Experimental and Numerical Aerodynamic Data

14th AIAA/AHI Space Planes and Hypersonic Systems and Technologies Conference

AIAA 2006-8031

Experimental and Numerical Aerodynamic Data Integration and Aerodatabase Development for the PRORA-USV-FTB_1 Reusable Vehicle. G. C. Rufolo*, P. Roncioni†, M. Marini‡, R.Votta§ CIRA, Italian Aerospace Research Center, 81043 Capua, Italy S. Palazzo** CIRA, Italian Aerospace Research Center, 81043 Capua, Italy

Main goal of this paper is to show the methodology of integration of the different sources of data adopted for the development of the aerodynamic data package of the Italian reusable experimental vehicle USV-FTB_1. Moreover, the aerodynamic characteristics of the vehicle are investigated in the whole range of foreseen flight conditions, from subsonic up to low supersonic regime with a deeper focusing on transonic region. USV-FTB_1 is a multimission, reusable vehicle under development at CIRA, the Italian Aerospace Research Center. The first USV-FTB_1 mission is aimed at experimenting the transonic flight of a reentry vehicle. In order to properly describe the aerodynamic characteristic of the USVFTB_1 it has been necessary to develop a suitable Aerodynamic Model, i.e. a mathematical representation of the physics of the problem, following the build-up approach for the description of global aerodynamic coefficients. Once the Aerodynamic Model has been defined, it has been necessary to gather a sufficient amount of data in order to explicit the functional dependencies of each piece of the model. Main data sources considered for the present activity are: Wind Tunnel and CFD. As a matter of fact, wind tunnel data do not allow a complete mapping of the analyzed phenomenology with respect to all the identified parameters. Typical example of this is the Reynolds number. In order to overcome this lack of information the experimental data base has been corrected by means of scaling laws obtained with CFD simulations. In particular, Navier-Stokes calculations at different Reynolds numbers allowed for the set up of scaling laws for the extrapolation to flight of wind tunnel data. Finally, in order to be able to perform Monte Carlo mission simulation studies, a structured model of uncertainties describing the range of variation of aerodynamic global coefficients has been developed.

I. Introduction

A

im of this paper is to provide an overview of the aerodynamic characteristic of the Unmanned Space Vehicle (USV) – Flight Test Bed 1 (FTB_1) vehicle. Moreover an outline of the Aerodynamic DataBase (ADB) development process is given. USV-FTB_1 is a multi-mission, reusable vehicle under development at CIRA, the Italian Aerospace Research Centre19. The first USV-FTB_1 mission is planned for the winter 2006/2007 and is aimed at experimenting the transonic flight of a re-entry vehicle. In addition, other missions are scheduled with the aim at extending the flight envelope up to Mach 2 in a fully supersonic regime. USV-FTB_1 is composed by a flying test bed and a carrier based on a stratospheric balloon. Most of data constituting the ADB has been produced within the CIRA Transonic Wind Tunnel (PT-1)15, and the DNW-TWG Wind Tunnel of Göttingen8,9. Several test campaigns have been conducted over a one-thirty model of the USV-FTB_1 vehicle, covering a consistent part of the flight envelope. Moreover, a CIRA CFD-solver (ZEN) has *

Ph.D., Research Engineer, Aerothermodynamics and Space Propulsion Lab., [email protected]. Ph.D., Research Engineer, Aerothermodynamics and Space Propulsion Lab., [email protected]. ‡ Ph.D., Research Engineer, Aerothermodynamics and Space Propulsion Lab., [email protected]. § Research Engineer, Aerothermodynamics and Space Propulsion Lab., [email protected]. ** Research Engineer, Research Engineer, PT1 -Transonic Wind Tunnel, [email protected]. †

1 American Institute of Aeronautics and Astronautics

Copyright © 2006 by CIRA - Italian Aerospace Research Center. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission.

been largely utilized22 in order both to fill gaps in experimental data and, mainly, to correct Wind Tunnel (WT) data for the effects of: Reynolds number, base flow (not accounted for in WT test) and model support system interference. As a result of the integration of all data sources an aerodataset covering the whole range of Mach number, Angle of Attack, Sideslip, Control surface deflections and Reynolds number of interest has been built. Namely, the extrapolation to flight Reynolds number has been done with referring to the mission nominal trajectory. Being the vehicle released from an altitude of 25Km, it spans the Mach number range two times: the first one during the acceleration phase at high altitude and low Reynolds number (105÷106) and the second one during the deceleration phase until the parachute opening at lower altitude and higher Reynolds number (106÷107). Within the paper the aerodynamic model built for a comprehensive description of the USV-FTB_1 aerodynamics is presented together with an insight on the aerodynamic characteristics of the vehicle. Finally, in order to be able to perform Monte Carlo mission simulation studies an uncertainties model describing the range of variation of aerodynamic global coefficients (and their derivatives) has been developed and it will be described within the paper.

II. Vehicle Geometry Description Generally speaking the USV-FTB_1 can be classified as a Winged Body Vehicle. In Figure 3 a schematic drawing of the vehicle is reported. The main body of the FTB_1 has an overall length of 8000 mm, from the nose apex (without considering Air Data Boom) up to the base plate. The front fuselage ends with a pointed nose constituted by a quasi-conical shape closed by an hemisphere of 1 cm radius. Afterwards the pointed nose, the windside part of the forebody geometry rapidly changes from a quasiX= 220 mm circular to a rounded-square shape. The mid-fuselage is X= 600 mm characterized by a quasi-constant section while the afterbody X=4200 mm ends with a boat-tailed truncated base. In Fig. 1 four X=8000 mm transversal sections of the fuselage are reported corresponding to a distance from the nose of respectively 220, 600, 4200 and 8000mm. The wing of the FTB_1 vehicle has a double delta shape with a main leading edge sweepback of 45° and a strake with a 76° sweepback leading edge. The trailing edge (TE) is characterized by a sweepforward angle of 6°. To improve lateral stability the USV-FTB_1 wing has a dihedral angle of 5° with referring to the Wing Reference Plane (WRP). Overall Figure 1. Fuselage Sections. wing span is 3.56 m, while the strake root chord is 2.8 m. A split elevon with both function of elevator and aileron is mounted on the FTB_1 wing. Elevon hinge line has no sweep angle. In Figure 2 wing sections normal to the WRP and corresponding respectively to the strake root station (a), the wing-strake junction (b), in the following indicated as kink and the wing tip (c) are shown together with chord length and maximum percentage thickness. To improve directional stability and control, a V-tail solution has been adopted for the USV-FTB_1. The two vertical tails have a dihedral angle of 40°, a sweepback angle of 45° and a span of 800 mm. The chord at root station is 1000mm while at the tip it 2820 mm reduces to 500mm. Fin airfoil section is symmetric with a 12% of mean thickness. τ =5.83% (a) Root A pair of full-span movable rudders is also implemented for directional control. Even 1804 mm if it is not foreseen at the moment, rudders τ =8 % (b) Kink could be also used as ruddervators in order to improve longitudinal control capabilities and as an energy management 677 mm device (speedbrake). (c) Tip τ =9% Moreover, in order to augment directional stability characteristics of the vehicle and to reduce possibilities of dutch-roll occurrence, a pair of full Figure 2. Wing Sections profiles. max

max

max


symmetric ventral fins has been added. The ventral fins, without movable surface, are characterized by a 55° sweepback angle, a root chord of 800mm with a taper ratio of 0.45 and a span of 418 mm (see Figure 3).

Figure 3. Three View of the USV-FTB_1 vehicle.

III. Reference Frames, Aerodynamic Actions definition, Sign Rules and Reference Quantities. In this section the reference frames currently utilized for the ADB development are described24. Moreover, the aerodynamic forces and moments used are described together with their sign rules. A. Reference Frames The Layout Reference Frame (LRF) has been used to define the USV-FTB_1 geometry and, in particular, the position of its centre of mass. With referring to Figure 4-(a), the origin {Oly} is placed in the nose apex of the USVFTB_1, the Xly axis is perpendicular to the USV-FTB_1 base plane and oriented from the nose toward the base plane, the Zly lie in the vehicle symmetry plane and is directed upward (from the wing plane to the fins), Yly completes the right-handed triad.

a)

b) Figure 4. (a) - Layout Reference Frame. (b) - Body Reference Frame.


The Body Reference Frames (BRF), depicted in Figure 4-(b), has the origin placed in the instantaneous centre of mass of the USV-FTB_1 and the axes parallel to the ones of LRF. For what concerns the axes orientation, the XB is positive towards the USV-FTB_1 nose, the YB is positive towards the right wing and the ZB completes the righthanded triad. The Wind Reference Frame (WRF) has the origin placed in the instantaneous centre of mass of the USVFTB_1; the XW parallel to the free-stream velocity and directed oppositely to it; the ZW orthogonal to the XW, lying in the USV-FTB_1 symmetry plane and oriented in such a way that the scalar product Z ly ⋅ Z w is negative;

(

Figure 5. WRF, SRF and BRF sketch.

)

the YW completing the right-handed triad. With referring to Figure 5, the Stability Reference Frame (SRF) (Xs,Ys,Zs) is obtained from the WRF with a rotation of an angle equal to the sideslip angle β around the ZW axis. The sideslip angle β is defined as positive when the wind comes from the right wing (right side of the pilot). The angle of incidence α is defined as positive when the wind comes from the bottom of the USV-FTB_1.

B. Definition of Aerodynamic Forces and Moments Sign Rules. Two sets of aerodynamic forces will be used in the following. The first one defined in the BRF as follows: NORMAL (N) Force, directed oppositely to the ZB axis; AXIAL (A) Force, directed oppositely to the XB axis; SIDE (Y) Force, directed like the YB axis. The second one defined in the SRF as follows: LIFT (L), directed oppositely to the ZS axis; DRAG (D), directed oppositely to the XS axis; SIDE (Y) Force, directed like the YS axis. (It coincides with the one previously defined). The aerodynamic moments will be always defined in the BRF as follows: ROLL (l), directed like the XB axis; PITCH (m), directed like the YB axis; YAW (n), directed like the ZB axis. For what concerns aerodynamic moments sign rules, it seems important to remark that ROLL is positive when tends to lower the right wing, PITCH is positive when tends to raise the nose and YAW is positive when tends to move the nose towards right. C. Control Surfaces Deflection. Sign Rules. As already stated in sec. II, USV-FTB_1 has two types of control surfaces: elevon and ruddervator. An elevon deflection, indicated as δ Ei =l ,r (with the apex i indicating left or right elevon), is considered positive when the TE moves downwards (Figure 6); a rudder deflection, indicated as δ Ri =l ,r (with the apex i indicating left or right rudder), is considered positive when the TE moves towards left (Figure 7). If not differently indicated, in the following the same deflection for left and right rudder, i.e.

δ R = δ Rl = δ Rr

will be assumed.

δ El ,r < 0

Zly

δ El ,r > 0 Xly Figure 6. Elevon deflection sign rule.


δ Rl , r < 0 Yly

δ Rl , r > 0

Xly

Figure 7. Rudder deflection sign rule.

D. Reference Quantities All the aerodynamic forces and moments reported in the present document have been normalized with the reference quantities reported in Table 1. Reference Surface Reference Chord Reference Span

Sref, m2 cref, m bref, m

3.60 1.05 3.56

Table 1. Adopted Reference Quantities. Nevertheless, it has to be noted that the above defined reference quantities can be not fully appropriate for the comparison of the USV aerodynamic coefficients with the ones of other similar vehicles. As a matter of fact, the adopted reference surface corresponds to that of the exposed wing/strake area while the commonly adopted reference surface is the wing planform area. For the USV case the wing planform surface Sw is 6.03 m2, i.e. 1.675 times larger than the Sref. In the same way the adopted reference length corresponds to the mean chord obtained from the relationship S ref = c bref , while the reference length commonly adopted for a winged-body vehicle is the mean aerodynamic chord. The ratio between the m.a.c. and the adopted cref is 1.79. Therefore, the reader must be aware that in performing comparison with other vehicles, e.g. X-34 or Space Shuttle Orbiter, it is strictly recommended to apply the above defined factors. The pole for moment reduction is the nominal Center of Mass (CoM) of the vehicle and is located at the 68.5% of the body length. The position of the CoM on the Zly axis of the LRF is -0.15m.

IV. Mission Description As already mentioned in the introduction the first USV-FTB_1 mission (DTFT-1, Dropped Transonic Flight Test -1), that is scheduled for the winter 2006/2007, is aimed at experimenting the transonic flight of a re-entry vehicle. Moreover, the USV-FTB_1 will perform additional flights, each of them simulating the final portion of a typical reentry trajectory. USV-FTB_1 is basically composed by a Flying Test Bed (FTB_1) and a Carrier based on a stratospheric balloon19. During the missions the balloon will carry the FTB_1 up to the desired altitude (20-25 Km for the first mission) and then, after having established a cruise horizontal trajectory, will release it from the gondola. At this moment USV-FTB_1 will start its proper flight following the designed trajectory. In the frame of a step by step approach, the USV-FTB_1 will reach during each subsequent mission an increasing Mach number, starting from Mach 1 during the first mission up to Mach 2 during the fourth flight. During the flight it will perform the experiments (Aerodynamics, Structure and Materials, Autonomous Guidance Navigation and Control), and by means of a pull-up maneuver it will decelerate in order to enter in the safe parachute opening regime. The final recovery will be performed from the sea by a ship of the National Research Council (CNR). Figure 8 reports an example of trajectory for a dropped controlled mission. It is possible to identify four characteristic phases for this kind of trajectory as described in the following:


18÷24 Km

1. DROP: Low Mach Number (< 0.5). Low dynamic pressure. Low Reynolds ( 0.85150 0.27600 0.01775 -0.32594 Rich. Extr. number of cells (representative of a mean value of the L2-L3 -> 0.86394 0.27076 0.01577 -0.34586 Level Diff. (L1-L2)/L2 -6.23 6.73 29.98 -29.52 cell dimension) with a suitable (second-order) (%) (L2-L3)/L3 -2.61 3.17 17.68 -11.04 polynomial. Figure 18 reports the case of the lift Eff. Ord. 1.219 1.130 0.997 1.250 L1-L2 Error (%) -5.87 7.08 37.64 -26.78 coefficient CL that at grid spacing zero is about 0.8760 L2-L3 Error (%) -2.45 3.34 22.19 -10.02 and is quite close to that obtained with the Richardson (L1-L2 RE) - (L3 CFD sim.) -0.58 0.86 5.92 -2.29 extrapolation formula. As a contribution to the whole Table 7: Main results of grid sensitivity analysis. uncertainty levels due to the grid dependence of global aerodynamic coefficients, it is possible to consider the value obtained with the formula of Richardson theory, the so called Grid Convergence Index, GCI (see ref Valencia) Table 7 reports the main results concerning the grid sensitivity analysis. The percentage error estimated with the GCI (L2-L3) is similar to the percentage difference between fine and medium grid levels for Lift, Drag and Pitching moment coefficients. The difference for the Friction Drag Coefficient (about 5.0 %) can be explained with the weakly convergent behaviour as it can be noted in Figure 19. M=1.40, AoA=10, AoS=0 L2-L3 Rich. Extr. & Error Bar

M=1.40, AoA=10, AoS=0 -0.1500

L1-L2 Rich. Extr. & Error Bar

Pitching Moment Coefficient

0.9600

Lift Coefficient

0.9200

0.8800

0.8400

0.8000

0.7600 0.0000

0.0050

0.0100

0.0150

0.0200

0.0250

-0.2500

-0.3000

-0.3500

-0.4000

-0.4500 0.0000

0.0300

(Cells number)^(-1/3)

a)

-0.2000

0.0050

0.0100

0.0150

0.0200

0.0250

0.0300

(Cells number)^(-1/3)

b)

Figure 18. Grid Sensitivity Analysis: (a) Lift Coefficient. (b) pitching Moment Coefficient. It is worthwhile to note also as the L1-L2 Richardson extrapolation is a good estimation of the Level 3 CFD computation (last line of Table 7). This means that, in general, after a good grid convergence analysis on a suitable subset of runs, it can be possible to accept results obtained on a medium grid level (associated with suitable grid convergence errors) or to extrapolate results from coarse and medium grid levels CFD computations (the CPU time of which is much lower than that of the fine grid level). As a conclusion of the grid sensitivity analysis we can see that, for the particular case considered (M=1.4, α=10°, β=0°), there is an under-estimation for CL and Cm (-2.45%, 10.02%) and an over-estimation for CD and CDf (3.34%, 22.19%). It must be said that, as a general rule for such complex geometry, the maximum number of cells used for the present simulations was chosen in accordance with an acceptable convergence CPU time estimation. 6. Time convergence criteria. Due to the complexity of flow pattern and grid topology used it is not always possible to obtain a standard convergence in terms of vanishing of residual of governing equations. For the above reason, the convergence criteria for all the analyzed cases was based on the achievement of steady values of global aerodynamic coefficients. An example of convergence history is reported in the Figure 19, in which is showed the oscillation of aerodynamic coefficients caused mainly by the base flow. In order to overcome this problem, when periodic oscillations were observed, an average of the coefficients over a suitable number of oscillations has been calculated. 18 American Institute of Aeronautics and Astronautics

Figure 19. An example of convergence history. 7. Results. In this section the results of the CFD simulations in terms of global aerodynamic coefficients directly used for the extrapolation to flight of experimental data are reported. The functional dependence versus Reynolds number is reported and stressed hereinafter in this section. The variations of aerodynamic coefficients CL and Cm versus Reynolds number in logarithmic scale are reported in Figure 20 and Figure 21 for M=1.05, 1.40. An asymptotic behavior with respect to the Reynolds number can be observed for lift and pitching moment at both angles of attack, with a major effect at α=10°. A not monotonic trend has been predicted for the drag coefficient CD in the Reynolds number dependence (Figure 22). The α=0°, β=8°, M=1.4 configuration, for example, exhibits a slight inversion. This can be explained by analyzing the lumped coefficients and the different contributions of the pressure and shear stress field to the aerodynamic drag (see Figure 23 and Figure 24). The analysis (for the M=1.4, α=0°, β=0° case) of the Reynolds number effect on the drag provided by the different part of the vehicle (lumped coefficients) shows a clear increasing trend with Reynolds of the base drag, differently from the other parts. Being friction drag due to the base negligible, the base drag is only caused by the pressure distribution which establishes over it, and for which the Reynolds number variation has an opposite effect wrt to friction drag, this being caused by the increase of expansion due to the reduction of boundary layer thickness. This is confirmed by the distributions reported in Figure 24, where the total pressure drag trend is similar to the base (pressure) drag trend (compare the green lines in both Figure 23 and Figure 24). Similar considerations can be done for the other cases. The trend of friction drag coefficient (CDf) versus Reynolds number is similar for all the cases reported in Figure 25, the more extended separated flow regions at higher attitude (for a fixed Mach number, M=1.40) are responsible for the lower values at the α=10°, β=0°. The functional dependency of the friction drag coefficient upon Reynolds number can be expressed with the power law CDf = a Re -b, similarly to the theoretical Blasius equation for the skin friction on a flat plate (in the hypothesis of turbulent boundary layer), i.e. Cf = 0.0592 Rex -0.2 f (compressibility corrections). The data fitting laws are powers of Reynolds with an exponent quite different from the Blasius’one (about -0.13 instead of -0.20) due to the effect of the actual vehicle shape and flow compressibility. The functional dependence, however, is preserved at all, and computed solutions appear coherent with theory and among themselves. The Lateral-Directional (L-D) aerodynamic analysis was performed at α=0° and β=8°. L-D results (CY, Cn, Cl) are reported in Figure 26 Figure 27. Increasing the Reynolds number causes an increase of both the lateral stability and directional stability at all Mach numbers (M=1.05, 1.40 in figure). Besides the information regarding the global aerodynamic coefficients, a detailed CFD analysis has been also useful in order to obtain a deeper understanding of the vehicle aerodynamics. As an example of the flow features that it is possible to identify with the help of CFD computations, in Figure 28-(a)-(b) stream-tubes together with isocontour of total pressure are shown for a case at M=0.70, AoA=10° and Rey=6.5E6. It is possible to note the formation of the wing leading edge vortex, typical of delta-wing configuration, and its interaction both with the wing-tip and the strake vortex. In Figure 28-(c) the deviation of the fuselage vortex due to non-zero sideslip angle it is clearly evident as well as the interaction with the V-tail. As we will see in sec. VIII this kind of interaction can cause non-linearity of the lateral-directional coefficients with the angle of sideslip. In Figure 28-(d) the effects of the elevon deflection on the vortex pattern are shown. 19 American Institute of Aeronautics and Astronautics

CL , Beta=0, M=1.40 CL, Beta=-8, M=1.40 CL, Beta=-8, M=1.05 0.0500 CMy Beta=0, M=1.40 CMy Beta=-8, M=1.40 0.0400 CMy Beta=-8, M=1.05 0.0300

AoA=0 0.0600

0.0500

AoA=10, Beta=0, M=1.40 0.8580

-0.3100 0.8540

0.0200

0.0400

-0.3150

CL

0.0000

CMy

0.0300

-0.0100 0.0200

0.8500

-0.3200

CMy

0.8520

0.0100 CL

-0.3050 CL CMy

0.8560

0.8480 -0.3250

-0.0200 0.8460

-0.0300

0.0100

-0.3300 0.8440

-0.0400 0.0000 100000

1000000

10000000

0.8420 100000

-0.0500 100000000

1000000

Figure 20: Lift and Pitch Coefficients. α=0°.

Figure 21: Lift and Pitch Coefficients. α=10°.

AoA=0, Beta=0, M=1.40 AoA=10, Beta=0, M=1.40 AoA=0, Beta=-8, M=1.40 AoA=0, Beta=-8, M=1.05

0.3000 0.2800

AoA=0, Beta=0, M=1.40 0.0500

0.2600

0.0450

0.2400

0.0400

0.2200

0.0350

0.2000

0.0300 CD

CD

-0.3350 100000000

10000000 Reynolds

Reynolds

0.1800

FUSE BASE WING VTAIL VFIN

0.0250 0.0200

0.1600

0.0150 0.1400

0.0100 0.1200

0.0050 0.1000 100000

1000000

10000000

0.0000 100000

100000000

Reynolds

1000000

10000000

100000000

Reynolds

Figure 22: Reynolds effect. Drag Coefficient.

Figure 23: Lumped coeff.: M=1.4, α=0°, β =0°. AoA=0, beta=0, M=1.40 AoA=10, beta=0, M=1.40 AoA=0, beta=-8, M=1.40 AoA=0, beta=-8, M=1.05 AoA=10, beta=0, M=1.40 fitting AoA=0, beta=-8, M=1.40 fitting AoA=0, beta=0, M=1.40 fitting AoA=0, beta=-8, M=1.05 fitting

AoA=0, Beta=0, M=1.40

0.0350 0.1600 0.1400

0.0300 0.1200

CD

0.1000

CD_fric

ALL FRIC PRESS

0.0800

0.0250

y = 0.1625x-0.1223 y = 0.1328x-0.1244

0.0600 y = 0.1389x-0.1281

0.0200 0.0400

y = 0.1445x-0.1334

0.0200 0.0000 100000

0.0150 100000 1000000

10000000

1000000

100000000

10000000

100000000

Reynolds

Reynolds

Figure 24: Drag coefficient. M=1.40, α=0°, β =0°.

Figure 25: Friction Drag Coefficient.

α=0°, β=-8°

α=0°, β=-8° -0.0500 100000 -0.0700

0.3300 0.3200

1000000

10000000

Cn, M=1.40 Cn, M=1.05 Cl, M=1.40 Cl, M=1.05

100000000 0.0700

-0.0900

0.3100

0.0600

-0.1100

M=1.40 M=1.05

0.0500

Cl

0.2900

-0.1300

Cn

CY

0.3000

-0.1500

0.2800

-0.1700

0.2700

-0.1900

0.0400

-0.2100

0.2600

0.0300

-0.2300

0.2500 100000

1000000

10000000

100000000

-0.2500

0.0200

Reynolds

Reynolds

Figure 26: α=0°, β =-8°. Side Force Coefficient.

Figure 27: α=0°, β =-8°. Yaw and Roll Coeff.


a)

b)

c)

d)

Figure 28. (a) M=0.70, AoA=10°, Rey= 6.5E6. Streamtubes and IsoContour of total pressure. (b) M=0.70, AoA=10°, Rey= 6.5E6. Wing Detail. Streamtubes and IsoContour of total pressure. (c) M=0.7 AoS=-8° AoA=10°. IsoContour of total pressure. (d) Streamtubes around the wing with the elevon deflected. M=0.70. AoA=10. δE=20°.

C. Approximate Methods As already said simplified numerical methodologies, i.e. Eulerian CFD linear panel method and semi-empirical method, have been used not only as a unique source for estimating the dynamic derivatives of the USV-FTB_1 vehicle but also in order to fill some gaps in existing WT data. Moreover, simplified methodologies have been also applied to the estimation of the contribution to the global aerodynamic coefficient of the ventral fin added to the vehicle in order to improve lateral-directional stability properties. See Refs. 1, 11,12 for any details. 1. Non Viscous Calculations. In this paragraph non-viscous CFD calculations are reported and analyzed. These results take part of the aerodynamic database of USV-FTB-1 and they have been also used for configuration studies. 21 American Institute of Aeronautics and Astronautics

In particular, an inviscid flow analysis has been performed in order to evaluate the influence of the ventral fins on lateral-directional derivatives. The following summarize the computed non-viscous calculations.

M 0.5, 0.7, 0.8, 0.95, 1.05, 1.13, 1.25, 1.4, 2

AoA [°] -5,0,5,10

β[°] 0, 4, 8

Configuration With/ without Ventral fins

Table 8. Computed non-viscous test matrix In order to assess the level of uncertainty induced by the non-viscous hypothesis, a cross check with a set of Navier-Stokes computations and Wind Tunnel experimental data has been performed. In Figure 29 (a)-(b) results of the comparison in prediction of lift and pitching moment are respectively reported for AoA=10° and ΑoS=0°, and a fair agreement should be noted. Similar considerations apply to others values of sideslip angles and angles of attack.

CL non-viscous; AoA=10° CL NS (WT); AoA=10° WT; AoA=10°

1.2

-0.2

Cm

CL

1 -0.4

0.8 -0.6

0.6

0.5

Cm non-viscous; AoA=10° Cm NS (WT); AoA=10° WT; AoA=10°

1

1.5

-0.8 0.5

2

M

1

1.5

2

M

Figure 29. (a) CL versus Mach; AoA=10°. (b) Cm versus Mach; AoA=10°.

0.1 WT Eulerian NS (WT); Re=400050 NS (Int.); Re=2097375 NS (Fl.); Re=11000062

0.05 0

CY

-0.05 -0.1

-0.15 -0.2 -0.25 -0.3

-2

0

2

4

6

8

10

β [°]

Figure 30. CY versus sideslip angle; M=2; AoA=0°. Figure 30 shows the CY behavior with respect to the sideslip angle for α=0° and M=2, as an example of a lateral coefficient. This figure shows a good match between Navier-Stokes computations and Eulerian ones for β=8°. A reasonable agreement between non-viscous calculations and wind tunnel results for all the computed sideslip angles has also been found.


It is important to remark how this Eulerian simplified approach is quite useful to provide suitable preliminary estimation of aerodynamic coefficients in transonic region, where aapproximate methods (Panel Method, Vortex Lattice, Datcom) are not able to provide satisfactory results. This is particularly evident for lateral- directional coefficients and derivatives25. The inviscid flow model represents a good compromise between accuracy (more detailed than panel methods) and computational cost (not so expansive as Navier-Stokes computations) 25.

VII. Extrapolation to flight As already said, CFD results have been used to complete the mapping of parameters needed to exhaustively describe the aerodynamics of the USV-FTB1 vehicle. In particular, scaling laws have been built in order to correct wind tunnel measurements21. The expression used for the calculation of the in-flight aerodynamic coefficients are the following:

CiFlight = CiWT + ∆CiSting + ∆CiRe press ,

{

i = L, Y, l, m, n

}

CDFlight = C DWT + ∆C DBase + ∆CDSting + ∆C DRe fric + ∆CDRe press

(20)

,

The left hand side terms in the Eq. (20) are the in-flight values, i.e. the value corresponding to the Reynolds number encountered along the nominal trajectory; the first terms of the right hand side are the coefficients measured in the wind tunnel test and the remaining terms are the CFD based numerical corrections. It can be noted that only for the drag coefficient the correction is composed by a summation of three contributions that take into account the effect of the Reynolds number over the fore-body pressure drag, the variation of the friction drag with Reynolds number and the contribution of the base Drag. The sting effect on the fore-body part of vehicle has been obviously neglected in supersonic regime.

A. Reynolds Number Effects. The corrections are described by analytical extrapolation laws obtained by using the numerical data. They depend on several parameters as Reynolds, Mach, angle of attack, etc. For what concerns the contributions of the Reynolds number to the pressure corrections of Eq. (20) a second order polynomial interpolation was found versus the logarithm of Reynolds: 2 Ci = a log10 (Re ) + b log10 (Re ) + c ,

(21)

It has been already said, in sec. B, that for the friction drag it is possible to use “Blasius’ form”: CDf = a Re –b. It must be remarked as these “analytical” laws are used to give the variation between flight and wind tunnel Reynolds number conditions, to be added to the experimental measurements, except for the base drag whose contribution to the total drag comes from CFD simulations only. As example, some scaling laws which describe the Reynolds number effect are reported in Figure 31 and Figure 32 for the case M=1.40, α=10°, β=0°. M=1.4, α =10° - CD scaling law

M=1.4, α =10° - CL scaling law

0.217

0.866

0.2165

0.864

0.216

0.862

0.2155

0.86

0.215

CL

CD

0.858

0.2145

2

CD=0.17153+0.011561log10(Re)+-0.0007341log10(Re)

0.856 2

CL=0.58491+0.077338log10(Re)+-0.0053622log10(Re) CFD

0.854

CFD 0.214

0.2135

0.852 0.213

0.85 0.2125

0.848

6

7

10 6

10 Reynolds

7

10

10 Reynolds

Figure 31: Lift Scaling Law with Reynolds. α=10°, β=0°, M=1.40.

Figure 32: Pressure Drag Coefficient Scaling Law with Reynolds. α=10°, β=0°, M=1.40.


B. Base Flow. The vehicle USV FTB-1, designed for the DTFT mission, is a not-propelled vehicle. The sting used in wind tunnel tests to support the scaled model, that could cross the nozzle throat in a propelled configuration, has to cross the base, thus altering the surrounding base flow. This makes the contribute of the base (to the global aerodynamic coefficients, mainly to the drag), if weighted by the balance, not directly usable. For this reason the WT balance only measures the resultant of the aerodynamic actions over the forebody. Residual contribution deriving from differences between the asymptotic and cavity pressure are depurated from the measured axial force. Namely, during the test the pressure acting within the model is measured and during postprocessing of the results the measured axial force is depurated by a terms equal to the difference between the cavity and asymptotic pressure multiplied by the base area. The contribution of the base flow has then to be numerically computed. Existing empirical correlation for Base Drag are strongly problem dependent. Even if it is known that CFD encounter a lot difficulties in well predicting large recirculation flow zone, it seems to be the most reliable way of correcting WT data for base drag effects. In Figure 33 Cp isocontours together with skin friction lines over the vehicle base are reported both at wind tunnel and at flight Reynolds number. Analogously, in Figure 34 Cp isocontours together with skin friction lines are reported for the case with the rear sting both at M=070 and at M=1.05.

Figure 33 – Cp iso-contours + skin friction lines. M∞=1.05, α=0 deg (Left: Wind Tunnel , Right: Flight).

Figure 34 – Cp iso-contours + skin friction Left : M∞=0.70, α=0 deg ; Right : M∞=1.05, α=0 deg .

lines.

Configuration


with

rear

sting.

C. Sting Effect. Obviously, sting presence alters the flow pattern (see Figure 35). At subsonic speed this has an effect on aerodynamic coefficient. Main difficult is to find out the best compromise between approximation in realizing the numerical model of the MSS and complexity in simulation. Nevertheless, correction functions were find out for only for longitudinal coefficients and for subsonic Mach number. For what concern lateral-directional coefficients the sting effect was not clearly achievable from numerical results so it has been preferred not to correct them.

Figure 35. Sting effect on vorticity distribution. Isocontour of total pressure. M=0.70 - AoA=10 - WT Re.

VIII. ADB Set-Up. Results and discussion. As showed, by correcting and integrating experimental results we have the possibility of generating a reliable set of data, that covers to a certain extent the variations of all the identified parameters, to be used to build the vehicle AeroDataBase. As already said in sec. V, the analysis of the gathered data allows for the determination of the functional dependencies of the AM by means of polynomials expressions whose unknown coefficients are determined by means of best-fitting algorithms. The approach followed in the present case is based on the identification, for each piece of the build-up, of a primary variable that drives the phenomenon. With respect to this variable a polynomial expression is written, while secondary dependencies are introduced directly into the polynomial coefficients. In the following, for each contribution to the aerodynamics coefficient, some details regarding the derivation of the polynomial expressions from the gathered data. Hereinafter, the general coefficient expression written in sec. V is reported again:

(

)

Ci M , Re,α , β , δ Er , δ El , δ R , αɺ , p, q, r = BL i

=C

β

δe

δr

αɺ

p

+ ∆Ci + ∆Ci + ∆Ci + ∆Ci + ∆Ci + ∆Ciq + ∆Cir

(22)

The general procedure adopted to derive each contribution can be summarized as follows: 1.

2.

Suitable sub-set of data are extracted from the set of experimental data (extrapolated to flight). In particular, data are chosen by selecting from the pool of data the ones characterized by a fixed combination of all the independent parameters except the driving one (see Figure 36). If necessary, small oscillation of Mach number are filtered out in order to have each sub-set of data at the same Mach number‡‡ by locally interpolating data versus M.

‡‡

Due to the strong variation of aerodynamic coefficients in transonic regime, Mach number differences of few thousands can be relevant. 25 American Institute of Aeronautics and Astronautics

3.

A Chi-Square type algorithm has been adopted for the best-fitting procedure. This kind of approach allows to take into account the standard deviation of each single sample of the set. Let us write the generic function y(x) as a linear summation over M basis functions Xk(x), that in our case are polynomial expressions: M

y ( x ) = ∑ ak X k ( x ) ,

(23)

k =1

It is possible to define a merit function as follows: (24)

2

 yi − ∑M ak X k ( xi ) k =1  . χ = ∑ σi  i =1   N

2

Where σi is the uncertainty associated with the single sample. In order to find out the ak coefficient it is 2

necessary to minimize the χ function. It has been choosen to use the Singular value Decomposition (SVD) to find least squares optimal solution. Without going into details, it has only to be said that by using the SVD is possible to derive the covariance matrix and then the uncertainty associated with each coefficient of the fitting. 4.

A fitting function is generated for each combination of the parameters for which data exist. It means that the dependency of the contribution by the secondary parameters is included within the fitting coefficients. For the parameters combination for which fitting functions do not exists suitable interpolation§§ of the fitting coefficients are performed.

β=0 δE=0/0 δR=0 XCM=5.48 ZCM=-0.15 2

1.5

α x=-5 α x=0 α x=5 α x=10 α x=15 α x=17

CL

1

0.5

0

-0.5

-1 0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

M

Figure 36. PT-1 Data. CL vs M at different AoA.

§§

Piecewise Cubic Hermite Interpolation has been generally used for coefficient interpolation in order to assure continuity of derivatives. 26 American Institute of Aeronautics and Astronautics

M=0.94 β =0 δE=0/0 δR=0 2

1.5

1.5

1

1

CL

CL

M=0.7 β =0 δE=0/0 δR=0 2

0.5 TWG - Re=542471 PT1 - Re=1000000 CFD - Re=784875 ADB - Re=1000000

0

0.5 TWG - Re=611840 TWG - Re=618154 PT1 - Re=1000000 CFD - Re=850500 ADB - Re=1000000

0

-0.5

-0.5

-1 -10

-5

0

5

10

15

20

-1 -10

25

-5

0

5

α (°)

a)

15

20

25

b) M=1.05 β =0 δE=0/0 δR=0

Re=1E6 - β=0 - δE = 0/0 - δR=0

2

2

1.5

1.5

1

1

CL

CL

10

α (°)

0.5

M=0.70

TWG - Re=641928 PT1 - Re=1000000 CFD - Re=929250 ADB - Re=1000000

0

0.5

0

M=0.94 M=1.05 M=1.20

-0.5

-0.5

M=1.52 M=2.00

-1 -10

-5

0

5

10

15

20

25

-1 -5

0

α (°)

5

10

15

20

α (°)

c)

d)

Figure 37. (a), (b), (c) CL vs AoA at M=0.70, M=0.94, M=1.05 respectively. Comparison between data sources (PT1, TWG, CFD) and the ADB. (d) CL vs AoA, ADB output at different Mach number, Re=1.e6. D. Baseline Contribution With referring to Eq. (22) the term CiBL (M , Re,α ) represents the baseline contribution to the global coefficient

Ci at zero-sideslip in clean configuration, i.e. with no-deflection of control surfaces (δ Er = δ El = δ R = 0 ) and with no

(

)

dynamics effects αɺ , p, q, r . As obvious, due to the symmetry of the geometry about the {Xly, Zly} plane, this contribution will appear only on the longitudinal actions. 2. Lift. From the analysis of different data sources (see Figure 37 (a)-(b)-(c)) it can be seen that the lift coefficient has a quasi linear behavior for all Mach numbers up to an AoA of about 12°. For subsonic Mach number (see Figure 37(a)) it is recognizable a small effect of vortex lift on the increase of CLα for 5°≤α ≤10° followed by a reduction of the same that tends to increase in transonic regime. For this reason fifth order polynomial comes out to be the best choice to fit data for M1 third order polynomial was used. The analytical expression for the lift coefficient is therefore the following: N N = 6, if M ≤ 1 C LBL = a (M , Re )α i − 1 , (25) i =1 i N = 4, if M > 1 where the ai coefficients depend upon Mach and Reynolds number. Still from Figure 37-(a)-(b)-(c) it is evident the quite good agreement existing between the different data sources, both experimental and numerical. It must be said that both the PT1 wind tunnel data and the CFD NS ones are referred to a vehicle configuration without the ventral fins. However, the effects of ventral fins over the lift

∑


coefficient is, obviously, quite small. In Figure 37-(b) lift curves, built from the ADB functions, for different Mach numbers are reported. It is clear the increase of slope in transonic regime with a maximum at M=1.05 and a subsequent decrease in supersonic regime. M=0.7 β =0 δE=0/0 δR=0

M=0.94 β =0 δE=0/0 δR=0

0.7

0.8 0.7

0.6 TWG - Re=542471 PT1 - Re=766561 CFD - Re=784875 ADB - Re=1000000

TWG - Re=611840 TWG - Re=618154 PT1 - Re=868509 CFD - Re=850500 ADB - Re=1000000

0.6

CD fore-CD friction

CD fore-CD fric

0.5

0.4

0.3

0.2

0.5 0.4 0.3 0.2

0.1

0.1

0 -10

-5

0

5

10

15

20

0 -10

25

-5

0

5

α (°)

a)

15

20

25

b) M=1.05 β =0 δE=0/0 δR=0

Re=1E6 - β=0 - δE=0/0 - δR=0

0.9

0.8

0.8

0.7

0.7

0.5 CD fore

0.5

M=0.70 M=0.94 M=1.05 M=1.20 M=1.52 M=2.00

0.6

TWG - Re=641928 PT1 - Re=867377 CFD - Re=929250 ADB - Re=1000000

0.6 CD fore-CD fric

10

α (°)

0.4

0.4 0.3

0.3 0.2

0.2

0.1

0.1 0 -10

-5

0

5

10

15

20

25

0 -5

0

α (°)

5

10

15

20

α (°)

c)

d)

Figure 38. (a), (b), (c) CD vs AoA at M=0.70, M=0.94, M=1.05 respectively. Comparison between data sources (PT1, TWG, CFD) and the ADB. (d) CD vs AoA, ADB output at different Mach number, Re=1.e6. 3. Drag. The drag coefficient exhibits a different behavior in subsonic and in trans-supersonic conditions. From Figure 38- (a)-(b)-(c) it is quite evident how the drag curve for -5° 0). The roll moment (Figure 45- (b)) has a typical behavior, clearly, the aileron effect is larger for positive deflection angles than for negative ones. Also note how the effectiveness decays for supersonic Mach numbers. From Figure 45- (c), it comes out that for subsonic Mach number prevails the effect of side force generated behind the CoM, while for supersonic Mach numbers the dominant effect is that of the drag produced by the deflected elevon that is always positive (i.e. tends to reduce the AoS).


Re=1E6 - α =5° - β=0 - δlE=0 - δR=0

Re=1E6 - α =5° - β=0 - δlE=0 - δR=0 0.05

ADB ADB ADB ADB ADB ADB

0.1

0.05

- M=0.70 - M=0.94 - M=1.05 - M=1.20 - M=1.52 - M=2.00

ADB ADB ADB ADB ADB ADB

0.04 0.03 0.02

∆ Cδl E

∆ CδYE

0.01 0

- M=0.70 - M=0.94 - M=1.05 - M=1.20 - M=1.52 - M=2.00

0 -0.01

-0.05

-0.02 -0.03

-0.1

-0.04

-20

-15

-10

-5

0

5

10

15

-0.05 -20

20

-15

-10

-5

δE (°)

0

5

10

15

20

δE (°)

a)

b) Re=1E6 - α =5° - β=0 - δlE=0 - δR=0 0.05 ADB ADB ADB ADB ADB ADB

0.04 0.03 0.02

- M=0.70 - M=0.94 - M=1.05 - M=1.20 - M=1.52 - M=2.00

∆ CδnE

0.01 0 -0.01 -0.02 -0.03 -0.04 -0.05 -20

-15

-10

-5

0

5

10

15

20

δE (°)

c)

Figure 45. (a), (b), (c) Contribution of right elevon deflection to CY, Cl and Cn coefficients respectively, for different Mach numbers. Re=1.e6, α=5°, δ El = 0 , δ Rl , r = 0 . I. Rudders effects on longitudinal actions As a matter of fact, the effect of the two fins with rudders deflected of the same angle tends to be small because of the V-Tail dihedral angle. Nevertheless, in order to make the AM predictions as accurate as possible it was also considered.

(

∆CδWTE = C WTE M , Re, α , β , δ R E

)

δ El ,r =0

~ − C WTE M , Re, α , β

(

)

δ R =δ EL ,R =0

,

(43)

∆CLδ R = ∑i =1 ai (M , α )δ R ,

(44)

∆CDδ R = ∑i =1 ai (M , α )δ R ,

(45)

∆Cmδ R = ∑i =1 ai (M , α )δ R ,

(46)

4

4 4

i −1

i −1 i −1


J. Rudders effects on lateral-directional actions By analyzing the existing wind tunnel data it comes out that the behavior of the lateral-directional coefficients with the rudder deflections is sufficiently linear. Moreover, even if it can seem unusual, the dependency of rudder effectiveness from the sideslip angle is much lower than the one of the angle of attack. The reason for this lies in the shield effects that the fuselage have on the flow impinging over the rudders and that strictly depends on the angle of attack.

(

∆CδWTE = C WTE M , Re, α , β , δ R E

)

δ El ,r =0

~ − C WTE M , Re, α , β

(

)

δ R =δ EL ,R =0

(47)

,

In Eqs. (48)-(49)-(50) the expressions for side force, roll and yaw moment contributions are reported together with the order of the fitting polynomials: 4 (48) i −1 δR

∆CY = ∑i=1 ai (M , α )δ R , ∆Clδ R = ∑i=1 ai (M , α )δ R ,

(49)

∆Cnδ R = ∑i =1 ai (M , α )δ R ,

(50)

4

i −1

4

i −1

From Figure 46 it can be seen that also in this case the effectiveness of the moving surface abruptly drops in supersonic regime. Re=1E6 - α =5° - β=0 - δE=0/0 0.03

0.1

0.02

0.05

0.01

∆ Cδl R

∆ CδYR

Re=1E6 - α =5° - β=0 - δE=0/0 0.15

0 ADB ADB ADB ADB ADB ADB

-0.05

-0.1

-20

-15

-10

-5

0

5

10

- M=0.70 - M=0.94 - M=1.05 - M=1.20 - M=1.52 - M=2.00

15

0 ADB ADB ADB ADB ADB ADB

-0.01

-0.02

-0.03 -20

20

-15

-10

-5

δR (°)

0

5

10

- M=0.70 - M=0.94 - M=1.05 - M=1.20 - M=1.52 - M=2.00

15

δR (°)

a)

b) Re=1E6 - α =5° - β=0 - δE=0/0 0.1 ADB ADB ADB ADB ADB ADB

0.08 0.06 0.04

- M=0.70 - M=0.94 - M=1.05 - M=1.20 - M=1.52 - M=2.00

∆ CδnR

0.02 0 -0.02 -0.04 -0.06 -0.08 -0.1 -20

-15

-10

-5

0

5

10

15

20

δR (°)

c)

Figure 46. (a), (b), (c) Contribution of rudder deflection to CY, Cl and Cn coefficients, respectively, for different Mach numbers. Re=1.e6, α=5°, δ Er ,l = 0 . 37 American Institute of Aeronautics and Astronautics

20

IX. Uncertainties Model. Therefore, the output of the AM is constituted by a functional representation of the aerodynamic characteristics of the space vehicle. As a matter of fact, even though the aerodynamics model prediction is aimed at being the best possible with the available tools and know-how, it is however only a representation of the actual phenomenology, and therefore it will be characterized by errors. In order to assess the AM output data and to make them useful, it is necessary to estimate the entity of such errors, by associating to the nominal values provided by the model the related uncertainty margins. The uncertainty model conceived for the USV-FTB_1 is characterized by a proper functional structure, and by a certain number of basic parameters. For example, in the case of the global aerodynamic coefficients the following uncertainty model has been associated to the AM:

(

)

unc unc unc unc ɺ C L = C *L M , Re, α , β , δ ER , δ EL , αɺ , q ± C unc L0 (M ) ± C Lα (M ) ⋅ α ± C Lδ e (M ) ⋅ δ e ± C Lαɺ ⋅ α ± C Lq ⋅ q

(51)

(

)

unc 2 unc unc C D = C*D M , Re,α , β , δ ER , δ EL , δ r ± C unc D0 (M ) ± C Dα 2 (M ) ⋅ α ± C Dδ e (M ) ⋅ δ e ± C Dδ r (M ) ⋅ δ r

(52)

(

)

unc unc unc unc unc ɺ C m = C*m M , Re,α , β , δ ER , δ EL ,αɺ , q ± C unc m0 (M ) ± C mα (M ) ⋅ α ± C mδ e (M ) ⋅ δ e ± C mδ r (M ) ⋅ δ r ± C mαɺ ⋅ α ± C mq ⋅ q

(53)

(

)

unc unc unc unc C Y = C*Y M , Re,α , β , δ ER , δ EL ,δ r , p, r ± C unc Yβ (M ) ⋅ β ± C Yδ a (M ) ⋅ δ a ± C Yδ r (M ) ⋅ δ r ± C Yp ⋅ p ± C Yr ⋅ r

(54)

(

)

unc unc unc unc C n = C*n M , Re,α , β , δ ER , δ EL , δ r , p, r ± C unc nβ (M ) ⋅ β ± C nδ a (M ) ⋅ δ a ± C nδ r (M ) ⋅ δ r ± C np ⋅ p ± C nr ⋅ r

(55)

(

)

unc unc unc unc C l = C*l M , Re,α , β , δ ER , δ EL , δ r , p, r ± C lunc β (M ) ⋅ β ± C lδ a (M ) ⋅ δ a ± C lδ r (M ) ⋅ δ r ± C lp ⋅ p ± C lr ⋅ r

(56) where the star terms represents the nominal value (the functional structure of each term is not reported here, and only the independent parameters are shown), while with the apex UNC the various terms of the uncertainty model are indicated. For istance, in the case of the lift coefficient, it has been made the hypothesis of a linear model of uncertainty with respect to the angle of attack. The terms

UNC C LUNC e C Lα are considered only depending upon Mach 0

number and constant wrt to all the other parameters. In practice, it has been made the hypothesis that the actual expression of lift coefficient can be the fitting polynomial (nominal function) plus/minus a linear function representing the uncertainty. Moreover, this is equivalent to state that we are doubtful about the intersection with the zero of the curve and with the slope*** and are quite confident about the shape. As a matter of fact this is not exactly true but represent a good compromise between accuracy and representation cleanness. Furthermore, also uncertainty terms related to the elevon deflection and to the dynamics derivative are considered. Each of the terms of uncertainty model is obtained as a sum of different contributions due to the different parts of the prediction model. Usually, the most common sources of errors are: ***

As a matter of fact, for the shape of the function we are dealing with, the linear term represent the major contribution to the first derivative of the curve. 38 American Institute of Aeronautics and Astronautics

− − −

Random experimental errors (repeatability) Systematic experimental errors (known and not removable errors ) CFD errors: computational grid, convergence, turbulence modeling, boundary conditions, etc.

To such error sources it must be added the uncertainty due to the ignorance, i.e. the incapacity to predict any unexpected phenomenology not foreseen by the AM during the flight. In practice, only by comparing pre-flight predictions and flight data it is possible to estimate the reliability of own prediction methods, and as a consequence improve them or at least increase the level of confidence of the estimated uncertainties. Before flight the only thing that can be done is to compare as much data sources as possible, i.e. different wind tunnel (PT-1, TWG), and CFD data. Finally, also existing literature data for similar vehicles are considered in order to assess the overall uncertainty level5. For instance, Figure 47 shows the uncertainties envelope included in the USV-FTB_1 Aerodatabase for Cm0 and Cmα coefficients. 0.070

0.006

0.050

0.004 0.002 UNC[C m α ]

UNC[C m 0 ]

0.030 0.010 -0.010

0.000 -0.002

-0.030

-0.004

-0.050

-0.006

-0.070 0.00

0.25

0.50

0.75

1.00

1.25

1.50

1.75

2.00

2.25

0.00

0.25

0.50

0.75

1.00

1.25

1.50

1.75

2.00

2.25

M

M

Figure 47. Uncertainty versus Mach number for Cm0 (Left) and Cmαα (Right).

One of the most important use of the uncertainty model rely in the MonteCarlo trajectory dispersion analysis. For this case it is necessary to associate with the uncertainty a probability distribution. As a matter of fact intrinsic differences in the data sources and the way of combining the different components of the uncertainty makes it not possible to apply a rigorous approach for the definition of the distribution. Let us say that, as a general rule adopted in this case, a Gaussian distribution is associated with the uncertainty. Even if there is no clear indication about the distribution of each single component, it can be reasonably assumed that the summation over a certain number of different error components tends to behave as a Gaussian distribution.

X. Conclusions. In the present paper a methodology for the integration of experimental and numerical aerodynamic data sources aimed at the development of the USV-FTB_1 Aerodatabase has been shown. Generally speaking, it is important to remark that the main goal of the activity was the development of a framework to be used not only for USV-FTB_1 aerodynamic needs but also for successive USV missions. Moreover, the entire process of set-up and verification of the methodology will take a great advantage by the inflight experiments that will be carried out during the DTFT missions. Global aerodynamic coefficients by means of inertial measurements and surface pressure distributions by means of 306 static ports will be acquired during flight. The possibility of performing a comparison between the prediction of the aerodynamic performance obtained by means of the AM and the in-flight measurements. Main benefits deriving from this kind of comparison can be recognized in: validation of predictive capabilities of Computational Fluid Dynamics (CFD) codes for a complex configuration in flight condition; verification of the suitability of the Wind-Tunnel Test methodology; Validation and tuning of the methodology for the extrapolation to flight condition of the experimental measurements; reduction of the uncertainty margins associated with the pre-flight prediction of the aerodynamic coefficients. 39 American Institute of Aeronautics and Astronautics

References 1

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