AERODYNAMIC CHARACTERIZATION OF A CANARD GUIDED ARTILLERY PROJECTILE

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1 45th AIAA Aerospace Sciences Meeting and Exhibit 8-11 January 27, Reno, Nevada AIAA AERODYNAMIC CHARACTERIZATION OF A CANARD GUIDED ARTILLERY PROJECTILE Wei-Jen Su 1, Curtis Wilson 2, Tony Farina 3, and Raymond Trohanowsky 4 U.S. Army RDECOM-ARDEC, Picatinny Arsenal, NJ [Abstract] An aerodynamic characterization of a 155mm canard guided artillery projectile was completed at the US Army RDECOM-ARDEC, Picatinny Arsenal, NJ. A parametric study was completed with various canard configurations. Initial configurations were modeled using different aerodynamic prediction software (PRODAS and Missile DATCOM). One configuration was modeled using commercially available computational fluid dynamics (CFD) software. Select configurations were fabricated and tested at the RDECOM-ARDEC wind tunnel facility. These characterizations provided a comparison between measured wind tunnel aerodynamic coefficients and estimated aerodynamic coefficients obtained from both aerodynamic prediction simulations and CFD model. The aerodynamic coefficients presented are essential for use in designing canard-guided projectiles. A AOA C C A C M C M C N C N CP F N F Nb F Nc L M b M c S V XCG XCP 6DOF Nomenclature = Canard deflection angle = Angle of Attack = Canard Chord = Axial force coefficient = Pitching moment coefficient (referenced from the XCG) = Pitching moment coefficient derivative = Normal force coefficient = Normal force coefficient derivative = Center of Pressure = Delta normal force = Normal force due to body = Normal force due to canard = Canard location = Moment due to body = Moment due to canard = Canard span = Velocity = Center of gravity = Center of pressure = Six degree-of-freedom I. Introduction he Department of Defense is continuously developing numerous types of precision guided projectiles. With the T advances of electronics systems and availability of guidance and control packages in a smaller envelope, the adaptation or minor modification to existing projectiles is feasible. This adaptation / modification of current projectiles will provide a means of converting a dummy projectile to a smart (precision guided) munition. 1 Aerospace Engineer, Aeroballistics Division, Picatinny Arsenal, NJ 786-5, Senior Member. 2 Aerospace Engineer, Aeroballistics Division, Picatinny Arsenal, NJ 786-5, Member. 3 Senior Aerospace Engineer, Aeroballistics Division, Picatinny Arsenal, NJ 786-5, Associate Fellow. 4 Aerospace Engineer, Aeroballistics Division, Picatinny Arsenal, NJ 786-5, Senior Member. 1 This material is declared a work of the U.S. Government and is not subject to copyright protection in the United States.

2 During preliminary design (trade-off study) of canard-guided projectiles, a quick, reliable, and accurate estimate of aerodynamic coefficient over different flight regimes is required. One of the main problems is that there is not enough experimental or CFD database of canard guided precision projectiles. Another problem is users rely on using the software and tools available to simulate the canard without conducting a comparison of different tools or experimental (wind tunnel) data and dangerously accept those results as factual. So, there is a need to expand the database and compare the different aerodynamics prediction simulation software with commercially available computational fluid dynamics (CFD) and experimental wind tunnel measurements. The present paper studied numerous canard (set of two canards) configurations for the 155 mm artillery projectile (M864 model) and different flight regimes. Two publicly available aerodynamics prediction simulation software tools were used: PRODAS 1, Missile DATCOM 2 and commercially available CFD: FLUENT 6 3 and compared with experimental results 4 obtained at the US Army RDECOM-ARDEC (Picatinny Arsenal) wind tunnel facility. The aerodynamic prediction module of PRODAS is based on empirical data and it is critical to stay within the limits of the database. Missile DATCOM is a publicly available Air Force aerodynamics coefficient software which use semi-empirical database. FLUENT 6 is a commercially available software. According to ANSYS/FLUENT, Inc.: FLUENT 6 is the CFD solver of choice for complex flows ranging from incompressible (low subsonic) to mildly compressible (transonic) to highly compressible (supersonic and hypersonic) flows. Providing multiple choices of solver options, combined with a convergence-enhancing multigrid method, FLUENT 6 delivers optimum solution efficiency and accuracy for a wide range of speed regimes. The wealth of physical modes in FLUENT 6 allows you to accurately predict laminar and turbulent flows, various modes of heat transfer, chemical reactions, multiphase flows, and other phenomena with complete mesh flexibility and solution-based mesh adaptation. The mesh generator used was TGrid for boundary layer mesh and GAMBIT for the rest of the mesh. The mesh generation and technical support was provided by the staff from ANSYS/FLUENT Inc. The US Army RDECOM-ARDEC wind tunnel facility has a 24 diameter test section with number regime of The facility is an inducted wind tunnel that operates with air stored at 12 psi. The angle-of-attack span is -2 to +2. Additional wind tunnels available on-site include: a 16 x16 transonic wind tunnel and a 9 x 9 supersonic wind tunnel. The number regime of the transonic wind tunnel is and the angle-of-attack span is -11 to +11. The number regime of the supersonic wind tunnel is and the angle-of-attack span is -1 to +1. Here is a brief explanation of how to guide a spin-stabilized projectile with canards. On a spin-stabilized projectile the normal force is in front of the center of gravity (fig 1a). Adding a deflected canard forces the projectile to fly with a body trim angle. This creates a net normal force that is used to maneuver the projectile. At trim: body pitching moment (Mb) is equal to canard pitching moment (Mc), the body center of pressure (CP) is closer to the CG than the canard center of pressure (CPc), thus the net normal force used to steer the projectile is the sum of the 2 normal forces, F N = F Nb + (-F Nc ) for a spin stabilized projectile (fig 1b). A control reversal occurs when the body center of pressure (CP) is farther from the CG than the canard center of pressure (CPc) and the net normal force used to steer the projectile, ( F N = F Nb + (-F Nc )), becomes negative (control reversal) (fig 1c). F Nb F Nb F Nb F N F NC F NC Mb Mc V Mb Mc V Mb Mc F N V - center of gravity - body normal force center of pressure - canard normal force center of pressure Figure 1a. Spin stabilized round F Nb - body normal force F Nc - canard normal force F N - net normal force V - velocity Mb - body pitching moment Mc - canard pitching moment Fig 1b. Spin stabilized round Fig 1c. Spin stabilized round w/ Canards w/ canards and CP ahead of nose 2

3 II. Procedure A parametric study was completed with various canard configurations. The baseline configuration is the M864, 155mm Artillery, projectile (Figure 2). Four different spans, three chord lengths, three canard locations, and three deflection angles were simulated to give a broad range of possible configurations (82 total configurations) (Table A). Figure 2. M864 Configuration Table 1. Attributes of Project Location (calibers) Location (inches) Configuration ID ¼ L1 ½ 3.51 L L3 Span (calibers) Span (inches) Configuration ID 1/8.763 S1 ¼ S2 ½ 3.51 S3 CFD Model S4 Chord (calibers) Chord (inches) Configuration ID 1/8.763 C1 ¼ C2 ½ 3.51 C3 Canard Pitch Angle Configuration ID (degrees) A1-4 A2-8 A3 To accommodate a valid comparison of attributes, several constraints were defined at the beginning of the project. The location is measured from the nose to the mid-chord. The span is defined as the exposed span, so for different locations, hence different body diameter, the same span is added. For this evaluation, it is assumed the canards will be used for end game maneuvers and would occur at high subsonic velocities. The XCG is assumed to be at calibers from the nose for all configurations. Two canards will be horizontally mounted and nonspinning with only pitch command capability. The canards are defined as 1/8 thick, rectangular flat-plate canards with sweep angle. The Missile DATCOM and PRODAS were used to estimate the aerodynamic performance of 82 configurations (Figures 3-5). A design of experiments matrix was developed to validate the conclusions of the mathematical analyses. These configurations were fabricated and tested at the ARDEC wind tunnel facility (Table 2). The wind tunnel model was scaled to 5% due to the size constraint of the subsonic tunnel. The test configurations were tested at.31 and.76. The baseline configuration (no canards) was tested at numbers.31,.48,.61, and.76. The configuration matching the configuration evaluated with CFD was tested at 3

4 numbers.69 and.76. Due to time constraints and availability of resources, the CFD analysis was completed on only one configuration (Figure 6). A wind tunnel model of one configuration is shown in figure 7. CHORD SPAN Figure 3. Span and Chord Configurations at Location 2 CHORD LOCATION Figure 4. Location and Chord Configurations at Span 2 4

5 SPAN LOCATION Figure 5. Span and Location Configurations at Chord 2 Table 2. Wind Tunnel Configurations Configuration Location Span Chord Deflection Angle Description, No canard Mid size canard mid location canard deflections With 2311 & canard locations Largest size canard 3 canard chords With canard spans CFD Configuration Figure 6. Solid Works Model of CFD configuration Figure 7. Wind Tunnel Model of Configuration

6 The FLUENT CFD was done with Reynolds Averaging of Navier-Stokes (RANS) equations type of realizable k- (2 equations) turbulent model. It was done with double precision in 3D. Boundary condition for front and back were pressure-based. The computational domain is the following: 18 cal. radial (31.13 body lengths,) 124 cal. forward of body (21.36 body lengths,) and 22 cal. rear of the body (34.8 body lengths.) The number of cells is 7.14 millions tetrahedral cells with boundary layer cells at the wall. Figures 8 to 1 show the mesh generation. The mesh designed for y + is showing in Figure 11. As one can see, the resolution is better at the nose, tail, canards and sharp corners. Figure 8. Surface Mesh Figure 9. Far Field Mesh Figure 1. Boundary Layer Mesh Figure 11. Surface y + CFD of the M864 baseline projectile (done by ANSYS/FLUENT Inc.) was performed first to validate CFD. Then, for configuration 1411, the CFD was performed at two numbers =.69 and.76 and at two AoAs of 2 and 4 deg. It was performed at altitude of 2,7 m using Standard Atmospheric Table. III.Results and Discussion A. Comparison comparisons of all the prediction methods were conducted on the M864, 155mm projectile, without any canards. Figures illustrate the aerodynamic coefficients obtained from PRODAS, and Missile DATCOM compared to the wind tunnel data and the existing coefficients from an existing 6-DOF simulation model. The CFD analysis was available at only AOA = 4 for the baseline configuration. The C N and C M demonstrate an excellent match between Missile DATCOM, PRODAS, wind tunnel data, CFD and the 6-DOF simulation model (all within 1%). The C A between PRODAS, wind tunnel data, 6-DOF, and CFD show excellent agreement, the Missile DATCOM estimation is approximately 25% higher. The wind tunnel data and CFD match for the XCP; PRODAS and Missile DATCOM match each other and is about.5 calibers forward, and the 6-DOF is about.4 calibers rearward. This analysis validates the baseline configuration for all four prediction methods. 6

7 Normal Force Coefficient WT MD PRO 6-DOF CFD Poly. (WT) Pitch Moment Coefficient WT MD PRO CFD 6-DOF Poly. (WT). AOA, deg. AOA, deg Figure 12. C N Figure 13. C M 5 3. Axial Force Coefficient WT 6-DOF MD PRO CFD Normal Force Center of Press (calibers from XCG) WT MD PRO 6-DOF CFD Poly. (WT) AOA, deg. AOA, deg Figure 14. C A Figure 15. XCP B. PRODAS Comparison Using PRODAS each element of the design was fixed and comparative plots were created to show the effects of holding one dimension constant. Figures show the plots for a fixed location (location 2) and fixed canard deflection angle ( ), while span and chord were varied. Location 2 Location Cx CN Figure 16. C A for Location Figure17. C N for Location 7

8 Location 2 Location CM Xcp Figure 18. C M for Location Figure 19. XCP for Location PRODAS shows for a fixed canard location, the smallest span had little effect on the pitching moment and normal force regardless of the chord length. For the two larger spans, the larger chord had a greater effect than the smaller chord on the pitching moment. At location 2, there is some critical span length between span 1 and span 2 in which the span produces minimal change to the normal force, and the length of the chord begins to dominate. Larger spans have more effect on axial than do larger chords. Figures 2-23 show the plots for a fixed span (span 2) and fixed deflection angle ( ), while location and chord were varied. Span 2 Span CX 2211 CN Figure 2. C A for Span Figure 21. C N for Span Span 2 Span CM 2211 Xcp Figure 22. C M for Span Figure 23. XCP for Span 8

9 PRODAS shows that for a fixed span 2, the axial coefficient for the baseline is higher than the axial coefficient for all cases at location 3. Obviously for span 2 and location 3, there is no empirical data in which PRODAS can use to more accurately calculate the axial coefficient. For a fixed span, different location and chord combinations show an increased pitching moment and normal force, but the values of pitching moment and normal force do not vary greatly. Figures show plots for a fixed chord (chord 2) and fixed canard deflection angle ( ) while location and span were varied. Chord 2 Chord CX CN Figure 24. C A for Chord Figure 25. C N for Chord Chord 2 Chord CM Xcp Figure 26. C M for Chord Figure 27. XCP for Chord PRODAS shows that for a fixed chord 2, configuration 3221 has a lower axial coefficient than the baseline. This probably is similar to the problem suggested for location 3. Larger spans have more effect on axial than does the location of the canard. For a fixed chord, span has more effect on the pitching moment and normal force than the location of the canard on the projectile. C. PRODAS challenges One challenge that occurred when dealing with PRODAS was that two canards cannot be pitched in such a way to create a pure pitching moment. When trying to pitch canards, the canards pitch opposite each other, thus creating a roll control command. Arrow Tech recommended evaluating only one canard to create a unit effect, then double the results for a two canard design. The other challenge dealing with PRODAS was how to properly define the canard. The canard must be created using a tip to tip canard length, but in doing so, the portion of the canard that is embedded in the projectile, still adds to both the moment and force coefficients. But if the canard is fully or partially embedded in the body root diameter, the effects of the canard on the body are not calculated. So to properly achieve the results, the canard must be drawn tip to tip, but there is an input that allows the projectile diameter at the root of the canard to be inputted, effectively eliminating the embedded portion. 9

10 D. Missile DATCOM Comparison Figures show plots for a fixed location (location 2). CA vs CN vs CA CN (deg) (deg) Figure 28. C A for Location Figure 29. C N for Location XCP vs XCP vs XCP (from CG) XCP (from CG) (deg) (deg) Figure 3. C M for Location Figure 31. XCP for Location Missile DATCOM shows for a fixed canard location, the smallest span had little effect on the pitching moment and normal force regardless of the chord length. The largest span and chord has about 75% higher C N. All configurations have approximately the same C A except the configuration with the largest span and the largest chord., which had a significantly higher C A at AOA =. Figures show plots for a fixed span (span 2). CA vs CA vs CA CA (deg) (deg) Figure 32. C A for Span Figure 33. C N for Span 1

11 CN vs CM vs CN CM (from CG) (deg) (deg) Figure 34. C M for Span Figure 35. XCP for Span Missile DATCOM shows that for a fixed span 2, different location and chord combinations show an increased pitching moment and normal force, but the values of pitching moment and normal force do not vary greatly. Figures show plots for a fixed chord (chord 2). CA vs CN vs CA CN (deg) (deg) Figure 36. C A for Chord Figure 37. C N for Chord CM vs XCP vs CM (from CG) XCP (from CG) (deg) (deg) Figure 38. C M for Chord Figure 39. XCP for Chord 11

12 `Missile DATCOM shows that for a fixed chord 2, spans have more effect on axial than does the location of the canard. For a fixed chord, span has more effect on the pitching moment and normal force than the location of the canard on the projectile. E. Missile DATCOM Challenges During the Missile DATCOM analysis, a limitation was observed as the span was increased. Once the span was increased beyond a limit, the prediction code will fail to provide a result. This may be contributed to the limitation of Missile DATCOM empirical database. Missile DATCOM was not able to evaluate a solution for some configurations, for example 1411 and To resolve this issue, the span was reduced until a solution could be obtained. Then three solutions were found for models defined with slightly smaller spans. A linear extrapolation of the results was conducted to get the data of the desire longer span. F. Wind Tunnel Comparison The wind tunnel configurations were tested in such a way that two variables, either location, span, or chord, were held constant while the remaining variables were changed to show the effects that each change would have on the total round. Below are plots of location 3, span 3, and canard deflection angle with varying chords (figs 4-43). Varying Chord Varying Chord CX CN Figure 4. C A for Varying Figure 41. C N for Varying Varying Chord Varying Chord CM Xcp Figure 42. C M for Varying Figure 43. XCP for Varying The wind tunnel showed that purely varying the chord of the canard had minimal effect on the axial coefficient while making large changes in the pitching moment and normal force coefficients. The coefficients increased as the chord increased in length. The center of pressure showed a similar trend. Figures show the plots for a fixed chord and fixed span, and fixed canard angle. 12

13 Varying Location Varying Location CX CN Figure 44. C A for Varying Figure 45. C N for Varying Varying Location Xcp Figure 46. XCP for Varying Data for a fixed chord and fixed span canard projectile showed that varying location had little effect on the axial coefficient. Location 1 and location 2 showed similar results for the pitching moment and normal force coefficients, but location three showed a considerable increase in the pitching moment and the normal force. For a fixed chord and fixed span, locations 1 and 2 yield practically the same results. Figures 47-5 show the plots for a fixed location and fixed chord. Varying Span Varying Span CX CN Figure 47. C A for Varying Figure 48. C N for Varying 13

14 Varying Span Varying Span CM Xcp Figure 49. C M for Varying Figure 5. XCP for Varying Wind tunnel data shows that for a fixed location and fixed chord, an increased span increases the axial coefficient by a considerable amount while having little or no effect on the pitching moment and normal force data. In general, chord seems to have the largest effect on pitching moment and normal force while span has the least effect on the axial coefficient. G. Wind Tunnel Challenges A few challenges were encountered when testing in the wind tunnel. Due to the size of the wind tunnel test section, the model had to be scaled to 5% of the actual projectile. Although the wind tunnel model was proportionate, the Reynolds number effects are not totally known. Another issue that arises when testing all projectiles in the wind tunnel is the asymmetries of the axial coefficient, normal force, and pitching moment data. Most wind tunnel tests require proper shifting and interpretation of the data to determine if the shifting or asymmetries are true functions of the projectile shape or natural variations that occur in all testing. The last problem that occurred was creating a matrix that would include enough data to make accurate analysis. It was not financially feasible to test all configurations. H. CFD Comparison Since the CFD baseline analysis matches the other aero prediction methods for the baseline, that clearly shows that the normal force without canard is predicted as well as one could hope for the given mesh and geometry. Once the baseline is established, the CFD simulation is completed with configuration Figures show the post-processing information. Refer to section I (Comparison of Configuration 1411) for the comparison of the coefficients from CFD with the results from the others tools. The C A from CFD was comparable with other prediction tools. The C N obtained from CFD was much lower than the results obtained from with the others tools. Analysis was done together with ANSYS/FLUENT Inc. to determine the cause of this discrepancy. It was confirmed that the shape of the model, Reynolds number, number, angle-of-attack and interpretation of aerodynamics coefficients were the same for the CFD model and the wind tunnel model. The lift force from CFD is 28% lower at.69, AoA = 4 deg. CFD shows that canard contributes C N =.12, compared with wind tunnel C N =.57, PRODAS C N =.138 and Missile DATCOM C N =.13. As a result, CM and XCp were different in CFD. The staff at ANSYS/FLUENT, Inc doesn t expect that a finer canard grid will change the lift by the required difference. 14

15 Figure 51. Dynamic Pressure Contour Figure 52. Total Pressure Contour Figure 53. Number Contour Figure 54. Velocity Magnitude Contour Figures show the canard is separated at AoA= and 4 degrees. The CFD says that the canard generates practically no lift at AoA= 4 deg. ANSYS/FLUENT, Inc suggested rationale to the observed difference in the lift due to the canards. The first explanation is that it may be a result of RANS models not doing absolutely well for such separated flows. The canard configuration was analyzed in 2D, and 2 out of 3 turbulence models say that (in 2D) the canard 'airfoil'at AoA=4 deg should actually generate down force. The SST model predicts a very small lift contribution. In CFD it was observed that the highest velocities occur on the lower side, and the pressure is also lower near the lower leading edge. The flow is mostly separated, except at the leading edge face. So, it is a RANS modeling issue (not FLUENT). Any RANS model would give such a behavior. Figure 55. Flow about Canard at AOA = Figure 56. Flow about Canard at AOA = 4 A second explanation is the infinitely sharp leading edge of the canard. The CFD model was assumed to have infinitely sharp corners. The wind tunnel model has very sharp corners, but it seems that the wind tunnel model does not separate as dramatically as CFD does. The 5% scale wind tunnel model has 1/16 thick canards. The authors assumed that the PRODAS and Missile DATCOM models do not have the flow separation issues. The third explanation is the interference effect of the flow due to the canard with the body and the vortex generated by the canard. It is possible that CFD is missing important flow physics. It is possible that the vortices 15

16 coming off the canard lower the surface pressure on the main body. If that is a significant mechanism in this case, then CFD is likely missing that, since the CFD model mesh is too coarse to resolve the canard wake. The baseline results show that this may be one of the causes of the difference between CFD and wind tunnel. PRODAS and Missile DATCOM account for interference effects. The accuracy of their equations is unknown. At the beginning of this program, the team decided to pursue a flat plate canard with the intention of simplifying the task. A flat plate would most likely not be used for a canard design. A canard design would either be an airfoil shape, a leading edge bevel or a leading edge radius. Since the wind tunnel model is a 5% scale, it probably models a flat plate more closely than the full scale CFD model. If the team had pursued an alternate canard design, the results of the CFD analysis may have been more successful. Another useful test would have been to conduct flow visualization testing in the wind tunnel to confirm whether the flow around the canard is separating. It is not certain that the RANS will be able to handle a hexagonal airfoil shape or if a leading edge radius or airfoil shape would be required for a good analysis. I. Comparison of Configuration 1411 Due to resource limitations, the CFD analysis was completed on one canard configuration (1411). Figures illustrate the aerodynamic coefficients obtained from PRODAS, and Missile DATCOM compared to the wind tunnel data and CFD analysis. The CN data shows a reasonable match between the wind tunnel data and PRODAS (within 1%), the Missile DATCOM estimate is about 25% higher than the wind tunnel data, and the CFD estimate is about 25% lower than the wind tunnel data. When compared to the wind tunnel data, the C M estimate with PRODAS is 2% higher, the C M estimate with Missile DATCOM is 45% higher and the C M estimate with CFD is 45% lower. The PRODAS and CFD estimates for C A match each other and are less than 1% higher than the wind tunnel data, the Missile DATCOM estimate is about 2% higher than the wind tunnel data. Since PRODAS and Missile DATCOM have higher C N and C M than the wind tunnel data and the CFD evaluation indicates almost total separation of flow around the canard, this implies the flow around the canard has partial separation in the wind tunnel test Normal Force Coefficient WT PRODAS MD CFD Linear (MD) Pitch Moment Coeff from XCG WT PRODAS MD CFD Linear (MD) AOA, deg. AOA, deg Figure 57. C N for Figure 58. C M for 5 Axial Force coefficient.15.1 WT PRODAs MD CFD AOA, deg Figure 59. C A for 16

17 J. Comparison of Configuration 2111 Figures 6-63 illustrate the aerodynamic coefficients obtained from PRODAS, and Missile DATCOM compared to the wind tunnel data for the smallest canard at location 2. The PRODAS calculation for CN is about 1% lower and the Missile DATCOM is less than 2% lower than the wind tunnel data. The CM shows a good match between the wind tunnel and Missile DATCOM, with PRODAS overestimating by about 1%. For C A, PRODAS estimates about 3% higher than the wind tunnel and Missile DATCOM estimates about 5% higher than the wind tunnel. For XCP, PRODAS estimates about calibers forward than the wind tunnel and Missile DATCOM estimates about.4 calibers forward than the wind tunnel. Since PRODAS and Missile DATCOM match the wind tunnel better for configuration 2111 than 1411, it is possible that the canard size falls within the empirical data for 2111 and outside the empirical database for Normal Force coefficient.15 WT PRODAs MD Pitch Moment (CG).3 WT PRODAs MD AOA, deg AOA, deg Figure 6. C N for Figure 61. C M for Axial Force coefficient.15 WT PRODAs MD XCP, calibers from XCG WT PRODAs MD AOA, deg AOA, deg Figure 62. C A for Figure 63. XCP for K. Canard Deflection To compare the effects of a deflected canard, a simulation in Missile DATCOM and a test in the subsonic wind tunnel were completed. For the wind tunnel analysis, configuration 221 (Location 2, Span 1, Chord 1) was tested and compared to the baseline results. In the wind tunnel results, both the pitching moment and normal force coefficients were slightly higher than zero at zero degrees angle of attack for both the baseline and configuration This vertical shift of the normal force and pitching moment coefficients is typical in wind tunnel testing for configurations that are symmetric about the pitch plane. The data is corrected by vertically shifting the normal force and pitching moment curves by the delta value at zero degrees angle of attack. Essentially, the normal force and pitching moment curves are purely shifted up or down, without affecting the slope. For the case of a deflected canard projectile, one would expect that at zero degrees angle of attack there to be a moment generated on the projectile due to the deflected canard. Configurations 2212 (4 deflected canard) and 2213 (8 deflected canard) had non-zero values for both the pitching moment and normal force coefficients at zero degree angle of attack. But to keep our data consistent, the delta values used for shifting configuration 2211 was applied to the deflected canard projectiles. This gives a one to one comparison of the deflected and non-deflected projectiles. Figures show the plots of the wind tunnel normal force and pitching moment coefficients for configuration

18 Figures show the plots of the Missile DATCOM estimates of normal force and pitching moment coefficients for configuration The results show significantly more change in both the C N and C M due to the deflected canards when compared to the wind tunnel data. This may imply the flow was separated in the wind tunnel configuration. Canard Deflection 221 Canard Deflection CN CM Figure 64. C N for Canard Figure 65. C M for Canard from wind tunnel data from wind tunnel data Canard deflection Canard deflection CN.15.1 ' CM (from CG).3 ' Figure 66. C N for Canard Figure 67. C M for Canard from Missile DATCOM from Missile DATCOM Appendices 1-3 include the aerodynamic coefficients of the various configurations. Appendix 1 is the aerodynamic coefficients generated from PRODAS for 81 configurations. Appendix 2 is the aerodynamic coefficients generated from Missile DATCOM for the 12 configurations that were tested in the wind tunnel. Appendix 3 is the aerodynamic coefficients measured from the wind tunnel test for the 12 configurations. 18

19 IV. Conclusions A database of the aerodynamic coefficients obtained from PRODAS, Missile DATCOM, and wind tunnel measurements is provided in Appendices 1-3. A comparison of the results obtained from these aero-prediction tools and CFD demonstrate a match of the C N and C M for the baseline configuration. PRODAS, CFD and wind tunnel data match for C A, and Missile DATCOM was about 2% higher for the baseline configuration. Results indicate different values given by PRODAS, Missile DATCOM, and CFD for the configurations with the canard. Two potential sources of variation in results include partial flow separation about the canard, and designing canards outside the limits of the empirical database. Each tool views the canard differently creating a variation in results. Each aero prediction tool has its own shortcomings and the user must be aware of the these and analyze the results with caution. For the computer simulations (CFD, PRODAS, Missile DATCOM) there is no easy way to validate how the program is solving the geometry and flow conditions. As for the wind tunnel test, only flow visualization would have provided the flow separation information required. In retrospect, the team should have chosen a canard that would be handled equally by all simulation tools. As mentioned previously, a canard with an airfoil shape or with a leading edge radius probably would have yielded more favorable results. This should serve as an emphasis as to why it is critical to use a variety of aerodynamic prediction codes, CFD analysis, experimental data and aeroballistic judgment to achieve a reliable aerodynamic estimate. 19

20 Appendix 1. Aerodynamic Coefficients Obtained with PRODAS Base

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26 Appendix 2. Aerodynamic Coefficients Obtained with Missile DATCOM CONFIG MACH.76 AOA C N C M C A CONFIG 1121 MACH.76 AOA C N C M C A XCP CONFIG 1221 MACH.76 AOA C N C M C A XCP CONFIG 1231 MACH.76 AOA C N C M C A XCP CONFIG 2111 MACH.76 AOA C N C M C A XCP

27 CONFIG 2121 MACH.76 AOA C N C M C A XCP CONFIG 2131 MACH.76 AOA C N C M C A XCP CONFIG MACH.76 AOA C N C M C A XCP CONFIG 2231 MACH.76 AOA C N C M C A XCP CONFIG 3121 MACH.76 AOA C N C M C A XCP

28 CONFIG 3221 MACH.76 ALPHA CN CM CA X-C.P CONFIG 3231 MACH.76 ALPHA CN CM CA X-C.P CONFIG 1411 MACH.76 ALPHA CN CM CA X-C.P CONFIG 1412 MACH.76 ALPHA CN CM CA X-C.P CONFIG 1413 MACH.76 ALPHA CN CM CA X-C.P

29 CONFIG 2131 MACH.76 AOA C N C M C A XCP CONFIG MACH.76 AOA C N C M C A XCP CONFIG 2231 MACH.76 AOA C N C M C A XCP CONFIG 3121 MACH.76 AOA C N C M C A XCP CONFIG 3221 MACH.76 AOA C N C M C A XCP

30 CONFIG 3231 MACH.76 AOA C N C M C A XCP CONFIG 1411 MACH.76 AOA C N C M C A XCP CONFIG 1412 MACH.76 AOA C N C M C A XCP CONFIG 1413 MACH.76 AOA C N C M C A XCP Run 1 Config Appendix 3. Aerodynamic Coefficients Measured with Wind Tunnel Test TP # MACH AOA C A AXIAL C N C M Xcp DRAG LIFT

31 Run 2 Config TP # MACH AOA C A AXIAL C N C M Xcp DRAG LIFT Run 3 Config TP # MACH AOA C A AXIAL C N C M Xcp DRAG LIFT

32 Run 4 Config TP # MACH AOA C A AXIAL C N C M Xcp DRAG LIFT Run 5 Config 2211 TP # MACH AOA C A AXIAL C N C M Xcp DRAG LIFT

33 Run 6 Config 2211 TP # MACH AOA C A AXIAL C N C M Xcp DRAG LIFT Run 7 Config 2212 TP # MACH AOA C A AXIAL C N C M Xcp

34 Run 8 Config 2212 TP # MACH AOA C A AXIAL C N C M Xcp Run 9 Config 2213 TP # MACH AOA C A AXIAL C N C M Xcp

35 Run 1 Config 2213 TP # MACH AOA C A AXIAL C N C M Xcp Run 11 Config 1311 TP # MACH AOA C A AXIAL C N C M Xcp DRAG LIFT

36 Run 12 Config 1311 TP # MACH AOA C A AXIAL C N C M Xcp DRAG LIFT Run 13 Config 3331 TP # MACH AOA C A AXIAL C N C M Xcp DRAG LIFT

37 Run 14 Config 3331 TP # MACH AOA C A AXIAL C N C M Xcp DRAG LIFT Run 15 Config 3311 TP # MACH AOA C A AXIAL C N C M Xcp DRAG LIFT

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