Comparison of Predicted Actuator Performance for Guidance of Supersonic Projectiles to Measured Range Data

Sidra I. Silton * U.S. Army Research Laboratory, Aberdeen Proving Ground, MD 21005-5066

A recent study showed that the complex 3-D shock/boundary layer interaction of a pin placed next to a fin produces an asymmetric lift force that can be utilized for flight control. This study was completed to validate this new technology. Specifically, a flight test was designed using this asymmetric lift to produce roll torque. The projectile was modeled, using high performance fluid dynamic computations and six degree-of-freedom trajectory simulations, to determine its flight characteristics prior to being flown in the US Army Research Laboratory’s Aerodynamics Experimental Facility. Analysis of the flight data determined that the projectiles with pins developed the expected rolling moments.

Nomenclature Clδ = Roll Torque Coefficient Clp = Roll Damping Coefficient Cmα

= Pitching Moment Coefficient Derivative Cmq = Pitch Damping Moment Coefficient CNα = Normal Force Coefficient Derivative CX0 = Zero Yaw Axial Force Coefficient φ = angle of revolution XCP = Axial Center of Pressure Location

I. Introduction

T HERE has been a recent interest in guided projectiles that operate in the high supersonic to hypersonic range for various missions. A possible scenario for missile defense assumes that medium caliber guns (35 mm to 75 mm)

with high rates of fire could fire multiple supersonic projectiles that may be guided into an incoming missile. For military programs that plan to utilize high speed guided munitions, large turning forces could be necessary due to the high closure rates between the projectile and an agile and maneuverable target.

The overall program discussed herein was conducted as an initial feasibility study for the use of strategically located actuators to provide the necessary turning force to maneuver a Defense Advance Research Project Agency (DARPA) command-guided, medium caliber projectile. Recent studies at Georgia Tech Research Institute (GTRI) have found that the introduction of pins on a projectile in the vicinity of the fins creates shock patterns that impinge on both the fins and body surfaces.† The forces created by the shock impingement are capable of providing control forces through asymmetric lift. Two pins placed close to adjacent fins can induce an angle-of-attack change, two diametrically opposed pins can induce a rotation.

The current effort was conducted to model and validate that placement of control pins next to the fins does indeed produce asymmetric lift for the DARPA Advanced Technology Office. Specifically, it was desired to determine if the diametrically opposed placement of the control pins could be used to induce projectile rotation by creating roll torque. The creation of a sufficient amount of roll torque produces measurable projectile rotation that can easily be measured in an aeroballistic facility. The current effort consisted of three parts:

1. computer simulations to predict projectile behavior due to the presence of the pins;

* Aerospace Engineer, Weapons and Materials Research Directorate, Ballistic and Weapons Concept Division, Aerodynamics Branch, AMSRD-ARL-WM-BC, Member AIAA. † The use of these pins or similar pins to produce steering forces and moments is a proprietary technology developed by the Georgia Tech Research Institute and is protected under US Patent Law. Used with permission. Patent Pending.

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22nd Applied Aerodynamics Conference and Exhibit16 - 19 August 2004, Providence, Rhode Island

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This material is declared a work of the U.S. Government and is not subject to copyright protection in the United States.

2. an experimental study conducted at the US Army Research Laboratory (ARL) Aerodynamic Experimental Facility (AEF) to determine the asymmetric lift produced by measuring the rolling moment; and

3. comparison of computational and experimental results for future use.

II. Blind Simulations Simulations were completed prior to experimental range testing (i.e. blind simulations) in support of the subscale

25 mm flight test in order to determine the expected roll characteristics of the projectile with control pins. Both high performance computations (CFD) and six de degree-of-freedom (6-DOF) simulations were completed on a full-scale model.

A. Computational Fluid Dynamics Computational fluid dynamic (CFD) simulations were conducted to obtain the roll torque coefficient and

determine the increase in axial force coefficient due to the presence of the control pins. 1. Solver

The CFD++ Solver1 was utilized for this study. CFD++ solves the Reynolds-averaged Navier-Stokes equations. The pointwise k-ε turbulence model2 was used for the computation of the turbulent flow. The equations are solved within a finite volume framework using an unstructured grid topology. Spatial discretization is accomplished using the cell face normal at the cell face centroid, which is obtained by reconstructing the cell centroid values. The point-implicit integration scheme was used to solve the steady-state simulation. The Courant number was ramped as large as possible to allow for quicker solution convergence. 2. Boundary Conditions

The far field boundary (including the inflow and outflow boundaries) is set to PV (pressure, velocity) temperature-based inflow/outflow. This boundary condition is a characteristic type that allows the solver to determine the conditions at the far field boundary (inflow, subsonic outflow or supersonic outflow) and either explicitly sets the boundary condition to free stream conditions (inflow, subsonic outflow) or extrapolates as necessary (supersonic outflow). Free stream pressure and temperature are set to 101.325 kPa and 288.15 K, respectively (i.e. standard sea level conditions). Density is then calculated from the perfect gas assumption. Velocity is varied between Mach 1.5 and 4.0. Angle of attack remained fixed at zero degrees. For the projectile body, fins, and control pins, when present, the boundary condition is set to be a no slip, adiabatic wall. 3. Geometry

The full scale 50 mm projectile with a tapered leading and trailing fin edge and sharp nose tip was modeled in the blind CFD simulations (Fig. 1). In order to determine the effect of the control pins on the drag coefficient, simulations were completed on three geometries; a projectile with no control pins, a projectile with diametrically opposed rectangular control pins, and a projectile with diametrically opposed parallelogram shaped (trapezoidal) control pins. These control pin shapes correspond to those optimized by GTRI for which limited CFD data had previously been obtained.3

Figure 1. 3-D renderings of geometry utilized inblind CFD calculations with aft view of controlpins.

4. Grid The grids for each geometry investigated were obtained

from Metacomp Technologies as the numerical grids had been previously constructed under contract from GTRI.3 Each grid was unstructured and contained mostly hexahedral cells along with a small number of triangular prisms. Each projectile contained approximately 2.9 millions cells.

B. Six Degree-of-Freedom Trajectory Simulations 6-DOF simulations were completed to determine the number of revolutions the projectile could be expected to

complete as it flew down the 100 m aeroballistic range. 1. 6-DOF Software

The PRODAS4 6-DOF fixed plane trajectory simulation was utilized in this study. PRODAS utilizes a database of aerodynamic coefficients as a function of Mach number. For these simulations, the database consisted of results from a previously completed flight test using a half scale 25 mm projectile fired from a rifled barrel5 augmented by

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the change in axial force and rolling moment coefficients due to the presence of the control pins obtained from the CFD. The physical characteristics of the projectile are specified within PRODAS. After initialization of the equations of motion based on input parameters, a fourth order Runge-Kutta numerical integration scheme is used to integrate the equation of motions in time. The time step is dynamically chosen in order to account for both pitch frequencies (usually 20 time steps per yaw cycle). 2. Initial Conditions

Initial conditions are specified for the gun and the projectile during setup of the 6-DOF simulation. The gun is set to have an elevation of 0.001° and no azimuth. Standard sea level meteorological conditions are used. The gun twist (the distance necessary for the projectile to rotate 360°) is made extremely large so that the spin at the muzzle is 0 Hz (i.e. smooth bore gun). The initial projectile velocity was varied between Mach 2.0 and Mach 3.0. The projectile starts at the coordinate system origin with no pitch angle, pitch rate, or yaw angle. The initial yaw rate was set to −15.0 rad/sec, as this is a typical value for small caliber projectiles.

III. Range Tests

A. Test Facility All experiments were conducted in the

ARL AEF. This facility is designed to evaluate the complete aeroballistics of projectiles as described by Braun.6 A schematic of the test setup, which is the standard system in the Aerodynamics Range, is shown in Fig. 2. A photograph looking towards the gun barrel is shown in Fig. 3.

Up to six high power, orthogonal x-rays were utilized to determine the structural integrity and launch dynamics of the projectile (Fig. 3) in a manner consistent with other programs.7,8, 9 The x-ray system is triggered by a piezoelectric gauge system that senses the precursor shock wave at the muzzle, then arms and waits for the main blast wave. The main blast wave arrives just after the projectile leaves the muzzle of the gun.

Figure 2. Schematic of ARL Aerodynamics ExperimentalFacility.

The range facility itself consists of 39 orthogonal spark shadowgraph stations (Fig. 4) arranged in 5 groups over 100 m of trajectory length. The first station is located approximately 4.57 m downrange of the muzzle. Infrared sensors detect the passage of the projectile and a computer system triggers the spark sources that project a vertical and horizontal direct shadow image of the passing projectile on 29.9 x 25.6 cm (11 x 14 in) film. The direct image technique allows the facility to produce high-quality spark shadowgraphs, but limits the size of the projectiles that can be tested (hence the 25 mm scaled projectile). The stations are surveyed into a fiducial system that is simultaneously imaged on the film with the projectile. The film is processed after each shot and read using a

Figure 3. Photo of orthogonal x-rays relativeto gun muzzle in AEF.

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Figure 4. Photo of dual plane (orthogonal) sparkshadowgraph stations with infrared sensor triggers andspark source.

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precision light table to produce the raw experimental data. These data include the measured special coordinates (range, deflection, altitude) and the angular orientation (pitch, yaw, roll) relative to the earth fixed range coordinate system, all as a function of the spark time. The data is then reduced for analysis.

The projectile was fired, using EXPRO propellant, from a modified 25 mm Bushmaster Mann barrel; the rifled barrel was bored out to create a smooth bore gun. Firing from a smooth bore gun allowed for easier determination of the roll torque development in this test. A charge establishment test was conducted on slugs of approximately the same mass as the final launch package in order to accurately determine the propellant charge weight necessary to achieve the desired velocity.

B. Test Model The complete launch package shot from the Mann barrel

consisted of a projectile and a sabot system (Fig. 5). The total package weight was approximately 120 g. 1. Projectile

The baseline projectile was a 25 mm sub-scale projectile with blunt fin leading and trailing edges, a relatively large fillet between the fins and the body and a blunt nose tip (0.635 mm radius). This projectile was the same as that utilized for the previously completed rifled test.5 For stability, the center-of-gravity (CG) was shifted forward byaluminum for the body and fins. The tungsten nose was a 46.0 body consisted of 2 tangent ogive sections 56.9 mm long and athick with a 25.76° sweep angle, a 24.9 mm span, a 22.4 mm edge was flush with the projectile base. A steel spin pin wprojectile roll position during analysis.

The roll torque models were created using a control pin ofthe optimized parallelogram shape3 investigated in the compuproof of concept experiment. The cylindrical control pins wmachined to 15.0 mm and 16.7 mm in length to produce the2.54 mm long control pin model (Fig. 7), respectively. A holecorrect placement of the diametrically opposed control pins (ap16° rotation from the fin). The appropriate length single rodcreate two equal length control pins.

2. Sabot System Figure 6. Photo of short pin model (a) complete project

A three piece sabot system was designed for use with the smpusher, and the obturator (Fig. 8). The four sabot petals weretogether to create a cylinder. Internally, the petals were contohad two slots cut out for the fins. The slots on two of the petals

The pusher cup (obturator) was also constructed of nylonpetals and projectile; slots were cuts for the fins. The exteriorfit with the barrel allowing for a consistent velocity to be maitself was manufactured from 17-4 stainless steel. The outside cup and a small hole was drilled to allow for the spin pin in the

C. Data Analysis Determination of the aerodynamic coefficients and derivat

measured in the ARL AEF. This is accomplished by pro

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Figure 5. Complete test model package as shotfrom the Mann barrel.

utilizing tungsten for the nose and hollowed out mm long tangent ogive. The hollowed out aluminum 2.6°, 22.4 mm long boat tail. The fins were 1.02 mm root chord and a 10.4 mm tip chord. The fin trailing as inserted in the projectile base to determine the

circular cross-section was utilized rather than that of ter simulations to ease machining requirements on a ere constructed of 1/16th inch diameter drill rod and 1.78 mm short control pin model (Fig. 6) and the

was drilled straight through the body to allow for the proximately 2.79 mm from the projectile base and a was fit through the predrilled hole and centered to

ile, (b) base view, and (c) close-up of fins.

ooth bore gun. It consisted of four sabot petals, the manufactured from nylon. Externally, the petals fit ured to the projectile shape. Each of the four petals were enlarged to accommodate the control pins. . The interior was sized to accommodate the sabot diameter near the base was flared for an interference intained for the charge weight utilized. The pusher diameter was fit to the interior diameter of the pusher base of the projectile.

ives is the primary goal in analyzing the trajectories cessing the raw data with ARFDAS.10 ARFDAS

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incorporates a standard linear theory analysis and a 6-DOF numerical integration technique. The 6-DOF routine incorporates the maximum likelihood method (MLM) to match the theoretical trajectory to the experimentally measured trajectory. The MLM is an iterative procedure that adjusts the aerodynamic coefficients to maximize a likelihood function.

Figure 8. Exploded 3-dimensional rendering ofthe sabot system with projectile.

Figure 7. Base view photo oflong pin model

Each projectile fired was initially analyzed separately (single fits), then combined in appropriate groups for simultaneous analysis using the multiple fit capability. The multiple fit approach provided a more complete spectrum of angular and translational motion than would be available from any single trajectory.

IV. Results and Discussion

A. Blind Simulations The results of the blind CFD and 6-DOF simulations are presented separately.

1. CFD Completing the CFD simulations between Mach 1.5 and Mach 4.0 insured data overlap with the previously

obtained experimental data.5 This range of Mach numbers also provided a broad range of aerodynamic coefficients to be used in the PRODAS database for the 6-DOF simulations.

While all force and moment data were obtained, the axial force (drag) and roll torque were of primary interest. Figure 9 shows how the zero yaw axial force coefficient (CX0) varies as a function of Mach number for the three simulated geometries. The pin geometries have larger drag over the entire range of Mach number, although the relative increase in drag due to the presence of the pins is much smaller at higher Mach numbers. The change in CX0 with the introduction of the control pins that is of primary interest, as CX0 is known for the baseline shape (no pin) from the previous range tests.5

Roll torque could also be easily obtained by the CFD. The CFD was completed with no angle-of-attack. Therefore, the roll torque can be directly determined from the axial moment. Figure 10 shows that the roll torque coefficient (Clδ) decreased by almost 75% over the range of Mach number investigated. As expected,3 the trapezoidal control pin created substantially more roll torque over the entire range of Mach numbers.

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2. 6-DOF

The aerodynamic coefficients from the rifled range test5 wcontrol pin for use by the 6-DOF simulations. After compl

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Figure 9. Computed Drag coefficient vs. Machumber.

ere modified by the CFD results of the rectangular eting the CFD for both the rectangular pin and the

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trapezoidal pin configurations, it was believed that the rectanthe cylindrical control pins in the planned range test.

The simulations were completed at Mach 2.0, 2.5, and 3range test to allow for an estimation of the roll characteriexpected to complete 8 to 10 turns during the flight down raare expected for the lower Mach number because the velocincreased a greater amount than the roll torque. Althougincrease in the number of revolutions is expected with anexpected.

B. Range Test Up to three Mach numbers were investigated for eac

projectile was shot for each nominal Mach number of 2.0, were shot for each nominal Mach number of 2.0, 2.5, and 3for the nominal Mach number of 3.0. This accounted for a to

Gun launch was successful. Consistent velocities werepetals cleanly separated upon muzzle exit – there was no inteof the projectile was maintained. (Fig. 12). Horizontal and vstation for each shot. Thus, aerodynamic coefficients were o

CX0 decreased nearly linearly with Mach number (Fig. projectile geometry. For a given Mach number, CX0 increaincreased with increased pin length. Both these trends were

The normal force coefficient, CNα, decreased with increaspin caused CNα to increase as did increasing the length of tlinear theory criterion for good data11 for CNα as the minimudid not meet the criterion, CNα was fixed to a reasonable valu

The pitching moment coefficient, Cmα, decreased (i.e. be15). Introduction of the control pins had minimal effect on be noticed with the pins present. Increasing the length of th

Figure 12: X-rays of sabot discard upon package e

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Figure 11. 6DOF revolution prediction forrectangular control pins.

Figure 10. Computed Roll Torque Coefficient vs.Mach number.

gular pin data would more likely be in like with that of

.0 corresponding to the Mach numbers of the planned stics. The results showed that the projectile could be nge depending on Mach number (Fig. 11). More turns ity at which the projectile is traveling downrange has h no dependency on pin length was investigated, an increase in pin length, as an increase roll torque is

h configuration. For the baseline configuration, one 2.5, and 3.0. For the short pin model, three projectiles .0. For the long pin model, three projectiles were shot tal of 15 shots. obtained for the charge weights utilized. The sabot rference with the projectile motion. Structural integrity ertical shadowgraph photographs were obtained at each btained for each shot. 13). The rifled data shown on the plot is the baseline sed with the introduction of the control pin. CX0 also

expected. ing Mach number (Fig. 14). Introduction of the control he control pin. Most, but not all, of the shots met the m acceptable yaw levels were exceeded. For shots that e. came less negative) with increasing Mach number (Fig. this coefficient, though a slight increase in stability can e pin had practically no effect. The minimal change in

xit from gun muzzle. Gun muzzle at left.

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Figure 13: Axial Force Coefficient vs. Machnumber.

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Figure 15: Pitching moment coefficient vs. Machnumber.

Cmα and a more pronounced change in CNα for the longer control pin indicates that the center of pressure, XCP, shifts closer to the center of gravity for the long pin model as compared to the short pin model.

Fn

The pitch damping moment coefficient, Cmq, was minimally effected by the introduction of the control pins or the length of the control pins as compared to the results of the rifled test (Fig. 16). This was expected as pin placement was chosen to have minimal effect on pitch damping. Cmq, like CNα, also has minimum acceptable yaw levels that are necessary to meet linear theory criterion for good data.11 These minimum acceptable yaw levels were met for most, though not all, shots.

Roll damping and roll torque were the main focus of this range test. For roll damping, the data from the previous rifled test5 was utilized for comparison. Similar to the rifled test, the roll damping coefficient decreased with increasing Mach number (Fig. 17). However, the magnitude of the roll damping coefficient, Clp, was found to increase with the introduction of the control pin when compared to a

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Figure 14: Normal force coefficient vs. Machnumber.

igure 16: Pitch damping moment coefficient vs.ach number.

igure 17: Roll damping coefficient vs. Machumber.

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projectile having no control pin. Increasing the length of the control pin, however, reduced the increase. This is likely due to the differences in the shock-shock interactions between the short pin model and the long pin model.

The diametrically opposed placement of the control pins created roll torque as expected (Fig. 18). Although Clδ for the baseline case was not exactly zero, the variation can be accounted for in experimental error. It is interesting to note that Clδ does not significantly vary with Mach number as is the case with the other aerodynamic coefficients. Additionally, the 50% increase in control pin length at Mach 3, nearly doubled the roll torque coefficient. This would allow for a much faster response from the projectile.

Figure 18: Roll torque coefficient vs. Mach number.

Figure 19: Roll rate as a function of down range distance.

Figure 19 shows that the roll rate increases as the projectile moves down range. At lower Mach number, the roll rate for the short pin model appears to reach an asymptote near the end of the range. This is not unexpected as the roll torque and the roll damping will reach an equilibrium at some distance downrange. As expected, based on roll torque, the difference in Mach number does not have a great effect on the roll rate. The increase in pin length, however, more than doubles the roll rate at the most down range locations. Comparing shadowgraphs at adjacent stations when the roll rate is small (Fig. 20) and further down range when a larger roll rate has been achieved (Fig. 21), the difference is quite noticeable. The spin pin has barely moved in between Fig. 20(a) and (b), where the round traveled from 6.7 m to 8.2 m, while later at least a 90° rotation has been achieved between Figures 21(a) and (b), where the round traveled from 90 m to 91.4 m. The degrees of rotation turned by the projectile is consistent with this.

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igure 20: Vertical shadowgraphs for shot 24096 stations (a) 22 and (b) 27.

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igure 21: Horizontal shadowgraphs for shot4096 at stations (a) 295 and (b) 300.

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C. Simulation and Range Test Comparisons

Figure 22: Axial force coefficient comparisonbetween range test and blind CFD.

Comparisons are made between the results of the range test and the blind simulations. Comparisons are also made between the range test and the 6-DOF simulations using updated aerodynamics coefficients. A final comparison is made between the range of aerodynamic coefficients and CFD using matched physical and atmospheric conditions. 1. Blind CFD and 6-DOF

It was desired to know how well the blind CFD and 6-DOF simulations predicted the range test results despite the differences in the geometric model. The differences were not just a scaled modeled for the CFD, but also fin leading and trailing edge taper (tapered vs. blunt), nose bluntness (sharp vs. blunt) and control pin shape (rectangular vs. cylindrical) and relative orientation (parallel vs. radial to the fin). The 6-DOF used this CFD as well as the aerodynamic coefficients determined for the baseline projectile shot from a rifled gun tube.5 This was not necessarily accurate.

Figure 23: Roll torque coefficient comparisonbetween range test and blind CFD.

If one first compare the CFD results, it is possible to compare CX0 and Clδ. A higher axial force coefficient is expected for the range test due to the bluntness of the fin leading and trailing edges as well as that of the nose tip. Keeping this in mind, the CFD does a reasonable job of predicting the axial force coefficient (Fig. 22). The CFD underpredicts the difference between the baseline model and the equivalent of the short pin model. This is likely due to the difference in pin shape and which changes the shock-shock interactions. However, by augmenting the rifled range test by this difference, a fair estimate of experimental CX0 for the short pin projectile is obtained.

CFD seems to do a better job predicting the roll torque despite modeling rectangular pins (Fig. 23) rather than the experimental cylindrical pins. The predictions are quite good at Mach 2.0 and 2.5 leading one to believe that the differences in control pin shape are insignificant at these Mach numbers. However, Clδ at Mach 3.0 is noticeably underpredicted indicating that the geometric differences become important at higher Mach numbers. As there were differences between the axial force, roll torque and roll damping coefficients assumed for the simulation and the actual values found in the range test, one expects there to be corresponding differences in the 6-DOF results. This was indeed the case. The predicted roll rate over the length of the range was overpredicted at Mach 2.0 and 2.5 and underpredicted at Mach 3.0 (Fig. 24).

The degrees of revolution turned by the projectile are consistent with the roll rate comparison. The number of revolutions achieved at Mach 3.0 was underpredicted while the number of revolutions at the lower Mach numbers was overpredicted. These discrepancies are easily accounted for by the differences between the assumed coefficients and the actual coefficients. Regardless, the 6-DOF simulations provided a fairly accurate idea of what could be expected to occur during the range tests.

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igure 24: Roll rate comparison between rangeest and blind 6-DOF simulations.

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2. Updated 6-DOF After completion of the data reduction from the range

tests, it was desired to confirm the accuracy of the 6-DOF simulations when accurate aerodynamic coefficients were utilized. Thus, the aerodynamic coefficients obtained from the range tests were used in the look-up table for the 6-DOF simulation. Very good agreement in both roll rate and number of revolutions was achieved indicating that accurate 6-DOF simulation results could be obtained for a similar projectile fired with different launch conditions.

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3. Updated CFD After completion of the range tests, two new CFD

models were created by Metacomp Technologies. One model had the geometric shape and dimensions of the short, cylindrical pin projectile that was flown in the range. The second model was identical to long, cylindrical pin model from the range tests. The CFD cases run by Metacomp matched the average conditions at 0° angle-of-attack for each Mach number investigated in the range,3 allowing for comparison of CX0 and Clδ.

The CFD accurately determined CX0 at all three Mach numbers for the short pin model as well as for the long pin model (Fig. 25). The scatter in the individual range data is due to small differences in angle of attack, which is negligible for the multiple fit data where angle of attack effects are accounted for.

CFD did a good job in modeling Clδ (Fig. 26). For the short pin model, the range test results show a small decrease in Clδ between Mach 2.0 and Mach 2.5 with a subsequent increase between Mach 2.5 and Mach 3.0 while the CFD predicts a continuous decrease. This causes an overprediction at Mach 2.5 and an underprediction at Mach 3.0. It is possible that a non-zero experimental angle-of-attack may be responsible for this discrepancy. For the long pin model, the CFD again underpredicts Clδ. Τhe scatter in the range test results suggests an angle of attack dependency, which supports the theory for the short pin discrepancy. Overall, the CFD does a remarkably good job in predicting the range results.

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V. Summary and A complete validation program for the use of diametr

completed. Blind CFD calculations were performed to obtanumbers with 0° angle of attack on the GTRI optimized augmented previously obtained rifled test data. This augmentrajectory simulations to approximate what would be seen dur

Flight hardware was then designed and built with circulaflight test was completed and good quality spark shadowgraptest analysis confirmed that the introduction of diametricaincrease in drag. As expected, the longer control pin produce

Comparison of the blind simulation results to the actualgeometry (nose, fins, control pins). This shows that 6-DOF prediction of the range performance, even when only a prerange safety and perhaps a smaller number of actual firings.

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igure 25: Comparison of updated CFD to rangeest axial force coefficient.

igure 26: Comparison of updated CFD to rangeest roll torque coefficient.

Conclusions ically opposed pins to produce asymmetric lift was in force and moment data over a large range of Mach control pin configuration. The results of the CFD ted data was input in a database for use by the 6-DOF ing range tests. r cross-section control pins for proof of concept. The h photography for data reduction was obtained. Flight lly opposed control pins creates roll torque with an d a greater amount of roll torque. range data was quite good considering differences in tool in combination with the CFD provides an accurate liminary design is available, thereby enabling greater When the exact geometry and flight conditions were

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simulated, agreement was quite remarkable. While the range tests were essential for validation of the concept, the agreement with CFD means the numerical solutions can be utilized to visualize the flow phenomena that could not otherwise be obtained or even investigate the effect of geometry changes on the flow prior to range testing.

Acknowledgments The author would like to acknowledge that funding for this project was provided by Dr. Michael Mattice of the

DARPA Advanced Technology Office. This work was supported in part by a grant of computer time from the Department of Defense High Performance Computing Major Shared Resource Center at the U.S. Army Research Laboratory. The author would like to thank Metacomp Technologies for providing the grid for the blind CFD and the results for the updated CFD. The author would also like to thank Dr. Kevin Massey of GTRI for providing further insight into the concept and working to develop the modifications necessary to the original idea in order to make the range test feasible. Finally, the author would like to thank Dr. Peter Plostins for all his help and guidance with the range test and subsequent data reduction.

References

1. Metacomp Technologies. “CFD++ User’s Manual.” Westlake Village, CA, 2000. 2. Goldberg, U. C., O. Peromian, and S. Chakravarthy. “A Wall-Distance-Free K-E Model With Enhanced Near-Wall Treatment.” Journal of Fluids Engineering, American Society of Mechanical Engineers, vol. 120, no. 3, pp. 457–462, September 1998. 3. Massey, K.C., Georgia Tech Research Institute, Private Communications, June-September 2003. 4. ArrowTech, “Prodas 2000 Technical Manual.” South Burlington, VT, 2001. 5. Whyte, R., Hathaway, W., and Steinhoff, M., Aerodynamic Analysis of the Hit-to-Kill (HK) NSWC / ARL Projectile.” ARL-CR-501, U.S. Army Research Laboratory, Aberdeen Proving Ground, MD, July 2002. 6. Braun, W.F., “The Free Flight Aerodynamics Range,” BRL-R-1048, U.S. Army Ballistic Research Laboratory, Aberdeen Proving Ground, MD, July 1958. 7. Plostins, P., Celmins, I., Bornstein, J. and Deibler, J.E., “The Effect of Front Borerider Stiffness on the Launch Dynamics of Fin-Stbilized Kinetic Energy Ammunition,” BRL-TR-3057, U.S. Army Ballistic Research Laboratory, Aberdeen Proving Ground, MD, October 1989. 8. Plostins, P., Bornstein, J. And Celmins, I., “The Effect of Sabot Wheelbase and Positions on the Launch Dynamics of Fin-Stabilized Kinetic Energy Ammunition,” BRL-TR-3225, U.S. Army Ballistic Research Laboratory, Aberdeen Proving Ground, MD, April 1991. 9. Bornstein, J., Celmins, I., Plostins, P., and Schmidt, E.M., “Launch Dynamics of Fin-Stabilized Projectiles,” Journal of Spacecraft and Rockets, vol. 29, no. 2, pp. 166-172, March-April 1992. 10. Arrow Tech Associate. “ARFDAS: Ballistic Range Data Analysis System.” User and Technical Manual, South Burlington, VT, May 1997. 11. McCoy, R.L., Modern Exterior Ballistic: The Launch and Flight Dynamics of Symmetric Projectiles, Schiffer Military History, Atglen, PA, 1999, p. 308.