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Research Papers

Magnus Effect: Physical Origins and Numerical Prediction

[+] Author and Article Information
Roxan Cayzac1

Associate Professor of the Universities, Head of Aerodynamics, Technical Direction, Nexter Munitions, 7 Route de Guerry, 18023 Bourges Cedex, France, Associate Professor of the Universities,  ENSIB/PRISME, 88 Boulevard Lahitolle, 18020 Bourges Cedex, Francer.cayzac@nexter-group.fr

Eric Carette

Research Associate in Aerodynamics, Technical Direction,  Nexter Munitions, 7 Route de Guerry, 18023 Bourges Cedex, Francee.carette@nexter-group.fr

Pascal Denis

Applied Aerodynamics Department,  Office National d’Études et de Recherches Aérospatiales, 29, avenue de la Division Leclerc, BP72, 92322 Châtillon Cedex, Francepascal.denis@onera.fr

Philippe Guillen

Applied Aerodynamics Department,  Office National d’Études et de Recherches Aérospatiales, 29, avenue de la Division Leclerc, BP72, 92322 Châtillon Cedex, Francephilippe.guillen@onera.fr

1

Corresponding author.

J. Appl. Mech 78(5), 051005 (Jul 27, 2011) (7 pages) doi:10.1115/1.4004330 History: Received November 22, 2010; Revised January 11, 2011; Published July 27, 2011; Online July 27, 2011

An overview of the Magnus effect of projectiles and missiles is presented. The first part of the paper is devoted to the description of the physical mechanisms governing the Magnus effect. For yawing and spinning projectiles, at small incidences, the spin induces a weak asymmetry of the boundary layer profiles. At high incidences, increased spin causes the separated vortex sheets to be altered. Vortex asymmetry generates an additional lateral force which gives a vortex contribution to the total Magnus effect. For finned projectiles or missiles, the origin of the Magnus effect on fins is the main issue. There are two principal sources contributing to the Magnus effect. Firstly, the interaction between the asymmetric boundary layer-wake of the body and the fins, and secondly, the spin induced modifications of the local incidences and of the flow topology around the fins. The second part of the paper is devoted to the numerical prediction and validation of these flow phenomena. A state of the art is presented including classical CFD methods based on Reynolds-averaged Navier–Stokes (RANS) and unsteady rans (URANS) equations, and also hybrid RANS/LES approach called ZDES. This last method is a recent advance in turbulence modeling methodologies that allows to take into account the unsteadiness of the flow in the base region. For validation purposes computational results were compared with wind tunnel tests. A wide range of angles of attack, spin rates, Reynolds and Mach numbers (subsonic, transonic and supersonic) have been investigated.

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Copyright © 2011 by American Society of Mechanical Engineers
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Figures

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Figure 3

Magnus effect on fins, (a) pressure ratio on the lee-side of the fins, (b) velocity vector at a longitudinal station, Mach 4.3, p*= 0.041, π = 7.7 Bar, Ti = 295 K, α = 4.22 deg

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Figure 4

Projectile geometry contribution to Magnus force, Mach 4.3, p*= 0.041 (100 rps), π = 7.7 Bar, Ti = 295 K, α = 4.22 deg

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Figure 5

ONERA S3MA wind tunnel, 4-component dynamic Magnus balance (a), 6-component static balance (b)

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Figure 6

RANS/LES computational sketch

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Figure 7

Longitudinal wall pressure coefficient distribution, Mach = 0.91 and α = 2 deg

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Figure 8

Longitudinal wall pressure coefficient distribution in the boattail region, Mach = 0.91 and α = 2 deg

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Figure 9

Magnus validation results for yawing and spinning projectile, Mach = 3 and p*= 0.0218 (a), Mach = 0.91 and α = 2 deg (b)

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Figure 10

ZDES boattail wake of yawing and spinning projectile, Q contours, Mach = 0.91 and α = 2 deg: nonspinning case p* = 0 (a), spinning case p* = 0.6 (b)

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Figure 11

CN and CY evolutions with angle of attach and non-dimensional spin rate, Mach 4.3, p*= 0 and 0.041, π = 7.7 Bar, Ti = 295 K, α = 4.22 deg

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Figure 12

Cn evolutions with angle of attack, Mach = 4.49, π =6 Bar, Ti = 356 K, TN = natural transition, TD = forced transition (TDO =TD on the ogive, TDO + F = TD on the ogive and TD on the fins)

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Figure 1

Physical aspects of the Magnus of spin-stabilized projectiles

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Figure 2

Resultant Magnus force coefficient distribution combined with the skin friction lines, Mach = 0.9, α = 17 deg, p = 138 rps

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