Computers & Fluids 38 (2009) 965–968

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Computers & Fluids

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Technical note

Numerical simulation of magnus force control for projectiles configurations

Franck Simon a, Sébastien Deck a, Philippe Guillen a, Alain Merlen b,*, Roxan Cayzac c

a ONERA-DAAP, 29 av. de la Division Leclerc, 92322 Châtillon Cedex, Franceb Joint European Laboratory in Magneto-acoustics (LEMAC), Laboratoire de Mécanique de Lille, UMR CNRS 8107, USTL, cité scientifique, bât. M3, 59655 Villeneuve d’Ascq Cedex, Francec Nexter Munitions, 7 Route de Guerry, 18023 Bourges Cedex, France

a r t i c l e i n f o a b s t r a c t

Article history:Received 13 June 2008Received in revised form 14 July 2008Accepted 15 September 2008Available online 25 September 2008

0045-7930/$ - see front matter � 2008 Elsevier Ltd. Adoi:10.1016/j.compfluid.2008.09.006

* Corresponding author. Tel.: +33 320 436 916; faxE-mail address: alain.merlen@univ-lillel.fr (A. Mer

Present paper proposes, through numerical simulations, some optimization possibilities for an innovativeconcept aimed to control the magnus effect induced by the high spinning velocity of a Secant–Ogive–Cyl-inder–BoatTail projectile. It appears that with a relatively small contra-spinning surface, the lateral forcecan be drastically reduced on a wide range of flight conditions. Present computations confirm experi-ments in supersonics and extend them for high subsonic and transonic regimes for small angles of attack.

� 2008 Elsevier Ltd. All rights reserved.

1. Introduction

There are still domains in aerodynamics where accurateexperiments are very difficult to carry out. This is the case forthe ballistic phase of an artillery spinning projectile. Computa-tional fluid dynamics is the most powerful tool for testing flowcontrol solutions on such configurations. It is well known that,to ensure the static stability of an artillery projectile, a spin isapplied to the body. This rotation, when combined with a non-zero angle of attack, leads to a distortion of the boundary layerand to an asymmetric pressure distribution with respect to thepitch plane. This generates a side force, commonly known asthe Magnus force [1]. Although of quite low magnitude com-pared to both the normal and axial forces, this lateral forcemay have major consequences on the dynamics stability duringflight [2,3]. To improve the capabilities of projectiles, it wouldbe interesting to control the Magnus force. Ahn and Chang [4]had numerically investigated an innovative concept to reducethe lateral force by having differentially spinning sections on aprojectile in the supersonic regime. They report a few examplesof missiles and projectiles having several spinning sections. Mostof the time, these smart munitions have been designed toachieve more efficient target search and reduce dispersion at im-pact by trajectory corrections. Present paper proposes to enrichthe study of those projectiles by providing additional numericalresults concerning an optimization of this novel concept. Onthe basis of RANS simulations, its effectiveness is evaluated notonly in the supersonic regime but also in the subsonic and tran-sonic regimes which correspond to the final phase of the trajec-tory just before the impact and for which no reliableexperiments exist.

ll rights reserved.

: +33 320 337 088.len).

2. Simulations overview

A classical 6-caliber projectile model is used in this study. Itis composed of a 3-caliber ogive, a 2-caliber cylinder and endswith a 7-degree boattail section. In the following, this projectilewill be referred to as SOCBT for Secant–Ogive–Cylinder–BoatTail.The computational grid, displayed in Fig. 1, has been built usingthe MESH3D software [5]. The total number of points is approx-imately equal to 3 millions. In the axial direction, the mesh is re-fined in order to properly capture the development of theboundary layer with 170 points along the projectile. In the radialdirection, the classical RANS requirements have been used witha shear dimensioned distance y+ � 1 at the wall. Finally, aftergrid convergence tests [6] and taking into account previous re-sults [7], a discretization of 73 plans (5� per cell) have been cho-sen. From a numerical point of view, RANS simulations havebeen performed with FLU3M, a multiblock Navier-Stokes solverdeveloped by ONERA [7,8] and adapted to this kind of flow[9,10]. The equations are solved using a second-order accurateupwind finite volume scheme and a cell-centered discretization.The Euler fluxes are discretized using the classical Roe scheme.The turbulence model of Spalart–Allmaras [11] (SA) has beenused. This numerical strategy has already been applied to projec-tiles computations by Péchier [7] with the Baldwin–Lomax tur-bulence model and more recently by Simon et al. [12], withthe SA model.

The freestream conditions in the supersonic regime are identi-cal to those used in some experimental tests which gather wall-pressure measurements [13], aerodynamic coefficients [14] andboundary layer velocity data [15,16]. The freestream Mach numberM1 is equal to 3. The stagnation pressure Pi and temperature Ti arerespectively set to 0.2985 MPa and 310 K with ReL = 7.3 � 10+6. Thedimensionless spinning velocity X� ¼ XD

U1is nearly equal to 0.19

which corresponds to 20,000 rpm.

Fig. 1. Computational grid of the SOCBT configuration.

α

CY

0 10 20 30

-0.015

-0.01

-0.005

0

0.005

0.01Experiment (global spinning)Computation (global spinning) Ogive non-spinningBoattail non-spinning

Fig. 2. Lateral force reduction for several angles of attack – M1 = 3.

966 F. Simon et al. / Computers & Fluids 38 (2009) 965–968

In the subsonic and transonic regimes, since no reliable experi-mental data is available for spinning projectiles numerical investi-gation is the only means to estimate the efficiency of any Magnuscontrol device. Here, the conditions tested are M1 = 0.70 and 0.91with Pi = 100,000 Pa and Ti = 320 K. X* is respectively set to 0.45and 0.36 (18,000 rpm).

3. Results and discussion

3.1. Results in the supersonic regime

The global Magnus force coefficient can be obtained byCY ¼

R 10 CYL dX where CYL(X) is the repartition coefficient of the

lateral force along the symmetry axis of the projectile andX = x/L, the dimensionless coordinate along this axis. Fig. 2 pre-sents a comparison of CY predictions between computationsand experiments for the global spinning cases (i.e. without con-trol). A good agreement is observed for the available wind-tun-nel data and an extensive comparison has been achieved bySimon [6] which demonstrates the predictions accuracy of thenumerical results. Preliminary results have also been added inthe controlled case to evidence the efficiency of the concept.Two series of computations have been performed by successivelyblocking the boattail rotation and the ogive rotation. In Fig. 2, itis clear that a variation of the boattail spin has no effect on CY

meaning that the Magnus force amplitude is largely independentfrom the boattail spin. On the contrary, when the ogive does notspin, a great reduction of the lateral force coefficient is observeddespite the fact that half of the integrated Magnus force comes

from the contribution of the boattail [7]. This result can be ex-plained by the fact that the Magnus force is highly dependenton the boundary layer history and on its influence downstreamon the boattail. This confirms previous results by Ahn and Chang[4]. Thus, by acting on the ogive, the spin-induced distortion isaltered compared to the single spinning case and a control effectis enhanced through the development of the boundary layer allalong the projectile.

x/R

CY

x

0 2 4 6 8 10 12-0.01

-0.008

-0.006

-0.004

-0.002

0

Ωogive /Ωcylinder

Ωogive /Ωcylinder

Ωogive /Ωcylinder

Ωogive /Ωcylinder

Ωogive /Ωcylinder

Ωogive /Ωcylinder

=1

=0.75

=0.50=0.00

=-0.50

=-1.00

Fig. 4. Partial lateral force coefficient for several Xogive=Xcylindervalues –

M1 = 3 � a = 6.34�.

Fig. 5. Magnus force reduction for different control parameters. Influence of thecontrol extent – M1 = 3. -e- a = 2�; -�- a = 6.34�; -O- a = 15�.

F. Simon et al. / Computers & Fluids 38 (2009) 965–968 967

3.2. Optimization

When performing numerical investigations, it is possible to setXogive to zero but it is rather impossible during real projectilesflights. Nevertheless, the case of different but not nil Xogive andXcylinder is perfectly realistic. That is why some additional simula-tions were achieved to estimate the control efficiency for severalXogive/Xcylinder ratios including negative ones. A few significant re-sults are displayed in Fig. 3) for three angles of attack. It can beobserved that CY varies quite linearly with the Xogive/Xcylinder ratio.

The partial lateral force coefficient CYX ¼R X

0 CYLð~XÞ d~X (X < 1)along the projectile is presented in Fig. 4 as a function ofx/R = 12X for a = 6.34�. It can be observed that very few differencesappear between the cases for x/R < 3. However, the boundary layerevolution amplifies those small differences downstream on the cyl-inder and the boattail, where the major part of the Magnus force iscreated. This figure also illustrates that the contribution of the noseof the ogive to CY is nearly equal to zero. Therefore, a control of thespin velocity on the nose (0 < x/R < 3) is probably inefficient.

This is confirmed for a = 2� and 6.34�, in an attached regime ofthe boundary layer on the nose, in Fig. 5 where the control extentLcontrol was varied (The ratio Lcontrol/Logive is measured from theogive/cylinder (x/R = 6) junction to an upstream location x/R < 6).It is also important to underline that this annular control deviceis much more suitable in practice for aerodynamic control thanthe whole ogive, the nose being generally a sensitive element ofthe projectile for other purposes. For the high incidence regime(a = 15�), the well-known existence of a vortex flow pattern onthe ogive restores the influence of the nose on the flow. However,the control remains efficient in this configuration but, here, themechanism is a reduction of the vortices asymmetry with respectto the pitch plane.

3.3. Results in the subsonic regime

In order to evaluate the control potentiality at the end of thetrajectory, simulations were performed in the subsonic andtransonic regimes. The results with a non spinning ogive are gath-ered in Fig. 6 in terms of control effectiveness 100�ð1� CYcontrol

=CYreferenceÞ. A comparison with the supersonic reference

at M1 = 3 shows that similar trends are observed with an increasein efficiency in the high subsonic regime for the smaller angle of at-tack. The possibility of a control by differential-spinning elementsis therefore demonstrated.

Fig. 3. Magnus force reduction for different control parameters. Influence of theogive spin. –e– a = 2�; -�-: a = 6.34�; -O-: a = 15�.

α

Eff

ecti

ven

ess

(%)

0 2 4 6 8 10 12 14 160

20

40

60

80

100

M∞M∞M∞

=0.70=0.91=3.00

Fig. 6. Control effectiveness measured as 100� ð1� CYcontrol=CYreference

Þ when thewhole ogive section is non-spinning.

968 F. Simon et al. / Computers & Fluids 38 (2009) 965–968

4. Conclusions

Present study investigated an innovative concept of Magnusforce reduction using RANS computations for an SOCBT projectileconfiguration. It is shown that with a relatively small contra-spin-ning surface at the right place, the lateral force can be drasticallyreduced on a wide range of flight conditions. As for all the Machnumbers investigated here, the Magnus force is mostly generatedby the spin-induced distortion of the flow on the ogive, the controlremains effective whatever the angle of attack is. This kind of con-trol is much more realistic for projectiles than microjets or micromechanical actuators that need microtechnologies which are notcompatible with the high accelerations due to the rotation. Sys-tems like coupled coil-magnets that can induce the spinning ofan annular element are not so sophisticated and could be consideras active control devices.

Acknowledgement

This study is partly funded by Nexter within the framework ofONERA/Nexter cooperation.

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