application of computational aeroelasticity to …

APPLICATION OF COMPUTATIONAL AEROELASTICITY TODESIGN OF HELICOPTER ROTOR BLADES

Marcello RighiZurich University of Applied Sciences, Technikumstrasse 9, 8401 Winterthur, Switzerland

Keywords: helicopter aeroelasticity aerodynamics structural dynamics

Abstract

Design of efficient and stable rotors must accountfor the reciprocal influence of aerodynamic andstructural forces. It is a challenging task, whichrelies on experience and on a few, validated tools,based on low fidelity models of structure andaerodynamics. Adopting high-fidelity modelingwould provide a more accurate load predictionand more direct correlation between design pa-rameters and rotor performances.

Numerical investigation of rotor flowfieldbased on Computational Fluid Dynamics (CFD)have been performed with increasing success inthe latest ten years. The aerodynamic solver isnormally a research code customised for rotorflow. However, rotor blades are normally mod-eled as beam elements. The potential for im-provement might be represented by a more ac-curate, unsteady modeling of turbulence and byhigh-fidelity mdoeling of the structure.

In the latest few years - outside of the heli-copter world - many software packages have beenmade available, which can couple Aerodynamicsand Structure. They do not account for a heli-copter control system and for helicopter trim ingeneral. However, dynamic mesh, accurate mod-eling of turbulence and flexibility in boundaryconditions might make them suitable also for ro-tor flow - provided they can be coupled to an ex-ternal ”trim” programme.

This paper presents the first incomplete re-sults of a test, where the applicability of two pow-erful general purpose simulation tools is assessedon rotors.

1 Introduction and motivation

The flow around a rotor blade can be unsteady,three dimensional, transonic with shocks (onthe advancing blade), reversed (on the retreatingblade). It can contain dynamic stalls and a vorti-cal wake. Its evolution depends not only on rigidmotion of the blade - rotation around the flap, lagand pitch hinges - but also on the elastic deforma-tions. The blade displacements - rigid and elastic- depend on airloads. The fully coupled aeroelas-tic problem must account for the mutual depen-dence between structure and aerodynamics. Be-sides, the problem is strongly nonlinear: a smallchange is one of the design parameters mightprovide a significant change in the dynamic re-sponse.

Traditionally, industry has relied on the so-called comprehensive codes, which are based onlow-fidelity models: a ”lifting-line” representa-tion of the blade aerodynamics and ”beam ele-ments” for the structure.

As Bousman pointed out in 1999 [6] com-prehensive codes are limited in their capabilityto mimic the aerodynamic phaenomena and theirinteraction with the rotor motion. This resultsin significant difference between predicted andmeasured airloads, especially on articulated ro-tors (i.e. where the motion is larger). As a con-sequence, the design process cannot rely on ananalysis tool able to conveniently link changes inparameters to changes in loads.

Rotor design is therefore a relatively slow andinefficient process, as compared to the one ofaerodynamic surfaces of fixed wing aircraft and

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of rotating elements in turbomachinery.However, the last ten years of research have

provided significant successes in the predictionof airloads on rotors. These prediction are basedon a numerical coupled approach, where the flowis simulated with the aid of Computational FluidDynamics (CFD) tools using prescribed movingboundary conditions.

The computations normally include a com-prehensive rotor code, coupled to Euler (referfor instance to [25] [1]) or Navier-Stokes (for in-stance [19] [20] [22] [21]) solvers.

The structure has been modeled in differentways but - as in comprehensive codes - mostlyrelies on a modified beam model or on monodi-mensional finite elements. In some cases ([12])Navier-Stokes equations are coupled to a rigid ro-tor.

In virtually all cases, simulations use ”rotor”CFD codes, i.e. research codes written or mod-ified especially to account for the characteristicsof rotor flow. The same can be said for the struc-tural modeling. If on one hand, customizationhas provided significant advantages in terms ofefficiency, it has on the other hand limited thebenefits of the latest developments in CFD andComputational Structure Dynamics (CSD) tools,such as more sophisticated modeling of turbu-lence and efficient adaptive grid refinement onthe CFD side and transient solutions togetherwith the flexibility to introduce a nonlinear ma-terial behavior on the CSD side. Moreover recentsoftware packages have been developed also withthe aim of having much simpler and more flexi-ble interfaces with external programmes as wellas a higher computational efficiency.

As open source software has greatly im-proved its reliability over the latest few years, itmay also be considered. It has the advantages ofincluding the “latest” algorithms and, by defini-tion, offering an endless flexibility. Refer for in-stance to [13] [14] [18] for OpenFOAM, [9] [8][7] for Overture, [29] for Nektar, [3] [2] [4] forPETs.

Open source CSD codes are also very power-ful. For instance they offer explicit integration intime. Refer for instance to [23] for Code ASTER.

The broad availability of these and other ”ad-vanced” features in simulation tools - which ad-dress a variety of industries - might let us wonderwhether also non-rotor specific tools can be em-ployed on the challenging problem of predictingrotor airloads and assess dynamic stability.

The aim of this work is to test the applica-bility of general purpose software packages tothis aim. Two test case are presented wherethe commercial package Ansys Multiphysics andthe open source package OpenFOAM have beenused and tested on simple cases. The test still isin an early phase and no comparison with exper-imental data can be shown at this stage. Thsi pa-per focuses therefore on a single deliverable: theapplicability of powerful general purpose tools.

This paper is organised as follows: The po-tential for improvement is described, in the formof a list of requirements for CFD, CSD and cou-pling. Two test cases are then presented. Thefirst one - involving an industry-standard carbonand glass composite tail rotor blade - relies onthe commercial package ANSYS which providesCFD, CSD and also the coupling between aero-dynamics and structure computational domains.In the second test case, the open-source softwarepackage OpenFOAM in a first temporary stage iscoupled to a helicopter ”trim” code, relying on afinite-elements description of the blade.

2 Potential for improvement in current CFD/ CSD rotor analysis

2.1 Potential for improvement in CFD

The improvement of CFD over ”lifting-line”models is recognized. CFD provides a nonlin-ear, unsteady description of the flow surround-ing the rotor. Nonlinearities include: high angleof attack, reverse flow, compressibility and wake.Unsteady phaenomena occur when the reducedfrequency of the system is small enough. Loadprediction at high speed (advance ratio µ' 0.40)is a typical ”difficult” test case, where CFD hasprovided results significantly more accurate thansimple models. Refer for instance to [11], [22].

However, the results are yet not perfect: com-

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APPLICATION OF COMPUTATIONAL AEROELASTICITY TO DESIGN OF HELICOPTER ROTORBLADES

parison with experiments still shows some phasedifferences in loads. The requirements for a suc-cessful CFD simulation of rotor flow could besummarizes as follows:

1. Correct representation of compressibilityeffects

2. Time accurate integration

3. Wake capturing and resolution

4. Correct representation of the flow on theblade, including boundary layer and detec-tion of flow separations

Whereas requirements 1 and 2 can be ”sim-ply” fullfilled with the use of unsteady, compress-ible solvers of the Navier-Stokes equations, re-quirements 3 and 4 require a slightly longer anal-ysis.

2.1.1 Wake Capturing

An additional item in the wishlist - requirement 3- is the capability to fully resolve the rotor wake.This means that the blade motion and loadingmust be accurately modeled in order to capturethe starting points and strength respectively ofthe vortices. Moreover, the vortex wake mustbe properly convected through the domain. Al-though in some cases the wake can be modeledand passed over to the CFD solver as boundaryconditions, being able to capture the wake in ageneral case, as part of the resolved flowfields, isone of the most interesting aspects of applicationof CFD to rotor flow. In forward flight solutionof the flowfields around the whole rotor is nec-essary together with the capability to rotate therotor inside the computational domain as the for-ward component of speed and wake do not ro-tate. As pointed out by [16], [10] and [26] thecapability to fully resolve tip vortices for the du-ration of their life until they meet the followingblade would require enormous computational re-sources. Note that an overset (chimera) grid ap-proach is necessary in forward flight. The rotorwake play a critical role. The effects of the wakevortices on the blade flowfields con be dramatic

in some flight conditions. It is well known thatblade-vortex-interaction (BVI) in descent flowis accountable for significant noise generation.Note that noise reduction is one of the most im-portant requirements in rotor design.

2.1.2 The Flow on the Blade

Flow separations and reattachments are correctlycaptured only if the turbulent phanomena areproperly represented in a way that is physicallymeaningful. Whereas two-equation models areto be considered as reliable, the more appropri-ate way to represent turbulent structures in ro-tor flow would be Large Eddy Simulation (LES).LES consists in explicitly solving large turbulentanisotropic structures and modeling the smallerones, which tend to be more homogeneous .

Rotor flow is characterised by large, unsteadyturbulent structures: the rotor wake ”built” by thevortices shed by the blades, the vortices producedin dynamic stall. In the ”turbulent wake” work-ing state of the rotor (see for instance [15]), theflow becomes a set of large, disorganized turbu-lent structures.

LES is being used for over twenty years in re-search ([17], [24] )and, more recently, in indus-trial applications.

In general, LES is more demanding thanRAS: it requires a finer mesh where turbulentstrctures are expected and time-accurate integra-tion. However, rotor flow requires in any case,time-accurate solution and sufficient resolution tocapture the rotor wake. The additional cost ofLES might not be that high.

Moreover, requirement 4, include the cor-rect and accurate representation of boundary mo-tion. Boundary motion is dictated by the rigidand elastic displacements of the blade, computedwith CSD and a ”trim” code. Dynamic mesh mo-tion is a feature which is normally included inCFD codes. It must be noted, however, that itmany cases it provides additional fragility to thenumerical solution.

Fulfillment of requirements 3 and 4 is de-manding: many of the coupled CFD/CSD anal-ysis published so far rely on simple algebraic tur-

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bulence model and prescribed wake.

2.2 Potential for improvement in CSD

Modal condensation and, in general, beam mod-els reliably represent the behavior of a rotorblade in terms of displacements and rotations ofthe reference line. The interaction with aerody-namic forces can be suitably reproduced. How-ever they do not allow a convenient and accu-rate reconstruction of stress and strain distribu-tion in the whole blade structure. Root and tipregions are ”notoriously” tridimensional in bothexternal shape and material layout. In a de-sign process and especially in an weight sav-ing exercise or in an optimization process (wherethe design parameters are systematically variedin given ranges) designers like to examine thestress and/or strain distribution in every compos-ite layer of every structural element.

It is useless to remind how the human intelli-gence and creativity is still superior to numericaldesign techniques, as far as geometrically com-plex composite parts are concerned. It is there-fore of the highest importance to provide seniordesigners and engineers with detailed informa-tion, as it is done in the design process of non-rotating parts.

A separate, completely different remark con-cerns the capability to reproduce the behaviorof the material in special conditions, outside ofthe ”normal” elastic range, such as the state ofstress due to ultimate loads or simulation of dam-aged conditions, where the material could en-ter the plastic range or the simulation could in-clude damage propagation - analysis normallyconducted on non-rotating parts. Simulation ofthe effects of ageing could also be a possibility.How many times discrepancies between flighttest measurements and theory are justified with”additional structural damping due to age of therotor”?

2.3 Potential Improvement in CFD / CSDCoupling

The displacement of the rotor blade includes arigid motion, dictated by the orientation of the

swashplate, and elastic deformation due to the ac-tion of aerodynamic and inertial loads. As theorientation of the swashplate (i.e. the controls)depends on the force balance on the whole ro-tor or on the whole helicopter, depending on thescope of the analysis, the rigid motion cannot ingeneral be resolved in a single-blade analysis.

The most pragmatic approach relies on a”trim” code - or comprehensive code - which pre-scribes the controls and the position of the blade.On a rigid rotor, this would mean collective andcyclic pitch, and a sufficient number of harmon-ics of rigid flap and lag. The description of themotion of a flexible rotor requires the harmonicsof a sufficient number of degrees of freedom, re-ferring either to nodal displacements (if FEM) ormodal or a combination.

A more ambitious option would consist incoupling CFD with a high-fidelity structuralmodel, typically a Finite Element (FE) model. Inthis case, either the FE software can include rigidmotion or a ”trim” code would still be necessary.

In all cases, coupling is a critical phase of theprocess. Coupling can be ”tight” (”strong”) or”loose” (”weak”). In the tight coupling method-ology, information between CFD and CSD istransferred at each time step. Subiterarion are of-ten necessary, in order to enforce consistence ofall flow and displacement fields.

In the loose coupling approach, loads and dis-placements (or velocities) are only periodicallypassed. In rotor analysis, typically once per rev-olution. Loose coupling has proven to be moreconvenient in a number of simulations. Detailsof one coupling framework can be found in theabove references or in [27] [28].

Potential for improvement lies in the possi-bility of coupling high fidelity structural mod-els with CFD, either directly or through a ”trimcode” which would become a sort of ”motionmanager”. Loose coupling normally assumes pe-riodic flow and motion. This is a good assump-tion for load prediction, as transient are normallya fraction of a revolution.

However, the capability to handle fully un-steady behavior might help understanding spe-cific flight conditions such as turbulent wake and

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autorotation flight states.

3 Evolution of the Requirements as a Func-tion of Rotor Evolution

The requirements stated above might becomemore significant if we consider the evolution ofrotors and helicopters. Tilt rotors and, possibly,compound helicopters, have ”rigid” rotors but flyat higher speed and experience potentially higherloads. The accurate prediction of compressibleeffects might become more important.

Accurate airloads prediction is critical to as-sess and reduce the vibratory and noise level -probably the highest priorities in design objec-tives.

4 Case study 1: hover flight analysed withAnsys Multiphysics

In a first test case, the turbomachinery moduleof Ansys has been used. The steady state optionhas been used. Airloads are computed by CFX(the CFD solver part of the Ansys package) onan undeformed blade geometry and passed overto Ansys FEM which computes the structural de-formations. The process is iterated until conver-gence is reached. Its application is straight for-ward; high-fidelity structural and aerodynamicsmodels are generated and used at reasonable cost.The blade chosen is an industry-standard tail ro-tor blade, made out of carbon and glas fibers.

The flowfield is plausible but no quantita-tive comparison of flow quantities has been con-ducted. Results impress for the abundance of in-formation, as it is documented in figure 4. Thehigh-fidelity structural (3) model provide a com-plete view on strain and stresses in every elementof the structure. This analysis methodology couldbe used in practice also in industrial environment;it can be easily set up and provides all the infor-mation designers need.

However, its practical use is limited to hoverflight, as we could not devise an easy way toproperly account for rotor dynamics in forwardflight. The aerodynamic mesh was not speciallyrefined in order to capture the rotor wake.

Fig. 1 Case study 1, the aerodynamic mesh

Fig. 2 Case study 1, flowlines computed in oneof the flight conditions tested

Fig. 3 Case study 1, a view of the FE mesh of theouter composite skin

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Fig. 4 Case study 1, dynamic stresses on one ofthe composite layers in one of the flight condi-tions tested

5 Case study 2: assessment of stability of arotor in forward flight using OpenFOAM

Analysis of forward flight is significantly moredemanding than hover flight. Loss of symmetrymakes the single-blade approach insufficient. Be-sides, at hight speed compressibility effects ariseon the advancing blade, pitch and flapping mo-tion relative to higher harmonics causes unsteadybehavior of the flowfields, the flow on a por-tion of the retreating blade reverses. Moreover,cyclic pitch excursion sets high requirements onthe mesh deformation algorithm.

This case study aims at testing the pre-diction of airloads with a CFD package. Atthis stage, boundary motion has been prescribed(taken from the solution of a helicopter ”trim”programme) as well as the rotor wake (modeledexternally). No high-fidelity structural model hasbeen used in the ”trim” code. Objective of thetest was the ease for the user to:

• Implement Dynamic boundary conditions,prescribed externally

• Implement the dynamic motion of the com-putational mesh

• Conduct a time-accurate simulation

• Provide a steady state converged solutionas starting point of the unsteady simulation

• Assess the sensitivity to mesh refinement

• Assess the effects of compressibility

• Assess the difference between different tur-bulent models

• Assess the compatibility of the above men-tioned parameters

The open source package OpenFOAM hasbeen chosen for its versatility in choosing solverand turbulence models and its flexibility in ac-cepting time varying, mapped boundary condi-tions.

A number of simulations have been con-ducted, testing various combinations of flowregimes and turbulent models, as well as meshmotion / deformation. Various solvers have beentested, they are listed in Tables 1 and 2. Note thatthe mesh has been generated analytically fromairfoil shape and twist distribution. Dynamicmesh motion has been implemented with no par-ticular difficulty despite geometrical complexityand a not-perfect-quality mesh. It must be said,though, that the mesh motion did not involvelarge displacements. Implementation of varioustwo-equation turbulent models was also possi-ble with no particular problem. The compress-ible solvers were also successfully tested but notwith dynamic mesh motion. The overall user’simpression is very positive. The case was set upwithin a few weeks by one person with long ex-perience on helicopters aeroealsticity but a verylimited one on OpenFOAM.

The figures 5 to 17 show some of the resultsobtained from an unsteady incompressible simu-lation, conducted for about one degree in azimuthin a flight condition where the blade undergoes anegative flapping motion and a positive pitch ro-tation. Various mesh sizes have been used. Thefigures shown have been obtained on a relativelycoarse mesh (about 1,4 million points). The com-putation has been carried out on a standard CoreDuo processor and has required about 9000 sec.

The rotor of an average light twin helicopterhas been taken as reference. The airfoil is theOA212 on the whole blade. The tip has been

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Solver FlowsimpleFoam steady state, incompressiblerhoSimpleFoam steady state, compressiblepisoFoam transient, incompressiblesonicFoam transient, compressible

Table 1 OpenFOAM fixed mesh solvers tested - inall cases were RANS and LES turbulence model-ing available

Solver FlowpimpleDyMFoam transient, incompressible

Table 2 OpenFOAM dynamic mesh solver tested- RANS and LES turbulence modeling are avail-able

modeled with higher than average droop andsweep. The blade is therefore realistic but notreal.

Fig. 5 Case study 2, The computational domain

6 Conclusions

Case studies 1 and 2 might contribute to pro-vide the confidence that general purpose simu-lation packages such as OpenFOAM and AnsysMultiphysics can be employed to analyse the he-licopter rotor in hover and forward flight. On theCFD front, the added value would be a more ac-curate modeling of turbulent structures and, pos-sibly, more efficient computations. Concerning

Fig. 6 Case study 2, Blade Surface

Fig. 7 Case study 2, Pressure distribution on theupper blade side

Fig. 8 Case study 2, Distribution of turbulent ki-netic energy on the upper blade side

Fig. 9 Case study 2, Distribution of turbulent dis-sipation ω on the upper blade side

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Fig. 10 Case study 2, Blade tip at start and finaltime

Fig. 11 Case study 2, Blade at start and final time

Fig. 12 Case study 2, Velocity flowfield at Y=40%




Fig. 16 Case study 2, Lift coefficient of the blade

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Fig. 17 Case study 2, Drag coefficient of the blade

CSD, high-fidelity models could provide the de-signers with a much better view on how designparameters influence rotor performances.

In the case of axial and hover flight, special“turbomachinery” modules, available for bothsoftware packages, provide the proper handlingof centrifugal and Coriolis forces for both struc-ture and airflow. Hovering rotor analysis cantherefore be managed as a special case of a tur-bomachinery rotating element, with much fewer,more slender blades, hinged in the case of articu-lated hub.

In the case of forward flying rotor, the avail-able off-the-shelf simulation codes must be cou-pled to a ”trim” programme, able to determine theposition of the swashplate (hence collective andcyclic pitch controls) corresponding to a givenflight condition (forward speed, thrust). Open-FOAM can very well cope with the requirementsfor a single blade flow simulation, includingcompressibility, turbulence, dynamic flow vari-ations, dynamic motion of the mesh. It canalso work with ”sliding” meshes and with over-set meshes, but not out-of-the-box, it must becoupled to additional software ([5]). Simulationof the whole rotor would therefore require ad-ditional effort. However, it must be noted thatOpenFOAM is not the only available tool and thatthe analysis in the present paper has been limitedto standard available solvers.

A secondary motivation for this work, is thatthe applicability of general purpose analysis toolsmight lower the ”entry fee” to rotor design. This

could be beneficial to related industries such aswind turbine and rotorcraft UAVs, which mightnot have the same resources that helicopter man-ufacturers have.

Copyright Issues

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Copyright Statement

The authors confirm that they, and/or their company ororganization, hold copyright on all of the original ma-terial included in this paper. The authors also confirmthat they have obtained permission, from the copy-right holder of any third party material included in thispaper, to publish it as part of their paper. The authorsconfirm that they give permission, or have obtainedpermission from the copyright holder of this paper, forthe publication and distribution of this paper as part ofthe ICAS2010 proceedings or as individual off-printsfrom the proceedings.

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