PREDICTION OF HELICOPTER MANEUVER LOADS - ICAS is

26th INTERNATIONAL CONGRESS OF THE AERONAUTICAL SCIENCES

PREDICTION OF HELICOPTER MANEUVER LOADS USING ACOUPLED CFD/CSD ANALYSIS

Jayanarayanan Sitaraman, Beatrice RogetNational Institute of Aerospace

Hampton, Virginia

Keywords: Helicopter, FSI, maneuver

Abstract

A fluid-structure analysis framework which cou-ples Computational Fluid Dynamics (CFD) andComputational Structural Dynamics (CSD) isconstructed to study the aero-mechanics of a he-licopter rotor system under maneuvering flightconditions. The CFD approach consists of thesolution of Unsteady Reynolds Average NavierStokes (URANS) equations for the near-field ofthe rotor coupled with the dynamics of trailedvortex wake that are computed using a free vor-tex method. The CSD approach uses a multi-body Finite Element method to model the rotorhub and blades. The analysis framework is usedto study the Utility Tactical Transport Aerial Sys-tem (UTTAS) pull-up maneuver of the UH-60Ahelicopter. Results shown illustrate the correla-tion of predicted performance, aerodynamic andstructural dynamic loading with measured flighttest data. The normal load factor and the peak-to-peak structural and aerodynamic loading showgood correlation with flight test data, indicatingthat the analysis framework is suitable for pre-liminary design purposes. Important phenomenasuch as advancing blade transonic effects and re-treating blade flow separation are predicted satis-factorily. However, deficiencies are noted in theaccurate resolution of stall incidence, reattach-ment and shock induced separation.

1 Introduction

Helicopter rotor systems operate in highly un-steady flow conditions which are characterizedby transonic flows, dynamic stall events and re-turning wake interactions. In addition, there isa large extent of aeroelastic coupling owing tothe slender construction of the blades. All thesefactors contribute to make the prediction of aero-dynamic and structural dynamic loading on he-licopter rotors a very challenging problem evenin steady forward flight. Maneuvering rotorcraftfurther augments this challenge, because of addi-tional aerodynamic and structural effects due tothe hub motion and associated wake transients.

The simulation tools for rotorcraft analy-sis (termed Comprehensive Aeroelastic Anal-yses) have historically been using lifting linebased aerodynamic models (with suitable en-hancements that use table lookup, unsteady flowand stall models). However, such models areknown to have inaccurate prediction capabili-ties [1]. There are two main reasons for theinaccuracies in the lifting line models. Thefirst is the inability to resolve unsteady tran-sonic effects and second is the inability to ac-curately resolve the returning wake effects [2].The advent of the CFD (Computational FluidDynamics)/CSD (Computational Structural Dy-namics) coupled approach replaces the liftingline aerodynamic model with a higher fidelityComputational Fluid Dynamic model that solvesthe Reynolds-Averaged Navier-Stokes (RANS)equations. This methodology has led to con-

1

JAYANARAYANAN SITARAMAN, BEATRICE ROGET

siderable improvements in the airload predic-tion as demonstrated by various research efforts[2, 3, 4, 5, 6]. The primary reason for the im-provement can be attributed to accurate predic-tion of aerodynamic loading, especially the pitch-ing moments caused by unsteady transonic flowsand improved representation of returning wakeeffects [3].

An important aspect of CFD based aerody-namic load prediction methodologies is the res-olution of the wake structures. There are twowell established methodologies that are in use atthe moment for wake predictions. They are a)wake coupling [7] and b) wake capturing [3, 4, 8].In the wake coupling methodology, the geometryof the vortex wake, circulation strength and coregrowth rate are computed externally by solvingthe vorticity transport equation. The wake posi-tions so obtained are embedded into the RANS-based CFD analysis using the field velocity ap-proach [9]. The wake capturing methodology, incontrast, models the entire rotor system and at-tempts to capture the wake structure as part ofthe solution. The advantages of the wake cou-pling methodology are computational efficiencyand ease of modeling. However, it suffers fromthe empiricism that is used to model the phys-ical diffusion of vorticity. The wake capturingmethodology has the advantage of being a first-principle based modeling technique without anyempiricism. However, it does suffer from highcomputational cost and numerical diffusion inpredicting the wake structure. An evaluation ofthe wake coupling and wake capturing method-ologies for prediction of steady flight conditionscan be found in Ref [10].

The main focus of most recent research ef-forts was on predicting rotor airloads in steadyflight conditions. The periodic nature of the flowfield and structural response facilitates the use ofthe so-called ’loose coupling’ approach for inter-facing the CFD and CSD analysis modules. Inthe loose coupling approach, the analysis mod-ules exchange relevant data only every rotor rev-olution. The inherent decoupling within a rev-olution provided a fast and robust way for estab-lishing aircraft trim and a fully periodic structural

response. In contrast, simulating an unsteady he-licopter maneuver necessitates the exchange offorces and motions at every time step between thefluid and structure methodologies.

Recently, Bhagwat et al. [11, 12] per-formed the seminal studies on computing air-loads and blade loads for the UH-60A pull-upmaneuver using a CFD/CSD analysis that cou-pled OVERFLOW-2 (wake capturing CFD) andRCAS (CSD+ comprehensive analysis) [4]. Re-markable improvements were demonstrated inthe prediction of aerodynamic and structural dy-namic loads compared to conventional compre-hensive analysis. This study triggered a lotof interest in the application of CFD/CSD cou-pling analysis to simulate helicopter maneuver-ing flight. Abhishek et al. [13] coupled asimplified aerodynamic model with multi-bodyCSD analysis. The results obtained were satis-factory for peak-to-peak loading especially forthe pushrod loads, however the details of load-ing waveforms showed unexplained phase differ-ences. Silbaugh et al. [14] used a wake capturingCFD approach coupled with a simplified struc-tural dynamic model. This study concentratedon isolating the differences between the time ac-curate and serial-staggered coupling approachesand performed simulations only for the first 15revolutions of the maneuver.

The objective of the present work is to fur-ther validate and enhance the analytical approachby constructing an analysis platform composedof another set of CFD/CSD analysis tools (UM-TURNS [15, 10] for CFD and DYMORE [16] forCSD). There are two main differences in the anal-ysis framework used in this paper compared tothat used by Bhagwat et al. [11]. The wake cou-pling methodology is utilized here in contrast tothe wake capturing methodology. In addition thecoupling of codes is performed using a pythonbased framework where all data exchange is per-formed using memory pointers rather than fileI/O making the coupling process efficient andseamless. The time evolution of the structural,fluid dynamic and vorticity transport equationsare consistently coupled to obtain an aeroelasticsolution for the unsteady maneuver.

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Prediction of Helicopter Maneuver Loads using a Coupled CFD/CSD Analysis

2 Methodology

2.1 CFD solver

The Navier-Stokes equations are solved in theirReynolds-Averaged form which has been provento be well-suited for high Reynolds number ex-ternal flow problems as in the case of helicopterflight. After Reynolds-averaging, the Navier-Stokes equations govern the variation of themean (time-averaged) flow quantities. Closureis achieved by accounting for turbulent fluctua-tions that are found using an adequate model thatis dependent on the mean quantities (algebraic orequation based).

The RANS (Reynolds Averaged Navier-Stokes) solver used as the CFD analysis is theUniversity of Maryland TURNS code [3, 8]which operates on meshes that follow structured-curvilinear topology. The UMTURNS code usesa finite volume numerical algorithm that evalu-ates the inviscid fluxes using an upwind-biasedflux difference scheme. The van Leer monotoneupstream-centered scheme for conservation laws(MUSCL) approach is used to obtain third orderaccuracy, with Koren’s differentiable flux lim-iters to make the scheme total variation diminish-ing. Viscous fluxes are computed using a 4th or-der central difference discretization. The Spalart-Allmaras one-equation model is used for the tur-bulence closure. The turbulence model equationsare solved segregated from the mean-flow solu-tions and the necessary implicitness and time-accuracy is achieved using sub-iterations.

The LU-SGS scheme suggested by Jamesonand Yoon [17, 18] is used for the implicit op-erator. Briefly, the LU-SGS method is a directmodification of the approximate lower-diagonal-upper (LDU) factorization to the unfactored im-plicit matrix. Though the (LU-SGS) implicit op-erator increases the stability and robustness of thescheme, the use of a spectral radius approxima-tion renders the method only first order accuratein time. Therefore, a second order backwards dif-ference in time is used, along with Newton-typesub-iterations to restore formal second order timeaccuracy.

UMTURNS uses the Arbitrary LagrangianEulerian (ALE) formulation for modeling un-steady flows with motion of the solid surfaces asin the case of helicopter flows. Calculation ofthe space and time metrics are the key require-ments for the ALE formulation. The present nu-merical scheme employs a modified finite vol-ume method for calculating the space and timemetrics. Finite volume formulations have the ad-vantage that both the space and time metrics canbe formed accurately and free stream is capturedaccurately [19]. Also, it is to be noted that thecomputations include not only aeroelastic defor-mations but also gust fields that are generated byhub motion and wake transients. The space andtime metrics are evaluated in such a manner thatthey implicitly satisfy the Geometric Conserva-tion Law(GCL) and also maintain order of accu-racy of the numerical scheme [9].

The computational domain is partitioned tofacilitate calculations in a distributed comput-ing environment. All parallel communicationsare achieved using the Message Passing Interface(MPI-2) standard.

2.1.1 Calculation of Space and Time metrics

The strong conservation-law form of the Navier-Stokes equations in cartesian coordinates can bewritten as [20]

qt + fx +gy +hz = σx +θy +ωz (1)

q = (ρ,ρu,ρv,ρw,ρE)T

E = e+u2 + v2 +w2

2

f = (ρu, p+ρu2,ρuv,ρuw,ρuH)T

g = (ρv,ρvu, p+ρv2, p+ρvw,ρvH)T

h =(ρw,ρwu,ρwv, p+ρww2,ρwH)T H = E + p/ρ

where u, v, w are the velocity components inthe coordinate directions x, y, z; ρ is the density,p is the pressure, e the specific internal energy;and σ, θ, ω represent the viscous stress and work

3


terms for each coordinate direction. Upon trans-forming to computational coordinates ξ, η, ζ withthe aid of the chain rule of partial derivatives,Eq.( 1) becomes:

qτ + fξ + gη + hζ = σξ + θη + ωζ (2)

q = Jq

f = ξtq+ ξx f + ξyg+ ξzh σ = ξxσ+ ξyθ+ ξzω

g = ηtq+ηx f +ηyg+ηzh θ = ηxσ+ηyθ+ηzω

h = ζtq+ ζx f + ζyg+ ζzh ω = ζxσ+ ζyθ+ ζzω

Here terms of form ξx,y,z, ηx,y,z and ζx,y,z arethe space metrics, ξt , ηt and ζt are the time met-rics in the computational domain, and J is the ja-cobian of the inverse coordinate transformation(i.e. J = det( ∂(x,y,z)

∂(ξ,η,ζ))).

2.1.2 Field Velocity Approach

For the computations presented here, the vortexwake is computed using time accurate solutionsof the vorticity transport equation. The effect ofvortex wake is then coupled to the fluid equationsusing the field velocity approach [9] which is away of modeling external velocity fields via ap-parent grid movement.

Mathematically, the field velocity approachcan be explained by considering the velocityfield, V , in the physical cartesian domain. It canbe written as

V = (u− xτ)i+(v− yτ) j +(w− zτ)k (3)

where u, v and w are components of the ve-locity along the coordinate directions and xτ, yτ

and zτ are the corresponding grid time veloc-ity component. Let the velocity induced by theexternal potential (e.g. that generated by thevortex wake) be represented by a velocity field(u′,v′,w′). Thus, the velocity field becomes

V = (u−xτ +u′)i+(v−yτ +v′) j+(w−zτ +w′)k(4)

The field velocity approach models thischanged velocity field by changing the grid ve-locities. The modified grid velocities are definedas

xτi+ yτ j+ zτk =(xτ−u′)i+(yτ−v′) j+(zτ−w′)k(5)

Once the modified grid velocities are obtained,the grid time metrics in the computational do-main (ξt , ηt ζt) are computed as:

ξt =−(ξxxτ + ξyyτ + ξzzτ)ηt =−(ηxxτ + ηyyτ + ηzzτ)

ζt =−(ζxxτ + ζyyτ + ζzzτ)

Detailed validation of this approach formodel problems as well as full helicopter simu-lations can be found in Ref [9].

2.2 CSD solver

In the present study, the CSD code DYMOREis used for structural modeling. DYMORE isa finite element based tool for the analysis ofnonlinear elastic multibody systems, developedat the School of Aerospace Engineering, Geor-gia Institute of Technology (Bauchau, Ref [16]).It includes a library of structural elements fromwhich models with arbitrarily complex topolo-gies can be built. The element library includesrigid bodies, cables, composite capable beamsand shells, and joint models which can includegeneric spring and/or damper elements. De-formable bodies are modeled with the finite el-ement method. The formulation of beams is ge-ometrically exact, i.e. arbitrarily large displace-ments and finite rotations are accounted for, butis limited to small strains. The equations of equi-librium are written in a Cartesian inertial frame.Constraints are modeled using the Lagrange mul-tiplier technique, resulting in a system of dif-ferential/algebraic equations (DAE). These equa-tions are then solved using a robust an efficienttime integration algorithm (Ref [21]).

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2.3 Time accurate wake computations

The aerodynamic model incorporated in DY-MORE utilizes 2-D airfoil theory augmentedwith airfoil table look-up. The inflow modelis based on the theory for unsteady flow overa circular disk with a pressure jump across thatdisk [22]. In the present work, a free wake analy-sis is devised in an attempt to improve the inflowmodeling and enhance the accuracy of rotor aero-dynamics predictions.

The dominant structures in the rotor flow fieldare the blade tip vortices. The present analy-sis considers a single tip vortex filament on eachlifting line of a rotor, released from each bladetip. The free wake problem is governed by thevorticity transport equation. Assuming that vor-tex elements convect with the fluid particles, theequation of evolution for the wake markers canbe written as:

d~r(ψ,ζ)dt

=~V (~r(ψ,ζ)) (6)

where~r defines the position vector of a wakemarker, located on a vortex filament that is trailedfrom a rotor blade located at an azimuth ψ, andwas first created when the blade was located at anazimuth (ψ−ζ), as represented in Figure 1.

Wake marker

Rotor Hub

Azimuth ψ

Azimuth ζ

Fig. 1 Representation of a wake free filament anda wake marker.

The vorticity transport equation can be writ-ten in the following partial differential form:

∂~r(ψ,ζ)∂ψ

+∂~r(ψ,ζ)

∂ζ=

~V (~r(ψ,ζ))Ω

(7)

The right hand side velocity accounts forthe instantaneous velocity field encountered by amarker on a vortex filament in the rotor wake.This includes the free-stream velocity, the in-duced velocities due to all the vortex filamentspresent in the wake, and also the induced contri-butions of the bound circulation representing thelifting rotor blades. This equation must be dis-cretized into a set of finite difference equationsthat can then be numerically integrated. The timemarching algorithm chosen is based on that sug-gested in Ref [23], and is modified to suit thepresent analysis framework [24].

The velocity term in the vorticity transportequation is computed from the Biot-Savart law:

~V (r) =Γ

4π

h2√h2 + r2

c

∫ d~l×d~r|~r|3

(8)

where ~V (r) is the velocity induced at a pointP located at r relative to the vortex element d~l.The integral is evaluated over the entire lengthof the vortex filament. Γ is the total strength ofthe filament, and d~l is an elemental unit vectoralong the vortex filament. The vortex core radiusis noted rc, and h is the perpendicular distanceof the evaluation point from the influencing vor-tex element. Viscous diffusion is modeled by thegrowth of the core radius given by [25]:

rc(ζ) =√

r2initial +4αδνζ/Ω (9)

where α is an empirical factor (α = 1.25643),δ is the apparent viscosity coefficient, and ν is thekinematic viscosity. The circulation Γ released atthe blade tip is assumed to be equal to the max-imum bound circulation along the blade. A nearwake is included in the model to improve the ac-curacy of modeling the distortions created by theblades on trailed vortex wake. The blade boundcirculation is fixed at the blade 1/4-chord and thenear wake trailers emanate from these locations.

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For operations within a table lookup based aero-dynamic modeling flow boundary conditions areenforced at the blade control points that are lo-cated at the 3/4-chord location. This method pro-vides a good first approximation to a lifting sur-face analysis, and is more accurate than a liftingline analysis [26].

For coupled operation with CFD, the bladebound circulations are computed based on theCFD aerodynamic loading and the enforcementof flow boundary conditions at 3/4 chord areturned off since they are implicitly satisfied bythe higher resolution flow field solution from theCFD.

After the velocity contributions (Equation( 8)) from both near and far wake are evaluatedand aggregated at each wake marker location,the ordinary differential equations that denotethe evolution of the wake markers are integratedin time using a 2nd order backward predictor-corrector algorithm (see Appendix in Ref [24]).

2.4 Fluid-structure interface

Since rotor blades have very little elasticity in thechordwise direction, they can be modeled quiteaccurately in the CSD methodology using a 1-Dbeam representation with flap, lag, axial and tor-sion degrees of freedom. In contrast, the entiresurface of the blade is represented in the CFDmesh within the limit of grid resolution. The dif-ference in geometry description of the CFD andCSD models requires specialized formulation forthe transfer of loads and displacements. In thispaper, we follow a rather simple approach ofone-dimensional interpolation of sectional aero-dynamic loading using cubic splines. Because ofthe structured nature of the grid, sectional aero-dynamic loading can be easily determined usingthe pressure and shear stress distributions on theCFD surface grid. These are interpolated usingcubic spline interpolation to the control points ofthe CSD model. As the span-wise resolution ofthe CFD mesh is commensurate (slightly higher)to that of the CSD control point distribution thereis very little inconsistency between the total load-ing integrated in either solvers (i.e. this method

is force-preserving within the limit of grid reso-lution). Additionally, local continuity of loadingis maintained because force/unit length is inter-polated as opposed to the lumped-force itself.

2.5 CFD-Wake interface

The Eulerian fluid-dynamic equations ( 1) andLagrangian wake equations ( 7) are interfaced us-ing the field-velocity approach. At any time step,the wake coordinates obtained from the wakesolver are used to evaluate the induced velocityfield (u′,v′,w′) at every grid point. The computa-tion of the induced velocity field is expensive ifa brute-force approach is followed. However, weutilize a fast-hierarchical approach [9] to accel-erate this calculation which brings the associatedcomputational overhead down to only about 10%of the total time step. Note that to prevent doublyaccounting for the near-wake region (i.e regiondirectly behind the blade), all the wake filamentsthat belong to a particular blade and are containedinside the CFD mesh belonging to that blade arenot included in the induced velocity calculations.The CFD aerodynamic loading on the bladedetermines the bound vorticity and hence theamount of vorticity shed into the wake markersas described in Section 2.3.In essence, the wake solver gives the wake po-sitions, their circulation strengths and vortex dif-fusion parameters to the CFD solver. The CFDsolver in turn provides the sectional aerodynamicloading to the wake solver such that the appropri-ate bound-vorticity profile can be computed.

2.6 Time integration procedure

The fluid, structure and wake equations are in-tegrated using the conventional serial-staggered(CSS) time stepping scheme as shown in Fig-ure 2. The CSS scheme was shown to pro-vide similar levels of accuracy as fully time-accurate simulation (sub-iteration based) for asmaller computational overhead by Silbaugh etal. [14]. Therefore, this method is adopted for thepresent study. The sequence of integration is asfollows: first the CSD solver computes convergedblade position using the provided aerodynamic

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converged

CFD (UMTURNS)

Free-wake

update

CSD (DYMORE)

no

yes

Structural

response

Aerodynamic

loading

Vortex wake

data

no

yes

Prescribed

Flight Dynamics

CFD sub-

iterations

CSD sub-

iterations

converged

time = tk

time = tk+1

Fig. 2 Schematic of the time-stepping sequenceused for integration of governing fluid, wake andstructural dynamic equations of the unsteady ma-neuver problem

loading, following that the wake solver computesnew wake locations based on this new blade po-sition as well as the provided aerodynamic load-ing. Once the new blade positions and wake lo-cations are obtained, the fluid equations are in-tegrated to generate the aerodynamic loading forthe next time step. Note that this method not onlydegrades in accuracy but also shows instabilitiesif large time steps are used. In the present work,an azimuthal step of 0.4 deg is used. This valueresults in similar level of overall accuracy whenusing the serial-staggered scheme compared tothe fully time-accurate simulation.The initiation of the fluid-structure solution oftencreates large transients in both physical systemsthat can be amplified by the combined time inte-gration procedure (because of its explicit nature)leading to destabilization. To prevent such desta-bilization from occurring, the CFD based aerody-namic loading is slowly introduced into the CSDloading using a smooth cosine decay scheme.The aerodynamic model (lifting-line based) ismaintained active in the CSD solver for the ini-tiation. This model is fully-coupled in the sub-iteration level and does not cause destabilization.

The aerodynamic loading from the CFD is slowlymixed with the lifting line aerodynamic loadingover half a revolution of the maneuver. After thefirst half a revolution the lifting line modeling iscompletely turned off and the CSD loading is ex-actly equal to the CFD aerodynamic loading.

2.7 Python based coupling framework

The data transfer between the CFD andCSD/Freewake codes are facilitated in a pythonbased framework. Python supports object-oriented programming and each participatingsolver is treated as an object (or module inFortran90 parlance). The infrastructure exe-cutes legacy solvers but only after the solversare “wrapped” with a socket-like Python layer.Python interfaces are compatible with other pro-gramming languages and there are freely avail-able tools for developing these Python interfaces,such as f2py and swig for codes in Fortran90and C/C++, respectively. Once wrapped, theparticipating solvers execute largely independentof one another following their own native paral-lel implementation. Different solvers can refer-ence each other’s data through the Python layerusing standard C-like pointers, without memorycopies or file IO. However, the different solversmust accommodate common shared data struc-tures maintained at the Python level for this towork efficiently. In essence, after the necessarywrapping procedures, the python script becomesthe driver for the entire CFD/CSD simulation andorchestrates the appropriate time stepping anddata exchange paradigms. In addition, it is alsopossible to run the Python wrapped code in par-allel under MPI using pyMPI or mympi, allowingone to use the large scale parallel computers tra-ditionally used for large-scale CFD calculations.

2.8 UH-60A aerodynamic and structural dy-namic models

The mesh system used for the UH-60A rotor fol-lows a C-O topology and is shown in Figure 3.The grid used for each rotor blade has 129 pointsin wrap around direction, 129 points in the span-wise direction and 65 points in the normal direc-

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Fig. 3 Mesh topology for UMTURNS wakecoupling methodology

tion respectively. The outer boundary of the gridextends about 3 chords from the blade surface.The full mesh system utilizes four such grids, oneeach for each rotor blade. Finer grid clustering isused in regions of high gradients such as the shedwake region (directly behind the trailing edge ofthe blade) and trailed wake region (at the root andtip of the blade). The wake coupling approachdescribed in the previous section is used for in-cluding the returning wake effects.

Figure 4 shows a representation of the UH-60rotor modeled using DYMORE. The rotor modelconsists of four elastic blades, each using 15 el-ements with cubic shape functions. The bladeroot articulation is modeled using three revolutejoints, coincident at 4.66% blade radius. A rigidmodel of the rotor control system is used, includ-ing the pushrods, pitch horns, rotating and fixedswashplates. The pushrods are modeled as rigidelements connected to a prismatic joint with lin-ear stiffness equal to 187792 lb/ft [11]. A modelof the lead-lag damper is also included by mod-eling the damper as a rigid element connected toa prismatic joint with non-linearly varying damp-ing coefficient.

The computations were conducted on a 16processor cluster with Intel 2.3MHz chipsets.The wall clock time required/time step (includingboth CFD and CSD) for computations is noted to

be 2.2 seconds.

2.8.1 Validation of Aerodynamic Modeling

Figure 5 illustrates the improved prediction ca-pabilities of the CFD based aerodynamic model-ing compared to traditional lifting line based ca-pabilities that are part of comprehensive analysiscodes. Results are shown for the high speed flightcondition of UH-60A helicopter. Identical set ofblade motions that are obtained by forcing thestructural model with measured flight test data isused for computation of aerodynamic loading inboth lifting line and CFD approaches. The plotsshown consist of aerodynamic loading (normalforce and pitching moment) variation towards thetip of rotor and are representative of the over-all quality of the results. It is evident that theCFD based aerodynamic modeling shows muchimproved agreement with experimental data forboth normal force and pitching moment wave-forms.

2.8.2 Validation of Structural Dynamic Model

The rotor blade frequency plot is shown in Fig-ure 6(a) and (b), which correspond to two dif-ferent values of pushrod stiffness, 62631 lb/ftand 187792 lb/ft, respectively. The larger stiff-ness value has been suggested as more accurateand is the one used in the present analysis [11].However, the frequency variation results are pre-sented for both stiffness values in order to allowcomparison with published results using differ-ent comprehensive analysis (Ref [27, 28]). Thepredicted natural blade frequencies compare wellwith results from other analyses. The main effectof stiffening the pushrod is to increase the firsttorsional frequency from about 3.8/rev to about4.2/rev. Other natural frequencies are not signifi-cantly affected.

3 UH-60A 11029 Maneuver description

The NASA-Army UH-60A Airloads Programinvestigated a wide range of flight conditions.Detailed measurements of blade aerodynamicsand structural dynamics load measurements were

8


Elastic blades: 10 Elastic blades (10 elements, order 3)

Control system

Lag damper(non-linear damper)

Elastic beam (5 elements, order 3)

Pitch link(linear spring)

Lag/Flap/Pitch joints

Fig. 4 Details UH-60A structural model used in DYMORE

0 90 180 270 360-300

0

300

600

900

0 90 180 270 360-250

0

250

0 90 180 270 360-180

-90

0

90

96.5% R 96.5% R

96.5% R

Azimuth, degs. Azimuth, degs. Azimuth, degs.

Lifting line

c8534

CFD

Normal force

(all harmonics)

Normal force 3-20/rev

(low pass filtered)

Pitching moment

(mean removed)

lb/ft

lb/ft

ft-lb/ft

Fig. 5 Comparison of aerodynamic loading obtained from CFD and lifting line models for highspeed forward flight condition

conducted which serve as a rich database for codevalidation. An extensive documentation of theflight test program can be found in Bousmanand Kufeld [29, 30]. The operating envelopeof the helicopters plotted as variation of vehicleweight coefficient with advance ratio is shownin Figure 7. The limiting factors for these flightconditions are the maximum thrust limit becauseof retreating blade stall and maximum sectionalairfoil lift that can be generated. McHugh etal. [31] determined the maximum thrust bound-

ary using wind-tunnel tests which is representedin the figure. Note that all the steady flight con-ditions lie below the McHugh boundary. Fig-ure 7 also shows the variation of weight coef-ficient with advance ratio for the UTTAS pull-up maneuver. The maneuver begins quite closeto the maximum level flight speed of the aircraftand achieves a peak load factor of 2.1g, which ex-ceeds the steady state McHugh boundary. There-fore the UTTAS pull-up maneuver is a challeng-ing flight condition in terms of predictive capa-

9


(a) Root spring stiffness = 62631 lbs/ft (b) Root spring stiffness = 187792 lbs/ft

(from Datta 2004)

DYMORE

UMARC (2002)

2GCHAS (1994)

CAMRAD/JA (1994)DYMORE

UMARC (from Datta 2004)F

requency, per

rev

Normalized rotor speed Normalized rotor speed

2/rev

4/rev

6/rev

8/re

v

2/rev

4/rev

6/rev

8/re

v

Lag 1

Flap 1

Flap 2

Tor 1

Lag 2

Flap 3

Flap 4

Lag 1

Flap 1

Flap 2

Tor 1

Lag 2

Flap 3

Flap 4

Fig. 6 Rotor frequency plot of UH-60A rotor obtained using the DYMORE structural dynamicmodel compared with those obtained from UMARC (Datta, 2005)

0.02

0.05

0.08

0.11

0.14

0.17

McHugh's Lift Boundary

High altitude, High thrustCounter 9017

0 0.1 0.2 0.3 0.4 0.5

Advance Ratio, µ

Level FlightTest Envelope

High speed flightCounter 8534

Counter 11029

UTTAS pull-up

Highest vibration

regimes

Low speed transitionCounter 8515

Picture courtesy

Bhagwat et. al (2006)

Rev 4Rev 12

Rev 20

Rev 28

Rev 36

nZ CW / σ

Fig. 7 UH-60A flight envelope and maneuver trajectory

bility. A schematic of the UH-60A pull-up ma-neuver is also shown in Figure 7 which consistsof a transition from a level flight condition to asteady climb condition in about 40 revolutions ofthe rotor (approximately 10 seconds).

4 Maneuver analysis

Simulation of free-flight maneuver requires theinclusion of a flight-dynamic model in the calcu-lation of the aeroelastic response of the complete

10


0 5 10 15 20 25 30 35 40-30

-20

-10

0

10

20

30

40

Angle

(deg)

θ

Flight path

curveγ

α

Horizon axis

FP axis

Body axis

α

γ

θ

Time (rotor revolutions)

(a) Vehicle attitude variation

0 5 10 15 20 25 30 35 400

50

100

150

200

250

300


Speed

(ft/sec)

U

Uh

Uv

θ

Flight path

curveγ

α

Horizon axis

FP axis

Body axis

U

Uh

Uv

(b) Flight path angle variation

0 5 10 15 20 25 30 35 40-15

-10

-5

0

5

10

15

Lateral

Longitudinal

Collective (data)Collective (analysis)

Pilo

t contr

ol in

puts

(deg)


(c) Pitch control variation

Fig. 8 Prescribed flight dynamics and controlsused for maneuver simulation

rotorcraft. A few simplifications are introducedin the present study to reduce the complexity ofthe entire problem and facilitate validation. First,the pitch control inputs are prescribed rather thancalculated in this analysis. Second, only the lon-gitudinal dynamics of the maneuver is prescribedas it is the dominant contributor to the fundamen-tal physical mechanisms.

The aircraft undergoes changes in attitudesas well as flight velocities owing to changes inflight path. In our approach, the attitude changesare modeled by actually rotating the grids to cor-respond to the vehicle orientation in space. Inthe Arbitrary Lagrangian Eulerian (ALE) CFDmethod, the rotational velocities and accelera-tions caused by attitude changes are computedusing second order discretizations based on gridpositions consistent with the geometric conserva-tion law. Note that these rigid motions of the gridsystem are in addition to the aeroelastic deforma-tions. The linear velocity changes are introducedusing the field velocity approach, i.e. the gridvelocities at all grid points are changed by thesame magnitude and direction as prescribed bythe flight dynamics at each time step. Note thatthese grid velocity changes are added to those in-troduced by the wake influence.

Figure 8 summarizes the variation of vehicleattitudes and pitch control variation. The angleof attack and pitch attitude response slightly lagsthe normal load factor response. The peak load-factor of 2.1g is achieved during revs 15-17 fol-lowed by peak pitch angle and angle of attack atrev 19-21. From revolution 19, the normal loadfactor diminishes gradually to 1 because of thegradual reduction of the aft cyclic input.

The collective control input is adjusted suchthat initial steady flight thrust levels are matchedbetween analysis and experiment, i.e the trimprocedure is performed only for matching thethrust and not the hub moments. Longitudinaland lateral cyclic controls are prescribed exactlyas they were measured in the flight test.

Since the authors do not have full access tothe actual experimental data base, the data shownin this paper are digitized from the publicationby Bhagwat et al. [11, 13, 14]. All the experi-

11


mental data shown in this paper have been pub-lished elsewhere before by other research groupsand could be considered public domain.

5 Results and discussion

5.1 Rotor performance

Figure 9 shows the comparison of the predictedrotor thrust compared with the total vehicle thrustcomputed using the normal load factor flightmeasurement. The normal load factor measure-ment includes contributions from fuselage/tailforces. The present analysis is restricted only tothe rotor system and the thrust changes caused bythe fuselage/tail aerodynamics are not modeled.Therefore, Figure 9 also includes the calculatedrotor thrust obtained by integrating the measuredsectional airloads.

The maneuver thrust is plotted as a functionof time in units of rotor revolution. The oscilla-tory nature of the analysis results is because ofthe combination of unsteady aerodynamic loadvariations and hub accelerations. The measureddata is statistically averaged over every revolu-tion and hence appears smoother.

The general qualitative feature lift waveform( rapid increase at the beginning of the maneuverand gradual decrease to steady state at the end ofthe maneuver) are captured quite accurately bythe analysis.

Some discrepancies in the quantitative com-parison are expected since the effects of the fuse-lage and tail planes are not modeled in the currentanalysis, especially leading to underprediction ofthe maximum lift. Additionally the thrust varia-tion during the recovery part of the maneuver isunder-predicted by about 30% compared to thethrust integrated from the flight test aerodynamicloading. The reason for this discrepancy is notclear at the moment.

5.2 Wake Dynamics

The prediction of the unsteady wake dynamics isillustrated in Figure 10. Predicted vortex wakegeometry follows expected qualitative trends cor-responding to the prescribed flight dynamics and

0 5 10 15 20 25 30 35 400.5

1

1.5

2

2.5

3

3.5x 10

4

time (rotor revolutions)

Ver

tical

hub

load

, Fz (

lbs)

AnalysisN

z*GW (total lift)

Measured airloads (rotor lift)

Fig. 9 Predicted vs Measured total lift for theentire duration of the pull-up maneuver

computed aeromechanics. At the initiation of themaneuver (rev 4), the operating condition is veryclose to steady high speed forward flight wherethe wake is convected away from the rotor sys-tem in the horizontal direction. Returning wakeeffects are minimal at this condition. The wakegeometry shows asymmetrical roll-up in the rearview because of the large difference in the aero-dynamic loading distributions on the advancingand retreating side of the rotor disk.

The aircraft angle of attack rapidly changesfrom nose-down to nose-up in the next 16 revolu-tions with the maximum angle of attack attainedat the time level of about 20 revolutions. Thevortex wake convects very close and even cutsthrough the rotor disk during this process. There-fore large unsteadiness can be noticed in the wakedynamics in the illustrations at rev 12 and rev20. The combination of high thrust, higher climbrate and decreased forward speed at around revo-lution 20 causes increased vertical convection ofthe wake.

From revolution 20, the aircraft pitch attitudedecreases gradually from its maximum value of30 degrees. The aircraft angle of attack how-ever decreases rapidly because of the increasein climb rate. The combination of aircraft pitchchange and increased climb rate causes the vor-

12


Rev 4

Rev 12

Rev 20

Rev 28

Rev 36

(b) Rear Views (c) Side Views

rev 4rev 12

rev 20

rev 28

rev 36

(a) Maneuver path

Fig. 10 Snap shots of unsteady wake dynamics during the course of the pull-up maneuver

13


tex wake to cut through the rotor-disk once againduring the course of the maneuver producing as-sociated aerodynamic loading perturbations. To-wards the end of the maneuver at rev 36 the air-craft is climbing at about two-third its forwardspeed causing the wake to be spread vertically.The wake dynamics are benign at this conditionbecause of the reduced thrust levels and a moreeven aerodynamic loading distribution on the ro-tor disk.

5.3 Aerodynamic loading prediction

The aerodynamic loading at various instancesof the unsteady maneuver are illustrated in Fig-ure 11 to Figure 14. Each figure shows the az-imuthal variation of sectional normal force andsectional pitching moment (mean removed) atfour chosen radial stations.

5.3.1 Sectional normal force prediction

Overall the sectional normal force variation arewell captured by the analysis for the entire ma-neuver. The normal force waveforms are domi-nated by the presence of advancing side negativelift gradient owing to transonics and retreatingside negative lift gradient owing to flow separa-tion. Fair prediction of the normal forces indi-cates that the analysis is able to predict the largerscale aeromechanics of this flight condition cor-rectly. However, specific details of the wave-form are not well captured, particularly the load-ing impulse on the advancing side, which may becaused by transonic stall. The normal forces areless sensitive to the actual aerodynamic loadingalong the airfoil compared to the pitching mo-ments. Therefore the pitching moment variationsconstitute a more accurate metric to gauge thequality of the analytical results.

5.3.2 Sectional pitching moment prediction

At the beginning of the maneuver (Figure 11), theoperating condition is very close to high speedforward flight. The main characteristics of thewaveforms of aerodynamic loading is the pres-ence of negative lift and negative pitching mo-ments on the advancing blade. From Figure 11 it

can be clearly seen that the CFD based aerody-namics predicts the pitching moment waveformquite accurately. This is because CFD providesaccurate modeling of the advancing blade tran-sonic effects (moving shock and shock relief to-wards the tip). Accurate prediction of sectionalpitching moment leads to improved prediction ofthe elastic torsional response leading to improvedprediction of effective angle of attack (which isa combination of control pitch, elastic torsionand inflow) at each blade section. Improved pre-diction of effective angle of attack in turn leadsto improved prediction of advancing blade liftwaveform.

As the aircraft engages on the longitudinalpull-up the pitch attitude and aircraft angle of at-tack increase leading to an increased thrust. Thehigher sectional angle of attack caused by thecombination of control pitch, aircraft pitch rateand inflow transients causes flow separation andeventual stall on the retreating side of the rotor.The high frequency torsional response caused bythe impulsive nose down pitching moment causesan elastic torsional response which relieves thehigh angle of attack momentarily causing theflow to reattach. However, within a few de-grees of azimuthal sweep the elastic torsional re-sponse becomes out of phase with the controlpitch inducing a higher sectional angle of attackand leading to another stall event. The presenceof these two distinct stall events are most pro-nounced in revs 12-24 of the maneuver when theaircraft attains the maximum thrust level. Thepitching moment excursions caused by the stallevents are clearly visible in the sectional pitch-ing moment plots (Figure 12(b), Figure 13(b) andFigure 14(b)). The analysis shows fair correla-tion in the prediction of these stall events. Inparticular, the magnitude of the stall events areunderpredicted and the second stall cycle showsphase error with the experimental data. Thereis a third stall event clearly visible in the ex-perimental data on the advancing side of the ro-tor disk. The analysis only predicts a weak stallevent on the advancing side when compared withthe experiment. This is consistent with the re-sults obtained by Bhagwat et al. [12]. The inac-

14


curacies in the inflow distribution from the singletip free wake model may contribute to this under-prediction. Moreover, unsteady RANS compu-tations suffer from large turbulence model sensi-tivities in resolving incidence of separation, reat-tachment and shock-boundary layer interaction,all of which are significant in this case.

As the aircraft recovers from the pull-up thehigher angle of attack is relieved by a nose-downpitching attitude and pitch rate. This results indecreased intensity of the retreating blade stallevents and disappearance of the advancing bladestall event (revolutions 23-24). The analysisshows improved correlation at these instances inresolving the pitching moment waveforms (Fig-ure 14(b)).

5.4 Structural loading prediction

Accurate prediction of rotor blade structuralloads is important for design considerations, andvery challenging for this demanding maneuver-ing flight condition.

Four rotating frame loads are presented forcomparison with test data: torsion moment at30% R, pushrod force, normal bending momentat 50% R, and edgewise bending moment at 50%R. In each case, the variation of the half-peak-to-peak amplitude is presented, followed by the de-tails of the waveform. For clarity and in order toallow comparison with published flight test data,the waveform plots are shown only for four se-lected 2-revolution frames spanning the maneu-ver: revolutions (1-2), (15-16), (19-20), and (23-24).

First, rotor blade torsion moment at 30%blade radius are represented in Figures 15 and 16.The torsion moment strongly correlates with thepushrod load, presented in Figures 17 and 18.Figure 15 shows that the peak-to-peak torsionmoment trend is predicted satisfactorily, howeverthe sudden increase in vibratory amplitude whichoccurs at around rev 7 in the test data is notpredicted until rev 12, possibly due to the inac-curacies in stall prediction. The maximum tor-sion moment amplitude is also over-predicted byabout 30%. However, details of the waveform

for key phases of the maneuver are well captured,as shown in Figure 16, which clearly shows thelarge stall-related oscillations on the retreatingside under high normal loading, especially for rev19-20.

The related pushrod load for blade 1 is shownin Figures 17 and 18, from which similar obser-vations can be made: satisfactory prediction ofthe peak-to-peak amplitude, however with a 5-revolution delay in the onset of the amplitude in-crease, and good prediction of the key features ofthe waveform.

Results for the rotor blade normal bendingmoment at 50% blade radius are shown in Fig-ures 19 and 20. For this blade load, both thepeak-to-peak amplitude variation and details ofthe waveform are very well predicted, consistentwith the accurate prediction of the sectional lift.However, the peak-to-peak amplitude of the nor-mal bending moment is slightly under-predictedat the end of the maneuver (by a factor of 0.7).This is also consistent with the under-predictionof final total rotor thrust seen in Figure 9.

Finally, results for blade edgewise bendingmoments at 50% blade radius are shown in Fig-ures 21 and 22. In this case, the peak-to-peakvariation trend is captured satisfactorily, withmaximum amplitude at around rev 20, but theamplitudes are the start and at the end of the ma-neuver are quite under-predicted (by a factor ofabout 0.4). Also, details of the waveform are notvery well predicted for the edgewise bending mo-ment compared to the other blade loads.

6 Conclusions

This paper presented correlation with test datafor a tightly coupled CSD/CFD analysis simulat-ing a maneuvering flight condition of the UH60Ahelicopter. The following conclusions could bedrawn on the overall accuracy of the simulation:

1. The total rotor thrust variation during themaneuver is well predicted for the pull-uppart of the maneuver, with a peak rotorlift close to 30000 lb. However, the rotorthrust variation during the recovery part of

15


the maneuver is under-predicted by about30%.

2. Main features of the sectional lift variationare well predicted compared to flight testdata for the entire duration of the maneu-ver. Advancing side transonics and retreat-ing side flow separation that occurs at highload factors are well captured.

3. Sectional pitching moments are not pre-dicted satisfactorily. The stall events oc-curring at high load factors on the retreat-ing side of the rotor disk are captured butnot resolved accurately; the advancing sidetransonic stall is not well captured.

4. Structural loads prediction is good for thenormal bending moment at 50% R (bothpeak-to peak variation and waveform), sat-isfactory for the torsion moment at 30%R and pushrod loads (increase in peak-to-peak amplitude delayed by about 5 revscompared to test data, good waveform pre-diction), and less than satisfactory for theedgewise bending moment at 50% R (largeunder-prediction of peak-to-peak ampli-tude).

This paper forms another link in the chain ofresearch looking at improving the state-of-the-artin rotorcraft aeromechanics prediction. The re-sults presented here agree with prior observationsand further confirm the efficacy of CFD/CSDanalysis in predicting aerodynamic and structuraldynamic loading behavior during unsteady ma-neuvers. Moreover, the present study shows thecapability of the wake coupling approach to pro-duce results with similar levels of accuracy as thewake capturing approach. The wake coupling ap-proach may be favored for preliminary design ap-plications because of its faster execution time.

Significant modeling challenges still exist infurther improving the prediction of rotorcraftaeromechanics. The most apparent ones that canbe noted from the present work are in the pre-diction of stall incidence and reattachment whichneeds to be addressed by studies with higher

grid resolution as well as improved turbulencemodeling. Moreover, current studies of rotor-craft maneuvers are still limited in scope becauseof they rely heavily on measured flight dynamicdata. Therefore, another improvement that can beconsidered is full integration with flight dynamicmodeling.

7 Acknowledgments

We acknowledge the support from the Army Re-search Laboratory with Dr. Mark Nixon andMatthew Wilbur as technical monitors. We thankDr. Olivier Bauchau at Georgia Tech for pro-viding the DYMORE code. We are grateful toDr. Hyeonsoo Yeo, Dr. Mahendra Bhagwat, Dr.Robert Ormiston and Dr. Robert Kufeld at NASAAmes for sharing their thoughts and permittingusage of the published experimental data. Wewould also like to thank Dr. James Baeder andBen Silbaugh from University of Maryland forreviewing the paper.

References

[1] William G. Bousman, “Putting the Aero BackInto Aeroelasticity”, 8th Annual ARO Work-shop on Aeroelasticity of Rotorcraft Systems,University Park, PA, October, 1999.

[2] Datta, A., Sitaraman, J., Chopra., I, and Baeder,J., “Analysis Refinements for Prediction of Ro-tor Vibratory Loads in High-Speed ForwardFlight”, American Helicopter Society 60th An-nual Forum, Baltimore, MD, June 2004.

[3] Sitaraman, J., Datta., A., Baeder, I. and Chopra,I., “Coupled CFD/CSD Prediction of RotorAerodynamic and Structural Dynamic LoadsFor Three Critical Flight Conditions”, 31st Eu-ropean Rotorcraft Forum, Firenze, Italy, Sep 13-15, 2005.

[4] Potsdam, M., Yeo, Hyeonsoo, Johnson, Wayne,“Rotor Airloads Prediction Using Loose Aero-dynamic/Structural Coupling”, American Heli-copter Society 60th Annual Forum, Baltimore,MD, June 7-10, 2004.

[5] Altmikus, A. R. M., Wagner, S., Beaumier, P.,and Servera, G., “A Comparison : Weak versusStrong Modular Coupling for Trimmed Aeroe-

16


lastic Rotor Simulation”, American HelicopterSociety 58th Annual Forum, Montreal, Quebec,June 2002.

[6] Pomin, H. and Wagner, S. “Aeroelastic Analy-sis of Helicopter Rotor Blades on DeformableChimera Grids,” Journal of Aircraft, Vol. 41,No. 3, May-June 2004.

[7] Sitaraman, J., Baeder J., D. and Chopra, I.,“Validation of UH-60 Rotor Blade Aerody-namic Characteristics Using CFD”, 59th An-nual Forum of the American Helicopter Society,Phoenix, 2003.

[8] Duraisamy, K., Sitaraman, J. and Baeder, J.,“High Resolution Wake Capturing Methodol-ogy for Improved Rotor Aerodynamic Compu-tations”, 61st Annual Forum of the AmericanHelicopter Society, Dallas, Texas, 2005.

[9] Sitaraman, J., Baeder J. D., and Iyengar, V.,“On the Field Velocity Approach and Geomet-ric Conservation Law for Unsteady Flow Sim-ulations”, 16th AIAA Computational Fluid Dy-namics Conference, Orlando, Florida, June 23-26, 2003.

[10] Sitaraman, J. and Baeder, J. D., “Evaluationof the Wake Prediction Methodologies used inCFD Based Rotor Airload Computations”, 24thApplied Aerodynamics Conference 5 - 8 June2006, San Francisco, California.

[11] Bhagwat, M., Ormiston, R., Saberi, H. andXin, H.,“Application of CFD/CSD Couplingfor Analysis of Rotorcraft Airloads and BladeLoads in Maneuvering Flight”, 63rd forumof the American Helicopter Society, VirginiaBeach, VA, May 1-3, 2007.

[12] Bhagwat, M. and Ormiston, R., “Examina-tion of Rotor Aerodynamics in Steady andManeuvering Flight Using CFD and Conven-tional Methods”, AHS Specialists Conferenceon Aeromechanics, San Francisco, CA, Jan. 23-25, 2008.

[13] Abhishek, A., Datta, A., and Chopra, I., “Com-prehensive Analysis, Prediction, and Validationof UH60A Blade Loads in Unsteady Maneuver-ing Flight”, AHS Specialists Conference of theAmerican Helicopter Society, Jan 23-25, SanFrancisco, 2008.

[14] Silbaugh, B., and Baeder, J.D., “CoupledCFD/CSD Analysis of a Maneuvering Ro-

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[15] Srinivasan, G.R., and Baeder, J.D., “TURNS:A Free-wake Euler/Navier-Stokes NumericalMethod for Helicopter Rotors,” AIAA Journal,31(5), 1993.

[16] Bauchau, O. A. and Kang N.K., “A MultibodyFormulation for Helicopter Structural DynamicAnalysis”, Journal of the American HelicopterSociety, Vol 38, No 2, April 1993, pp 3 - 14.

[17] Jameson, A., and Yoon, S., “Lower-Upper Im-plicit Schemes with Multiple Grids for the EulerEquations”, AIAA Journal, Vol. 25, No. 7, 1987,pp. 929-935.

[18] Yoon, S. and Jameson, A., “An LU-SSORScheme for the Euler and Navier Stokes Equa-tions”, AIAA paper 1987-600, Aerospace Sci-ences Meeting, 25th, Reno, NV, Jan 12-15,1987.

[19] Vinokur, M., “An Analysis of Finite-Differenceand Finite-Volume Formulations for Conserva-tion Laws”, Journal of Computational Physics,Vol.81, No.2, March 1989, pp. 1-52.

[20] Pulliam, T. and Steger, J., “Implicit FiniteDifference Simulations of Three DimensionalCompressible Flow”, AIAA Journal, Vol.18, No.2, 1980, pp. 159-167.

[21] Bauchau, O.A., Bottasso, C.L., and Trainelli,L., “Robust integration schemes for flexiblemultibody systems”, Computer Methods inApplied Mechanics and Engineering, 192(3-4):395-420, 2003.

[22] Peters, D.A., and He, C.J., “Finite state inducedflow models. Part II: Three-dimensional rotordisk”, Journal of Aircraft, Vol.32, 1995, pp.323-333

[23] Bhagwat, M. and Leishman, J. G., “Stabil-ity, Consistency and Convergence of Time-Marching Free-Vortex Rotor wake Algorithms”,Journal of American Helicopter Society, Jan-uary 2001, pp 59-71.

[24] Roget, B.,”Simulation of Active Twist and Ac-tive Flap Control on a Model-Scale HelicopterRotor”, 24th Applied Aerodynamics Confer-ence 5 - 8 June 2006, San Francisco, California.

[25] Squire, H. B., “The Growth of a Vortex in Tur-

17


bulent Flow”, Aeronautical Quarterly, Vol. 16,August 1965, pp. 302-306.

[26] Weissinger, J., “The Lift Distribution on Swept-Back Wings”, NACA TM 1120, March 1947.

[27] Datta, A., “Fundamental Understanding, Pre-diction, and Validation of Rotor VibratoryLoads in Steady Level Flight”, Ph.D. thesis,University of Maryland at College Park, 2004.

[28] Kufeld, R. M., Johnson, W., “The Effects ofControl System Stiffness Models on the Dy-namic Stall Behavior of a Helicopter”, Amer-ican Helicopter Society 54nd Annual Forum,Washington, D.C., May 20-22.

[29] Bousman, G., and Kufeld, R. M., Balough, D.,Cross, J. L., Studebaker, K. F., Jennison, C. D.,“Flight Testing the UH-60A Airloads Aircraft”,50th Annual Forum of the American HelicopterSociety, Washington, D.C., May, 1994.

[30] Kufeld, R. M., “High Load Conditions Mea-sured on a UH-60A in Maneuvering Flight”,Journal of the American Helicopter Society,Vol. 43, (3), July 1998, pp. 202-211.

[31] McHugh, F.J., “What are the lift and Propul-sive Force Limits at High Speeed for the Con-ventional Rotor ?”, American Helicopter Soci-ety 34th Annual Forum, Washinton D.C., May1978.

Copyright Statement

The authors confirm that they, and/or their com-pany or institution, hold copyright on all of theoriginal material included in their paper. Theyalso confirm they have obtained permission, fromthe copyright holder of any third party materialincluded in their paper, to publish it as part oftheir paper. The authors grant full permission forthe publication and distribution of their paper aspart of the ICAS2008 proceedings or as individ-ual off-prints from the proceedings.

18


0 0.5 1 1.5 20.05

0.1

0.15

0.2

0.25

Cn*M

2

r/R=0.6750

0 0.5 1 1.5 2−0.1

0

0.1

0.2

0.3r/R=0.8650

0 0.5 1 1.5 2−0.2

−0.1

0

0.1

0.2

0.3

Time (rotor Revolutions)

Cn*M

2

r/R=0.9200

0 0.5 1 1.5 2−0.2

−0.1

0

0.1

0.2

0.3


r/R=0.9650

DataAnalysis

(a) Normal force variation

0 0.5 1 1.5 2−0.01

−0.005

0

0.005

0.01

Cn*M

2

r/R=0.6750

0 0.5 1 1.5 2−0.02

−0.01

0

0.01r/R=0.8650

0 0.5 1 1.5 2−0.03

−0.02

−0.01

0

0.01

0.02


Cn*M

2

r/R=0.9200

0 0.5 1 1.5 2−0.03

−0.02

−0.01

0

0.01

0.02


r/R=0.9650

DataAnalysis

(b) Pitching moment variation (mean removed)

Fig. 11 Non-dimensional sectional force variation with azimuth for the first two revolutions of themaneuver

19


14 14.5 15 15.5 160.1

0.2

0.3

0.4

0.5

Cn*M

2

r/R=0.6750

14 14.5 15 15.5 160

0.2

0.4

0.6

0.8r/R=0.8650

14 14.5 15 15.5 16−0.2

0

0.2

0.4

0.6


Cn*M

2

r/R=0.9200

14 14.5 15 15.5 16−0.2

0

0.2

0.4

0.6


r/R=0.9650

DataAnalysis


14 14.5 15 15.5 16−0.04

−0.02

0

0.02

0.04

Cn*M

2

r/R=0.6750

14 14.5 15 15.5 16−0.1

−0.05

0

0.05

0.1r/R=0.8650

14 14.5 15 15.5 16−0.06

−0.04

−0.02

0

0.02

0.04


Cn*M

2

r/R=0.9200

14 14.5 15 15.5 16−0.04

−0.02

0

0.02

0.04


r/R=0.9650

DataAnalysis


Fig. 12 Non-dimensional sectional force variation with azimuth for the revs 15-16 of the maneuver

20


18 18.5 19 19.5 200

0.1

0.2

0.3

0.4

Cn*M

2

r/R=0.6750

18 18.5 19 19.5 20−0.2

0

0.2

0.4

0.6r/R=0.8650

18 18.5 19 19.5 20−0.2

0

0.2

0.4

0.6


Cn*M

2

r/R=0.9200

18 18.5 19 19.5 20−0.2

0

0.2

0.4

0.6


r/R=0.9650

DataAnalysis


18 18.5 19 19.5 20−0.03

−0.02

−0.01

0

0.01

0.02

Cm

*M2

r/R=0.6750

18 18.5 19 19.5 20−0.05

0

0.05r/R=0.8650

18 18.5 19 19.5 20−0.05

0

0.05


Cm

*M2

r/R=0.9200

18 18.5 19 19.5 20−0.06

−0.04

−0.02

0

0.02

0.04


r/R=0.9650

DataAnalysis



21


22 22.5 23 23.5 240

0.1

0.2

0.3

0.4

Cn*M

2

r/R=0.6750

22 22.5 23 23.5 24−0.2

0

0.2

0.4

0.6r/R=0.8650

22 22.5 23 23.5 24−0.4

−0.2

0

0.2

0.4

0.6


Cn*M

2

r/R=0.9200

22 22.5 23 23.5 24−0.2

0

0.2

0.4

0.6


r/R=0.9650

DataAnalysis


22 22.5 23 23.5 24−0.04

−0.02

0

0.02

Cm

*M2

r/R=0.6750

22 22.5 23 23.5 24−0.05

0

0.05r/R=0.8650

22 22.5 23 23.5 24−0.05

0

0.05


Cm

*M2

r/R=0.9200

22 22.5 23 23.5 24−0.05

0

0.05


r/R=0.9650

DataAnalysis



22


0 5 10 15 20 25 30 35 400

200

400

600

800

1000

1200

1400

Tor

sion

mom

ent a

t 30%

R,

1/2

pea

k−to

−pe

ak (

lb−

ft)


dataanalysis

Fig. 15 Torsion moments at 30%R, half peak-to-peak variation

0 0.5 1 1.5 2

−1000

0

1000

time (rotor revolutions)14 14.5 15 15.5 16

−1000

0

1000


18 18.5 19 19.5 20

−1000

0

1000

Tor

sion

mom

ent a

t 30%

R (

lb−

ft)


−1000

0

1000

Tor

sion

mom

ent a

t 30%

R (

lb−

ft)


dataanalysis

Fig. 16 Torsion moments at 30%R, time histories (mean removed)

23


0 5 10 15 20 25 30 35 400

500

1000

1500

2000

2500

3000

Pus

hrod

#1

load

, 1/2

pea

k−to

−pe

ak (

lb)


dataanalysis

Fig. 17 Pushrod 1 load, half peak-to-peak variation

0 0.5 1 1.5 2

−2000

0

2000


−2000

0

2000


18 18.5 19 19.5 20

−2000

0

2000

Pus

hrod

#1

load

(lb

)


−2000

0

2000

Pus

hrod

#1

load

(lb

)


dataanalysis

Fig. 18 Pushrod 1 load, time histories (mean removed)

24


0 5 10 15 20 25 30 35 40200

300

400

500

600

700

800

900

1000

1100

1200

Nor

mal

ben

ding

mom

ent a

t 50%

R,

1/2

pea

k−to

−pe

ak (

lb−

ft)


dataanalysis

Fig. 19 Normal bending moment at 50%R, half peak-to-peak

0 0.5 1 1.5 2

−1000

−500

0

500

1000


−1000

−500

0

500

1000


18 18.5 19 19.5 20

−1000

−500

0

500

1000

Nor

mal

ben

ding

mom

ent a

t 50%

R (

lb−

ft)


−1000

−500

0

500

1000

Nor

mal

ben

ding

mom

ent a

t 50%

R (

lb−

ft)


dataanalysis

Fig. 20 Normal bending moment at 50%R, time histories (mean removed)

25


0 5 10 15 20 25 30 35 400

1000

2000

3000

4000

5000

6000

7000

Edg

ewis

e be

ndin

g m

omen

t at 5

0%R

, 1

/2 p

eak−

to−

peak

(lb

−ft)


dataanalysis

Fig. 21 Edgewise bending moment at 50%R, half peak-to-peak

0 0.5 1 1.5 2

−5000

0

5000


−5000

0

5000


18 18.5 19 19.5 20

−5000

0

5000

Edg

ewis

e be

ndin

g m

omen

t at 5

0%R

(lb

−ft)


−5000

0

5000

Edg

ewis

e be

ndin

g m

omen

t at 5

0%R

(lb

−ft)


dataanalysis

Fig. 22 Edgewise bending moment at 50%R, time histories (mean removed)

26

Date post:	11-Feb-2022
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PREDICTION OF HELICOPTER MANEUVER LOADS - ICAS is

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