Numerical Study Of Out-of-plane Force And Moment For Spinning Finned Projectiles In Supersonic Flow

Spinning projectile has been widely used as tactical weapons.For a spinning projectile,angle of attack will induce out-of-plane force,which is perpendicular to the attack angle plane,and out-of-plane moment,which produces a rotation out of the attack angle plane.The out-of-plane force and moment can influence the flight status,and may induce a diverged coning motion.Therefore,the analysis of the flow mechanism of the out-of-plane force and moment is important to the aerodynamic study of spinning projectile.However,the flow structure of the spinning finned projectile is complex,and exhibits significant unsteady effect comparing with that of the non-finned projectile.Thus,the mechanism analysis of the out-of-plane force and moment of the spinning finned projectile is difficult.In recently years,numerical methods have been remarkably developed,which makes the study of the transient flow of the spinning finned projectile possible.This paper studies the out-of-plane force and moment characteristics of spinning finned projectile in supersonic flow by using the numerical method,and the flow mechanisms are analysed.The results of this paper can be used for projectile design and aerodynamic analysis.First,the out-of-plane force and moment characteristics of the spinning projectile with straight tail fins are studied.The flow over a projectile with four straight tail fins in supersonic conditions is simulated by using the dual time stepping method.The influence of the static aerodynamics is removed by using a nonlinear aerodynamic model and the steady simulation results,and the flow mechanisms of the time-averaged out-of-plane force and moment are analysed.The results show that the flow mechanisms of the out-of-plane force and moment are significantly influenced by the Mach number,and the out-of-plane force and moment are mainly induced by the fore-body cover effect and the influence of spinning on the shocks produced by the fins.Moreover,the interaction between the shock waves and expansion waves around fins also influences the time-averaged out-of-plane force and moment.The out-of-plane force and moment characteristics of the projectile with straight tail fins in combined spinning and coning motion are also studied.The spinning motion and the coning motion are defined and computed by the rigid body dynamic mesh method and the moving reference frame method,respectively.The flow over the aforementioned four fins projectile in supersonic conditions is computed.The results show that when the Mach number is close to 1,the superposed results of out-of-plane force and moment of the one freedom motions show obvious difference with those of the combined motion,which indicates significant aerodynamic coupling effects occur.However,when the Mach number is increased or the spin and coning rates are reduced,the influence of the aerodynamic coupling effects is weakened or eliminated.The flow analysis shows that the aerodynamic coupling effects are mainly induced by the interaction between the leading edge shock of the fin and the expansion waves which are produced by other fins in low supersonic Mach number.Furthermore,the out-of-plane force and moment characteristics of a spinning projectile with four wrap-around tail fins,which is asymmetric to the angle of attack plane,in supersonic flow are also studied.The results show that the difference of the out-of-plane force and moment between the projectile with the wrap-around tail fin and the projectile with the straight tail fin is mainly produced by the static aerodynamics induced by the asymmetry of the wrap-around fins.However,the characteristics of the out-of-plane force and moment induced by the spin rate are similar for the projectiles.The analysis of the shape of the projectile with wrap-around tail fin and the computed flow indicates that the static out-of-plane force and moment of the projectile with wrap-around tail fin are induced by the interaction between the curvature of the fins and the fin-fin and fin-body interferences.Furthermore,when the Mach number increases,the change of the static out-of-plane force and moment coefficients of the body significantly influences the time-averaged out-of-plane force and moment coefficients of the projectile.Lastly,because the flow of the spinning finned projectile is periodic,the harmonic balance method,which is designed for solving the periodic flow,is introduced to simulate the flow over a spinning finned projectile.The flow of the spinning projectile with four straight tail fins in supersonic flow is simulated by the harmonic balance method,and the computed side force and yaw moment coefficients are compared with the results of the traditional dual time stepping method and wind tunnel experiment.Moreover,the characteristics of the computed flow and the influence of the number of harmonics are analysed.The results show that the flow of the spinning finned projectile at angle of attack can be simulated by the harmonic balance method,and the accuracy of the computed side force and yaw moment is reasonable.The number of the harmonics significantly influences the accuracy of the computed aerodynamic coefficients and the details of the computed flow.