Trajectory Control of a Small Caliber Projectile UsingActive Transpiration

S. K. R. Patil∗ and T. Terry Ng†

University of Toledo, Toledo, OH 43606

Mehul P. Patel‡

Orbital Research Inc., Cleveland, Ohio 44103

A method to generate aerodynamic control forces for steering a small caliberprojectile using flow transpiration channels on a boattailed afterbody is numeri-cally investigated. Steady state simulations are conducted at Mach 2 from 0 to 10deg angles of attack with zero sideslip angle using Reynolds Averaged Navier-Stokesequations and Reynolds Stress turbulence model. Results show that the interac-tion of the jet exiting from the transpiration channels with the main stream flowresults in a complex three-dimensional shock wave structure on the projectile baseyielding coherent vortex structures downstream of the primary interaction shock.The asymmetry induced in the flow due to three-dimensional coherent structuresgenerated by natural flow transpiration near the projectile surface results in a con-siderable force which can be used for steering a small caliber projectile.

I. Introduction

RECENTLY there has been much interest in alternative flight control methods for steeringsmall and large caliber projectiles as conventional control surfaces such as fins, wings or other

protrusions from the projectile body can result in conflicting design requirements and increaseddrag. At high speeds, in particular, it is desired that control surfaces are small and thin to min-imize aerodynamic drag penalties, but this can pose significant structural integrity problems dueto severe aerodynamic and thermal loading. For small caliber projectiles, conventional controls aredifficult, if not impossible, to implement due to stringent volume and power constraints. Tech-nological advances and breakthroughs in the areas of Microelectromechanical Systems (MEMS),materials and computing, in the past decades, have opened up realm of opportunities in applyingunconventional flow control techniques to steer small projectiles at subsonic and supersonic speeds.

References [1—9] provide examples of a few unconventional flow control techniques investigatedby different researchers. Work by Patel et al. [1—3] discusses the use of forebody and afterbodydeployable mechanical actuators for aerodynamic steering of missiles and projectiles. DeSpirito etal. [4] conducted a detailed numerical study on a canard-controlled missile with planar and grid finsin supersonic flow. Massey et al. [5] studied the feasibility of deployable pin actuators to generateturning force to steer a supersonic missile. In this approach, a control pin is placed near theprojectile fin, which, at supersonic flows, leads to the complex shock interaction between the pinand the corner of the body and fin at supersonic speeds, thereby creating a strong asymmetric forcethat can be used for control. Momoda et al. [6] discusses a compact hybrid actuator device based

∗Graduate Research Assistant, Dept. of Mechanical, Industrial and Manufacturing Engineering, Member AIAA.†Professor, Dept. of Mechanical, Industrial and Manufacturing Engineering, Senior Member AIAA.‡Director, Aerodynamics Group, Senior Member AIAA.

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on the concept of combining high power density and high bandwidth of the thin-film shape memoryalloys with hydraulic rectification and dense power electronics technology to enable guidance andcontrol of hypersonic missiles. McMichael et al. [7] discusses the use of synthetic jet actuators forcontrolling a spinning projectile using the Coanda effect. Apostolovski and Andreopoulos [8] discussthe use of microballoons (inflatable microactuators) to generate control forces by changing the localpressure distribution on the projectile. Mostly all these control techniques rely on passive or activemechanical actuators to alter the base state of the flow in a controllable fashion to effect a desiredchange. The present approach, transpiration channels, is derived from recent study performed byPatel et al. [9] and Lopera et al. [10] on the use of a reconfigurable porosity technique for flowcontrol over airfoils and projectiles.

A schematic of the present flow transpiration control concept for projectile steering is shown inFig. 1(a).

Array of 8 MicrovalvesArray of 8 Microvalves

MEMS Microvalves

air

air

(b)

(c)

(a)

Array of 8 MicrovalvesArray of 8 Microvalves

MEMS Microvalves

air

air

air

air

(b)

(c)

(a)

Figure 1. (a) projectile steering concept using flow transpiration at the boattail; (b) open andclosed positions of a MEMS microvalve11, enabling the control concept; (c) a photograph showingan array of eight microvalves packaged on a single chip.

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In this concept, the fluid, powered by the natural pressure distribution around the projectile’ssurface, propagates through transpiration channels that are regulated using an internal MEMSmicrovalve [11]. The projectile used in the present study is 137.5 mm long and 25 mm in diameter.The forebody is 30 mm in length and the boattail section (20 deg slope) is 7.5 mm in length.The transpiration channels are 2 mm in diameter and the boat tail angle is 20 deg. Owing to thenatural pressure differences induced by the shape of the projectile air flows through the transpirationchannels, redistributing the pressure and causing a local asymmetry in the flow. By opening andclosing an internal MEMS valve, a controlled asymmetry, and thus a turning force can be produced.

The flow through the channel can be actuated by a MEMS microvalve, which in turn can becontrolled by a closed loop control system. Reliable flow control techniques need to employ aclosed loop feed-back control mechanism which can adapt to the changing conditions in order tobetter track the desired output trajectory (or force generation). At supersonic speeds, the systemdemands quick fast response times and robustness. Recent developments in MEMS have resultedin microvalves that can be operated at high pressures and activated at high frequencies with goodreliability [11]. A schematic of a MEMS microvalve with optical micrographs of the valve in openand closed positions are shown in Fig. 1(b). In this design, the electrostatic microvalve is open inits natural state (with no voltage applied) and closes upon excitation to the top diaphragm. Therelative size of the microvalves is compared to a coin in Fig. 1(c). The small size of the valvesmakes them attractive for potential use in small caliber weapons. The advantages of the presentcontrol method are the absence of any moving control surfaces on the skin of the projectile and theuse of a low voltage source for activating MEMS valves.

II. Numerical Method

The concept of flow transpiration for projectile steering is validated numerically by solvingsteady three dimensional Reynolds Averaged Navier-Stokes (RANS) equations at Mach 2 usingReynolds Stress Model (RSM) for turbulence modeling. The grid and the computational domainused for simulations are shown in Fig. 2. The projectile is centered in a cylindrical computationaldomain of diameter 50D, where D is the diameter of the projectile. Unlike subsonic speeds, atsupersonic speeds the disturbances downstream cannot influence the flow upstream, and hence thefluid upstream is independent of the conditions downstream. This gives the freedom to place theinlet of the computational domain near the body. The inlet is placed at 2D from the nose of theprojectile. The effect of the wake on the projectile is neglected as the present approach does notderive its control from flow field in the wake. The outlet of the computational domain is thereforesituated precisely at the end of the projectile aft section.

Boundary layer with a propagation ratio of 1.07 is created with 15 and 30 orthogonal elementson the projectile surface for coarse grid (grid 1) and fine grid (grid 2), respectively. The first elementsize at the wall is 1 x 10−6D resulting in a y+ value of less than 1. This value of y+ eliminates theuse of standard wall functions and resolves the turbulent boundary layer up to the wall resultingin a high fidelity solution. A tetrahedral grid is generated around the boundary layer to fill thecomputational domain. The circumference of the inlet and exit holes of the transpiration channelare meshed with 30 and 60 elements for grid 1 and grid 2, to capture the interaction of natural flowtranspiration with the main stream flow. The coarse mesh contained 2.1 million and 3.2 millioncells for the baseline and control cases, respectively; whereas, the fine mesh dimensions resulted in6.3 million and 7.8 million cells for the baseline and control cases, respectively.

Far-field boundary condition with a Mach number of 2 is used on all the faces of the compu-tational domain except for the wall of the projectile where no slip boundary condition is applied,and the outlet face where a pressure outlet boundary condition is applied. The pressure at theexit is calculated by extrapolating the pressures from the adjacent cells upstream. Fluent 6.2, awell-tested computational fluid dynamics code, is used to solve the RANS equations with RSMturbulence model. A coupled-implicit, cell-based steady state compressible solver is utilized. Thespatial derivatives are discretized using a third order MUSCL scheme. The system of discretizedgoverning equations are solved using a point-implicit, Gauss-Seidel relaxation along with an alge-braic multigrid (AMG) method to accelerate solution convergence. The RSM turbulence model used

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employs enhanced wall treatment with corrections for pressure gradient and thermal effects [12].Viscous heating is also calculated for energy balances. An inviscid solution is first obtained. Then,Spalart-Allmaras turbulence model is used to converge the viscid solution. This converged solutionis used with RSM model to obtain the final solution. The solver and the turbulence model arefully parallelized. Simulations were performed in parallel on 8 dual processor machines at the OhioSupercomputer Center.

Figure 2. Computational domain and grid structure for the projectile using orthogonal boundaryelements and tetrahedral outer elements.

III. Validity of RANS and Turbulence Model

The use of RANS methods, as an alternative to LES or DNS, for predicting unsteady flows thatcontain vigorous organized, periodic components may lead to under-resolved and dissipated results.Much uncertainty arises due to the potential of interaction between turbulence-related unsteadi-ness and the external perturbation. The interaction is likely to be significant if the perturbationfrequency is of the order of that associated with turbulence-generation mechanisms, or comparableto any influential process within other parts of the spectrum of turbulent motion. It is importantto note that the control technique investigated in the present study does not rely on controllingthe unsteady vortex structures or other high frequency turbulence mechanisms. Also, the effect ofwake on the projectile is neglected. RANS methods have been used previously [4,13—15], to reliablypredict the supersonic flow fields over projectiles. Hence steady RANS method used in the presentstudy is justified. Reynolds Stress Model (RSM) is used for closure of the turbulence model asit takes into account the anisotropy of the Reynolds Stresses resulting from natural transpirationthrough the skin of the projectile.

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IV. Results

Figure 3 shows the axial variation of pressure coefficient on the surface of the baseline projectilefor the coarse grid (grid 1) and fine grid (grid 2). Although the pressure predicted using the coarsegrid coincides well with that obtained by the fine grid, as shown in Fig. 3, only the fine grid wassuccessful in resolving the near wall flow structures. Therefore, all the results reported in this studywere obtained using a fine grid of 6.3 million and 7.8 million cells for the baseline and control cases,respectively.

Figure 3. Grid convergence on the baseline projectile.

Figure 4 shows the Mach number contours at mid-plane for the projectile at 0 deg angle ofattack with and without control. As expected, the projectile has a bow shock in front of the noseand expansion waves at the start and end of the cylindrical section. The fluid on the cylindricalsection is at a higher pressure before the expansion wave and expands to a low pressure high velocityflow over the boat tail. To take advantage of this pressure differential, three transpiration channelsare made to connect the high pressure region ahead of the boat tail with the low pressure regionon the boat tail. The pressure difference created naturally by the shape of the projectile drives theflow through the transpiration channels. The high pressure fluid passing through the transpirationchannels meets the main flow at the exit of the channel.

The fluid exiting the channel is hereafter referred to as a jet. The interaction and expansionof the jets with the main flow gives rise to complex, coherent, three-dimensional structures. Theinset in Fig. 4 shows the effect of natural transpiration on the local flow field near boat tail forbaseline and control cases. In the controlled case, the expansion wave structure is modified nearthe transpiration channel; however, the expansion structure is similar to the baseline case on thediametrically opposite side. The flow is supersonic at the entrance of the transpiration channel, anddecelerates as it passes through the narrow channel and then expands at the exit of the channel.The shocks generated due to the discontinuity can be seen at the entry and exit of the transpirationchannel (inset of Fig. 4). The expanding jet changes the velocity flow field locally at the surfacenear the channel exit as shown in Fig. 5.

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Baseline With controlBaseline With control

Figure 4. Mach contours at midplane on the projectile with and without control at freestream Mach2 and 0 deg angle of attack. The inset shows Mach number contours near the projectile boattail.

δ

δ

(a)

(b)

Flow direction

δ

δ

(a)

(b)

Flow direction

Figure 5. Velocity vectors colored by Mach number at freestream Mach number of 2 and 0 deg angleof attack; (a) velocity vectors on the boattail downstream of the transpiration channel; (b) velocityvectors on the bottom half of the boattail where no transpiration channel is present. Arrowsindicate thickness of the boundary layer.

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This causes local low pressure regions starting at the channel exit and extending till the endof boat tail, as shown in Fig. 6a. Figure 6b shows static pressure contours at cross-stream planeAA0 on the boat tail. There exist three low pressure regions on the surface of the projectile,corresponding to the three transpiration channels. This pressure imbalance on the surface of theboat tail provides the turning force for a nose-down pitching moment for this configuration oftranspiration channels. The angular position of the activated transpiration channels can be variedto obtain different desired controls (pitching and yawing monents, and rolling moment thoughinteractions with fins).

The expanding jet at the channel exits disrupts the boundary layer on the boat tail. Figure 5bshows the thickening of the boundary layer on the boat-tail surface when no control is implemented.The boundary layer thickens gradually owing to adverse pressure gradient and separates at the endof the boat-tail (not shown in the figure). On the contrary, the thickness of boundary layer nearthe control increases rapidly (Fig. 5a) when compared to the same region on boat-tail withoutcontrol. This phenomenon is local to the region near the transpiration channel exit. The boundarylayer returns to its baseline thickness away from the jet. The slow moving jet at the channel exitacts like an obstruction to the high velocity main stream flow. The interaction between the slowjet exiting at an angle to the high velocity main flow results in an interaction shock structure. Thestructure starts just upstream of the exit hole where the two flow streams meet, and extends tillthe end of the boat-tail, as shown in Mach number contours of Fig. 7b. The shock waves generatedby the presence of two adjacent jets also interact and form a complex, three-dimensional shockwave structure. Downstream of this primary shock wave structure, regions of varying velocity andpressure distributions exist. Figure 8b shows the path lines of flow immediately upstream of theexit hole. Immediately downstream of the exit hole, a low pressure region exits due to the “lift-up”of the main flow by the jet (see Fig. 6a and region 1 in Fig. 8b). This lifting up of the main streamflow can be clearly seen in region 3 of Fig. 8b. The jet obstructs the flow and causes it to curvearound it. This results in a narrow region for flow passage as shown in region 2 of Fig. 8b. Themanifestation of this process can be seen in the Mach number contours between two jets in Fig.7b. Region 1 of Fig. 8b shows the interaction of the jet with the main flow resulting in a threedimensional elongated capsule like structure. The Mach number contours in Fig. 8a clearly showthe velocity variations in this capsule like structure. Away from this three-dimensional structure,the boundary layer and velocity contours are similar to the baseline case, as shown in the Machnumber contours between two exit holes in Fig. 8a. A weaker shock wave structure is also formedupstream of the boat-tail as a result of suction through the holes into transpiration channels (seeFig. 7a).

Streamwise vorticity with opposite sense of rotation develops inside the transpiration channel.This streamwise vorticity at the exit interacts with the oncoming flow and generates streamwisevorticity with opposite senses of rotation near the projectile surface, as shown in Fig. 9a. Figure 9bshows the in plane velocity vectors at the channel exit. Two counter rotating vortices can be seenextending out of the boundary layer. The streamwise vorticity exists near the surface of the boattail and decreases in strength downstream due to diffusion process. For a particular jet exit angleand pressure, there could be a formation and growth of streamwise vortices in the main flow astypically seen in jets injected normally into a flow. In this particular case, however, the streamwisevorticity is confined to a region downstream of the primary shock wave structure inside the lowvelocity elongated capsule region (region 1 of Fig. 8b).

The vorticity strength depends on the interactions of the jet with the main flow and the boat-tailangle. Blowing tangentially along the surface accelerates the boundary layer and makes it thinner,while blowing perpendicularly could create local separation and then reattachment downstream.The three-dimensional interaction shock wave structure, elongated capsule region and vortex struc-tures depend on the jet exit angle, shape and pressure. Hence the design (cross section shape andexit angle) of transpiration channel is of high importance. A detailed study on the jet exit location,angle, shape, pressure and transpiration channel design is needed to optimize the present controltechnique for maximizing the turning force.

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A

A’

(a)

(b)

A

A’

(a)

(b)

Figure 6. (a) Static pressure contours on the surface of the projectile; (b) static pressure contoursin a cross-stream plane at section AA0. Units are in Pascals.

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Interaction shock

(a)

(b)

Flow direction

Interaction shock

(a)

(b)

Interaction shock

(a)

(b)

Flow direction

Figure 7. Mach number contours above the surface of the projectile near suction regions (a) andon the boattail (b) at freestream Mach number of 2 and 0 deg angle of attack.

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1

2

3

(a)

(b)

Flow direction

1

2

3

1

2

3

(a)

(b)

Flow direction

Figure 8. (a) Mach number contours at different cross-stream planes on the boattail of the projectile;(b) pathlines of the fluid just upstream of the transpiration channel exit. Freestream Mach number= 2; 0 deg AoA.

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(a)

(b)

Flow direction

(a)

(b)

Flow direction

Figure 9. (a) Streamwise vorticity contours at different cross-stream planes on the projectile boat-tail; (b) in-plane velocity vectors on a cross-stream plane located near the exit of the transpirationchannel. Freestream Mach number = 2; 0 deg angle of attack.

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-0.02

0.03

0.08

0.13

0.18

0 2 4 6 8 10

Angle of attack (deg)

CM

Baseline

With Control

Figure 10. Pitching moment coefficient as a function of angle of attack with and without controlat Mach 2.

The moments at different angles of attack obtained from simulations for baseline and controlcases are given in Tables 1 and 2, respectively. The center of gravity of the projectile is assumed tobe at half the projectile’s length. Pressure moment is due to pressure forces and viscous moment isdue to viscous forces. Total moment is the sum of pressure and viscous moments in the respectivedirections. As seen from Tables 1 and 2, viscous pitching moments are orders of magnitude lessthan pressure pitching moments, as expected. The roll and yaw moments are orders of magnitudeless than pitching moments and do not vary substantially with angle of attack, which suggests thatthe two moments are a result of numerical round off error in the calculation.

Table 1. Pressure, viscous and total moments for the projectile with no control at different anglesof attack. All moments are in Nm. AOA denotes angle of attack. Freestream Mach number = 2.

In the absence of tail fins the baseline projectile is unstable in pitch. At 0 deg angle of attack,

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Table 2. Pressure, viscous and total moments for the projectile with control at different angles ofattack. All moments are in Nm. AOA denotes angle of attack. Freestream Mach number = 2.

the pitching moment is zero for baseline case as the flow is symmetric about the projectile’s axis(see Fig. 10). With control on, the projectile pitches down due to pressure imbalance created at theboat tail. As the angle of attack increases, the bow shock is no longer symmetric about the axis.This creates a high pressure region at the bottom of the projectile nose and a low pressure regionon the top. At increasing angles of attack, the force at the nose due to bow shock asymmetry andthe force at the boat-tail due to the control reduce the overall nose-up pitching moment comparedto the baseline case (see Fig. 10 and Table 3).

Table 3. Pitching moment coefficient (CM) for baseline and controlled case.

The transpiration channels at +90 or -90 deg to the existing ones can be activated to obtain apositive or negative yawing moment even at high angles of attack to steer the projectile. Furthersimulations are being planned with this configuration to quantify the yawing moment effect.

The turning moment generated by the aerodynamics forces can be used to calculate the turnangle using the relation M = I d

2θdt2, where M is the difference between the moments of baseline and

control case obtained from the simulations; I is the mass moment of inertia along the moment axisand θ is the turn angle. The turn angles in the pitch direction thus obtained are plotted in Fig.11. It can be seen from the Fig. 11 that considerable deflection can be obtained with the presentcontrol after 0.1 sec of activation. The turn angle decreases with the density as expected. Thesehigh turn angles reinforce the feasibility of this new control technique for supersonic small caliberprojectiles.

V. Conclusions

A new control method employing naturally-powered flow through transpiration channels forsteering a small caliber projectile is numerically investigated. Steady state compressible simulationsare conducted at Mach 2 for 0 to 10 deg angles of attack with zero sideslip angle using ReynoldsAveraged Navier-Stokes equations and Reynolds Stress turbulence model to study the effects of

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Figure 11. Angular position versus projectile density after 0.1 sec of activating transpiration control.Freestream Mach number = 2.

control on a projectile. Results show that the interaction of the jet exiting from the transpirationchannels with the main stream flow results in a complex three-dimensional shock wave structureon the projectile base yielding coherent vortex structures downstream of the primary interactionshock. The asymmetry induced in the flow due to three-dimensional coherent structures generatedby natural flow transpiration near the projectile surface results in a considerable force which can beused for steering a small caliber projectile. The turn angles calculated up to 10 deg angle of attackshow high rate of maneuverability at supersonic speeds. Detailed transpiration channel designimprovements addressing the optimum channel shape, exit diameter, exit jet angle and exit shapeare expected to further improve the efficiency of the presented flow control technique. Benefits of theproposed control approach is that no plumbing (suction/blowing) is required; control is implementedsolely through flow transpiration channels powered by the natural pressure distributions aroundthe projectile body and regulated via an internal microvalve.

VI. Acknowledgment

The authors thankfully acknowledge the support of the Ohio Supercomputer Center for provid-ing computational resources during this work.

References

[1]Patel, M. P., Tilmann, C. P., and Ng, T. T., “Closed Loop Missile Yaw Control Via Manip-ulation of Forebody Flow Asymmetries,” J. of Spacecraft and Rockets, Vol. 41, No. 3, pp. 436-443,May-June 2004.

[2]Patel, M. P., DiCocco, J. M., Lopera, J., and Ng, T. T., “Active Boattailing and Aerody-namic Control Fins for Maneuvering Weapons,” AIAA Paper 2004-2696, June 2004.

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[3]Patel, M. P., Sowle, Z. H., Ng, T. T., and Toledo, W., “Hingeless Flight Control System ofa Smart Projectile Using Miniature Actuators,” AIAA Paper 2005-5258, June 2005.

[4]DeSpirito, J., Vaughn, M., Washington, W.D. “CFD Investigation of Canard-ControlledMissile With Planar and Grid Fins in Supersonic Flow,” AIAA Paper 2002-4509, August 2002.

[5]K. C. Massey , K. B. Guthrie, and Sidra I. Silton, “Optimized Guidance of a SupersonicProjectile using Pin Based Actuators,” AIAA 2005-4966, June 2005.

[6]Momoda, L., Carman, G., and Williams, D., "Compact Navigation, Guidance and Con-trol Actuator for Miniature Kinetic Energy Missiles," presentation to DARPA Smart StructuresTechnology Interchange Meeting, CHAP Kickoff Meeting, Baltimore, MD, June 2000.

[7]McMichael, J., Lovas, A., Plostins, P., Sahu, J., Brown, G., and Glezer, A., “MicroadaptiveFlow Control Applied to a Spinning Projectile,” AIAA Paper 2004-2512, July 2004.

[8]Apostolovski, G. and Andreopoulos, Y., "Microactuators for Projectile Flight Control Sys-tems," a Feasibility Study, Journal of Aircraft, Vol. 41, No. 6, pp. 1336-1346, Nov-Dec 2004.

[9]Patel, M. P., DiCocco, J. M., Prince, T. S., and Ng, T. T., “Flow Control Using Reconfig-urable Porosity,” AIAA Paper 2003-3665, June 2003.

[10]Lopera, J., Ng, T. T., Patel, M. P., and DiCocco, J. M., “Experimental Investigation ofReconfigurable Porosity for Aerodynamic Control,” AIAA Paper 2004-2695, June 28 — July 1,2004.

[11]Patel, M. P., Skebe G., Ng, T. T., and Lisy, F. J., “Development of a MEMS Based Mi-crovalve for Flow Control Using Active Dimples, AIAA 2002-270, 2002.

[12]“Fluent 6.2 user guide”, Fluent Inc, Lebanon, New Hampshire, USA.[13]DeSpirito, J., Edge, H. L., Weinacht, P., Sahu, J., and Dinavahi, S. P. G. “Computational

Fluid Dynamics Analysis of a Missile With Grid Fins,” J. of Spacecraft and Rockets, Vol. 38, No.5, 2001, pp. 711—718.

[14]DeSpirito, J., and Sahu, J. “Viscous CFD Calculations of Grid Fin Missile Aerodynamicsin the Supersonic Flow Regime,”AIAA Paper 2001-2057, Jan 2001.

[15]Jubaraj Sahu, Sidra I. Silton, and Karen R. Heavey, “Numerical Computations of SupersonicFlow over Non-Axisymmetric Configurations,” 2004, AIAA 2004-5456.

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