PERFORMANCE IMPROVEMENT OF A COMPOUNDHELICOPTER ROTOR HEAD BY AERODYNAMIC SHAPE

OPTIMIZATION

P. Pölzlbauer∗ , D. Desvigne∗∗ , C. Breitsamter∗∗Technical University of Munich , ∗∗Airbus Helicopters

Keywords: Design Optimization, CFD, Helicopter Aerodynamics, Blade-Sleeve Fairing, RACER

Abstract

Within the present publication, the rotor head of acompound helicopter known as Rapid And Cost-Effective Rotorcraft (RACER) is investigated. Inparticular, the aerodynamic design optimizationof the RACER blade-sleeve fairings is conducted.For this purpose, an isolated rotor head is gen-erated featuring a full-fairing beanie, the blade-sleeve fairing and a truncated rotor blade. More-over, a steady rotor is investigated and averagedflow conditions according to the RACER cruiseflight are applied. The automated aerodynamicdesign optimization is performed by means ofa previously developed optimization tool chain.A global multi-objective genetic optimization al-gorithm is applied for the given problem. Dur-ing preliminary work, a two-dimensional aero-dynamic design optimization of selected blade-sleeve sections was conducted. These optimizedairfoils represent the design variables for the cur-rent optimization problem. The shape modifica-tion of the three-dimensional fairing is realizedby exchanging specific airfoils at certain span-wise sections.

1 Introduction

Europe and its aviation industry have definedvery ambitious goals regarding the developmentof future air transportation concepts. The reduc-tion of the environmental impact as well as theperformance improvement of future vehicles arethe key challenges to be tackled. Especially, the

reduction in CO2 and NOx emissions as well asthe decrease of the noise footprint are in focus.At the same time, a seamless door-to-door mobil-ity is required by the growing population. How-ever, conventional aircraft require a large groundinfrastructure and rotorcraft do not achieve thecruising speed, payload and range of such an air-caft. Therefore, the gap between those two con-figurations can only be closed by the develop-ment of a novel aircraft concept. One of theseconcepts is represented by the new compoundhelicopter configuration known as Rapid AndCost-Effective Rotorcraft (RACER), which is de-veloped within the European Clean Sky 2 JointTechnology Initiative (CS2-JTI). The RACERcombines the beneficial characteristics of a fixed-wing aircraft with the ability of a helicopter forvertical take-off and landing (VTOL). Further-more, the predicted cruising speed is around 220knots, which is approximately 50 percent higherthan for a conventional helicopter. Due to thehigh cruising speed, aerodynamic efficiency be-comes an important topic during the RACER de-velopment. Regarding a conventional helicopter,the rotor head represents a major drag source,which offers potential in terms of drag reduction.Hence, one possibility is to design fairings forcertain rotor head components, which was com-prehensively investigated within the Clean SkyGreen RotorCraft Research Program [1, 2].

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P. PÖLZLBAUER , D. DESVIGNE , C. BREITSAMTER

Moreover, the importance of hub drag min-imization is reflected by a large number of ex-perimental [3, 4, 5] and numerical investigations[6, 7] that have been conducted over the lastdecades. The present work is related to the CleanSky 2 project FURADO (Full Fairing Rotor HeadAerodynamic Design Optimization), which dealswith the aerodynamic design optimization of asemi-watertight full-fairing rotor head by meansof CFD simulations. For this purpose, the rotor-head fairings are divided into three main com-ponents, the blade-sleeve fairing, the full-fairingbeanie and the pylon fairing. The present pub-lication deals with the aerodynamic design op-timization of the RACER blade-sleeve fairing.During preliminary work, two-dimensional air-foils were aerodynamically optimized for se-lected sections of the blade-sleeve fairing. Theseairfoils yield a database of supporting geome-tries, which are used for the modification of thethree-dimensional fairing shape. Furthermore, aglobal multi-objective genetic optimization algo-rithm is applied and selected supporting airfoilsrepresent the design variables for the given opti-mization problem.

2 RACER Compound Helicopter

The innovative demonstrator RACER provides aconcept allowing to expand the flight envelope ofhelicopters towards higher cruising speeds. Thedevelopment of this new configuration is basedon the experience gained through the X3 demon-strator program of Airbus Helicopters [8]. It of-fers a common demonstrator platform for newtechnologies and it is developed within a Euro-pean framework of industrial and academic part-ners. Figure 1 gives an overview on the RACERcompound helicopter configuration. The maindifferences, compared to a conventional heli-copter, are given by the innovative box-wing de-sign holding two lateral rotors as well as the hori-zontal and vertical stabilizers in H-type architec-ture. Moreover, a classical five-bladed main ro-tor is used enabling vertical take-off and landing.Concerning cruise flight, a significant part of thelift is generated by the wings. Hence, the main

rotor can be unloaded and its rotational speed isdecreased, which keeps the tip Mach-number ofthe advancing rotor blade low enough to avoidtransonic effects. Furthermore, the stabilizers areequipped with rudders and provide pitch and yawstability during cruise flight. The propellers de-liver additional thrust, generate anti-torque andenable yaw control in hover.

Fig. 1 : Clean Sky 2 demonstrator RACER [9].

The expected RACER performance is definedby a 50% higher cruising speed and a cost reduc-tion of 25% per nautical mile compared to con-ventional helicopters from the same class. Con-sidering the high cruising speed, aerodynamic ef-ficiency becomes an important topic during theRACER development. Especially drag reductionis one of the major challenges to be tackled inorder to achieve the predicted goals. Therefore,highly efficient wings, a low-drag fuselage and afully faired main rotor are employed.

3 Geometry

Within the present publication, the aerodynamicdesign optimization of the RACER blade-sleevefairing is at focus. Figure 2 shows a simpli-fied CAD model of the rotor head, which con-sists of three components. These include the full-fairing beanie (FFB) in green, the blade-sleevefairing (BSF) in orange and a truncated rotorblade (RB) in blue. Hence, an isolated rotor headis taken into account and its interference effectswith the fuselage as well as the pylon fairing areneglected.

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Performance Improvement of a Compound Helicopter Rotor Head by Aerodynamic Shape Optimization

Additionally, the dampers between the ro-tor blades are omitted, which reduces the com-plexity in terms of mesh generation. The junc-tion between the blade-sleeve fairing and the full-fairing beanie as well as the transition to the rotorblade are geometrically fixed. Hence, these sec-tions keep their shape throughout the optimiza-tion process. Furthermore, the cross-sections ofthe supporting airfoils, which represent the ba-sis for the three-dimensional blade-sleeve fair-ing, are depicted in Fig. 2. The shape variationof the blade-sleeve fairing is achieved by replac-ing the supporting airfoils. For this purpose, adatabase of selected two-dimensional geometriesis employed, which was generated during previ-ous work within the FURADO project [10]. Thefour supporting airfoils (S1-S4) are located in aregion of 0.078 ≤ r/R ≤ 0.149, where R corre-sponds to the rotor radius.

Fig. 2 : CAD model applied for the design opti-mization of the RACER blade-sleeve fairing.

4 Optimization Approach

Within this section, the aerodynamic design op-timization process for the RACER blade-sleevefairing is described. This includes an introduc-tion to the applied optimization tool chain, a de-scription of the optimization problem and a briefoverview on the selected optimization algorithm.A general introduction to optimization formu-lation and different optimization techniques isgiven in [11]. During the first phase of the FU-RADO project, the optimization tool chain allow-ing for fully automated aerodynamic shape opti-mization was developed. It consists of five mainmodules, which can be divided into optimization,

shape generation, mesh generation, flow simula-tion and design evaluation. A detailed descriptionof the applied tool chain is provided in [10].

4.1 Optimization Problem

During preliminary work, the two-dimensionalblade-sleeve sections were aerodynamically opti-mized for cruise flight, which is the most relevantflight condition in terms of drag reduction. Forthis purpose, the local flow conditions for eachsection were taken into account, which vary dueto the circumferential velocity and the flow de-flection caused by the fuselage. Two different az-imuthal positions of the rotor were investigated,which are shown in Fig. 3 and correspond to theadvancing and retreating rotor blade.

(a) Advancing rotor blade at Ψ = 90◦.

(b) Retreating rotor blade at Ψ = 270◦.

Fig. 3 : Comparison of the flow conditions for theinvestigated azimuthal rotor positions.

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P. PÖLZLBAUER , D. DESVIGNE , C. BREITSAMTER

Previous investigations at TUM-AER re-vealed that the highest drag values are obtainedat these azimuthal rotor positions [12]. Typicalflow-velocity profiles for cruise flight are givenin Fig. 3a and Fig. 3b. The flow conditions arecharacterized by high Mach numbers in the tipregion of the advancing rotor blade and a back-flow region in the vicinity of the rotor axis forthe retreating rotor blade. Regarding the RACERdemonstrator, the rotational speed of the main ro-tor is adapted for each flight condition to keepthe tip Mach number within a permissible rangeduring cruise flight and to provide sufficient liftduring hover. The design optimization of thetwo-dimensional blade-sleeve sections representsthe basis for the current optimization problem.Therefore, similar objective functions are appliedand their mathematical description is given byEq. 1 and Eq. 2. The main objective is to re-duce the drag caused by the blade-sleeve fairingsduring cruise flight. However, lift is taken intoaccount as well in the objective function for theadvancing rotor blade. In terms of overall drag,any additional lift generated by the blade-sleevefairings would have a beneficial effect on the en-tire configuration. Moreover, the minimizationof drag is considered as the objective function forthe retreating rotor blade, which is located withina back-flow region.

maximize f1(x) =CL/CD (Adv. Blade) (1)minimize f2(x) =CD ·S (Ret. Blade) (2)

Four discrete design variables representingspecific geometries of the supporting airfoils areapplied:

x = {S1,S2,S3,S4} (3)

For each section (S1-S4), twelve airfoils orig-inating from the two-dimensional design opti-mization are selected. Figure 4 exemplarilyshows the objective space for the final popula-tion of one blade-sleeve section. Both objectivefunctions are normalized by a symmetric refer-ence geometry. The designs close to the Pareto

front can be divided into three main regions. De-signs with low drag values regarding the retreat-ing blade case are located in the blue colored re-gion and geometries offering a compromise be-tween both objective functions can be found inthe orange colored region. Moreover, the greencolored region contains designs with high lift-to-drag ratios concerning the advancing blade case.From each of the three regions, four airfoils areselected for each of the blade-sleeve sections.Hence, a database containing 48 optimized air-foils is created, which corresponds to 20736 pos-sible shape combinations. Evaluating all possi-ble shapes of the blade-sleeve fairing is not pos-sible within a reasonable time-frame. Hence, amulti-objective design optimization is employedto find a feasible geometry. During the prelim-inary optimization of the blade-sleeve sections,design constraints regarding the available designspace were applied. Therefore, these constraintsare automatically met by the three-dimensionalblade-sleeve fairing and an unconstrained opti-mization can be performed.

Fig. 4 : Exemplary objective space for the finalpopulation of the two-dimensional design opti-mization showing the three main regions of thePareto front.

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Performance Improvement of a Compound Helicopter Rotor Head by Aerodynamic Shape Optimization

4.2 Optimization Algorithm

The selection of the optimization algorithmfor a given optimization problem is based onthe characteristics of the design space and theapplied constraints. In convex search spaces,gradient-based optimization algorithms effi-ciently navigate into a local optimum close tothe starting point. However, these algorithms arenot suited for multi-modal problems, becausethey could get caught in such a local optimum.Therefore, derivative-free global evolutionary al-gorithms offer a robust alternative in non-convexsearch spaces or whenever the characteristicsof the search space are unknown. However,global optimization algorithms require a largenumber of function evaluations compared togradient-based algorithms. Concerning thepresent optimization problem, similar concurringobjective functions as for the two-dimensionaldesign optimization are employed. However,they slightly differ, because the force-coefficientsare multiplied by the reference surface S for thethree-dimensional investigations. Moreover, theflow around the rotor head fairing represents acomplex flow problem and the properties of thesearch space are unknown. Therefore, a robustmulti-objective genetic algorithm (MOGA) isused for the aerodynamic design optimizationof the RACER blade-sleeve fairing. Geneticalgorithms (GAs) use the principles of naturalselection, which means that they are based onDarwin’s theory of survival of the fittest. Thesealgorithms start their search for the optimalsolution from a population of designs and notfrom a single one. In combination with aparameter sampling method, which is applied forthe initialization of the first population, a widerange of the design space can already be coveredat the beginning of the optimization process.Moreover, GAs only use objective functionsto determine the fitness of a design. Hence,they do not require any auxiliary information,like gradients or Hessians. The transition fromone population to a subsequent one depends onprobabilistic rules.

The main operations used within a GA are re-production, crossover and mutation. Dependingon the objective function of a candidate, it hasa certain probability of being selected for con-tributing offspring in the next generation. Withinthe next step, a mating pool of candidates is gen-erated and they are combined in pairs crossingover genetic information. Additionally, a muta-tion operator is employed to randomly change thevalues of coded design variable strings in orderto prevent the optimization algorithm from los-ing important genetic information [13, 14].

5 Numerical Setup

Within this section an overview on the investi-gated flow conditions, the computational meshand the applied flow solvers is given. As men-tioned in Sec. 4.1, two different flow condi-tions are examined yielding the advancing andretreating rotor blade case. In order to sim-plify the optimization process, a stationary rotoris investigated. Therefore, an averaged circum-ferential velocity is superposed with the cruisespeed of the helicopter, which corresponds toVCruise = 220 kts. Furthermore, an averaged an-gle of attack is applied for all sections, which isdefined by the collective pitch, the longitudinalcyclic-pitch and an averaged local angle of at-tack due to the flow deflection of the fuselage.Additionally, the employed ambient conditionsare representative for a sea-level cruise flight inICAO standard atmosphere [15].

5.1 Computational mesh

The applied computational mesh is generatedwith Ansys ICEM. A block-structured hexahe-dral mesh consisting out of 182 blocks is created.The dimensions of the computational domain areillustrated in Fig. 5. The quantity dFFB representsthe diameter of the full-fairing beanie, whichis shown in green. The size of the domain isbig enough to ensure that no influence from theimposed boundary conditions can be observed inthe flow field near the geometry.

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P. PÖLZLBAUER , D. DESVIGNE , C. BREITSAMTER

In order to minimize the computational timeon the one hand and to ensure low numerical dis-sipation due to the spatial discretization on theother hand, mesh independence studies were con-ducted to find the required mesh size. As a result,a computational mesh featuring 7.2 million ele-ments was selected for the numerical investiga-tions. Furthermore, the boundary layer is fullyresolved by selecting a dimensionless wall dis-tance of y+ ≈ 1 for the initial cell height and amesh expansion ratio of 1.2. On the front, top,back and bottom of the computational domain,farfield boundary conditions are applied. A sym-metry boundary condition is used on the surfaceconnected to the investigated geometry. For theremaining side of the domain, a free-slip wall ischosen. The initial mesh is generated for a base-line geometry of the blade-sleeve fairing, whichuses airfoils yielding the best compromise of bothobjective functions. Subsequent meshes are auto-matically generated by updating the geometriesand reassociation.

Fig. 5 : Computational domain used for the CFDsimulations.

5.2 Flow solvers

This section summarizes the numerical setup ofthe applied flow solvers. Ansys FLUENT aswell as the DLR TAU-Code were used for thenumerical investigations within the present pub-lication. The preliminary aerodynamic designoptimization of the blade-sleeve fairing sectionswas conducted using Ansys FLUENT. Further-

more, all time-accurate results for detailed analy-sis were produced with this flow solver, becausefaster convergence was observed in terms of un-steady flow simulations. The DLR TAU-Codewas employed for the three-dimensional designoptimization of the blade-sleeve fairing.

5.2.1 ANSYS Fluent

The numerical flow simulations dealing withthe two-dimensional design optimization of theblade-sleeve fairing sections were conductedwith Ansys FLUENT. Furthermore, selectedthree-dimensional blade-sleeve fairing designswere investigated with this flow solver. Dueto Mach numbers within a range of 0.3-0.4,compressibility effects are taken into account.Therefore, the compressible, unsteady Reynolds-Averaged Navier-Stokes equations (URANS) areconsidered. The initialization of the transientflow simulation is performed by the applicationof a steady state solution. Furthermore, the k-ω SST model [16] is employed for turbulencemodeling. Moreover, the SIMPLEC algorithmis applied for the treatment of pressure-velocitycoupling, which allows for increased under-relaxation. The pressure interpolation is achievedby the standard pressure scheme of FLUENT. Re-garding the spatial discretization, second-orderupwind schemes are chosen for density, momen-tum, turbulent kinetic energy, specific dissipa-tion rate and energy. Further, a least-squarescell-based formulation is applied for the gradientcalculation and a bounded second-order implicitscheme is used for the temporal discretization[17]. The time-step size for the time-accuratesimulations was set to ∆t = 10 −4 s, which cor-responds to a resolution of 130 points per periodregarding the observed oscillation of forces. Fur-thermore, all normalized residuals were reducedby at least four orders of magnitude. Dependingon the investigated geometry, this was achievedwithin approximately ten inner iterations per timestep. During preliminary tests regarding the sim-ulation setup, it was observed that doubling thetime-step size leads to approximately 60 percentmore inner iterations.

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Performance Improvement of a Compound Helicopter Rotor Head by Aerodynamic Shape Optimization

Further, a more stable setup could be obtainedwith the smaller time-step. The applied fluid isair ideal gas and its properties are set accordingto a sea-level cruise flight.

5.2.2 DLR TAU-Code

The numerical investigations for the evalua-tion of the objective functions concerning thethree-dimensional design optimization are con-ducted with the DLR-TAU Code. This CFDsolver was developed at the DLR (GermanAerospace Center) and solves the compressiblesteady or unsteady Reynolds-Averaged Navier-Stokes (RANS) equations. The flow calculationis based on a dual grid approach and a cell vertexgrid metric is employed. Turbulence modelingis achieved by the SST k-g model, which rep-resents a re-implemented version of the MenterSST model [16, 18]. The standard TAU aver-age of flux central scheme is selected for the dis-cretization of the meanflow equations. Further-more, a Roe second-order scheme is applied forthe convective fluxes of the turbulence equationsand a Green-Gauss algorithm is chosen for thegradient reconstruction. The system of equationsis solved by a Lower-Upper Symmetric-Gauss-Seidel (LU-SGS) method and scalar dissipationis used for the numerical dissipation scheme. Anoverview of the hybrid RANS solver TAU isgiven in [19]. Regarding the convergence of theflow simulations, the normalized density residualwas reduced by three orders of magnitude.

6 Results

The present section introduces the applied opti-mization setup and shows the intermediate resultsof the currently ongoing blade-sleeve fairing op-timization. The Automated Aerodynamic ShapeDevelopment (AASD) tool chain, which was de-veloped at TUM-AER, was used in combinationwith a multi-objective genetic algorithm to gen-erate the data.

The investigated objective functions are givenby the maximization of the lift-to-drag ratio(CL/CD) for the advancing rotor blade (Ψ = 90◦)and the minimization of drag CDS for the retreat-

ing rotor blade (Ψ = 270◦). Four discrete designvariables, which correspond to specific designsfrom an airfoil database, span the available de-sign space. Twelve airfoils were selected for eachsection, which yields a design variable range of1 ≤ S1,S2,S3,S4 ≤ 12. Regarding the ranking ofthe designs, a domination count is used to orderthe population members and to determine theirfitness. One design is dominating another one,if it is better in both objective functions. Thedesigns that are kept for the subsequent gener-ation are selected by a below limit replacementvalue of six. This means that the number of can-didates dominating a specific design has to belower than the replacement value, otherwise thisdesign is rejected. Furthermore, the reduction ofthe population size is controlled by a shrinkagepercentage of 95%. This value specifies the num-ber of candidates, which have to continue to thenext generation. Hence, it prevents an excessivedecrease in the population size. Furthermore,the below-limit selector is adapted, if the algo-rithm does not find sufficient designs to fulfillthe shrinkage percentage requirement. Addition-ally, a differentiation along the Pareto-frontier isachieved by employing niching during the opti-mization. The initial population contains 150 de-signs, which were randomly generated by the ap-plied optimization tool-box DAKOTA [20]. Re-garding the optimization results, an evaluation ofthe objective space is conducted and one design isselected to be investigated in more detail. More-over, an overview on the prevailing flow field isgiven and the occurring flow phenomena are de-scribed. For this purpose, a baseline design isintroduced, which features airfoils offering thebest compromise between the objective functionsfrom the two-dimensional design optimization.

6.1 Evaluation of the objective space

Within this section, the evaluation of theblade-sleeve fairing designs is presented. Theinvestigated geometry yields a bluff body and anunsteady flow field can be observed in its wakeregion.

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P. PÖLZLBAUER , D. DESVIGNE , C. BREITSAMTER

However, time-accurate flow simulations re-quire a significant amount of time, which is unde-sired in terms of the automated design optimiza-tion. Therefore, a comparison between a time-accurate and a steady-state flow simulation wasconducted for a representative test-case using theDLR-TAU Code. Figure 6 shows the results forthe time-accurate simulation (red), the averagedtime-accurate simulation (green) and the steady-state simulation (blue). All results are normalizedwith the final value of the averaged time-accuratesimulation.

tsim

[s]

(CLS

) re

l [-]

0.1 0.15 0.2 0.25 0.3

0.8

1

1.2

1.4Unsteady SimulationAveraged Unteady SimulationSteady Simulation

(a) Normalized lift coefficient (CLS)rel.

tsim

[s]

(CDS

) re

l [-]

0.1 0.15 0.2 0.25 0.30.9

0.95

1

1.05

1.1Unsteady SimulationAveraged Unteady SimulationSteady Simulation

(b) Normalized drag coefficient (CDS)rel.

Fig. 6 : Comparison of an averaged time-accurateflow simulation with the results from a quasisteady-state flow simulation.

The total simulation time was Tsim = 0.3 s andthe applied time-step was ∆t = 2 · 10−4s. Re-garding the normalized lift-coefficient (CLS)rel,which is illustrated in Fig. 6a, a deviation of0.9 percent can be observed between the steady-

state and the averaged time-accurate simula-tion. Furthermore, a difference of 3.5 percentwas obtained for the normalized drag-coefficient(CDS)rel, which is shown in Fig. 6b. The devia-tion from the time-accurate simulation is consid-ered to be within a reasonable range and there-fore, a steady-state simulation setup is used forthe current optimization task. A steady-state flowsimulation with 22000 iterations is performed tocalculate the objective functions for the designevaluation. During the first phase of the de-sign optimization, 334 designs have been eval-uated. An overview on the objective space isgiven in Fig. 7. Both objective functions arenormalized with reference values from the base-line design of the blade-sleeve fairing. Hence,the performance of a candidate is evaluated rela-tive to this reference geometry. The feasible ob-jective space is defined in a region of −0.63 ≤(CL/CD)rel ≤ 1.14 and 0.89 ≤ (CDS)rel ≤ 1.2.Furthermore, the baseline design, which is lo-cated at (CL/CD)rel = 1 and (CDS)rel = 1,is marked with a blue symbol. Any design thatis better than the reference, is located within thehighlighted region, in the bottom-right corner ofFig. 7a. A detailed view on the currently bestperforming designs is given in Fig. 7b. Can-didate C1 achieves the highest lift-to-drag ratio(CL/CD)rel and candidate C2 provides the low-est drag (CDS)rel. The relative performance im-provement of C1 and C2 is summarized in Ta-ble 1.

Design f1 f2 ∆ f1 [%] ∆ f2 [%]C1 1.136 0.954 +13.6 -4.6C2 1.101 0.897 +10.1 -10.3

Table 1: Comparison of the objective functionsfor the designs C1 and C2.

Connecting the designs C1 and C2 leads tothe utopia point UP for the current set of re-sults. This point represents a theoretical designthat combines the best of both objective func-tions. However, this point cannot be reached,because there is always a trade-off between theconcurring objective functions.

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Performance Improvement of a Compound Helicopter Rotor Head by Aerodynamic Shape Optimization

The distance between UP and any other de-sign is taken into account to find a geome-try, which offers a good compromise betweenboth objective functions. The geometry with thesmallest distance to UP is given by candidate C2,which is marked by a green symbol in Fig. 7.Moreover, this design is investigated in more de-tail and compared to the baseline geometry.

(a) Overview on the entire objective space.

(b) Detailed view on the designs featuring the best ob-jective functions.

Fig. 7 : Objective space showing the evalu-ated designs from the multi-objective design op-timization.

In order to exemplarily show the differencebetween the baseline geometry and the selecteddesign C2, the chordwise pressure distribution isdetermined at the second radial blade-sleeve sec-tion S2. This section was chosen, because only

minor interference effects with a large flow sep-aration originating from the transition region be-tween the full-fairing beanie and the blade-sleevefairing are present. The sectional shapes of thebaseline design and candidate C2 are depictedin Fig. 8. Additionally, the design constraints,which were applied during the two-dimensionaldesign optimization, are shown by red and bluelines. It can be observed that both designs areclose to the minimum permissible design space.

Fig. 8 : Comparison between the sectional shapesof the baseline design and candidate C2 at the ra-dial position S2.

Figure 9 shows the chordwise pressure dis-tribution Cp(x/c) for the selected candidate C2 incomparison to the baseline design. The data wasextracted from the second radial section S2. Theresults for the advancing rotor blade are shownin Fig. 9a and for the retreating rotor blade theyare given in Fig. 9b. The pressure distributionin Fig. 9b is mirrored, because reversed flow ispresent for the retreating blade. Regarding thepressure distribution on the upper surface of theblade-sleeve fairing, which is represented bysolid lines in both figures, no big differences canbe observed. This is caused by the fact that thecontour on the upper surface is quite similar forboth designs. Hence, the same suction peak canbe observed at x/c = 0.65 for the advancing andthe retreating rotor blade, which is related to astrong curvature in the geometry.

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P. PÖLZLBAUER , D. DESVIGNE , C. BREITSAMTER

Concerning the bottom surface of the base-line design in Fig. 9a, a pressure drop canbe identified at 70 percent of the chord-length,which is related to a region of separated flow. Theonset of flow separation is triggered by a strongcurvature at x/c = 0.7. Furthermore, the smoothedcontour of the optimized design C2 leads to a de-layed flow separation within this region. Consid-ering the retreating blade case in Fig. 9b, a signif-icant suction peak can be seen on the lower sur-face of the baseline design. In comparison to this,moderate pressure levels are obtained for candi-date C2.

x/c [-]

Cp [

-]

0 0.2 0.4 0.6 0.8 1

-2.5

-2

-1.5

-1

-0.5

0

0.5

1

S2 Baseline Adv TopS2 Baseline Adv BottomS2 Design C2 Adv TopS2 Design C2 Adv Bottom

(a) Advancing rotor blade.

x/c [-]

Cp [

-]

0 0.2 0.4 0.6 0.8 1

-3.5

-3

-2.5

-2

-1.5

-1

-0.5

0

0.5

1

S2 Baseline Ret TopS2 Baseline Ret BottomS2 Design C2 Ret TopS2 Design C2 Ret Bottom

(b) Retreating rotor blade.

Fig. 9 : Comparison of the chordwise pressuredistribution between the baseline design and theselected candidate C2 at section S2.

6.2 Flow field visualization and 3D effects

At first, a general view on the prevailing flowfield and the occurring flow phenomena is given.For this purpose, the simulation results of thebaseline design are shown, which are represen-tative for candidate C2 as well. The flow fieldis visualized by means of the averaged, axialflow velocity VX, mean, which is normalized bythe free-stream velocity V∞. Figure 10 showsfour slices in chordwise direction, which are lo-cated within a range of 0.5 ≤ x/c ≤ 1.5. More-over, the results for the advancing and the re-treating rotor blade are illustrated in Fig. 10aand Fig. 10b. The cutoff values for the contourplots are set according to (VX ,mean/V∞)min = 0and (VX ,mean/V∞)max = 1. Additionally, an iso-surface is drawn at VX ,mean/V∞ = 0 for both cases.By means of this iso-surface, a large region ofseparated flow can be identified, which featuresreversed flow inside. The onset of flow separa-tion is located in the transition region between theblade-sleeve fairing and the full-fairing beanie, atapproximately half of the chord length. Further-more, the first blade-sleeve section S1 is influ-enced by this flow separation and reduced pres-sure levels are obtained compared to the two-dimensional simulation results. Moreover, theflow separation is larger for the retreating bladecase, which can be seen in Fig. 10b. Startingfrom a spanwise position of y/ly = 0.5, almostundisturbed wake flow fields can be observed.Furthermore, y-slices showing the averaged andnormalized axial flow velocity are depicted inFig. 11. These slices are located at the radialpositions of the four supporting airfoils (S1-S4).In comparison to the wake flow field of sectionS1, the region of reduced axial flow velocity ismuch smaller for the remaining sections S2-S4.In Fig. 11b, the results for the retreating rotorblade are shown. Concerning section S3, it canbe observed that the flow separates earlier on thebottom surface, which leads to a flow deflectionin downward direction. Additionally, the veloc-ity deficit is more pronounced for the sections S1and S2 compared to the advancing blade case inFig. 11a.

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Performance Improvement of a Compound Helicopter Rotor Head by Aerodynamic Shape Optimization

(a) Advancing rotor blade. (b) Retreating rotor blade.

Fig. 10 : Baseline Fairing: Normalized axial flow velocity VX, mean/V∞ shown at four evenly distributedx-slices within the region 0.5≤ x/c≤ 1.5.

(a) Advancing rotor blade. (b) Retreating rotor blade.

Fig. 11 : Baseline Fairing: Normalized axial flow velocity VX, mean/V∞ shown at the four blade-sleevesections S1-S4.

In order to determine the influence of thethree-dimensional effects, the results from thepreliminary airfoil optimization are compared tothe results from the three-dimensional flow sim-ulations. For this purpose, the chordwise pres-sure distributions are considered for the sectionsS1 and S3, which can be seen in Fig. 12. Re-garding section S1, a large discrepancy betweenthe airfoil pressure distribution and the three-dimensional result is present. The flow field

in this region is dominated by the flow sepa-ration between the blade-sleeve fairing and thefull-fairing beanie, which strongly influences thepressure distribution at this spanwise location.Hence, almost constant pressure is obtained over60 percent of the chord length for the advancingas well as the retreating blade case.

11

P. PÖLZLBAUER , D. DESVIGNE , C. BREITSAMTER

x/c [-]

Cp [

-]

0 0.2 0.4 0.6 0.8 1

-2.5

-2

-1.5

-1

-0.5

0

0.5

1

S1 3D Baseline Adv TopS1 3D Baseline Adv BottomS1 2D Baseline Adv TopS1 2D Baseline Adv Bottom

x/c [-]

Cp [

-]

0 0.2 0.4 0.6 0.8 1

-3

-2.5

-2

-1.5

-1

-0.5

0

0.5

1

S1 3D Baseline Ret TopS1 3D Baseline Ret BottomS1 2D Baseline Ret TopS1 2D Baseline Ret Bottom

x/c [-]

Cp [

-]

0 0.2 0.4 0.6 0.8 1

-3

-2.5

-2

-1.5

-1

-0.5

0

0.5

1

S3 3D Baseline Adv TopS3 3D Baseline Adv BottomS3 2D Baseline Adv TopS3 2D Baseline Adv Bottom

(a) Advancing rotor blade.

x/c [-]

Cp [

-]

0 0.2 0.4 0.6 0.8 1

-4

-3.5

-3

-2.5

-2

-1.5

-1

-0.5

0

0.5

1

S3 3D Baseline Ret TopS3 3D Baseline Ret BottomS3 2D Baseline Ret TopS3 2D Baseline Ret Bottom

(b) Retreating rotor blade.

Fig. 12 : Comparison of the two-dimensional (2D) and the three-dimensional (3D) simulation resultsconsidering the pressure distribution Cp(x/c) at the sections S1 and S3.

Regarding the pressure distributions of sec-tion S3, good agreement between the two-dimensional (2D) and three-dimensional (3D) re-sults can be observed for both cases. However,a significant difference can be identified in thefront region of the bottom surface for the retreat-ing blade case, which is depicted in Fig. 12b.Nevertheless, the present investigations show thata preliminary, two-dimensional design optimiza-tion is reasonable for such an optimization task.Furthermore, a sound database of airfoils is avail-able for the three-dimensional design optimiza-tion, which significantly reduces the number ofrequired design variables.

Figure 13 shows the spanwise pressure dis-tribution Cp(y/ly) for the baseline design as well

as candidate C2. The results are derived fromthe center of the fairing (x/c = 0.5). The stationy/ly = 0 corresponds to the most inboard part ofthe blade-sleeve fairing and y/ly = 1 representsthe transition to the rotor-blade. Furthermore, theresults for the advancing rotor blade are depictedin Fig. 13a. Between 45 and 75 percent of thefairing length, an almost constant pressure gradi-ent can observed for the upper surface of both de-signs. Moreover, the largest pressure differencebetween the upper and the lower surface is lo-cated at approximately 80 percent of the fairinglength and design C2 reveals a bigger pressuredifference than the baseline design on almost theentire length of the fairing.

12

Performance Improvement of a Compound Helicopter Rotor Head by Aerodynamic Shape Optimization

Furthermore, a significant pressure differencecan be seen in the region 0.5 ≤ y/ly ≤ 1. Hence,the largest lift contribution is provided by thispart of the blade-sleeve fairing. Regarding theretreating blade case, which is shown in Fig. 13b,lower pressure differences between the upper andthe lower surface are obtained for both geome-tries. Additionally, the pressure gradient on theupper surface is reduced compared to the advanc-ing blade case. At y/ly = 0, almost the samepressure levels can be found for both cases. Fur-ther, design C2 provides a larger pressure differ-ence between the upper and the lower surface inFig. 13b.

y/ly [-]

Cp [

-]

0 0.2 0.4 0.6 0.8 1

-1.2

-1

-0.8

-0.6

-0.4

-0.2

Baseline Adv TopBaseline Adv BottomDesign C2 Adv TopDesign C2 Adv Bottom

(a) Advancing rotor blade.

y/ly [-]

Cp [

-]

0 0.2 0.4 0.6 0.8 1

-1.2

-1

-0.8

-0.6

-0.4

-0.2

Baseline Ret TopBaseline Ret BottomDesign C2 Ret TopDesign C2 Ret Bottom

(b) Retreating rotor blade.

Fig. 13 : Spanwise pressure distribution Cp(y/ly)at the center of the fairing (x/c = 0.5) for the base-line design and candidate C2.

7 Conclusion

Within the present publication, the three-dimensional aerodynamic design optimization ofthe RACER blade-sleeve fairing is described andfirst results of the ongoing optimization processare shown. An isolated rotor head featuring afull-fairing beanie, a blade-sleeve fairing and atruncated rotor blade is examined. Furthermore,the parameterization of the blade-sleeve fairing isrealized by four supporting airfoils, which wereaerodynamically optimized during previous workin the FURADO project. For each blade-sleevesection, twelve of the best performing airfoilsfrom the two-dimensional design optimizationwere selected yielding the design variables forthe present optimization problem. The shape ofthe blade-sleeve fairing is modified by replac-ing the supporting airfoils. The applied objectivefunctions are represented by the maximization ofthe lift-to-drag ratio for the advancing rotor blade(CL/CD) and the minimization of drag (CDS) forthe retreating rotor blade. The optimization isconducted by means a multi-objective genetic al-gorithm and 334 designs have been evaluated sofar. In order to be able to measure the perfor-mance improvement for a given design, a base-line candidate is generated for comparison. Thisbaseline geometry is composed out of airfoils,which yield the best compromise regarding bothobjective functions from the two-dimensional de-sign optimization. Additionally, the objectivespace is evaluated and a detailed view on the bestperforming geometries is given. In comparisonto the baseline design, a maximum increase of(∆CL/∆CD)rel = 13.6 % was observed for the ad-vancing blade case (Design C1) and a reductionof (∆CDS)rel = 10.3 % could be achieved for theretreating blade case (Design C2). Moreover, de-sign C2 represents the best compromise for bothobjective functions and it was selected to be in-vestigated in more detail. For this purpose, thesectional shape as well as the chordwise pres-sure distribution of the second blade-sleeve sec-tion (S2) are compared to the baseline design.Additionally, the spanwise pressure distributionis examined at x/c = 0.5 for both designs.

13

P. PÖLZLBAUER , D. DESVIGNE , C. BREITSAMTER

Furthermore, a description of the flow fieldis given for the baseline geometry, which is rep-resentative for candidate C2 as well. There-fore, the averaged and normalized axial flow ve-locity is examined in four chordwise and span-wise slices. In order to determine any three-dimensional effects, a comparison of the two-and three-dimensional simulation results is per-formed. Therefore, the sectional pressure dis-tributions are derived for the first and the thirdblade-sleeve section (S1 and S3) of the baselinedesign.

Acknowledgements

The authors would like to thank the EuropeanUnion for the funding of the FURADO researchproject within the framework of Clean Sky 2 un-der the grant agreement number 685636. Fur-ther, the fruitful collaboration and valuable sup-port of the project partner AIRBUS Helicoptersis highly acknowledged. Special thanks are ad-dressed to ANSYS and the DLR for providingthe flow simulation software. The authors grate-fully acknowledge the Gauss Centre for Super-computing e.V. (www.gauss-centre.eu) for fund-ing this project by providing computing time onthe GCS Supercomputer SuperMUC at LeibnizSupercomputing Centre (www.lrz.de).

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8 Contact Author Email Address

Patrick Pölzlbauermailto: patrick.poelzlbauer@aer.mw.tum.de

Copyright Statement

The authors confirm that they, and/or their companyor organization, hold copyright on all of the origi-nal material included in this paper. The authors alsoconfirm that they have obtained permission, from thecopyright holder of any third party material includedin this paper, to publish it as part of their paper. Theauthors confirm that they give permission, or have ob-tained permission from the copyright holder of thispaper, for the publication and distribution of this pa-per as part of the ICAS proceedings or as individualoff-prints from the proceedings.

15

IntroductionRACER Compound HelicopterGeometryOptimization ApproachOptimization ProblemOptimization Algorithm

Numerical SetupComputational meshFlow solversANSYS FluentDLR TAU-Code

ResultsEvaluation of the objective spaceFlow field visualization and 3D effects

ConclusionContact Author Email Address