Reprint of: Stochastic modeling of a freely rotating disk facing a uniform flow

Abstract

The fluid–structure interaction between a thin circular disk and its turbulent wake is investigated experimentally and described with a low-order stochastic model. The disk faces a uniform flow at Reynolds number Re=133 000 and can rotate around one of its diameters. It is equipped with instantaneous pressure measurements to give the aerodynamic loading: moments and center of pressure of the front and base sides. When the disk is fixed and aligned, symmetry-breaking vortex shedding is observed and all orientations are visited with equal probability, yielding axisymmetric long-term statistics. Very-low-frequency antisymmetric modes as recently observed by Rigas et al. (2014) are not observed unless the disk shape is modified into that of a bullet, showing the importance of the separation angle. It suggests that these modes are linearly stable for the disk while they are unstable for the bullet shape. When the disk is fixed and inclined, the base center of pressure (CoP) shifts preferentially towards one side of the rotation axis. Finally, when the disk is free to rotate, the front moment is proportional to the disk inclination (aerodynamic stiffness), while the base moment is well correlated with the disk inclination. From these observations, a low-order model is derived that couples (i) the CoP, forced stochastically by the turbulent flow, and (ii) the disk inclination, as a linear harmonic oscillator forced by the base moment. The model captures well the main statistic and dynamic features observed experimentally. One difference lies in the distribution of the disk inclination (which features exponential tails in the measurements but is Gaussian in the model), suggesting a possible refinement with non-linearities or time delays. The model is expected to capture coupled dynamics in other systems involving turbulent wakes behind freely rotating bluff bodies.