Numerical investigation on aerodynamic and inertial couplings of flexible spinning missile with large slenderness ratio

There are aerodynamic and inertial couplings in rigid-body motion and structural vibration of a flexible spinning missile in flight, and when slenderness ratio is larger, the couplings are more obvious. As for the flexible spinning missile with large slenderness ratio, aerodynamic and inertial couplings should be considered. Based on rigid-motion mesh and radial-basis-function (RBF) mesh deformation techniques, unsteady Reynolds-averaged Navier-Stokes (URANS) Equations and flight dynamics equations of flexible spinning missile derived from Lagrange equation are coupled simultaneously to simulate the dynamic response of flexible spinning missile with large slenderness ratio. The URANS equations are solved by Computational Fluid Dynamics (CFD) technique with the in-house code. Not only the aerodynamic coupling between rigid-body six degree of freedom (DOF) motion and structural vibration are included in the flight dynamics equations of flexible spinning missile, but also the variation of inertia tensor and extra moment terms caused by structural vibration are included, too. More importantly, the extra force term caused by angular acceleration of rigid-body motion, Coriolis and centrifugal loading terms caused by angular velocity of rigid-body motion are included. The rigid-motion mesh and RBF mesh deformation techniques are both based on unstructured mesh. The rigid-motion mesh is adopted to treat the large rigid-body motion due to flight dynamics, while the RBF mesh deformation is employed for flexible structural deformation caused by aeroelasticity. Numerical results of free flight case and aeroelastic case are well agreed with the experimental results, which validates the numerical method. A missile model with X-X configuration is constructed to quantitatively investigate the aerodynamic and inertial couplings between rigid-body motion and structural elastic vibration, and aerodynamic force, extra generalized force terms caused by rigid-body motion and extra moment terms caused by structural vibration are all investigated. Final results show that for the critical stable case studied in this paper, the aerodynamic force plays a major role in coupling effects between rigid-body motion and structural vibration, and the inertial coupling terms in rigid-body motion caused by structural vibration are negligible compared with the aerodynamic force. However, the inertial coupling terms in structural vibration due to rigid-body motion are not negligible compared with the aerodynamic force.