.

NASA Technical Memorandum 100066 USAAVSCOM Technical Report 88-A-001

Some Rototcraft Applications ofComputational Fluid DynamicsW. J. McCroskey

DTICr.--,LECTE 1

Dist~utin U~imio~ AUG1 8198DDSTFISUTION STATEMENTAApprpved for public release4

Distribution Unlimited

March 1988

usARM YVAVIATION

SYSTEMS COMMANDNational Aeronautics and AVLATION RESEARCH ANDSpace Administration TECHNOLOGY ACTVrTY

88 8 18 "

PI

NASA Technical Memorandum 100066 USAAVSCOM Technical Report 88-A-001

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Some Rototcraft Applications ofComputational Fluid DynamicsW. J. McCroskeyAmes Research Center and Aeroflightdynamics Directorate, U.S. Army Aviation Research andTechnology Activity, Ames Research Center, Moffett Field, California

March 1988

NASAMNational Aeronautfics and ATMVSpace Administation SYSTEMS COMMAND

AVIATION RESEARCH ANDAm.. Research Center TECHNIOLOGY ACTIVITYMoffett Fied, Calffornia 94W35 MOF~ETT FIELD, CA 94305-10gg

SOME ROTORCRAFT APPLICATIONS OF COMPUTATIONAL FLUID DYNAMICS

W.J. McCrookey

Ames Research Centerand

Aeroflightdynamics Directorate

U.S. Army Aviation Research and Technology Activity

ABSTRACT of these simpler "building blocks." In recentyears, computational fluid dynamics (CFD) has

The growing application of computational aerody- begun to offer new tools to the rotorcraft commun-

namics to nonlinear rotorcraft problems is out- ity; and Reference (5), in particular, emphasizes

lined, with particular emphasis on the development some pioneering applications of CFD to transonic

of new methods based on the Euler and thin-layer tip flow on the advancing side of the rotor disc.

Navier-Stokes equations. Rotor airfoil character-

istics can now be calculated accurately over a Computational fluid dynamics has had a major

wide range of transonic flow conditions. However, impact on fixed-wing aircraft design, but for a

unsteady three-dimensional viscous codes remain in variety of reasons, comparable applications to and

the research stage, and a numerical simulation of payoffs for rotorcraft lag by a decade or more.the complete flow field about a helicopter in Nevertheless, the combination of fixed-wing suc-

forward flight is i.ot currently feasible. Never- cesses and rapid advances in modern supercomputer

theless, impressive progress is being made in software and hardware have begun to attract the

preparation for future supercomputers that will attention of both government and industry manage-

enable meaningful calculations to be made for ment. Consequently, fresh challenges and newarbitrary rotorcraft configurations. opportunities ire arising for scientists and engi-

neers engaged in rotorcraft research and

development.I. INTRODUCTION

Significant applications of CFD are already underThe flow fields of rotorcraft provide a rich vari- way at several laboratories, universities, and

ety of challenging problems in applied aerodynam- heicopter companie-. including 4:,vpstigatinns

ics. It is well known that much of the flow of descri3ed at this conference. This paper is notthe rotating blades is nonlinear, three- intended to be a review of these activities.

dimensional, and often unsteady, with periodic Instead, it selectively highlights a few of the

regions of transonic flow near the blade tips, and joint Army/NASA efforts by the author and his

with dynamic stall pockets inboard. The blades colleagues to develop, adapt, and apply the latest

also shed complex vortical wakes, and serious CFD technology to rotorcraft. The overall, long-aerodynamic interactions may arise between the term objective of this work is to develop andmajor rotating and nonrotating components. validate advanced CFD codes for three-dimensional,

unsteady viscous flews about arbitrary, elastic

For many years, helicopter engineers have rotorcraft configurations. It must be noted that

addressed these difficult problems with a mixture we have no illusions of building an all-inclusive,of simplified linear aerodynamic theories, wind comprehensive analysis system based on CFD.tunnel data, and design charts. At the same time, Rather, the goal is to provide a complete numeri-

a small community of research scientists has sys- cal simulation of realistic rotorcraft flow fields

tematically explored the details of individual with as few physical approximations as possible.pieces of the overall problem, indicated by the This predictive capability will help to reduce the

sketches in Figure (1). References (1) and (2) risks for new rotorcraft designs and will provideprovide an overall picture of the practical side improved tools to help engineers increase perform-of helicopter aerodynamics, and References (3), ance and efficiency and reduce noise and(4), and (5) summarize many of the recent studies vibrations.

In pursuing this goal, a twofold approach is cur-

rently being taken at the Ames Research Center:1) Mature CFD methods are being coupled withintegral wake models and simplified structural

Presented at the Second International Conference intel for moderind signland s s usinon BsicRotocrat Rsearh, ollee Prkmodels for engineering design and analysis usingon Basic Rotorcraft Research, College Park, current or almost-available supercomputers.

Maryland, Feb-uary 1988. 2) New CFD codes are bein developed and validated

I

for selective calculations of rotorcraft configu- the advancing blade in high-speed forwardrations using future supercomputers. flight. An extensive study was made of the accu-

racy and sensitivity of the results to the variouiBy way of explanation, the relatively mature corm- numerical parameters and approximations, andputational methods used in the first approach favorable comparisons were made with a large bodyinclude the transonic small-disturbance and full- of experimental data.potential flow solvers that have been used rou-tinely by the fixed-wing industry for years, but Figures (2) and (3) give representative exampleswhich are only now becoming useful to helicopter from Reference (6) for lift, drag and pitching-engineers. Their approximations may limit their moment coefficients. Of particular interest toscope and accuracy, but they run fairly easily and the helicopter community is the variation of' Cefficiently, and they can provide extremely va]u- with Mach number. For example, the large negativeable information to a skilled user. peak in the value of Cm at M 0.88, called

"Mach cuck," is well predicted by ARC2D, as shownIn the second approach, which is the subject of in Figure (3). Stall and maximum lift at low Machthis paper, the new codes and their associated number were not addressed, however, and thistechnology employ Euler and Navier-Stokes flow important problem remapnq' unsolved for highsolvers. Today these are mostly being implemented Reynolds-number flows. However, this is mainlyin a pure research mode. That is, they are cur- because of the turbulence modeling, and notrently nursed along by CFD specialists for highly- because of computational barriers.specialized cases, at an inordinate expense in CPUtime on the most power-ful supercomputers avail- More recently, Holst [9] examined in detail theable, and the results may or may not be realis- capabilities and limitations of APC2D, alonp withtic. Whenever possible, useful and practical numerous other transonic airfoil codes, and heinformation is derived from these exploratory concluded that codes of this type are capable ofresults, but the main purpose is to build toward producing airfoil data that are as accurate asfuture capabilities. While we must refrain from wind tunnel measurements. This new capability isunrealistic projections, such as replacing wind beginning to be exploited by specialists in thetunnels by computations, or designing new rotor- helicopter industry, as a tool complementary tocraft automatically by expert systems, the fixed- airfoil testing.wing legacy clearly shows that today's CFDresearch codes become tomorrow's design tools. B. Airfoil-Vortex Interactions

The lessons learned from the preceding experiencesII. INDIVIDUAL COMPONENTS with the quasi-zteady version of ARC2D and from

the adaptation of the unsteady transonic small-The building-block approach depicted in Figure (1) disturbance code ATRAN2 to inviscid airfoil-vortexprovides a framework for building sophisticated interactions [10] led us to apply time-accurateCFD codes in manageable steps, with some early Euler and Navier-Stokes algorithms [11-13] to thisapplications and practical dividends along the two-dimensional approximation of blade-vortexway. This section describes some of the recent interaction. Figure (4) shows the Navier-StokesCFD developments at the Ames Research Center for results from Reference (11), using the so-calledthese individual components, prescribed vortex approach and unsteady solution-

adaptive gridding. In this example, the structureA. Static Airfoil Characteristics of the vortex was prescribed and maintained

throughout the calculation, but its convected pathThe author and his colleagues began their long- in space was computed as part of the solution.range program of applying Navier-Stokes algorithms This technique, which is somewhat analogous toto rotorcraft problems with the two-dimensional shock fitting in thc uum .'irnl analysis of tran-airfoil calculations described in Reference (6). sonic and supersonic flows, is designed to over-In this study, the aerodynamic section character- come the tendency of most numerical schemes toistics of several helicopter profiles were com- dissipate artificially tle soiepn o-AiP'ts with:-nited using the existing NASA-Ames code AtCdU t7J, the vortex.which solves the Reynolds-averaged, thin-layerNavier-Stokes equations with the Baldwin-Lomax There was no significant shock-wave/boundary-layereddy-viscosity model to approximate boundary-layer interaction in the case shown in Figure (4).turbulence [8]. A wide range of Mach number, Therefore comparisons with other numerical tech-angle of attack, and Reynolds number was examined niques [14] revealed that the Navier-Stokes equa-in Reference (6), with particular emphasis on tions were not necessary to obtain the correcttransonic separated flow conditions relevant to time-dependent airloads in this case - they just

2

required much more CPU time to solve. On the crucial role in helicopter aerodynamics and that

other hand, the solution-adaptive grid used in their structure is closely related to the blade-

Reference k11) provided such fine resolution near tip geometry. However, past efforts to alter tip

the moving shock wave that a lambda structure was shapes and vortex structure have been largely by

observed during the vortex encounter, whereas this trial and error, with mixed results, and r, con-

structure was not revealed in other calculations, census has emerged on the optimum blde geom-

etry. This seems to be an area where computa-

The prescribed-vortex approach of References (10), tional fluid dynamics can improve our understand-

(11), and (14) is appropriate to cases in which ing of the basic phenomena and help design and

the core of the vortex bypasses the airfoil or analyze better blade tips. In addition, we envi-

rotor blade, but it cannot treat a direct, head-on sion that accurately-computed vortex structures

encounter that would significantly alter the vor- will be used as inputs to wake modeling efforts

tex structure. However, Rai [13] has developed a and/or prescribed-vortex methods for calculating

vortex-capturing method with very low numerical the complete vortical wake development For several

dissipation for such cases, using a higher-order rotations of the blades.

differencing algorithm for the Euler or Navier-

Stokes equations and a special grid structure. Srinivasan, et al. [16,171 have extended the pio-

Rai's method is also suitable for capturing weak neering efforts of Mansour [18] and Kaynak, et al.

disturbances, such as acoustic waves. (19,20] for viscous three-dimensional wings byconcentrating on the tip region and the vortex

In fact, a major motivating factor in studying formation process, using the Reynolds-averaged

airfoil-vortex interactions is the acoustics of thin-layer Navier-Stokes equations. The planforms

helicopter blade-vortex interaction, and a central shown in Figure (7) have already been investi-

question here is the capability of "conventional" gated, and the British Experimental Rotor Program

CFD techniques to capture the far-field acoustic (BERP) configuration, Figure (8), is currently

radiation due to the nonlinear shock-wave undergoing detailed study.motiin. This issue is being addressed by James

Baeder, with the aid of Rai's method described Figure (9) shows the computed streamline pattern

above, and he has reported his preliminary find- for a swept-tip configuration designed by ONERA.

ings in References (12) and (15). Baeder is cur- This example is nonrotating and is at a free-

rently comparing the effects of the numerical stream Mach number of 0.85. The swept tip reduces

algorithms on the results in the near field of the the shock wave strength, but it increases the

airfoil, where the reactive components of the concentration of vorticity and the peak velocitiesfluctations are dominant, and in the intermediate in the tip vortex.

field, where the radiative components begin to

dominate. Although the surface airloads are not Representative results for a rectangular wing at

significantly different, Figure (6) from Refer- low speeds are shown in Figure (10) from Refer-

ence (12) shows that the different levels of ence (16). An interesting result of this series

sophistication in the various codes produce dif- of calculations was the sensitivity of the

ferences in the acoustic pressure throughout the detailed flow features to the geometry of the tip

field. At present, a fifth-order-accurate Euler cap, and the importance of using different compu-

code seems to be the best overall compromise tational grid topologies in modeling the different

between accuracy and cost of the computations. tip-cap shapes, e.g. Figure (11). Generally, good

Baeder [12] also studied the effect of vortex core agreement was obtained with experimental results,

size, miss distance (including head-on encoun- including the qualitative differences between the

ters), and Mach number, and he is currently exam- different tip caps. However, the peak suction

ining various airfoil shapes to see whether BVI levels that were measured in the extreme tip

noise can be alleviated by changing the airfoil region were not obtained in the calculations. The

geometry. The results so far indicate that the reason for this clear but relatively minor dis-

Mach number and miss distance are the most impor- crepancy in the numerical results has not been

tant paramieters in determining the radiated noise. identified; it may be due to the turbulence model,

to inadpquate local grid rsolution, or to' the

lp Flows ai2 Tip-Vortex Formation thin-layer approximation in the governingequations.

The formation and subsequent rollup of tip vor-

tices from blade tips is an important fundamental Another shortcoming of the tip-vortex calculations

problem that provides an ideal opportunity to done up to now is the distortion and diffusion of

extend the capabilities of the Navier-Stokes codes the vortex structure downstream of the blade tip,

to a practical component of the total rotor flow due to the effects of the sparse grids in the far

field. It is well known that tip vortices play a field and the numerical dissipation used to

3

enhance the stability of the code. For this rea- Figure (13) shows the instantaneous pressure dis-son, the vorticity contours in the wake and the tributions computed with the same Euler solver forcalculated rollup process can only be considered a particularly difficult forward flight case. Thequalitative at this time. New, special grid topo- results, particularly the unsteady shock-wavelogies and solution-adaptive grid generation formation and its rapid decay in the second quad-strategies will be required to overcome this limi- rant, agree better with the experiment than in anytation, as discussed in Section V. previous numerical study.

B. Results for a Lifting Rotor in HoverIII. ISOLATED ROTOR BLADES

As reported in Reference (22), C.L. Chen recently

The numerical methods of the preceding section for computed the flow for a lifting two-bladed rotorstudying blade tip flows and tip vortices and the with no wake modeling. Instead, the vortical wakeexperience gained in working with them are now was captured approximately by his Euler codebeing applied to rotating blades. However, the through the use of a periodic boundary conditionextension is not a small step, as the complexities between grid zones containing the blades. Fig-of the flow field and the computer resources ure (14) summarizes his solution and shows tnerequired are significantly greater in these importance of this periodic boundary condition.cases. In this section, a brief overview is given After several revolutions of the blades, solutionof some recent results, current activities, and converged with the several individual tip vorticesfuture directions for several aspects of flows on more or less merged into one vortical blob thatrotor blades. induced approximately the correct downwash near

the blade tips. Consequently, the agreement withTwo aspects of our current research should be experimental data in the tip region is quitepointed out. First, the codes are being developed good. However, the accuracy of the solutionto treat hover and forward flight in a unified deteriorated in the inboard region, where themanner, for arbitrary blade motion. Therefore, as induced downwash was too small and the resultingexplained in References (17), (21), and (22), we blade-element lift was too large. Much more workhave chosen to solve the unsteady Euler and thin- remains to be done on this problem, but theselayer Navier-Stokes equations in an inertial frame preliminary results with no wake modeling areof reference, rather than in blade-fixed coordi- encouraging.nates. This results in some increases in CPU timefor hovering cases, where non-time-accurate Chen and McCroskey [22] calculated the flow pastconvergence-acceleration techniques might other- this hovering rotor for MT = o.41, 0.794, andwise be used, but it allows the same general for- 0.877, with the best agreement with the experimen-mulation and code to be used for both hover and tal results occurring at the two lower Mach num-forward flight. bers. The results at MT = 0.877 were in close

agreement with the Euler solution of Agarwal andSecond, as discussed in Section IV, our long-term Deese [241, which was obtained using a simple wakegoal is to include arbitrary rotor-body combina- model. Both Euler solutions produced a strongtions and to calculate the aerodynamic interac- shock wave that was significantly farther rearwardtions between rotating and non-rotating compo- than in the experiment. However, Srinivasan andnents. This has influenced our preliminary choice McCroskey [17] computed this same case using aof grid topologies to insure this capability. Navier-Stokes code and Agarwal's wake model, andAlso, the topology chosen readily lends itself to they found almost perfect agreement with thea straightforward treatment of multiple-blade experimental shock wave position and strength, asrotors and to wake-capturing in hover, shown in Figure (15). It should be mentioned that

the three solutions [17,21,24] were obtained withA. Results for Nonlifting Hover and Forward Flight three different codes on three different grids,

and differences due to these purely numericalIn the absence of lift on the rotor, the vexing factors cannot be discounted. Nevertheless, these

problems of the wake are avoided. Figure (12) are strong-shock conditions that would be expected

from Reference (21) shows two Euler solutions for to produce significant shock-wave/boundary-layera six-bladc! rotor in hover, at transonic tip interaction, and it is our opinion that thesespeeds just below and just above the conditions comparisons substantiate this speculation. Offor the onset of the aeroacoustic phenomenon known course, it remains puzzling that Strawn and

as delocalization [23]. The effects of blade-to- Caradonna [25] achieved almost as good agreementblade thickness interference were studied for two, with the experimental results using a full-

four, and six blades. potential code, neglecting viscous effects

entirely.

pM

Srinivasan and McCroskey [17] also examined sev- Fortunately, other engineering problems have

eral nonrotating configurations that are sometimes spawned research activities that are relevantproposed to simulate rotor blade tips in conven- here; for example, rotor-stator interactions in

tional wind tunnels. In this exercise, the span- turbomachinery and store separations of fixed-wing

wise distribution of circulation of the hovering aircraft. Representative two-dimensional examples

rotor described in the preceding paragraph was of grid topologies and data-transfer strategies

approximately matched in two nonrotating simula- for these two problems [26,27] are indicated

tions: 1) by a linear vd, iation in the spanwise schematically in Figure (17). The patched-grid

Mach number distribution with a constant blade method on the left, in which a single plane sepa-

pitch angle of 4.20, and 2) by a linear spanwise rates the two zones, seems intuitively attractive

twist distribution at a constant Mach number of for many rotorcraft configurations. However, the

0.877. overset-grid method on the right, in which onegrid system sweeps through the interior of

The computations for this strong transonic case another, may allow more flexibility for the grid

are shown in Figure (16). These results show that topologies for the individual components in some

the variable Mach-number simulation is a good cases. The idea of overset grids is also attrac-

representation of the rotating blade in the tip tive for capturing tip vortices that move relative

region. However, the more conventional approxima- to the blade-fixed grid zones, such as for thetion of variable twist at constant Mach number is wakes in forward flight. Both strategies are

not even qualitatively correct anywhere on the being studied at the Ames Research Center and

blade, under these transonic conditions. The elsewhere.

differences inboard are to be expected, since the

flow on the rotating blade is completely subsonic The research of C.L. Chen [21,22) described in

there, but it is rather surprising that the nonro- Section III has been tailored to the patchcd-grid

tating solution is so different in the tip concept, particularly regarding the grid topolo-region. On the other hand, it should be noted gies. This is illustrated in Figure (18). Here

that this overall conclusion is limited to tran- the "outer" cylindrical grid zones have identical

sonic conditions; both types of nonrotating simu- circumferential grid lines at the interface,

lations agreed well with the rotating solution and thereby minimizing the complexities at the moving

with the rotor test data at subsonic tip speeds. boundary between the rotating and nonrotiting

In any case, this investigation was a striking outer zones. "Inner" zones that are more appro-

demonstration of the flexibility and power of CFD priate for the local flow past the actual blades,

to gain physical insight, study novel ideas, and fuselage, wing, etc. can be imbedded within each

examine various possibilities that might be diffi- cylindrical block. For example, a C-mesh topology

cult or even impossible to set up in physiqal for the viscous region on the blade and in the

experiments, near wake is shown. In such cases, the interfacesbetween the inner and outer zones are likely to be

more complex; but as they are not in relativeIV. ROTOR - BODY COMBINATIONS motion, they can be treated by conventional zonal

methods [28].The aerodynamic interactioo between rotating and

nonrotating components is an important distin- The implementation of this overall strategy has

guishing feature of rotorcraft that produces con- not yet been accomplished. The work described in

siderable additional complications for CFD analy- References (21) and (22) is a limited first step;

ses. This is because the inner boundaries of the the Euler equations have been solved in the outer

computational grids of most codes today conform to rotating zone only. However, the inclusion of

and move with the surface of the respective compo- inner, viscous-layer and vortical-wake zones, as

nents, and the flow field around each object is well as nonrotating components, has high prioritycontained within the interior of one or more of in our research plans.these grid zones. The art of transferring numeri-

cal data accurately across grid zone boundaries as

the solution develops is by no means mature for V. LIMITATIONS AND CRITICAL ISSUES

fixed-wing configurations, and it is in itsinfancy for problems with relative motion between Although the growth trends of supercomputer tech-

the various grid zones around the individual com- nology and overall CFD capability are well estab-

ponents. Therefore, much creative work remains to lished, it will be some time before the Euler and

be done in this aspect of CFD for rotorcraft Navier-Stokes methodologies outlined in Sections

applications. III and IV will offer a significant competitive

edge over simpler approaches. As noted in the

Introduction, the two overriding issues today are,

5

first, that the CPU time and memory are excessive FLOPS = no. floating-point arithmeticand, second, that the accuracy of the results is operations per unit timeoften questionable. Major improvements in super-computer hardware and software, numerical grids The efficiency factor, A, is introduced to emphni-and algorithms, turbulence models, and vortical size that the code may not take full advantage of'

wake-capturing capabilities are urgently required, the computer being used. In practice, it is aas briefly discussed below. Other essential cap- function of the programming efficiency, the degreeabilities which are not addressed in this paper of vectorization, the coupling between the gridinclude improved graphical displays, better pre- and the solution algorithm, user experience,and post-processing of the enormous data struc- etc. Ideally, its value should approach unity;tures, and aerodynamic/structural coupling, but especially with the advent of supercomputersFinally, there is an acute shortage of both with novel architecture, it could be much larger.structural-dynamics engineers and technical man-agers who understand CFD. The number of arithmetic operations per grid point

per time step, WGT, is a strong function of theA. Computer Speed and Memory Requirements numerical method; that is, of the flow equations,

the boundary conditions, the solution algorithm,In addition to crucial three-dimensional effects, and the grid. The quantity NC represents theunsteadiness is an important, complicating aspect number of grid points for a finite-differenceof flows past rotor blades. This feature is method, the number of elements for a finite-shared by the fixed-wing aeroelasticity and turbo- element method, or the number of panels for amachinery communities. These groups have helped panel method. Consequently, WGT NG representsto extend the methodologies of quasi-steady aero- the number of arithmetic operations that must bedynamics, generally a few years after they were performed at each iteration or time step, althoughfirst introduced. However, existing time-accurate in some instances with panel methods, N. log NGcodes tend to have stability restrictions that or Nm is a more accurate representation thanrestrict the time steps to values which are much NG.

smaller than necessary for accurate resolution ofthe relevant unsteady physics of the flow. As Ideally for rotorcraft applications, the totaldiscussed in Reference (29), such restrictions number of time steps, NT, would simply be theincrease the CPU time by an order of magnitude or number of time steps per blade revolution multi-more for Euler and Navier-Stokes calculations; and plied by the number of revolutions needed totherefore, they must be overcome before complete determine the aerodynamic characteristics. How-rotor flow fields can be computed on a routine ever, many nonlinear aerodynamics codes have sta-basis. bility or accuracy limits that are determined by a

nondimensional time step, AT = UAt/L. Thus theIt is instructive to examine the factors that maximum permissible value of AT typicallydetermine the CPU time for various CFD approaches, depends upon the complexity of the problem, thewhich can be estimated from the following formula algorithm, the grid, and the desired accuracy.from Reference (29):

Finally, the computing speed, FLOPS. is a functionCPU A . WGT ' NG x NT/FLOPS (1) of the computer clock speed and architecture, the

data management techniques of the code, the memorywhere: A "numerical inefficiency" requirements (in-core or external memory), and the

factor, >1.0 solution algorithm. Thus it is clear that manydifferent factors determine the CPU time, and

WGT : number of floating-point hence the cost, of an aerodynamic calculation.operations per grid point per timestep In Reference (29), a detailed analysis was made of

the solution times that would be required to per-NG = no. grid points form fixed-wing flutter analyses, using a wide

range of contemporary time-accurate methods onNT no. time steps modern supercomputers. This information is at

least qualitatively relevant to rotorcraft appli-(no. ref. lengths/revolution) x cations. Table 1, reproduced from that investiga-(no. rev.)/AT tion, shows a breakdown of the factors in Equa-

tion 1 for a wing of moderate complexity under-AT : nondimn. time step going 3 cycles of oscillatory motion and 25 chord-

lengths of travel per cycle, running on a computer

with a nominal sustained rate of 80 million

6

Table 1. Computational Requirements for Various 3-0Time-Accurate Methods

CPU, Memory,Flow model WGT NG AT minutes million words Notes

Nonlinear panel WGT Nm 2 - 106 0.05 60 2.0 a,cSmall disturbance 100 105 0.06 8 0.6 b,dFull potential 600 105 0.04 23 2.0 d,e

Full potentialand integral B.L. 630 105 0.02 50 2.0 d,e,f

Euler 3000 100 0.01 450 3.0 d,e

Euler and finite

difference B.L. 2000 2 x 105 0.01 600 6.0 d,e,gThin-layer

Navier-Stokes 3600 106 0.005 11,000 30 d,eReynolds-averagedNavier-Stokes 4500 2 o 106 0.004 35,000 60 d,e

Notes: a. A 2b. A 3c. AT for time accuracyd. AT for stability limitationse. WGT includes 100 for grid generationf. 5% increase in WGT for boundary layerg. WGT = 500 in viscous layer, 3000 in inviscid region

floating-point operations per second. Several of A 1.5the additional assumptions are noted in the foot-note to Table 1. The solution-time requirements WGT 4000are compared graphically in Figure (19). Ofcourse, all of these results are very approximate, NG 106

accurate to one significant figure at best.AT 0.025

It should be mentioned that a time step limit ofAT C G 05 was assumed as a rather subjective NT 5000estimate o' what is required to resolve accuratelyunsteady transonic effects on a wing, includingsignificant shock wave motion. Also, the esti- Then Equation 1 yields CPU = 80 hours for amates of the stability limitations on AT are 100-megaflop supercomputer, and approximately

very approximate, and the numbers given are 30 million words of memory would be required forintended more to give a sense of the relative this problem. At the present time, everyone hasvalues of the various methods, than the absolute difficulty achieving even this level of perform-values. The important point is that, the more ance on simpler problems. These results illus-sophisticated the method, the more severe is the trate the magnitude of the challenge. Only thestability restriction on AT for highly nonlinear largest machines, such as the Cray 2, have ade-problems. quate main memory, and its speed is insufficient

for more than a few showcase solutions. It seems

Estimates for rotorcraft applications are more clear that the megaflop rates of even the nextdifficult to determine. For two revolutions in generation of supercomputers will be a limitingforward flight of a two-blade rotor with blades of factor for practical CFD computations of helicop-aspect ratio 10 above a simple fuselage, and for a ter aerodynamics.typical implicit thin-layer Navier-Stokes codewith algebraic eddy-viscosity modeling of turbu- B. Improvements in Grid Generationlence, the following values might be (optimis-tically) appropriate: An essential step in solving rotorcraft problems

using computational aerodynamics is the generation

7

of a suitable grid. Although a significant reduced by a factor of two or more by dynamic g'.dadvantage of some panel methods and of the tran- adaption. However, this will require a signif:-

sonic small-disturbance method is that the appro- cant and specialized effort.priate boundary conditions can be applied on non-

aligned grids, most of the more sophisticated C. Turbulence Models

methods rely on body-conforming grids. The zonalmodeling, or multi-block, concept appears espe- The simulation of the dynamics of turbulencecially attractive for complex configurations. remains the foremost challenge in fluid mechanicsThis is one of the most rapidly growing areas of today, and turbulence modeling is nrobab!y the

CFD, and there have been several meetings in weakest link in the chain of computational aerody-recent years devoted exclusively to grid genera- namics technology. For conventional helicopter.,tion. The recent surveys by Thompson [28,30) are retreating-blade stall is probably the practicelparticularly noteworthy, and another major inter- aerodynamic problem most impacted by turbulencenational conference on grid generation will be 'odeling, while for tilt-rotor configurations,held in Miami in December 1988. accurate predictions of the separated flow associ-

ated with rotor-wing interactions in hover areFor computational efficiency, algebraic and hyper- next to impossible today.bolic schemes seem better suited to the classes ofunsteady problems that require regenerating the Because of the limitations of the computationalgrid at each time step. High efficiency is neces- power available in the foreseeable future, turbo-sary to exploit the concept of adapting the grid lence modeling throughout the aeronautics commun-to some feature of the solution, such as cluster- ity has taken the approach of single-point closureing grid points in regions of Large gradients, so of the Reynolds-averaged Navier-Stokes equations,as to obtain the maximum accuracy with the least and no single turbulence model exists that can benumber of grid points. As noted earlier in con- applied to a wide variety of flows. An overviewnection with Figure (4), dynamic solution-adaptive of the range of possible turbulence models, rang-grids have been successfully used in two dimen- ing from essentially no modeling at all, to thesions, and comparable capability will be essential hypothetical full simulaton of turbulence, isfor computing three-dimensional vortical wakes given in Table 2. As no universal turbulenceaccurately. We believe that the grid pointrequirements, and hence the CPU times, can be

Table 2. Summary of Turbulence Models

Physical NumericalModel Generality Compatibility Remarks

Viscous wedge Very low Very high Shock-B.L. interactionIntegral B.L. Low High Very good when highly tunedEddy viscosity

Zero equation Low High Needs more tuning

2-equation Medium Low to high AWGT a 20%, AT ?Reynolds stress equations High Low 3-D separation?Large eddy simulation Very high Low (?) Guidelines for above modelsComplete simulation Complete nth generation supercomputers

Are the more complex models any better?

8

model exists, most contemporary researchers are simplicity and generality. Some of the mndels in

focusing their attention on creating a catalog of this category lead to stiff equations, arid this

models based on fundamental building-block experi- raises again the problem of restrictive values

ments. Most of these models are being carefully of AT in Equation 1.

tested computationally to determine their capabil-

ities and limitations. From this brief overview, it is clear that turhij-

lence modeling will remain a primary pacing item

As shown in Table 1 and Figure (19), enormous in computational aerodynamics over the next dec-

comruter resources are required to solve time- ade, for both fixed-wing and rotorcraft

dependent problems with finite-difference simula- applications.tions of the Reynolds-averaged Navier-Stokes equa-tions, even with simDIc turbulence models. Fur- D. Modeling Vortical Flowsthermore, even those solutions that have beenpublished for steaoy flows have used grids whose Whereas the treatment of shock waves in transonic

fine spacing is limited to the single direction flow was a major focal point for computational

nearly normal to the body, and hence fall within aerodynamics in the 1970's, compressible flow

the spirit of the thin-layer approximation. This fields with embedded regions of concentrated vor-resulting computational process qualitatively ticity are gaining prominence today. Again, the

simulates separated flows and flows with large- key role is being played by the fixed-wing commun-

scale unsteady behaviors, but the accuracy of such ity. Some interest comes fron adverse effects of

simulations is still controversial, trailing wing-tip vortices, but the vortical flowsshed from sharp leading edges of tactical aircraft

At the Ames Research Center we are well aware of at high angles of attack are the principal driver.

their limitations and we are always looking for

something better, but we have only used the zero- The helicoidal vortical wakes of rotor blades have

equation eddy-viscosity model of Baldwin and Lomax a much larger influence in hover and at low for-

[8] and the thin-layer approximation "'or rotor- ward speeds than do the trailing vortices of

craft problems up to now. Holst [10] and Kaynak fixed-wi.g aircraft. These wakes are complex in

and Flores [20] showed a few examples in which geometry and structure, and treating them accu-

improved turbulence models had some influence on rately and efficiently is one of the greatestthe shock wave location on airfoils and wings, but challenge- in helicopter aerodynamics today.our transonic airfoil studies [6] did not indicate Possible special treatments include 1) couplinga serious deficiency in the Baldwin-Lomax model some form of wake modeling with the finite-for rotorcraft applications below stall. The main difference computations, as in Reference (5),concern that we have uncovered so far is in the 2) three-dimensional extensions of the prescribed-details of the tip separation and early stages of vortex or split-potential methods discussed intip-vortex formation. As discussed in Section II Section I, as in References (25), (31), and (32),in connection with Figure (10), we not have been 3) adapting a refined computational grid to theable to reproduce quantitatively the measured concentrated vortical regions as they are beinglocal suction peaks outboard of Y/B = 0.96. computed, 4) developing new vortex-preserving

schemes that reduce the inherent numerical dissi-In the larger arena of applied aerodynamic compu- pation in current codes which rely on vortex cap-tations for fixed-wing aircraft, however, more turing, as in Reference (13), or 5) combinationssophisticated models are beginning to be used that of these.are "tuned" in conjunction with the numericalprocedure for a specific class of flow problems. The flow fields of rotors are inherently vorticalAs a result, validations by means of experimental and three-dimensional, and three-dimensional com-2omparisons are mandatory, and confidence in the putations are inherently expensive. Furthermore,

absolute values of the numerical predictions the results of the numerical simulations will

remains low for flows with significant separation, generally be no better than the predictions of the

including stall, of course. vortical wake structure. Therefore, it is

extremely important to establish what minimumIn principle, the more general models in Table 2 level of complexity in the governing equations

should cover a wider range of flows with less will suffice and to determine the most expeditious

"tuning," but helicopter engineers will probably way either to model or to capture vortices within

remain suspicious of the idea that "bigger is the computational domains. This topic is one of

better." Nevertheless, in some rotorcraft prob- the most fruitful and opportune areas for creative

lems which involve three-dimensional flow separa- research, and it seems destined to be an extremely

tion, the two-equation eddy-viscosity models may active one for the next few years.

turn out to be the best compromise between

9

VI. SUMMARY AND CONCLUSIONS 2. Harris, F.D., "Rotary Wing Aerodynamics -

Historical Perspective and Important Issues,"

The rotorcraft industry appears to be entering a American Helicopter Society Specialists' Meetirg

new era in which computational fluid dynamics will on Aerodynamics and Aeroacoustics, Ft. Worth,play an increasingly important role in the design Texas, Feb. 1987.and analysis of advanced aircraft. A major effortis unoer way at the Ames Research Center to hasten 3. McCroskey, W.J., and Baeder, J.D., "Somethis process and to capitalize on the arrival of Recent Advances in Computational Aerodynamics for,future generations of supercomputers. Helicopter Applications," International Symposium

on Computational Fluid Dynamics, Tokyo, Japan,

Airfoil codes are now available that can be used Sept. 1985; also NASA TM 86777, Oct. 1985.

to complement wind tunnel testing. The accuracy

of the numerical simulations is comparable to that 4. Johnson, W., "Recent Developments in Rotary-

of airfoil data, but the entire flow field struc- Wing Aerodynamic Theory, "AIAA Journal, Vol. 24,

ture can now be readily examined. The cost for (8), Aug. 1986.

the calculation of each condition is probably

greater than that of an individual test point, but 5. Caradonna, F.X., and Tung, C., "A Review of

the geometry of the airfoil can be changed much Current Finite-Difference Codes," American

more easily in the computer than in the wind Helicopter Society 42nd Annual Forum, Washington,

tunnel. D.C., June 1986.

The major focus at Present is on obtaining more 6. McCroskey, W.J., Baeder, J.D., and Bridgeman,

accurate and less costly three-dimensional solu- J.O., "Calculation of Helicopter Airfoil

tions. Although impressive progress has been Characteristics for High Tip-Speed Applicitions,"made, a finite-difference simulation of the com- Journal of the American Helicopter Society,plete flow field about a helicopter in forward Vol. 31, (2), Apr. 1986.

flight is not currently feasible. The principal

CFD limitations are the computer speeds and memory 7. Pulliam, T.H. and Steger, J.L., "Recent

capacities, algorithm and solution methods, grid Improvements in Efficiency, Accuracy, and

generation, turbulence models, and vortex model- Convergence for Implicit Approximate Factorization

ing. Other important limitations are the inade- Algorithms," AIAA Paper 85-0360, Re o, Nevada,

quate structural and aerodynamic coupling, and a Jan. 1985.

shortage of engineers and scientists who are

skilled in both CFD and helicopter aerodynamics 8. Baldwin, B.S., and Lomax, H., "Thin Layer

and dynamics. Nevertheless, the potential bene- Approximation and Algebraic Model for Separated

fits of CFD to the rotorcraft industry are even Turbulent Flows," AIAA Paper 78-257, Huntsville,

larger than tho that have already accrued to the Ala., Jan. 1978.

fixed-wing industry, and the ever-increasing

applications of this new tool must continue to be 9. Hoist, T.L., "Viscous Transonic Airfoilencouraged. Workshop - Compendium of Results," AIAA Paper 87-

1460, Honolulu, Hawaii, June 1987.

VII. ACKNOWLEDGEMENTS 10. McCroskey, W.J., and Goorjian, P.M.,

"Interactions of Airfoils with Gusts and

This paper draws heavily from the research accom- Concentrated Vortices in Unsteady Transonic Flow,"

plishments of my coworkers, J.D. Baeder, C.L. AIAA Paper 83-1691, Danvers, Mass., July 1983.

Chen, E.P. Duque, and G.R. Srinivasan, and their

ideas and contributions are gratefully acknowl- 11. Srinivasan, G.R., McCroskey, W.J., and

edged. Also, the stimulating discussions and Baeder, J.D., "Aerodynamics of Two-Dimensionalsuggestions of M.L. Green, T.L. Holst, J.L. Blade-Vortex Interaction," AIAA Journal, Vol. 24Steger, and R.C. Strawn are deeply appreciated. (10), Oct. 1986.

12. Baeder, J.D., "Computation of Non-LinearVIII. R ERENCES Acoustics in Two-Dimensional Blade-Vortex

Interactions," 13th European Rotorcraft Forum,1. Johnson, W., Helicopter Theory, Princeton Arles, France, Sept. 1987.Univeriity Press, NJ, 1980.

10

13. Rai, M.M., "Navier-Stokes Simulations of 23. Schmitz, F.H., and Yu, Y.H., "Transonic Rotor

Blade-Vortex Interaction Using High-Order Accurate Noise - Theoretical and Experimental Comparison,"

Upwind Schemes," AIAA Paper 87-0543, Reno, Nev., Vertica, Vol. 5 (1), Jan. 1981.

Jan. 1987.24. Agarwal, R.K., and Deese, J.E., "Euler

14. Srinivasan, G.R., and McCroskey, W.J., Calculations for Flowfield of a Helicopter Rotor

"Numerical Simulations of Airfoil-Vortex in Hover," Journal of Aircraft, Vol. 24 (4), Apr.

Interactions," Vertica, Vol. 11 (1/2), Jan. 1987. 1987.

15. Baeder, J.D., Srinivasan, G.R., and 25. Strawn, R.C., and Caradonna, F.X.,

McCroskey, W.J., "Acoustic Propagation using "Conservative Full Potential Model for Unsteady

Computational Fluid Dynamics," American Transonic Rotor Flows," AIAA Journal, Vol. 25 (2),

Helicopter Society 42nd Annual Forum, Washington, Feb. 1987.

D.C., June 1986.26. Rai, M.M., "Unsteady Three-Dimensional

16. Srinivasan, G.R., McCroskey, W.J., Baeder, Navier-Stokes Simulations of Turbine Rotor-Stator

J.D., and Edwards, T.A., "Numerical Simulation of Interaction," AIAA Paper 87-2058, San Diego, Cal.,

Tip Vortices of Wings in Subsonic and Transonic June 1987.

Flows," AIAA Paper 86-1095, Atlanta, Ga., May

1986. 27. Dougherty, F.C., Benek, J.A., and Steger,

J.L., "On Applications of Chimera Schemes to Store

17. Srinivasan, C.R., and McCroskey, W.J., Separation," NASA TM 88193, Oct. 1985.

"Navier-Stokes Calculations of Hovering Rotor

Flowfields," AIAA Paper 87-2629, Monterey, Cal., 28. Thompson, J.F., "Grid Generation Techniques

Aug. 1987. in Computational Fluid Dynamics," AIAA Journal,Vol. 22 (11), Nov. 1984.

18. Mansour, N.N., "Numerical Simulation of the

Tip Vortex off a Low-Aspect Ratio Wing at 29. McCroskey, W.J., Kutler, P., and Bridgeman,

Transonic Speed," AIAA Journal, Vol. 23 (8), Aug. J.0., "Status and Prospects for Computational

1985. Aerodynamics for Unsteady Transonic ViscousFlows," Paper No. 9, AGARD CP-374, Toulouse,

19. Kaynak, U., Holst, T., Cantwell, B.J., and France, Sept. 1984.

Sorenson, R.L., "Numerical Simulation of TransonicSeparated Flows over Low-Aspect Ratio Wings," 30. Thompson, J.F., "Review of the State of the

Journal of Aircraft, Vol. 24 (8), Aug. 1987. Art of Adaptive Grid Generation," AIAA

Paper 84-1606, Snowmass, Col., June 1984.

20. Kaynak, U., and Flores, J., "Advances in the

Computation of Transonic Separated Flows over 31. Steinhoff, J.,"A Vortex Embedding Method for

Finite Wings," AIAA Paper 87-1195, Honolulu, Free Wake Analysis of Helicopter Rotor Blades in

Hawaii, June 1987. Hover," 13th European Rotorcraft Forum, Arles,

France, Sept. 1987.

21. Chen, C.L., McCroskey, W.J., and Ying, S.X.,

"Euler Solution of Multiblade Rotor Flow," 13th 32. Roberts, T.W., and Murman, E.M.,"Euler

European Rotorcraft Forum, Arles, France, Sept. Solutions for the Flow Around a Hovering

1987. Helicopter Rotor," AIAA Paper 86-1784CP,

San Diego, Cal., June 1986.

22. Chen, C.L., and McCroskey, W.J., "NumericalSimulation of Helicopter Multi-Bladed Rotor Flow,"

AIAA Paper 88-0046, Reno, Nev., Jan. 1988.

11

2-D M.3-D 3-D 3O W D2-I. (NONROTATING) (ROTATING) FRIGRT

jTEADY

UNSTEADYORR

Figure 1. Development of rotor blade aerodynamics from simpler cases

1.0 M LIFT DRAGa 0.50 0.6.0-M

.8 00.8 0.6.058 0 0.6

010.8

.6 .04

CL CD

.4

.2

0-2 4 6 8 10 0 2 4 6 8 10

a, dog a, dog

0 INVISCID.1-oIVSD.30- 0 NAVIER.STOKES 0 INVIESCD E

- EPEIMNT A EXPERIMENTS 0

dCL/da -CDO 0

.04-

00 i a ,,

.2 .4 .6 .8 1.0 .2 .4 .6 .8 1.0

Figure 2. Calculated NACA 0012 airfoil characteristics, Re 6 -106

12

-1.2 M -0.6 M -0.88 M= 1,10

UPPER

1. GL--OWER0 1.0 0 1.0 0 1.0

xIC xIC x/C0

-. 02

CM -04 .F0 0 NAVIER-STOKES,

-. 6- 0 NAVIER-STOKES,EXPERIMENTAL Re

*EXPERIMENT (x-.08 . II I I a lm p

.2 .4 .6 .8 1.0M_

Figure 3. Pitching moment vs. Mach number for the VR-8 airfoil at CL 0

13

PRESSURE DISTRIBUTION

-1.2 x v0.2 xV,=0.5 XV 1.0

,C P ,C ' I_ ;N

-- UPPER

-LOWER

1.2 (a) (b) (C) (d)

ADAPTIVE GRID.6- x0 x 02x 0.5 x =1.0

y0

(a) (b-.6 C()C) (d)-2 x1.0 -. 2 1.0 -.2 1.0 -. 2 1.0

MACH CONTOURS

0 Vxv 0.5 -v x1.0

I 0

- 1 (a) (b) (C)___ (d) _ _

-. 5 1.5 .8 1.2 -.5 1.5 -. 2 1.8

Figure 4. Airfoil-vortex interactions for NACA 0012 airfoil at M =0.80 (a) instantaneouspressure distributions, (b) solution-adaptive grid (c) instantaneous pressurecontours

xv 2.0 x.4 .00

x8 00

Figure 5. Disturbance-pressure contours for an airfoil-vortex interaction

- NAVIER-STOKES 4M_ -......EULER 0-

LINEARIZED TRANSONIC SMALL DISTURBANCE 7 --- TRANSONIC SMALL DISTURBANCE0 R

30' ABOVE

.10 2 6 10 30' BELOW

.1 26 10

.056

-- -_ -- 44i

-. 1 1 L I I I I I I I9 11 13 5 17 19 21 9 11 13 15 17 19 21

TIME, 7 -xv + 10 TIME,? r Xv + 10

Figure 6. Time-histories of scaled acoustic disturbances by various computational methods

15

y

(b) WING CB/C 0.83

(a) NACA 0015RECTANGIILAR WINGB/C =2.5

(c) ONERA WING (d) MODIFIEDB/C * 5.0 ONERA WING

B/C - 5.0

Figure 7. Planform and surface grids of four wings for tip vortex simulations

16

Figure 8. Planform and SLr'face grid for the BERP blade tip

Figure 9. Streamlines and tip vortex of' the ONERA swept-tip blade at M 0.85 and a 50

17

---- CALCULATIONS SQUARE

A EXPERIMENTS TIP

S=09ROUND TIP-CALCULATIONS

3.0

24

1.8 Y/B= 0.970

1.2---Cp .6 Y/B 3.82

0 - FI~f

-.6 I '. _ I I ROUND TIP-EXPERIMENT

0 .2 .4 .6 .8 1.0x

Figure 10. Surface pressure distributions and streamline patterns on an NACA 0015 wing atM = 0.17 and a = 120

A A B B C C

PLAN VIEW

SECTION AA SECTION BB SECTION CCSQUARE TIP ROUNDED TIP BEVELLED TIP

WITH H-H GRID WITH 0-0 GRID WITH H-H GRID

Figure 11. Schematic of tip caps and grid topologies for tip-vortex studies

18

Figure 12. Mach-number contours on a non] ifting rotor. (a) MT 0.85 (b) MT =0.90

-1.0ll 3' 0 =120o

.5 00

0

20

CP 0 0 0 0

.5

1.0

-1.0-0 o =60o 0 ~ /150-

-.5

1.0

-.5

p 0 0CP 0

~0 go.5 -EULER CALCULATIONSI ~ EXPERIMENTAL DATA

1.0_______ 1_ (CARADONNA et al.). 204. -. 4 -. 6 -.8 .4 .2 0 -2 -.4 -.6 -.8

X!C XIC

Figure 13. Surface pressure distributions on a two-blade nonlifting rotor in forward flight;MT = 0.80, p 0.20, AR =7

19

-1.5 WITH..... W/o

-1.0 'EXP.

=/ 0.80 Y/8 0.89 Y/R 0.96

C0

.5

1.00 .2 .4 .6 .8 1.0 0 .2 .4 .6 .8 1.0 0 .2 .4 .6 .8 1.0

x/C x/C xC

Figure 14. Streamlines and pressure distributions on a two-blade rotor in hover; Euler

solution, MT 0.794, 8 80, AR =6

NA VIE R-STOK ESSV EXPERIMENTS

1.2 - ylr =0.80 yR09

.8-

.4-

-

-.8-(b) d

0 .2 .4 .6 .8 1.0 0 .2 .4 .6 .8 1.0

Figure 15. Surface streamlines and pressure distributions on a two-blade rotor in hover;Navier-Stokes solution, MT =0.877, e = 80, AR = 6

20

M(tlp) =0.877 Mwy M(root) =0.146

-RTATING BLADEx

M ,I(tip) =0.87 MAY) M,(root) =0.146

1.2

.8 . -"FIXED BLADE-VARIABLE MACH NUMBER

j0. Jf(tip) =4.20 M. 0.877 0(root) =0.70

0 .2 .4 X.6 .8 1.0 FIXED BLADE-VARIABLE PITCH (TWISTED)

Figure 16. Rotating and nonrotating simulations of a rotor in hover; Navier-Stokes solution,HT1 = 0.877, 6 8o, AR = 6

PATCHED GRIDS OVERSET GRIDSROTOR - STATOR INTERACTIONS WING -STORE SEPARATION

Figure 17. Example of grid interfaces in relative motion

21

.0V

ROTATING OUTER GRID

ROTAT1N.x INNER GRID ROTATING SLADE

Figure 18. Representative grid topology for rotor-body combinations

CPU MINUTES HIGH aTRANSONIC

104 week

103 day ?

102

hour -' TRANSONIC0 CRUISE

10 13J, heI~

+ cc I

1minute-.' _j Z Zz n cc4w _ j L-

cc 2

<eon -' - - > SUBSONIC__ w i.- CRUISE

Figure 19. Estimated solution times for an oscillating wing using different CFD methods

22

NASA Report Documentation PageI.kR rt No. 2. Government Accession No. 3. Recipient's Catalog No.NASA TM-100066US4AVSCOM TR 88-A-001 ,

4. Title and Subtitle 5. Report Date

Some Rotorcraft Applications of Computational March 1988Fluid Dynamics 6. Performing Organization Code

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

W. J. McCroskey A-88094

10. Work Unit No.

9. Performing Organization Name and Addrs 992-21-01Ames Research Center and Aeroflightdynamics 11. Contract or Grant No.Directorate, U.S. Army Aviation Research andand Technology Activity, Ames Research CenterMoffett Field, CA 94035-1099 13. Type of Report and Period Covered

12. Sponsoring Agency Name and Address Technical Memorandum

National Aeronautics and Space AdministrationWashington, DC 20546-0001 and U.S. Army Aviation 14. SponsoringAgencyCodeSystems Connand, St. Louis, MO 63120-1798

15. Supplementary Notes

Point of Contact: W. J. McCroskey, Ames Research Center, MS 258-1Moffett Field, CA 94035 (415) 694-6428 or FTS 464-6428

Paper presented at the Second International Conference on Basic Rotorcraft Researchin College Park, Maryland, in February 1988.

16. Abstract

The growing application of computational aerodynamics to nonlinear rotorcraftproblems is outlined, with particular emphasis on the development of new methodsbased on the Euler and thin-layer Navier-Stokes equations. Rotor airfoil character-istics can now be calculated accurately over a wide range of transonic flow condi-tions. However, unsteady three-dimensional viscous codes remain in the researchstage, and a numerical simulation of the complete flow field about a helicopter inforward flight is not currently feasible. Nevertheless, impressive progress isbeing made in preparation for future supercomputers that will enable meaningfulcalculations to be made for arbitrary rotorcraft configurations.

17. Key Words (Suggested by Authors)) 18. Distribution Statement

Rotorcraft aerodynamics Unclassified-Unl imitedNavier-Stokes applications

Subject Category - 02

19. Security Clasi. ('of this report) 20. Security Claesif. (of this page) 21. No. of pages 22. Price

Unclassified Unclassif'ied 24 A02

NASA FORM 1i11 OCT U6 For sale by the National Technical Information Service, Springfield, Virginia 22161r~ 0NMZ&"

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