ADVANCES IN ROTORCRAFT SIMULATIONS WITH

UNSTRUCTURED CFD

Jennifer N. Abras∗ C. Eric Lynch† Marilyn J. Smith‡

Georgia Institute of TechnologyAtlanta, Georgia 30332-0150

Abstract

Advances have been made in the development ofunstructured solver methods suitable for fixed winganalyses, as well as rotary-wing applications, includ-ing interaction aerodynamics. This paper demon-strates the ability of an unstructured overset solver,FUN3D, to resolve the viscous compressible equationsof motion for rotor-fuselage interactions and rotor-alone configurations. The solver is capable of model-ing fully-articulated rotors (prior work was limited torotation and flapping) and CFD-CSD loosely-coupledsolutions including trim, using overset approaches.Initial results with the UH60A rotor indicate thatthe unstructured solver provides similar loading toits structured solver counterparts. Additional devel-opment of efficient domain connectivity interface rou-tines are warranted to provide the ability to performtightly-coupled rotor simulations.

∗PhD Candidate and Graduate Research Assistant,School of Aerospace Engineering. Student Member, AHS.E-mail: gtg503s@mail.gatech.edu

†PhD Candidate and Graduate Research Assistant,School of Aerospace Engineering. Student Member, AHS.E-mail: gte258v@mail.gatech.edu

‡Associate Professor, Member, AHS. E-mail: mari-lyn.smith@ae.gatech.edu

Presented at the American Helicopter Society 63rdAnnual Forum, Virginia Beach, VA, May 1-3, 2007.

c©2007 by Jennifer N. Abras, C. Eric Lynch, andMarilyn J. Smith.

Nomenclature

a axis of rotationA rotor disk areac center of rotationCT thrust coefficient, CT = T

(0.5ρ∞AΩ2R2)

Cp pressure coefficient, Cp = p−p∞(0.5ρ∞V 2)

Mx roll moment, ft-lbsMy pitch moment , ft-lbsMz yaw moment , ft-lbsr radial coordinateR rotor blade radiusT rotor thrustu, v, w velocity in the x, y, z Cartesian directions,

respectivelyV velocity vector, (u, v, w)T

x, y, z Cartesian components in the stream, sideand normal directions, respectively

X, Y, Z Cartesian components in the stream,side and normal directions, respectively,nondimensionalized by reference length, L

Greek

α angle of attackβ blade flap angle, β = β0 + β1ssinψ +

β1ccosψδ lead–lag angleρ fluid densityψ blade azimuth angleµ advance ratio, µ = V∞

ΩRω nondimensional vorticityΩ rotor rotational velocityσ solidityθ blade pitch angle, θ = θ0 + θtw

rR

+θ1ssinψ + θ1ccosψ

Subscripts

s shaftT tip0 mean or root1s 1st cyclic sine coefficient1c 1st cyclic cosine coefficient∞ free stream

Introduction

Accurate, yet efficient prediction of rotary-wing air-loads has been a topic of interest for the past twentyto thirty years within the rotorcraft community. Therotor flow field is a complex interaction of unsteadyviscous-dominated subsonic and transonic aerody-namics, that is further complicated via interactionswith the flexible rotor blade. The wake system thatdevelops from the lifting blade shed wake can remainin the near-field of the rotor and fuselage, introducingadditional unsteady loading. Thus an accurate pre-diction of the airloads on a rotary-wing vehicle relieson the accurate prediction of the rotor structural dy-namics, wake geometry, and unsteady aerodynamics,including vortex-surface interactions.

This dichotomy has yielded two lines of aerody-namics research in an attempt to resolve accuracyand computational expense. A detailed discussion ofthe history of the development of airloads numericalmethods can be found in Refs. 1 and 2; a short syn-opsis of the state of the art is presented here for thereader.

The focus of practical computations for many yearshas been on the development of comprehensive codescharacterized by the finite-element structural meth-ods combined with efficient, low-fidelity aerodynam-ics and trim models. The aerodynamic models forthese methods are typically chosen from lifting-line,dynamic inflow, and prescribed or free wake sim-ulation techniques. Among the most popular ofthese codes are UMARC (Ref. 3), CAMRAD II(Ref. 4), DYMORE (Ref. 5), and HOST (Ref. 6).Kunz (Ref. 2) has presented a detailed discussion ofthe current capabilities of these comprehensive codes,with the exception of the HOST code.

As computational hardware has matured with af-fordable options such as highly-parallelized Linuxclusters, the viability of computational fluid dynam-ics (CFD) methods to provide detailed airloads anal-ysis has become a realistic option in production envi-ronments. Applications of CFD to rotorcraft have,in the past, yielded airloads that were inadequatefor engineering utilization due to the lack of accu-rate aeroelastic blade response, poor wake resolution,

and the inability to model complex configurations.These deficiencies have been addressed via a numberof improvements. First, the coupling of CFD withcomputational structural dynamics (CSD) codes nowpermits the modeling of the articulated rotor withelastic response. This is not a new idea. As early asthe 1980s, full-potential aerodynamic methods havebeen coupled with comprehensive codes (Ref. 7), withsome success, but continuing problems resolving thepitching moments have limited the usefulness of full-potential methods. In the early 1990s, Smith (Ref. 8)coupled an Euler Navier-Stokes method with the non-linear beam model of Hodges and Dowell (Ref. 9), butgrid resolution due to computational memory limita-tions was still a concern.

More recently, using the impetus of the UH60Aairloads workshop, CFD-CSD coupling has en-joyed a resurgence, this time with much betterresults due to the improvement in computa-tional power. Using a loosely-coupled approachfor level flight, a number of CFD methods havebeen successfully coupled with comprehensivecodes, such as CAMRAD-OVERFLOW (Ref. 10),DYMORE-OVERFLOW (Ref. 11), RCAS-OVERFLOW (Ref. 12), UMARC-TURNS (Ref. 13),and HOST-elsA (Ref. 14).

These CFD solvers typically resolve the Reynolds-Averaged Navier Stokes (RANS) equations, and areformulated using three distinct grid-topologies. MostRANS codes utilize a structured scheme, since thenatural ordering of the nodes reduces the requiredmemory and solution time. However, creating astructured grid can take weeks for very complex con-figurations. Chimera and/or overset grids partiallyalleviate this problem, and their success in resolv-ing complex rotorcraft is well documented (for ex-ample, Refs. 10 and 14). Initial research to applyCartesian-based structured grid methods is also un-derway (Ref. 15), although recent research has fo-cused on utilizing these methods with adaptive meshrefinement (AMR) capabilities for wake refinement,coupled with more mature solvers for the near-fieldsimulations. Unstructured grid techniques offer theadvantage of reduced grid generation time, along withthe ability to make rapid configuration changes. Withthe recent advances in parallel computing, the in-creased overhead per node required by unstructuredmethods is no longer as important an issue, and theadditional run time per node can be partially com-pensated by reduced grid density in areas far fromthe vehicle. Much of the focus with unstructuredmethodologies has been for the resolution of complexfuselage geometries and rotor-fuselage interactions, asillustrated in Refs. 15, 16, 17, 18 and 19 .

Rotor-fuselage interaction computational fluid dy-namics (CFD) methods have focused primarily lower-fidelity rotor modeling, as the emphasis has been onpredicting the fuselage loading. This lower-fidelitymodeling usually takes the form of a rotor actuatordisk, where discrete sources are inserted into the gridwith magnitudes that include the influence of the ro-tor, obtained typically from momentum or blade el-ement theory or a comprehensive code. New imple-mentations include a closed feedback loop that per-mit interaction between the rotor and fuselage. Thismodeling has been shown to be accurate when steadyairloads are required for fuselage design and analysis(e.g, Refs. 16, 20, and 21), and unsteady actuatorblades appear to hold promise for unsteady fuselageloading (Refs. 16, 22).

These simulations appear to be sufficient if the em-phasis is on fuselage loading. However, the mostphysically correct analysis requires that all surfacesbe accurately modeled via the time-accurate Navier-Stokes equations. Full RANS rotor modeling addsa level of additional complexity since each rotor re-quires a rotating frame and the fuselage requires astationary frame, which must co-exist within the sim-ulation. Two methodologies have emerged for mixedframe problems using unstructured methods: oversetand/or chimera grids, and sliding boundaries. Parkand Kwon (Refs. 23, 24) have demonstrated via theEuler equations, the solution of a rotating main rotorcylindrical grid that fits within a background rectan-gular grid that contains the fuselage and remainderof the control volume. The two grids communicatevia a sliding boundary that forms the interface be-tween the two grids. The primary drawback to thisapproach is the restriction imposed on the type ofconfigurations that can be modeled. Multiple over-lapping rotors, such as compound rotors, cannot bemodeled. The second approach utilizes a combinationof overset or chimera grids to generate smaller gridsaround each rotor blade, which then rotate througha background Cartesian or unstructured grid, as il-lustrated in Fig.1 from Ref. 16. This overset ap-proach, utilizing structured grids has been used tocorrectly capture the general experimental trends onseveral configurations by Hariharan (Ref. 21), Pots-dam et al (Ref. 10) and Duque (Ref. 25). Recentpublications by OBrien and Smith (Ref. 22) andO’Brien (Ref. 16) have demonstrated this technologyutilizing an unstructured method for the solution ofthe compressible RANS equations to resolve fuselageloading.

This paper extends these unstructured demonstra-tions of O’Brien and Smith to include overset rotorswith full rigid body motion and introduces CFD-CSD

Figure 1: Robin rotor–fuselage unstructured oversetgrid (Ref. 16).

coupling concepts for unstructured grids. Emphasishere includes not only the fuselage loading reportedearlier, but also explores the ability of the unstruc-tured methods to correctly capture blade loading viacorrelation with experimental data and structuredcomputational results (OVERFLOW).

Methodology

This section first provides a short review of the base-line computational aerodynamic and structural dy-namics methodologies, as well as the libraries thatare utilized to effect the overset coupling.

Unstructured Methodology: FUN3D

The unstructured methodology that is utilized andextended within this effort is the FUN3D code de-veloped at the NASA Langley Research Center (Ref.26, 27, and 28). FUN3D can resolve either the com-pressible or incompressible RANS equations on un-structured tetrahedral meshes. The incompressibleRANS equations are simulated via Chorin’s artifi-cial compressibility method (Ref. 29). A first-orderbackward Euler scheme with local time stepping hasbeen applied to steady-state applications, while asecond-order backward differentiation formula (BDF)has been utilized for time-accurate simulations. Apoint-implicit relaxation scheme resolves the result-ing linearized system of equations. FUN3D solves theRANS equations on the non-overlapping control vol-

umes surrounding each cell vertex or node where theflow variables are stored. Inviscid fluxes on the cellfaces are computed via Roes flux-difference-splittingscheme (Ref. 30), while viscous fluxes are computedwith a finite volume formulation to obtain an equiv-alent central-difference approximation.

The FUN3D methodology was originally developedfor fixed-wing applications. It has been extendedto evaluate rotary-wing applications of interest byO’Brien and Smith (Refs. 16, 15, 20, 22). It hasbeen shown by these researchers that FUN3D’s in-compressible formulation is not only robust for low-speed flight regimes, but results comparable to struc-tured methods are obtained when the grids are lo-cally comparable on the surface and boundary region.During these studies on rotor-fuselage interactions,an overset formulation of FUN3D was developed forcomparison of lower-fidelity rotor models.

Overset Rotor Blade Model

Overset grid modeling in FUN3D is achieved usingthe Donor Interpolation Receptor Transaction Li-brary (DiRTlib) (Ref. 31) library and Structured,Unstructured, and Generalized overset Grid Assem-bleR (SUGGAR) (Ref. 32) code, developed at ARLby Dr. Ralph Noack. DiRTlib provides a libraryof interface function that enable the flow solver per-form overset computations without major modifica-tions to the solver. DiRTlib’s primary function isto interpolate the data at the fringes of the compo-nent meshes using the domain connectivity informa-tion (DCI) generated by the grid assembly program,SUGGAR. SUGGAR generates a single compositegrid from the individual grids by determining thenodes in each domain (grid) that need to be blanked,and it identifies the locations where flow informationneeds to be interpolated. These interpolation nodelocations are stored in data connectivity interpola-tion (DCI) files. As SUGGAR is a stand-alone code,interactions between SUGGAR and the solver can beproblematic. Prior to this work, the rigid rotor blademotions for each test case were known prior to therun, and the motion was simulated by a reduced setof rigid blade motion equations (flap without bladeoffsets) to the FUN3D solver as required. Prior toeach FUN3D run, the DCI files for the known timeincrement for each iteration were pre-computed andstored in the run directory. This process is adequate(though not optimum) if only a reduced set of rigidblade motions is needed.

Nonlinear Elastic Multibody Dynam-

ics: DYMORE

In order to facilitate the CFD-CSD coupling thatis described later in this work, a CSD methodol-ogy needed to be selected. The code selected forthis demonstration is the DYMORE code, developedat Georgia Tech (Ref. 5). DYMORE is a multi-body finite element analysis code that can be appliedto arbitrary nonlinear elastic systems, and has beenproven in recent work (Ref. 11) using the OVER-FLOW methodology as a suitable CSD methodologyfor CFD-CSD coupling. DYMORE includes an ex-tensive library of multibody components that can beutilized to model mechanical components of a rotorsystem. This library is comparable to the componentlibraries in popular finite element methods for nonlin-ear elastic structural dynamics analysis. DYMOREcan be applied to new topological designs with ex-isting library elements or by the addition of new el-ements. Its modular approach allows the basic com-ponents to be validated independently. For flexiblestructures, DYMORE applies geometrically exact fi-nite elements along the blades with limiting assump-tions of the deflection values. It includes elementsbased on the work of Berdichevsky (Ref. 33), as ex-tended to beams (Ref. 34) and shells (Ref. 35), whichare very important for composite rotors and fuselagecomponents.

Aerodynamically, DYMORE includes internal un-steady 2D airfoil computations, as well as optionsto utilize airloads from an external source, such asa CFD methodology. Trimming is achieved usingan auto pilot method (Ref. 36), which has beensuccessfully utilized in CFD-CSD couplings withOVERFLOW (Ref. 11) and a free wake methodol-ogy (Ref. 37). This method controls the zeroth andfirst harmonics of the blade pitching function via areference jacobian matrix and three perturbationsto compute function gradients. The function gra-dients are computed with the lower-fidelity aerody-namic methods found in DYMORE. Trim targets areachieved by applying the gradients along with thecomputed loads in DYMORE’s aerodynamic modelplus the frozen delta between the input higher-fidelityand lower-fidelity loads.

Advances in the Unstructured

Overset Techniques

Fully-Articulated Rotor Motion

As previously discussed, in prior demonstrations ofthe unstructured overset methodology, rotor blademotion was limited to rotation and blade flappingreferenced to the hub (center of rotation). Thishas been extended to allow fully-articulated motionwhere flap, pitch and lead-lag motion, along withhinge offsets, are modeled. Collective changes toeffect trim convergence are also permitted. Thesemotions are implemented via Fourier coefficientsto prescribe the periodic motion of each degree offreedom, and then applying these coefficients toharmonically reconstruct the motion at each timestep. The hinge offsets are included through thecomputation of the center of rotation of each degreeof freedom. Finally, using the combination of centerof rotation, axis of rotation, and angle of rotation,a set of transformation matrices is obtained whichthrough matrix multiplication is combined to formone transformation matrix to specify the motion ofeach rotor blade: The RBM equations are computedin steps. The first step is to determine the axes ofrotation and their corresponding centers of rotation.These will be denoted as ~aη and ~cη, where η is aplace holder for the rotation type of interest. Thematrix that defines the rotation of the system abouta specific axis will be denoted as Aη and is defined as,

Aη =

(1 − cos(η)) ∗ a2ηx + cos(η)

(1 − cos(η)) ∗ aηx ∗ aηy + sin(η) ∗ aηz . . .(1 − cos(η)) ∗ aηx ∗ aηz − sin(η) ∗ aηy

(1 − cos(η)) ∗ aηx ∗ aηy − sin(η) ∗ aηy(1 − cos(η)) ∗ a2

ηy + cos(η) . . .(1 − cos(η)) ∗ aηx ∗ aηy + sin(η) ∗ aηx

(1 − cos(η)) ∗ aηx ∗ aηz + sin(η) ∗ aηy(1 − cos(η)) ∗ aηy ∗ aηz − sin(η) ∗ aηx

(1 − cos(η)) ∗ a2ηz + cos(η)

(1)

The centers of rotation and axes of rotation aredefined for this specific case to include the contribu-tions of hinge offsets and shaft tilt :

~aψ = (−sin(−αs) ∗ sn, 0.0, cos(−αs) ∗ sn)~cψ = (x0, y0, z0)~aθ = (cos(−αs) ∗ sn, 0.0, sin(−αs) ∗ sn)~cθ = (x0 + PH ∗ cos(−αs), y0, z0+

PH ∗ sin(−αs))~aδ = (−sin(−αs), 0.0, cos(−αs))~cδ = (x0 + LH ∗ cos(−αs), y0, z0

+LH ∗ sin(−αs))~aβ = (0.0,−1.0, 0.0)~cβ = (x0 + FH ∗ cos(−αs), y0, z0

+FH ∗ sin(−αs))

Where (x0, y0, z0) is the hub center, PH, FH, LH arethe pitch, flap, and lag hinges of the rotor, and αs isthe shaft tilt angle. The variable sn is either 1 or -1depending on the direction of rotation of the rotor.The angles are computed by reconstructing user inputfourier coefficient data:

β = β0 + β1s ∗ sin(ψ) + β1c ∗ cos(ψ) + ...θ = θ0 + θ1s ∗ sin(ψ) + θ1c ∗ cos(ψ) + ...δ = δ0 + δ1s ∗ sin(ψ) + δ1c ∗ cos(ψ) + ...

The total rotation matrix is then constructed bythe set of sequential equations,

R′ = AθIR′′ = AδR

′

R′′′ = AβR′′

Rtot = AψR′′′

Where R′,R′′,R′′′ are intermediate steps and Rtot isthe total rotation matrix. The corresponding dis-placements are finally computed as,

~dx = −Aθ(~cθ) + ~cθ~dx

′′= Aδ( ~dx

′− ~cδ) + ~cδ

~dx′′′

= Aβ( ~dx′′− ~cβ) + ~cβ

~dxtot

= Aψ( ~dx′′′− ~cψ) + ~cψ

Where ~dx′, ~dx

′′, ~dx

′′′are intermediate steps and ~dxtot

is the resulting displacement vector. These compo-nents are used to relate the initial point to the de-formed point as follows,

~xnew = Rtot~xold + ~dxtot

(2)

This expression is applied to every grid point in thegrid attached to the flexible surface at each time step,resulting in fully-articulated rotor motion.

Rigid blade motions are implemented by an inputdeck that permits the user to define the motion via

a set of motion commands. For example, blade pitchmotion is achieved using the equation of motion:

θ = θ0 + θ1ssinψ + θ1ccosψ (3)

where the user inputs the coefficients θ0, θ1s, θ1c thatare applied within the rotor module of FUN3D.

Elastic blade motions are implemented slightly dif-ferently. The user will still input the rotor motioncoefficients so that the basic rotor motion is properlyupdated in the blade motion routines. The elastic ro-tor motion is updated from a file that contains boththe blade deflections and rigid motions. This file isoutput from DYMORE, and is formatted using thestandard proposed by Nygaard et al (Ref. 38) sothat the selection of the CSD module is not limitedto DYMORE.

CFD–CSD Coupling

Prior to this effort, FUN3D already included thecapability for aeroelastic flexibility via NASTRAN,however rotorcraft have specialized concerns in thisarea. Using comprehensive or multi-body dynamicscodes, the rotor is typically modeled as one or morebeams that must include not only the elastic beamdeflections, but rigid body motion as well, so thatthe rotor may be trimmed to approximate the correctperformance. The coupling process is being demon-strated with DYMORE, which has been successfullycoupled at Georgia Tech to OVERFLOW (Ref. 11).A delta loads trim process, which has become a defacto standard among the rotorcraft community, isbeing utilized in this work.

Once elastic blades are introduced into the system,the overset methodology becomes much more com-plex. At every time step, a new DCI file that hasbeen updated with the blade deflections is needed.Depending on the coupling strategy, this may requirethat SUGGAR be called and instructed to generatethe new DCI file for the next time step. When SUG-GAR finishes, the flow solver can advance the solutionto the new time step.

One way around this problem is to apply a loose-coupling strategy. In rotorcraft applications, loosecoupling has been taken to mean that loads and de-flections data are exchanged for an entire rotor rev-olution, as illustrated in Fig. 2. First, the initializa-tion of the trimmer jacobian and initial deflectionsis computed in DYMORE. The blade deflections arepassed to FUN3D, which has been coupled with SUG-GAR to generate a composite grid using the deflec-tions and connectivities via the DCI files. These DCIfiles and composite grid are then passed to FUN3Dwhere the run is integrated for some fraction of a

revolution until the blade loading over a revolution isperiodic. The azimuth fraction discussed above de-pends on the number of blades and the number oftime steps required to reach a periodic solution. Toillustrate, consider a four-bladed rotor, such as theUH60A. The minimum length of time that the CFDcode needs to be run is 1

4 of a revolution, as this frac-tion multiplied by the four blades is equivalent to afull revolution. If the loads at each quarter-revolutiondo not match at the boundaries, then the CFD sim-ulation must be run for another quarter-revolution.This must be repeated until the loads are repeatableand have (near) Co continuity at the run boundaries(e.g., for a four-bladed rotor at 0o, 90o, 180o, 270o, and360o).

Figure 2: Overset FUN3D–DYMORE Loose Cou-pling Scheme.

At this point, the loads can be sent back to the CSD

methodology (DYMORE) to evaluate how close totrim the current rotor configuration approaches. Us-ing the delta airloads approach (Ref. 10), the differ-ence between the input CFD and CSD aerodynamicloads is computed. The rotor is then trimmed us-ing a set of input targets (e.g., thrust, pitch and rollhub moments) and one of the lower-fidelity aerody-namics options found in the CSD methodology un-til a converged solution is obtained. If the targetsare predicted within preset tolerances – or the val-ues are no longer changing between iterations – thesolution is considered to be “converged to trim”. Ifthe computed targets are not within the trim targettolerances, the resulting blade deflections, which im-plicitly contain the control angles, are passed backto FUN3D where a new set of airloads is computed.As a result trim adjustments that are computed us-ing the DYMORE trimmer at each step are used inthe CFD code. This cycle is repeated until a solutionthat is “converged to trim” is achieved.

This loose-coupling strategy provides solutionsthat are adequate for many level-flight simulations.Problems have been encountered for flight conditionsthat have aperiodic loading (highly separated flows)or are located on the edge of the operation envelope.For these flight conditions, as well as maneuvers,a tight-coupling strategy is needed. For the tight-coupling strategy, the previously discussed strategymust occur at a much smaller fraction of the azimuth;updates may be needed within azimuthal changes ofone or two degrees in order to capture the transients.For this strategy, the grids and connectivity informa-tion will need to be created at each of these updates.Given the current situation where SUGGAR remainsan independent code, this process is too user time-intensive to be practical. Two potential solutions tothis problem would be to rewrite SUGGAR as a par-allel library, as has been done for DiRTLib, or toforgo the utilization of SUGGAR as a facilitator andreplace it with routines specific for use in FUN3D.

Test Cases

Georgia Tech Rotor–Fuselage

Experimentalists at Georgia Tech (GT) have per-formed a series of studies (Ref. 39) for the aerody-namic interaction between a teetering rotor and asimplified fuselage, as shown in Fig. 3. A fuselageconsisted of a 0.067m radius and 1.3716m cylindercapped with a hemispherical nose. The rotor was atwo-bladed, teetering rigid rotor mounted indepen-dently of the fuselage using a strut extending fromthe ceiling. Each rotor blade consisted of a rectangu-

lar planform with a constant, untwisted NACA 0015airfoil section. The blade radius was 0.4572 m with a2.7 percent cut out and a chord of 0.086m. The ro-tor rotation rate was 2100 rpm. The hub was located1 rotor radius downstream of the nose and 0.3 rotorradii above the fuselage centerline.

Figure 3: Georgia Tech rotor–fuselage test model(Ref. 16).

An advance ratio of 0.1 with a rotor shaft tilt angleof 6o and fixed blade pitch of 10o was chosen for thiswork. The flap angle defining the blade motion is

θ = −2.02osinψ − 1.94ocosψ (4)

For the test case chosen here, the thrust coefficient(CT ) was measured to be 0.00945. It should be notedthat the experimental tip path plane shifts to the sidesince the rotor could not be trimmed given the lackof cyclic pitch control.

The computational grid utilized for this simulationconsists of a fuselage grid with 1,870,639 nodes with36,119 nodes on the fuselage. The overset blade gridconsisted of 420,709 nodes and had total 15,784 nodeson the blade surfaces. Therefore, the composite gridhad 2,291,348 nodes and 51,903 surface nodes.

UH60A Rotor in Level Forward Flight

The UH60A helicopter flight test database (Ref. 40)has become the correlation standard for CFD-CSDcoupling. For illustration here, the high speed case(C8534) has been chosen as the verification case.For the C8534 case, the flight conditions are µ =0.368, CT

σ= 0.084,M∞ = 0.236,Mt = 0.642, αs =

−7.31o, and an altitude of 3273 ft. Target trim val-ues are 17,944 lbs. of thrust, –6884 ft.–lbs. of rollingmoment and a 2583 ft.–lbs. of pitching moment.While many of the discrepancies in the data havebeen resolved (Refs. 41, 42), discrepancies betweenthe thrust and moments from measured and rotor

pressure gauge integrations create uncertainties in thetrim condition. Since the experimental mean airloadvalues may be different from computed values, loadsare usually shown with the mean values removed.

Each of the UH60’s four blades was modeled us-ing its physical properties described in Ref. 43.The blade was modeled using ten cubic beam ele-ments, and the hub-rotor connection was modeledwith three segments permitting lag, flap, and pitchrotations. The physical characteristics of the bear-ing were simulated by springs and dampers in thejoints. This structural dynamics model has been cor-related within DYMORE and UMARC using experi-mentally measured airloads and has been previouslypresented (Refs. 37, 44).

The overset grid utilized for these computations in-cludes five different volumes comprised of tetrahedralelements for the four near-field blade grids and thebackground grid. There were a total of 18.3 millioncells (3.2 million nodes) in the entire grid, with 2.4million cells (414 thousand nodes) in each blade gridand 8.8 million cells (1.5 million nodes) in the back-ground grid. Fifteen thousand triangles (8000 nodes)were used to model each rotor blade surface, as seenin Fig. 4. The overlay of the near-field blade gridand the background grid is illustrated in Fig. 5. Thenearfield blade grid extended about the blade with a0.22 blade radius, while the outer grid extended out-ward more than 30 blade radii. Normal spacing atthe surface was approximately 1 × 10−6 chords.

Figure 4: FUN3D UH60 blade surface grid.

Results

Georgia Tech Rotor–Fuselage

The Georgia Tech rotor–fuselage configuration hasbeen utilized to verify the new rigid body motionroutine. Fig. 6 verifies that the implementation of therigid body motion file is correct for the teetering rotorconfiguration. Both the overset time-averaged pres-sure coefficients for the hard-coded motion (Ref. 16)and the motion computed from the rigid body motionmodule result in the same pressure distribution overthe body given the same grid and numerical input se-lections. In addition to the overset simulations, theresults from the unsteady actuator blade (Ref. 16) are

Figure 5: FUN3D UH60 near– and far–field oversetgrids.

included for comparison.There are some interesting pressure pulses that oc-

cur only with the overset computations. Further in-vestigation shows that the tip vortices intersect thefuselage in the areas where the pressure pulses oc-cur. As observed in Fig.7, vorticity from the rootarea tends travel sharply downward and impinge nearthe rotor hub (X/R = 1.0). The tip vortices travelaft and downward, moving more rapidly downwardon the left side, as expected. The influence of the tipvortex as it approaches the fuselage on the left sideis first felt about X/R = 1.5. When it impinges onthe fuselage at about X/R = 2.3, the influence is feltaround the entire fuselage.

There are no extant data for the rotor blade loadsfor this configuration. However, if the pressure co-efficients for the blade are plotted, as in Fig. 8, oneobserves that the pressure distributions have the ap-proximate magnitude and shape expected from thisairfoil at the estimated angles of attack.

UH60A Blackhawk Rotor

The UH60A Blackhawk rotor is utilized to verify theability of the unstructured FUN3D code to computethe loads about a rotating system. In order to testthe ability of FUN3D without the additional sourceof error from coupling, a rigid body simulation wasrun and compared with a comparable OVERFLOWsimulation to allow correlation since the experimen-tal data inherently includes flexible blades and istrimmed. Table 1 compares the hub loads for each

(a) Upper

(b) Right

(c) Left

Figure 6: GIT rotor–fuselage time-averaged center-line fuselage pressures.

simulation, as well as the experimental data. Thethrust predictions for the two computational method-ologies are very close, within 3% of one another, al-though there is significant deviation as expected with

(a) Orthogonal View

(b) Side View

Figure 7: Wake vorticity for the GIT rotor-fuselageat a µ = 0.10.

the experimental data without flexibility or trim. Themoment data, which are typically the most sensitiveof the integrated parameters, show very large devia-tions from experiment and one another. The reasonsfor the integrated moment differences are due to thefact that FUN3D shows a tendency to separate inthe third and fourth quadrants, as well as near thetip, as illustrated by the selection of pressure coeffi-cients shown in Fig.9. These pressure coefficients ver-ify that the solution obtained by the FUN3D solverwith the overset grids is comparable to its structured

counterpart, OVERFLOW. Although each was runusing the Spalart-Allmaras turbulence model, differ-ences in the pressures can be easily accounted for bygrid differences and possibly, numerical input selec-tions. FUN3D very closely matches the suction peakpredictions for all of the spans examined. Pressuretrends throughout the blade disk are very well pre-dicted using OVERFLOW as a guide, and indicatethe viability of FUN3D to predict rotor loads.

Proceeding to a flexible simulation (CFD-CSD cou-pling), the implementation discussed earlier has beentested within FUN3D. Using the DYMORE deflec-tions and controls, the blade is successfully deflected,as illustrated in Fig. 10. If the near-field bladegrid remains fixed with respect to the rotor tip pathplane so that the blade motion within the near-fieldgrid includes flexibility and rigid motions, care mustbe taken that the grid outer boundaries remain farenough from the blade so that the grid does not gen-erate unwanted dense spots (e.g., the upper portionof the grid in Fig. 11). If only the elastic motionsare updated within the near-field grid, so that thegrid moves with the rigid blade motions is anotherway to alleviate this problem. As illustrated in Fig.12, the CFD-CSD formulation implemented withinFUN3D provides smooth Co blade deflections, as ex-pected from the physics of the problem.

Conclusions

Advancements in the utilization of unstructured CFDmethodologies have been demonstrated via imple-mentations in the FUN3D code. Rigid body motionand CFD-CSD coupling have been demonstrated viaseveral test cases of interest to the rotary-wing com-munity. Preliminary results shown here are compara-

Parameter Target OVERFLOW FUN3D

Blade Flexible Rigid RigidTrim Yes No NoFx (lbs) — 857 887Fy (lbs) — -507 -940Fz (lbs) 17944 25445 24472Mx (ft-lbs) 6884 80266 102238My (ft-lbs) -2583 5405 96096t Mz (ft-lbs)

— -64132 -82951

CT 0.007247 0.01028 0.009884CT

σ0.08714 0.1236 0.1204

Table 1: UH60A Integrated parameters from rigidblade simulations.

ble to structured overset code results, within the po-tential errors introduced by differences in the grids.Further research to optimize the domain connectivityinformation, as well as the most accurate way to up-date the overset grids needs to be investigated. Thiswork continues to show the viability of unstructuredmethods for rotary wing applications.

Acknowledgements

This work is sponsored in part by the National Ro-torcraft Technology Center (NTRC) at the GeorgiaInstitute of Technology. Dr. Michael Rutkowski hasbeen the technical monitor of this center. Computa-tional support for the NTRC was provided throughthe DoD High Performance Computing Centers atMHPCC, ERDC and NAVO through an HPC grantfrom the US Army. Dr. Roger Strawn is the S/AAAof this grant.. The computer resources of the De-partment of Defense Major Shared Resource Centers(MSRC) are gratefully acknowledged. The FUN3DDevelopers Group at NASA Langley Research Centeris also acknowledged for their help with FUN3D pro-gramming and numerous discussions on rotary-wingmodeling. The aid of Dr. David O’Brien of AED inHuntsville, AL to help the first two authors continuein his footsteps is appreciated, as well as the use ofhis GIT and UH60 blade grids. The late nights de-bugging and plotting by Mr. Chirag Talati and Mr.Nick Burgess are also much appreciated.

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-2-1.5

-1-0.5

00.5

1

0 0.5 1

Cp

, P

si =

0 d

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FUN3DOverflow

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-1.2

-0.8

-0.4

0

0.4

0.8

0 0.5 1

Cp

, P

si =

0 d

eg

-1

-0.5

0

0.5

1

0 0.5 1

Cp

, P

si =

90

de

g

-1.4

-1

-0.6

-0.2

0.2

0.6

0 0.5 1

Cp

, P

si =

18

0 d

eg

-0.9

-0.6

-0.3

0

0.3

0.6

0 0.5 1x/c

Cp

, P

si =

270 d

eg

Figure 8: Pressure coefficients for the GIT rotor at aµ = 0.10.

(a) Undeflected grid

(b) Deflected grid

Figure 10: Comparison of an undeflected and de-flected blade grid.

Figure 11: Large blade deflections along with rigidblade motions can cause problems in a deforminggrid.

Figure 12: Comparison of an undeflected and de-flected blade surface.