SURFACE TOPOLOGY EFFECTS ON THE TRANSVERSE GALLOPING BEHAVIOR OF RECTANGULAR CYLINDERS

The effect of geometry on the transverse galloping behavior of rectangular cylinders was studied experimentally for Reynolds numbers between 1,000 and 10,000. In particular, a comparison was made between a rectangular cylinder with rounded corners and a smooth surface, and the same baseline geometry with added surface topology synthesized from two-dimensional Fourier-modes. The effect of the amplitude of the topological surface height was investigated. From measurements of the normal (galloping direction) force coefficient variation with angle-of-attack, it was found that the added surface topology generally had a destabilizing effect relative to the smooth cylinder. At the lowest Reynolds number, the smooth cylinder was stable, while the cylinders with added topology were unstable with respect to galloping. For Reynolds numbers from 5,000 to 10,000, the added topology did not cause a similar instability. However, there was a monotonic increase in the slope of the normal force coefficient at zero angle-of-attack with increasing surface height amplitude, thus moving the geometry closer to the instability threshold. This effect diminished as Reynolds number increased. Overall, for the range of parameters investigated herein, the cylinder with larger topology amplitude exhibited more favorable galloping resistance characteristics than the one with smaller topology. INTRODUCTION An elastically mounted cylinder with non-circular cross section may be susceptible to a flow-induced oscillation known as galloping. This is a result of the fact that the aerodynamic forces acting on the body vary with its orientation to the oncoming flow. This is described schematically in Figure 1 for a rectangular cylinder elastically mounted in the transverse direction (y-direction). The lift and the drag forces, FL and FD, respectively, will be oscillatory in time due to the oscillation of the body at a velocity ẏ. The normal force coefficient in the y-direction is related to the lift and the drag coefficients, viz: Cy = Fy 1/2ρU2 ∞dl =− 1 cos2 α (CL cosα +CD sinα), (1) where CL = FL/(1/2ρU reldl) and CD = FD/(1/2ρU 2 reldl) are the lift and the drag coefficients, respectively, α is angleof-attack, U∞ is the steady freestream velocity, Urel is the instantaneous oncoming velocity relative to the cylinder, ρ is the density, d is the cylinder width and l is the cylinder span. If the oscillation is such that Cy increases with α , this produces negative fluid damping and the structure may become unstable. Mathematically, the necessary aerodynamic condition for transverse galloping is ∂Cy/∂α > 0. This phenomenon can affect structures such as ice coated power lines, bridge decks and stalled wings (Blevins, 2001). Another type of structure that may be susceptible to galloping is the parachute suspension line used in precision airdrop systems. A typical suspension line has a non-circular cross section that resembles a rectangle with side ratio c/d = 2 – 3 (where c is chord length) and rounded corners (Siefers et al., 2013). The unsteady forces arising from potential galloping of the suspension lines could contribute substantially to the overall aerodynamic performance of the airdrop system, since the lines have been shown to significantly affect the total drag (Bergeron et al., 2009). Understanding the galloping behavior of such a geometry is therefore fundamental to the prediction and mitigation of this aero-elastic instability.