COMPUTATIONAL ANALYSIS OF ROTOR-FUSELAGE

INTERACTIONAL AERODYNAMICS USING SLIDING-PLANE CFD

METHOD

R. Steijl and G. Barakos

CFD Laboratory, Department of Engineering, University of Liverpool, L63 3GH, U.K.

Abstract

Aerodynamic interactions between the main rotor,fuselage and tail rotor must be considered duringthe design phase of a helicopter and their effect onperformance must be quantified. Regardless of itsimportance, interactional helicopter aerodynamicshas so far been considered by very few researchers.This is due to the geometric complexity and com-plex flow physics involved in the flow field analy-sis of a full helicopter geometry. The aim of thepresent work is the development of a CFD methodcapable of accurately simulating the flow arounda full helicopter and to improve the understand-ing of helicopter interactional aerodynamics. In thepresent work, the Helicopter Multi-Block (HMB)flow solver[1, 2, 3] of the CFD Laboratory at Liv-erpool University is used. The present work inves-tigates the flow around two generic rotor-fuselagetest cases, i.e. the GeorgiaTech rotor-cylinder testcase and the ROBIN rotor-fuselage test case, beforemoving on to a more realistic full helicopter geom-etry under investigation in the European Commis-sion Framework 6 GOAHEAD project. A compari-son of the results obtained using the HMB methodwith experimental data shows that the method iscapable of resolving the main interactional flow fea-tures for the generic cases. A similar comparisonfor the GOAHEAD test case has not yet been con-ducted, but the obtained results show that even fora test case of high complexity, state-of-the-art ro-torcraft CFD methods are capable of providing re-alistic results.

1 Introduction

Aerodynamic interactions between the main rotor,tail rotor and fuselage are an important part of theaerodynamic characteristics of a helicopter. Re-gardless of its importance, interactional helicopteraerodynamics has so far been considered by very fewresearchers. There are a number of reasons for this.First, the aero-mechanics of an isolated rotor is stilla very challenging area, since it constitutes a com-plex multi-disciplinary problem involving complexvortical wake flows, transonic flow regions, rotor

blade dynamics and blade elastic deformation. Nat-urally, understanding interactional helicopter aero-dynamics requires a good level of understanding ofrotor aero-mechanics. The second reason for thelimited number of studies in interactional aerody-namics is the geometric complexity and even morecomplex flow physics involved in the flow field anal-ysis of a rotor-fuselage geometry, and in particu-lar, a full helicopter geometry. Therefore, most ofthe published works concern wind tunnel experi-ments with a generic helicopter rotor mounted onan idealised fuselage, e.g. the rotor-cylinder testcase at GeorgiaTech[4, 5] and the ROBIN test caseat NASA[6, 7, 8]. In the first example, the airframeis represented by a circular cylinder with hemispher-ical nose, while the ROBIN fuselage is closer to areal helicopter fuselage shape, but tail planes, en-gine inlets and exhausts, etc. are ignored.

However, the importance of helicopter interac-tional aerodynamics, combined with the progressin CFD algorithms and the availability of ever morepowerful affordable computers, encouraged severalrecent CFD studies[9, 10, 11, 12, 13, 2]. These in-vestigations have not yet reached the maturity ofnumerical investigations of hovering rotors or iso-lated rotors in forward flight. There are a numberof contributing factors for this. First, the geometriccomplexity of a rotor-fuselage and, in particular, afull helicopter geometry, and the resulting challengein creating good quality meshes. Secondly, the al-gorithmic complexity of the CFD methods due tothe need to handle relative motions of rotor bladeand the fuselage. However, a major factor has beenthe lack of adequate wind tunnel flight test data forvalidation purposes.

Therefore, an urgent need exists for a databaseof high quality experimental data, which can actas validation for the state-of-the-art CFD meth-ods. To address this need, the European Com-mission funded the Framework 6 Program GOA-HEAD, with the aim to create such an experi-mental data base and to validate state-of-the-artCFD methods. The CFD Laboratory at LiverpoolUniversity is involved in the CFD work packageof this project, using the Helicopter Multi-Block

75.1

(HMB) flow solver[1, 2]. The Helicopter Multi-Block (HMB) solver employs a sliding-grid tech-nique to handle the relative motion of the rotor(s)and the helicopter fuselage. The CFD package com-prises a pre-wind tunnel test phase, in which thepartners provide CFD results using predicted testconditions, and a post-wind tunnel test phase, dur-ing which the wind tunnel results are available. TheCFD results for the blind pre-wind tunnel test phasewere presented last year in Ref.[14].

The present paper is structured as follows. First,a review of published experimental numerical inves-tigations into helicopter interactional aerodynamicsis presented in Section 2. Then, the CFD methodused in the present study is described in Section 3.Section 4 present the results for the Georgia Techteetering rotor test case, while the ROBIN rotor-body test case is described in Section 5. Resultsfor the NH90-like geometry under investigation inthe GOAHEAD project are presented in Section 6.Finally, conclusions are drawn in Section 7, alongwith future research planned for the near future.

2 Review of previous work

In the present work, the well-known GeorgiaTechrotor-cylinder interaction experimental data is usedboth for validation of the present CFD method waswell as in the analysis of interactional aerodynam-ics for simple fuselage shapes. In the GeorgiaTechexperiments, a simple two-bladed teetering rotor isconsidered mounted on a cylindrical airframe withhemispherical node. The surface pressure measure-ments for this series of experiments were presentedby Brand, McMahon and Komerath[4]. The resultsfrom velocity field measurements in the GeorgiaT-ech rotor-cylinder interaction test case were pre-sented in the late eighties by Liou, Komerath andMcMahon[15, 16].

Kim and Komerath[5] present a summary of ex-perimental work for the interaction of the wake ofsimple two-bladed rotors with a circular cylindricairframe. In addition, the work present compar-isons of the experimental results with results fromtheoretical modelling of the interaction. The paperdescribed the differences between the wake fuselageinteraction at the front of the rotor disk with that atthe aft part of the rotor disk. Building on potentialflow models, the authors describe the wake-fuselageinteraction in two-phase, i.e. a pre-collision phasein which the wake vortex trajectory is modified bythe presence of the fuselage and a collision phasedominated by complex vortex-boundary layer in-teractions. The pre-collision phase can be modelledwith potential flow theory while the collision phaseobviously requires viscous flow models. The forwardshaft tilt in the rotor-cylinder test cases considered

and hence the closer proximity of the rotor disk andthe cylinder at the front of the disk, as comparedto the separation of the rotor disk from the cylin-der at the back, leads to a qualitatively differentbehaviour of the vortex path modification resultingfrom the presence of the cylinder. In the theoreticalmodel discussed by Kim and Komerath[5], the vor-tex wake descent is significantly decelerated relativeto the isolated rotor wake development at the frontof the rotor disk, while the deceleration is absent atthe back. In the potential flow model, the interac-tion with the cylinder is different due to the oppo-site sense of vortex rotation at the front and back ofthe rotor disk, i.e. at the front of the disk, the vor-tex can be expected to proceed directly to collidewith the surface, while at the back, the vortex canbe expected to have a less direct interaction, withthe vortex travelling along the surface. Naturally,vortex-boundary layer interactions will play an im-portant role, particularly when the interaction leadsto flow separation on the cylinder/fuselage. Hence,the difficulty in developing theoretical models basedfor wake-fuselage interaction. In more recent stud-ies, theoretical models including viscous effects havebeen discussed by Affes and co-workers[17, 18].

CFD investigations of the rotor-cylinder inter-action have been presented previously by vari-ous researchers. An early numerical investigationbased on potential flow methods was presented byKomerath and co-workers[19]. More recent worksinclude research efforts in which the rotor effectis modelled using an actuator disk and in CFDinvestigations using a full simulation of the time-dependent rotor-cylinder problem with moving ro-tor mesh(es). The latter category mainly involvesworks based on overset mesh methods, for examplethe work of Hariharan and Sankar[20]. Park andKwon[10] presented results for this test case usingan unstructured-mesh sliding-plane method. Inter-estingly, the predictions based on the Euler equa-tions by both Hariharan and Sankar[20] and Parkand Kwon[10] under-predict the peak in averagedpressure present at the back of the rotor disk rela-tive to the experimental data.

3 Sliding-plane CFD method

The Helicopter Multi-Block (HMB) CFD code [1, 2,3, 13] was employed for this work. HMB solves theunsteady Reynolds-averaged Navier-Stokes equa-tions on block-structured grids using a cell-centredfinite-volume method for spatial discretisation. Im-plicit time integration is employed, and the re-sulting linear systems of equations are solved us-ing a pre-conditioned Generalised Conjugate Gra-dient method. For unsteady simulations, an im-plicit dual-time stepping method is used, based on

75.2

Jameson’s pseudo-time integration approach [21].The method has been validated for a wide range ofaerospace applications and has demonstrated goodaccuracy and efficiency for very demanding flows.Examples of work with HMB can be found in refer-ences [1, 2, 13, 22, 23, 24]. Several rotor trimmingmethods are available in HMB along with a blade-actuation algorithm that allows for the near-bladegrid quality to be maintained on deforming meshes[1].

The HMB solver has a library of turbulence clo-sures which includes several one- and two- equa-tion turbulence models and even non-Boussinesqversions of the k − ω model. Turbulence simula-tion is also possible using either the Large-Eddy orthe Detached-Eddy approach. The solver was de-signed with parallel execution in mind and the MPIlibrary along with a load-balancing algorithm areused to this end. For multi-block grid generation,the ICEM-CFD Hexa commercial meshing tool isused and CFD grids with 10-20 million points andthousands of blocks are commonly used with theHMB solver.

The underlying idea behind the sliding-mesh ap-proach can be explained using Figure 1 which showsthe definition of two layers of halo cells around theboundary surface of each block. In the sliding planealgorithm, this concept is extended to deal withgrids which are discontinuous across the interfaceand can also be in relative motion. Figure 1(b)presents a situation where two adjacent blocks havenon-matching cell faces. If the halo cells of eachblock are populated with interpolated values of theflow field variables, the solver will have no difficultyin updating the flow solution. The application ofthe sliding-plane algorithm to non-matching gridsas well as grids in relative motion will result innon-matching cell faces as sketched in Figure 1(b).There are three main steps involved in populatingthe halo cells: i) identification of the neighbour-ing cells for each halo-cell, ii) interpolation of thesolution at the centroids of the halo cells and iii)exchange of information between blocks associatedwith different processors. The last step is importantfor computations on distributed-memory machinesonly. Regardless of the identification and interpo-lation methods employed, the halo-cell values arecomputed using:

φhalo =i=n∑

i=1

wiφi (1)

where φ represents any flow field variable, wi is theweight associated with the ith neighbour of the halocell and n is the number of neighbours.

The distance-based interpolation (shown in Fig-ure 1(c)) computes a weighted sum of flow field data

of neighbouring cells within an interaction radius.The weights are inversely proportional to the dis-tance of the cell centre from the projected point onthe sliding plane interface and are scaled to sumup to one. Figure 1(d) shows the cell-face over-lap interpolation, in which case the weight for eachneighbour is directly proportional to the fractionof the projected cell face area that overlaps withthe cell face of this neighbour cell. In the contextof finite-volume discretisation methods for conser-vation laws based on numerical fluxes through cellfaces, the cell-face overlap interpolation is the pre-ferred method. However, an interpolation methodbased on the overlap weighting of Figure 1(d) doesnot necessarily enforce conservation and due to dif-ferences in grid sizes on both sides of the sliding-plane interface may acts as a spatial filter.

The present implementation of the sliding-meshalgorithm is based on the cell-face overlap interpo-lation method presented in Figure 1(d). Sliding-mesh interfaces can be of arbitrary shape and forthis reason the contributing cell surfaces must allbe projected on the curvilinear ξ, η, ζ axes as usedin the present finite-volume solver. This step canbe combined with a transformation from to conser-vative variables so that flux-weighted summationscan also be computed.

4 GeorgiaTech teetering-rotor test case

The first rotor-fuselage test case considered in thepresent work, is the experiment conducted at Geor-gia Institute of Technology for a idealised fuselageinteracting with a two-bladed teetering rotor[4]. Forthis test case, unsteady surface pressure measure-ments, as well as, particle-image velocimetry flowfield measurements are available in the literature.This availability and the low geometric complexityof the considered wind tunnel model make this awell-established test case for investigation into in-teractional aerodynamics as well as CFD code val-idation. The configuration consists of a 134mm di-ameter cylindrical idealised airframe with a hemi-spherical nose. It is supported by a wind tunnelsting, independent of the two-bladed rotor that isdriven by a shaft projecting down from the windtunnel ceiling. In the present work, both the windtunnel supper for the airframe as well as the rotordrive shaft are neglected. Figures 3(a) and (b) showthe idealised geometry considered in the present in-vestigation. The rotor centre was located 1.0 rotorradius behind the centre of the hemispherical nosecone and 0.3 rotor radius above the centre line ofthe airframe. The rotor consists is a teetering un-twisted rotor with NACA0015 section and 86 mmchord and 450 mm radius. The grid used has a totalof 514 blocks and 2.5 · 106 cells. The rotor grid has

75.3

324 blocks and 1.6 · 106 cells. Therefore, the background grid containing the airframe has 190 blockswith an O-type topology around the cylindrical air-frame with hemispherical node and 0.9 · 106 cells.The test case has an advance ratio of 0.10, lead-ing to CT = 0.0090. Collective and cyclic controlswere eliminated in the experiment, while the ro-tor is mounted with a 6o forward shaft tilt. Since,the simulations for this test case are mainly con-ducted to validate the present sliding-plane CFDmethod[2], the rotor mesh motion and deformationmethod used for fully articulated rotors[1] was usedhere as well. Therefore, in the simulations, the one-piece rotor from the experiment was replaced by arotor with small root cut-out and a simple ellip-soidal rotor head. The far-field boundaries consid-ered in the simulations are formed by a rectangu-lar box. The rotor grid has a flat upper and lowerboundary and a cylindrical outer boundary surface.This cylindrical mesh is embedded in a cylindricaldrum-shaped cavity in the stationary airframe-windtunnel grid. The sliding-plane method is employedon drum-shaped surface surrounding the rotor grid,as sketched in Figures 3(c) and (d). The surfacemesh for the airframe and rotor is also shown inFigure 3. In the present simulations, the first-harmonic flapping motion of the teetering rotor wasreplaced by a cyclic pitch motion and modified ro-tor shaft inclination, using the pitch-flapping equiv-alence. The flapping coefficients were obtain frompublished work[10]. The motivation behind the re-moval of the flapping motion is that the close prox-imity of the rotor and the cylinder for ψ = 180o, i.e.at the front of the rotor disk, leads to a rotor gridwith a lower domain boundary close to the rotorplane. The flapping motion would have given riseto a much more significant grid deformation of therotor grid than the equivalent pitching motion.

Figure 4 presents the chordwise surface pressuredistribution in six spanwise stations of the rotorfor ψ = 0o, 90o, 180o and 270o. The plots clearlyshow that the effect of the flapping of the rotor is toincrease the effective blade incidence at retreatingside as well as the rear part of the rotor disk. Thelow tip Mach number of 0.295, combined with themoderate advance ratio of 0.10 render the flow sub-sonic, including in the outboard stations on the ad-vancing side. The first rotor-fuselage interactionalaerodynamic effect considered here is the change inthe time-averaged pressure distribution along thecrown line of the cylinder compared to the steadystate pressure without the rotor. Figure 5 shows theresults from two Euler simulations compared to theexperimental data for this averaged pressure. Thefigure shows two distinct peaks in pressure near thetip of the rotor blades. For this untwisted rotor,the rotor clearly carries most of the load in the out-

board stations of the rotor. The stagnation of theinduced velocity component normal to the cylindersurface gives rise to a pressure increase. The Eu-ler simulations obviously do not include the effectsof the viscous interaction of the vortex wake of therotor with the cylinder boundary layer. Also, theexperimental data indicate that the flow will haveseparation in the nose region (where the cp has aplateau) through at least part of the rotor revolu-tion, an effect absent from the simulations. Figure 5clearly shows the effect of the flapping on the cylin-der surface pressure. Consistent with the increasedrotor loading on the advancing side and rear partof the rotor disk shown in Figure 4, this increasedrear loading increases the surface pressure increasein the second peak, while the reduced loading at thefront of the disk due to flapping reduces the firstpressure peak. The instantaneous surface pressurealong the crown of the cylinder is shown in Figure6. The figure compares the Euler results includingthe blade flapping with experimental data. Figure6(a) and (b) shows the situation when the blade ispassing over the nose of the cylinder, for blade az-imuth 180o and 185o, respectively. The simulationdoes resolve the sharp rise surface pressure well,considering the absence of viscous effects and thecoarseness of the used mesh. The pressure increasedue to the rotor induced flow far exceeds the stag-nation pressure of the freestream flow. The plotsalso show the strong azimuthal dependency of theinstantaneous pressure, which means that a slightshift in phasing relative to the experimental datacould lead to serious discrepancies in comparisonswith the experiment. Figure 6(c) and (d) show thepressure for blade azimuth 145o and 155o, respec-tively. This is the situation 35o and 25o degreesazimuth before the blade passage. Clearly, the in-duced pressures are significantly lower than before,since no direct interaction with the blade occurs forthese azimuths.

5 ROBIN test case

The first rotor-fuselage test case involves theROBIN model helicopter model [6, 25, 26]. Theoverall configuration is shown in Figure 7(a). Thefour-blade rotor has an aspect ratio of 13 and con-sists of a NACA0012 section, with a linear twistof 8o. In the experimental setup, the rotor issuspended from the wind tunnel roof, while thefuselage has a floor-mounted wind-tunnel support.Both supporting structures are omitted in the ge-ometry used here. The rotor hub is modelled asan ellipsoidal surface. The geometry includes the2-inch rotorshaft offset from the fuselage centreline,and the 3o forward tilt of the rotor shaft. Figure7(b) shows the locations of the surface pressure taps

75.4

and inflow flow measurements from the NASA ex-periments, which are used here. The test case con-sidered here has a rotor tip Mach number of 0.5, theadvance ratio is 0.15 and the rotor thrust coefficientwas CT /σ = 0.0656 in the experiment. The rotortrim state is that reported by Park and Kwon[9],with collective, longitudinal and lateral cyclic pitchangles of 6.0o, −2.2o and −2.0o, respectively. Theinviscid flow simulations were conducted on multi-block structured grids with the sliding plane inter-face located one blade chord below the rotor disk.The fuselage grid has an O-type topology in the di-rect vicinity of the fuselage, embedded in a domainwith a cylindrical side surface, with the same di-ameter as the rotor grid far-field boundary, and anupper surface orthogonal to the rotor shaft. Thegrid has 240 blocks and 4.0 · 106 cells. The topol-ogy and mesh are shown in Figure 7(c). The ro-tor grid has a C-H topology, with 456 blocks and5.5 · 106 cells. The rotor grid has 50 cells in thespanwise direction of each blade, 45 cells in the sur-face normal direction, 150 cells around the bladechord and 40 cells in the streamwise direction be-tween the blades. The simulation was run for 4 ro-tor revolutions using azimuthal steps of 1.0 degree.For the 4th rotor revolution, the thrust coefficientwas CT /σ = 0.0066, which is within 0.6% of thevalue for the 3rd revolution, indicating a sufficientlevel of convergence, confirmed by surface pressureplots for the 3rd and 4th revolution discussed later.The neighbours searches and interpolation weightswere pre-computed as discussed in Ref.[2], requiringabout 5% of the total CPU time. The sliding-planemethod added an additional 5−6% communicationoverhead for the parallel simulation conducted on40 Pentium 4 processors of a Linux cluster.

Figure 8 compares the time-averaged inducedflow field components in the stream-wise and rotor-disk normal direction from the experiment[7] withCFD data averaged over one rotor revolution.The agreement is favourable, with a slight over-prediction of the stream-wise component. This isan encouraging result, since any loss of continuityacross the sliding plane would have an effect on theobtained velocity field.

Time-averaged surface pressure coefficients areshown in Figure 9 for the cross-sections x/L=0.35and x/L=1.17. The small discrepancy at the lowersurface for x/L=1.17 can be (partly) attributed tothe absence of the wind tunnel support in the CFDgeometry. Figure 10 compares the predicted time-dependent surface pressure coefficients with the ex-perimental data[26]. The pressure in the four cen-treline positions defined in Figure 7(b) are shown inFigures 11(a)-(d). The pressure in probe locationson the side of the fuselage fairing is shown in Figure11(a) and (b), for the retreating and advancing side

of the rotor, respectively. The peak-to-peak pres-sure fluctuations agree favourably with the exper-iment. Also, the obtained results favourably withthe results of Park and Kwon[9], which are shownhere for comparison.

6 GOAHEAD rotor-fuselage test case

A second rotor-fuselage test case demonstrates thecapability of the method to handle more complex,realistic helicopter geometries. The case consideredhere is the wind-tunnel model of a medium-weightgeneric helicopter with the 4-bladed ONERA 7ADrotor, equipped with anhedral tips and parabolictaper, and the BO105 2-bladed tail rotor. This con-figuration is under investigation for the GOAHEADEC 6th Framework Research Project. Figure 12shows the geometry and the multi-block struc-tured mesh used for the Reynolds-Averaged Navier-Stokes simulations. For this full helicopter geom-etry, both main and tail rotor are placed withina drum-shaped sliding-plane interface, as shown inFigure12(a-b). The close proximity of the main andtail rotor planes are notable in the figure, whichleads to a additional challenge in the generation ofthe multi-block structured meshes used here. Themain rotor drum has the 5o forward tilt of the mainrotor shaft, while the tail rotor drum is tilted aboutthe x-axis as well as the z-axis (in the tail rotorhub-centred coordinate system) to provide a smallforward and upward tail rotor thrust component.The multi-block mesh used here, consists of 3786blocks and approximately 27 · 106 cells. The meshin the y = 0 plane is shown in Figure12(c-e). Thecase considered corresponds to an economic cruisecondition, for which the free-stream Mach numberis 0.204 and the tip Mach number of the rotor 0.62.A representative rotor trim schedule is used in thesimulation, i.e. the rotor has cyclic pitch change aswell as a harmonic blade flapping. The multi-blocktopology of the rotors is designed to handle the griddeformation as discussed in Ref.[1]. This test casewas run in parallel processors on the Hector super-computer at EPCC in Edinburgh. The simulationswas run for three rotor revolutions with a time-stepcorresponding to 0.25o rotor rotation and the k−ωturbulence model was used.

Figure 13(a) shows the instantaneous surfacepressure distribution at main rotor azimuth 90o ofthe third revolution for the economic cruise condi-tion at µ = 0.3. The effect of the blade passing onthe surface pressure distribution of the front partof the fuselage is shown in detail in Figure 13(b),where x = 0.75 plane is shown. The main rotorblade passing through the front of the rotor diskclearly induces a (delayed) pressure rise on the for-ward fuselage, as discussed previously in Ref.[2].

75.5

The interaction of the tail rotor with the fin isshown in Figure13(c), showing the cp contours inthe z = 0.775 cross section. The tail rotor blade isat ψ = 0o, which corresponds to the downward ver-tical position. For the rotation direction of the tailrotor used here, this position is in the retreating sideof the tail rotor disk. The blade stagnation pres-sure in the selected cross-section is therefore onlyaround twice the fin stagnation pressure. In addi-tion to the direct impulsive effect, the tail rotor-fininteraction also includes the effect of the tail rotorinduced velocity on the flow around the side-forcegenerating fin, by effectively changing the flow an-gle in a time-periodic fashion. This effect is moredifficult to analyse than the pressure impulse effectshow in the figure. A comparison of simulation re-sults with and without tail rotor would clearly showthis contribution.

7 Conclusions

A computational analysis of helicopter interactionalaerodynamics is currently under way at the CFDLaboratory at the University of Liverpool. Thepresent paper showed results obtained using theHMB CFD method, which has recently been ex-tended with a sliding-mesh algorithm enabling sim-ulations of flows around full helicopter configura-tions. A comparison of the results obtained usingthe HMB method with experimental data showsthat the method is capable of resolving the maininteractional flow features for the generic cases. Asimilar comparison for the GOAHEAD test casehas not yet been conducted, but is planned for thenear future in the framework of the European UnionFramework 6 GOAHEAD project. The results ob-tained for the GOAHEAD test case show the capa-bility of the CFD method to handle flow simulationsfor complex helicopter configuration in demandingflight conditions.

Acknowledgements

During this work, R. Steijl was supported by the Eu-ropean Union under the Integrating and Strengthen-ing the European Research Area Programme of the 6thFramework, Contract Nr.516074 (GOAHEAD project).

References

[1] R. Steijl, G.N. Barakos, and K.J. Badcock. AFramework for CFD Analysis of Helicopter Rotorsin Hover and Forward Flight. Int. J. Numer. Meth.

Fluids, 51:819–847, 2006.

[2] R. Steijl and G.N. Barakos. Sliding Mesh Al-gorithm for CFD Analysis of Helicopter Roto-Fuselage Aerodynamics. accepter for publicationin Int. J. Numer. Meth. Fluids, December, 2007.

[3] K.J. Badcock, B.E. Richards, and M.A. Woodgate.Elements of computational fluid dynamics on blockstructured grids using implicit solvers. Progress in

Aerospace Sciences, 36:351–392, 2000.

[4] A.G. Brand, H.M. McMahon, and N.M. Komerath.Surface Pressure Measurements on a Body Subjectto Vortex Wake Interaction. AIAA journal, 27(5),1989.

[5] J.M. Kim and N.M. Komerath. Summary of theinteraction of a Rotor Wake with a Circular Cylin-der. AIAA journal, 33(3), 1995.

[6] C.E. Freeman and R.E. Mineck. Fuselage Sur-face Pressure Measurements of a Helicopter Wind-Tunnel Model with a 3.15-Meter Diameter SingleRotor. Technical Report TM-80051, NASA, 1979.

[7] J.W. Elliott, S.L. Althoff, and R.H. Sailey. InflowMeasurements Made With a Laser Velocimeter ona Helicopter Model in Forward Flight - Volume I:Rectangular Planform Blades at an Advance Ra-tio of 0.15. Technical Report TM-100541, NASA,1988.

[8] J.W. Elliott, S.L. Althoff, and R.H. Sailey. InflowMeasurements Made With a Laser Velocimeter ona Helicopter Model in Forward Flight - Volume II:Rectangular Planform Blades at an Advance Ra-tio of 0.23. Technical Report TM-100541, NASA,1988.

[9] Y. Park, H.J. Nam, and O.J. Kwon. Simulationof unsteady rotor-fuselage aerodynamic interactionusing unstructured adaptive meshes. American He-licopter Society 59th Annual Forum, Phoenix, Ari-zona, May 6-8., 2003.

[10] Y. Park and O. Kwon. Simulation of unsteady ro-tor flow field using unstructured adaptive slidingmeshes. J. American Helicopter Society, 49(4):391–400, 2004.

[11] H.J. Nam, Y. Park, and O.J. Kwon. Simulationof unsteady rotor-fuselage aerodynamic interactionusing unstructured adaptive meshes. J. American

Helicopter Society, 51(2):141–148, 2006.

[12] T. Renaud, C. Benoit, J.-C. Boniface, and P. Gar-darein. Navier-stokes computations of a completehelicopter configuration accounting for main andtail rotor effects. 29th European Rotorcraft Forum,Friedrichshafen, Germany, September, 2003.

[13] G. Barakos, R. Steijl, K. Badcock, and A. Brockle-hurst. Development of CFD Capability for Full He-licopter Engineering Analysis. 31st European Ro-torcraft Forum, 13-15 September 2005, Florence,Italy, 2005.

[14] O. Boelens, G. Barakos, M. Biava, A. Brocklehurst,M. Costes, A. D’Alascio, M. Dietz, D. Drikakis,J. Ekatarinaris, I. Humby, W. Khier, B. Knutzen,F. Le Chuiton, K. Pahlke, T. Renaud, T. Schwarz,R. Steijl, L. Sudre, L. Vigevano, and B. Zhong. TheBlind-Test Activity of the GOAHEAD Project.33rd European Rotorcraft Forum, Kazan, Russia,September, 2007.

75.6

[15] S.G. Liou, N.M. Komerath, and H.M. McMahon.Velocity Measurements of Airframe Effects on aRotor in Low-Speed Forward Flight. AIAA jour-

nal, 26(4), 1988.

[16] S.G. Liou, N.M. Komerath, and H.M. McMahon.Velocity Field of a Cylinder in the Wake of a Rotorin Forward Flight. AIAA journal, 27(9), 1989.

[17] H. Affes, A.T. Conlisk, J.M. Kim, and N.M.Komerath. Model for Rotor Tip Vortex-AirframeInteraction, Part 2: Comparison with Experiment,Vortex Wake Interaction. AIAA journal, 31(12),1993.

[18] H. Affes, Z. Xiao, A.T. Conlisk, J.M. Kim, andN.M. Komerath. Model for Rotor Tip Vortex-Airframe Interaction, Part 3: Viscous Flow on Air-frame, Vortex Wake Interaction. AIAA journal,36(3), 1998.

[19] N.M. Komerath, D.M. Mavris, and S.G. Liou. Pre-diction of Unsteady Pressure and Velocity over aRotorcraft in Forward Flight. Journal of Aircraft,28(8), 1991.

[20] N. Hariharan and L.N. Sankar. Unsteady OversetSimulation of Rotor-Airframe Interaction, CircularCylinder. AIAA journal, 40(4), 2003.

[21] A. Jameson. Time Dependent Calculations UsingMultigrid, with Applications to Unsteady Flowspast Airfoils and Wings. AIAA Paper 1991-1596,10th Computational Fluid Dynamics Conference ,Honolulu, Hawai, June 24-26, 1991.

[22] R. Morvant, K.J. Badcock, G.N. Barakos, andB.E. Richards. Aerofoil-Vortex Interaction Usingthe Compressible Vorticity Confinement Method.AIAA J., 43(1):63–75, 2004.

[23] A. Spentzos, G. Barakos, K. Badcock, B.E.Richards, P. Wernert, S. Schreck, and M. Raffel.CFD Investigation of 2D and 3D Dynamic Stall.AIAA J., 34(5):1023–1033, 2005.

[24] R. Steijl and G.N. Barakos. A ComputationalStudy of the Advancing Side Lift Phase Problem.Journal of Aircraft, 45(1):246–257, 2008.

[25] M.S. Chaffin and J.D. Berry. Navier-Stokes andPotential Theory Solutions for a Helicopter Fuse-lage and Comparison with Experiment. TechnicalReport TM-4566, NASA, 1994.

[26] R.E. Mineck and S. Althoff Gorton. Steady andPeriodic Pressure Measurements on a Generic He-licopter Fuselage Model in the Presence of a Rotor.Technical Report TM-2000-210286, NASA, 2000.

75.7

Sliding−plane interface

Halo 2 Halo 1 Cell 1

Block 2 Block 1

Halo 2

Halo 2

Halo 1

Halo 1

Cell 1

Cell 1

Block 1

Block 2

Sliding−plane interface

(a) Halo cells and matching cells (b) Non-matching cells along interface

12

34

(x, y, z)

(II) area−based interpolation

12

34

(x, y, z)3

21

4

(ξ, η, ζ)

(c) Distance-based interpolation (d) Face area-based interpolation

Figure 1: Sliding plane interface with matching and non-matching cell faces. (a) matching halo cells,(b) non-matching interface, (c) sketch of distance-based interpolation, (d) sketch of cell-area weightedinterpolation.

Halo 2

Cell 2

Cell 1

Halo 1

Cell 1

Cell 2

Mesh 1

Mesh 21

23

Cell 2

Cell 1

Cell 1

Cell 2

Halo 1

Halo 2 Mesh 1

Mesh 21

23

(a) First layer of halo cells (mesh 1) (b) Second layer of halo cells (mesh 1)

Figure 2: Sliding-plane algorithm employing ’direct’ interpolation. The cell face is projected on thesliding-mesh interface. The cell-face overlap determines the interpolation weight for each of the donorcells.

75.8

(a) (b)

(c) (d)

Figure 3: GeorgiaTech test case. The two-bladed teetering rotor is mounted above an idealised airframewith cylindrical shape. The boundary surface and block boundaries along these surface are shown in (a),while (b) shows the surface mesh. The rotor grid outer surface forms a cylindrical drum (c) placed withina matching drum-shaped cavity in the background mesh (d).

75.9

x/c

M2C

p

-0.25 0 0.25 0.5 0.75

-0.05

-0.025

0

0.025

0.05

r/R = 0.35r/R = 0.45r/R = 0.55

x/c

M2C

p

-0.25 0 0.25 0.5 0.75

-0.1

-0.05

0

0.05

0.1

r/R = 0.75r/R = 0.85r/R = 0.95

(a) ψ = 0o, inboard (b) ψ = 0o, outboard

x/c

M2C

p

-0.25 0 0.25 0.5 0.75

-0.05

-0.025

0

0.025

0.05

r/R = 0.35r/R = 0.45r/R = 0.55

x/c

M2C

p

-0.25 0 0.25 0.5

-0.1

-0.05

0

0.05

0.1

r/R = 0.7r/R = 0.8r/R = 0.9

(c) ψ = 90o, inboard (d) ψ = 90o, outboard

x/c

M2C

p

-0.25 0 0.25 0.5 0.75

-0.05

-0.025

0

0.025

0.05

r/R = 0.35r/R = 0.45r/R = 0.55

x/c

M2C

p

-0.25 0 0.25 0.5 0.75

-0.1

-0.05

0

0.05

0.1

r/R = 0.75r/R = 0.85r/R = 0.95

(e) ψ = 180o, inboard (f) ψ = 180o, outboard

x/c

M2C

p

-0.25 0 0.25 0.5 0.75

-0.05

-0.025

0

0.025

0.05

r/R = 0.35r/R = 0.45r/R = 0.55

x/c

M2C

p

-0.25 0 0.25 0.5 0.75

-0.1

-0.05

0

0.05

0.1

r/R = 0.75r/R = 0.85r/R = 0.95

(g) ψ = 270o, inboard (h) ψ = 270o, outboard

Figure 4: GeorgiaTech test case (µ = 0.10, CT = 0.0090). Chordwise surface pressure distribution for 6spanwise stations at different rotor azimuths.

75.10

x/R

Cp

0 0.5 1 1.5 2 2.5 3 3.5 4-1

-0.5

0

0.5

1

1.5

2

Figure 5: GeorgiaTech test case (µ = 0.10, CT = 0.0090). Revolution averaged pressure along thecrownline of the cylindrical body. CFD results with and without flapping are compared with experimentaldata.

x/R

Cp

0 0.25 0.5 0.75 1 1.25 1.5 1.75 2-1

0

1

2

3

4

5

6

7

8

experiment: ψ = 180o

Euler (flapping): ψ = 175o

Euler (flapping): ψ = 180o

x/R

Cp

0 0.25 0.5 0.75 1 1.25 1.5 1.75 2-1

-0.5

0

0.5

1

1.5

2

2.5

3

3.5

4

experiment: ψ = 6o

Euler (flapping): ψ = 0o

Euler (flapping): ψ = 5o

(a) ψ = 180o (b) ψ = 5o

x/R

Cp

0 0.25 0.5 0.75 1 1.25 1.5 1.75 2-1

-0.5

0

0.5

1

1.5

2

2.5

3

3.5

4

experiment: ψ = 144o

Euler (flapping): ψ = 145o

x/R

Cp

0 0.25 0.5 0.75 1 1.25 1.5 1.75 2-1

-0.5

0

0.5

1

1.5

2

2.5

3

3.5

4

experiment: ψ = 154o

Euler (flapping): ψ = 155o

(a) ψ = 145o (b) ψ = 155o

Figure 6: GeorgiaTech test case (µ = 0.10, CT = 0.0090). Instantaneous pressure along the crownline ofthe cylindrical body for different rotor azimuths.

75.11

(a) ROBIN configuration and (b) Pressure tap and inflowsliding-plane interface measurement locations

(c) Fuselage and symmetry plane mesh

Figure 7: ROBIN configuration used in the present CFD study. The wind tunnel supports for the floor-mounted fuselage and the roof-mounted rotor are omitted. (a) sliding-mesh interface is located 1.0 bladechord below the rotor disk. (b) location of pressure taps and inflow measurements used in the presentwork.

75.12

r/R

µ i(m

ean)

0 0.2 0.4 0.6 0.8 1 1.2-0.05

-0.04

-0.03

-0.02

-0.01

0

0.01

0.02

0.03

0.04

0.05

CFDExperiment

r/R

µ i(m

ean)

0 0.2 0.4 0.6 0.8 1 1.2-0.05

-0.04

-0.03

-0.02

-0.01

0

0.01

0.02

0.03

0.04

0.05

CFDExperiment

(a) µi, ψ = 0o (b) µi, ψ = 180o

r/R

λ i(m

ean)

0 0.2 0.4 0.6 0.8 1 1.2-0.07

-0.06

-0.05

-0.04

-0.03

-0.02

-0.01

0

0.01

0.02

0.03

CFDExperiment

r/R

λ i(m

ean)

0 0.2 0.4 0.6 0.8 1 1.2-0.05

-0.04

-0.03

-0.02

-0.01

0

0.01

0.02

0.03

0.04

0.05

CFDExperiment

(c) λi, ψ = 0o (d) λi, ψ = 180o

Figure 8: Robin rotor-fuselage test case (µ = 0.15). In-plane (µi) and normal (λi) velocity ratios at 0o

(a,c ) and 180o (b, d) azimuth angles. The velocity was extracted above the rotor disk plane at z/c = 1.1.The thrust coefficient was cT = 0.0065, Mtip = 0.51, advance ratio µ = 0.15

z/L

time-

aver

aged

Cp

-0.15 -0.1 -0.05 0 0.05 0.1 0.15-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

Experiment, advancing sideExperiment, retreating sideCFD, 4th rev., advancing sideCFD, 4th rev., retreating side

X/L = 0.35

z/L

time-

aver

aged

Cp

-0.15 -0.1 -0.05 0 0.05 0.1 0.15-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

Experiment, advancing sideExperiment, retreating sideCFD, 4th rev., advancing sideCFD, 4th rev., retreating side

X/L = 1.17

Figure 9: Robin rotor-fuselage test case (µ = 0.15). Time-averaged surface pressure coefficient. Thrustcoefficient cT = 0.0065, Mtip = 0.51, advance ratio µ = 0.15

75.13

ψ[deg]

Cp

0 45 90 135 180 225 270 315 3600

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8 CFD: 3rd revolutionCFD: 4th revolutionExperimentPark&Kwon

D6

ψ[deg]

Cp

0 45 90 135 180 225 270 315 360-0.1

0

0.1

0.2

0.3

0.4

0.5

0.6 CFD: 3rd revolutionCFD: 4th revolutionExperiment

D8

(a) centreline, x/L = 0.096 (b) centreline, x/L = 0.201

ψ[deg]

Cp

0 45 90 135 180 225 270 315 360-0.4

-0.3

-0.2

-0.1

0

0.1

0.2 CFD: 3rd revolutionCFD: 4th revolutionExperiment

D22

ψ[deg]

Cp

0 45 90 135 180 225 270 315 360-0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7 CFD: 3rd revolutionCFD: 4th revolutionExperimentPark&Kwon

D15

(c) centreline, x/L = 0.896 (d) centreline, x/L = 1.368

Figure 10: Robin rotor-fuselage test case (µ = 0.15). Centreline surface pressure distribution for ROBINtest case.

ψ[deg]

Cp

0 45 90 135 180 225 270 315 360-0.3

-0.25

-0.2

-0.15

-0.1

-0.05

0

0.05 CFD: 3rd revolutionCFD: 4th revolutionExperimentPark&Kwon

D19

ψ[deg]

Cp

0 45 90 135 180 225 270 315 360-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1 CFD: 3rd revolutionCFD: 4th revolutionExperimentPark&Kwon

D25

(a) x/L = 0.896, y/L = -0.07, z/L = 0.125 (b) x/L = 1.368, y/L = 0.07, z/L = 0.125

Figure 11: Robin rotor-fuselage test case (µ = 0.15). Surface pressure in probes left and right of thefuselage fairing for ROBIN test case.

75.14

(a) Geometry and sliding planes (b) Surface mesh and sliding planes

(c) Mesh in y = 0 plane

(d) Zoom of nose region of mesh in y = 0 plane (e) Zoom of tail region of mesh in y = 0 plane

Figure 12: GOAHEAD full helicopter geometry. (a-b) the main and tail rotors are placed within drum-shaped sliding-plane interfaces. (c-e) The mesh in the y = 0 plane is shown, which does not constitutea symmetry plane. The rotor meshes are not shown for clarity. The mesh has 3786 blocks and 27 · 106

cells. (a) global view of mesh, (b) detail of mesh in nose region, (c) close-up of mesh in tail region.

75.15

(a) Surface pressure coefficient at ψ = 90o

Sliding plane

Sliding plane Sliding plane

Sliding plane

(b) main rotor-fusselage interaction (c) tail rotor-fin interaction

Figure 13: GOAHEAD full helicopter geometry. Economic cruise condition. Instantaneous pressurecoefficients are shown. (a) instantaneous surface pressure coefficient at main rotor azimuth 90o, (b) mainrotor-fuselage interaction, x = 0.75 cross section (approx. mid span of blade), (c) tail rotor fin interaction,z = 0.775 cross-section, at base of fin.

75.16