AIAA Paper 2009-6273 - CFD4Aircraft

Framework for Establishing the Limits of TabularAerodynamic Models for Flight Dynamics AnalysisM. Ghoreyshi ∗ , K.J. Badcock † , A. Da Ronch ‡ S. Marques § A. Swift and N. Ames ‖Department of Engineering, University of Liverpool, Liverpool, UK, L69 3GHThis paper describes the use of Computational Fluid Dynamics for the generation andtesting of tabular aerodynamic models for flight dynamics analysis. Manoeuvres for theAGARD Standard Dynamics Model wind tunnel geometry for a generic fighter are consideredas a test case. Wind tunnel data is first used to validate the prediction of static anddynamic coefficients at both low and high angles, featuring complex vortical flow, with goodagreement obtained at low and moderate angles of attack. Then the generation of aerodynamictables is described based on an efficient data fusion approach. An optimisation isused to define time optimal manoeuvres based on these tables, including level flight trim,pull-ups at constant and varying incidence, and level and 90 degree turns. The manoeuvredescription includes a definition of the aircraft states and also the control deflections toachieve the motion.The main point of the paper is then to assess the validity of the aerodynamic tableswhich were used to define the manoeuvres. This is done by replaying them, including thecontrol surface motions, through the time accurate CFD code. The resulting forces andmoments can be compared with the tabular values to assess the presence of inadequatelymodelled dynamic or unsteady effects. The agreement between the tables and the replayis demonstrated for slow manoeuvres. A study for the pull-up at increasing rates showsdiscrepancies which are ascribed to vortical flow hysteresis at elevated motion rates.I. IntroductionThe flight mechanics analysis of combat aircraft requires a nonlinear and unsteady aerodynamic modelvalid for rapid and large amplitude manoeuvres. 1,2 The source of nonlinearity and unsteadiness is mainlydue to shock waves, separation and vortices at high angles of attack. 3 These phenomena impact aircraftperformance but developing a model of these flows is difficult due to the complexity of the flow simulation andthe limitations of existing dynamic wind-tunnel test facilities. 4 Attempts at exploiting CFD for predictingS&C derivatives were reported in references. 5–8The aerodynamic model for flight dynamics analysis considered in this paper is tabular in form. Tables,in contrast to stability derivatives, are not linearized, and are consistent with quasi-steady aerodynamics fora wide range of flight conditions. There are several difficulties associated with aerodynamic tables. First,a large number of table entries must be filled. The brute-force calculation of the entire table using CFD isnot feasible due to computational cost. Sampling and data fusion methods have been proposed to overcomethis. 9 Secondly, the pre-computed nature of tables lacks the ability to describe hysteresis of the aerodynamicphenomena. That flow hysteresis impacts on the manoeuvering aircraft was first recognized by Harper andFlanigan 10 in 1950. They showed that there is a substantial increase of aircraft lift force if the aircraftis pitched at a rapid rate. It is well known that aerodynamic forces and moments of aircraft responding∗ Research Assistant† Professor, SMAIAA, corresponding author. Tel. : +44(0)151 794 4847 , Fax. : +44(0)151 794 6841, Email :K.J.Badcock@liverpool.ac.uk‡ Research Assistant§ Research Assistant PhD Student‖ Undergraduate Student1 of 22American Institute of Aeronautics and Astronautics

to sudden changes of flow around aircraft not only depends on the instantaneous values but also the timehistory of the motion. 11–14CFD tools are becoming credible for the computation of aerodynamic time history effects. The flight dynamicsof a manoeuvering aircraft could be accurately modelled by coupling the Reynolds-Averaged Navier-Stokes (RANS) equations and the dynamic equations governing the aircraft motion. First attempts werelimited to two-dimensional test cases, 15–19 while recently the coupled CFD-flight dynamics of a full aircrafthas been studied. 20 The 6DoF CFD-coupled simulations take substantially longer than when taking theforces and moments from look-up tables raising the open question of when time hysteresis of the aerodynamicsis required for flight dynamics analysis.In the present paper a framework for investigating the limits from flow unsteadiness of aerodynamic tablesis investigated. The particular demonstrations of this framework are made for a generic (and sharp leadingedge) fighter performing time optimal manoeuvres with the aerodynamics given by the Euler equations.The paper first reviews the flow solver and how the manoeuvres are computed. Then the test case isdescribed and the aerodynamic predictions validated. The generation of the aerodynamic tables and theapproach to defining the time optimal manoeuvres is then given. The evaluation of the aerodynamic tablesfor these manoeuvres is then made by replaying them directly through an unsteady CFD calculation. Finally,conclusions are given.A. Flow CodeII. CFD FormulationThe flow solver used for this study is the University of Liverpool PMB (Parallel Multi-Block) solver. TheEuler and RANS equations are discretised on curvilinear multi-block body conforming grids using a cellcentredfinite volume method which converts the partial differential equations into a set of ordinary differentialequations. The equations are solved on block structured grids using an implicit solver. A wide varietyof unsteady flow problems, including aeroelasticity, cavity flows, aerospike flows, delta wing aerodynamics,rotorcraft problems and transonic buffet have been studied using this code. More details on the flow solvercan be found in Badcock et al 21 and a validation against flight data for the F-16XL aircraft is made inreference. 22B. Motion ReplayThe key functionality for the CFD solver in the current application is the ability to move the mesh. Twotypes of mesh movement are required. First, a rigid rotation and translation is required to follow the motionof the aircraft. Secondly, the control surfaces are deflecting throughout the motion. The control surfacesare blended into the geometry in the current work following the approach given in reference. 23 After thesurface grid point deflections are specified, transfinite interpolation is used to distribute these deflections tothe volume grid.The rigid motion and the control deflections are both specified from a motion input file. For the rigidmotion the location of a reference point on the aircraft is specified at each time step. In addition the rotationabout this reference point is also defined. Mode shapes are defined for the control surface deflections. 24 Eachmode shape specifies the displacement of the grid points on the aircraft surface for a particular control surface.These are prepared as a preprocessing step using a utility that identifies the points on a control surface,defines the hinge, rotates the points about the hinge and works out their displacements. The motion inputfile then defines a scaling factor for each mode shape to achieve the desired control surface rotation.The desired motion to be replayed through the unsteady CFD solution is specified in the motion inputfile. The aircraft reference point location, rotation angles and control surface scaling factors are needed.The rotation angles are obtained straight from the pitch, yaw and bank angles. The aircraft reference pointvelocity v a is then calculated to achieve the required angles of attack and sideslip, and the forward speed.The velocity is then used to calculate the location. The CFD solver was originally written for steady externalaerodynamics applications. The wind direction and Mach number are specified for a steady case. If the initialaircraft velocity is denoted as v 0 , then this vector is used to define the Mach number and the angle of attackfor the steady input file. Then the instantaneous aircraft location for the motion file is defined from therelative velocity vector v a − v 0 .2 of 22American Institute of Aeronautics and Astronautics

III. Test Case and ValidationThe Standard Dynamics Model (SDM) is a generic fighter configuration based on the F-16 planform. Themodel includes a slender strake-delta wing, horizontal and vertical stabilizers, ventral fin and a blocked offinlet section. The three view drawing is shown in figure 1. This geometry has been used for an internationaleffort to collect wind tunnel data. 25–28Figure 1. Standard Dynamic Model(SDM) layout. 29In the current paper Euler calculations are used to generate the aerodynamic forces and moments.A multiblock mesh was generated using the commercial package ICEMCFD. The geometry was slightlysimplified by removing the blocked off intake and the ventral fins. Since the main interest here is on theimpact of vortical flow on the upper lifting surfaces these were considered reasonable simplifications. A fineEuler mesh was generated with 5.6 million points, and a coarse mesh was obtained with 701 thousand pointsby omitting every second point. The calculations described are for the coarse mesh unless otherwise stated.Mesh block faces were placed on the control surfaces and the mesh points on these faces were deflectedto define the control surface mode shapes. The control surfaces are blended into the airframe as describedabove, and views of the surface mesh for the deflected control surfaces are shown in figure 2.The geometric, mass, inertial and engine properties of SDM are obtained from data in Winchenbach etal. 30 Their free-flight model is 0.1325:1 scale of the studied model in this paper resulting in scaled-up valuesof:S = 27.87 m 2 m = 9295.44 kgc = 3.45 m I xx = 12874.0 kgm 2b = 9.144 m I yy = 75673.0 kgm 2T m = 26.24 KN I zz = 85552.0 kgm 2where T m is the maximum total thrust force assumed to cross the centre of gravity. The thrust is assumedto remain unchanged with altitude and flight speed, and to vary linearly with the engine throttle.The lifting surfaces all have sharp leading edges. This allows the Euler equations to predict the developmentof vortical flow since the separation points are fixed at the leading edge. A complex interaction of thestrake and wing vortices develops as the incidence is increased, as illustrated in figure 3 for low speed and nosideslip conditions. At ten degrees the vortices form, remain unbroken and do not interact over the airframe.At fifteen degrees the two vortices wind around each other towards the trailing edge of the wing. At twentydegrees the wing vortex appears to breakdown quickly after formation, whereas the strake vortex is coherent3 of 22American Institute of Aeronautics and Astronautics

Figure 2. View of Deflected Control Surfaces on the Surface Grid.4 of 22American Institute of Aeronautics and Astronautics

for longer. Finally at thirty degrees there is no sign of coherent vortices. Note that these calculations wereall run as steady state although vortical interactions and the separated flow field would almost certainly beunsteady. The assumption is that the mean flowfield from unsteady calculations would resemble the steadyresult shown here.These vortex dominated flow fields cause nonlinear variations in the aerodynamic forces and moments.Figure 4 compares DATCOM 31 and CFD results with available experimental data 29 at low speed and zerosideslip conditions. The figures show that there is a good agreement between the Euler predictions and themeasurements for angles of attack below 20 degrees. Above 20 degrees the disagreement in the magnitudeof the longitudinal quantities increases and the sign of the slope of the lateral quantities is wrong. At theseconditions it was seen that the vortical flow is lost, and the lateral forces and moments will be stronglyinfluenced by the separated flow adjacent to the vertical fin. The Euler simulations will not predict thisflowfield properly, and Detached Eddy Simulation is a better option. The DATCOM predictions in somerespects are adequate (eg for the pitching moment and normal force coefficient), but it should be noted thatthe empirical database which underlies these predictions is for a conventional aircraft which would not featurevortical flow. This can be seen in the predictions of the normal force coefficient which show a conventionalaircraft stall. The lateral coefficients are generally not well predicted by DATCOM in this case.AoA = 10 DegAoA = 15 DegAoA = 20 DegAoA = 30 DegFigure 3. SDM-Flow Field Visualization. The calculations are for a Mach number of 0.3 and zero degreessideslip. The streamtraces are coloured by pressure coefficient.For fast manoeuvres the dynamic contributions to the forces and moments are required. The estimation ofthe quasi-steady dynamic derivatives is achieved by imposing a forced sinusoidal motion around the aircraftcentre of gravity. For the extraction of longitudinal dynamic derivative values from time-histories of theforces and moments, it is assumed that the aerodynamic coefficients are linear functions of the angle of5 of 22American Institute of Aeronautics and Astronautics

3.02.01.5Digital DATCOMPMB (Euler)Exp1.01.0C m0.0-1.0C N0.5-2.00.0-3.0-4.0Digital DATCOMPMB (Euler)Exp.-0.5-1.0-5.0-20 -10 0 10 20 30AoA (Deg)-20 -10 0 10 20 30AoA (Deg)0.060.041.00.8Digital DATCOMPMB (Euler)0.020.6C rol0.00C D-0.020.4-0.04Digital DATCOMPMB (Euler)EXp.0.2-0.06-20 -10 0 10 20 30 40AoA (Deg)0.0-20 -10 0 10 20 30AoA (Deg)0.100.050.100.05Digital DATCOMPMB (Euler)EXp.0.00C n0.00C Y-0.05-0.05Digital DATCOMPMB (Euler)EXp.-0.10-0.10-20 -10 0 10 20 30AoA (Deg)-0.15-20 -10 0 10 20 30AoA (Deg)Figure 4. Static Aerodynamic Predictions- Lift, drag and pitching moments are for zero degrees sideslip,V 0 =100 m/s. The lateral figures are for five degrees of side-slip and V 0 =100 m/s. The experimental data arefrom reference. 29 6 of 22American Institute of Aeronautics and Astronautics

attack, α, pitching angular velocity, q, and rate, ˙q.The increment in the lift coefficient with respect to its mean value during the applied sinuisoidal motion isformulated as∆C L = C Lα ∆α + l V C L ˙α˙α + l ( ) 2 lV C L qq + C LV˙q˙q (1)where V is the magnitude of the aircraft velocity vector and l is the characteristic length, here the wing rootchord. The pitching moment is treated in an analogous way.The harmonic motion defines the following relationsEquation (1) can be re-written as∆α = α A sin (ω t)˙α = α A ω cos(ω t) (2)˙q = −α A ω 2 sin (ω t)∆C L = α A(CLα − k 2 C L ˙q)sin (ω t) + αA k ( C L ˙α+ C Lq)cos(ω t) (3)where k = lω/V is the reduced frequency of the applied motion. The in-phase and out-of-phase componentsof ∆C L , respectively indicated as ¯C Lα and ¯C Lq , can be defined as¯C Lα = C Lα − k 2 C L ˙q(4)¯C Lq = C L ˙α+ C Lq (5)∆C L = α A ¯CLα sin (ω t) + α A k ¯C Lq cos(ω t) (6)These coefficients can be obtained by taking the first Fourier coefficients of the time history of C L .The longitudinal dynamic derivatives were computed for the SDM. Periodic motions with five degreesamplitude and a reduced frequency of 0.0493 were applied for six cycles to reach a periodic state.Figure 5 shows the comparison with wind tunnel and range data from Winchenbach. 30 A good agreementis obtained up to about 17 degrees. DATCOM cannot predict the variation with angle of attack.A. Aerodynamic TablesIV. Generation of ManoeuvresThe flight dynamics predictions requires a vector of aerodynamic forces and moments[C L , C D , C m , C Y , C l , C n ] Trepresenting wind axis coefficients of lift, drag, pitching-moment, side-force, rolling moment and yawingmoment coefficient, respectively. This vector depends on the aircraft state and control variables. In thispaper, this dependency is represented in look-up tables. For a slow motion, the aerodynamic forces andmoments are assumed to depend on angle of attack, Mach number, side-slip angle and three control surfacedeflection angles. The tables are arranged with three parameters in each: Mach number, angle of attack andone other variable. Around 6000 entries are required to define the variations in each table, leading to a largenumber of calculations required if a brute force method was used.An alternative approach is used to fill up the tables. The brute-force calculations were used to providethe values with respect to the angle of attack and Mach number ( referred to here as the baseline table). Thedependence of the longitudinal forces and moments on other parameters is assumed to be an increment of thebaseline table and the Co-Kriging data fusion approach 9 is used to include this variation in a computationallyefficient way. The baseline table describes the general trends of longitudinal aerodynamic forces and moments.This table consists of 156 conditions, with the angle of attack ranging from -14 0 to 28 0 , and the Mach numberfrom 0.1 to 0.4. With just 15 additional samples the variation with the elevator, side-slip angle, aileron andrudder was included in the tables.For the lateral coefficients a different approach is needed since all the lateral coefficients in the baselinetable are zero. Instead the DATCOM lateral coefficients are used as low fidelity data for Co-Kriging andthen a few Euler results are used to generate updated tables using co-Kriging.For the dynamic derivatives, these are assumed to be independent of Mach number, and to vary withangle of attack.7 of 22American Institute of Aeronautics and Astronautics

2015Digital DATCOMPMB (Euler)Exp.1510Digital DATCOMPMB (Euler)Exp.105Cz q+Cz α.50Cm q+Cm α.0-5-5-10-10-155 10 15 20 25AoA (Deg)-150 5 10 15 20 25AoA (Deg)0PMB (Euler)Exp.1.0PMB (Euler)Exp.-50.5Cm q+Cm α.-10Cn p0.0-15-0.5-200.2 0.4 0.6 0.8 1Mach-1.00 5 10 15 20 25AoA (Deg)Figure 5. Dynamic Derivative Aerodynamic Predictions. The Mach number in the upper figures is 0.3 andthe angle of attack in the lower-left figure is zero. The experimental data is from reference 308 of 22American Institute of Aeronautics and Astronautics

B. Time Optimal ManoeuvresThis paper aims to investigate the validity of aerodynamic tables for the generation of time-optimal manoeuvres.Manoeuvre flight (sometimes named accelerated flight 33 ) is the response of the aircraft to thepilot’s applied control inputs starting from one trimmed flight condition to another. The manoeuvre timeis the flight period between the initial and final trim points, and this should be minimised for aerial combatmanoeuvres.The optimal control problem finds the optimal controls that transfer a system from the initial state tothe final state while minimizing (or maximizing) a specified cost function. 32 The optimal control aims tofind a state-control pair x ∗ (), u ∗ () and possibly the final event time t f that minimizes the cost function∫ tfJ[x(), u(), t 0 , t f ] = E(x(t 0 ), u(t f ), t 0 , t f ) + F(x(t), u(t), t)dt (7)t 0where E and F are endpoint cost and Lagrangian (running cost),respectively. For the problem of an aircraftoptimal time manoeuvre, the general aircraft equations of motion detailed in Etkin 34 and Stevens and Lewis 35serve as one of the constraints. Also, the initial and final state parameters are fixed with trimmed flightconditions, but the rest of the manoeuvre is out of trim conditions.For the solution of the optimal control problem the DIDO code 36 and MATLAB 37 are used. In DIDO,the total time history is divided into N segments. The boundaries of each time segment are called nodes.The value of N is normally in the range 5 to 150. The optimal state and control pair are calculate at thenodes.The optimization uses the solution of the 6DoF equations as a constraint. This solution derives theaerodynamic forces and moments from the look-up tables. Hence, the predictions from these tables need tobe realistic for the manoeuvre itself to be valid. The tables can be limited from a number of sources:• too coarse a representation which misses nonlinear variations• inadequate representation of the dynamic derivatives• significant hysteresis in the aerodynamics.The main contribution of this paper is to consider how to evaluate the limitations by replaying the motionthrough a time accurate CFD simulation. The predicted forces and moments can then be compared withthe tabular model values to evaluate the consistency between the two sets of values.A. OverviewV. Testing of Manoeuvre ReplayThis section shows the comparison between the prediction of the aerodynamic forces from the static tabularmodel and the motion replay. This is done for slow motions where exact agreement would be expected. Themotions used are trimmed level flight, pull-ups with constant and varying angle of attack, wing-over and90-degree turns. The comparisons test the CFD formulation of the manoeuvre replay, which is done in atime accurate fashion with control surface deflections. Throughout this section the replay predictions arereferred to on the figures as Coupled Model.B. Level FlightThe first manoeuvre is for steady wing-level straight flight at 3,000 ft and 350 fps. To define this manoeuvrethe constraints are set for the time rates of angle of attack, pitch angle and flight speed with upper and lowervalues of ±1.0 × 10 −5 . The altitude is also set as a constraint. The solution gives a trim angle of attack7.67 0 and elevator deflection angle of 1.69 0 . In order to verify the optimal criteria and validate the solution,the Hamiltonian function and flight altitude during flight are shown in figure 6. During the 85 seconds offlight computed the altitude remains unchanged as required. In addition the Hamiltonian values are nearlyconstant, showing that the solution is optimum.It is possible to define the replay calculation through the CFD in different ways. As described in the CFDformulation section the important quantity to be specified is v a − v 0 where v 0 is a fixed vector specified9 of 22American Institute of Aeronautics and Astronautics

3500-0.94-0.96Alt. (ft)3000Hamiltonian-0.98-1.00-1.02-1.04-1.0625000 20 40 60 80Time (sec)0 20 40 60 80Time (sec)10.8V 0=400 ft/sV 0=350 ft/sV 0=300 ft/sTable0.6C L0.40.200 20 40 60 80Time (sec)Figure 6. Level Flight Trim Solution and Replay Test.10 of 22American Institute of Aeronautics and Astronautics

through the initial steady state conditions given to the CFD solver and v a is the instantaneous velocityvector of the aircraft in an axis system moving with the initial steady velocity. We are free to choose anysteady velocity vector. To test the replay calculation the magnitude of this vector was set to three differentvalues, namely V 0 = 350, V 0 = 300 and V 0 = 400 fps, where V 0 is the magnitude of the vector v 0 . Theaircraft velocity was then set to achieve the desired relative velocity and angle of attack. The calculationof the lift coefficient for these three cases is shown in figure 6 and all three cases give identical values asrequired.C. Fixed α Pull-Up ManoeuvreNext two pull-up manoeuvres are considered. The first pulls up faster at 8 deg/sec at a fixed value of 18 0angle of attack and the second is a slow pitch up case with 2 deg/s pitch rate at a fixed value of 9.5 0 angleof attack. For these manoeuvres, the upper and lower boundary values of the time rates of angle of attack,pitch rate and flight speed are set to ±1.0 × 10 −5 . The boundaries of angle of attack and pitch rate arechanged in the code in order to achieve two different manoeuvres. Also, the elevator deflection angles arelimited to ±25 0 .The solution for the slow pitch up is shown in figure 7. This shows the trajectory and Hamiltonian. Inaddition the tabular and replay values for the lift coefficient are shown and are in perfect agreement. Finallythe surface pressure contours are shown, with the effect of the weak leading and strake vortices visible. Thesame plots are shown in figure 8 for the higher rate pull-up. Again the tabular and replay results are inagreement for the lift coefficient, and the footprint of the stronger vortices are apparent in the pressurecontour plot.D. Varying α Pull-Up ManoeuvreRemoving the constraints imposed to time-rate changes of angle of attack and pitch rate for the fixed αpull-up results in a pull-up with varying angle of attack. In order to find a slow pull-up, the upper boundaryof pitch rate is set to two degrees per second.The optimum solution results in a pull-up with varying angle of attack from 4.7 0 to 11.5 0 in 30 seconds.This means that dynamic effects are expected to be small. The elevator varies throughout the motion up todeflections of 5 0 . The time variation of the angle of attack and the elevator angle are shown in figure 9. Thecomparison of the tabular and replay values of the lift and drag coefficients are also shown and are in closeagreement.E. Wing-overNext manouevres featuring lateral motions are considered. A wing-over manoeuvre in 130 seconds is defined.The predicted time-optimal manoeuvre changes the heading of the aircraft from 0 to 180 0 , while the finalvalues of the velocity, altitude and latitude (x) are fixed with the initial-time ones. The aircraft gains altitudeby increasing its angle of attack, while banking at the same time. At its minimum speed, rudder is appliedto change the heading and then the aircraft starts to dive.The start and final speed and altitude of minimum time manoeuver are set to 300fps and 3,000ft, respectively.The code is free to choose initial and final angles of attack, but they need to be below 20 degrees.Also, throughout time, the angles of attack should not exceed the upper limit of 20 degrees. The elevator,aileron and rudder deflection values are also limited to ± 20 0 . All the rotation angular speeds are limited tosmall value, resulting a slow moving manoeuvre.Figure 10 depicts the predicted manoeuvre. The definition of the angles of attack and sideslip are givenin figure 11, together with the control surface deflections. The comparison between the tabular aerodynamicswith the replay predictions shows good agreement.F. Turn 90The final manoeuvre is a 90 degree turn in 200 seconds, shown in figure 12. The aircraft returns to itsoriginal position but with its heading changed by 90 0 . In such a manoeuvre the final values of the velocity,altitude, latitude(x) and longitude (y) are fixed with the initial-time values. The predicted angles of attackand sideslip are shown in figure 12, together with the control surface deflections. The lift, drag and sideforce coefficients are also shown in figure 13 for the replay and the tables and again are in close agreement.11 of 22American Institute of Aeronautics and Astronautics

38003236001Alt (ft)3400Hamiltonian0-13200-230000 500 1000 1500 2000X (ft)-30 1 2 3 4 5 6Time (sec)1.0Coupled ModelTable0.80.6C L0.40.20.00 2 4 6Time (sec)Figure 7. Steady Pull-Up Manoeuvre at 2 deg/s pitch rate and a fixed angle of attack of 9.5 0 .12 of 22American Institute of Aeronautics and Astronautics

3100230801Alt (ft)30603040Hamiltonian0-1-23020-3-430000 100 200 300 400 500 600X (ft)0 0.5 1 1.5Time (sec)1.4Coupled ModelTable1.2C L1.00.80.60 0.5 1 1.5Time (sec)Figure 8. Steady Pull-Up Manoeuvre at 8 deg/s pitch rate and a fixed angle of attack of 18 0 .13 of 22American Institute of Aeronautics and Astronautics

124102AoA (Deg)8Elev. (Deg)06-2-440 5 10 15 20 25 30Time (sec)0 5 10 15 20 25 30Time (sec)0.400.35-0.920.30-0.96Mach0.250.20Hamiltonian-1.00-1.040.15-1.080.100 5 10 15 20 25 30Time (sec)0 5 10 15 20 25 30Time (sec)1Coupled ModelTable0.2Coupled ModelTable0.80.150.6C LC D0.10.40.20.0500 5 10 15 20 25 30Time (sec)00 5 10 15 20 25 30Time (sec)Figure 9. Slow Pull-Up Manoeuvre with varying angle of attack.14 of 22American Institute of Aeronautics and Astronautics

Figure 10. Wing-over Manoeuvre visualization.VI. Fast ManoeuvresHaving demonstrated the agreement between the static tabular and replay predicted aerodynamics forslow motions, we now consider faster manoeuvres where we would expect significant dynamic and unsteadyeffects. Increasingly fast pull-up manoeuvres are considered in this section. Dynamic terms are added tothe static tabular values. The aim is to evaluate the importance of the dynamic terms, and the presence ofunsteady terms that are not represented in the tables.The pull-up with time varying angle of attack, described above, is considered as the baseline manoeuvre.This is referred to as the Low angle of attack pull-up ( Figs 9). Also, a high angle of attack pull-up was definedwith the range of angle of attack going from 12.7 0 to 19.5 0 . Faster versions of both of these manoeuvreswere obtained by reducing the duration from 30 seconds to 3 seconds and then to 0.3 seconds (to test theaerodynamic predictions rather than to asses a realisable manoeuvre).The time variation of the lift coefficient for the six resulting manouevres is shown in figure 14. Lookingfirst to the left column in this figure for the low angle of attack case, agreement between the static tabularpredictions and the replay is obtained for the slow 30 sec motion. The dynamic tabular terms are notrequired at the rates in this motion. Small discrepancies are observed between the static tables and thereplay values for the 3 sec motion. The addition of dynamic tabular terms gives agreement with the replayvalues. Larger differences are observed with the static tabular predictions for the 0.3 sec manouever , bitthe dynamic terms again bring the tabular predictions into agreement with the replay results.The story is the same for the high angle case for the 30 sec and 3 sec motions. However, for the 0.3 sec caseadding the dynamic corrections do not bring the tabular predictions into line with the replay predictions. Toinvestigate this further the pressure distributions at the time of maximum discrepancy are plotted in figure15. The time is marked by the red symbols in figure 14. The time accurate replay result is shown on topand the quasi-steady prediction at the conditions at this time is shown below. Note that this calculation15 of 22American Institute of Aeronautics and Astronautics

3020AoABeta30 Elev.Ail.Rud.20Flow Angles in Degree100-10-20Control Deflections in Degree100-10-20-300 20 40 60 80 100 120Time (sec)-300 20 40 60 80 100 120Time (sec)-0.92-0.96-1.00Hamiltonian-1.04-1.08-1.12-1.16-1.200 20 40 60 80 100 120Time (sec)1.50.510.40.50.3C LC D00.2-0.5Coupled ModelTable0.1Coupled ModelTable-10 20 40 60 80 100 120Time (sec)00 20 40 60 80 100 120Time (sec)Figure 11. Wing-Over Manoeuvre definition and replay solution.16 of 22American Institute of Aeronautics and Astronautics

Figure 12. Turn-90 Manoeuvre visualisationincludes both the static and dynamic effects in the solution, and the red symbol in figure 14 is the steadystate value obtained. This is in perfect agreement with the tabular value calculated from separate estimatesof the static and dynamic effects included in this figure as a solid dot. This agreement builds confidence inthe static and dynamic tables. The motion replay solution shows a weaker leading edge vortex which leadsto the lower value of the lift coefficient. The angle of attack is increasing at this point in the motion and thesolution for the replay appears to be lagging the time accurate solution.VII. ConclusionsThis paper describes a framework for generating optimal manoeuvres based on CFD generated tabulataerodynamic models, and then testing the aerodynamic model by replaying the manoeuvre using an unsteadyCFD calculation to check the consistency of the aerodynamic forces and moments. The CFD solver uses twotypes of mesh movement, namely rigid motion, and transfinite interpolation for the control surfaces. Datafusion was used to allow the generation of the aerodynamic tables in a feasible number of static and forcedmotion CFD calculations.The test case used was the SDM generic fighter. Sharp leading edges for the lifting surfaces allowedthe Euler equations to be used. A validation was made against available experimental data which showedthat the predictions fail to predict static lateral forces and moments above 20 degrees when the flowfield isno longer dominated by coherent vortices. The longitudinal dynamic derivatives showed agreement up to17 degrees. To improve the agreement at higher angles viscous modelling is required, with Detached EddySimulation a good candidate. However, the agreement at lower angles means that the Euler equations canbe used to demonstrate the replay framework, with credible flow physics and predictions being present inthe test case.A number of slow longitudinal and lateral manoeuvres were used to demonstrate that the tabular and17 of 22American Institute of Aeronautics and Astronautics

3025AoABeta3025Elev.Ail.Rud.2020Flow Angles in Degree151050-5-10-15Control Deflections in Degree151050-5-10-15-20-20-250 50 100 150 200Time (sec)-250 50 100 150 200Time (sec)21.5Coupled ModelTable10.8Coupled ModelTable10.6C L0.5C D00.4-0.50.2-10 50 100 150 200Time (sec)00 50 100 150 200Time (sec)0.60.4Coupled ModelTable0.2C Y0.0-0.2-0.4-0.60 50 100 150 200Time (sec)Figure 13. Turn 90 Manoeuvre definition and replay solution.18 of 22American Institute of Aeronautics and Astronautics

0.8Coupled ModelStatic Tables1.2Coupled ModelStatic Tables0.61C LC L0.40.80.210 15 20 25 30Time (sec)Low AoA 30 sec Pull-up0.610 15 20 25 30Time (sec)High AoA 30 sec Pull-up0.8Coupled ModelStatic TablesStatic- Dynamic Tables1.2Coupled ModelStatic TablesStatic Dynamic Tables0.61C LC L0.40.80.21 1.5 2 2.5 3Time (sec)Low AoA 3 sec Pull-up0.61 1.5 2 2.5 3Time (sec)High AoA 3 sec Pull-up0.8Coupled ModelStatic TablesStatic- Dynamic Tables1.2Coupled ModelStatic TablesStatic Dynamic Tables0.61C LC L0.40.80.20.1 0.15 0.2 0.25 0.3Time (sec)Low AoA 0.3 sec Pull-up0.60.1 0.15 0.2 0.25 0.3Time (sec)High AoA 0.3 sec Pull-upFigure 14. Comparison of Pull-ups replay at different rates.19 of 22American Institute of Aeronautics and Astronautics

Instantaneous Replay SolutionQuasi-steady SolutionFigure 15. Surface pressure contours for the high angle of attack 0.3 second manoeuvre at the time instantmarked by the red symbol on figure 14.20 of 22American Institute of Aeronautics and Astronautics

eplay aerodynamics agreed closely as expected. Then a number of higher rate manoeuvres for a pull-upwere used to investigate the influence of dynamic and unsteady terms. At moderate rates the addition ofdynamic tabular terms brought the tabular predictions into agreement with the replay values. However, fora high angle of attack, high rate motion, the dynamic terms were not adequate to achieve agreement. Aquasi-steady calculation confirmed that the tabular prediction is correct, and so the disagreement is due tothe influence of the history in the unsteady replay manoeuvre. This example shows the usefulness of theframework in investigating the limits of the static and dynamic tables.Future work will extend this study to include DES flow modelling to try to capture high angle of attackvortical flows more realistically than was achieved with the Euler modelling in this study. The frameworkwill be applied to a fighter trainer aircraft with flight test data to compare with. Finally, the impact ofvortical flow history effects will be investigated, and previous work on modelling these effects reconsidered.VIII. AcknowledgementsThis work was supported by the Engineering and Physical Sciences Research Council and the Ministryof Defence under EP/D504473/1. AR was supported by the SimSAC project under funding from the SixthFramework programme of the European Union, AS by a BAE SYSTEMS/ Engineering and Physical SciencesResearch Council studentship and SM by the European Union under the Marie Curie Excellence TeamECERTA, contract MEXT-CT-2006 042383References1 Hamel, P. G. and Jategaonkar, R. V., Evolution of Flight Vehicle System Identification, Journal of Aircraft, Vol. 33, No.1 pp. 9-282 Jouannet, C. and Krus, P., Lift Coefficient Predictions for Delta Wing Under Pitching Motions, AIAA-2002-2969, June20023 Katz, J. and Schiff, L. B., Modeling Aerodynamic Responses to Aircraft Manoeuvres: A Numerical Validation, Journalof Aircraft, Vol. 23, No. 1, pp. 19-254 Greenwell, D. I., A Review of Unsteady Aerodynamic Modelling for Flight Dynamics of Manoeuvrable Aircraft, AIAA-2004-5276, August 20045 Green, L. L. and Spence, M., Applications of Computational Methods for Dynamic Stability and Control Derivatives,AIAA-2004-377, January 20046 Simon, J. M., Dynamic Derivative Data for High-Angle-of-Attack Simulation, AIAA-92-4355, Aug. 19927 Blake, W. B., Dixon, C. J., and Adler, C. O., Development of a High-Angle-of-Attack Stability and Control PredictionCode, AIAA-92-4354, August 1992.8 Park, M. A. and Green, L. L., Steady-State Computation of Constant Rotational Rate Dynamic Stability Derivatives,AIAA-2000-4321, August 20009 Ghoreyshi, M., Badcock, K. J. and Woodgate, M., Accelerating the Numerical Generation of Aerodynamic Models forFlight Simulation, Journal of Aircraft, Vol. 46, No. 3, pp. 972- 98010 Harper, P.W. and Flanigan, R.E., The Effect of Change of Angle of Attack on the Maximum Lift of a Small Model,NACA TN-2061, March 1950.11 Tobak, M. and Schiff, L.B., Aerodynamic Mathematical Modeling: Basic Concepts, AGARD Lecture Series on DynamicStability Parameters, Lecture No. 1, March 1981.12 Levy, L.L. and Tobak, M., Nonlinear Aerodynamics of Bodies of Revolution in Free Flight, AIAA Journal, Vol. 8, Dec.1970, pp. 2168-2171.13 Tobak, M. and Schiff, L.B., Generalized Formulation of Nonlinear Pitch-Yaw-Roll Coupling: Part 1:NonaxisymmetricBodies, AIAA Journal, Vol. 13, March 1975, pp. 323-326.14 Tobak, M. and Schiff, L.B., Generalized Formulation of Nonlinear Pitch-Yaw-Roll Coupling: Part 2:Nonlinear Coning-Rate Dependence, AIAA Journal, Vol. 13, March 1975, pp. 327-332.15 Ballhaus, W.F. and Goorjian, P.M., Computation of Unsteady Transonic Flow by the Indicial Method, AIAA Journal,Vol. 16, Feb. 1978, pp. 117-124.16 Rizzetta, D.P., Time-Dependent Response of a Two-Dimensional Airfoil in Transonic Flow, AIAA Journal, Vol. 17, Jan.1979, pp. 26-32.17 Chyu, W.J. and Schiff, L.B., Nonlinear Aerodynamic Modeling of Flap Oscillations in Transonic Flow: A NumericalValidation, AIAA Journal, Vol. 21, Jan. 1983, pp. 106-113.18 Steger, J.L. and Bailey, H.E., Calculation of Transonic Aileron Buzz, AIAA Journal, Vol. 18, March 1980, pp. 249-255.19 Gallaway, C.R. and Hankey, W.L., Free-Falling Autorotating Plate, AIAA-84-2080, Aug. 1984.20 Schutte,A. , Einarsson, G., Raichle,A., Schoning,B., Mnnich, W. and Forkert, T., Numerical Simulation of ManoeuvreingAircraft by Aerodynamic, Flight Mechanics, and Structural Mechanics Coupling, Journal of Aircraft Vol. 46, No. 1, January-February 200921 Badcock, K.J., Richards, B.E. and Woodgate, M.A. Elements of Computational Fluid Dynamics on Block StructuredGrids using Implicit Solvers. Progress in Aerospace Sciences, vol 36, 2000, pp 351-392.21 of 22American Institute of Aeronautics and Astronautics

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