Normal forces exerted upon a long cylinder oscillating in an axial flow

Abstract

AbstractThis work aims to improve understanding of the damping induced by an axial flow on a rigid cylinder undergoing small lateral oscillations within the framework of the quasistatic assumption. The study focuses on the normal force exerted on the cylinder for a Reynolds number of $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}\mathit{Re}=24\, 000$ (based on the cylinder diameter and axial flow velocity). Both dynamic and static approaches are investigated. With the static approach, fluid forces, pressure distributions and velocity fields are measured for different yaw angles and cylinder lengths in a wind tunnel. It is found that for yaw angles smaller than $5{^\circ }$, the normal force varies linearly with the angle and is fully dominated by its lift component. The lift originates from the high pressure coefficient at the front of the cylinder, which is found to depend linearly on the angle, and from a base pressure coefficient that remains close to zero independent of the yaw angle. At the base, a flow deficit and two counter-rotating vortices are observed. A numerical simulation using a $k\mbox{--}\omega $ shear stress transport turbulence model confirms the static experimental results. A dynamic experiment conducted in a water tunnel brings out damping-rate values during free oscillations of the cylinder. As expected from the linear dependence of the normal force on the yaw angle observed with the static approach, the damping rate increases linearly with the axial flow velocity. Satisfactory agreement is found between the two approaches.