Predictions of Fluid-Induced Self-Excited Oscillations by the Time-Spectral CFD

Abstract

The time-spectral (TS) method to numerically predict self-excited oscillation due to the fluid dynamics-- rigid body dynamics coupling is developed and validated through the comparison with the time-marching (TM) method. A residual of the TS equation of motion of a rigid body is found to be a useful indicator to realize limit-cycle oscillations. It is minimized by repeating the frequency update by the Newton iteration, where the gradient of the residual with respect to the frequency is obtained from the flow simulation, and the displace update by solving the TS equation of motion. The developed method is validated by two problems: one is an oscillating cylinder due to the Karman vortex, and another is a transonic, pitching wing due to the movement of the shock wave around the wing. In both problems, the TS methods quantitatively reproduce free oscillations by the TM method. The simulation time is shortened by a factor of 4 for the transonic wing problem.