is to r ted wake geometry i f necessary. The induced ve loc i ty ( a l l three components i n general 1 i s evaluated a t the three-quarter-chord, excluding the cont r ibu t ion of the bound vortex (which i s already accounted for in the matching).

A comparison of the various formulations i s use+ul. Let 8 be the geometric angle o f at tack of the wing, The inner problem problem can be solved ana ly t i ca l l y , as f o r a th in a i r f o i l ; or numerically, perhaps using a i r f o i l tables:

t h i n a i r f o i l r = nc(U6 - V)

r = 1 UccR(e-v/U) tab les

The outer problems ca lcu lates the induced ve loc i t y v a t the quarter-chord or three-quarter-chord, excluding the bound vortex. Note tha t f o r a t h i n planar wake, the induced v e l o c i t y a t the quarter-chord is:

16

- - - J 1 (dr/drr)ds c/4 4n Y - n

V

order perturbation method obtains v from ro = ncUB: The first

Prandtl’s + r o m r:

r-

integral equation is also first order, but obtains v

The common implementation of liftinq-line theory for rotors is also first order (using v instead of thin airfoil theory for the inner solution:

but airfoil tables are used /4)

r- I I

nc 2r which is the method used in CAMRCID. For the present investigation, second order liftinq-line theory is introduced, in which the induced velocity is evaluated at the three-quarter- chord:

This comparison should also consider Weissinger’s L-theory, in which the induced velocity is calculated at the three-quarter- chord, including the contribution from the bound vortex at the quarter-chord, and equated to the geometric angle of attack. This is equivalent to using thin airfoil theory for the inner solution in second order lifting-line theory:

3.2.2 Sweep and Yawed Flow

A +ixed w i n g with sweep and yawed flow is shown in figure 3-1. The spanwise line m(y) and the chord c<y) are both m e a s u r e d perpendicular to the y-axis. and the wing sweep is m’ = tan%. allowed, but it is assumed that the wing curvature is small enough 50 its effects are second order: m’ and % order 1, mw order E . This assumption on the curvature is required in order for the inner a1 problem (the wake-induced velocity effect) to remain two-dimensional. It is generally a good assumption for rotor blades, except at kinks. At kinks the expansion is invalid to any order (the integral formulation and spanwise discretization are relied on to keep the loading solution well behaved) .

The free stream has yaw angle %, Large sweep and yaw are

The matching process gives for the inner ~1 a new term in 1 the boundary condition at infinity, which is proportional to r’tanA (an effect of the edge of the wake vwtex sheet). It can be shown that if these sweep terms are neglected and the induced velocity 15 calculated at the three-quarter-chord, then the

17

second order solution gives the correct lift but introduces a moment error. Experience shows that this is a good approximation for the second order theory applied to swept wings.

Hence a practical theory has for the inner problem a two- dimensional airfoil in a uniform flow, consisting of the swept free stream and the wake induced velocity. The outer problem is a vortex wake from the bound vortex at the quarter-chord. The induced velocity is evaluated at the three-quarter-chord, excluding the contribution of the bound vortex. The inner problem is an infinite wing with crossflow. It is preferable however to define the geometry relative to the straight y-axis, which gives an infinite wing with yaw and crossflow for the inner problem.

3.2.3. Unsteady Loading

The matching process produces the following results for the case of a fixed wing with unsteady loading.

a) Inner 9 : unsteady two-dimensional airfoil with shed wake, in a yawed ?re= stream.

b) Outer a1: solution.

a lifting line; the shed wake matches the inner

c) Inner 9 : the boundary condition at infinity has a regular part from tAe wake-induced velocity, and a singular part from sweep; both the bound vortex and the inner shed wake must be excluded in evaluating the induced velocity.

If the shed wake is considered as part of the inner solution boundary conditions, instead of part of the inner problem, then only the bound vortex is excluded in evaluating the induced velocity. In this case, the shed wake is omitted from the inner 9 problem. 0

It is natural to include all of the wake in the outer problem when the induced velocity is being calculated numerically. Then the shed and trailed wake are treated identically: the induced velocity is evaluated at the three- quarter-chord and treated as a uniform flow for the inner problem. The assumption that the shed-wake induced velocity is constant over the chord is a significant approximation however. With the induced velocity evaluated at a single point, the shed wake model should be modified as required to obtain unsteady loads correctly. It is found (Johnson, 1980a) that if the shed wake is started a quarter-chord aft of the collocation point, then the Theodorsen and Sears functions are well approximated (at least for small reduced frequency k, and reasonably well up to about k = 1) .

For small reduced frequency, k order e , the unsteady part the induced velocity is of the same order as the steady part;

of

18

while for k order I , the unsteady part of the induced velocity (three-dimensional effect) is higher order. Hence it is consistent to have the unsteady inner solution accurate to k order 1, and the unsteady outer solution accurate to k order e.

Hence a practical theory has f o r the inner problem a two- dimensional airfoil with no shed wake. The outer problem is a vortex wake from the bound vortex at the quarter-chord. The induced velocity is evaluated at the three-quarter-chord, including all the shed wake but excluding the contribution of the bound vortex. The trailed wake starts at the bound vortex, while the shed wake is created a quarter-chord a-Ft of the collocation point .

3-2.4 Compressible, Transonic, and Viscous Flow

For an unswept wing with steady loading, the compressible solution is obtained simply using the Prandtl-Blauert scaling. For the swept and unsteady case, compressibility introduces new terms but does not change the basic structure and order of the solution. A practical lifting-line theory includes compressibility in the inner solution, and calculates t h e induced velocity from an incompressible wake model.

For transonic flow, it is necessary to first introduce tsyQsonic scaling of the equations, and expand the potential in 7 (where 7 is a measure of the disturbance produced by thicknesz 1y5 angle of attack). i n E = r c/R (note that a larger aspect ratio is required in transonic flow for the same order lifting-line expansion). Transonic scaling requires moderately small sweep and small reduced frequency a5 well. Matching gives the following results:

Then the solution can be expanded

transonic two-dimensional equation. 0: a) Inner (0

b) O u t e r 9 - subsonic equation (linear).

c) Inner transonic two-dimensional equation, linearized about

Nonlinearity does not enter the matching at first order. The outer solution is still a lifting-line, and the inner boundary condition is still the induced velocity. If the inner a0 and 0 solutions are not combined, then it is also necessary to introhuce perturbations of the shock jump relation and shock position. A practical lifting-line theory includes transonic flow in the inner solution, and calculates the induced velocity from an incompressible wake model.

1-

For viscous flow, it is assumed that the outer limit of the inner problem is still irrotational, so the matching results are the same a5 for inviscid flow. The inner boundary conditions on the wing are now no-slip, which introduces nen effects for a yawed wing. For a practical method it is required that with

19

viscous flow the inner problem still be an infinite wing (yawed and swept, unsteady, transonic). To achieve this in the equations of motion (spanwise derivatives second order or smaller) requires only that the Reynolds number be order E for a swept wing, In fact the Reynolds number is much larger, so the lifting-line assumption is good as far as viscous transport is concerned. It is also necessary to consider the geometry of the flow field that results from the introduction of viscous effects (e.g, large scale separation) - The liftinq-line assumption requires that such geometry vary slowly in the spanwise di recti on .

-1

3-2.5 Rotary Wing

Rotation as well as translation of the wing introduces some extra complications, but does not siqnif icantly increase the level of approximation (because so much has been assumed or neglected already). Using a rotating and translating coordinate frame, the wing geometry can still be described as in figure 3-1. Now the free stream velocity U and yaw angle vary with y. Small curvature is still assumed- Note that k i 5 order E for l/rev variations, while k is order 1 for higher harmonics, For the incompressible case only the boundary conditions and wake configuration change; moreover, the inner limit of the outer problem is the same as for the fixed wing. For compressible flow, there are additional Coriolis and centrifugal type terms in the equations.

20

3.3 Summary of Wake and Wing Model

The following is a practical implementation of second order lifting-line theory for rotors. The outer problem is an incompressible vortex wake behind a lifting-line, with distorted geometry and rollup. The lifting-line (bound vortex) is at the quarter-chord (the quadrupole-line approximation, for second order loading). The trailed wake begins at the bound vortex, while the shed wake is created a quarter-chord aft of the collocation point on the wing (the lifting-line approximation for unsteady loading). Three components of wake-induced velocity are evaluated at the collocation points, excluding the contribution of the bound vortex. The collocation points are at the three- quarter-chord, in the direction of the local flow (the approximation for linearly varying induced velocity, from the second order wake).

The inner problem consists of unsteady, compressible, viscous flow about an infinite aspect-ratio wing; in a uni+orm flow consisting of the yawed free stream and three components of induced velocity. This problem is split into several parts: two-dimensional, steady, compressible, viscous flow (rir+oil tables); plus corrections for unsteady flow (small angle noncirculatory loads, but without any shed wake), dynamic stall, and yawed flow (equivalence assumption for a swept wing).

This formulation is generally second order (in e = c/R) accurate for lift, including the effects of sweep and yaw, but less accurate for moment. Note that placing the collocation points at the quarter-chord gives a first order lifting-line theory.

The geometry of the wing will be defined by the quarter- chord (aerodynamic center) and chord as a function of r , measured perpendicular to a straight reference span axis. The inner problem (at radial station r ) is an infinite aspect-ratio wing w i t h the local chord and sweep, in yawed flow. The outer problem has the bound vortex at the quarter-chord, and the collocation points at the three-quarter-chord (in the trailed wake direction, i.e. the direction of the local velocity).

3.4 Near Wake Model

Implementation of this lifting-line theory primarily involves the CAMREID near wake, which is defined as the wake lattice directly behind the reference blade (where the induced velocity is being calculated). The circulation distribution and resulting wake panels for the near wake are illustrated in figure 2-4. The blade bound circulation r(r ,*) is evaluated at the aerodynamic radial stations (where the induced velocity is calculated also) and at a discrete set of azimuth angles. A piecewise-linear variation of r implies vortex sheet panels, with shed and trailed vorticity that have strength varying linearly along their direction (see Johnson, 1980b, figures 14 and 16).

2 1

With a stepped variation of r , or as an approximation for the sheets, vortex lines in the middle of the panels are obtained.

It follows that the geometry in the near wake is defined in terms of these wake panels; that the vortex lines should be placed in the middle of the panels (radially and azimuthally); and that the vorticity strength varies linearly along its direction. However, sheet elements are not used for the near wake model being developed here. The discretization of the wake is not well controlled using sheet elements, because of edge and corner si ngul ari ti es, particularly when pl anar-rectanqul ar elements are used. Also, the most important case of the downwash from the two sheet panels adjoining the collocation point would require a higher order element or some other special treatment. Hence a vortex lattice representation of the near wake is used.

The wake panel geometry is defined by the positions of the blade root, tip, and aerodynamic radial stations, convected from azimuth stations *-ak and Y-ak+l (with self-induced distortion) where y i is the current blade azimuth (time) and 8 is the wake age. The trailed lines are placed in the middle of the panels (interpolated from the positions of the corners), or at the root/tip for the most inboard/outboard panels. Specifically, the end points 0.F the trailed line are on the panel leading and trailing edges, at the radial stations that define the edges of the aerodynamic segments of the blade (see Johnson, 1980b, section 2.4.1). Then the collocation points (in the middle of the aerodynamic segments) are always equidistant from the nearest trailed lines.

The shed lines are placed in the middle of the panels (interpolated from the positions of the corners), and moved aft by 3c/4 (c/4 if the collocation points are on the quarter-chord). Specifically, the end points of the shed line are on the panel side edges, 3c/4 aft of the mid points.

The collocation points are at the three-quarter-chord, for the aerodynamic radial stations. Specifically, they are on the side edges of the first wake panels, c/2 aft of the leading edge (the geometry of the wake is thus being used to obtain the local flow direction) -

The liftinq-line is placed at the quarter-chord of the blade, i.e. x a+t of the blade reference axis. Hence an increment in ehe blade position of A F ~ = x ? is required (see Johnson, 1980b, section 3.1.3). The c/2 sffift 0.C the aerodynamic center in reverse flow is ignored here (only for the purpose of defining the wake geometry; the loads are properly applied to the blade in reverse flow). The option of a straight lifting-line is also implemented, by omitting this x A term.

The geometry of this discretization is well controlled. Still, with vortex lines and the distorted, skewed, helical geometry of the rotor wake it is necessary t o be concerned about the singular velocities that could occur with lines too near

22

collocation points (most likely to occur near the reverse flow boundary). A solid-body-rotation viscous core is used for the near wake line segments in order to avoid such sinqularities. The baseline core sire is

r = (panel width115 C

so the core should not influence the induced velocities in normal situations.

The tip vortex is rolled up substantially by the time it reaches the trailing edge, even with highly tapered tips. Most of the effects o+ this rollup can not be obtained with lifting- line theory, but it is important that radial station of the

be included in the model. The near wake model has rollup, r trailed lines at the aerodynamic segment boundaries and at the tip. Hence it is possible to force the bound circulation to be trailed at rTV by using the factor

TV

m a x ( 0 , min(1, (r - r . ) / ( r -r.) 1 ) TV 1 i+l 1

on the lift coefficient cR at aerodynamic radial station r is midway between t h e aerodynamic segment edges r . and r . Ai Note that if rTV equals some r then there will be exa&fy zero i' bound circulation and hence zero strength wake outboard of that

This factor is similar to that used for the tip loss factor r in the uniform inflow model (Johnson, 1980b, section 2.4.51, but here it actually models the physical rollup position.

(rAi 1 -

i'

23

4. LIFTING-SURFACE THEORY CORRECTION

4.1 Objective

This chapter describes a second method for improving the wing model for blade-vortex interactions: a lifting-surface theory correction. Note that the lifting-surface correction is an alternative to the second order lifting-line theory developed in the preceding chapter; the two methods should not be used simultaneously.

The basis fo r the lifting-surface theory correction is the model problem shown in figure 4-1: an infinite wing encountering a straight infinite vortex with intersection angle A. The wing and vortex lie in parallel planes with separation h. The wing semichord is b. The intersection angle A is 90 deg for a perpendicular encounter and 180 deg for a parallel encounter (angles between 0 and 90 deg are treated by symmetry considerations) . The wing spanwise variable r is measured from the intersection with the vortex: so (r SinA) is the distance to the vortex line.

Johnson (1971b) derived a lifting-surface theory solution for this model problem, and developed an approximation suitable for vortex-induced loads. By applying a Fourier transform to the vortex-induced downwash and lift, the problem becomes finding the loading produced by a sinusoidal gust. A numerical solution to this problem was approximated by a series that has an analytical inverse transform. This produced an approximate lifting-surface solution L for vortex-induced loads. 1s

CAMRAD uses this liftinq-surface solution in the following manner (Johnson, 1980b, section 3.1.7). A similar expression is introduced for the vortex-induced load that would be obtained

Then the induced-velocity of each from lifting-line theory, line segment of the tip vor iex in the wake model is multiplied by t h e factor L /L By this m e a n s , the li+ting-line calculation of the vortex-inhced loads should give the lifting-surface theory result. Calculations performed with CCIMRAD do not however show a significant effect of this lifting-surface theory correction (e.9. Yamauchi, Heffernan, and Gaubert, 1988). Therefore the method has been reviewed and revised in the present investigation.

1'

I S

4.2 Lifting-Surface Theory Expression

This section summarizes the results of the lifting-surface theory solution for the model problem (Johnson, 1971b). The vortex-induced downwash on the wing, for the perpendicular interaction, is:

-r - - w/v 2 r/2~nbV r2 + h

I PRECEDING PAGE BLANK NOT FILMED

25

where r and h are scaled with b. To include a viscous core. a distributed vorticity model is used, such %ha% the circulation at a distance r from the vortex is Y = rrA/(rL+rL)- Then the vortex-induced downwash is still given by the above expression, if an effective separation distance h

C

is used: eff

The Fourier transform decomposes the downwash w(r) into sinusoidal gust of amplitude w ( v ) , where v is the wave number:

Application of the Fourier transform gives the spectrum of the vortex-induced downwash:

i -vh e - - - W/V

r/2nbV 2

Eased on this equation, wavenumbers in the range v = 0 to 5 were considered relevant for vortex-wing separations greater than a quarter-chord (h 5 - 5 )

The lift produced by a sinusoidal gust can be written in L: terms of a lift deficiency function g

c(v) = -2n~Vb W ( V ) 9 ( V I L

for the perpendicular interaction. The lift deficiency function is similarly defined for all intersection angles A. For the parallel intersection (two-dimensional unsteady airfoil 1 , the wavenumber becomes the reduced frequency k. and g is the Sears f unct i on . L

The lift deficiency function is approximated by a sum of exponentials:

gL 3 exp(-c v ) - i sin(b v ) a' exp(-c'v) 0 0 0 0 2 4 + exp(i(b v-b 1 ) (-a u exp(-clu) + a+ exp(-c,v))

1 2 1 L L

This form is chosen because it (and its product with the vortex sprectrum) has an analytical inverse (see Johnson, 1980b, section 3-1.7 for the result). The exponentials decay too quickly, so any finite series of this form will be too small at high v. The approximation is acceptable however over the required range of v (i.e. because g is multiplied by exp(-vh) from the vortex spectrum) . Linear liftinq-surface theory was solved numerically for g , and the results used to identify the coefficients in this expression as a function of intersection angle A and Mach number.

L

L

CAMRAD uses this expression for zero Mach number (an incompressible interaction). Note that there is an error in the coefficients used by CAMRAD; bo should be

26

bo = 8.88 - 1.88 ( A / 9 0 )

(Johnson, 1980b, page 167). This correction has no effect for the perpendicular interaction, and does not greatly change the peak blade-vortex interaction loads in any case. If there is a problem with this method, it must be sought in the corresponding lifting-line solution used by CEIMRAD.

4 - 3 Lifting-Line Theory Expression

The lifting-line theory equation for an infinite wing with downwash w (the perpendicular interaction) is:

- iur

= F/2rrbw = l/(l+y)

For a sinusoidal gust, w = we , the solution is n

gL

This result assumes a continuous trailed wake sheet, For a discretized wake, with trailed lines uniformly spaced a distance d apart, the result is

For rotor analyses, usually d/R = -02 to -06 on the outer part of the blade, so d/c = .& is typical.

For the parallel interaction, it is necessary to consider the lifting-line approximation for two-dimensional unsteady aerodynamics (Johnson, 1980a). With the induced velocity calculated at a single point, the Theodorsen function is approximately matched by starting the shed wake c / 4 behind the collocation point:

For a sinusoidal gust, t h e corresponding approximation for the Sears function is

= S ( k ) z eik/2 (C + ik/2) 9L This is a low frequency approximation, good to about k = 1/2. Note that to order k, the real part of g is L

Re(gL) 1 1/(1+3)

which is identical to the perpendicular interaction result.

For the perpendicular interaction, CCIMRCID approximates the lift deficiency function as

n 2 2 1 1 gL B exp(--w) - a Y exp(-c Y )

27

with al = -.&&2 and c and u = 2.

= 1.296 obtained by matching gL at u = 1 1

Figure 4-2 shows the lift deficiency function g for the L perpendicular interaction; figure 4-3 shows the normalized gust spectrum, exp(-vh); and figure 4-4 shows the product, gLexp(-vh), for h/b = 1. The lifting-surface solution is significantly smaller than the lifting-line solution, particuarly with a discretized wake. It is observed that the spanwise resolution in the discretized wake should be less than d/c = .5 for a blade- vortex separation of about 112 chord; a corresponding azimuthal resolution is also required. The CAMRAD expression for the lifting-line solution is reasonable to about v = 2, but is too small for larger wavenumbers (figure 4-21. When multiplied by the gust spectrum, the errors in the CAMRAD expression are not very important though (figure 4-41, as long as d/c is not too large. A better approximation can be developed, by matching the discretized lifting-line result for d/c and using a third term. The revision is not expected to have much of an effect on the peak vortex-induced loads however.

For non-perpendicular interactions, the CAMRAD lifting-line expression was obtained by simply replacing r by (r SinA). For the parallel interaction, this is equivalent to assuming that

which is a good approximation to order k for the real part of the Sears function, but ignores the phase shift. It is the phase shift that leads to a significant asymmetry in the blade-vortex interaction peak loads for the parallel interaction, with the first peak (in time) being much larger than the second peak, particularly for small separation. By using a real g this asymmetry is absent in the CAMRAD lifting-line expression used in the lifting-surface correction. The result in fact is that L /Lll as calculated in CAMRAD is greater than one for the first peak, which CAMRAD then replaces by Lls/L = 1, i .e. there is no lifting-surface correction for the first peak. A nonzero phase exists for any non-perpendicular interaction, and is significant even for interactions 30 deg from perpendicular. Consequently, for most interactions the CAMRAD lifting-line expression results in no lifting-surface correction for the first peak. This is the major problem that must be corrected.

LS

1s 1 1

4.4 Revised Lifting-Line Theory Expression

The revised lifting-line theory expression will be based

L’ directly on the lifting-surface theory expression for g assuring that the phase shift will exist, and improving the approximation at higher wavenumbers as we1 1 . The approach was to adjust the constants from the lifting-surface expression in order to match the lifting-line g for the perpendicular interaction (the discretized wake resulk for d / c about - 6 ) and the parallel

28

interaction (up to about k = 1, the limit of the validity of the lifting-line approximation). The low frequency limit in both cases gives c = n / 2 . The factors a and a, were increased in order to mat& the magnitude of gL for wavefiumbers around 1. The factor a' was decreased for the parallel interaction, in order to match the peak phase shift at very low frequency. Finally, for the parallel interaction b = 0 and b = .5 are used, to match the phase of g Hence the expression for the lifting-surface theory lift LIS (Johnson, 1980b, page 167) is used with:

1

0

2 for wavenumbers arounA 1. L

t = 1.571 0

a = (1.25 + -5 sinA) (a 1 1 1 1s

a = (2.5 + SinA) (a2Ils 2

I75 1 5

(bl)ls bl = .5

11' The result is a revised expression for L

Figure 4-5 shows the revised lift deficiency function f o r the perpendicular interaction, and figure 4-6 shows the corresponding vortex-induced load. The revised lifting-line expression is an improvement (compare figures 4-5 and 4-21, but still the product of g and the vortex spectrum shows that the difference is not too important, as long as d/c is not too large. L

Figure 4-7 shows the magnitude and phase of the lift deficiency function for the parallel interaction. The CAMRAD lifting-line expression has no phase shift, and it5 magnitude is close the the lifting-surface theory expression. The revised lifting-line expression has a nonzero phase. and matches both the magnitude and phase reasonably well. It should be noted that the lifting-surface theory phase shows s o m e distortion that is a result of the approximate expression used; and that the accuracy of the lifting-line theory result is deteriorating at k = 1.

The vortex-induced loads along the wing span can be calculated from the lifting-surface theory and lifting-line theory expressions, and the peak load5 found as a function o+ vortex-blade separation h/b. The normalized section lift is L / P V r , where r is the strength of the vortex. N o t e that the two- dimensional lift is L = -pVb2nw, so for the vortex-induced downwash 2D

and the peak loads are L /pur = ?1/2h, occuring at r = +h. The vortex-wing separation s?i!uld be considered the effective value

which has a minimum value equal to the core size r hi3ff, C.

29

Figure 4-8 shows the peak lift magnitude and its spanwise location f o r the perpendicular interaction. The effect of the revised lifting-line expression is evident only for very small h.

= -74 for the peaks at The lifting-surface correction is L h = .5b. interaction. The negative peak occurs first (in time), then the lift goes through zero and the positive peak occurs. With no phase shift, the CCIMRCID lifting-line expression gives the same magnitude for the positive and negative peaks, and hence implies a correction factor greater than one f o r the negative peak. The revised lifting-line theory always gives a correction factor less than one. The liftinq-surface correction is .61 for the positive peak at h = .5b.

(L 1 Figure 4-9 shows the peak ?'if& for the parallel

Figure 4-10 shows the peak lift for an interaction with the vortex 30 deg f r o m perpendicular, which may be considered a typical r o t o r blade-vortex interaction case. Again the CCIMRAD lifting-line expression gives a lifting-surface correction greater than one for the negative peak, while the revised expression gives a correction significantly less than one. Hence with the phase shift accounted for in both the liftinq-surface and lifting-line expressions, this result is similar to that for the p e r p e n d i c u l a r interaction, The lifting--sur+ace correction 15 here -70 for the positive peak and -78 for the negative peak at h = .5b.

30

5. OUTLINE OF CALCULATIONS AND CORRELATIONS

5.1 CAMRAD Modif icat ions

The new wake model described above has been incorporated i n t o the CAMRAD computer program. Appendix A describes the code modifications, and defines the new input parameters. The analysis was run for nine t e s t cases, t o check t h a t t he modif icat ions were functioning as intended. These checks establ ished the fol lowing resul ts ,

a) With the three-quarter-chord co l loca t ion point, a smaller value of the re laxat ion fac to r f o r the c i r c u l a t i o n i t e r a t i o n i s required (compared t o tha t required w i th the quarter-chord co l loca t ion po in t ) . b) N e a r wake core sizes from .0005 t o .5 times the panel width were t r i e d ( the defaul t value is -2). For the low speed cases, t he r e s u l t s were ident ica l f o r .OOOS t o -2, but d i f f e r e n t f o r - 5 ; there were no convergence problems. For the high speed cases, t he analysis would not converge w i t h the smallest factors, and t he r e s u l t s f o r -05 t o -2 d i f f e r e d somewhat. (An in f luence of t h i s core s ize on the r e s u l t s usual ly means po ten t ia l problems w i t h the discret izat ion.) It was concluded tha t the basel ine value of .2 i s appropriate: small enough not t o a f f e c t normal configurations, and large enough t o ensure convergence.

c ) W i t h the dual-peak wake model, two i t e r a t i o n s between the wake geometry and t r i m so lu t ions were s u f f i c i e n t f o r r t o converge. It was noted tha t changes i n the mean in f l ow (which defines the v e r t i c a l convection f o r r i g i d wake geometry) had as much e f f e c t i n these i t e r a t i o n s as changes i n rGI.

G I

5.2 Rotors Analyzed

The capab i l i t i es and l i m i t a t i o n s o+ the n e w w a k e m o d e l were established by comparison of the ca lcu lat ions wi th measured hel icopter r o t o r air loads data. Outlined below are the invest igat ions tha t w i l l be described i n the remainder of th is report.

The focus of t h i s inves t iga t ion was on high speed forward f l i g h t , but a t high speed there are many fac to rs besides the wake t h a t inf luence the ro to r loads. Therefore spec i f i c features of t he new wake model, p a r t i c u l a r l y the treatment of blade-vortex in teract ion, were i n i t i a l l y examined by considering low speed cases:

1) Hovering ro to r c i r c u l a t i o n d i s t r i bu t i on . T h i s case wa6 used on ly to establ ish the inf luence and proper use of rTV, t he parameter def in ing the r a d i a l loca t ion of the t i p vortex a t the blade t r a i l i n g edge.

31

21 Lateral flapping wind tunnel test. Lateral flapping in low speed forward flight is a sensitive measure of blade-vortex interaction. No airloads data were available for this case.

3) S A 3 4 9 / 2 helicopter flight test. One low speed case that exhibits significant blade-vortex interaction was considered. This case and the lateral flapping data were used to examine the capabilities of the new wake model: the second order lifting- line theory (three-quarter-chord collocation point). and the lifting-surface theory correction.

4) Swept tip calculations. No measured data from a rotor with a swept tip is available. Calculations were performed to examine the capabilities of the new wake model: first order or second order lifting-line theory, straight or swept bound vortex.

Then the modified analysis was used to calculate the airloads for comparison with several flight tests and wind tunnel tests:

5) Boeing model 360 scale rotor test. Application of the new wake model to the high speed results of this wind tunnel test was a primary objective of the investigation.

6) H-34 rotor w i n d tunnel test. This t e s t has been a primary source of information and speculation about rotor airloads at high speed. Model 360 and H-34 cases were therefore used to examine the influence of various features of the new wake model on the calculated airloads at high speed.

7) AH-1G helicopter flight test. Although only one radial station was instrumented in this test, it includes high speed operating conditions.

8 ) H-34 helicopter flight test. This test has long been a standard for rotor airloads data, but did not include the high speed conditions that are of interest for the present investigation. For completeness, and in order to re-examine the quality of the measured data, the airloads were calculated fo r low speed and moderate speed cases.

9) UH-60A rotor calculations. No data is available yet for this rotor. The calculations were performed to examine the results of the new wake model for a rotor with a swept tip and a large (and unusual 1 twist . The report concludes by considering some special topics.

10) Harmonic content of airloads data. The available data are examined to determine the azimuthal resolution required for airloads tests.

11) Review of measured rotor airloads data. A summary of the problems and limitations observed in the existing rotor airloads data sets is provided. The review included tests that were not the subject of correlation in the present investigation: NACA

32

model wind tunnel test ; and CH-47, HU-lA, XH-SlA, NH-ZA, and CH-S3A f l i g h t tests.

5.3 Format of Data Presentation

Most of the cor re la t ion between the measured and calculated aerodynamics w i l l be f o r the ro to r blade sect ion l i f t . The section l i f t a t a pa r t i cu la r rad ia l s ta t i on i s obtained experimentally by measuring the pressure a t several chordwise stations, and numerical ly in tegrat ing along the chord. The wind tunnel and f l i g h t t e s t s considered vary g rea t l y i n the number of r a d i a l stat ions, number of chordwise stat ions, and use of d i f f e r e n t i a l ar absolute pressure measurements. The corre la t ion w i l l concentrate on the loading on the outboard p a r t of the blade, t y p i c a l l y f o r r a d i a l stat ions near 75%, 85%, and 95% R. The section l i f t w i l l be presented i n dimensionless form:

d(CT/c)/dr = L / ( P ( O R ) ~ C ~ )

where L i s the sect ion l i f t i n l b / f t , and c i s the l i f t coef f ic ient . The quant i ty obtained from the measured pressures i s actual ly the normal force coef f ic ient , whi le the analysis gives d(C /a) /dr i n shaft axes; t h i s d i f fe rence i s ignored.

2

T The experimental data is presented w i t h t he best azimuthal

resolut ion avai lable, which ranges from 10 harmonics t o 1024 samples per rev. The analysis gives the calculated blade l i f t a t twenty-four azimuth stations, i.e. 15 deg resolut ion. The calculated l i f t i s p lo t ted by connecting the po in ts every 15 deg wi th s t ra igh t l i n e s and then smoothing the corners s l i g h t l y . This is accomplished by using a 15-harmonic respresentation of the piecewise-1 inear curve connecting the calculated points. The resu l t i ng smooth curve nearly passes through a l l the calculated poi n t s, w i thout i ntroduci ng spur i ous overshoots or osc i 1 1 a t i ons.

Blade to rs iona l moments are also presented i n dimensionless form:

' m t l u "t /

where Mt i s the moment i n f t - lb .

33

6. HOVERING ROTOR CIRCULATION DISTRIBUTION

T h i s case is c o n s i d e r e d t o e s t a b l i s h t h e i n f l u e n c e and p r o p e r u s e of r , t h e pa rame te r d e f i n i n g t h e r a d i a l location of t h e t i p v o r t e x i? t h e b l a d e t r a i l i n g edge. B a l l a r d , O r l o f f , and Luebs (1979) o b t a i n e d t h e bound c i r c u l a t i o n f o r a m o d e l rotor i n hove r , u s i n g a two-component laser v e l o c i m e t e r t o measure t h e c i r c u l a t i o n around a box e n c l o s i n g t h e b l a d e a t v a r i o u s r a d i a l s t a t i o n s . The rotor p r o p e r t i e s and o p e r a t i n g c o n d i t i o n are a s f 01 l o w s -

number of b l a d e s r a d i u s s o l i d i t y c h o r d , c / R t w i et airf oi 1

C p

M t i p

2 3.43 f t -0464 ( r e c t a n g u l a r ) , -0396 (ogee) . 073 -11 deg NACA 0012

. 10 -22

F i g u e 6-1 compares t h e measured and c a l c u l a t e d c i r c u l a t i o n , r/nR , fo r r e c t a n g u l a r and ogee t i p planforms. Two v a l u e s of r are used f o r t h e c a l c u l a t i o n s i n each case.

5 TV

The n e a r w a k e model c o n s i s t s of a v o r t e x la t t ice , w i t h t h e trailers a t t h e e d g e s of t h e b l a d e aerodynamic segmen t s and t h e c o l l o c a t i o n p o i n t s i n t h e m i d p o i n t s of t h e b l a d e aerodynamic segments . The m o s t ou tboa rd trailer is a t t h e t i p , r / R = 1. With r = l . , t h i s m o s t o u t b o a r d trailer is t h e t i p v o r t e x . FigureTX-l shows t h a t t h e l o a d i n g is n o t a c c u r a t e l y c a l c u l a t e d u s i n g r = 1. With rTV less t h a n 1, t h e a n a l y s i s sets t h e b l a d e

TV' s e c t i o n T y i f t t o zero f o r aerodynamic segments o u t b o a r d of r T h e c o m p l e t e near w a k e la t t ice still e x i s t s , b u t t h e t railers o u t b o a r d of r have zero s t r e n g t h , so e f f e c t i v e l y t h e t i p v o r t e x is formed on #e b l a d e a t radial s t a t i o n rTV. When i n f i g u r e 6-1 r is set t o t h e measured t i p v o r t e x rollup p o s i t i o n , good correlation w i t h t h e measured c i r c u l a t i o n is o b t a i n e d . I t is also -Found t h a t r h a s a s i g n i - F i c a n t i n f l u e n c e on t h e c a l c u l a t e d induced power.

T V

TV

C a r e must b e t a k e n i n p o s i t i o n i n g r r e l a t i v e t o t h e b l a d e TV aerodynamic segments. I f t h e r e are o n e or m o r e segments hence ou tboa rd of t h e t i p v o r t e x , c o m p l e t e l y ou tboa rd of r

t h e y w i l l see a large p o s i t i v e induced ang le -o f -a t t ack , which w i l l increase t h e p r o f i l e power and d e c r e a s e t h e -Figure of m e r i t . F o r a r e c t a n g u l a r planform b l a d e t h i s e f f e c t s h o u l d b e avoided, which c a n be accomplished by h a v i n g t h e l as t aerodynamic segment large enough t o i n c l u d e rTV. For a h i g h l y t a p e r e d t i p ( s u c h as t h e ogee p lan fo rm of f i g u r e 6-11 t h e effect may b e realistic, a l t h o u g h it is a d e t a i l t h a t is p r o b a b l y beyond t h e c a p a b i l i t y of 1 i f t i ng -1 i n e theo ry .

TV'

PRECEDING PAGE BLANK NOT FlLMED 35

The calculations shown in figure 6-1 were obtained with first order lifting-line theory (quarter-chord collocation point) and without the lifting-surface theory correction. Second order lifting-line theory or the lifting-surface theory correction reduces the loading variation produced by the vortex, hence reduces the peak circulation. The result 15 worse correlation than shown in figure 6-1-

36

7. LATERAL FLAPPING WIND TUNNEL TEST

Lateral flapping in low speed forward flight is a sensitive measure of the effects of the rotor wake. The lateral tip-path- plane tilt of an articulated rotor depends primarily on the longitudinal gradient of the induced velocity distribution over the disk. The induced velocity in forward flight is larger at the rear of the disk than at the front, which produces larger loads at the front, hence an aerodynamic pitch moment on the rotor. An articulated rotor responds to this moment like a gyro, so the tip-path-plane tilts laterally, toward the advancing side. In forward flight there is also a small lateral flappinq contribution proportional to the coning angle.

The lateral flapping is underpredicted when uniform inflow is used, and even when nonuniform inflow based on undistorted wake geometry is used. Below an advance ratio of about 0.16, it is necessary to include the free wake calculation in order to obtain a good estimate of the lateral flapping (Johnson, 1986a). There is significant self-induced distortion of the tip vortices, resulting in numerous blade-vortex interactions in which the vertical separation is a faction of the blade chord. The result of such distortion is a much larger longitudinal gradient of the induced velocity, which produces the observed lateral flapping. In the case considered here, the free wake geometry places the tip vortices so close to the blades that the calculated flapping is sensitive to the value of the tip vortex core radius, which determines the maximum velocity induced by the vortex. There are a number of factors that influence the magnitude of the vortex- induced loading, including: the extent of the tip vortex rollup; the tip vortex strength: the viscous core size; lifting-surface effects on the induced blade loading; and possibly even vortex bursting or vortex-induced stall on the blade. The core size used in the analysis accounts for all such effects that are not otherwise modelled. The present investigation improves the calculation of the vortex-induced loading, using methods equivalent to lifting-sur+ace theory. Hence it is expected that a smaller core size, closer to the physical viscous core radius, will be needed for good correlation with the improved model.

The flapping in low speed was measured by Harris (19721, on a model rotor in a wind tunnel. The rotor parameters and operating condition are as follows.

number of blades radius sol i di ty chord, c/R twist airf oi 1

4 2.73 ft . 0891 . 070 -9.14 deq VZ3010-1,58

C,/C a' &PP tip

. 08 1 deg . 40

37

Figure 7-1 compares the measured and calculated lateral flapping, for three models of the blade-vortex interaction loads:

a) First order lifting-line theory (c/4 collocation point) and no lifting-surface correction. This model will require a larger core size.

b) Second order liftinq-line theory ( 3 ~ 1 4 collocation point) and no lifting-surface correction.

c) First order lifting-line theory (c/4 collocation point), with the lifting-surface theory correction.

For each case the tip vortex core sire is varied. Figure 7-2 shows the corresponding longitudinal flapping.

For case (a), a core size of about .05R (70% chord) appears best; but at low advance ratio the lateral flapping magnitude is overpredicted, and the longitudinal underpredicted, regardless of the core size. With either the 3c/4 collocation point or the lifting-surface correction, a core size of about .035R (50% chord) appears best. These two approaches produce about the same results, but w i t h di++erences in details. The liftinq-surface theory correction is nearly equivalent to simply increasing the core size by Ar = -015 R = - 4 3 b (20% chord). For advance ratios below about -06, the liftinq-surface correction does not improve the correlation, while t h e 3c/4 collocation point gives good results over the entire speed range shown.

C

In general therefore the best model is the second-order liftinq-line theory. The core size appropriate with this model is still relatively large, which might be a Reynolds number effect on the actual viscous core.

The calculations were performed using four revolutions of the rotor wake for all speeds. The free wake geometry (self- induced distortion) was calculated for the f irst two revolutions, and extrapolated fo r the last two. Using three revolutions of calculated free wake geometry produced poorer correlation with the measurements. Below an advance ratio of about -04 the free wake geometry used is not accurate. It is possible that the large errors in flapping prediction at advance ratios below -06 with the c/4 collocation point are associated with the influence o+ the core size (directly or through the circulation) on the wake geometry. Airloads and wake geometry measurements are needed to pursue these questions-

58

8. SA349/2 HELICOPTER FLIGHT TEST

In order to examine the capability of the wake model to calculate blade-vortex interactions without the additional complications of high speed flight, a low speed case that exhibits siqnif icant blade-vortex interaction is considered.

Flight tests of an SC1349/2 helicopter were reported by Heffernan and Gaubert (1986). Flight test case 2 is considered here (condition number 1 of Yamauchi, Heffernan, and Gaubert, 1988). The lift coefficient was measured at radial stations 75%, 88%. and 97% R. There were 9-11 pressure gages on the upper surface and 6-7 on the lower surface. Heffernan and Gaubert (1986) present 10 harmonics of the lift, for six revolutions and averaged over the six revolutions. Time histories of the lift with an azimuthal resolution of 2 deg w e r e obtained from the Rotary Wing Aeromechanics Branch, NASA Ames Research Center. The measured lift shows considerable variation from rev to rev for this flight condition. However. an examination of the blade- vortex interaction peaks in the individual revolutions showed that the amplitude of the peaks in the averaged data were only 3- 5% less than the mean of the amplitude of the peak in the original data; and the peak amplitudes in the original data vary by 27-16% from the mean amplitudes. Hence it is acceptable to base the correlation with analysis on the averaged lift data.

The principal characteristics of the rotor and the operating condition are as follows.

number of blades 3 radius 5.25 m solidity -0637 chord, c/R . 0667 ai rf oi 1 06209 twist -7.3 dog ( 0 outboard 91% radius)

CT/tF advance rat i o

-065 14 -72

Heffernan and Gaubert (1986) give CAMRAD input parameters for this rotor.

It is known that the free wake geometry must be used in order to accurately calculate the blade-vortex interaction loads for this low speed flight condition (Yamauchi, Heffernan, and Gaubert, 1988). Figure 8-1 compares the measured airloads with calculations using the present wake model, showing the influence of nonuniform inflow and the free wake geometry. Figure 8-2 shows the corresponding calculated wake geometry. These calculations involved the following features:

a) c/4 collocation point, with liftinq-surface correction;

39

b) tip vortex core sire .015 R (22.5% chord);

c) core size of -100 R for radial stations inboard of 80% R (transitioninq to -015 R at 90% R ) , to suppress the bl ade-vor t ex i nter act i ons i nboard .

The amplitudes of the blade-vortex interaction peaks are well predicted. The calculated load is low in the second quadrant for 97% R, and high in the third quadrant for 88% R.

Figures 8-3 to 8-5 compare the measured airloads with calculations using tip vortex core sizes of -015, -025, -035, and -045 R (22.5% to 67.5% chord). For these calculations the same core size was used for both inboard and outboard portions of the blade. Three wake models are considered:

a) first order lifting-line theory (c/4 collocation point), and no lifting-surface correction;

b) second order lifting-line theory (3c/4 collocation point), and no lifting-surface correction;

c) first order lifting-line theory, with the lifting-surface theory correction.

For the loading at 97% R, the best core size is -025 R (37.5% chord) for case (a), or .015 R (22.5% chord) with either the 3c/4 collocation point or the lifting-surface correction. The correlation suggests that the actual core radius varies with azimuth, being larger for vortices created on the retreating side of the disk. The calculations also significantly overpredict the blade-vortex interactions for the inboard radial stations (particularly 75% R here). The core size is increased for collocation points on the inboard part of the blade in order to eliminate (but not explain) this problem. Note that the calculations of Yamauchi, Heffernan, and Gaubert (1988) used a model similar to (a); they concluded that the best core site was 0.035 R, considering inboard stations as well as the tip.

Figure 8-6 shows the loading calculated using these three wake models, with the best core radius for each. All three models give similar results, although the details of the calculated loading vary. Note that the lifting-surface theory correction is nearly equivalent to simply increasing the core radius by A r = - 0 1 R = - 3 b (15% chord). With either second order liftinh-line theory or the lifting-surface theory correction, the required core size of 22.5% chord is in the expected range for the physical viscous core radius.

fipplication of the lifting-surface theory correction is controlled by the parameter dls. and applied for a vortex line segment if the distance between the collocation point and the center of the segment is less than

dlsR. doubles the time required to compute the wake influence

The correction is calculated

Using the correction for all segments in the tip vortices

40

coeff ic ients. For th is case i t was found t h a t t he calculated load5 were unchanged f o r d varying from 100. t o 0.5, and were near ly the same f o r d were of ten the s a m e as without the corre~t ion. '~Hence i t i s concluded tha t i t i s possible t o apply the l i f t i n q - s u r f a c e correct ion w i t h d = 0.5, which increases the in f luence coe f f i c i en t compukztion time by only 5%.

= b72; however, w i t h d = 0.1 the load5 Is .

Figure 8-7 shows the e f fec t of the core s i z e used f o r inboard co l locat ion po in ts on the calculated loads. I f the same t i p vortex core s i ze i s used f o r a l l blade co l l oca t i on points, then the blade-vortex in te rac t ion loads are s i g n i f i c a n t l y overpredicted a t 75% R. While the existence o f th is e f f e c t has been known f o r a long t ime (Johnson, 1971~11, the physical nature o f the phenomenon remains speculative. Figure 8-7 shows tha t using a larger core s i ze when the co l locat ion po in ts are on the inboard par t of the blade w i l l improve the corre la t ion; no explanation of the physics i s intended. More de ta i l ed measurements, inc lud ing measurements of the wake geometry, are needed t o explore t h i s phenomenon.

Figure 8-8 compares the calculat ions (using the l i f t i n g - surface correct ion) w i th three revolut ions o f the unaveraged data. The unsteadiness and noise i n the measured data d o not change the basic conclusions of the correlat ion, but i t i s c lear t h a t f i n e d e t a i l s m u s t be ignored. The data f o r 75% R suggest t h a t the unsteadiness may be p a r t i a l l y responsible f o r the decreased blade-vortex in te rac t ion peaks i n the averaged data.

41

9. SWEPT TIP CALCULATIONS

The new wake model improves the capability to analyze rotors with swept tips, by introducing the second order lifting-line theory. No measured airloads data are available for rotors with swept tips. Calculations were performed to examine the effects of the features in the wake model. The rotor considered had the following properties and operating condition: I

number of blades 4 sol i di ty -0748 CT/U . 10

-5 deq 3 e g n c e ratio -2

(similar t o the S-76 main rotor). Three tip configurations were analyzed:

1) tapered planform, 30 deg sweep at 95%R; 2) rectangular planform, 30 deg sweep at 95%R; 3) rectangular planform, 45 deg sweep at 90XR.

In the tip region, the edges of the blade aerodynamic panels are at r / R = -88, -91, -935, -955, -97, -985, and 1. The only blade motion included was coning and first harmonic rigid flapping. The influence of a swept tip on the dynamics of a rotor blade, particularly the elastic torsion motion, is significant. That influence is suppressed here so that the influence of the wake model on the aerodynamic load can be assessed separately.

The analysis options that implement the near wake model allow four cases:

a) c/4 collocation point, straight lifting-line;

b) 3c/4 collocation point, straight lifting-line;

c) c/4 collocation point, swept lifting-line;

d) 3c/4 collocation point, swept lifting-line. I .

For a swept tip, model (a) is first order lifting-line theory and model ( d ) is second order lifting-line theory. The second order theory also has an influence in yawed flow, which will be given by model (b) as well as model (d).

Figure 9-1 shows the calculated loading at two stations on the tip, 92% and 98% R. Note that even for the tapered, 30 deq swept tip, model (c) has a significant effect on the calculated load. Model (c) however is not a consistent implementation of lifting-line theory, and should not be used. Comparing models (a) and (d), it is seen that second order lifting-line theory has a significant effect on the tip loading. A concern with discretized lifting-line models in yawed or swept flow is the

43

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posibility of singular behavior of the loads, particularly near the kinks in the span axis. No such problems were encountered with the cases investigated.

The wake model has s o m e influence on the calculated rotor induced power, as shown in the following table.

ratio induced power to ideal induced power model = (a) (b) (C) (d)

tip 1 1.38 1.49 1.20 1.44 tip 2 1.38 1.49 1.19 1.45 tip 3 1.37 1.46 1-00 1.32

Again, model (c) is not appropriate.

The 3c/4 collocation point and the lifting-surface correction are alternative methods to improve the calculation of blade-vortex interaction loads. The results o+ the preceding chapters show that these two methods are indeed comparable. However, only second order lifting-line theory influences the swept tip loads; the lifting-surface theory correction has no role in the aerodynamics of the swept tip or yawed flow.

44

10. BOEING MODEL 360 SCALE ROTOR TEST

A scaled model of the Boeinq model 360 main r o t o r was tested i n the DNW wind tunnel (Dadone, Dawson, Boxwell, and Ekquist, 1987). The high t w i s t and low aspect r a t i o of the blades should increase the ef fects of negative loading on the advancing t i p ( f o r a given blade loading C /a, the bound c i r c u l a t i o n i s T proport ional t o the blade chord). Hence th is i s a good choice f o r appl icat ion of the new wake model for high speed f l i g h t .

The prel iminary t e s t data, ro to r properties, CAMRAD input parameters, and a i r f o i l tab les were obtained from the Aerof lightdynamics Directorate, U.S. Army Aviat ion Research and Technology Ac t iv i t y . The data provided were sect ion l i f t a t 88% and 95% R r a d i a l s t a t i o n ( including p l o t s of t he ind iv idua l pressures), and the to rs iona l moment a t 23% R. There were 6-8 pressure gages on the upper surface and 5-6 on the lower surface, a t the fo l lowing chordwise locations:

upper :;/c = -06, -12, .18, -25, -35, -508, -70, -858 lower x/c = .03*, .06, -28, .35, -50, - 8 5 s

( 8 not f o r 95% R) ( * a t 89% and 94% R)

Air loads data averaged over 64 revolutions, and two revolut ions o f the tors ional moment data were provided, w i t h 1024 points per revolut ion.

The model 360 r o t o r has tapered planform, h igh t w i s t blades w i th dynamics optimized f o r high speed f l i g h t . The p r inc ipa l character is t ics of the r o t o r are as follows:

number of blades radius s o l i d i t y chord, c / R

t w i s t

a i rf o i 1

4 5.052 f t . 10725 -0872 inboard 90% R, -0279 a t t i p -11.65 deg inboard 86X R, -17.28 deg outboard 8KL R VR12 inboard 85% R, VRl5 a t t i p

The blade had the p i t c h a x i s a t 20.2% chord; t he center of g rav i t y and e l a s t i c ax i s a t approximately 25% chord; and the aerodynamic center and tension center a t approximately 27% chord. A s the control system s t i f f n e s s was unknown, the blade r i g i d p i t c h motion was not used and the p i t c h ax i s was ignored. The baseline analysis assumed tha t the center of grav i ty , tension center, e l a s t i c axis, and a i r f o i l tab le reference ax is were a l l at 25% chord ( the a i r f o i l tables account f o r t he aerodynamic center shi f t from the a i r f o i l t ab le reference axis) . The r o t o r had no lag damper.

45

The f i v e operating condi t ions ( i d e n t i f i e d by run number) considered are as follows. Run 195 was i n the open t e s t section, and the other runs were i n the closed section.

R u n 195 222 244 250 279 ~~ ~ ~~

a -5.60 -6.70 -7.95 -12.01 -10.23 -0699 -0695 .OS07 . O S 0 8 -0691

c /a . 0054 1 -00557 . 00607 . 00687 . 0 1078 agvance r a t i o . 356 I359 . 398 .366 . 456

S CT/lT

-86 -83 . a7 I93 . 90

CX/C -. 0042 -. 0041 -. 0049 -. 0051 -. 0067 fo rce angle -3.43 -3.40 -5.54 -5.73 -5-50 r o t o r L/D 6.4 6.1 4.9 3.7 4.1

The propuls ivq force -X/q i s about 0.65 f t 2 f o r run 250, and about 0.55 ft' fo r the other runs. The "force angle" i s the angle of the resul tant r o t o r fo rce from ver t i ca l , pos t ive a f t . The angle of the resu l tan t fo rce r e l a t i v e the shaf t i s thus 2.2 t o 6.3 deg a f t f o r these runs. It was reported t h a t run 195 had a s p l i t tip-path-plane. Generally, the r o t o r was operated w i t h t he tip-path-plane n o r m a l t o the sha-ft, but the r o t o r +lapping was not measured. Non-zero f lapp ing was observed f o r some runs. I n pa r t i cu la r , i t was reported t h a t BlC 3 1.6 deg f o r run 244.

The ca lcu lat ions trimmed the r o t o r thrust t o the measured value, and the first-harmonic f lapp ing r e l a t i v e the shaf t t o zero. The r o t o r shaft angle of a t tack was set t o the measured value. (The calculated power matches the measured power be t te r f o r f i x e d shaf t angle than w i t h t he drag force trimmed t o the measured value.) The blade motion considered was ten harmonics of the f i r s t si;: f lap- lag bending modes ( including the r i g i d f l a p and l a g modes) and the f i r s t e l a s t i c to rs ion mode.

Figure 10-1 shows the in f luence of the f a r wake model on the calculated a i r loads a t r a d i a l s ta t i ons 80%, 88%, and 95% R f o r run 222 (advance r a t i o .36). The wake model has a s i g n i f i c a n t e f f e c t on the t i p loading. A s i n g l e peak model using the maximum bound c i r c u l a t i o n has both the s ign and strength of t he v o r t i c i t y wrong when the t i p loading i s negative. The dual peak model has a d i f f e r e n t inboard wake s t ruc tu re than the model using the outboard c i r c u l a t i o n peak; i n addi t ion, changes i n the loading w i l l feed i n t o the t i p vortex s t rength and increase t h e d i f ferences between these two models. Consequently the m i n i m u m loading and the azimuth a t which i t occurs var ies g r e a t l y f o r the th ree models. Figure 10-2 examines the convergence of the dual- peak model, f o r which the wake s t ruc tu re depends on the r a d i a l s t a t i o n of the inboard peak. The r o t o r i s f i r s t trimmed using uniform inf low; t h i s so lu t ion provides a mean i n f l o w and the l oca t i on of inboard peaks, to be used i n ca lcu la t ing the nonuniform in f l ow inf luence coef f i c ien ts . Then the r o t o r i s trimmed using nonuniform i n f l o w ( the f i r s t i t e r a t i o n ) . W i t h the

46

resu l t i ng updated mean in f low and loca t i on of the inboard peaks, the in f luence coef f i c ien ts are recalculated. The the r o t o r i s again trimmed using nonuniform in f l ow ( the second i t e ra t i on ) . The wake s t ruc tu re f o r the dual-peak model i s converged i f the r a d i a l loca t ion of the inboard peak i n the current c i r c u l a t i o n so lu t ion matches tha t used i n the wake geometry t o ca lcu late the inf luence coef f ic ients . Figure 10-2 shows tha t two i t e r a t i o n s are required f o r such convergence, w i t h some di f ferences between the a i r loads from the two i te ra t ions . Figures 10-3 and 10-4 g ive the corresponding resu l t s for run 279 (advance r a t i o -46 ) . The inf luence o f the wake model i s s t i l l s ign i f i can t , even w i t h a tip-path-plane angle of attack o f -10.2 deg.

Figures 10-5 to 10-7 show f o r runs 222 and 279 the in f luence on the a i r loads of the near wake model; r o l l u p of the inboard t r a i l e d wake; and blade e l a s t i c motion. The e f f e c t of t he near wake model ( f i g u r e 10-5) i s Sign i f icant . T h i s i s the e f f e c t of second order l i f t i n g - l i n e theory f o r t h i s low aspect-ratio blade, and f o r t he large yawed f low t h a t t he blade sees i n high speed forward f l i g h t . The calculat ions used a t i p vortex core s i ze of 0.02 R (23% chord). Decreasing the core s ize t o -01 R had no e f fec t : c lose blade-vortex i n te rac t i on i s not a fac to r f o r these high speed cases. Similarly, r o l l u p o f the inboard t r a i l e d wake when the t i p loading is negative had l i t t l e e f f e c t i n the loading ( f i g u r e 10-6; an inboard core s i z e of -03 R was used). Res t r i c t i ng the calculated blade motion t o just l / rev r i g i d f lapping had some e f fec t on the loads ( f i g u r e 10-7). T h i s e f f e c t i s p r i m a r i l y produced by the la rge e l a s t i c to rs ion calculated f o r the blade, as shown i n f i gu re 10-8.

The measured and calculated a i r loads are compared f o r the f i v e runs i n f i g u r e 10-9. The behavior of the measured air loads, of the calculated airloads, and of the d i f ference between the two i s consistent. The calculated mean loads tend t o be high. A l l ,

the measured loads have a peak around 60 deq azimuth, whi le the calculated loads are decreasing i n the f i r s t quadrant. Regarding the m i n i m u m loading a t azimuths from 90 t o 135 deq, the measurements have osc i l l a t i ons and are sometimes relatively +lat; whi le the calculat ions are smoothly varying with a d i s t i n c t m i n i m u m . For high advancing t i p Mach number (runs 250 and 2791, the measured loading i s much more negative than the calculated loading f o r 95% R; and the d i f ferences between the measured and calculated loading are greater f o r 95% R than f o r 88% R.

The t ime h i s to r i es of the blade pressures were examined t o determine what i s occuring i n the measured l i f t . The features o f i n t e r e s t are the constant or increasing l i f t f o r azimuths from 45 t o 75 deq; the negative loading a t azimuths 90 t o 135 deg, w i t h a f l a t or reversed minimum; and the o s c i l l a t i o n s a t azimuths from 105 t o 150 deg. Basical ly these e f f e c t s are being produced by shocks, which cause jumps i n the pressure as a funct ion o f Y.

Upper surface shocks appear when the section Mach number

The shock moves a f t as the Mach number increases w i t h reaches -72--74, hence a t 9 = 20 t o 45 deg, depending on r and

Mat.

47

azimuth. Thus there i s a large negative pressure a t the nose, w i t h a sharp drop somewhere i n the f i r s t 25% or 35% of the chord. The resu l t i s a p o s i t i v e l i f t , the e f f e c t of the shock countering the e f fec t of the angle of attack decreasing w i t h 9. L o w e r surface shocks occur f o r VJ = 90 t o 135 deg, the negative pressure ahead of the shock producing negative l i f t . The shock occurs on the f i r s t or second, o r even t h i r d quarter of the chord,

For low Mat, the upper surface shock t' depending on M disappears a t $ around 100 deg, which helps produce a sharp drop i n the l i f t . 9 around 150 deg, producing osc i l l a t i ons i n the l i f t .

For high Mat, the upper surface shock disappears a t

The analysis being used sees the e f f e c t s o f transonic aerodynamics only through the a i r f o i l tables. Figure 10-10 p l o t s the a i r f o i l t ab le data f o r t h i s case ( the a i r f o i l a t 88% and 95% R i s the V R 1 5 1 , which exh ib i t the expected behavior. What the measured l i f t impl ies i s c roughly constant w i t h decreasing angle of attack but increasing Mach number, a f t e r shocks f i r s t appear around M = -73. It i s possible t h a t the measured l i f t r e f l e c t s three-dimensional transonic ef fects , requ i r i ng a CFD analysis t o capture.

Q

While the pressure measurements are accurate, i t i s questionable +or these runs whether there is s u f f i c i e n t chordwise resolut ion t o obta in the section l i f t . The shocks tend t o remain between two pressure gages f o r many degrees o f azimuth. Without information about the movement of the shock between gages, the chordwise i n teg ra t i on produces nearly constant l i f t coef f ic ient , which i s responsible fo r the f l a t cQ i n the f i r s t quadrant (from upper surface shocks) and near the negative m i n i m u m (from lower surface shocks). When a shock passes a gage, i t produces a rap id change i n the pressure there, which then appears i n the integrated l i f t also. It i s concluded t h a t t he chordwise resolut ion of the measured pressures on the forward 25% t o 50% of t he a i r f o i l i s not s u f f i c i e n t to obtain an accurate l i f t coe f f i c i en t .

Figure 10-11 compares the measured and calculated to rs ion moment a t 23% rad ius ( the analysis and data correspond t o the air loads comparison i n f i g u r e 10-9) . The operating condi t ion does not in f luence much the shape of e i t he r the calculated or measured moment, and even the amplitudes are s i m i l a r (except f o r the highest speed, run 279). The measured and calculated r e s u l t s are qu i te d i f f e r e n t however. Note tha t a moment coe f f i c i en t of A C ~ ~ / ~ = -0002 corresponds t o a blade e l a s t i c t w i s t def lect ion a t the t i p of about 1 deg. Two observations can be made: the o s c i l l a t i o n s of t he measured moment on the r e t r e a t i n g s ide are a t around 4.6/rev, whi le the calculated to rs ion frequency i s b.O/rev; and the measured behavior looks l i k e a blade approaching p i tch- f lap f l u t t e r . The calculat ions were made assuming that there was no f l e x i b i l i t y i n the control system; a contro l system so f t enough t o lower the fundamental t o rs ion /p i t ch mode frequency below S/rev would not be unreasonable. To inves t iga te the inf luence of the to rs ion frequency, the blade GJ was reduced t o give a calculated e l a s t i c tors ion frequency of 4.8/rev ( s t i l l

48

with no control system flexibility). In addition, the blade center of gravity was shifted aft from 25% chord to 27% chord in the analysis. Figure 10-12 compares the original and modified calculations with the measured torsion moment for run 222, and shows the influence of the modified input parameters on the calculated lift. The input parameter changes do improve the correlation with the torsion moment. The increased oscillation of the calculated torsion moment is also evident in the calculated blade airloads. To proceed further it would be necessary to obtain a better description of the rotor physical proert i es.

49

11- H-34 ROTOR WIND TUNNEL TEST

A n H-34 main ro to r was tested i n the 40- by 8O-Foot Wind Tunnel (Rabbott, Litak, and Paglino; 1966a, 1966b). This t e s t covered a l a rge range of operating condi t ions (advance r a t i o s from -29 t o -45, tip-path-plane angles from -5 t o 5 deg), and has been the focus f o r much work on high speed r o t o r air loads (Hooper , 1984 .

The sect ion l i f t was measured a t n ine r a d i a l stations: r / R = -25, -40, -55, -75, -85, -90, -95, -97, -99. For rad ia l s ta t ions from 75% t o 95%, d i f f e r e n t i a l pressure measurements were made a t 7 chordwise locations:

x / c = -017, -090, .168, -233, -335, -625, -915

except f o r 85% radius, which used 4 addi t ional gages (11 t o t a l ) at:

x/c = -040, -130, -500, -769

The other r a d i a l s ta t ions had only 3-5 gages- The report g ives 10 harmonics o f the integrated sect ion l i f t a t these r a d i a l stations. For presentation here, a measurement system phase l a g of A+ = 5.3 deg was accounted fo r .

The proper t ies of the H-34 r o t o r blade are given by Rabbott, Lizak, and Paglino (1966a). The p r inc ipa l character is t ics of t he r o t o r are a5 follows:

number of blades rad ius so l i d i t y chord, c/R t w i s t a i r f o i l

4 28 f t - 0622 -0488 -8 deg NACA 0012

The operating condit ions f o r shaf t angle of attack as = 0 are as f 01 1 ows:

advance r a t i o . 284 I394 I450 . 73 . 79 . 83 . 0570 I0594 . 0497 I00022 - 00169 . 00289 - 5 -. 5 -1.0

-2.8 -3.6 -3.7

and f o r a = -5 deg: . 288 -396 I449 5 advance r a t i o

PRECEDING PAGE BLANK NOT FILMED

I73 . 79 -83 . 0573 0596 (. 0484 -- 00529 -. 00443 -.00172

- 7 1.0 -. 2 -3.5 -4.4 -4.4

5 1

The ca lcu lat ions trimmed the r o t o r thrust , and the longi tudinal and l a t e r a l f lapping t o the measured values. The r o t o r shaft angle of attack was set t o the measured value. With t h i s t r i m method, the calculated ro to r drag force and power were close to the measured data. The blade motion considered was ten harmonics of the f i r s t seven f lap-lag bending modes ( including the r i g i d f l a p and l a g modes) and the f i r s t e l a s t i c to rs ion mode. Rig id wake geometry w i th a t i p vortex core s i ze of -03 R was used.

Figure 11-1 shows the inf luence of the f a r wake model on the calculated a i r loads a t r a d i a l s ta t ions 75%, 85%, and 95% R f o r II = -39 and a = 0, The wake model has a s i g n i f i c a n t e f f e c t on the loading. Tse dual peak model and the s ing le peak model using the outboard c i r c u l a t i o n peak give s imi la r resul ts , implying tha t the inboard wake s t ruc tu re i s not very important. The wake model also influences the calculated induced power:

r a t i o induced power t o idea l induced power II = .29 -39 I45

dual -peak m o d e l 1.64 2.41 2.36 1.65 2.18 2.29 1.79 2.42 3.17

s i ngl e-peak, single-peak,

___________---------------------------------------

rO max

dual-peak, 1st i t e r 1.44 2.19 2.33

Figure 11-2 examines the convergence of the dual-peak model, f o r which the wake s t ruc tu re depends on the r a d i a l s t a t i o n of the inboard peak. The wake st ructure f o r the dual-peak model i s converged i f the r a d i a l locat ion of the inboard peak i n the current c i r c u l a t i o n so lu t ion matches tha t used i n the wake geometry t o ca lcu la te the inf luence coef f ic ients . Figure 11-2 shows that two i t e r a t i o n s are required f o r such convergence, wi th s o m e dif ferences between the air loads from the two i terat ions.

Figures 11-3 and 11-4 show the inf luence on the air loads of the near wake model; blade e las t i c motion; t i p vortex core size; and r o l l u p of the inboard t r a i l e d wake. Each o f these has some e f f e c t on the air loads. The near wake model (c/4 or 3c/4 co l locat ion po in t ) inf luences the l i f t i n g - l i n e ca lcu la t ion o f the loads i n yawed -Flow. The r i g i d blade analysis on ly used f i r s t harmonic r i g i d f l a p motion. Decreasing the t i p vortex core s i r e had only a small e f fec t , but r o l l u p of the inboard t r a i l e d wake changed the loads ~ i i g n i f i c a n t l y ( f i gu re 11-4). For the l a t t e r case, a core s i z e o f -05 was used f o r t he inboard t r a i l e d wake when the t i p loading was negative. These features also influenced the calculated induced power ( f o r a = 0):

5

52

r a t i o induced power t o ideal induced power u = -29 I39 I45

base1 i n e 1.64 2.41 2.36

smaller core s i z e 1.64 2.23 2.37 inboard r o l l e d up 0.70 2.34 2-45

...................................................

c/4 c o l l po in t 1-52 1.96 2.24

Note tha t the induced power was less than idea l fo r JA = -29 and the inboard t r a i l e d wake r o l l e d up; tha t would not be an appropriate model

Calculat ions were a lso performed using a f r e e wake geometry; trimming the r o t o r drag fo rce t o the measured value; and w i t h a dynamic s t a l l model. L i t t l e change i n the ca lcu lated a i r loads was found.

The measured and calculated a i r loads are compared i n f i g u r e 11-5 f o r JA = .39 and as = 0. The dual-peak wake model i s needed f o r the negative loading a t 95% R (see f i g u r e 11-11. The measured and calculated a i r loads are compared i n f i g u r e 11-6 f o r u = -39 and a = -5 deq. For the th i s case, w i t h a t ip-path- plane angle 07 attack of -6 deg, the r i g i d wake geometry keeps t h e t i p vor t i ces wel l below the blades; the f ree wake geometry ca lcu la t ion give the same resu l t , Figure 11-6 a lso shows the calculated a i r loads w i t h the prescribed wake geometry adjusted t o leave the wake i n the tip-path-plane, i n order t o maximize the inf luence of the wake. Note tha t the measured t ime h i s t o r i e s are constructed from only 10 harmonics, so the h igh frequency o s c i l l a t i o n s observed i n f i gu res 11-5 and 11-6 do not f u l l y r e f l e c t the actual events. Figure 11-7 compares the measured and calculated a i r loads (c 1 f o r a l l s i x cases considered here.

J?

The cor re la t ion between calculated and measured a i r loads i s not very good. The fo l low ing fac to rs may be involved.

a) The wake geometry used by the ca lcu lat ions may be incorrect . Figure 11-6 suggests t h a t the wake might be closer to the r o t o r disk. The f ree wake geometry method being used has not been modified t o include the dual-peak model. Hence whi le i t i s using the correct t i p vortex s ign and strength, i t does not have the correct inboard wake model; i.e. the wake geometry ca lcu la t ion i s based on a s ing le peak model, using the outboard peak value a t best. W i t h a dual peak model i n the wake geometry calculat ion, the increased strength of the inboard (pos i t i ve) t r a i l e d wake would tend t o push the t i p vortex closer t o the r o t o r disk. A l ess l i k e l y p o s s i b i l i t y i s t h a t the proximity o f the wind tunnel wa l ls a f fec ts the wake geometry.

b) The wake may not be a major influence. F igure 11-8 shows the inf luence of shaft angle (hence tip-path-plane angle of attack) on the measured airloads. The zero shaf t angle data i s expected t o show much more wake in f luence than the -5 deg (forward ti lt) data. Differences between the two cases could be a t t r i b u t e d t o wake ef fects. I n f a c t t he measured a i r loads f o r t he two shaf t

53

angles are very s i m i l a r .

c) The chordwise resolut ion of the pressure measurements may not be s u f f i c i e n t f o r an accurate sect ion l i f t wi th shocks on the blade. Generally the measured l i f t i n the f i r s t quadrant i s higher than the calculated l i f t . Some of the cases (e.9. f i g u r e 11-51 have near ly constant l i f t c o e f f i c i e n t on the t i p i n the f i r s t quadrant, s imi lar t o the behavior observed on the model 360 r o t o r (chapter 10). With an NACA 0012 a i r f o i l a t these speeds, there are ce r ta in l y shocks on the blade. although they are d i f f i c u l t t o discern i n d i f f e r e n t i a l pressure measurements.

d) The pressure measurements may be incorrect. The chordwise pressure d i s t r i bu t i ons exh ib i t some unusual behavior. Examples are given i n f i g u r e 11-9. The presence of shocks might produce some of t h i s behavior, but systematic e r ro rs are also possible.

e) The t e s t was conducted wi th a s p l i t tip-path-plane (Rabbott, Lizak, and Paglino, 1966b) . A r o t o r cont ro l system modi f icat ion produced kinematic coupling such t h a t two adjacent blades ( the instrumented blade and the blade proceding i t ) had d i f f e r e n t c y c l i c p i t c h than the other two. Hence there was a s p l i t t i p - path-plane when c y c l i c p i t c h was applied, t y p i c a l l y about 1 deg di++erence i n the +lapping. The longi tud ina l c y c l i c p i t c h used increased wi th speed and with forward shaf t tilt. The unusual aerodynamic environment of a s p l i t tip-path-plane was not included i n the analysis. Moreover, the control system might have introduced higher harmonics of control, i n addi t ion t o the d i f ferences i n l / r e v pitch.

54

12. AH-16 HEICOPTER FLIGHT TEST

An AH-1G hel icopter wa5 tested i n f l i g h t wi th three blade sets having d i f f e r e n t a i r f o i l s (Morris, 1978). The three a i r f o i l s had the fol lowing properties:

It wa5 found tha t the a i r f o i l used had an e f f e c t on the measured p i t c h moment coe f f i c i en ts and o s c i l l a t o r y p i t c h l i n k loads ( the l a t t e r were h igh enough with the RC-SCZ t o l i m i t the f l i g h t speed). The air-Foi l used had l i t t l e e f f e c t on the measured power, mean p i t c h l i n k load, l i f t coef-ficients, and to rs ion moment. The f l i g h t tes ts were conducted f o r advance r a t i o s from 0.12 to 0.37; negative loading on the advancing t i p was measured f o r advance r a t i o s of 0.33 and above.

The data were reported by Morris, e t a1 . (1979-1982) . The section l i f t was measured at a s ing le r a t i a l stat ion, 90% R. There were 7-8 pressure gages on the upper surface and 6 gages on the lower surface:

upper x / c = -02, -10, -20, -35, -50 , -70, .80, .90 lower x/c = -02, -10, -20, .SO, -70, -90

The 35% chord upper surface gage was inoperable f o r the NLR-1T a i r f o i l . The 70% chord lower surface gage was inoperable f o r t he RC-SCZ a i r f o i l , and replaced by in te rpo la ted data. Time h i s t o r i e s o f the pressures, l i f t coef f i c ien t , and moment coe-f+icient are given with an azimuthal reso lu t ion of 2 deq.

The proper t ies of the modified AH-16 r o t o r blades tested are given by Morris, Tomaine, and Stevens (1979, 1980a, 198Ob). The p r inc ipa l character is t ics of the tee ter ing r o t o r are as fol lows:

number of blades 2 rad ius 22 f t so l i d i t y -0651 chord, c/R -1023 t w i s t -10 deg

The blade to rs ion frequency w a s 15.5 Hz (2.8&/rev) wi th the NLR-1T a i r f o i l , and 16.7 Hz (3.131rev) w i t h the other two sections. The RC-SCZ blade needed counterweights on the p i t c h horns, t o counter larger mean to rs ion moments i n hover; o s c i l l a t o r y p i t c h l i n k loads l i m i t e d the maximum advance r a t i o t o 0.35 wi th t h i s section.

55

One case. a t the highest speed tested, i s considered here f o r each of the three blades. The operating condi t ions are as f 0 1 1 ow5.

RC-SC2

94-11 I345 . 89 . 0808

.- - - -- - -

-6. 1 1.3 1.1 .00657

Note tha t the measure4 tip-path-plane angles imply an a i r c r a f t drag area of 14-17 ftL.

The ca lcu lat ions trimmed the ro to r thrust, and the longi tud ina l and l a t e r a l f lapping t o the measured values. The r o t o r shaft angle of attack was set t o the measured value. Because of the lack of two-dimensional data, p a r t i c u l a r l y a t the proper Reynolds numbers, no a i r f o i l tables were ava i lab le f o r these three sections. The calculat ions were performed using the tab le f o r the VR15 a i r f o i l of the Boeing model 360 r o t o r 0.835, CRmax = . 1-21, w i t h drag and moment coe f f i c i en t increments. The blade motion considered was ten harmonics o f t he teeter mode, the f i r s t s i x f lap- lag bending modes, and the f i r s t e l a s t i c to rs ion mode. R ig id wake geometry w i t h a t i p vortex core s i t e of 0.02 R was used. Using f r e e wake geometry or dynamic s t a l l had l i t t l e e f fec t on the calculated t i p airloads.

- (PIdd -

Figure 12-1 compares the measured and calculated air loads f o r the three cases. The corre la t ion was improved by adding a nose-down p i t c h moment increment t o the a i r f o i l t a b l e data. 4 drag increment was a lso used, i n order t o match the measured r o t o r power:

The measured l i f t coe f f i c i en ts are s imi la r i n character to the other high speed t e s t data examined i n th is invest igat ion. Note the roughly constant l i f t i n the f i r s t quadrant. The o s c i l l a t i o n s around y. = 120 de9 are caused by shocks moving past ind iv idual pressure gages (pa r t i cu la r l y lower surface gages a t 20% and 50% chord).

Figure 12-2 shows the inf luence of the f a r wake model on the calculated airloads. The wake model has some e f f e c t even f o r t he large tip-path-plane angles of these cases. The inboard wake appears t o be as important as the t i p vort ices. The wake inf luence on the f irst-quadrant a i r loads can be increased by

56

moving the prescribed geometry closer t o the r o t o r di5k. Figure 12-3 shows the inf luence of the near wake model (c/4 or 3c/4 co l loca t ion point ) , Figure 12-4 shows the in f luence o f the blade motion, which i s substantial. The blade i s r e l a t i v e l y sof t i n to rs ion (frequency about 3/rev) , so the calculated e l a s t i c t o rs ion motion i s very large. Figure 12-5 shows the blade e l a s t i c de f lec t ion a t the t i p , which has the fo l l ow ing composi t i on :

mean -4 t o -5 deg l / r e v amplitude 2 t o 3 deg Wrev amp1 i tude 1.3 deq 3/rev amplitude 0.4 deg

T h i s to rs ion def lect ion i s produced by the aerodynamic p i t ch ing moments on the blade, so the lack of a i r f o i l tab les i 5 a serious problem. Figure 12-6 shows the measured and calcuated p i t c h m o m e n t coef f ic ients . The measured cm shows more higher harmonic content than the calculated data, implying t h a t a uni form c increment i s not s u f f i c i e n t . It i s also l i k e l y however thaF the chordwise resolut ion of the pressure data i s not s u f f i c i e n t f o r an accurate measurement o f c .

m

Typical measured chordwise pressure d i s t r i b u t i o n s are shown i n f i g u r e 12-7. The absolute pressures i n p a r t i c u l a r show the presence of shocks, on the a f t par t of the chord fo r these sect ions and high M a t '

13. H-34 HELICOPTER FLIGHT TEST

A n H-34 hel icopter was tested i n f l i g h t (Scheiman and Ludi, 1963; Scheiman, 1964). This t e s t has long been a standard f o r r o t o r a i r loads data, b u t d i d not include the high speed condi t ions tha t are of i n t e r e s t i n the present invest igat ion. For completeness, and i n order to re-examine the q u a l i t y of the measured data, the a i r loads w e r e calculated f o r low speed and moderate speed cases from t h i s data.

The section l i f t was measured a t seven r a d i a l stat ions: r / R = -25, -40, -55, -75, -85, -90, -95 ( the wind tunnel t e s t added r a d i a l s ta t ions -97 and -99). For r a d i a l s ta t ions from 75% t o 95%, d i f f e r e n t i a l pressure measurements were made a t 7 chordwise locations; except f o r 85% radius, which used 11 gages. The other r a d i a l s ta t ions had only 5 gages. The data from osci l lograph records was averaged over three revolut ions. Time h i s t o r i e s of t he l i f t are given with an azimuthal resolut ion of 15 deg. For presentation here, a measurement system phase l a g of AJ. = 4.5 deg was accounted for, a5 well as a 6 deg s h i f t of the zero azimuth pos i t i on f o r some cases.

The propert ies of (1%4), including data horn geometry, and lag character i st i cs of the

number of blades rad ius s o l i d i t y chord, c/R t w i s t a i r f o i l

the H-34 r o t o r blade are given by Scheiman on t h e cont ro l system f l e x i b i l i t y , p i t c h damper character ist ics. The p r i n c i p a l r o t o r are as follows:

The blade had a t r a i l i n g edge h e t w e e n 85% and 90% I?.

4 28 f t . 0622 . 0488 -8 deq NACA 0012

tab, deflected 4 deq upward,

The low speed case considered i s condi t ion I11 of Scheiman and Ludi (1963); the high speed case i s f l i g h t 19 of Scheiman (1964). The operating condi t ions are as follows.

advance r a t i o . 178 -287 M I70 . 78 C?f, -0817 I 0907 a -2.5 -6.8 5 . 55 -. 97 -. 58 -. 61 # l C

# l s

The calculat ions trimmed the r o t o r th rus t (obtained by i n teg ra t i ng the a i r loads data), and the longi tud ina l and l a t e r a l f lapping t o the measured values. The r o t o r shaft angle o f attack was set t o the measured value. The blade motion considered was ten harmonics of the f i r s t seven f lap- lag bending modes

PRECEDIKG PAGE BLATX NOT FILMED 59

(including the rigid flap and lag modes), the rigid pitch mode, and the first elastic torsion mode. To account for the trim tab, a pitch moment increment of Ac = .03 was used outboard of 75% R. The blade was relatively stiffmin torsion: frequencies w w e 15.6/rev for the rigid pitch motion (control system flexibility), and 7.l/rev for the elastic torsion mode. Three revolutions of the wake w e r e used, with a tip vortex core site of - 0 1 R (20.5% chord). For collocation points on the inboard part of the blade, the core site was increased to -100 R (with a transition region from 72% to 86.5% R).

the calculated

Figure 13-1 compares the measured and calculated airloads at radial stations 75%, 85%, 90%, and 95% R for JJ = -18, showing the influence of nonuniform inflow and the free wake geometry. Figure 13-2 shows the corresponding calculated wake geometry. These calculations used the lifting-surface theory correction, with the quarter-chord collocation point, A larger core size on the retreating side and a smaller core sire on the advancing side would improve the correlation.

Figure 13-3 shows the influence of the near wake model, 1.e. the three methods for treating blade-vortex interaction: the lifting-surface correction, 3c/4 collocation point, or a larger core s i z e . A l l three give generally similar results, but with differing details. With the lifting-surface correction or the 3c/4 collocation point, a core size of about 20% chord is good, just a5 for the SA349/2 calculation. The liftinq-surface correction is roughly equivalent to increasing the core size by A r = -007 R = -3 b (15% chord, as for the SA349/2). Figure 13-4 shgws the effect of the core size for inboard collocation points on the calculated loads. Suppressing the blade-vortex interaction inboard is essential for good correlation. Figure 13-5 s h o w s the influence of blade elastic motion- by considering calculations using only f irst harmonic rigid flap motion.

Figure 13-6 compares the measured and calculated airloads at radial s t a t i o n s 75%. 95%, 90%. and S5% R for ?.! = - 2 9 , showing the influence of nonuniform inflow. At high speed there is less blade-vortex interaction apparent (so free wake geometry has little effect), but nonuniform inflow is still required to predict the loads. Note that the "uniform inflow" inflow results shown include the e+fect of a linear variation of the inflow across the rotor disk. These calculations used the lifting- surface theory correction, with the quarter-chord collocation point. Figure 13-7 shows the influence of the near wake model. Since there is little blade-vortex interaction, the differences shown are produced by the treatment of yawed flow using first order (c/4 collocation point) and second order (3c/4 collocation point) lifting-line theory. Figure 13-8 shows the e-ffect of blade elastic motion on the calculated airloads, which is greater for this moderate speed case than for the low speed case.

60

14. UH-60A ROTOR CALCULATIONS

The UH-60A r o t o r has a swept t i p and a l a rge (and unusual) t w i s t , so i s an i n te res t i ng case f o r app l i ca t ion of the new wake model. No t e s t data i s avai lable f o r t h i s ro to r , although both small scale wind tunnel and f u l l scale f l i g h t t e s t s are planned. CAMRAD input parameters f o r the UH-60A he l i cop ter are given by Shanley (19861, and a i r f o i l decks were provided by the Aerof lightdynamics Directorate, U.S. Army Aviat ion Research and Technology Ac t i v i t y . The pr inc ipa l cha rac te r i s t i cs of the r o t o r are as follows:

number o f blades radius s o l i d i t y chord, c / R a i rf o i 1

t i p sweep

4 26.83 f t -0821 004545 SC1095 f o r 0 t o 30% R, SC1095R8 for 30% t o 87.4% R, SC1095 f o r 87.4% R t o t i p 20 deg at 92.9% R

Figure 14-1 shows the blade b u i l t - i n t w i s t d i s t r i bu t i on . To ensure t h a t t he analysis has the p i t c h bearing outboard of the f l a p and l a g hinges, rFA = -047 was used. loads were included, a5 they are a p r i n c i p a l source of p i t c h damping. The number of col locat ion funct ions f o r the blade modes were increased t o 12 f o r bending and 5 f o r tors ion. For a f r e e + l i g h t t r i m case, other changes t o the input parameters would also be required. Whether the input parameters represent a good physical descr ip t ion of the a i r c r a f t was not assessed.

Noncirculatory blade

Two operating condit ions were considered, low speed and h igh speed cases a t t y p i c a l thrust and propuls ive force:

The ca lcu lat ions trimmed the ro to r l i f t and propuls ive forces (wind axes) t o the required values, and the longi tud ina l and l a t e r a l f lapp ing t o zero, by ad just ing the c o l l e c t i v e and c y c l i c p i t c h and the r o t o r shaft angle.

The blade motion considered fo r the basel ine cases was ten harmonics of t he f i r s t s i x f lap-lag bending modes ( including r i g i d f l a p and l a g motion), the r i g i d p i t c h motion, and the f i r s t two e l a s t i c t o r s i o n modes. Two revolut ions o f r i g i d wake geometry were used f o r the high speed case, and three revolut ions o f f ree wake geometry f o r the low speed case, w i t h a t i p vortex core s ize of -015 R (23% chord). The basel ine ca lcu lat ions use the dual-peak wake model, 3c/4 co l loca t ion point , and no l i f t i n g -

61

surface correction.

Figure 14-2 shows the inf luence o f nonuniform in f l ow and wake geometry on the calculated a i r loads a t rad ia l s ta t ions 75%, 86.5%, and 95% R, f o r V = 60 knots. A s expected, the f r e e wake geometry increases the blade-vortex i n te rac t i on loads. Because of t he l a rge t w i s t , the blade-vortex i n te rac t i on produces negative loading on the t i p a t 9 = 75 deg. Figure 14-3 shows the r a d i a l bound c i r c u l a t i o n d i s t r i b u t i o n around the disk, f o r t he f r e e wake geometry case. The in f luence of both blade-vortex i n te rac t i on and the ref lexed t w i s t i s evident a t the blade t i p . Note tha t on the advancing side the peak c i r cu la t i on occurs around 40% R, and tha t the t i p loading changes rap id l y from p o s i t i v e t o negative t o pos i t i ve around Y = 75 deg. Such behavior probably does not produce a s t rongly rolled-up t i p vortex .

Figure 14-4 shows the inf luence of the f a r wake model, i.e. f o r t h i s case whether the t i p vortex strength from e = 75 deg i s p o s i t i v e (single-peak, maximum bound c i r cu la t i on ) or negative ( the other two cases). The e f f e c t shown might be measurable, although a l a rger t i p vortex core could el iminate the negative loading. Figure 14-5 shows the inf luence of e l a s t i c blade motion on the ca lcu lated load; the e++ects are comparable to those o f the wake model .

Figure 14-6 shows the in f luence of the swept t i p aerodynamic model on the a i r loads a t 91% and 95% R ( the sweep occurs a t 92.9% R ) . Only the f i r s t harmonic r i g i d f l a p motion i s considered fo r these calculat ions, i n order t o examine just the aerodynamic e f fec ts without changes associated w i th the to rs ion dynamics. There i s l i t t l e di f ference between the swept and s t ra igh t l i f t i n g - l i n e m o d e l s . The c/4 co l loca t ions point increases the blade-vortex i n te rac t i on loads, because the t i p vortex core s i z e was not changed (chapters 8 and 13 showed tha t the core s i te should be increased by 15% chord f o r th is option). I n general, 20 deg s w e e p is not large enough t o produce cignl+izant aerodynamic e f f e c t s associated w i t h t he wake model .

Figures 14-7 t o 14-11 show the corresponding r e s u l t s f o r t he high speed case, V = 160 knots. Free wake geometry has l i t t l e e f f e c t now, but nonuniform in f l ow i s s t i l l required ( f i g u r e 14- 7). The r a d i a l c i r cu la t i on d i s t r i b u t i o n shows the e f f e c t o f reverse f low inboard, wi th l i t t l e blade-vortex i n te rac t i on ( f i g u r e 14-8). The e f fec t of t he re f lexed t w i s t a t the t i p i s evident. The peak c i r cu la t i on occurs around 35% R on the advancing s i d e (a r e s u l t of the l a r g e t w i s t ) , again suggesting t h a t the t i p vortex r o l l u p would be r e l a t i v e l y weak. The inf luences of t he f a r wake model ( f i g u r e 14-91 and blade e l a s t i c motion ( f i g u r e 14-10) are comparable. D i f fe ren t wake r o l l u p would a f f e c t t he r e s u l t s i n f i g u r e 14-9. The e f fec t of t he swept t i p aerodynamic model i s s t i l l small f o r t h i s high speed case ( f i gu re 14-11).

62

15. HARMONIC CONTENT OF AIRLOADS DATA

An important issue in planning and executing a rotor airloads test is the question of the azimuthal resolution needed for a complete, or at least sufficient, representation of the aerodynamics. The quantity of interest here is the section lift or circulation, which determines the rotor wake characteristics. Moreover, most present rotary wing analyses use liftinq-line theory for the blade aerodynamics and a nonlinear beam theory for the blade structural dynamics, hence need the section lift for correlation. The harmonic content of the predictions from such analyses suggest that 10 or 12 harmonics is sufficient.

A different approach is to examine the harmonic content of the measured airloads, to see what actually occurs on rotors. Several of the existing airloads data sets have azimuth resolutions of 2 deq or lese, and so are appropriate examples. The time histories of this data will be compared with representations consisting of 10 or 15 harmonics.

Figure 15-1 shows the averaged airloads data measured on the SA349/2 helicopter, and figure 15-2 shows the unaveraged data. It appears that 15 or m o r e harmonics would be required in this case, but figure 15-3 shows that conclusion to be inappropriate. The unaveraged data exhibits significant unsteadiness and high frequency noise.

Figure 15-4 shows the airloads data measured on the Boeing model S A 0 scale rotor. In order to capture the oscillations around 120 deg azimuth, 15 or more harmonics are needed. However, these measured oscillations in lift are produced by shocks moving past individual pressure gages, The measured oscillations would probably b e smoother with gages at more chordwise locations. Figure 15-5 shows a similar result for the airloads data measured on the AH-16 helicopter.

Too few harmonics can produce undesirable e++ects h o w e v e r . Figure 15-6 shows the airloads data measured in flight on the H- 34 helicopter. While 10 harmonics clearly contain all the information of the original data (with a 15 deg azimuthal resolution), the Fourier analysis produces high frequency oscillations that are misleading.

The above results suggest that 15 or 20 harmonics are sufficient to describe the aerodynamic phenomenon of rotor airloads. Several factors require that more data be taken:

a) Unanticipated phenomena may be encountered that produce faster changes in the blade section lift.

b) Oscillations produced by the Fourier analysis rather than by the aerodynamics are undesirable.

c) A high sample rate allows analog filters to be used

63

simply for noise attenuation rather than for antialiasing purposes.

It is concluded that a sample rate of 64 or 72 per revolution, with a filter corner frequency of 30-40/rev, is sufficient for airloads data (5-6 deg resolution of the filtered data).

Other considerations are as important as the azimuthal resolution:

a) Unsteadiness and high frequency noise must be minimized.

b ) The chordwise resolution must be sufficient to accurately obtain the section lift and moment, particularly with shocks or b 1 ade-vortex i nteract i on . c) The radial resolution must be sufficient to define the wake structure and measure the total rotor lift.

64

16. REVIEW O F MEASURED ROTOR AIRLOADS DATCS

The present investigation involved correlation between measured and predicted rotor airloads data, using many of the published data sets. In all cases this effort was made m o r e difficult by the lack of some information or data. This chapter summarizes the problems and limitations observed in these data sets. For completeness, tests that were not part of the current correlation work are alsa included in the summary. This summary wi 11 be the basi 5 for recommendations regarding future rotor airloads tests.

A general consequence of any airloads correlation work is questions about wake geometry and rollup. None of the published airloads data sets includes information on the rotor wake st rut ture.

The following identifies the problems and limitations observed in the airloads data sets.

A ) SA349/2 helicopter (Heffernan and Gaubert, 1986)

1) only three radial stations 2) unsteadiness and high frequency noise 3) shaft angle of attack and flapping measurements not

4) control system stiffness not measured accurate

B) Boeing model 360 scale rotor (Dadone, Dawson, Boxwell, and Ekquist, 1987)

1) insufficient chordwise resolution of pressure measurements to obtain section lift when shocks are present

2) concern about rtructural dynamic Froperties 3) control system stiffness not measured

H-34 wind tunnel test (Rabbott, Lizak, and Paglino, 1966a)

1) only 10 harmonics 2 ) concern about chordwise pressure distribution 3) split tip-path-plane during test 4) control system stiffness not measured

CIH-1G he1 icopter (Morris, 1978)

1) only one radial station 2) no airfoil tables 3) control s y s t e m stiffness not measured

65

E) H-34 f l i g h t t e s t (Scheiman, 1964)

1) azimuthal resolut ion only 15 deg 2) r o t o r torque not measured

F) NACA model wind tunnel t e s t (Rabbott and Churchi l l , 1956)

1) propulsive force not accurate 2) no s t ruc tu ra l dynamic p roper t ies given

6 ) HU-1A hel icopter (Burp0 and Lynn, 1962)

1) azimuthal resolut ion a t best 15 deg; 30 deg f o r most of the data

2) r o t o r torque not measured

HI CH-47 hel icopter (Pruyn, e t al, 1967)

1) no tabulated data

I ) XH-S1A compound hel icopter (Bartsch and Sweers, 1968)

1) propuls ive force not measured 2) shaf t angle of attack measurement not accurate 3) problem wi th zeros of pressure measurements 4) instrumented blade operating a t lower l i f t than other

5 ) no s t ruc tu ra l dynamic proper t ies given blades

J) NH-3A compound hel icopter (Fenauqhty and Beno, 1970)

1) =haf t Xntyle o f attack measurement not = c c ? ' ~ a t e (propulsive force not accurate)

2) only 5 chordwise pressure measurements 3) concern about chordwise pressure d i s t r i b u t i o n 4) no s t ruc tu ra l dynamic proper t ies given

K) CH-536 hel icopter (Beno, 1970)

1) s i m i l a r t o NH-3A 2) no microf iche of tabulated data avai lab le

66

17. CONCLUSIONS AND RECOMMENDATIONS

17.1 Conclusions

An improved rotor wake model for helicopter rotors has been developed. The emphasis was on wake effects (including blade- vortex interaction) in high speed flight, considering in particular cases with negative loading on the advancing tip.

Two alternative approaches for blade-vortex interaction were considered: second order lifting-line theory, and a lifting- surface theory correction. Good correlation with measured rotor data was shown for cases involving significant blade-vortex interaction. For full scale data, the vortex core site required for the correlation was about 20% chard. This is in the range of measured core sites for rotors. but is probably still too large. The core size must account for not only the physical viscous core radius, but also all those aspects of the blade-vortex interaction that are not otherwise included in the analysis. Factors that would cause the core size in the analysis to b e too large include:

a) Discretization of the wake: generally the radial and azimuthal resolution in the discretized wake are too large, producing an overprediction of vortex-induced loads.

b) Partial tip vortex rollup: contrary to the assumptions of the analysis, the tip vortex may not be completely rolled up by the time it reaches the following blade; i-e. the strength may be less than the value o+ the peak bound circui ati on.

c) Unsteadiness and noise in the data: particularly if the azimuth angle of the blade-vortex interactions changes + r o m rev to rev, the averaging process : d i l l r2duce t h e measured peak 1 odds.

Factors that would cause the core size in the analysis to be too small i ncl ude:

a) Discretization of calculated lift: the blade section loading i 5 calculated here with an azimuthal resolution of 15 deg, which would generally have the effect of reducing the apparent peak loads.

The common approach of using a larger vortex core radius to account for lifting-surface effects was quantified: the core radius should be increased by about 15% chord if neither second order lifting-line theory nor the lifting-surface correction is used -

The capability was developed to modal the wake created by dual-peak span loading (inboard and outboard circulation peaks,

67

of opposite sign), optionally with multiple rollup of the trailed vorticity. The calculated airloads showed a significant effect of this wake model. By using the outboard circulation peak rather than the maximum bound circulation, the tip vortex has the correct sign and strength. While that is a major factor in calculating the advancing tip loads, the inboard wake is also influential. Hence the dual-peak model is best for these cases. The wake structure for the dual-peak model depends on the radial location of the inboard peak. Two iterations between the influence coefficient calculation and the trim solution were required for convergence of the inboard peak location. In some cases, the calculated loads were affected by the extent of the rollup of the inboard (positive) trailed wake.

Generally the correlation with measured airloads at high speed was not good however. The measured data showed some consistent behavior:

a) The measured loading in the first quadrant is higher than the calculated loading. Often there is a peak in the measured loading, or at least relatively constant lift coefficient, while the calculated loads tend to decrease with azimuth.

b) The model 360 data often show a flat or even reversed lift behavior in the middle of the negative loading region on the advancing tip. The calculated loading shows a distinct minimum.

c) The measured loading in the second quadrant has sharp changes and oscillations, while the calculated loading is smoothly varying.

This behavior of the measured loading is generally associated with shocks occurring on the blade. It appears likely that the chordwise resolution of the measured pressures is not sufficient to obtain an accurate li+t coef+icient in t h e presence of shocks. However, if the chordwise resolution is sufficient, then errors in the analytical wake geometry and rollup are possible causes of the discrepancies. It in clear in any case that the effects of compressibility and blade dynamics are as important as wake effects for high speed flight.

The dual-peak wake model is relevant to flight conditions besides high speed helicopter operation. With a large enough twist, blade-vortex interaction at low speed can result in small areas of negative loading on the blade. Also, a tiltrotor in airplane mode cruise can have negative loading on the inboard part of the blade and positive loading on the tip; and in helicopter mode flight it will have negative loading on the advancing tip even at low speed.

The second order lifting-line theory also improves the modeling of yawed flow, swept tips, and low aspect-ratio blades. The influence of the theory in yawed flow is significant for

68

ro to rs a t h igh advance ra t io . While the analys is i s apparently funct ioning properly, t e s t data are not ava i lab le t o ve r i f y the treatment of yawed f low and swept t ips.

17.2 Recommendations: L i f t Measurement a t High Mach Number

It has been postulated here that the e x i s t i n g a i r loads data a t high speed are inaccurate because the chordwise resolut ion of the pressure measurements i s not s u f f i c i e n t t o obta in the section l i f t i n the presence o f shocks. It i s recommended tha t an invest igat ion be conducted with the fo l lowing objectives:

a) Establ ish whether or not the ex is t ing sect ion l i f t data are accurate.

b) Establ ish requirements f o r measurements i n f u t u r e tests.

The approach would be t o calculate the a i r f o i l pressure d i s t r i b u t i o n using ex i s t i ng two-dimensional f in i te-d i f ference codes. Then the calculated pressures a t a set o f chordwise pos i t ions gives an equivalent experimental measurement, which can be integrated t o obtain a l i f t coef f ic ient . Comparing the calculated and equivalent-experimental l i f t coe f f i c i en ts gives a quant i ta t ive assessment of the accuracy of t he process.

The a i r f o i l s , operating conditions, and chordwise s tat ions used i n previous and proposed ro to r a i r loads t e s t s should be considered. It would a lso be useful t o examine the calculated d i f f e r e n t i a l pressure d is t r ibut ions, t o resolve some of the concerns about ex i s t i ng measured data.

I f there prove5 t o be a problem w i t h the chordwise resolut ion i n previous tests, i t would be poss ib le t o use the above approach t o def ine a tranform t o be appl ied t o the calculated sect ion l i f t . Then meaningful comparisons of experiment and theory could be made.

17.3 Recommendations: Wake Geometry and Rol lup

Discrepancies between analysis and t e s t data suggest tha t the d is tor ted wake geometry, t i p vortex formation, and wake r o l l u p m u s t be invest igated further. T h i s conclusion i s a universal conclusion of any a i r loads co r re la t i on work. Information i s needed about the self-induced d i s t o r t i o n of the e n t i r e wake; the t i p vortex core s izes and strength; and the s t ructure of the inboard wake.

Questions and observations from the present invest igat ion include the fol lowing. The corre la t ion f o r blade-vortex in te rac t ion cases suggests tha t the core s i n e i s larger for vor t ices formed on the re t rea t ing s ide than f o r those formed on the advancing side. Something i s happening on t h e inboard par t o f the blade t o reduce measured the vortex-induced loads. The

69

wake geometry may be incorrect for the high speed airloads calculations, particularly since the free wake geometry method was not revised to include a dual-peak model (with a dual-peak model the inboard trailed wake strength would be increased, tending to push the tip vortex upward). The distorted geometry of the inboard wake is not being calculated at all. Examination of the spanwise circulation distributions for both low and high speed, particularly with highly twisted blades, suggests that the tip vortices may not be strongly rolled up on the advancing side. With a dual-peak circulation distribution however, multiple rollup of the trailed wake is a possibility.

Both theoretical and experimental investigations are recommended. The phenomena involved in rotor wakes will remain speculative until measurements are available for at least:

a) the positions of the tip vortices;

b) the structure and extent of the wake rollup.

Wake measurements should be made simultaneously with airloads measurements, and at full scale Reynolds numbers. The theoretical work need not wait for the test data however, since there are clear de+iciencies in the existing w a k e geometry and rol lup calculations.

17.4 Recommendations: Airloads Measurements and Correlation

The rotor airloads data sets examined in the present investigation will continue to be useful:

Boeing model 360 scale rotor test. A better de+inition of the rotor structural dynamic properties is needed.

SA349/2 helicopter flight test. The unsteadiness and noise in +he data limitc corrslatian to t he majsr event s.

H-34 rotor wind tunnel test. The fact that the test was run with a split tip-path-plane makes it difficult to draw conclusions from poor correlation, and raises questions about good correlation.

H-34 helicopter flight test. The large azimuthal resolution limits correlation to the major events.

AH-1G helicopter flight test. Airfoil tables are needed for the three sections tested, and might be obtained using two-dimensional f inite-difference computations.

The data sets include many flight conditions, and structural load measurements. All the information available should be used (by the research community, if not in any single investigation).

70

Further correlations are recommended. First however it must be established whether the lift coefficient data at high Mach numbers is accurate. Improvements in the wake geometry and rollup calculations are a logical next step.

There is a clear need for further rotor airloads measurements, particularly considering the def i ci enci e5 observed in the available data sets. For high speed flight conditions, measurements must be made with sufficient chordwise resolution of the pressure gages. It is also recommended that high advance- ratio wind tunnel tests be conducted at both design tip speeds and at Mach numbers low enough to avoid shocks. By this means information will be available to separate the effects of the rotor wake, blade dynamics, and transonic flow at high speed.

17.5 Recommendations: Future Airloads Tests

Finally, the requirements for future airloads tests are summarized, based on the deficiencies observed in existing data sets.

a) Accurately measure the rotor operating condition, including: shaft angle-of-attack, flapping, torque; lift and drag in a wind tunnel; data on the helicopter drag and engine thrust for flight tests; rotor cyclic and collective pitch.

b) Collect sufficient data: enough chordwise pressure measurements to obtain lift and moment coefficients, particularly with shocks; enough radial stations to define the wake structure and for a reasonable measure of the rotor thrust: 64 to 72 samples per revolution.

c) Report sufficient data: use a good chordwise integration method; present 15-20 harmonics of data, along with the time hi stor i es . d) Document the rotor and aircra+t properties: the usual quantities; control system stiffness and torsion stiffness; airfoil tables. This information should be checked for consistency by using it in calculations.

e ) Publish all performance data, much structural loads and airloads data, and a few good points of the pressure data. Use a medium that ensures the data will be available in the future.

Appendix A. CAMRAD PROGRAM MODIFICATIONS

A. 1 New and Revised Input

The complete CAMRAD input is given in the user's manual (Johnson, 1980~). The new input parameters are read in namelist NLWAKE (they are not included in the binary input file). Parameters in namelist NLWAKE that are not used by the new model are: MRL, NL, MRG, NG, OPRTS, OPNWS, FNW. The new input parameters

OPNW

OPBPXA

FRCNW

RTVTX

OPFW

OPRGI

RGI (MPSI 1

OP I VTL

are as follows.

integer

integer

real

real

integer

integer

real

integer

RC I VTL real

wake configuration: near wake and lifting-line 0 collocation point at c/4,

straight 1 if ti ng-1 ine 1 collocation point at 3c/4,

straight lifting-line 2 collocation point at c/4,

swept 1 if ti nq-1 ine 3 collocation point at 3 ~ 1 4 ,

swept lifting-line

0 to suppres twist in x offset of swept lifting-line A

factor on near wake core size; 1. for baseline value

radial station of tip vortex at blade

wake configuration: far wake rollup 0 one circulation peak, 1 one circulation p e a k , L ~ = a r d r 2 two circulation peaks

source of inboard circulation peak radial station (r for wake geometry: o to calculate, l G l o use input

-1. for single peak model GI ' input r

inboard rolled up trailed wake model 0 use WKMODL(7) 1 stepped line segment 2 linear line segment

core radius for inbaord rolled up trailed wake (line model only)

73

A . 2 New and Revised Common Blocks

The following common block for the wake influence coefficients was revised. The influence coefficients CI for the inboard peak were added. The matrix sizes were increased, to allow the use of more radial stations and a larger near wake extent.

COMMON /WKClCM/MR,ML,MI,MW,MH,MV,MO.CO(3,300~~),CI(3,3~~0~), CNW ( 3,45000 1

The following new common blocks contain the new input parameters for the far wake and near wake models.

COMMON /WNlDAT/OPNW,OPBPXA,RTVTX,FRCNW INTEGER OPNW,OPBPXA

COMMON /WF1DAT/OPFW,OPRGI,OPIVTL,RCIVTL,RGI~36~ INTEGER OPFW,OPRGI,OPIVTL

The following new common block contains the blade position r (rhi,@.) at the aerodynamic radial stations and a l l azimuth skations: which is required f o r the near wake model.

COMMON /WNlCM/RBRA (3,30,36)

The following new common block contains the circulation peak information (as a function of azimuth station) required for the far wake model.

COMMON /WFlCM/CIRC0(36),CIRC1(36), RCIRC (361, RCIRCO (36) , RCIRCI (361, RHOGI (36) ,COOLD(36) ,CIOLD(36)

where

rO CIRCO

CIRCI

RC I RC r for rmax RC I RCO r for ro

RCIRCI r for rI RHOGI

COOLD old ro for inflow (lagged) CIOLD old rI for inflow (lagged)

pGI used in wake geometry

74

A- 3 Revised Subroutines

General revi si ons

I NPTW 1 namelist read of new input parameters (NLWAKE)

PRNTWl print new input parameters

FILEJ store new commons; change C to CO, use CI;

INITRl check input RGI; zero RCIRCO, RCIRCI; set RHOGI=-1.; set MRL=MRA, MRG=MRA

CHEKRl increase dimension of influence coefficients

Far wake model

PERFR 1 print CIRC' s, RCIRC' s, RHOGI

AEROF 1 calculate circulation peaks

RAMF use CIRCO, CIRCI in circulation convergence

GEOMR 1

GEOMF 1

WAKEC1

WAKEN 1

Near wake model

GEOMR 1

calculate RHOGI; use r or ro for wake geometry max

or ro for wake geometry rmax change C to CO; calculate CO and CI for rolling up and far wake models

change C to CO; lag CIRCO. CIRCI: calculate inflow +rom r and rI

0

calculate FTIP from RTVTX; call WAKEBl; calculate RBREI

t e r m s ; always calculate X A WAKEBl use OPBPXA, cal cul ate at all aerodynamic radial stations

GEOME 1 calculate wake geometry at aerodynamic radial stations

GEOMP 1 call GEOMEl

LOADR 1 call GEOMEl

WAKEC 1 call GEOME1; calculate collocation points; calculate CNW +or near wake model

WAKECZ call WAKEBl

REFERENCES

Ballard, J.D.; Or lo f f , K.L.; and Luebs, A.B. (1979) "Ef fect of Tip Planform on Blade Loading Character is t ics f o r a Two- Bladed Rotor i n Hover." NASA TM 78615, November 1979.

Bartsch, E.A. , and Sweers, J.E. (1968) " I n f l i g h t Measurement and Correlat ion w i t h Theory of Blade Air loads and Responses on the XV-51A Compound Helicopter Rotor." U.S. Army Aviat ion Materiel Laboratories, USAAVLABS TR 68-22, May 1968.

Beno, E.A. (1970) "CH-53A Main Rotor and S t a b i l i z e r Vibratory Air loads and Forces. I' Sikorsky A i rc ra f t , Report SER 65593, June 1970.

Burpo, F.B., and Lynn, R.R. (1962) "Measurement o f Dynamic Air loads on a Ful l -sca le Semirigid Rotor." U.S. Army Transportation Research Command, TCREC 62-42, December 1962-

Dadone, L.; Dawson, S.; Boxwell, D.; and Ekquist, D. (1987) "Model 360 Rotor Test a t DNW -- Review of Performance and Blade Ai r load Data." Annual National Forum o+ the American Helicopter Society, 1987.

Fenaughty, R- , and Beno, E. (1970) "NH-3A Vibratory Air loads and Vibratory Rotor Loads. 'I Sikorsky A i rc ra f t , Report SER 611493, January 1970..

Ham, N.D. (1975) "Some Conclusions from an Invest igat ion of Blade-Vortex In teract ion. " Journal o f t he American Helicopter Society, vo l 20, no 4 (October 1975).

Harris, F.D. (1972) "Ar t icu la ted Rotor Blade Flapping Motion a t Low Advance Ratio. Is Journal of the American Helicopter Society, vol 17, no 1 (3anuary 1972).

He++ernan, R.M., and Gaubert, M. (1986) "St ructura l and Aerodynamic Loads and Performance Measurements of an SA34912 Helicopter w i t h an Advanced Geometry Rotor." NASA TM 88370, November 1986.

Hooper, W.E. (1984) "The Vibratory Air loading o f Helicopter Rotors." Vertica, vo l 8, no 2 (1984).

Johnson, W. (1971a) "Appl icat ion of a L i f t ing-Sur face Theory t o the Calculat ion of Helicopter Airloads. In Annual National Forum of the American Helicopter Society, 1971.

Johnson, W. (197lb) "A L i f t ing-Surface Solut ion f o r Vortex- Induced Airloads." A I A A Journal, vo l 9, no 4 (Ap r i l 1971).

Johnson, W. (1980a) Helicopter Theory. Pr inceton Univers i ty Press, Princeton, New Jersey, 1980.

PRECEDiNG PAGE BLANK NOT FILMED 77

Johnson, W. (1980b) "A Comprehensive Analy t ica l Model of Rotorcraf t Aerodynamics and Dynamics. 'I NASA TM 81 182, June 1980.

Johnson, W. ( 1980~) "A Comprehensive Analy t ica l Model of Rotorcraf t Aerodynamics and Dynamics. ID NASA TM 81183, Ju ly 1980.

Johnson, W. (1981) "Comparison of Calculated and Measured Helicopter Rotor Lateral Flapping Angles. 'I Journal of the American Hel icopter Society, vol 26, no 2 (Ap r i l 1981).

Johnson, W. (1986a) "Assessment of Aerodynamic and Dynamic Models i n a Comprehensive Analysis f o r Rotorcraf t . I D Computers and Mathematics wi th Applications, vol 12A, no 1, (January 1986) .

Johnson, W. (1986b) "Recent Developments i n Rotary-wing Aerodynamic Theory." A I A A Journal, vo l 24, no 8 (August 1986) .

Mi l l e r , R.H. (1985) "Methods for Rotor Aerodynamic and Dynamic Analysis. ID Progress i n Aerospace Science, vo l 22 (1985) .

Mi l l e r , R.H., and E l l i s , S.C. (1986) "Predict ion of Blade Air loads i n Hovering and Forward F l i g h t Using Free Wakes. ID

European Rotorcraf t Forum, Germany, September 1986.

Morris, C.E.K., Jr . (1978) "Rotor-Ai r fo i l F l i g h t Investigation: Prel iminary Results. ID Annual National Forum of the American Helicopter Society, 1978.

Piorris, Z.E,k-. , 2r . (1981) " A F l i g h t Invest igat ion o+ Blade- Section Aerodynamics f o r a Helicopter Main r o t o r Having 10-64C A i r f o i l Sections. 'I NASA TM 83226, November 1981.

M o r r i s . C.E.K. , Jr. !l?S2) ''9 Flight Inves t iga t icn zf Elade- Section Aerodynamics for a Helicopter Main r o t o r Having RC-SC2 A i r f o i l Sections." NASA TM 83298, March 1982.

Morris, C.E.K., Jr.; Stevens, D.D.; and Tomaine, R.L. (1980) " A F l i g h t Inves t iga t ion of Blade-Section Aerodynamics f o r a Helicopter Main r o t o r Having NLR-1T A i r f o i l Sections. 'I NASA TM 80166, January 1980.

Morris, C.E.K., Jr.; Tomaine, R.L.; and Stevens, D.D. (1979) "A F l i g h t I nves t t i ga t i on of Performance and Loads f o r a Helicopter w i t h NLR-1T Main Rotor Blade Section." NASA TM 80165, October 1979.

Morris, C.E.K., J r . ; Tomaine, R.L.; and Stevens, D.D. (1980a) " A F l i g h t I nves t t i ga t i on of Performance and Loads f o r a Helicopter w i t h 10-64C Main Rotor Blade Section." NASA TM 81871, October 1980.

78

Morris, C.E.K., Jr.; Tomaine, R.L.; and Stevens, D.D. (1980b) "A Flight Investtigation of Performance and Loads for a Helicopter with RC-SC2 Main Rotor Blade Section." NASA TM 81898, December 1980.

Pruyn, R.R., et al. (1967) "Inflight Measurement of Rotor Blade Airloads, Bending Moments, and Motions, Together with Rotor Shaft Loads and Fuselage Vibration, on a Tandem Rotor Helicopter. ' I U.S. Army Aviation Materiel Laboratories, USAAVLABS TR 67-9, May 1967.

Rabbott, J.P. , Jr., and Churchill, G.B. (1956) "Experimental Investigation of the Aerodynamic Loading on a Helicopter Rotor Blade in Forward Flight." NACA RM L56107, October 1956.

Rabbott, J.P., Jr.; Lizak, A.A.; and Paglino, V.M. (1966a) "A Presentation of Measured and Calculated Full-Scale Rotor Blade Aerodynamic and Structural Loads. 'I U.S. Army Aviation Materiel Laboratories, USAAVLABS TR 66-31, July 1966.

Rabbott, J.P., Jr.; Liiak, A.A.; and Paglino, V.M. (196613) "Tabu1 ated Si korsky CH-34 E1 ade Surf ace Pressures Measured at the NASA/Ames Full-scale Wind tunnel. 'I Sikorsky Aircraft, Report SER-58399, January 1966.

Scheiman, J. t 1964) "A Tabulation of He1 icopter Rotor-Blade Differential Pressures, Stresses, and Motions as Measured in Flight." NASA TM X-952, 1964.

Scheiman, J., and Ludi, L.H. (1963) "Qualitative Evaluation of Effect of Helicopter Rotor-Blade Tip Vortex on Blade Airloads." NASA TN D-1637, May 1963.

Scully, M.P. (1975) "Computation of Helicopter Rotor Wake Geometry and Its Influence on Rotor Harmonic Airloads." Massachusetts I n r - t i t e t e cf Tschnoiogy, ASRL Tli 178-1, March 1975 .

Shanley, J.P. (1986) "Application of the Comprehensive Analytical Model of Rotorcraft Aerodynamics and Dynamics to the UH-60A Aircraft." Sikorsky Aircraft, Report SER 72126, February 1986.

Tung, C.; Caradonna, F.X.; and Johnson, W. (1986) "The Prediction of Transonic Flow5 on an Advancing Rotor." Journal of the American Helicopter Society, vol 31, no 3 (July 1986).

Yamauchi, G.K.; Heffernan, R.M.; and Gaubert, M. (1988) "Correlation of SA349/2 Helicopter Flight Test Data with a Comprehensive Rotorcraft Model . ' I Journal of the American Helicopter Society, vol 33, no 2 (April 1988).

79

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9iJ

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CAMRAD rolled up wake

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Figure 2-5. Possible wake models for dual-peak loading case.

9 1

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rO

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I T

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32

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Report Documentation Page 1. Fie crt No. NA5i! Cfi 177507

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

t'SAVSCW TR-88-A-008 4. Title snd Subtitle

Mvember 1988 6. Performing Organization Code

Wake &lode1 for Helicopter Rotors in High Speed Flight

5. Report Date

7. Authorts) I 8. Performing Orqanization Reoort No. I

9. Psrforming Organization Name and Address

Johnson Aeronautics

Wayne R. Johnson I

rrrOP #505-61-51 11. Contract or Grant No.

10. Work Unit No.

2. Sponsoring Agency Name and Address

NASA Axes Pesearch Center Zlerofliqhtciymni.tmics Directorate

Pbffett Field, CA 94035

Contract R e p r t 14. Sponsoring Agency Code

P.O. Eox 1253 Palo Alto, CY. 94302

20. Security Classif. (of this page) 21. No. of pages 9. Security Classif. (of this reportJ

Unclassified 1 4 3 Unclassified

I

22. Price

A07 I

- -1r7 mTL%?-lL 1 4 ,

13. Type of Report and Period Covered

I 5. Supplementary Notes

D r . Chee Tung Aeroflightdynamics Directorate NASA PEES Research Center Moffett Field, CA 94035

6. Abstract

Two alternative approaches are developed to calculate blade-vortex interaction airloads on helicopter rotors: surface theory correction. radius t o account for lifting-surface effects is Fant i f ied. lifting-line theory also improves the mdelinq of yawed flow and swept tips. Calculated results are compared with wind tunnel measurerents of la te ra l flapping, and with f l igh t test masuremnts of blade section l i f t on SA349/2 and H-34 helicopter rotors. the f l ight test data is a b u t 20% chord, which is wi th in the range of measured viscous core s i zes for helicopter rotors.

second order liftin?-line theom, and a l if t ing- The c o m n approach of usinq a larger vortex core

The second order

The t i p vortex core radius required for good correlation with

7. Key Words (Suggested bv Authorrsl) I 18. Distribution Statement I

Rotor Wakes, Blade Vortex Interaction, a t o r Airloads

Unlimited - l i n c l a s s i f i e d

-_

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