Galloping of Prismatic Bodies With Different Afterbody Shapes

Many offshore and polar structures consists of slender prismatic bodies with different cross-sectional shapes. In an ISOPE-93 article by Yazdani et. al (1993) it was shown that at a mean angle of attack [a] of zero degrees square cylinder become unstable to galloping oscillation. However, at this same condition, trapezoidal and triangular cylinders exhibit a stable and neutrally stable condition to galloping oscillation respectively. In the present paper, the conditions of galloping stability of cylinders with the same three shapes are examined experimentally at both zero and non zero α. All the experiments were carried out in an open loop wind tunnel. At the experimental wind speed the level of turbulence in the tunnel was no more than 0.5%, which is considered equivalent to a calm sea-state. Dynamic tests, where the cylinder was forced to oscillate in a direction that is transverse to the free stream, were also carried out at amplitude [a], oscillation frequency [f_N] and free stream velocity [U_∞]. While a/d (d = cylinder cross-stream dimension) was kept constant at a value of 1 in the experiment, f_N and U_∞ were varied over the range of 1 Hz to 3 Hz and 5 m/s to 20 m/s respectively. The reduced velocity [U. = U_∞/ (f_N d)] and Reynolds number therefore varied in the range of 33.34 to 400 and 1.5 X 104 to 6.0 X 10⁴ respectively. By analyzing the normal force [C_N] versus a curves and in particular the sign and magnitude of ∂C_N/∂αat different α, it was observed that there exists several ranges of α within which galloping instability for these three shapes becomes possible. For the square cylinder the low end of the unstable range is 0°, while for the trapezoidal and triangular cylinders, it is about 10°. (Formulas are shown in the paper)