Aerospace Science and Technology 20 (2012) 12–20

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Aerospace Science and Technology

www.elsevier.com/locate/aescte

Comparing and benchmarking engineering methods for the prediction of X-31aerodynamics

Michael R. Mendenhall a,∗,1, Stanley C. Perkins Jr. a,2, Maxmillian Tomac b,3, Arthur Rizzi b,4,Raj K. Nangia c,5

a Nielsen Engineering and Research, 2700 Augustine Dr, Suite 200, Santa Clara, CA 95054, USAb Department of Aeronautical and Vehicle Engineering, Royal Institute of Technology (KTH), Teknikringen 8, Stockholm, 100 44, Swedenc Nangia Aero Research Associates, 78-Queens Road, Clifton, Bristol, BS8 1QU, UK

a r t i c l e i n f o a b s t r a c t

Article history:Available online 7 May 2012

Keywords:Engineering methodsAerodynamicsLongitudinal stabilityX-31 aircraftPrediction methods

A number of useful engineering methods are available for fast and economic estimates of theaerodynamic characteristics of complex flight vehicles. This article investigates the application of threespecific engineering methods to the X-31 fighter configuration, and CFD, wind tunnel, and flight testdata are used for comparison and evaluation purposes. The emphasis is on static longitudinal stabilityaspects up to high angles of attack; however, selected asymmetric and unsteady effects are considered.Results from the engineering methods are in good agreement with experiment and CFD for angles ofattack up to 15◦ for most cases and higher angles for some cases. Results for pitching moment are ingood agreement with CFD, but many of the nonlinear characteristics of the airplane are not predictedby the engineering methods. The quality of the longitudinal stability results is discussed in terms of theprediction of the center of pressure on the vehicle. The results provide improved understanding of thecontinued usefulness of engineering methods as an analysis tool during the design phase and into theflight test diagnostic phase of a new aircraft.

© 2012 Elsevier Masson SAS. All rights reserved.

1. Introduction

An assessment of Stability and Control Prediction Methods forNATO Air and Sea Vehicles was conducted in RTO AVT-161. Theassessment includes the use of advanced CFD methods; however,a number of useful engineering methods are available for fast andeconomic estimates of the aerodynamic characteristics of complexflight vehicles [9].

Fast and reliable engineering tools that can predict the flyingand handling qualities of a high-performance aircraft at the earlyconceptual design stage of a project are essential for the under-standing of flight characteristics early in the design cycle. Theyare also useful later in the design cycle for configuration designchanges or flight test planning and analysis. The foundation forthese engineering predictions involves the coupling of the aero-dynamic characteristics with the flight dynamics behavior of theaircraft to determine the flying and handling qualities. This article

* Corresponding author. Tel.: +11 408 727 9457; fax: +11 408 727 1428.E-mail addresses: mrm@nearinc.com (M.R. Mendenhall), scp@nearinc.com

(S.C. Perkins Jr.), maxtomac@kth.se (M. Tomac), rizzi@kth.se (A. Rizzi).1 President and CEO.2 Senior Research Engineer.3 Research Assistant.4 Professor.5 Consulting Engineer.

1270-9638/$ – see front matter © 2012 Elsevier Masson SAS. All rights reserved.http://dx.doi.org/10.1016/j.ast.2012.05.001

describes various computational engineering methods to predictthe aerodynamic characteristics required for stability and controlanalysis.

The highest fidelity model available for aerodynamic analysis isthe numerical solution of the Navier–Stokes equations; however,these solutions are often impractical for use in preliminary design.There is still a need for fast and accurate engineering methodswhich can provide aerodynamic characteristics quickly and eco-nomically. Engineering prediction methods are simplifications ofthe advanced CFD models, and they can vary in fidelity from em-pirical or handbook methods like DATCOM, to physics-based linearpotential-flow models, to Euler-equation solvers for more realisticinviscid flow calculations. Three different engineering methods areconsidered for comparison and discussion in this article.

The first of these is the Nangia Aero method based on a po-tential panel code enhanced with models for leading-edge vortexflow separation and eventual vortex breakdown. The second is theSHAMAN code based on a vortex-lattice solver with an advancedarray of empirical models to enhance its capability to model thephysics of the flow at high angles of attack. The third method isCEASIOM, a framework tool that integrates discipline-specific toolsfor aircraft conceptual design.

This article benchmarks all three approaches against wind tun-nel data for the X-31. The wind tunnel experiments performed onthe detailed X-31 model provided an excellent data set for vali-dation and comparison purposes. This data set has been provided

M.R. Mendenhall et al. / Aerospace Science and Technology 20 (2012) 12–20 13

Nomenclature

c chordCD drag coefficientCL lift coefficientCm pitching-moment coefficientCN normal-force coefficientL reference length

p,q, r rotation rates

t time

Xcp longitudinal center of pressure

Xmrc pitching-moment reference center

α,β angles of attack and sideslip

Fig. 1. X-31 in flight.

by DLR (Deutsches Zentrum fur Luft-und Raumfahrt) to the par-ticipants within the NATO RTO task group AVT-161 Assessment ofStability and Control Prediction for NATO Air & Sea Vehicles [7].

2. X-31 description

The X-31 is an experimental high-angle-of-attack delta-wingcanard configuration aircraft with lex, strake, and flaps. The air-craft was designed to test thrust vectoring technology and con-trolled flight at high angles of attack as seen in Fig. 1. The fullscale aircraft has a length of 13.2 meters (including thrust vector-ing paddles) and a total wingspan of 7.3 meters. The DLR windtunnel model has a length of 1.7 meters and a total wingspan of1.0 meter (7.3:1.0 scale). The engine inlet has been replaced by aplug for wind tunnel tests. Gaps between slats, flaps, and controlsurfaces have been sealed in the CFD model. Sealing of gaps wasdone since earlier investigations have shown that these gaps havea negligible effect at angles of attack below 12◦ [1].

In addition to the DLR wind tunnel data described above, inde-pendent wind tunnel data from a sub-scale test at NASA [5] andflight test data from DARPA are compared with SHAMAN results todemonstrate specific features of that method.

3. Engineering analysis methods

This article describes the results from three different and in-dependent engineering analysis methods, each with its advantagesand disadvantages. The three methods are briefly described below,and results from each method are presented in Section 4.

3.1. Nangia Aero panel code

Nangia [4] used linear theory and surface singularity methods(panel codes) to assess their applicability on the X-31 class ofconfigurations. The emphasis was on longitudinal stability aspects;however, consideration was also given to selected asymmetric ef-fects. The panel code is a “first-order” type method. Similar in

Fig. 2. X-31 configuration paneling.

formulation with other panel codes, elements on the outer surfacesof the aircraft components carry distributions of sources and dou-blets. The canard and wing wakes can be relaxed in this method,a feature considered important in view of the presence of a ca-nard on the X-31. The effect of the relaxed trailing vortex wake onthe canard and wing span load distribution at moderate angle ofattack is shown in a previous publication [9].

An example of the panel representation of the X-31 is shown inFig. 2. The intake is faired over as in the experimental model, andthe forward and aft body strakes are included in this model.

The preferred analysis technique with this engineering methodis to strictly follow a component build-up approach. Start with awing alone, then add a canard, and follow that with the addition ofa fuselage and tail fins. With this approach, the accuracy of resultscan be assessed at every stage.

3.2. SHAMAN engineering analysis method

SHAMAN [3] is a preliminary design prediction and analysissoftware tool applicable to configurations operating in pre- andpost-stall flow conditions. Its approach is a direct coupling of fluiddynamics and flight mechanics for use in the flight regimes wherethe flow phenomena are dominated by vorticity and separationassociated with high angles of incidence and large values of roll,pitch, and yaw rotational rates. Under these flow conditions, non-linear forces and moments caused by boundary layer separationand mutual interference between configuration components candominate the aerodynamic characteristics of the maneuvering ve-hicle. Traditional linear prediction methods are highly developed

14 M.R. Mendenhall et al. / Aerospace Science and Technology 20 (2012) 12–20

Fig. 3. SHAMAN flow diagram.

for low-angle flow conditions, but these same methods are not al-ways suited to all aspects of the difficult problems associated withmaneuvering vehicles because of the influence of the vortical flowfield around the vehicle.

An analytically based method to predict the nonlinear aerody-namic forces and moments on a general configuration undergoingsteady and unsteady maneuvers is contained in the SHAMAN code.The major physical flow phenomena over the vehicle at high inci-dence angles are simulated, including the fuselage leeside separa-tion vorticity and the trailing vortex wakes from control surfaces.Post-stall flight regimes are handled with empirical correlations ofwing data. The mutual interactions between the vehicle geometry,its motion, and the time-dependent wake are considered in theprediction of the unsteady aerodynamic characteristics. SHAMANcan be used to predict specified vehicle motions or flow conditions,or it can be coupled with a six-degree-of-freedom equation-of-motion solver to predict flight trajectories and transient perfor-mance.

The simulation of the flow phenomena and of the major phys-ical features of the flow field requires an appropriate flow modelfor each component of the configuration. The fuselage wake is rep-resented with the vortex cloud model which provides a means toconsider unsteady flow conditions. The unsteady development ofthe wake from a moving vehicle and the motion of the wake rela-tive to the vehicle are calculated. In a trajectory, the history of theflow conditions and the motion of the vehicle dictate the instanta-neous state of the vorticity at every instant in time. The unsteadyvortex field is a result of time-varying flow conditions which are afunction of the motion of the vehicle. The capability to analyze thedetails of a trajectory calculation enables the user to investigateflow phenomena which can dominate trajectory characteristics andto better understand the physics of such phenomena. The resultingmethod contained in SHAMAN is applicable to generic configura-tions, it is not dependent on specific empirical information, and itis economical to use. A simple flow diagram of the SHAMAN codeis shown in Fig. 3.

The objective of the use of empirical modeling is to achieve auseful design/analysis method for preliminary design that can treatcases with high angle of attack, high rotational rates, and post-stallflight. The features included in the SHAMAN vortex-lattice panelingare:

• Relaxed wake for both steady and quasi-steady motion• Vortex cloud model (fuselage vorticity)• Predicted separation line on the fuselage• Wake vortex tracking and interference effects• Wing and canard stall models (empirical)• Vortex bursting (empirical)

3.3. CEASIOM multifidelity framework system

The philosophy underlying the construction of the CEASIOMaerodynamic model differs from that of the two previous methods.Instead of adopting just the potential-flow model and then en-hancing it with highly refined empiricism, CEASIOM uses adaptive-fidelity CFD, either a vortex-lattice method, a panel method, or anEuler solver. The selection depends on the level of fidelity neededto capture the inviscid flow physics under consideration. There isonly secondary reliance on empirical modeling to enhance that re-alism further. CEASIOM also contains a RANS solver for highestfidelity and DATCOM for the lowest fidelity to complete the suiteof methods.

Today there is an increasing interest in running CFD compu-tations earlier in the design stage to estimate static and dynamicforces and moments acting on the aircraft, as a precursor to windtunnel testing, in order to get a head start on the controls design.For this strategy to succeed, the simulation methods must be fast,reasonably accurate, and easy to use, so that changes in the air-craft configuration can be assessed at acceptable costs. These threerequirements can be addressed by adaptive fidelity CFD, low-ordermethods in the low-speed linear region, and higher-order solverswhen it is necessary to consider the high-speed and nonlinearflight regions.

The CEASIOM framework, developed in the SimSAC project[10,8,2] and today open-source project (http://www.ceasiom.com/),integrates discipline-specific tools for the purpose of aircraft con-ceptual design. These include CAD, mesh generation, CFD, stability& control, and aeroelasticity. However, this article will only focuson adaptive CFD with the range of models described above andthe scripting tools which are integrated into the AMB-CFD module(Fig. 4).

The CFD solver is Edge, an edge- and node-based Navier–Stokes flow solver applicable to unstructured grids. Edge is basedon a finite-volume formulation where a median dual grid formsthe control volumes with the unknowns allocated in the cen-ters. The governing equations are integrated to steady state, with

Fig. 4. AMB-CFD module for aerodynamic model building in CEASIOM framework system.

M.R. Mendenhall et al. / Aerospace Science and Technology 20 (2012) 12–20 15

Fig. 5. Multifidelity X-31 meshes generated for the CEASIOM methods.

a line-implicit approach in areas with highly stretched elements,and explicitly elsewhere with a multistage Runge–Kutta scheme.The steady state convergence is accelerated by FAS agglomerationmultigrid.

The Tornado VLM code is an open source Matlab implementa-tion of a modified horse-shoe vortex singularity method for com-puting steady and low reduced frequency time-harmonic unsteadyflows over wings. The lifting surfaces are created as unions ofthin, not necessarily flat, quadrilateral surface segments. Effects ofairfoil camber and leading edge control surfaces are modeled bysurface normal rotation. The modification to the horseshoe vor-tices allows trailing edge control surface deflection by actual meshdeformation. The steady wake can be fixed in the body coordi-nate system or relaxed to follow the free stream. Overall effectsof compressibility at elevated Mach numbers are assessed by thePrandtl–Glauert scaling, and zero-lift drag estimates are obtainedby Eckert’s flat plate analogy. The fuselage may be modeled bycombinations of flat plates or Munk’s slender body singularitymethod; however, the choice of the proper geometry for suchmodels requires experience. Most analyses are done by simply re-placing the portion of the lifting surface covered by the fuselage bya flat plate with zero incidence. The basic flow solver is wrappedby user interfaces to create tables of aerodynamic coefficients, aswell as stability derivatives, for export to flight simulators andflight-control system design software.

Fig. 5 illustrates a hierarchy of different X-31 meshes gener-ated for the different fidelity methods. The very simple mesh forVLM simulations, Fig. 5(a), takes into account the canard, wing andvertical tail. More detailed geometry has been built and meshedfor Euler simulations shown in Fig. 5(b). The mesh was gener-ated automatically with the CAD and mesh tool SUMO [2], andthe CFD solutions were obtained by running the CFD code Edgein Euler mode. The highest fidelity X-31 model is meshed semi-automatically with ICEM CFD driven by the script tool for RANSsimulations, Fig. 5(c). The solutions in this case are also obtainedby running the CFD code Edge in RANS mode.

4. X-31 results

The three engineering methods were applied to the X-31 fighteraircraft configuration representing the DLR wind tunnel data for awide range of angles of attack. The longitudinal aerodynamic char-acteristics from the three methods are compared with wind tunneldata and higher fidelity CFD methods from CEASIOM to assesstheir longitudinal aerodynamic prediction capabilities. In addition,SHAMAN was applied to a sub-scale model of the X-31 in post-stall flight at very high angles of attack to illustrate its capabilityfor aerodynamic prediction under these extreme flight conditions.Finally, SHAMAN was applied to the full-scale X-31 in a flight testmaneuver at high angles of attack for which flight test data areavailable to illustrate the use of this engineering method for flightmechanics diagnostic analysis.

4.1. Longitudinal aerodynamic characteristics of the DLR model

For the initial results, all of the methods described above wereapplied to the X-31 model tested by DLR [9]. The basic X-31configuration is considered with flaps and canard at zero deflec-tion angles. Longitudinal aerodynamic coefficients on the X-31were obtained using all the different fidelity methods in CEA-SIOM, the Nangia panel method, and SHAMAN, and these resultsare compared with wind tunnel data in Fig. 6. For the engi-neering methods, the wakes are relaxed and interacting. For theSHAMAN results, fuselage vortex shedding and wing and canardstall are included. An example of the complex vortex field asso-ciated with the X-31 at high angles of attack is shown in a laterfigure.

As shown in Fig. 6(a), all methods predict the CL slope quitewell in the linear range, and this is not an unexpected result.There is some disagreement in the angle for zero lift for allthe methods and the experiment, but this is a sensitive param-eter which may depend on subtle geometric characteristics ofthe model which are not represented by the prediction meth-ods. When the canard and wing begin to stall, the linear meth-ods differ more from the experiment. The SHAMAN results, withan empirical stall model included, begin to indicate effects of ca-nard and wing stall earlier than the data because of a deficiencyin the stall model. If data were available on the high angle ofattack post-stall characteristics of the X-31 canard and wing air-foil sections, these could be included in SHAMAN to improve theoverall lift prediction. This information was not available for thisstudy.

The drag coefficients from all the methods are compared withexperiment in Fig. 6(b). Note that the RANS method is the onlyprediction which includes viscous drag, and these results are gen-erally in better agreement with experiment than the other meth-ods. The Euler and engineering methods under-predict the dragat low lift, which is not surprising since they do not take intoaccount viscous effects. The results from the Tornado VLM andSHAMAN give zero drag at zero lift as would be expected froman inviscid method at these flow conditions. The general char-acter of the predicted drag is similar to the measurements, butit is clear that all of these methods, with the exception of theRANS solutions, are not appropriate for accurate drag predic-tion.

The predicted pitching moment coefficients are not in goodagreement with the measurements as shown in Fig. 6(c). In gen-eral, the results from the RANS simulations are better than thelower-fidelity methods, but no engineering method predicts themoment curve slope well over the complete alpha range. The VLMmodel is sensitive to small changes in geometry; in this case thewing tip twist was altered by a few degrees. The Euler results missthe effect causing the drop in pitching moment at 15–20◦ angle ofattack; however, this effect seems to be delayed to a higher angleof attack in the Euler results. The SHAMAN results after canard and

16 M.R. Mendenhall et al. / Aerospace Science and Technology 20 (2012) 12–20

(a) Lift coefficient

(b) Drag coefficient

Fig. 6. X-31 configuration force and moment coefficients.

wing stall do not exhibit the highly nonlinear character of the data,but these results do approach the experimental results at very highangles of attack. Some of the nonlinear behavior of the pitchingmoment is explained in the next figure showing the longitudinalcenter of pressure.

A comparison of longitudinal center of pressure results inFig. 6(d) shows a general lack of agreement between the predictionmethods and experiment, and much of the extreme nonlinearityin the data is not seen. It should also be noted that these resultsare very small numbers, an indication that the center of pressureis very near to the center of moments for the experiment. Theinteresting result from this comparison is that all the methodsare predicting the position of the longitudinal center of pressurewithin a few percent of the mean aerodynamic chord. The resultsat low angle of attack are not shown because of the lack of accu-racy in this calculation when the lift or normal force approacheszero.

4.2. Sub-scale high angle-of-attack aerodynamic characteristics

A selected set of results from the engineering method SHAMAN[3,6] is presented for another sub-scale wind tunnel test of theX-31 [5] to illustrate how this method can be used at very highangles of attack. It should be noted again that SHAMAN is essen-tially the same level of engineering method as the panel methodsdiscussed previously; however, SHAMAN has included empiricaltechniques which will permit investigation at high angles of attackin the post-stall region, and SHAMAN also includes a forebody vor-tex shedding model, essential for high angles of attack.

The measured and predicted normal force characteristics on amodel of the X-31 at very high angles of attack are shown inFig. 7(a). For this calculation, it was critical that the SHAMAN wingstall model be used to represent the loss of lift at higher anglesof attack, and it was important that the nonzero canard deflectionand leading edge flap angles be modeled correctly. These results

M.R. Mendenhall et al. / Aerospace Science and Technology 20 (2012) 12–20 17

(c) Pitching-moment coefficient

(d) Longitudinal center of pressure

Fig. 6. (continued)

are similar to the previous comparisons in that the predicted on-set of stall of the canard and wing appears to occur at a lowerangle of attack than that measured. The general character of thepredicted normal force coefficient is in reasonable agreement withthe data. More details on this result are available elsewhere [6].

The comparison of pitching moment coefficients is shown inFig. 7(b) where the agreement between SHAMAN and the mea-sured data is very reasonable for an engineering method. The de-tails of the predicted pitching moments over the large range ofangle of attack are not particularly good, but the general characterof the pitching moment approximates that exhibited by the data.The extreme difference in the character of the pitching momentcoefficients in Figs. 6(c) and 7(b) is explained in the following fig-ure.

In Fig. 7(c), the measured and predicted locations of the longi-tudinal center of pressure with respect to the moment referencecenter are compared. Notice in these results, the moment refer-ence center is a much larger distance from the center of pressure,thus reducing the sensitivity of the pitching moment results tosmall changes in center of pressure. The error in the measuredand predicted center of pressure location is about the same forboth cases.

4.3. Maneuvering aerodynamic analysis

SHAMAN has application as a diagnostic tool for the assessmentof aerodynamics and flying characteristics of flight test aircraft. Ina flight test maneuver of the X-31, the aircraft is flying in trimat approximately 25◦ angle of attack. The maneuver begins with

18 M.R. Mendenhall et al. / Aerospace Science and Technology 20 (2012) 12–20

(a) Normal force coefficient

(b) Pitching moment coefficient

(c) Longitudinal center of pressure

Fig. 7. Measured and predicted aerodynamic characteristics on an X-31 sub-scale model at high angles of attack.

M.R. Mendenhall et al. / Aerospace Science and Technology 20 (2012) 12–20 19

Fig. 8. Measured flow conditions during a flight-test maneuver of the X-31.

Fig. 9. Measured and predicted forces on an X-31 in a flight-test maneuver.

a 180◦ roll around the velocity vector followed by a rapid pullup. In the flight test, the X-31 departs from the intended trajec-tory at about 55◦ angle of attack (t = 15 s). SHAMAN was appliedto this maneuver by forcing the aircraft through the actual mea-sured flight conditions and control deflections. Careful examinationof the forces and moments on the vehicle and the associated flowfield can provide some insight into the flow phenomena whichmay be responsible for the departure.

The flow angles and angular rates measured during the ma-neuver are shown in Fig. 8. These conditions are imposed on theX-31 configuration in SHAMAN as the vehicle is forced throughthe actual maneuver and the vortex field is allowed to build andevolve with the changing flight conditions. The measured and pre-dicted aerodynamic forces on the X-31 are compared during themaneuver in Fig. 9. The two arrows in Figs. 8 and 9 mark two keyflight conditions, one prior to departure and the other after depar-

ture, which are examined in more detail to better understand thefeatures of the aircraft flow field at this critical time during themaneuver.

In Fig. 10, the predicted vortex field is shown on the X-31 be-fore and after departure. Because of the high angle of attack, thevortex field is moving away from the airplane at a high angle, butthere are still significant interference effects of the vorticity on thevehicle. Note that the rudder is engulfed in part of the forebodyvortex field just prior to departure. After departure, there is moreasymmetry in the vortex fields because of the high angles of in-cidence and sideslip (shown in Fig. 10), and most of the forebodyand wing vorticity is above the rudder. As part of the diagnosticanalysis of this maneuver, SHAMAN provides the time history ofthe loads on each component of the aircraft to help understandthe changing loads as the flow field changes.

20 M.R. Mendenhall et al. / Aerospace Science and Technology 20 (2012) 12–20

Fig. 10. Predicted vortex field for the X-31 in a maneuver.

5. Concluding remarks

A discussion of the application of three engineering analysismethods to the prediction of aerodynamic characteristics of theX-31 aircraft is presented. The methods are compared with wind-tunnel data, flight-test data, and advanced CFD methods to demon-strate the feasibility of the use of these simpler methods to providefast and economic analysis results for complex aircraft configura-tions. The main emphasis is on the longitudinal stability aspectswith component contributions; however, selected asymmetric ef-fects are also considered, including a full-scale flight test maneuvercase exhibiting six-degree-of-freedom motion at high angles of at-tack.

For the symmetric cases, the predictions have provided goodagreement with experiment and CFD for lift and normal force upto angles of attack of about 15◦ . With empirical enhancements,one of the methods has application to higher angles of attack. Forpitching moment, agreement with other CFD results is good up toangles of attack of about 15◦ , but the experiments show more non-linear behavior at angles of attack above 10◦ . It is demonstratedthat comparison of center of pressure location may be more reli-able than comparison of pitching moment coefficients which ex-hibit greater nonlinearity.

The application of these engineering methods is encouraging,and they have the potential to assist in improved understandingof the aerodynamics of complex configurations with strongly in-teracting and separating vortical flows. They have the advantage ofbeing practical for use early in the design cycle of flight vehiclesbefore CFD results may be available.

It was demonstrated that a useful portion of the overall as-sessment of the aerodynamic stability and control of a complexconfiguration can be achieved rapidly using engineering methods.Viscous effects can be introduced through empiricism to identifypossible flow-break onsets requiring further investigation. This al-lows more costly high-order methods and wind tunnel testing to

be focused on key areas. Configuration refinements can be intro-duced where necessary before very costly model manufacture isundertaken.

Acknowledgements

The work described in this paper is part of current in-houseR & D activities for the three organizations involved. No externalfinancial support has been received. The authors acknowledge thework of DLR in supplying Wind Tunnel results. Any opinions ex-pressed are those of the authors who have been privileged to bemembers of the RTO AVT-161 task group.

References

[1] O.J. Boelens, CFD analysis of the flow around the X-31 aircraft at high angle ofattack, AIAA-2009-3628, 2009.

[2] D. Eller, Mesh generation using sumo and tetgen, SimSAC Delivery report D2.3-5, Royal Institute of Technology, Stockholm, 2009.

[3] M.R. Mendenhall, S.C. Perkins Jr., Predicted high-alpha aerodynamic character-istics of maneuvering aircraft, AIAA 96-2433, 1996.

[4] R.K. Nangia, X-31 vector aircraft, low speed stability & control, comparisons ofwind tunnel data & theory (focus on linear & panel codes), AIAA-2009-3898,2009.

[5] NASA Langley Research Center, Private communication with J.M. Brandon, 1992.[6] S.C. Perkins Jr., M.R. Mendenhall, Prediction of post-stall aerodynamic charac-

teristics of maneuvering aircraft, AIAA 99-3115, 1999.[7] A. Schuette, M. Cummings, T. Loeser, Dan D. Vicroy, Integrated computa-

tional/experimental approach to UCAV and delta-canard configurations regard-ing stability & control, in: 4th Symposium on Integrating CFD and Experimentsin Aerodynamics, 2009.

[8] M. Tomac, A. Rizzi, Creation of aerodynamic database for the X-31, AIAA Paper-2010-501, 2010.

[9] M. Tomac, A. Rizzi, R.K. Nangia, M.R. Mendenhall, S.C. Perkins Jr., Comparingand benchmarking engineering methods on the prediction of X-31 aerodynam-ics, AIAA 2010-4694, 2010.

[10] R. von Kaenel, A. Rizzi, J. Oppelstrup, T. Goetzendorf-Grabowski, M. Ghoreyshi,L. Cavagna, A. Berard, CEASIOM: Simulating stability & control with CFD/CSM inaircraft conceptual design, in: 26th Int’l Congress of the Aeronautical Sciences,Anchorage, Alaska, Sept 2008 (ICAS-Paper 061).