numerical tools for contra-rotating open-rotor …

NUMERICAL TOOLS FOR CONTRA-ROTATINGOPEN-ROTOR PERFORMANCE, NOISE AND VIBRATION

ASSESSMENT

M. Laban, J.C. Kok, B.B. PranantaNational Aerospace Laboratory NLR, Amsterdam, the Netherlands.

Keywords: Contra-Rotating Open-Rotor, CFD, CAA, FEM

Abstract

Increasing the by-pass ratio of turbofans was suc-cessful in the past decades to increase the propul-sive efficiency. The ultimate in this sense is theContra-Rotating Open-Rotor (CROR) which of-fers a potential of 20% fuel burn reduction rela-tive to classical turbofan engines in service today.Mitigating the inherent noise & vibration issuesassociated with this propulsion concept, calls forhigh-fidelity analysis tools. This paper highlightsthe development of CFD/CAA/FEM-based toolsto address these issues.

1 Introduction

The aeronautical industry faces the challengeto counter the environmental impact due to thegrowth of air transport with low fuel burn in-novative products. The Advisory Council forAeronautical Research in Europe (ACARE) setsa 50% CO2 emission reduction target for the year2020. The past decades have shown a gradualincrease of the by-pass ratio of turbofan engineswhich was a successful measure working towardsthis goal. However, the growth of the by-pass ra-tio is accompanied by larger and heavier nacelles.At a certain point, the associated nacelle weightincrease and drag penalty outweighs the growthin propulsive efficiency. The Contra-RotatingOpen-Rotor (CROR) offers a breakthrough. Op-erating without the drag&weight penalty of alarge nacelle, the by-pass ratio is no longer alimiting factor. Operating two contra-rotating

Fig. 1 Potential 2020 transport aircraft layoutfeaturing a T-tail configuration and CROR inpusher configuration.

"stages" allows to eliminate swirl losses inher-ent to the classical "single-stage" propeller. TheContra-Rotating Open-Rotor can achieve propul-sive efficiencies of 85% at cruise conditions. Thisoffers a potential of 20% fuel burn reduction rela-tive to classical turbofan engines in service today.

Operating without a nacelle, the open-rotoris intrinsically noisier than a turbofan at equiva-lent thrust setting. The interference between thetwo rotor stages introduces rotor interaction tonesunknown for the classical single-stage propeller.For tail-mounted pusher configurations, see Fig-ure 1 for an illustration, the pylon wake inflowinto the rotor again presents an additional noisesource.

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M. LABAN, J.C. KOK, B.B. PRANANTA

Experimental and operational CROR’s in theUSA and Russia have shown that noise and vibra-tion levels of these propulsion devices are criticalindeed. Hence, the fuel burn reduction potentialis in conflict with another ACARE target: 50%reduction on perceived noise levels by the year2020.

This paper describes how FEM/CFD/CAA-based numerical tools, combined with massivelyparallel computing, can be configured towardsthe analysis of CROR concepts. Applications ofthese tools to generic rotors are included to il-lustrate how far field sound pressure levels, rotorvibrations, rotor blade loads, and rotor propul-sive efficiency can be computed. With these toolsavailable, potential noise & vibration reductionstrategies can be assessed numerically.

2 The Computational Fluid DynamicsModel

Rotor loads, vibrations and acoustics find theresource in the aerodynamics of the rotor. AContra-Rotating Open-Rotor shares some basicfeatures with the classical propeller, for whichvarious numerical techniques do exist. However,it is the vortex and viscous wake interaction be-tween the pylon and the rotors and between thefront-rotor and the aft-rotor which make the pic-ture more complex. A representation of the phys-ical phenomena specific to a Contra-RotatingOpen-Rotor requires to propagate the (tip) vor-tices and viscous wakes through the various rotorstages.

Although it is quite well possible to extendexisting propeller codes, e.g. based on lifting-lineor lifting-surface theory, to tackle this challenge,the authors have chosen to apply ComputationalFluid Dynamics (CFD) techniques.

2.1 Modeling Options

The various parts of the geometry (pylon, first-rotor, second-rotor) have their own rotation direc-tion & velocity. This can be handled by decom-posing the geometry in three separate domains.Between the domains, the flow solver data trans-

fer can be setup by means of Sliding Interfaces[1]. Two options now present themselves:

• Solve the flow around a single front and asingle aft rotor blade by means of steady-state computations in each Rotating Refer-ence Frame. Apply periodic boundary con-ditions on the domain side faces to modelthe effect of the neighboring blades in thesame rotor stage. Apply data averagingin azimuth direction over the sliding inter-faces to couple the two rotor domains.

• Expand the single blade numerical meshesto a full rotor stage. Solve the flow in time-accurate mode, in which the front and aftrotor meshes are rotated at each time step.Apply spline-based data interpolation overthe sliding interfaces to couple all three do-mains.

The first modeling option is essentially a steady-state solution which retains some averaged flowfeatures of the rotor only. The Sliding Inter-face between the two rotor stages now functionsrather as Averaging Interface which effectivelysmears out the viscous and vortical wakes be-tween the rotor stages. This approach offers veryshort problem turn around times and can be use-ful e.g. for a quick view of the rotor propulsiveperformance. Yet, this approach does not fullyaddress the issues specific to Contra-RotatingOpen-Rotors.

The second option allows for a characteriza-tion of the rotor physics at a fairly complete level.The vortical and viscous wake interaction be-tween the rotor stages can be retained. Also, non-uniform inflow into the rotor (e.g. due to a pylon)can be modeled. However, this comes at the costof a high computational effort demanding paral-lel computing to keep problem turn-around timesacceptable.

2.2 Grid Generation

Computational Fluid Dynamics computations areperformed on multi-block boundary-conformingstructured grids. The grids feature three individ-

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Numerical Tools for Contra-Rotating Open-Rotor Performance, Noise and Vibration Assessment

Fig. 2 Details of the multi-block grid near therotor blade root at the fine grid level.

ual domains (far-field, first-rotor, second-rotor)that form non-overlapping sliding grids.

A dedicated algorithm is build to automati-cally wrap an O-O block topology around a ro-tor blade. In this process, the blade number,blade row spacing and blade pitch angle are takeninto account to arrive at optimally shaped blockedges. Automating this process holds the advan-tage that blade pitch angle changes can be accom-modated without requiring manual effort.

Grid density and stretching factors are setparametrically along all block edges. This needsto be done manually once for a representative ro-tor blade. These settings are stored and appliedto all subsequent rotor blade variants. Grid di-mensions along the block edges are typically amultiple of 8, such that a sequence of sub-levelgrids are available. In practice, three grid levels(fine, medium, coarse) are used with respectively640 ·103, 80 ·103 and 10 ·103 cells per blade do-main. Figure 2 provides an example.

For time-accurate computations, the individ-ual blade grids are copied and rotated to form afull rotor stage. The outer-domain, containinge.g. a pylon or even the complete airframe, ishandmade and connects to the sliding interfaceboundaries of the rotor domains. Figure 3 showsa domain decomposition around the Smart FixedWing Aircraft project’s Contra-Rotating Open-

Fig. 3 Multi-block topology around the SFWA-CROR wind-tunnel test rig.

Rotor wind tunnel test rig. The grid features atotal of 38 ·106 cells on the finest grid level.

2.3 Flow Solver

The CFD computations are based on theReynolds-Averaged Navier-Stokes (RANS)equations combined with an explicit algebraicReynolds stress turbulence model [5, 2].

2.3.1 Rotating Reference Frame Solutions

Fig. 4 CROR propulsive efficiency map com-puted using the rotating reference frame solutiontechnique.

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Fig. 5 SFWA-CROR surface pressure distribu-tion computed with the time-accurate full-rotorsolution technique.

Figure 4 provides an example of a solution ofthe Navier-Stokes equations in the rotating ref-erence frame for the front & aft rotor blades inwhich an azimuthal data averaging is performedover the sliding grid interface. The rotor perfor-mance map shown in Figure 4 is based on com-putations for multiple blade angle settings. Engi-neering accuracy can be obtained on the mediumgrid level for which problem turn around timesare in the order of 10 minutes per data point.

2.3.2 Time-Accurate Full-Rotor Solutions

Figure 5 provides an example of the time-accurate full-rotor solution technique. A fourthorder accurate finite-volume scheme [4] is usedto solve the RANS equations. This scheme isdispersion-relation and symmetry preserving, re-sulting in low numerical dispersion and dissipa-tion. Such properties are essential to capture therotor-rotor interaction effects which result fromthe shed front rotor vortical & viscous wakes.Figure 6 shows an example of the propagationof trailing vorticity computed at the medium gridlevel (5 ·106 cells).

The temporal resolution is tuned to the spatialgrid resolution over the sliding grid interfaces.For medium grid computations this results in atime step equivalent to a rotor blade azimuth rota-

Fig. 6 Iso-vorticity contours showing the spatialpropagation of trailing vorticity shed by the rotorblades.

tion step of 0.5◦. A number of full rotor rotationsare required before the solution becomes peri-odic. The computational load of this approachis relatively high, about 10 days of computing perrotor revolution at the medium grid level employ-ing 8 CPU cores working in parallel. Note thatcomputations at the fine grid level, which is actu-ally required for a sufficient resolution of the ro-tor physical phenomena, would increase the com-putational load with a factor of 16.

2.3.3 Computing Hardware

Capturing the rotor physical phenomena bymeans of time-accurate full-rotor CFD is compu-tationally expensive. This calls for applying mas-sively parallel computing platforms. On a SiliconGraphics Altix ICE computing server with 512CPU cores, the turn-around time of a full-rotorcomputation at the fine grid level is expected tobe one week.

3 The Computational Aero Acoustics Model

A number of specific acoustic sources can beidentified for a Contra-Rotating Open-Rotor. Theapproach taken by the authors concentrates on asubset only, namely tonal noise originating fromthe steady and unsteady pressures acting on the

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Fig. 7 Kirchhoff surface keeping a certain dis-tance to the two rotors of the pylon/centre-bodymounted SFWA-CROR showing the instanta-neous pressure distribution.

rotating blades. This approach includes the so-called rotor alone tones, complemented with in-teraction tones which result from blade pressurevariation due to pylon-to-rotor and rotor-to-rotorvortical & viscous wake interactions. Also in-cluded is the sound wave propagation through thenon-uniform flow in the direct vicinity of the ro-tor blades where high gradients in the flow ve-locity persist. Shielding and reflections by theengine cowling and pylon potentially affect theacoustic source directivity and are accounted for.However, as soon as the sound waves leave theimmediate vicinity of the rotor, a straightforwardpropagation through uniform flow to the far-fieldis assumed.

Currently not included is broadband noiseoriginating from the core engine intake and ex-haust as well as broadband noise due to turbulentboundary layers. Hence, the current acoustic pre-diction will underestimate the actual rotor noise.

3.1 The Sound Source

The time-accurate CFD solution, described inChapter 2, contains both the sound generationand the propagation of the sound through thenon-uniform flow field in the immediate vicin-

Fig. 8 Far field overall sound pressure level anddirectivity.

ity of the rotor. Sound waves are captured accu-rately by employing a fourth-order finite-volumescheme with low numerical dissipation and dis-persion. The maximum frequency content is de-termined by the temporal (CFD time step) as wellas the spatial discretisation (CFD grid cell spac-ing). As a rule of the thumb, a minimum of 8grid cells per wave length are deemed necessaryto propagate a sinusoidal sound wave. Thereforethe CFD mesh size needs to be relatively small inthe region around the rotor and the surfaces (na-celle & pylon) which are to be taken into accountfor shielding/reflecting.

3.2 Sound Propagation to the Far Field

A direct approach in which CFD carries thesound waves all the way to the far field is bothprohibitively expensive and unnecessary. CFDmeshes tend to loose resolution when approach-ing the far-field and this will cause the soundwaves to dissipate numerically. Also, the flowsoon becomes quite uniform so that the wavepropagation does not require relative "expensive"solutions of the Euler equations. A practical ap-proach is to wrap a closed surface, a so-calledKirchhoff surface, around the rotor on which toextract the flow variables (pressure and pressuregradient) as function of time. A Kirchhoff inte-gral method in the frequency domain is used tocompute the sound propagation from the Kirch-hoff surface to any desired location in the far

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Fig. 9 Front rotor tone pressure waves propagat-ing over NACRE’s noise shielding U-tail.

field.Figure 7 illustrates the Kirchoff surface

around a pylon/centre-body mounted CROR. Forthis application, part of the Kirchhoff surface co-incides with the sliding mesh interface used bythe CFD solver to exchange information betweenthe rotating and stationary flow domains. Figure8 shows the corresponding far field overall soundpressure levels as function of polar angle.

3.3 Accounting for Airframe Shielding Sur-faces

Depending on the aircraft configuration, acous-tic shielding and/or reflection due to the airframesurfaces can have a significant impact on the per-ceived far field noise levels. If these need to beincorporated in the acoustic analysis, an inter-mediate modeling technique can be placed "inbetween" the full time accurate Navier-Stokesmodel around the rotor (Section 3.1) and theKirchhoff surface from which the data is extrap-olated to the far field (Section 3.2). This interme-diate model is based on time accurate solutionsof the linearized Euler equations using again afourth-order finite volume scheme as well as afourth-order Runge Kutta scheme. It does requirea volumetric meshing of the 3D space around theairframe. The mesh is boundary conforming andpreferably isotropic with 8 grid cells per wavelength to be propagated.

Figure 9 shows an illustration of a front ro-

Fig. 10 Effect of NACRE’s acoustic shieldingU-tail on far field sound pressure levels due to asingle frequency front rotor tone.

tor tone propagating over a noise shielding U-tail, computed in the context of EU-project NewAircraft Concepts REserach (NACRE). Figure 10shows the differential effect (shielding) on the farfield sound pressure levels.

4 The Aeroelastic Model

For maximum propulsive & acoustic perfor-mance, rotor blades tend to be very thin. Atthe same time, the rotor blade inflow is highlydistorted due to the pylon & upfront rotor bladewakes that impinge on the downstream blades.This leads to static as well as dynamic rotor bladeaeroelastic deformations that can be relativelylarge and may impact the rotor loads, vibration,performance and acoustic behavior. The aeroe-lastic effects are taken into account in the CFDmodel (Chapter 2) through a fluid-structure inter-action in modal space [7].

4.1 The Blade Finite Element Model

Full-scale flight CROR blades commonly featurea complex structure, comprising a metallic sup-port structure complemented with a carbon fiberlaminate skin. Scaled CROR models for windtunnel experiments usually feature a solid tita-nium or a solid carbon fiber structure.

The numerical representation of solid metal-lic CROR blades in Finite Element codes (e.g.

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Fig. 11 FE-computed first three mode shapes ofa metallic wind-tunnel model scale rotor blade.

MSC-NASTRAN) is rather straightforward. Theblade geometry is meshed using hexahedral(CHEXA) elements. The titanium materialis represented with isotropic material propertycards (MAT1). The blade root is constraint tothe rigid outer world using appropriate boundaryconditions (SPC’s).

The dynamic properties of a rotating bladeare influenced by the centrifugal, the Coriolis andthe aerodynamic forces. The centrifugal & aero-dynamic forces affect the eigenfrequencies andthe mode shapes by the change of the stiffnessproperty due to static deformation of the bladesunder these forces, i.e. the so-called pre-stressingeffect. The Coriolis force introduces damping inthe system. The dependency to these forces im-plies that the eigenfrequencies and mode shapesof rotating blades depend on the speed of rota-tion. In most cases the eigenfrequencies raisewith the increase of speed of rotation leading to astiffening effect.

To take the pre-stressing effect into account,the computation of the eigenfrequencies andmode shapes starts from a statically deformedstate as a function of the speed of rotation. Sincethe most important effect influencing the eigen-frequencies and the mode shapes comes from thecentrifugal force, the aerodynamic force is ne-glected. The computation of the static deforma-tion due to centrifugal force is carried out using

Fig. 12 The FE-mesh, the numerical versus ex-perimental eigenfrequencies, and the Cambell di-agram of a metallic wind-tunnel model scale ro-tor blade.

the RLOAD card of NASTRAN. The solution isused in a subsequent eigenvalue analysis usingspecial DMAP macros. When damping due tothe Coriolis force is included, a complex eigen-value solver has to be used (SOL107 of NAS-TRAN), otherwise a real eigenvalue solver canbe used (SOL103).

Figure 11 illustrates the FE-computed firstthree mode shapes (first bending, second bend-ing, first torsion) of a representative titaniumwind-tunnel model scale CROR blade. Figure 12illustrates the computed versus measured ("pingtest") eigenfrequencies at zero rotation rate. Thenumerical predictions match the experimentallymeasured eigenfrequencies within a few percentmargin. The first three eigenmodes are of par-ticular interest as the associated eigenfrequenciesusually lay well within the range of potential ro-tor excitation frequencies due to rotor inflow dis-tortions. This information is presented in a so-called Cambell diagram, Figure 12. It also high-lights the centrifugal stiffening effect on the com-puted eigenfrequencies.

For carbon fiber CROR blades, the finite el-ement modeling is more complex and is sub-ject of research. The current approach is to useanisotropic shell elements (CQUAD4) represent-ing each individual laminate layer. In the nearfuture, the authors expect to have data on the cor-

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relation with experimental values to validate thismodeling approach.

4.2 Aero-Elastic Coupling with the FlowSolver

To compute the dynamic aeroelastic deforma-tions of the blades, the structural model must becoupled to the CFD flow solver. Given the aero-dynamic forces, the structural model determinesthe dynamic deformations of the blades, whichare passed to the flow solver. Given the defor-mations, the flow solver computes the aerody-namic forces, which are passed back to the struc-tural model. An iterative scheme, based on aprediction-correction method [6], is used to solvethis dynamic fluid-structure interaction process.In practice, a small number of iterations is re-quired to obtain sufficient convergence in eachtime step.

The structural model computes the dynamicdeformations in the space spanned by the modeshapes of the blades. The dynamic equationsin modal space are driven by so-called general-ized aerodynamic forces. This generalized forceis obtained by projecting the aerodynamic forcesworking on the aerodynamic surface on eachmode shape. In order to transfer the structuraldeformations back to the physical space used inthe flow solver, the volume spline method [3] isused to deform both the aerodynamic surface gridand the CFD volume grid.

5 Conclusions

Massively parallel computing systems have be-come affordable today. This allows to run a nu-merical simulation of a Contra-Rotating Open-Rotor which captures all the relevant physicalphenomena. This paper illustrated the basic in-gredients to setup such an analysis. With the nu-merical capability in place, engineers can start toaddress some of the ideas that are currently on thetable to reduce the CROR perceived noise levels.If this challenging issue can be solved success-fully, the Contra-Rotating Open-Rotor can makea very significant contribution to reduce the envi-

ronmental impact of the future transport aircraft.

5.1 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.

5.2 Acknowledgement

This research is 50% funded by the European Unionin the 6-th framework programme New Aircraft Con-cepts REsearch (NACRE), in the 7-th framework pro-gramme by the Clean Sky Joint Technology Initia-tive’s Smart Fixed Wing Aircraft ITD (Grant Agree-ment No CSJU-GAM-SFWA-2008-001), and 50% byNLR’s programmetic research "Kennis voor Beleid"and "Kennis als Vermogen".

References

[1] Boelens O. J, van der Ven H, Kok J. C, andPrananta B. B. Rotorcraft simulations using asliding-grid approach. Proc European RotorcraftForum 34 ??, 2008.

[2] Dol H. S, Kok J. C, and Oskam B. Turbu-lence modelling for leading-edge vortex flows.Proc 40th Aerospace Sciences Meeting & Exhibit,Reno, Nevada, 14–17 January 2002.

[3] Hounjet M. H. L and Meijer J. J. Evaluation ofElastomechanical and Aerodynamic Data Trans-fer Methods for Non-planar Configurations inComputational Aeroelastic Analysis. Proc Pro-ceedings of 1995 CEAS International Forum onAeroelasticity and Structural Dynamics, pp 11.1–11.24, Manchester, June 1995. Royal Aeronauti-cal Society, also NLR-TP-95690, NLR, 1995.

[4] Kok J. C. A high-order low-dispersion symmetry-preserving finite-volume method for compress-ible flow on curvilinear grids. Journal of Compu-

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tational Physics, Vol. 228, pp 6811–6832, 2009.NLR-TP-2008-775.

[5] Kok J. C and Spekreijse S. P. Efficient and accu-rate implementation of the k–ω turbulence modelin the NLR multi-block Navier–Stokes system.Proc ECCOMAS 2000, Barcelona, Spain, 11–14September 2000. NLR-TP-2000-144.

[6] Prananta B. B and Hounjet M. H. L. Largetime step aero-structural coupling procedures foraeroelastic simulation. Proc Proceedings of 1997CEAS International Forum on Aeroelasticity andStructural Dynamics, Vol. 2, pp 63–71, Rome,June 1997. Associazione Italiana di Aeronau-tica ed Astronautica, also NLR-TP-97619, NLR,1997.

[7] Prananta B. B, Kok J. C, Spekreijse S. P, HounjetM. H. L, and Meijer J. J. Simulation of limit cy-cle oscillation of fighter aircraft at moderate angleof attack. Proc International Forum on Aeroelas-ticity and Structural Dynamics, Amsterdam, theNetherlands, 4–6 June 2003. NLR-TP-2003-526.

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