Numerical Investigation of the Vibration of a Circular Cylinder in Oscillatory Flow in Oblique Directions

The response of an elastically mounted circular cylinder vibrating in an oscillatory flow oblique to the flow direction is investigated. Simulations are conducted for vibration angles ranging from 0° to 90°, with 0° and 90° corresponding to the cases where the vibration is inline and perpendicular to the flow direction, respectively. One mass ratio of 2, one Reynolds number of 150, and two Keulegan–Carpenter (KC) numbers of 5 and 10 and a wide range of frequency ratios that cover the lock-in regime are considered. The frequency ratio is the ratio of the oscillatory flow frequency to the natural frequency. The maximum vibration amplitude is highest when the cylinder vibrates in the flow direction (vibration angle = 0°) and gradually decreases with the increase of the vibration direction. All the identified flow regimes are mapped on the frequency ratio versus vibration angle space. In addition to the flow regimes that exist for a stationary cylinder, two variants of Regime F (F1 and F2), a new flow regime R and an unstable regime D/F are found. The vortex street directions of Regime F1 and F2 are the opposite to and the same as the direction of the vibration, respectively, Regime R is a regime where a dominant vortex circles around the cylinder and Regime D/F is an unstable regime where the flow changes between Regime D and F frequently. The contribution of the higher harmonics in the vibration increases with the increase of the vibration direction angle. As a result of the strong contribution of higher harmonics at large vibration angles and small frequency ratios, local peak values of the vibration amplitude are found at frequency ratios of 0.4 and 0.25 for KC = 5 and 10, respectively.