INVESTIGATION OF A HIGH-DRAG SPOILER PLATE AS A RANGELIMITING DEVICE: COMPARISONS OF RANGE AND CFD
CALCULATIONS
T. Gordon Brown (1), Harris L. Edge (2)
(1,2) U.S. Army Research Laboratory, Weapons and Materials Research Dir.,AMSRL-WM, Aberdeen Proving Ground, MD 21005-5066
Abstract
The design of a device that provides over 50%range reduction for a 155-mm artilleryprojectile is discussed. The mechanical designof a spoiler plate used to increase drag isdiscussed. A complete set of three-dimensional(3-D), time-dependent, Reynolds-averaged,thin-layer Navier-Stokes equations is solvednumerically to obtain a solution for the zeroangle of attack aerodynamics of a 155-mmprojectile with protruding circular ring (spoilerplate) located at the nose. A simulatedtrajectory of the calculated aerodynamics iscompared to radar data measured duringflight. Issues concerning kinematics, stability,and overall performance are discussed.
Introduction
Operational and developmental testing ofmunitions is a critical part in the DODacquisition system. Government test facilitiesbuilt 60 years ago were designed for muchshorter ranges than are achievable today.Over the years, test facilities such as AberdeenProving Ground (APG) have not increased insize, yet the associated distances thatmunitions travel have greatly increased.Typical maximum ranges of 155-mm artilleryshells have increased from 10 km in 1921 toabout 40 km today. Since the proving groundshave not increased in size, some limitationsmust be made on range of firing if the newprojectiles are to be investigated.
This paper is declared a work of the U.S.Government and is not subject to copyrightprotection in the United States.
U.S. firing tables from 1921 indicate themaximum range that a 155-mm Mark 1Shrapnel shell shot from the model 1918howitzer could achieve 9.9 km with the highexplosive (HE) version extending to 11.4 km.In 1940, the M101 shell shot from the M1917howitzer would normally go to 14.7 km, butwith a supercharged propellant could extend to18.4 km. In 1942, the Ml howitzer was used tofire an M101 HE shell to 23.5 km with thesupercharged propellant. In 1944, the M107HE projectile extended the maximum range to15 km shot from the Ml howitzer. Today,NATO rounds are reaching to 40 km. At APG,the maximum range is about half what isrequired for optimal testing.
This report describes a simple and inexpensivedevice (spoiler plate) to limit the range of a155-mm projectile. A fully viscous Navier-Stokes calculation is performed to compute thezero angle of attack drag of a spoileredprojectile. A comparison of actual flight datato computational predictions is provided.
Figure 1. Fuze with spoiler plate.
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A circular disk (spoiler plate), much like alarge washer, is placed between the fuze andogive of the 155-mm projectile. The fuzethreads into the ogive, thereby locking thespoiler plate without modification to the fuzeor ogive. A picture of the spoiler and fuze isshown in figure 1. Figure 2 shows the spoiler asit appears assembled to a 155-mm projectile.
Figure 2. Projectile with spoiler plate.
The spoiler plate concept is not new. In fact,test ranges have used a smaller device formany years with some effect. The difference inthis design is the size of the plate. The oldspoilers were limited in size because the highacceleration loading experienced during launchwould damage the plate if made too large. Thenew plate is much lighter than the old steel
plate. The new design is in the process ofgaining a patent because of its efectiveness as arange reduction device.
Trajectory Simulation
A six degree of freedom (6-DOF) simulation isused to model the trajectory of the computedaerodynamics and the actual flight testmotion. Fitting of the simulated motion to themeasured motion can be minimized viaautomatic iteration of various unknownaerodynamic coefficients. Since the intent is tocompare computed aerodynamics with flightdata, no iterations of the aerodynamics to fitthe measured data are performed. A lineartheory analysis can be performed over the firstfew seconds of flight to produce a startingsolution for the modified 6-DOF. A descriptionof attributes of Linear Theory can be found in"Free-Flight Motion of Symmetric Missiles,"(Murphy [1963]). The polynomial expansions ofthe aerodynamic coefficients are
Qr=CAo
CNa=Cm
C = C
C, = C1S8
mtf ^mq tnqiP — C 4-P ff2 4-P^• ~ ^- T ̂ c T ̂
where,e = sina
(1)(2)(3)(4)
(5)(6)(7)(8)
(9)
Atmospheric table computation is utilizedwhen meteorological (MET) data as a functionof altitude are not measured. Minimumrequirements for the computation are sea levelpressure (millibars), temperature (C), winddirection (degrees from north), and velocity(m/s).
Presented in this report is radial velocity. Torepresent the output data from the simulationas radial velocity, the change in slant rangewas calculated between subsequent points anddivided by the associated time.
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The complete set of time-dependent, Reynolds-averaged, thin-layer Navier-Stokes equationsis solved numerically to obtain a solution tothis problem. The numerical technique used isan implicit, finite-difference scheme. Steady-state calculations are made to numericallycompute the flow field for a projectile.
Governing EquationsThe complete set of three-dimensional (3-D),time-dependent, generalized-geometry,Reynolds-averaged, thin-layer Navier-Stokesequations for general spatial coordinates £, TI,and £ can be written as follows (see Pulliamand Steger [1982]):
(10)
where,
% (x, y, z, t) - longitudinal coordinate;r\(x, y, z, t) -circumferential coordinate;C (*/ y/ z/ 0 - nearly normal coordinate;T - time
In Equation 1, q contains the dependentvariables: density, three velocity components,and the energy; and F, G, and H are fluxvectors. The thin-layer approximation is usedhere, and the viscous terms involving velocitygradients in both the longitudinal andcircumferential directions are neglected. Theviscous terms are retained in the normaldirection, £, for the projectile and segments,
^
and are collected into the vector 5. In the
wake or the base region, similar viscous termsare also added in the streamwise direction, £.For computation of turbulent flows, theturbulent contributions are supplied through analgebraic eddy viscosity turbulence modeldeveloped by Baldwin and Lomax [1978].
Numerical TechniqueA zonal grid was used to model a 155-mmprojectile with spoiler. The projectile shapeconsists of a rounded nose, a flat disc, an ogive,a cylinder, and an aftbody section that includesthe boattail and flat base. The zonal gridpreserves the actual comers in the spoiler andbase area. In application of the zonalapproach, the zone interior solution wasobtained through solution of the thin-layerNavier-Stokes equations with an implicitapproximately factored scheme that employscentral differencing in the normal andcircumferential directions and upwinding inthe streamwise direction for each individualzone (Steger, Ying, and Schiff [1986]).
Figure 4. Computational grid (central planed
Once the zone interior solution is obtained, theboundary conditions are explicitly imposed. Atthe body surfaces, an adiabatic, no-slipboundary condition is used. The body surfacepressure is calculated by solving a combinedmomentum equation. Free-stream boundaryconditions are used at the inflow boundary.The boundary condition imposed on the outerboundary was modified with changes in theMach number. For the solutions obtained atMach 0.95 and Mach 1.2, the computationalgrid outer boundary was placed at a distanceaway from the body such that a free-stream
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boundary condition could be used. At Mach 1.5the grid outer boundary was much closer to thebody and a nonreflecting boundary conditionwas used at the outer boundary. The initialcomputations were made at zero degrees angleof attack, which allowed for only threecircumferential planes to be used to model theaxisymmetric body. The circumferentialplanes were spaced five degrees apart. Asymmetry boundary condition was imposed onthe first and third circumferential planes. Atthe computational model axis of symmetry,extrapolation and symmetry were used todefine the boundary condition.
After the boundary conditions are computed,information is exchanged between adjacentzones. The zonal grids are overlapped by asingle cell with the neighboring grids withoutany mismatch. Thus, interzone informationexchange does not require any interpolation orcomputation. Only data transfer is involved a tzonal interfaces. Once the information transferis complete, another iteration begins with thesolution of the thin-layer Navier-Stokesequations.
Several thousand iterations were required forconvergence of the solution. Convergence wasdetermined by monitoring the residuals andthe rate of change of the aerodynamiccoefficients computed from the flow fieldsolutions.
Computational ResultsSteady-state calculations have been performedto numerically simulate the flow field about aprojectile with a spoiler plate. Computationswere run for free-stream velocities of Mach0.95, Mach 1.2, and Mach 1.5 at sea-levelatmospheric conditions. All computations weremade at zero degrees angle of attack.
Figures 5,6, and 7 are Mach contours of the flowfield about the spoilered projectile at thevelocities of Mach 0.95, Mach 1.2 and Mach 1.5respectively. The Mach contours indicate thedifference in shock strength and position at therespective Mach numbers. The Mach contoursalso give a good indication of the length of thewake generated by the spoiler and the base ofthe projectile. The length of the spoiler wakeis indicative of the flow field conditions seenby ogive and cylinder portions of the projectile.
At zero degrees angle of attack, the spoilergenerates a large region of recirculating flow inits wake. Within the spoiler wake, a largeportion of the projectile sees flow velocities ina direction opposite that of the free-streamvelocity. As indicated in figures 5,6, and 7 thehigher the velocity, the smaller the spoilerwake. This point should be noted in studyingthe contribution of each projectile component tothe total drag.
0.00 0.40 t.80 1.20 1.60
Figure 5. Mach Contour. M=0.95
».M 0.50 1.00 1.50 2.00
Figure 6. Mach Contour. M=1.2
•JM (U2 1.25 1.88 2.50
Figure 7. Mach Contour. M=1.5
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Figures 8a, 8b, and 8c are pressure contours ofthe surfaces of the spoilered M549 projectile a tthe velocities of Mach 0.95, Mach 1.2 andMach 1.5 respectively. The pressure contoursindicate that, as expected, the largestdifferences in pressures seen by the projectile a tdifferent velocities will be at the nose andspoiler. While the pressures computed on theogive and cylindrical portions of the bodyindicate little difference in magnitude.
c.
0.0 0.5 1.0 1.5 2.0 2.5
Figure 8. Pressure Contour. M= 0.95.1.2.1.5
As stated earlier, the largest difference inpressures for the various Mach numbers are a tthe projectile nose and spoiler. This region alsoprovides the greatest positive contribution tothe total drag. The base of the projectile alsocontributes positively to the drag, but to amuch lesser degree than the spoiler plate. Themain body of the projectile, which includes the
ogive, cylinder, and boattail, provides anegative contribution to the drag. The lowerthe Mach number, the lower the dragcoefficient of the projectile body. The totaldrag coefficients for the spoilered roundcomputed for Mach numbers 0.95, 1.2, and 1.5were 0.6939, 1.1892, and 1.3778, respectively.The combined drag coefficients for the ogive,cylinder, and boattail portions of the body forMach numbers 0.95, 1.2, and 1.5 were -0.2391,-0.1573, and -0.0672 respectively. Again itshould be stressed that the computations weremade at zero degrees angle of attack. It is clearthat the large flow recirculation region aft ofthe spoiler plate creates the conditions for thenegative body drag coefficients. At nonzeroangles of attack, one could speculate that thespoiler wake flow would be significantlydifferent and the main body of the projectilewould contribute positively to the total dragcoefficient. Hopefully, computations atnonzero angles of attack will be performed inthe future to study this point further.
Table 1. Computed Drag
MachNumber
0.951.21.5
Total DragCoef. forSpoilerRound0.6941.1891.378
Main BodyDrag Coef.
-0.2391-0.1573-0.0672
Flight Test of Spoilered Projectiles
InstrumentationMany types of data can be incorporated into aflight test. Generally, the more data taken,the better the understanding of results.Unfortunately, the fiscal constraints alwaysdictate the test diagnostics. In this study, theprimary tool used for diagnostics was a radar.The rest of the data was augmented bycomputer simulation and computation.
A Weibel Radar Model 1000 tracking Dopplerradar was used to obtain slant velocity andslant range data. The radar was operated bythe U.S. Army Aberdeen Test Center (ATC)(formerly the Combat Systems Test Activity
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[CSTA]) at Wallops Island, VA. The Dopplerradar data (radial velocity with respect totime) provide radial velocity with aresolution better than 1 m/s. The radarposition, with respect to the gun, is recorded tocorrect for any offsets (parallax errors). Thedata presented are adjusted for the offset ofthe radar w.r.t. the gun.
Flight Test ResultsTwo projectile types were fired with andwithout a spoiler plate. Two of each type werefired for each case. A range data summary foreach of the eight flights is found in Table 2.The unspoilered rounds were not tracked toimpact.
Figure 9 represents the drag profile for anunspoilered and spoilered round as well aswind tunnel data for a blunt cylinder (Hoerner[1965]). Table 1 shows the calculated drag atthree Mach numbers. A curve was fittedthrough the calculated drag to use in thesimulation.
Figures 10 and 12 compare the simulatedtrajectory to the measured data for type 1 andtype 2, respectively. The range data were notfully recorded for the unspoilered round, so asimulation of the trajectory is used forcomparison. Similarly, figures 11 and 13include the velocity history for type 1 and 2,respectively.
I
0.00 0-50 1.50 200 250M»ch Number
3.50 4.00
Figure 9. Drag comparison.
The effectiveness of the spoiler plate issummarized in Table 3. For the two roundtypes flown with the spoiler plate, 57.7% and63.6% loss in range were achieved. Types 1 and2 were shot at quadrant elevations of 804 and787 mils, respectively.
Overall the study of limiting the range of a155-mm projectile was successful. Thetrajectory analysis employing the CFD-predicted drag compares well with actualflight data. In general it was found that aspoiler plate follows a similar drag profile tothat of a circular cylinder at zero degrees angleof attack. However, some inconsistencies existbetween the simulation and the flight testresults. A number of the results point to large3-D effects.
The most noticeable 3-D effect would be themagnus moment and the associated drift. Whenthe magnus moment of an unspoilered round wasused for the magnus in the simulation of thespoilered round, the drift was less than whatwas measured in flight. In other words, thespoilered round drift is higher for the range
test. A 3-D CFD calculation at an angle ofattack could account for this difference.
Another noticeable difference between therange results and simulations is the velocityhistory. This occurrence can be explained by anunstable flight history. No data support orrefute this explanation. Another possibility isan inconsistent comparison of radial and actualvelocity.
Table 3. Spoiler Plate Effectiveness
Type
TypelType 2
NominalRange
(m)1808122617
MeasuredRange
(m)76458244
Effectiveness(%)57.763.6
Summary and Conclusions
Comparisons of flight performance between anartillery round shot with and without aspoiler plate indicate at least 50% reduction inrange. In fact, the range was reduced by 57%and 63% for two round types near maximumquadrant elevation.
The zero angle of attack drag was calculatedfor a 155-mm projectile with a large spoilerplate at the interface between the fuze andogive. The computed drag was used to simulatea near maximum range trajectory. The rangeprediction with the spoiler plate was within13% of an actual flight case.
Whether or not stability was affected isquestionable. It is difficult to make definitiveconclusions as to the stability without furtherinvestigation. To verify the stability, moreelaborate testing is needed, such as on-boardinstrumentation that measures the attitude ofthe projectile continuously during flight. TheARL yawsonde, which utilizes a telemetrylink and on-board sensors, is a likely system(Brown, et al. [1997]).
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Brown, T. G., Brandon, F. J, Harkins, T. E., andHathaway, W. H., "Flight Testing of a 2.75-INCH Rocket," Proceedings of the 35th AIAAAerospace Sciences Meeting and Exhibit,AIAA-97-0634, January 1997.
Murphy, C. H., "Free Flight Motion ofSymmetric Missiles," Ballistic ResearchLaboratory, MR-1216, July 1963.
Baldwin, B. S., and Lomax, H., "Thin LayerApproximation and Algebraic Model forSeparated Turbulent Flows." AIAA Paper No.78-257, January 1978.
Sahu, J., "Numerical Computations ofTransonic Critical Aerodynamic Behavior."AIAA Journal, vol. 28, no. 5, pp. 807-816, May1990 (also see BRL-TR-2962, December 1988.
Sahu, J., Nietubicz, C. J. and Steger, J. L.,"Navier-Stokes Computations of ProjectileBase Flow With and Without Base Injection."AIAA Journal, vol. 23, no. 9, pp. 1348-1355,September 1985.
Sahu, J., and Steger, J.L., "NumericalSimulation of Three-Dimensional TransonicFlows." AIAA Paper No. 87-2293, AtmosphericFlight Mechanics Conference, Monterey, CA,August 1987.
Steger, J. L., Ying, S. X., and Schiff, L.B., "APartially Flux-Split Algorithm for NumericalSimulation of Compressible Inviscid andViscous Flows." Proceedings of the Workshopon Computational Fluid Dynamics, Institute ofNonlinear Sciences, U. of California, Davis,CA, 1986.
Hoerner, S. F., Fluid Dynamic Drag, publishedby author, Midland Park, New Jersey, Chapter16, pp 13-14,1965.
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