Magnus Effect: Physical Origins and Numerical Prediction

Abstract

An oven'iew 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, ai 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 asymmetiy 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. Firsilw the interaction between the asymmetric houndary layer-wake of the hody 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, .^pin rates. Reynolds and Mach numbers (subsonic, transonic and supersonic) have heen investigated.

Body-fin interference on the Magnus effect of spinning projectile in supersonic flows

“…Thus, the Magnus effect of a nonfinned projectile in supersonic flows can be calculated using steady algorithm with the addition of a moving surface boundary condition, and good results are obtained compared with experimental data. Different from the quasi-steady Magnus effect of nonfinned projectile, the lateral force and yawing moment of finned projectile change with time and have obvious unsteady characteristics (Cayzac, Carette, Denis, & Guillen, 2011).…”

Effect of elastic deformation on the aerodynamic characteristics of a high-speed spinning projectile

“…Flight tests have shown that, elastic deformation of a projectile body can reach the same order of magnitude as its radius [1,7]. Spin can cause Magnus forces and moments with the distorted boundary layer, the coupling of the elastic deformation and rolling movement of a projectile body will produce a more complicated phenomenon than those previously discussed [2][3][4]. Studies have shown that, non-linear aerodynamic moments can be obtained even with linear aerodynamic theory; these moments will further cause non-linear movements such as spin lock-in and roll-pitch resonance [5][6][7].…”

Canards interference on the Magnus effect of a fin-stabilized spinning missile

“…The dominating flow mechanism of the Magnus effect of non-finned projectiles includes the surface boundary layer distortion, the asymmetrical flow separation, and the asymmetrical transition. 2 For finned projectiles, additional angle of attack of tails induced by spin rate and the impact of fore-body separation vortices on tails would produce additional influence. 3,4 Although the lateral force is only 1/100 to 1/10 of the normal force, the coupled longitudinal and lateral motions can be induced and is characterized as coning motion.…”