Development and validation of a vortex lattice method to calculate

(1)

EIGHTEENTH EUROPEAN ROTORCRAFT FORUM

B- 06

Paper N• 72

DEVELOPMENT AND VALIDATION OF A VORTEX LATTICE

METHOD TO CALCULATE THE FLOW FIELD OF A

HELICOPTER ROTOR INCLUDING FREE WAKE DEVELOPMENT

L. ZERLE, S.WAGNER

UNIVERSITAT STUTTGART

GERMANY

September 15-18, 1992

AVIGNON, FRANCE

(2)

(3)

DEVELOPMENT AND VALIDATION OF A VORTEX LATTICE METHOD TO CALCULATE THE FLOWFIELD OF A HELICOPTER ROTOR INCLUDING FREE

WAKE DEVELOPMENT

L. ZERLE and S. WAGNER Institut fiir Aerodynamik und Gasdyna.mik

Universitat Stuttgart

Pfaffenwaldring 21, D-7000 Stuttgart 80 Federal Republic of Germany

ABSTRACT

Calculated helicopter rotor inflow velocities in forward flight are presented and compared to laser doppler anemometer measurements. Basing on linear potential theory, the code works as a time-stepping simulation program, using vortex lattice method. Wake prolongation at blade trailing edge is performed during each timestep, shedding blade doublet strength

int<> the wake. Additional wake self-induction is calculated and added to wake motion.

Unsteady wake roll up, even at the inboard lattice parts, are observed. With the exception of the vortex core model, there is no empirical input to obtain the results. Improved blade vortex interaction (BVI) and rotor-fuselage interference predictions are the expected bene-fits of the free wake model. Comparisons demonstrate that the inflow velocity field is very

well represented in tendency. Flow speed values in the outer radial rotor region also agree

also well with measurement. Neglecting the missing fuselage in the calculation, results in

differences at the inner rotor area.

1. INTRODUCTION

Progress in helicopter aerodynamics requires sufficient wake modelling. A wide span of prob-lems stemming from the rotor wake is given by blade vortex interaction, aerodynamic noise pro-duction and vibratory loads. Compact and light helicopter construction requires knowledge about Rotor Fuselage Interference (RFI) effects, espe-cially at canopy, rear rotor and fin area. Improved predictions in these cases are expected benefits by application of rotor free wake models. Increasing computer capabilities and arising CPU power un-der relative low costs allow application of aerody-namic rotor codes, working with fully free devel-oped wake systems. A lot of research is published, using prescribed models for rotor downwash han-dling. They require empirical input data. Im-portant for code development is an experimental database for comparisons and validation, to check the implied models. More than about 10 years, free wake technics are used in fixed wing appli-cations, especially for delta wings [1]. Free wake methods are used in helicopter aerodynamics, too. Several research groups are working in this direc-tion [2, 3]. Good historical review is given in the

introductions of [4, 5).

Modern Laser Doppler Anemometry (LDA) flow measuring technics allow velocity measurements without placing any disturbing probe or hot wire equipment. Rotor inflow in forward flight was measured by NASA [6] using LDA. These results are used here for first comparisons with code cal-culations. The inhouse developed computer pro-gram for isolated rotor [7], was generally refined and expanded to forward flight within the Pi-lot Phase of BRITE EURAM research program [8]. Further measured data bases at different he-licopter model sections were generated in this re-search phase, and will be used for comparisons in a later development step.

2. GENERAL CODE DESCRIPTION

Based on the theory of 3-dimensionallinear po-tential flow, a vortex lattice method is used to de-termine time dependent flow field and wake geom-etry generation. The developed code is a timestep simulation program in FORTRAN 77 language. Flow conditions are calulated at every timestep, using the information of the former step to deter-mine the new solution. Obtained timestep

(4)

solu-tions consit of two parts: 1. The local singular-ity strength at the blade panel, produced by full-filling the boundary condition at the blade con-trol points (i.e. no velocity perpendicular to the blade). 2. Displacement, prolongation and new positioning of the wake networks, which are lo-cating the wake representing vorticies. During the timestep, quasi steady state potential flow condi-tions and a frozen geometry system are assumed, to calculate the new flow field and new wake ge-ometry at the end of the timestep.

2.1 Coordinate Systems

Two coordinate systems are used. B-System is the blade fixed system, that represents the ro-tor blade in defined 0 - pitch angle position (Fig. 2.1). The other one, called System K is non ro-tating, rotorshaft axis and fuselage fixed, with lo-cation in the rotor center (Fig. 2.2). All calcu-lations are performed in K system, fuselage and free stream are represented here also.

2.2 Blade Handling

For the first step thin blades were used, covered with a vortex doublet ring at every panel. At the blade control points all actual active velocities, i.e. free stream, wake induced, and rotor movement caused are added. After skalar multiplication of the velocity vectors with the unit vectors normal to the panel surface they build the right hand side of a system of linear equation.

a1,1 a2,1

a3,1

aN,l

+

a1,2 a1,N It! R1

az,z az,N ll-2 R2 a3,2 a3,N !1-3 R3 aN,2 aN,N !1-N RN (1) -iik. ( Uoo(f, t) -

n

X Tk

+

~ ~

free tJtream motion of rotorblade

V¢vs(r,

t)

~ wake induced velocitietJ

). (2)

The blade panel doublet strength p. is

deter-mined by simultaneously solving the linear equa-tion, using the blade-panel to blade-panel in-fluence coefficient matrix aki, at the end of the timestep. Beginning each timestep, the complete rotor is generated by coordinate transformation

and multiplication, regarding the actual pitch and flapping angles at the destinct blade positions. 2.3 Wake Handling

Wake discretisation is done by sheets of quadri-lateral ring vorticies (wake doublets). Every two neighboured doublets build the vortex strength at the vortex filament between them, by balanc-ing their doublet strength. Usbalanc-ing this superposi-tion, we obtain the well known 'horse shoe' vor-tex system of a lift producing wing with finite span. During every timestep a new wake row is produced at the blade trailing edge, where the KUTTA- condition is postulated. The new wake panels are shedded down from the blade with the same span wise blade panel discretisation, and are loaded with the doublet strenght of the abuting blade trailing edge panels. Therefore, in case of a steady state moving wing, the vortex at blade's trailing edge is extinguished by balancing the dou-blet strength of blade and wake along the trail-ing edge. Unsteady wtrail-ing movements, as usual in helicopter aerodynamics, cause alternating dou-blet strength on the blades. In this case the wake network is covered with a local varying doublet strength in quasi chord direction, and a vortex activity remains at the spanwise filaments. Dou-blet strength on each particular wake panel is kept constant during all timesteps.

For wake motion and distorsion during the timestep, displacement influence portion of free stream and every singularity (i.e. blade and wake vorticies) is calculated. Vortex induced displace-ment contributions are determined by application of a special transportation model, including the 3-dimensional BlOT- SAVART law. More detailed Info.rmation is given in chapter 2.6.1 and [9, 7].

2.4 Code Working Procedure

The code runs in the following way: After read-ing the input files and some precalculations the timestep loop is entered, with at first two steps for calculation of the startup. Oth. step: Rotor is in starting position, facing the freestream and the blade moving speed only.

1st. step: Rotor moves to new position and pro-duces the first wake row in spanwise direction. The shedded doublet strength for the first wake row is the blade doublet strength solution ob-tained at step 0. Now the panel control points are affected by freestream, blade moving velocity

(5)

and the vorticies of the first panel row.

2nd. and further steps: Timestep loop works now in full configuration with additional displacement calculation at all free wake lattice nodal points. The wake length of each blade grows now step by step, influencing itself, too. Therefore, computing time increases timestep by timestep. At the end of each timestep loop specific output is written to a file for postprocessing. After the treatment of all scheduled timesteps final file output is done and the procedure ends. An additional illustra-tion is given by the flowchart in Fig. 2.3

2.5 Timestep Length

Rotor speed and rotor moving angle step de-termine timestep length. Practicable angle steps depend on two detalls, wake shedding model and the desired result resolution in time and space. Concerning the applied wake prolongation model, increasing angle steps produce increasing misposi-tion of wake vorticies nearby blade's tralling edge. The experience shows that 15 Degree rotor angle movement steps are acceptable. For special in-vestigations a smaller angle step of 5 Degrees was used. A sensitivity test was done, to look how the results are affected by varying the timestep length. See chapter 3.2.4 .

2.6 Special View to Applied Models

Some model expansions are necessary, to avoid unrealistic flow conditions and to achive stability in the whole procedure.

2.6.1 Circular Transport of an Allocation Point by a Vortex Filament

Nature shows that a single vortex transports particles along a circle around its vortex core, and not along a line indicated by the tangential veloc-ity direction. This prinziple (9] is used to model the transport mechanism in a vortex flow field (Fig. 2.4). The collocation point moves within the timestep along the circle from location Q to the target point P, depending on the circumferen-tial speed given by the BIOT-SAVART law. Vec-tor QP represents the displacement contribution of this vortex filament within the timestep, in-stead of a transversal dislocation to point P' away from the vortex core.

2.6.2 Vortex Core Model

Approaching to the vortex core, theory gives in-finitely high induced circumferential speed, which is neither realistic nor observed in nature. There-fore a core model with exponential velocity damp-ing is applied. It ensures steady velocity reduction down to zero, by approach to vortex core within the damping radius. This damping radius is the single empirical code input parameter. It is set to half of the minimum span wise blade panel size. 3. RESULTS

3.1 Important Development Step Results First forward fight calculations were performed with an untwisted testblade, used for blade pan-elisation testing and discretisation optimisation. The test run worked with constant rotor speed after impulsive start, with a moving angle of 15 degrees during each timestep, and an advance ra-tio of 0.20. Blade 1 of the 2-bladed rotor starts in rear positon, and the rotor completes the revolu-tion after every 24 timesteps.

3.1.1 Wake Structure

Fig. 3.1 gives an impression about the wake geometry after the first rotor revolution. Typi-cal outer (tip) vortex rolling up effects in the free wake are clear visible. The crossing of retreat-ing blade 1 with the wake of blade 2 is remark-able, too. Blade 1 hits the tip vorticies nearly parallel at timestep 19. Wake plots in fig. 3.2 represent the actual wake structure after 3 rotor revolutions. Wake lattice distorts heavily, but a kind of systematical wake wrapping is obsered, The wake activity on the starboard side (positive y-area) is not symmetric to the other one. This demonstrates the necessity to include cyclic pitch capability to the rotor free wake code.

3.1.2 Blade Doublet Strength Oscillations Calculated doublet strength of blade 1 is shown in isoline plot (Fig. 3.3a). After the start at t=O up to time step 28 the doublet strength is domi-nated by a startup process in the fiowfield. The following rotation cycles show very similar pat-terns in this diagram. Doublet strength versus time step at relative radial position (0.8 R) is de-tailed in figure 3.3b. This line diagram can be

(6)

subdivided to 3 typical areas:

1) Startup process until timestep 28 (i.e. first revolution) 2) Line peak, if the blade is in advanc-ing position (timestep 30, 54 and 78) 3) Wake in-fluenced doublet strength oscillations, if the blade passes by or crosses the wake in the rear rotor disk section.

Such fast 1-period oscillations as calculated during the time steps 42-50 and 66-74 are typical indications for noise generation ation, induced by wake- blade interference. That is one of the main results of this free wake rotor code.

3.2 Code Run and Results Comparison Us-ing the 2MRTS Rotor

3.2.1 Measured Inflow Data Base

Published LDA data from NASA-Langley con-sist of rotor inflow data, measured one chord length above the tip path plane (TPP). The wind-tunnel model is a full rotor fuselage configuration, with 0.86 m rotor rad.ius. It was tested at three d.ifferent advance ratios (0.15, 0.23, 0.30). Ac-cord.ing to [6] the rotor was trimmed to a cond.i-tion without blade flapping. Published velocities are already preprocessed by subtraction of the free stream component, and by relating to the blade tip speed. Two velocity components are given: 1. LAMDA- value represents the velocity compo-nent in perpend.icular direction to the TPP (pos-itive is upwind in postive z-direction).

2. MUE - value is a tip speed related veloc-ity component, directed simultaneous parallel to TPP and x-z plane of the K-coordinate system (positive in rear direction).

The given time averaged measurement data were used for code result comparison. Also given instantaneous data will be used for further inves-tigations.

3.2.2 Blade Discretisation

The twisted 2MRTS blade is modeled fiat with 14 panels spanwise and 1 panel chordwise. The aerodynamic panels are shifted 0.25 chordlength downsteam, to position the blade bounded span-wise vortex on the 0.25 chord position and the blade control point to the 0. 75 chord position. The panels are non equispaced, to obtain a good spanwise vortex strength resolution. Fig. 2.1

3.2.3 Code Run with 2-Bladed Rotor A 2MRTS rotor with two baldes was calculated at an advance ratio of 0.15 for one rotor revolu-tion, to see how the wake develops during startup situation. Two blades were used only, keeping a good overview with respect to the wake lattice (Fig. 3.4). In forward flight, tip vortex rollup at retreating blade side is similar strong at advanc-ing blade side. That's a cyclic pitch effect. Addi-tional to the tip vortex rollup, we also see rolling up activity at the inboard wake structures. 3.2.4 4-Bladed Rotor Application

Next investigations were performed with 4 blades, running 4 rotor revolutions. Using con-stant timesteps with 15 degrees stepwise rotor movment, 96 timesteps must be calculated. A fully free developed wake is shown in figure 3.5a

. All four wakes wrap heavily into each other.

About one and a half revolutions behind the rotor position the helical lattice structure is dissolved. A kind of global tip vortex roll up remains at the longitud.inal border lines of the total wake

sys-tem. The extracted wake part of a single blade (Fig. 3.5b) underlines the d.isintegration of the vortex lattice. It is important that the simulated wake system shows stable behaviour and no wake exploding occurs.

Blade doublet strength development versus time is given in four d.iagrams, one for each blade (Fig. 3.6). After the startup process the isoline pattern of all four blades are equal, with respect to phase displacement. That is a further demonstration that the simulation code works stable.

Timestep length variation effects were investi-gated by a special test run. Two revolutions after start, the timestep length was derated from 15 degrees to 5 degrees, to calculate the next quar-ter rotor turn. Afquar-ter that, the timestep length was switched back to 15 degrees. Blade 1 dou-blet strength devolpment of this special run was now compared to a normal run, using 15 degree timestep ouly. Isoline diagrams of both test cases (Fig. 3. 7) show, that in the timespace after the slow down procedure the same doublet strength

pattern is produced. Corresponding timestep

numbers for the same rotor position are 66 with, and 54 without timcstep length variation.

(7)

but don't cause changes in the wake system. Dif-ferent solutions on the rotor blades during the follow-on timesteps were not observed.

First investigations of aerodynamic coupling ef-fects were done, by including a simple body con-figuration to the isolated rotor code. The actual clwsen body for this test is a half-infinite one. It. is built by one point source under freestream only, simulating a rotation symmetric body (Fig. 3.8) Position and dimensions are similar to the real used wind tunnel model.

3.3 Rotor Inflow Data Comparisons

Calculation results of mean LAMDA and MUE are presented in disk diagrams with isolines to give an overview (Fig. 3.9-3.10), and in x-y like diagrams at distinct radial and circumferen-tial positions (Fig. 3.11-3.13) to show the results in detail. Values in the plots represent NASA-Langley measurements (NL Meas.), free wake iso-lated rotor (FW Calc.) calculations and free wake results with simple body simulation by a single point source (FW +Body). Investigations were performed for three different advance ratios: 0.15, 0.23, 0.30 . A complete set of all result diagrams is given in [10].

3.3.1 Lamda Results

Isoline patterns look very similar to their mea-sured counterparts. Unsymmetric downwash in the rear disk area is also represented as the tip vortex induced upwash in the disk front section. This observed similarity indicates that the wake vortex system is calculated well. Local differences between measured and calculated data are visible in line diagrams (Fig. 3.11-3.13). In the outer ra-dial disk area the isolated rotor calculations agree with the NASA full configuration (i.e. rotor and fuselage) measurements. At the inner areas the calculated Lamda values are lower, but it is im-portant that they follow the measured result line in the same tendency. If we take into account, that there is no panelised displacement body used in the calculations, the theoretical results are too low, which is correct.

Local improvements were achieved by applica-tion of the body simulating 3D-point source. In the disk front area, especially at 180 degree and

r/R

<

0.5 (Fig. 3.11c, 3.12c) the point source <ec-tivity 'lifts' the lamda very near to the rneilsured

value. This result is qualitative only, and was a

first study of fuselage to rotor influece.

3.3.2 MUE Results

Line diagrams of mue value (Fig. 3.13) show in radial direction the same tendency between mea-surement and calculation. Compared to lamda re-sults the tendential agreement is weaker, and the relative difference is higher. A probable explana-tion is the following: Mue values are very sensi-tive to the vortex z-position in the K-coordinate system. Wake vorticies with high activity (i.e. blade tip vortex) are almost parallel to the rotor disk. Small differences in the z- position affect the Mue value strongly. Additional simple body simulation don't ensure result improvement. Ten-dential improvements are sometimes observed in the diagrams.

4. Conclusions

Free wake method application to rotor aerody-namics improve basic knowledge of rotor wake be-haviour and its influence to other rotorcraft com-ponents. The achieved conformity between rotor inflow calculations and experiment indicate, that even details of the wake induced flowfield are rep-resented well. First coupling attempts with a sim-ple fuselage simulation show local improvement. Code expansion to a paneled fuselage with full rotor-wake coupling is necessary, to obtain im-portant wake effects at fuselage surface.

References

[1) D. Levin and J. Katz. Vortex-Lattice Method

for the Calculation of the Nonsteady Separated

Flow over Delta Wings. Journal of Aircraft,

18(12):1032-1037, December 1981.

[2) G.L. Crouse, Jr., J.G. Leishman, and Napei Bi.

Theoretical and Experimental Study of Unsteady

Rotor/Body Aerodynamic Interactions. Journal

of the American Helicopter Society, 37(1):55-65, January 1992.

[3) D.R. Clark and B. Maskew. A Re-Examination

of the Aerodynamics of Hovering Rotors

Includ-ing the PrcBence of the Fuselage. In International Technical Specialists' Meeting on Rotorcraft Basic

Research, Atlanta, GA, 30332 USA, March 1991.

(4) A. Baron, M. Boffadossi, and S. De Ponte.

Nu-merical Simulation of Vorlcx Flow.9 Pa8i !mpu/w

(8)

Dy-namics Panel Symposiutn1 Schevcningen,

Nether-lands, October 1990. Paper 33.

[5] D.R. Clark and B. Maskew. Calculation of Un-steady Rotor Blade Loads and Blade/Fuselage In-terference. In Second International Conference on Rotorcraft Basic Research, University of Mary-land, College Park, Maryland USA, February 1988.

[6] J .\-\'.Elliott, S.L. Althoff, and R.H. Sailey. Inflow

Measurement Made with a Laser Velocimeter on

a Hdicopter Model in Forward Flight. Technical

Memorandum TM 100541-100543, NASA

Lang-ley Research Center, Hampton, Virgina

23665-5225, 1988.

[7] A. Rottgermann, R. Behr, Ch. Schott!, and

S. Wagner. Calculation of Blade- Vortex

Inter-action of Rotary Wings in Incompressible Flow by an Unsteady Vortex-Lattice Method Including Free Wake Analysis. In Hackbusch W., editor, Notes on Numerical Fluid Mechanics, pages 153-166, Braunschweig, 1991. Vieweg Verlag.

[8] L. Zerle and S. Wagner. Progress Reports in

BRITE EURAM Aero 0011 C(A) 'SCIA' Project 1990-1992. Technical report, Institut fiir Luft-fahrttechnik und Leichtbau, Universitat der

Bun-deswehr Miinchen, 8014 Neubiberg, Germany,

1991.

Blade Panelisation 14 x 1

Local. blade own!;(! Coordinate System 8

/Real Blade y B

·--- ---

-·

---1

Lj _

_L_

--1---1-

-l-- l-l-l Wll

l

~

Aocodynamic Panolisation

Coordinate System K

~ rotor shaft I fuselage fixed

~ non rotating -rotor disk centered

Fig. 2. 1

y

Fig. 2.2

[9] H. Behr and S. Wagner. A Vortex-Lattice Method

for the Calculation of Vortex Sheet Roll-Up and ·wing- Vortex Inter-action. In E.H. Hirschel1

ed-itor 1 Finite Approximations in Fluid Aftchanics

II, volume 251 pages 1-13. F'ricdr. Vicwcg & Sohn1

I3raunschwcig und \Viesbadcn1 1989.

[10] L. Zcrlc and S. Wagner. Final Technical

Re-port BRITE EURAM Aero 0011 C{A) 'SCIA' Project 1990-1992. Technical report, lnstitut fiir Luftfahrttcchnik und Leichtbau, Universitiit

der Bundeswehr Miinchen, 8014 Neubiberg,

Ger-many, 1992.

[11] A. Lesching and S. Wagner. Theoretical Model to Calculate Aerodynamic Interference Effects be-tween Rotor and Wing of Tiltrotors. In Proceed-ings of the 16. European Rotorcraft Forum,

Gla.s-gow,UK, September 1990. Paper No. 11.2.

[12] O.A. Kandil. Steady and Unsteady

Incompress-ible Free- Wake Analysis. In L. Morino, editor, Computational Methods in Potential Aerodynam-ics, pages 631-677. Springer Verlag, Berlin, 1985.

(~-"'-S'-'lt a"-r \,____)

Read inD'JI:

Blade goometry Code ~\t>eling d

j

Roto1 moVJng data

Precalculatoon~ S.:>tting of con~tants

~==':::;m:::":::":::':::':::"":::'=;J:\-:::0:::.

":::'

=====::;'""-~cut ate di$.Diaco:.>m0flt of wakG netwo1k nodal point~ h'.ove 10101 to now po!.itbn Displace wake to now pos.iton

Calculate ~lie am vokx:ily al blade con\101 points, by u~in9:

Fre-e silOam, b!aOO movh9 spood, and wako induction &iifd and ~olve equation systom. to obtain bladQ panol

dovt>lel sl!ongth

[ _ Wlito lim()step dopQndon\ output

(9)

i

/,/'

/

-{

r

\

_\ Q

\,~~-/

Fig. 2. 4 w. L.t p

Blade 1 (Xw..OI.<( Stt...,.h OeYelopmenl

2 ~ Rocor in Forward Aqll mu~0.20 . _ _

...

...,.

"

0 3!>0 0 325 0.300 -() 21~

""

ons 0>00

Elade 1 Do<.bl<11 Strength a1 R.., • 0.60 Ko;.e Fl01or 1t1 F<.:n<atd Hlf1t mu.0.20

P'

' 0.

f Ha f ... 0 tl• c • "

·---···-·--·-· -... 1

2 Rl..,. Ro<O<' •II~ ~~ nm .. iep• l

w .... lx><h • .,~ ' - - : {

Fig. 3.1

c-.-.. w .... , _ . _ . , _ . _ _ , _ Top V>ew

'---"I

_v ... c....o__..,_ _'

·:· :;; 1

~

.,.

i

: ::: I

I

: ::: I

-~-~ I ooo i I

. :: l \

--1

.. i \

I

~~---1 Fig. 3. 2 n

~·

% I' '"---~--Fig.

=-~-c-~~---·---Calculated Rotor Free Wake

2 - 6lade1 MATS· Isolated Rotor in Forward Fliijhl

Adva11co Ratio mu a 0.15 lr!Clld<ng cydic Pilch

Starling up Process af10f OOQ Rovoli.J.ion

(10)

Wake of 4-Biaded Rotor after 4 Revolutions mu = 0.23

Doublet Strength Variation

mue .. 0.23 Blade No.1 ~-• <U

.

_• '" _ou ' '" • 1 ....

.

'" _'"

.

'" ' ou ' '" 11 J• :w ... oo n -... " 24 -nrr-•f" p..- f\.wokA\on No. o( ~~ Fig. 3.6 Fig. 3 .Sa Fig. 3.5b

Doublet Strength Variation

"""'. 0.23 r....-~~-~...!~!!-~ .coo~t. 15doo9"-fW.ot:~p.«T...-ep ot.oo •;·66 s ~-Roo.«~~>« r..-00

.

·-

'" ¥ ~ n u " - - cl ~ r.u.c:::::""c___"'·_· ,...._~ _ __j Fig. 3.7

,---··

I

_I Fig. 3.8

(11)

""

N I

"'

,---···-·-···---~---~~---· S Ul

"

g 0. ~

Mean Rotor Inflow Data Ffee Wake Calculalon

Larnda lsolines v.,...Jv~

Advance Aalio rnu"' 0.23

l"""•' lAM(!(} M _'~~ 0 OW{l(J l)i)IY.) (1(\lf)(! 0

"""

'

·=

•

<00"> A .CNOO <Q-()11-0 n~Voo

.,"

"'"'

~ ..¢;:;:~ <<><oo ~ .(l (>C$Q 'l -¢{600 405:.0 ·10!·, ~ I 10

3_:2_~

·1.0 -<l.5 0.0 0.5 x/R Position

Mean Rotor Inflow Data NASA· langley Measuremenl

g ; 0 ·~

2 .

a. ~ Larnda Jsolines v'nll,lv, Advance Ratio mu "'023 l"'"'' 1,..';>.(00 H

"'"'

0

'""'

0 (ll!>Q {1(1!00 0 000~ c ·00000

" '"'"'

A o{l(/j(\0 ~ -.()01$1) -<:~0700 -{1(1?!.(1 .(')1\.lC.) -{I OJ~

l

i

t

~~~4/

:

;;E

.

I

.,o

₁ _'

~

_~..c:::: _t _!

<""'

I

L

-u.J --o.s oc o.s "u 3 1 Ob I

X/R PotJIIOf1 • __)

---~--- ---·

,--·

---·--·--·~--~

I

Mean Rotor Inflow Data

c

-~

0

a. ~

Free Wake Calculaion

~

-~~'

-D . . S 0-CJ O.S U) xJR Posit10n

I

_g 1i n. '{ -1.0

Mean Rotor Inflow Data

NASA· Langley Meas\Jrement

l_:,~

.•

~--~~.0~5~.~--~~--_.--~---"-_uo _o.s _Ul "#?. Posilion Larnda lsolines v_/v"" Advance Ralio mu ., 0.1 S """' V#I!O

'

jJ f.IZ"'...Y G

'"""

'

CblY.

'

~')1~

•

(;(l'l"J.,

'

ovm

'

-:irh'..t; ' .C!i•~ -:IC!!.:l ..;~ -:.?-;~ ./.:C.r:f,',· .()~ -':'~~ .;;-:,.v. .il')'Y/. .C~Y.: 3.9b

(12)

Mean Rotor lnftow Data Comparison cr-o,,..,t .. ~~~ oc.g.-M-i~R•oo""-'•Qt!> 000 fWCNG NLM..o .. - - fWolk><ly a

Mean Rotor Inflow Data Comparison

CJC>.>tf"ht~Jfl~W ...__-.~ Pou>on: 1&0 Dt?-Ntou.cc Raloa,...., • 0.\S 000 0.00 - - - o -fW CU:-. NLM-.. - - - fWtBoOy c

R~ Radial u..-.r-..aort ~ ~~ • 0_40

~- FWCaJ.:;.

Mv"NA R..lo:> IY'O,t .. c. 15

.

NLMe .... ~ _fW•BOOy ~·v-lv,. 00~

o=

. .

_{. .}

.

__;._

·=

_~·

.

~

.

-..

-

0 ~ •oo _·~ ~ ~ = =

C.-cumi<.<....- PQO.<t.on fD<o9<-l

R.!M"" R.o,doal ~..., Pc.+t>oo 1~ • O.li)f

Moi&I>I:A Rail<) In</. 0 15

----<>-- FW C&Jc Nl 1.1-. - - - FWo6o<.ty

U

--~=~~

'=

·=

·~

-e

Munn notor Inflow Data Compa!iSOil

<>0.'>

C..cun'ht..-....1 "'..._..~ Po..a.on: 240 ~

~ano.Ruomu•0.15

000

'"

/>.ll(;llh-9 A~ ~WOOO( f>ou>oorfi'l• 0.78 ~~mu•0.15 Lt.-nd.;o •v-/v,.

o=

_~

.

v

.

·=

·~ 0 ~ •oo _·~ ~ 000 tWC.&!>: N( M.u.o fW •t»Jr b

..

.

d ~ FWC...

.

kl~. ~- fW,aooy

.

.._,___:___ =

,.

Ci<cutm.o<<M"(""' ~~-I f

Figure

3.ii

l_AMOA

_{Inflow Data}

(Vertical to

T1p

Path Plane)

(13)

c~cvmlerOO<"oo..r ~ .. nwn~ ~oo

oo.,.--·-

fWCak:. -'<!""""" RMIO rrou • O.ZJ

.

_{Nl ""-.o} ~ _{FW •Uody} L..-naa • v...,lv,.

..

~

·=

~-..

"

~t::st::::tl

·~. 000 '" ••

'"

• 00 R..._ R..,.. ROIO< ~ r~ a Mean Rotor Inflow Data Comparison

Clf<:UTI!<w..n~.W M-..:our..,...n~ p~· t80 ~·" ~ _fWC&lc. Mv.nc-Rlllll ll'w.l • O.l!

.

_NLMu..a. ~ FW•B~ ~-"-'"·

o=

.

·=

.

. .

·=

000

••

'"

>00

R~~ R.ado.a.l Rolol Po woo·~

c Mean Rotor Inflow Data Comparison

R~ ~ ~Gme<t Poo:<lJO<lrJl'l. • 0.40

~ FWCi>l<=. Advanc.<~ f\al.:) mu • 023

.

_NL_{M&.aa •}

-

FW•BOOy L.om::la•v .... tv,. Q.Q..,.,

·=

.

. .

.

~.

.

.o.o-...

""<>-.q.

' ~ ,00

...

₌ ~ = ~

c.-cum..,.~ Pc.won ~""•I

Mean Rotor Inflow Data CompaJison

.,

e ---<>-FW C~. Nll.!oua. - - - o - -FW •BO<:Jf

---

--··---·--···--···---·

--Mean Rotor Inflow Data Comparison

C•c""'hol.,lw.l M...,...,.,,..~ ~t.:>n \l<.l Ooov<- ---<>--fWC.w.. NNWY-•II"""'""""OlJ

.

_Nl_t.l.u•

--

IW •lw.Jy Lolm<:la•v.,.lv,. ·~· ·~

.

~/

·~· ~.

·-

000 _'" •• _'" 'W ~R..o..o~f\OCU<f'<.>r.~r,fi b

Cn:um~ ....,...,~ Po.A~Qt~: 170 D+>~rno

~ _FWCU:.

NNN>t:• R•bO rrou • 023

.

_{Nl Mu.~}

~ Fw.~ La.rro::S& • v...,lv.,

o=

_.

.

o=

_:.

_{. . .}

_..

_...

_.

.

·=

₀₀₀ '"

••

'·" 'OO

R.bo~ ~Ill Rolo< Po...:.on t.f'l

d

RW!Ih"'!Rild<OII~<il<T>OO(~r~•0.78

-

FWC<ok.

Nfv'OIICfl R~ ffiY • 023

.

_NLJ.I.l..u

-

FW·-Utnda • v .... lv,. om>

.

_~

_.

·=

.

v

.

.O.<XIS ~

"'

·-

_•

_..

,00

.•

₌ _'" ₌ '" Cwcuml<>"·•·o~..,. ~ {0<-;;r.-..j f

Figure 3.12

LAMDA

Inflow Data

(Vertical to Tip Path Plane)

Advance Ratio 0.23

(14)

Mean Rotor lnftow Data Comparison Crcuom!.,..~~-'IIP\:oo.ol;o.;l<'l:

'""'-

--rwc~to~c. Adv...,.A.oho~n<~•O.lS

.

_NLIMIII. - - - fW+6<.>dy Mvo•v_tv,.

..

~

..

~

.

· 0 -

.

..

0~ 0~ o• on _·~ fl~ Rad.al Rotoo ~ r!fl

A.<N~ Raloomu • 0.1$

o=

_...

000

Rto!a!M~fU.do.:al~....-t~tiR• 0.4-0 !Wv"""""R<o!Kirnu•O\S !.l.al.v_tv,.

o=

o= r-

_.

. .

.

·=

0

•

.oo

.•

₌ ₌ a ----o-- FW Calc.

..

~

.

~

.

~ Nllol..u. FW t&>dy fWCWc, NLM<o..,_ c

fW·-.

~ c;.,...,..,.._.,.~ P<:>Mion 10<-?-1

ROII<~~~w• R~~ ~...,_.. Poo.t>o<~ r,fl "0.96 Ai.1vo.NAR...loomu•O.I5 ~FWCak:. NLM..a1. ~ FW•B<.Kiy e g

co~""""""''"'" M.»u~ .. ~ '~"' 1)0 o""~'-

--

_fWCak:.

Nl ... Raloornu•0.\5

.

_Nl_M..lo ~ fW•U<»y r.w.•v-lw,. 0 -0~ s~~

.

..

_.

.

.,

.

·~.

.

. .

0~

·~ •• _{A - ' - Radw.l A<>101}"' _{f>o ....}_oon..oo _<ill

~~ M.-..,._... f'oWon: 2-40 o.v ...

/.dv~R..loclmu•0.\5

0.1~

R~A""'""~tt<n«ll~r.fl.•0.76 N:lv;or,:;.eRil!>Omu•O.tS Moo ·•-lv.,

o=

""

_{. .}

_.

.

...,.

.

·=

0 • _•oo

.•

₌

,.

. .

•. oo ~

.

~

.

' ~ b FWC... NLIMu. F W -d fWC~. NL~ . fW•80<ty ~ C~G>Jml<><"'~...t POUK>ro !D<>\}1.,...1 f

Figure 3.13

MUE

Inflow Data

(Parallel to Tip Path Plane and

xK- zK

Plane)

Advance Ratio 0.15