rotary-wing aerodynamics, volume i

380 Pages·012.85 MB·English

N79-22039
ROTARY-WINAGERODYNAM-ICVSOLUMEI
BASICTHEORIESOFROTORAERODYNAMICS
(WITHAPPLICATIONTOHELICOPTERS)
Boeing Vertol Company
Philadelphia, PA
Jan 79

NASA Contractor Report 3082 N79-22039
Rotary-Wing Aerodynamics
Volume I - Basic Theories of
Rotor Aerodynamics (With
Application to Helicopters)
W. Z. Stepniewski
Boeing Vertol Company
Philadelphia, Pennsylvania
Prepared for
Ames Research Center
under Contract NAS2-7007
N/ A
National Aeronautics
and Space Administration
Scientific and Technical
Information Office
1979

2. Gov_nmonl _ No. 3. Iqacil_mt's Cmmog No.
RNepAorStA NCo.R-3082 ! N7f-
4. T_ie end Subtitle I. Ilopon Date
January 1979
Ro_ry-Wi_ Aerodynamics
Voiu_ne I - Basic Theories of Rotor Aerodynamics (with _plication $. _ O,_,_x_ion Code
to Helicopters)
7. Amber{s}
|. Porfocm_l Orpr_zatio. Repwt No.
W. Z. Stepniewski
I0. Work Onit No.
9. IKw_rnsn_OrganJ_tionNarnelndAdd,'esm
Boeing Vertol Company
Philadelphia, Pa. !I. Gmm_-t o¢G,r'at No.
NAS2-7007
I_L Tvlm of Rel_Ort and Period Co_¢ed
12.S_omoring A41encv Name and Addrou
t Contractor Report
National Aeronautics and Space A__is_nation
Washington, D. C. 20546 14. SponsoringAgency Code
iS. Supplementary Notes
16 Abstracl
Chapter I, Introduction, includes a Aefinition of rotmr-,-wing a'ircraft and their comparison to
other transport vehicles regarding energy consumption, :-..lementary consideration of blade and
rotor d>Tumics, rotor control, and a review of rotary-:.ing configurations. Chapter II is devoteJ
to the moment%oa theory, with application to such prob], _ as prediction of thrust and ideal
power of single and tandem rotor configurations in var _us regimes of flight, axxl induced
velocity distribution along the disc in inplane transl;-tion. Ompter Ill deals primarily with
app]ication of the combined momentum-blade-element the ties to problems previously considered
in Chapter II. In Chapter IV, various aspects of wort:._ theory are discussed with application
to the determination of induced velocities around the cisc--both under static conditions and
inplane translation. The so-called local momentum the:ry is presented as am mppendix. Chapter V
explains the velocity and acceleration potential theor;._s and their application to rotor
aerodynamic problems--analogous to those considered in, ':ha@ter IV. In addition, flow determination
about non-rotating bodies is briefly out/ined. Rmdame_ta/ theories of both thin sad thick
airfoil sections are presented in Chapter VI, followe_ by discussion of u_steady aerod)mamics
and contributions of airfoil characteristics to merod),nmic efficiency of rotors and helicopters
in hover and horizontal flight.
t NATIONAL -TECttNICAL
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17. Key Wocm (SuggestedbyAuthor(s}} llL Dm• ¢._ Smemem
P_tary-_:ihg Ae_od)_namics, l_ment_m Theory, -Unclassified
Combined Blade-element and ICaaen1_m Theory,
Vortex Theory, Potential Theory, and Airfoil
Theory
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"Foe sadebytheNot_n_ T_dm,,"_ Infom_tion Ser_. Sil_qlT_Md, Viq_ 22161
IASA-La_! e.y, IS79

FOREWORD
In recent years,there hasbeenanincreasingvolume of reports, articles,papers,and
lectures dealingwith variousaspectsof rotary-wing aircraft aerodynamics. To hose who
enter this domain, either as graduate students with some background in general aero-
dynamics, or thosetransferring from otherfields of aeronautical ornonaeronauticaJengi-
neering activities, this vastamount of literature becomesa proverbial haystackof infor-
mation; often with the result of looking for aneedle that isn'tthere. Buteventhosewho
are professionally engagedin someaspects of rotary-wing technoloiP/may experience a
need for areference text on basicrotor aerodynamics.
Through my experience both asan educator and practicing engineer directly in-
volved invariousaspects of industrial aeronautics,it becamedouble apparent that there
wasa need for atextbook that would fulfill, if not all, at leastsomeof theabove require-
ments.
With this goal in mind, the text entitled Rotory-W/ng Aerodynamics waswritten
under contract from USAAMRDL/NASA Ames.On onehand,theobjective isto provide
an understanding of the aerodynamic phenomena of the rotor and on the other, to
furnish tools for a quantitative evaluation of both rotor performance and the helicopter
asawhole.
Although the material deals primarily with the conventional helicopter and its
typical regimes of flight, it shouldalso provide a comprehensiveinsight into otherfields
of rotary-wing aircraft analysisaswell.
In order to achieve this dual aim of understanding and quantitative evaluation,
variousconceptual modelswill bedeveloped. The modelswill reflect physicalaspectsof
the considered phenomena and, at the sametime, permit establishment of mathematical
treatmenL To more strongly emphasize this duality of purpose, the adjectiveph,vsico-
mothemat/co/will often beusedinreferring to thesemodels.
It shouldberealized atthispoint that similar to otherfieldsof engineeringanalysis,
conceptual models-no matter how complicated in detail--still represent asimplified pic-
ture of phys,cal reality. It is obvious, hence, that the degreeof sophistication of the
physicomathematical modelsshould begearedto the purposefor whichthey areintended.
When faced with the taskof developingsuch a model, one may beadvised to first ask
the following two questions: (1) whether the introduction of new complexities truly
contributes to a better understanding of the physicsof the considered phenomena and
their qualitative andquantitative evaluation, and (2) whether thepossibleaccuracyof the
data inputsissufficiently highto justify these additional complexities.
In this respect, one should determine whether amore complex model would truly
leadto amore accurate analysis of the investigatedphenomena orjust,perhaps,that the
procedureonly looks more impressivewhile mathematical manipulation would consume
more time andmoney. Furthermore, it shouldbe realized that often inthe more complex
approach,neither intermediate stepsnor final results canbeeasilyscrutinized.
Withrespectot rotary-winagerodynaminicgseneraal,ndperformance
predictions
in particular, one shouldrealizethat aerodynamic phenomena associatedwith thevarious
regimesof flight of aneven idealized, completely rigid rotor arevery complicated. Fur-
thermore, the level of complexity increasesdueto the fact that in reality, every rotor is
non-rigid becauseof the elasticity of itscomponents and/or built-in articulations. Asa
result, a continuous interaction existsbetween aerodynamics and dynamics, thus intro-
ducing new potential complexities to the taskof predicting aerodynamic characteristics
of the rotor. Fortunately, evenconceptually simple models often enableoneto geteither
accurate trends or acceptable approximate answersto many rotary-wing performance
problems.
Byfollowing the development of basicrotor theories-from thesimplemomentum
approach through the combined momentum and bladeelement theory,'vortex theory,
and finally, potential theory-the reader will be able to observe the evolution of the
physicomathematical model of the rotor from its simplest form to more complex ones.
It will alsobe shown that anunderstanding or explanantion of the newly encountered
phenomena may require modifications andadditions andsometimes, a completely new
approach to the representation of the actual rotor by itsconceptualmodel. Bythesame
token, a better feel isdeveloped with respectto the circumstancesunderwhich asimple
approach may still suffice. Finally, these simpler and more easilyscrutinized methods
may serve as a meansof checking the validity of the resultsobtained by potentially
accurate, hut alsomore complicated wayswhich may be prone to computational errors.
Presentation of the above-outlined theories, plusconsiderations of airfoils suitable
for rotary-wing aircraft constitutes the contents of Vo; I."Reduction to practice" of the
material presentedin Vol I isdemonstrated in Vol II, where complete performance pre-
dictions are carried out for classical,winged, and tandem configurations including such
aspectsasperformance guaranteesandaircraft growth.
The existing need for a text conforming to the aboveoutlined philosophy was
recognized by representativesof USAAMRDL and in particular, by Mr. Paul Yaggy,
then Director of USAAMRDL, and Dr. I. Statler, Director of Ames Directorate whose
support madepossiblethe contract for the preparationof the firsttwo volumes.
To perform this task, a team was formed it BoeingVertol consisting of He under-
signed as Editor-in-Chief and author of Vol I; Mr. C.N. Keysasthe principal author of
Vol II; and Mrs. W. L. Metz as Associate Editor. The courseof thework wasmonitored
by Mr. A. Morse and Dr. F.H. Schmitz of Ames Directorate; while Mr. Tex Jonesfrom
USAAM RDL-Langley Directorate provided his technical assistance andexpertise by re-
viewing the material contained in both volumes. Thanks l_e extended to the above-
mentioned aswell asthe otherrepresentatives of USAAMRDL. Finally, my asr_oclatesand
I wish to thank the managementof BoeingVertol; especially,Messrs.K.Grina, J.Mallen,
W. Walls,andE. Ratz for their support, understandingand patience.
There are, of course many more people from this country and abroadwho signifi-
cantly contributed to the technical contents. Their individual contributions are more
specificallyacknowledged inthe prefacesof the individual volumes.
W.Z.Smpnlexwkl
• ' RldleyPerk,Pro.
/i i.,_ a_,to_
PREFACE
II II
Volume I of the text entitled Rotory-W/ng Aerodynomic$ isdevoted in principle
to Boslc Theories of Rotor Aerodynomlcs. However, the exposition of the material is
preceded by an introductory chapter wherein the concept of rotary-wing aircraft in
general isdefined. This isfollowed by comparisonsof the energyeffectivenessof heli-
copters with that of otherstatic-thrust generatorsinhover;aswell aswith variousair and
ground vehicles in forward translation. While the most important aspects of rotor-blade
dynamics and rotor control are only briefly reviewed, they should still provide asuffi-
cient understanding and appreciation of the rotor dynamic phenomena related to aero-
dynamicconsiderations.
The reader is introduced to the subject of rotary-wing aerodynamics inCh II by
first examining the very simple physicomathematical model of the rotor offered by the
momentum theory. Here, it isshown that eventhis simpleconceptual model mayprove
quite useful incharting basicapproaches to helicopter performance predictions; thus pro-
viding some guidanceto the designer.However, the limitations of themomentum theory;
i.e., its inability to account for suchphenomena asprofile dragandlift characteristicsof
blade profiles and geometry, necessitatedthe development of a more sophisticated con-
ceptual rotor model.
Thecornblned b/ode-elementond momentum theory presentedinCh IIIrepresents
a new approach which demonstrates that indeed, greater accuracy in performance pre-
dictions isachieved,and this would alsobecomeasourceof more.detailed guidelinesfor
helicopter design. Even with this improvement, many questions regarding flow fields
(both instantaneousandtime averaged)aroundthe rotor still remainunanswered.
In the vortex theory discussedin Ch IV, a rotor blade ismodeled by meansof a
vortex filament(s) or vorticity surface; thus opening almost unlimited possibilities for
studying the time-averageand instantaneous flow fields generatedby the rotor. Unfor-
tunately, the price of this increased freedom was computational complexity usually
requiring the useof high-capacitycomputers.
It appears that some of the rotor aerodynamic problems amenable to the treat-
ment of the vortex theory may be attacked with a somewhat reduced ¢omputationai
effort by usingthe approachesoffered by the velocity ondocceJerotlonpotentlol theory.
This subject is presentedin Ch V which also contains a brief outline of the application
of potentiai methods to the determination of flow fields around three.dimensional, non-
rotating bodies.
Considerations of o/rfoll sections suitable for rotors, aspresentedin Ch VI, com-
pletesthe sequenceonfundamentals of rotary-wing aerodynamics.Thismaterial provides
a basisfor development of the methods for helicopter performance predictions usedin
Vol II.
iii
In order to create a complete series on Rotary-Wing Aerodynamics the author
anticipates a third volume devoted to the application of the basic theories established in
Vol I. This volume would include (1) selected problems of helicopter flight mechanics
(e.g., ground effect, flight maneuvers, performance limitations, and autorotation); (2)
establishment of a link between aerodynamics and design optimization; and (3) develop-
ment of techniques leading to performance maximization of existing helicopters. In
fairness to the aeronautical engineers and designers who have been anxioudy awaiting
for the publication of this series, the first two volumes are being released prior to the
writing of the proposed third volume.
Returning to the present volume, the reader's attention is called to the fact that
both $1 metric and English unit systems are used in parallel; thus expediting an acquain-
tance with the metric approach for those who are not yet completely familiar with this
subjecL
in conclusion, I wish to express my indebtedness to the following persons who
generously contributed to this volume: Professor A. Azuma of the University of Tok_,o,
Japan for his review of the appendix to Ch IV; and to Drs. R. Dat and J.J. Costes of
ONERA, France for their valuable inputs and review of Ch V.
W. Z. Stepniewski
iv