Data-driven stability analysis via the superposition of reduced-order models for the flutter of circular cylinder submerged in three-dimensional spanwise shear inflow at subcritical Reynolds number

Abstract

In this paper, we present a novel data-driven theory for the stability analysis of a flow-induced vibration (FIV) system consisting of an elastically mounted circular cylinder submerged in three-dimensional (3D) spanwise shear inflow at a subcritical Reynolds number. The presented data-driven theory separates the cylinder into several elements along the spanwise direction and treats the aerodynamics of each element as a two-dimensional (2D) situation subject to a uniform inflow. An eigensystem realization algorithm is constructed to obtain the separate 2D flow reduced-order model (ROM) for each element, and then, the superposition of those 2D ROMs (SROM) is processed to obtain the simplified 3D flow ROM. The simplified 3D flow ROM is coupled with the structural model to perform a linear stability analysis of the FIV system under study. The proposed data-driven technique demonstrates high consistency with the high-fidelity full-order model (FOM) with regard to the prediction of flutter lock-in boundaries while being more time-efficient, whereas the traditional direct 3D data-driven analysis involves significant errors. The growth rate obtained using SROM is negatively correlated with the lagging time (reflected in the FOM calculation) for the FIV system to evolve from the initial stationary state to the final equilibrium state. The evolution of the structural instability range with the variation in the mass ratio is analyzed/predicted by the proposed data-driven theory. The determination of the lock-in regime using the FOM is accompanied by a careful discussion of the associated dynamical responses, including phase differences, structural oscillation frequencies, lift coefficients, and wake patterns.