Numerical Investigation of Cross-Flow Over Oscillating Tandem Cylinders with Two Degrees of Freedom

Abstract

Two elastically mounted cylinders with two degree of freedom (2-DOF) in tandem is numerically investigated at constant Reynolds number 3900 within the subcritical range, and fixed spacing ratio (L/D) = 4. The two cylinders are identical with a moderate mass ratio m*=7, and mass damping parameter (m∗ + 1)ζ= 0.0117. Delayed Detached Eddy Simulation (DDES) model is utilized in the simulation. Eight reduced velocities (Ur ) of (3, 5, 6, 6.6, 7, 8, 12, 14) are investigated to find the effect of the upstream cylinder (UC) to vibrate with 2-DOF on the response of the downstream cylinder (DC). In addition the associated wake patterns are investigated to study the flow behavior in stream wise and spanwise direction.

It is noticed that the response of the downstream cylinder have a different behavior than typical wake induced vibration (WIV), especially at low reduced velocities (synchronization range), where there is a high amplitude vibrations of UC in the transverse direction. The upstream cylinder is initially in tandem with the downstream, before they both are allowed to vibrate. It is not as a build-up process like the case when a fixed UC cylinder is used. Therefore, the mechanism of the concept “wake stiffness” is behaving differently. Thus in the cases when the two cylinders had a synchronized motion, the wake is much complex than the case of a fixed upstream cylinder.

However, the downstream cylinder inline amplitude response is significantly higher the case when vortex induced vibration occurs at a single cylinder. Moreover, a completely different mechanism happens to describe the downstream oscillation when the two cylinders’ motion are not synchronized.

Dynamics of UC and the relative position between the two cylinders at the low region of the reduced velocities (Ur = [3 − 8]) within this study, have a paramount effect on the response of the DC. At this region, mix of wake flutter (WIF) and wake induced vibrations (WIV) dominates the behavior of the DC and both the inline and transverse vibration frequencies coalescence into the cylinder’s natural frequency. This leads to the presence of the elliptical orbits of the DC motion. At this phenomenon, it is believed that the steady forces in the wake is dominating. The unsteady vortex interaction has been found to play a vital role of the amplitudes of DC. Where and when it interacts with DC matters. The relative position between the two cylinders defines how this interaction will be significant.

The DC lift force has been found to be increased up to Ur=7, then it is decreased at Ur=8, where it is the end of the wake-induced flutter of the studied range of reduced velocities. The further increment of lift forces is not leading to higher amplitudes at Ur = (12, 14) as there is no congruent frequencies of the inline and transverse vibrations. The behavior is found to be described by the concept of “wake stiffness” which is a mechanism of wake-induced vibrations (WIV). This is consistent with the fact that the UC vibration amplitudes are reduced at this range of reduced velocities. Both DC lift and drag forces are dependent on the unsteady interaction between the vortices of the UC and the body of the DC whether it enhances it or hinders its movement in the respective direction.

Date of Award	13 Jul 2024
Original language	American English
Supervisor	Md Didarul Islam (Supervisor)