Aerodynamic Loads on External StoresSaab 39 Gripen

Evaluation of CFD methods for estimating loads on external stores

Christian Spjutare

September 21, 2009

ii Christian Spjutare

Master Thesis

September 2009

LIU-IEI-TEK-A09/00686SE

Department of Management and Engineering

Division of Applied Thermodynamics and Fluid Mechanics

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AbstractExternal stores mounted on aircraft generate loads which need to be estimatedbefore first takeoff. These loads can be measured in a wind tunnel but since thepossible store configurations are basically endless, testing them all is neither eco-nomically feasible nor time efficient. Thus, scaling based on geometrical similar-ity is used. This can, however, be a crude method. Stores with similar geometri-cal properties can still behave in different ways due to aerodynamic interferencecaused by adjacent surfaces.

To improve the scaling performance, this work focuses on investigating twoCFD codes, ADAPDT and Edge. The CFD simulations are used to derive thedifference in aerodynamic coefficients, or the ∆-effect, between a reference storeand the new untested store. The ∆-effect is then applied to an existing wind tunnelmeasurement of the reference store, yielding an estimation of the aerodynamicproperties for the new store.

The results show that ADAPDT, using a coarse geometry representation, haslarge difficulties predicting the new store properties, even for a very simple storeconfiguration on the aircraft. Therefore it is not suited to use as a scaling tool inits present condition. Edge on the other hand uses a more precise geometry rep-resentation and proves to deliver good estimations of the new store load behavior.Results are well balanced and mainly conservative. Some further work is neededto verify the performance but Edge is the recommended tool for scaling.

iv Christian Spjutare

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PrefaceThis thesis was carried out in the Loads Department at Saab Aerosystems inLinkoping as part of a master’s degree in Mechanical Engineering at LinkopingUniversity.

I would like to express my gratitude to my supervisors at Saab Aerosystems,Jenny Poovi and Mickael Stenborg. They provided invaluable support by dis-cussing different ideas and by answering all of my questions. My supervisors atLinkoping University, Roland Gardhagen and Matts Karlsson, have also providedmany thoughts for which I am very grateful. Furthermore I would like to thankAnders Lindberg and Bengt Mexnell at Saab Aerosystems for taking the time todiscuss options and for providing expert opinions. Many thanks also go out toPer Weinerfelt for introducing me to the ADAPDT software and for highly appre-ciated insights to the mathematical modelling of the problem. The task has alsoinvolved many of the other employees in the Loads Department and the StructuralDynamics, Flutter & Separation Department at Saab Aerosystems and I wouldlike to thank all of them for the enthusiasm they have shown and for every piecethey have contributed. I would also like to mention David Eller at KTH RoyalInstitute of Technology, who generously helped me with the modelling softwaredwfSumo.

Finally, I want to thank my near and dear ones, especially Asa, for patienceand constant loving support during this work.

Linkoping, August 2009Christian Spjutare

vi Christian Spjutare

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Table of Contents1 Introduction 1

1.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Purpose . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.3 General Definitions . . . . . . . . . . . . . . . . . . . . . . . . . 31.4 Delimitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2 Pilot Study 52.1 Simulation Tools . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2.1.1 ADAPDT . . . . . . . . . . . . . . . . . . . . . . . . . . 62.1.2 Edge . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

3 Work Process 83.1 ADAPDT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83.2 Edge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93.3 Postprocessing . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

4 Results 124.1 Selecting Appropriate Models for ADAPDT . . . . . . . . . . . . 124.2 Mesh Independence for Edge . . . . . . . . . . . . . . . . . . . . 134.3 CFD vs. Wind Tunnel Data . . . . . . . . . . . . . . . . . . . . . 144.4 Scaling Using the CFD Results . . . . . . . . . . . . . . . . . . . 15

4.4.1 Mach 0.6, Alpha Sweep . . . . . . . . . . . . . . . . . . 164.4.2 Mach 0.8, Alpha Sweep . . . . . . . . . . . . . . . . . . 174.4.3 Mach 0.6, Beta Sweep . . . . . . . . . . . . . . . . . . . 17

5 Analysis 195.1 General Performance . . . . . . . . . . . . . . . . . . . . . . . . 195.2 Higher Speed Scaling . . . . . . . . . . . . . . . . . . . . . . . . 205.3 Errors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

6 Discussion 216.1 Improving the Results Further . . . . . . . . . . . . . . . . . . . 216.2 Recommendations for Continued Work . . . . . . . . . . . . . . 226.3 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

7 Summarising the Methodology 237.1 Modelling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 237.2 Preprocessing . . . . . . . . . . . . . . . . . . . . . . . . . . . . 237.3 Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 247.4 Postprocessing . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

viii Christian Spjutare

References 25

A CFD Values, Store1, Mach 0.6, Alpha Sweep I

B CFD Values, Store2, Mach 0.6, Alpha Sweep IV

C CFD Values, Store1, Mach 0.8, Alpha Sweep VII

D CFD Values, Store2, Mach 0.8, Alpha Sweep X

E CFD Values, Store1, Mach 0.6, Beta Sweep XIII

F CFD Values, Store2, Mach 0.6, Beta Sweep XVI

G Scaling at Mach 0.6, Alpha Sweep XIX

H Scaling at Mach 0.8, Alpha Sweep XXII

I Scaling at Mach 0.6, Beta Sweep XXV

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Nomenclature

α Angle of attack [°]β Angle of sideslip [°]CC Side force coefficient [-]CD Drag force coefficient [-]CL Lift force coefficient [-]CN Normal force coefficient [-]CT Axial force coefficient [-]CMX Roll moment coefficient [-]CMY Pitch moment coefficient [-]CMZ Yaw moment coefficient [-]M Mach number [-]

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Saab Aerosystems 1

1 IntroductionSaab Aerosystems, a part of the Saab Group, offers advanced airborne systemsand services throughout the product life cycle to defence customers and aerospaceindustries. The main product is the Gripen fighter.

The Loads Department is responsible for generating load data as a basis forstress analyses of the aircraft hull and subsystems. The data include loads forstatic dimensioning as well as load spectra for dimensioning against fatigue anddamage resistance.

Aircraft are complex technical systems; especially military aircraft which havea large flight envelope including high speed, great altitude and rapid manoeuvres.Additionally, they need to carry a large amount of external equipment, also calledexternal stores. The performance of an aircraft is highly dependent on its aerody-namic properties and when equipped with bombs, missiles and external fuel tanksthe aerodynamics change drastically. This introduces new loads on the aircraftstructure and they need to be determined to assure structural integrity.

1.1 Background

When new external stores are to be integrated on the aircraft, it is important todetermine the loads they generate and study the corresponding effects on the air-craft. This applies to both aerodynamic and inertial loads and this report focuseson the aerodynamic loads. These loads can be estimated in a variety of ways. Oneof the more accurate methods would be to perform a wind tunnel measurement ofthe store mounted in the desired pylon on the aircraft.

The Gripen fighter, as it looks today, has five pylon stations for external stores.Together with more than thirty different types of bombs, missiles, drop tanks andother equipment, this generates a huge number of possible store configurations onthe aircraft. See Figure 1. All of these cannot be tested in a wind tunnel since windtunnel measurements are very expensive, time consuming and require meticulouspreparations.When integrating a new kind of store it is important to be able to produce goodload results in a fast way and a wind tunnel measurement does only meet thefirst half of those requirements. Therefore it is appealing to use some form ofscaling technique to estimate the loads on the new store based on wind tunnelmeasurements for other stores.

Generally, aerodynamic data for free flight conditions is provided by the man-ufacturer of the store. If not, a program such as Missile DATCOM can be used[1, 2, 3]. However, data for free flight conditions may differ a lot from data ob-tained from wind tunnel measurements with the store mounted on the aircraft.This is a result of interference effects between the store, the wing and stores

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Figure 1: A large number of stores can be mounted on the aircraft, making windtunnel measurements a costly business. Copyright Gripen International.

mounted in adjacent pylons. These effects must be considered, thus data for freeflight conditions is not enough to predict the aerodynamic loads.

The scaling at Saab Aerosystems currently consists of a number of differentactions, for which geometrical similarity is the basis. If a new external store hasa similar appearance to a previously wind tunnel measured one, it is assumed tobehave in a similar way. The scaling methods include, for instance, comparingfree flight aerodynamics and geometric scaling from existing wind tunnel mea-surements, based on reference areas and lengths.

To improve the accuracy of the current scaling, the interest has increased fordeveloping a scaling methodology based on simulation of the flow field around thebodies using computational fluid dynamics (CFD). For this task two CFD codeswere selected for evaluation; ADAPDT and Edge.

1.2 Purpose

The purpose of this Master thesis is to outline the basis for a new load scalingmethodology. To do so, the CFD codes ADAPDT and Edge are investigated froma load scaling perspective to determine if they are suited to use as scaling tools inthe Loads Department at Saab Aerosystems.

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1.3 General Definitions

The coordinate system used throughout this report is basically a standard systemfrom flight mechanics, as can be seen in Figure 2. The angle of attack, α and theangle of sideslip, β, are defined positive in positive y and z directions respectively.Out of the five force coefficients shown above, only two are used throughout thisreport, CC and CN . Forces in the x direction are not measured in the wind tunneland therefore not considered here.

Figure 2: Defining positive directions for forces, moments and angles.

1.4 Delimitations

Investigating different methods is a time consuming task, hence the large amountof store configurations available needed to be reduced into a narrow range to per-form the simulations and scaling on. Initially, two different stores were chosen.These were selected based on two criteria:

• Two types of stores with some geometrical similarity.

• Previously wind tunnel measured.

Figure 3 shows an example of what geometrical similarity may involve. The storesselected are here referred to as Store1 and Store2 and they are geometrically sim-ilar to some extent. Identical wind tunnel measurements existed for these storesmounted on the Gripen wing. The wind tunnel measurements were used as a base

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(a) A simple store (b) A more complex store

Figure 3: Two stores which have identical central body sections but different nosecones, tails and fin assemblies. They are considered geometrically similar.

for the scaling and also as a reference to evaluate the scaling results. All resultspresented in this report are normalised.Due to time constraints associated with the work process of scaling aerodynamicloads at the Loads Department, the use of the Navier-Stokes equations in Edgewas deemed unrealistic. The CFD simulations must be carried out within hoursrather than days.

This report focuses on the simulation and scaling of aerodynamic loads. Iner-tial loads are not considered. Any mention of loads refers to purely aerodynamicloads.

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2 Pilot Study

Aerodynamic scaling is a difficult topic and most of the research done in the fieldis focused on scaling wind tunnel data from small scale models to full-size ap-plications [4, 5, 6]. Scaling data from one full size application to another withsimilar appearance is a sparsely investigated field.

Applying a single scale factor for an entire range of α or β is not sufficient.It is easy to illustrate the difficulties associated with this form of scaling. Figure4 shows a comparison of wind tunnel measured CMZ coefficients for Store1 andStore2. Multiplying one of the curves by a constant scale factor will never resultin a curve that resembles the other. Thus, scaling with a constant factor throughoutthe α-range is too crude a method.

Figure 4: The dotted curve represents the scaling result of the Store2 curve multi-plied by a constant factor -2.

In aerodynamics, basic scaling can be performed using different rules of thumband the moment coefficients are generally more difficult to scale than the force co-efficients [7, 8]. Some rules that may be applied are that the side force coefficientCC and the roll moment coefficient CMX can be scaled using the relation betweenthe bodies’ wingspans squared. In this case, due to the existence of interferencefrom other bodies, these rules may range from fairly accurate to useless.

Interference effects caused by surfaces in the vicinity of the store are highlyirregular and difficult to predict [9, 10]. Therefore the interference effects on astore are hard to estimate by simply applying an interference effect from a similarstore. A slight change in position or size can result in fundamentally different flowfields.

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2.1 Simulation ToolsCFD is an umbrella term for different methods to simulate flow fields aroundobjects in a fluid [6, 11, 12]. All CFD methods suffer from lack of precision inpredicting complex flow fields, at least when computational times are required tobe short. When ∆-effects are considered they are generally considered able todeliver acceptable results.

The ∆-effect is the difference in aerodynamic loads between two simulations.The general assumption is that the error produced in each of the two different sim-ulations will be approximately the same, eliminating each other when consideringthe ∆-effect instead of the raw CFD values.

2.1.1 ADAPDT

ADAPDT (Aero Dynamic Analysis and Preliminary Design Tool) is an in-housedeveloped panel code based on the vortex lattice potential flow theory [13, 14, 15].The vortex lattice method models surfaces as infinitely thin sheets of vortices tocalculate the loads. The theory neglects viscous effects, making it valid only forsubsonic speeds and low angles of attack [16]. The fast computation time is themain benefit of this theory.

Panel methods can be used with both two and three dimensional body repre-sentations and ADAPDT uses the simpler, two dimensional representation. Suc-cessful attempts to integrate three dimensional representation in ADAPDT havebeen made but they are not yet implemented in the available code.

In ADAPDT, bodies are approximated with thin sheets in one plane or in across configuration, see Figure 5. Each sheet is then divided into a number ofsmaller panels.

(a) Cross model (b) Flat sheet model

Figure 5: Front views of the two model types.

2.1.2 Edge

Edge is developed by the Swedish Defence Research Agency, FOI, and it uses theEuler or Navier-Stokes equations to solve flow problems [17]. The Euler equa-tions are a simplification of the Navier-Stokes equations, neglecting viscous ef-

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fects in the flow and speeding up calculation times. This also imposes the sameconstraints on the test envelope as mentioned for ADAPDT. Despite the lack ofviscous effects in the flow solver, it has been pointed out that for predicting ∆-effects for stores on aircraft, the use of the Euler equations may in fact be moreprecise than the Navier-Stokes equations [18].

In contrast to ADAPDT, Edge makes full use of three dimensional geometries.To model the geometries and generate the mesh, dwfSumo and TetGen was used[19, 20].

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3 Work Process

The basic idea behind this thesis is to employ CFD methods to simulate the flowaround both the new store as well as the wind tunnel measured reference storewhen mounted on the aircraft. The differences in aerodynamic loads, the ∆-effect,between these two simulations can be viewed as a scaling unit between the stores.This unit depends on angle of attack, angle of sideslip and Mach number and isapplied to the wind tunnel measurement data for the reference equipment. Theresult is an estimation of the aerodynamic loads for the new equipment.

Scaling was performed using Store1 as the scaling base; the known referencestore. Store2 was used as the unknown, new target store for which accurate loadswere required. The two stores investigated have the same reference areas andlengths, making the resulting coefficient curves for the stores directly comparable.On the other hand, the reference points used in the two wind tunnel measurementsare different. The wind tunnel reference point is the point in the tested modelwhere the loads are measured. To achieve fully comparable loads between the twowind tunnel measurements, the loads for Store2 had to be moved to correspond tothe reference point of Store1 before scaling was performed.

Despite the α and Mach number limitations of the potential flow theory and theEuler equations, both theories were tested for higher angles of attack and speedsto investigate if the ∆-effect could be used there as well.

3.1 ADAPDT

ADAPDT has the disadvantage of not using a three dimensional representationof the geometries. This leaves large room for interpretation of how a body ismodelled accurately. For this reason several different models were initially madeand compared with aerodynamic data for free flight to achieve models that actedas much as the actual store as possible.

Two major designs were tested for the stores; body-shaped sheet design (BSD)and rectangular sheet design (RSD), shown in Figure 6. The RSD was based onusing the smallest possible rectangle to fit the planform. The RSD is currently

(a) Body-shaped sheets (b) Rectangular sheets

Figure 6: Side views of one of the stores modelled with body-shaped and rectan-gular sheets.

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used at Saab Aerosystems for various simulations with good results. The BSDwas chosen to evaluate if using the contours of the body would improve upon theresults of the RSD design. The two designs were tested using the cross model andflat sheet configurations mentioned i section 2.1.1. The number of panels in eachsheet was also varied to find the most suitable combination. This was done byseparately altering the number of panels in the direction of flow and the directionof span from 2 to 32 panels by doubling, 2-4-8-16-32. Consequently, each modelwas simulated 25 times using different panel densities. Finally, the RSD wastested with different sizes of the sheets. The total number of models tested was inthe end somewhere around 15 to 20 per store, resulting in a total of at least 750simulations.

A prefabricated model of the aircraft existed in the Aerodynamics Depart-ment. Pylons 2 and 3 were added and the store models with the best free flightdata agreement were installed on the aircraft wing, Figure 7, and used for the sim-ulations. ADAPDT was tested using both a linear and a nonlinear option at Mach0.6 and 0.8 with an α-sweep between -4° and 20° and a step size of 2°.

Figure 7: The aircraft modelled as a cross model with a store mounted in pylon 2.

3.2 Edge

Three dimensional geometry representation made modelling a simpler task for theEdge calculations. Based on drawings, the stores were modelled as accurately aspossible using the dwfSumo software.

Since no previous dwfSumo models existed and the software lacks the abilityto import CAD geometry, every body had to be modelled, including the Gripenfighter, see Figure 8. Fine details were excluded to keep the mesh size to a min-imum. Also, the vertical stabiliser was removed, since its effect on the store wasassumed to be negligible. The meshes were generated focusing on refinement inthe region of interest; close to the store.

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Figure 8: The aircraft modelled in dwfSumo with a store mounted in pylon 2.Fine details are removed, as well as the vertical stabiliser.

The mesh size was approximately 700,000 nodes, varying with store complexity.Mesh independence was tested using the Edge ’hadaption’ feature which refinesthe mesh based on gradients in the flow parameters. For more information regard-ing this feature, please view the Edge manual [17]. Figure 9 illustrates the meshrepresentation in the vicinity of the store.

Figure 9: Mesh representation close to the store

Boundary conditions were manually placed on the air intakes and exhaust. Inreality the mass flow through the engine would vary with engine thrust. Here thenormal flow velocities were specified at the intake surfaces and were assumed tobe equal to the aircraft velocity. The exhaust boundary condition was calculatedaccordingly, assuming constant mass flow. All other boundary conditions, suchas those on the aircraft surfaces and on the farfield boundary were automaticallyspecified by the mesh generation software.

Simulations were performed at Mach 0.6 and 0.8, using an α-sweep rangingfrom 0° to 15° and a step size of 3°. Edge was executed on a Beowulf clustercomputer, using 8 or 16 processor cores per simulation. Maximum number ofiterations was set to 5,000. The number of simulations performed, including meshindependence study, was close to 120.

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3.3 PostprocessingThe postprocessing step was similar for both ADAPDT and Edge. Scripts for ex-tracting force and moment coefficients were applied to the resulting data, generat-ing MATLAB coefficient libraries. The reference store data was subtracted fromthe new unknown store equivalent to produce the ∆-effect. It was then appliedto the reference store wind tunnel measurement. Finally, plots were generated,showing both scaling results and raw CFD values.

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4 Results

ADAPDT calculations lasted somewhere between 1 to 5 minutes depending on theamount of panels in the model and which method was used; linear or nonlinear.Modelling the store itself was a simple and fast process since the RSD was chosen.The most time consuming task was the adjustment of the ADAPDT models to freeflight data, which required several different models and showed no discerniblepattern.

Edge Euler calculations lasted 20 to 80 minutes, representing up to 50% of thetotal time for modelling, simulation and postprocessing.

4.1 Selecting Appropriate Models for ADAPDT

The cross model design was chosen over the single flat sheet design based on thefirst tests made. The single flat panel design resulted in a greatly underestimatedside force which could not be compensated with altered panel densities or sheetsizes without interfering with the other force and moment coefficients. Thus thedesign was abandoned.

Nonlinear calculations in ADAPDT resulted in numerical errors above α =10°, see Figure 10. This problem was general and occurred for all models. Theresults of the linear and nonlinear calculations were similar for low angles of at-tack, thus the linear method was used.

Figure 10: The nonlinear ADAPDT option generated numerical errors at highangles of attack.

Tests on the BSD model showed that panel density increases, both in length andspan directions, did not make the results converge towards a stable solution. Fig-

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ure 11a shows an example of this, where the curves change directions and magni-tude arbitrarily.

The RSD model generated results that converged towards a stable solution andthe tests showed that panel density on the body should be chosen low in the lengthdirection. Optimal density was at 2 panels. Span density was optimal between8 to 32 panels and was chosen as 8 panels since the differences in results weresmall and few panels reduce the calculation time. Figure 11b shows an exampleof panel density variations in the RSD model compared to free flight data.

(a) Non-converging BSD model of Store1 (b) Converging RSD model of Store1 with goodfree flight data agreement

Figure 11: Panel density was varied in the span direction from 2 to 32 panels.Curve names are defined as (length density-span density), e.g. 2-2.

Fin density was evaluated next and the span density was optimal at 2 panels.Length direction density was found best at 32 panels. To further improve theload behavior of the rectangular models, the sizes of the panels were altered inboth length and span direction. Best correspondence was found by increasing therear fin set span. For Store1 the increase stayed at 5% while for Store2 the in-crease was 65% for optimal results. Thus, selected for final testing were the RSDcross models with increased rear span which provided converging results and bestpossible free flight data agreement.

4.2 Mesh Independence for EdgeThe original 700,000 node meshes were refined to investigate whether a moredense grid would improve the results. This was done using the Edge ’hadaption’feature. Relatively little was gained by increasing the mesh density. The largestrefinements were done in regions of low mesh density far from the store, thus onlyaffecting the flow field around the store to a small extent. After two refinements

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the loads on the stores had only changed 4% from the original values, thus theoriginal meshes were chosen for the final simulations.

4.3 CFD vs. Wind Tunnel Data

Comparisons between raw CFD values and wind tunnel measurements were madeto investigate if the simulation tools could capture the loads for the stores whenmounted on the aircraft. The results for the α-sweep at Mach 0.6 are presented inthis section.

The examples in Figure 12 display a trend for both ADAPDT and Edge wherethe roll moment coefficient is overestimated. Figures 12a and 12b are zoomed into visualise the shapes of the curves. Original curves are available in appendicesA and B, showing the large exaggeration of ADAPDT.

(a) CMX for Store2 (b) CMX for Store1

Figure 12: Roll moment coefficient comparison for wind tunnel, ADAPDT andEdge

Figure 13 shows the pitch moment coefficients for the two stores. For Store2, Fig-ure 13a, ADAPDT has predicted the slope in the right direction but exaggerates themagnitude. In Figure 13b, ADAPDT predicted an erroneous slope direction. TheEdge simulations captured the overall load behavior of both Store1 and Store2.The normal force coefficient proved a difficult task for both ADAPDT and Edge.Edge managed to pinpoint the location of the Store2 curve well, Figure 14a. Turn-ing to Store1 in Figure 14b, the result was overestimated but Edge kept predictingthe direction of the slope in the right way. ADAPDT consistently exaggerated themagnitude of the normal force coefficient and also predicted the direction of theslope wrong in both cases.

See appendices A and B for all charts presenting the raw values delivered byEdge and ADAPDT for the α-sweep at Mach 0.6 and appendices C and D for the

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(a) CMY for Store2 (b) CMY for Store1

Figure 13: Pitch moment coefficient comparison for wind tunnel, ADAPDT andEdge.

(a) CN for Store2 (b) CN for Store1

Figure 14: Normal force coefficient comparison for wind tunnel, ADAPDT andEdge.

α-sweep at Mach 0.8. Appendices E and F show results from a β-sweep at Mach0.6.

4.4 Scaling Using the CFD ResultsThe ∆-effects generated by the CFD codes were added to the Store1 referencewind tunnel measurement which resulted in two different scaling curves; one forADAPDT and one for Edge. These were plotted against the wind tunnel measure-ment for Store2 to evaluate the accuracy of the scaling methods. The charts in thissection also include the wind tunnel measurement for Store1 to get a notion of thescaling starting point. All scaling charts are also available in detail in appendicesG, H and I.

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4.4.1 Mach 0.6, Alpha Sweep

With an α-sweep at Mach 0.6, CC was predicted well by both Edge and ADAPDTscaling, with a slight underestimation (Figure 15a). ForCN in Figure 15b, ADAPDTexaggerated the result and generated an erroneous direction of the slope. Edgeoverestimated the magnitude of the curve at high α but with good overall resem-blance.

(a) Scaling of CC (b) Scaling of CN

Figure 15: Force coefficients at Mach 0.6, α-sweep

The trend for CN continues in Figure 16 for both CMX and CMY where theADAPDT scaling overestimated the size of the coefficients and Edge kept pre-dicting both the slope and the order of magnitude well.

(a) Scaling of CMX (b) Scaling of CMY

Figure 16: Roll and pitch moment coefficients at Mach 0.6, α-sweep

For CMZ , neither Edge, nor ADAPDT did well in scaling the order of magnitudeof the Store2 curve but Edge managed to capture the shape which resulted in a

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parallel displaced curve. See appendix G for this figure and the other scalingresults for the α-sweep at Mach 0.6.

Figure 17: Scaling of CMZ at Mach 0.6, α-sweep

4.4.2 Mach 0.8, Alpha Sweep

Moving to the α-sweep at Mach 0.8, the scaling performance of Edge and ADAPDTwas very similar to the Mach 0.6 case. Only minor differences were seen, forinstance in CC , where Edge performed slightly better than at Mach 0.6 and gener-ated a scaling without underestimation. ADAPDT improved upon its CMZ resultat Mach 0.6 and delivered a slightly more well adjusted scaling. These charts canbe viewed in appendix H.

4.4.3 Mach 0.6, Beta Sweep

The promising performance of Edge led to an additional test; a β-sweep at Mach0.6. Charts showing raw Edge values are available in appendices E and F. Theforce scaling performance, in Figure 18, was generally good, where CC was ade-quate and CN had fair shape resemblance and magnitude.Scaling was less accurate for yaw and roll moments, Figure 19. The slopes of thecurves were overestimated in both cases but Edge picked up the opposite directionof slope for the yaw moment. The pitch moment, Figure 20, was well predictedin shape but slightly underestimated, mainly for positive β. All β-sweep scalingcharts are available in appendix I.

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(a) Scaling of CC (b) Scaling of CN

Figure 18: Force coefficients at Mach 0.6, β-sweep.

(a) Scaling of CMX (b) Scaling of CMZ

Figure 19: Roll and yaw moment coefficients at Mach 0.6, β-sweep.

Figure 20: Scaling of CMY at Mach 0.6, β-sweep

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5 AnalysisThe results from the scaling tests were very different for the two CFD meth-ods. Edge performed relatively well for most aerodynamic coefficients, deliveringloads resembling the wind tunnel measured results. ADAPDT performance on theother hand left much to be desired in terms of both shape and magnitude for allbut one coefficient.

Looking at the time consumed for the total scaling process, the two CFD meth-ods were comparable. The slower simulation times of Edge were compensated bya long and complicated process for adjusting the ADAPDT models to fit free flightaerodynamic data.

5.1 General Performance

ADAPDT only managed to deliver side force coefficient curves that could be con-sidered usable from a scaling perspective. The results for the other coefficientswere unpredictable in both magnitude and shape.

The poor performance should probably be addressed to the coarse geometryrepresentation. The thin sheets may be a good starting point in preliminary evalu-ation of new aircraft and flying bodies but they are not suited for use in a complexflow field as the present one. A plausible explanation for this lies in the theoreticalformulation of the potential flow theory. A closed body with rotational symmetryhas in potential flow no normal force at all. The thin sheets on the other handgenerate a significant normal force in potential flow. The actual normal force ex-erting on the body is neither zero, nor of the magnitude predicted by ADAPDT,but somewhere in between.

Looking at the raw values delivered by ADAPDT, it becomes obvious why thescaling results are not sufficient. ADAPDT rarely managed to capture the shapesof the force and moment curves which in turn means that it could not predict saidshapes in the scaling. This would not necessarily be a problem. If the raw valuepredictions were consistently over or underestimated and the slope directions wereaccurate, the ∆-effect could still be approximately right, delivering a scaling witha good overall magnitude.

Edge delivered values and curve shapes that were generally close to thosemeasured in the wind tunnel. The scaling results presented were well adjusted tothe desired shapes. They were also predictable. For example, Edge showed goodability to foresee changing slope directions. For CMX and CMZ in the β-sweep,Edge scaling was slightly less accurate but the results were mainly conservative.For all test cases, Edge overestimated the maximum curve magnitude by a factor2.5 at most. For ADAPDT, the same factor was in the range of 25 to 30, at leastten times higher.

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5.2 Higher Speed ScalingAt Mach 0.8, where compressible effects are more intrusive, the scaling perfor-mance of both ADAPDT and Edge was very similar to the Mach 0.6 case. ForEdge this looks promising since it may indicate the possibility of using the soft-ware for higher Mach scaling as well. Thus, the ∆-effect may in fact be fairlyaccurate even though the underlying theory is not entirely valid for higher speeds.This will require further investigations to be confirmed.

5.3 ErrorsFor both ADAPDT and Edge the absolute scaling errors increase at high α. Inmost cases, above α = 10° Edge starts to overestimate the magnitude of thecurves. This is expected since the theory applies only to low angles of attack.ADAPDT on the other hand has a steadily growing error throughout the α-range.This generates clearly exaggerated results already at α = 5° in most cases.

It is interesting to note that the error produced by Edge is generally well be-haved and with tests on more stores it may be possible to deduce a correctionfactor for higher alphas. In the case of CMZ a parallel displacement coefficientcould be used to move the whole curve to a more appropriate level. It could beargued that also ADAPDT would benefit from deduction of correction factors butthere is no clear shape correlation between the ADAPDT scaling and wind tun-nel curves. Edge manages this well without corrections. Also, ADAPDT doesin the case of CN predict the slope in the opposite direction. There is no way ofknowing this without having a wind tunnel measurement at hand for comparison.Thus ADAPDT would be an unreliable scaling tool and Edge has proved moreconsistent in this investigation.

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6 DiscussionThe time frame for the complete scaling process using ADAPDT and Edge isnot that different. Edge requires more time during the computer simulations andADAPDT during model adjustments to fit them to free flight data. In the end,the difference is negligible and the choice of method comes down purely to thescaling performance.

When generating the volume mesh for Edge using dwfSumo, it was difficultto get Edge to accept any mesh file exceeding 80 MB. Whether the problem lies indwfSumo or TetGen is unknown but fortunately, the simple configurations chosenin this thesis meant that the mesh files were below that limit. If more complexconfigurations are investigated there is a risk of passing the 80 MB limit whichwill require an investigation of the problem.

It is of great importance that the scaling tool is reliable and ADAPDT shows nosigns of stability in the scaling results. Since, in the actual scaling situation, therewill be no wind tunnel measurements available for the second store, ADAPDTsimply cannot be trusted to predict the new loads. Edge gives a more reassuringimpression and the scaling performance can be considered good. It delivers a veryaccurate scaling when α < 10° for most coefficients.

The Edge scaling was mainly conservative, which is a positive feature. How-ever, a too conservative result is not good and can lead to over-dimensioning orlimitations to the use of the store. ADAPDT was conservative as well but an over-estimation of a factor 25 to 30 would impose restrictions to the flight envelope.

6.1 Improving the Results Further

ADAPDT nonlinear simulations resulted in numerical errors. The cause is un-known and perhaps resolving it could lead to more accurate ADAPDT resultsusing the nonlinear instead of the linear solver.

Implementation of full three dimensional geometry representation in ADAPDTcould possibly improve the results to such extent that it would produce a satisfac-tory scaling. Also, it would simplify the body modelling process and eliminate thetime consumed for adjusting the models to free flight data. This of course requiresadditional work to be done in the ADAPDT code. Using an alternative potentialflow solver would pose an option.

For the Edge simulations, refining the aircraft model would further improvethe scaling results. The model used throughout this work was roughly modelledusing pictures and certain important measures. Details, such as the saw tooth onthe Gripen wing were omitted and the aerofoil was chosen as a standard highspeed thin profile. Thus, the model was far from accurate but still delivered anacceptable scaling performance.

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6.2 Recommendations for Continued WorkBefore implementing a three dimensional geometry representation in ADAPDT,it would be of interest to compare its performance to a potential flow solver usingsaid representation. An example of such a code is dwfSolve [21]. This wouldhelp to determine whether implementation of three dimensional representation inADAPDT is worth the efforts.

Since only one scaling case with two stores has been investigated during thisstudy, several more should be made to verify the results. For example, an inves-tigation of scaling performance for missiles and other bomb shapes. It is alsovery important to investigate more complex store configurations on the aircraft.In this case the stores were mounted in pylon 2 with an empty pylon 3. Mountingadditional stores in adjacent pylons will further increase the complexity and it isimportant to investigate if Edge manages to predict the loads in these cases.

Another vital task is to further investigate how Edge performs as a scaling toolat higher Mach numbers. If it can be established that Edge ∆-effects are relativelycorrect also for transonic speeds it would increase the usefulness of this scalingmethod.

Finally, correction factors for high α should be investigated, as well as paralleldisplacement coefficients for the yaw moment.

6.3 ConclusionsBased on the results presented in this report, there is little reason to choose theADAPDT software as the scaling tool for the Loads Department at Saab Aerosys-tems. ADAPDT predicted only one out of five coefficients well. The results forthe other coefficients were unpredictable and exaggerated. However, it would bevaluable to repeat the scaling performance test if three dimensional geometry wasimplemented. Currently, ADAPDT shows no advantages over Edge. Scaling re-sults are less accurate and the total amount of time for the scaling is basically thesame due to the long process of model adaption.

Edge results were consistent and proved to deliver fairly accurate results alsoin raw CFD values. Scaling performance was good throughout the tests. Caseswith less accuracy were mainly conservative and never overestimated by morethan a factor 2.5 at maximum value.

Edge will be a good choice for a scaling tool if some time is spent verifyingthe results for more store configurations. Overall, this scaling method will mostlikely improve the accuracy of the scaling performed at Saab Aerosystems and,more importantly, make the scaling process more efficient.

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7 Summarising the MethodologyFour main steps are needed to perform the scaling using Edge. Modelling, wherethe geometries are created. Preprocessing, which generates the mesh and preparesit for the simulation. The actual simulation and then postprocessing, where thedata is managed. See Figure 21 for an illustration of the work flow, including aniteration for investigating the mesh independence.

Figure 21: Illustrating the steps of the work process. To check mesh indepen-dence, iterations are performed after the initial simulation.

7.1 ModellingThe first step is the modelling of the geometry. This step is performed in thedwfSumo software. The geometry is defined by specifying a number of crosssections throughout the length of the store. Fins, rudders, air intakes and otherprotruding parts are added separately. When finished, the store is moved to thecorrect position in the aircraft coordinate system and is finally added to the aircraftmodel.

7.2 PreprocessingThe surface mesh for the entire aircraft, including the store selected for evalua-tion, is generated within dwfSumo. Mesh size parameters are specified for eachof the modelled surfaces. A fine representation is chosen close to the store, grad-ually coarsening moving away. Based on the surface mesh, the volume mesh isgenerated using the built-in TetGen interface.

An Edge input file is defined by specifying parameters for the Edge simulation.These parameters include, for instance, solver algorithms, number of iterations,convergence criteria and velocities. One input file is required for each angle in anα-sweep. Depending on the level of precision needed and the time available, thestep size in the sweep can be adjusted accordingly. Finally, the Edge preprocessorprepares the mesh for the simulation using the input files.

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7.3 SimulationThe simulations are initiated by executing Edge. Each angle in a sweep requiresits own simulation, but when executed on a cluster all simulations can run si-multaneously. The time frame for simulations of this size was 20 to 80 minutesdepending on convergence speed and number of processors used.

7.4 PostprocessingEdge generates coefficients for the entire model in the mesh. Thus, a script has tobe executed to extract coefficients for every body defined in the model. The coef-ficients for the relevant bodies of the store are added, generating the aerodynamiccoefficients for the entire store. These are stored in a MATLAB library which canbe used for plotting.

Once the libraries for both the new store and the old reference store are gen-erated, the ∆-effect can be extracted. Subtracting the reference store coefficientdata from the new store equivalent results in a ∆-effect which can then be addedto the existing wind tunnel measurement data and finally be plotted.

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References[1] Sooy, Thomas J. & Schmidt, Rebecca Z. (2005). Aerodynamic Predictions,

Comparisons, and Validations Using Missile DATCOM (97) and Aeropre-diction 98 (AP98). AIAA Inc.

[2] Vukelich, Steven R. & Jenkins, J. E. (1984). Missile DATCOM: Aero-dynamic Prediction of Conventional Missiles Using Component Build-UpTechniques. AIAA Inc.

[3] Vukelich, Steven R. (1985). Aerodynamic Prediction of Elliptically-ShapedMissile Configurations Using Component Build-Up Methodology. AIAAInc.

[4] Grimes, R. & Walsh, E. & Quin, D. & Davies, M. (2005). Effect of GeometricScaling on Aerodynamic Performance. AIAA Journal, Vol. 43, No. 11.

[5] Hansen, Heikki & Jackson, Peter & Hochkirsch, Karsten (2002). Compari-son of Wind Tunnel and Full-Scale Aerodynamic Sail Force Measurements.High Performance Yacht Design Conference, Auckland.

[6] Petterson, Karl & Rizzi, Arthur (2006). Aerodynamic Scaling to Free FlightConditions: Past and Present. Elsevier Ltd.

[7] Lindberg, Anders (2009). Personal communications at Saab Aerosystems.

[8] Mexnell, Bengt (2009). Personal communications at Saab Aerosystems.

[9] Nelson, H. F. (1989). Wing-Body Interference Lift for Supersonic Missileswith Elliptical Cross-Section Fuselages. AIAA Inc.

[10] Sahu, Jubarai & Heavey, Karen R. & Ferry, Earl N. (1998). ComputationalModeling of Multibody Aerodynamic Interference. Elsevier Science Ltd.

[11] Anderson, John D. Jr. (2007). Fundamentals of Aerodynamics. McGraw-Hill.

[12] Jiyuan Tu & Guan Heng Yeoh & Chaoqun Liu (2008). Computational FluidDynamics, A Practical Approach. Elsevier Inc.

[13] Weinerfelt, Per (2005). Metodik for aerodynamisk analys och design avlagsignaturfarkoster. Saab Aerosystems.

[14] Weinerfelt, Per (2005). Validering och anpassning av metodik for aerody-namisk analys och design av lagsignaturfarkoster. Saab Aerosystems.

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[15] Nordin, Erik (2006). Development of Body and Viscous Contribution toa Panel Program for Potential Flow Computation, Aero Dynamic Analy-sis and Preliminary Design Tool. Department of Mechanical Engineering,Linkoping University.

[16] Munk, Max M. (1922). Technical Note No. 104. Notes on AerodynamicForces - II. The Aerodynamic Forces on Airships. National Advisory Com-mittee for Aeronautics.

[17] FOI (2009). Edge. [www] http://www.foi.se/edge. 2009-04-22.

[18] Persson, Ingemar & Lindberg, Anders (2008). Transonic Store SeparationStudies on the Saab Gripen Aircraft Using Computational Aerodynamics.ICAS 2008.

[19] Eller, David (2007). dwfSumo. [www] http://fdl8.flyg.kth.se/dwf/sumo.html. 2009-04-21.

[20] Hang Si (2007). TetGen, A Quality Tetrahedral Mesh Generator andThree-Dimensional Delaunay Triangulator. [www] http://tetgen.berlios.de/ 2009-04-21.

[21] Eller, David (2007). dwfs. [www] http://fdl8.flyg.kth.se/dwf/dwfs.html. 2009-04-21.

Saab Aerosystems I

A CFD Values, Store1, Mach 0.6, Alpha Sweep

CC for Store1

CN for Store1

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CMX for Store1

CMY for Store1

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CMZ for Store1

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B CFD Values, Store2, Mach 0.6, Alpha Sweep

CC for Store2

CN for Store2

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CMX for Store2

CMY for Store2

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CMZ for Store2

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C CFD Values, Store1, Mach 0.8, Alpha Sweep

CC for Store1

CN for Store1

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CMX for Store1

CMY for Store1

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CMZ for Store1

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D CFD Values, Store2, Mach 0.8, Alpha Sweep

CC for Store2

CN for Store2

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CMX for Store2

CMY for Store2

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CMZ for Store2

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E CFD Values, Store1, Mach 0.6, Beta Sweep

CC for Store1

CN for Store1

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CMX for Store1

CMY for Store1

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CMZ for Store1

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F CFD Values, Store2, Mach 0.6, Beta Sweep

CC for Store2

CN for Store2

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CMX for Store2

CMY for Store2

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CMZ for Store2

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G Scaling at Mach 0.6, Alpha Sweep

Scaling of CC

Scaling of CN

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Scaling of CMX

Scaling of CMY

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Scaling of CMZ

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H Scaling at Mach 0.8, Alpha Sweep

Scaling of CC

Scaling of CN

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Scaling of CMX

Scaling of CMY

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Scaling of CMZ

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I Scaling at Mach 0.6, Beta Sweep

Scaling of CC

Scaling of CN

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Scaling of CMX

Scaling of CMY

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Scaling of CMZ