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Exterior Ballistics

Investigation of the Magnus Effect of a Generic Projectile at Mach 3 Up to 16 Degrees Angle of Attack

[+] Author and Article Information
D. Klatt

Ph.D. Student
Aerodynamics and Wind Tunnels Group,
French-German Research Institute of Saint-Louis (ISL),
5 rue du Général Cassagnou,
P.O. Box 70034,
68301 Saint-Louis, France
e-mail: daniel.klatt@isl.eu

R. Hruschka

Researcher
Aerodynamics and Wind Tunnels Group,
French-German Research Institute of Saint-Louis (ISL),
5 rue du Général Cassagnou,
P.O. Box 70034,
68301 Saint-Louis, France
e-mail: robert.hruschka@isl.eu

F. Leopold

Head of Aerodynamics and Wind Tunnels Group
Aerodynamics and Wind Tunnels Group,
French-German Research Institute of Saint-Louis (ISL),
5 rue du Général Cassagnou,
P.O. Box 70034,
68301 Saint-Louis, France
e-mail: friedrich.leopold@isl.eu

Manuscript received July 31, 2012; final manuscript received January 14, 2013; accepted manuscript posted January 18, 2013; published online April 19, 2013. Assoc. Editor: Bo S. G. Janzon.

J. Appl. Mech 80(3), 031603 (Apr 19, 2013) (9 pages) Paper No: JAM-12-1359; doi: 10.1115/1.4023434 History: Received July 31, 2012; Revised January 14, 2013; Accepted January 18, 2013

Abstract

The Magnus effect on a generic 6.37 diameter long tangential-ogive-cylinder type projectile was studied by means of 3D Reynolds-averaged Navier–Stokes (RANS) simulations and wind tunnel measurements. The nominal Mach number was 3 and the Reynolds number, based on the model length, was 1.09 × 107. The simulations provided a profound insight into the flow structure and revealed a shift of the cross-flow separation lines as a consequence of the spin. This was shown to be the primary source of the Magnus side force for the higher angles of attack in the investigated range. The nonlinear dependence of the Magnus side force on the angle of attack was analyzed and reached a maximum value between 10 and 15 deg before decreasing again. The occurrence of secondary vortices in this range of angles of attack is presented as an explanation for a locally negative Magnus side force portion acting on the model.

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Figures

Fig. 1

Model geometry: tangential-ogive-cylinder projectile

Fig. 2

Topology of a cut through the central plane of the mesh M3 used for the investigation of the influence of the mounting structure: (a) structured mesh for the sting-mounted model; (b) zoom into the region near the model

Fig. 3

Visualization of the vortex system at a 9 deg angle of attack: (a) visualization for the nonspinning model; (b) visualization for the spinning model

Fig. 4

Contour lines of the vortices for the spinning and nonspinning test case at a 9 deg angle of attack

Fig. 5

Normal force coefficient for a model at a dimensionless spin rate of p¯ = 0.000 and p¯ = 0.107

Fig. 6

Magnus side force coefficient versus angle of attack

Fig. 7

Density field at a position of x = 0.75 diameters upstream of the base for a Mach number of 3 and an angle of attack of 2 deg: (a) model spin rate, p¯ = 0.000 (b) model spin rate, p¯ = 0.107

Fig. 8

Density field at a position of x = 0.75 diameters upstream of the base for a Mach number of 3 and an angle of attack of 6 deg: (a) model spin rate, p¯ = 0.000; (b) model spin rate, p¯ = 0.107

Fig. 9

Density field at a position of x = 0.75 diameters upstream of the base for a Mach number of 3 and an angle of attack of 9 deg: (a) model spin rate, p¯ = 0.000; (b) model spin rate, p¯ = 0.107

Fig. 10

Density field at a position of x = 0.75 diameters upstream of the base for a Mach number of 3 and an angle of attack of 12 deg: (a) model spin rate, p¯ = 0.000; (b) model spin rate, p¯ = 0.107

Fig. 11

Normalized circumferential pressure distribution for a 2 deg angle of attack

Fig. 12

Normalized circumferential pressure distribution for a 6 deg angle of attack

Fig. 13

Normalized circumferential pressure distribution for a 9 deg angle of attack

Fig. 14

Normalized circumferential pressure distribution for a 12 deg angle of attack

Fig. 15

Normalized circumferential pressure difference between the spinning (p¯ = 0.107) and the nonspinning model for different angles of attack

Fig. 16

Distribution of the normalized pressure difference on the model for an angle of attack of 6 deg and a spin rate of p¯ = 0.107

Fig. 17

Magnus side force coefficient distribution along the model longitudinal axis for a spin rate of p¯ = 0.107 at different angles of attack

Fig. 18

Vortex formation for angles of attack of 9 deg and 14 deg at a spin rate of p¯ = 0.107 and a position of x = 0.75 diameters upstream of the base: (a) α = 9 deg, p¯ = 0.107; (b) α = 14 deg, p¯ = 0.107

Fig. 19

Normalized circumferential sum of pressure and shear distribution in the side force direction at a position of x = 0.75 diameters upstream of the base

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