Magnus effects on a differentially spinning projectile have been numerically analyzed using the three-dimensional thin-layer Navier-Stokes equations for Mach numbers ranging from 2.0 to 4.0 and angles of attack of α = 4° and 7°. The projectile model is a 6-caliber long, secant-ogive-cylinder-boattail (SOCBT) shape. Differential Magnus effects have been investigated for the spin cases where one of the projectile sections does not spin while the other two are spinning at the same rate. Three spin cases have consequently been considered. The three-dimensional supersonic flow around the SOCBT projectile has been computed using an implicit, approximately-factored, partially flux-split algorithm. The accuracy of the present Navier-Stokes code has been validated by comparing the computational results with experimental data for the single-spinning SOCBT projectile at supersonic speeds. Good agreements could be obtained at small and moderate angles of attack.
Computed results have shown that there is indeed noticeable change in Magnus forces and moments due to the differential spinning. Changes of surface pressure, circumferential and longitudinal wall shear stresses by the differential spin, relative to the single-spinning case, are presented in the circumferential direction on three sampled sectional locations. Magnus forces generated by the surface pressure and wall shear stresses are plotted in the longitudinal direction for the three different spin cases. Computations have also shown that the position of the Magnus center of pressure varies noticeably due to the differential spinning. Numerical results indicate that, contrary to Magnus effects, the normal forces and pitching moments remain nearly independent of the spin cases considered in this study.
