The numerical simulations of flow over a spinning finned projectile at angles of attack ranging from 4 • to 30.3 • in supersonic conditions were carried out to investigate the flow mechanism of the Magnus effect. The finite volume method, a dual-time stepping method, and a γ − Re θ transition model were combined to solve the Reynolds-averaged Navier-Stokes (RANS) equations. The validation of temporal resolution, grid independence, and turbulence models were conducted for the accuracy of the numerical method. The numerical results were in certain agreement with archival experimental data. A comparison of the transient lateral force and time-averaged Magnus force between the body of finned projectile and the nonfinned body, the projectile fin and single fin was given. The key lies in the analysis of the reasons for the production of the Magnus force. The simulation provided a profound insight into the flow structure and revealed the following. The fin leading edge shock contributes to the unsteady interference on body lateral force, while the time-averaged body Magnus force is similar to that of the nonfinned body. At α = 30.3 • , the shielding effect of body on crossflow weakens the time-averaged body Magnus force induced by asymmetrical flow separation, the magnitude of which is reduced to the value at α = 8 • . The leeward separation vortices and the resistance on wingroot flow are responsible for the nonlinear interference of the projectile body on fin Magnus force at different angles of attack. When the low pressure region of the vortex core is equivalent to the size and position of fin, leeward separation vortices contribute more the time-averaged Magnus force and induce high frequency variation to the transient fin lateral force. ARTICLE HISTORY

Reynolds-averaged simulations of flow over spinning finned missiles with and without canards were carried out at Ma = 0.6, 0.9, 1.5, and 2.5; a= 4°, 8°, and 12.6°; and v = 0:025 to investigate different mechanisms of the Magnus effect. An implicit dual-time stepping method and the g À Re ut transition model were combined to solve the unsteady Reynolds-averaged Navier-Stokes equations. Grid independence study was conducted, and the computed results were compared with archival experimental data. The transient and time-averaged lateral force coefficients were obtained, and the flow field structures were compared at typical rolling angles. The results indicate that in subsonic conditions, the canards interference intensifies the asymmetrical distortion of the body surface boundary layer and flow separation at different angles of attack, doubling the absolute value of the time-averaged body lateral force; the wash flow effect strengthens on the leeward tail due to the canards interference, increasing its time-averaged lateral force; in supersonic conditions, the shock and expansion waves induced by canards, the vortex system, and the flow separation are responsible for the fluctuation of the body lateral force; the direction of the canard induced wash flow alters as angle of attack increases, increasing first and then decreasing the time-averaged tail lateral force.

Based on the three-dimensional Navier–Stokes (N–S) equations, using unsteady numerical technology, flow over a dual-spin projectile was simulated to investigate its aerodynamic characteristics during flight. Spin was achieved via the sliding mesh method. The influence laws of the aftbody spin rate, Mach number, and angle of attack on the aerodynamic characteristics of the projectile are presented, and the flow mechanisms for the laws are revealed. The results demonstrate that the influence of the aftbody spin rate on the normal force coefficient is very small, whereas, on the lateral force coefficient, it is larger. With the increase in the Mach number, the time-averaged normal force coefficient and lateral force coefficient increase, while the fluctuation quantities of the normal force coefficient and the lateral force coefficient decrease. The variation of angle of attack will influence the size, distribution, and interference effect of the shedding vortices.

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