Self-excited dynamics of an elastically restrained slender rigid body in uniform compressible laminar flow

Abstract

In this research, we employ a computational methodology to investigate the self-excited angular dynamics of an elastically restrained rigid body in uniform compressible laminar flow. We investigate the onset of vortex-induced vibration of a two-dimensional slender rigid body configuration with a torsion spring at the leading edge and investigate the fluid–structure interaction of a three-dimensional ogive–cylinder body restrained by three torsion springs in the pitch, roll, and yaw directions. The methodology combines the implicit finite-difference Beam and Warming algorithm for the Navier–Stokes equations and a fourth-order Runge–Kutta solver for the rigid body equations of motion. The results for a fixed body reveal a critical angle-of-attack beyond which the two-dimensional flow becomes unsteady culminating with periodic drag and lift forces due to an asymmetric vortex pair shed at the body free edge. Numerical analysis of a two-dimensional pitch motion yields periodic limit cycles for a low Reynolds number flow. These self-excited oscillations evolve to ultrasubharmonic, quasiperiodic and non-stationary chaotic-like dynamics with increasing Reynolds number. Numerical analysis of three-dimensional coupled angular dynamics reveals a similar bifurcation structure for finite Reynolds number flow which includes quasiperiodic and non-stationary dynamics with increasing angles-of-attack.