Oscillating rectangular and octagonal profiles: Modelling of fluid forces

Fluid forces acting on rectangular and octagonal cylinders oscillating without (alpha = 0 degrees) and with (alpha = 10 degrees) a mean incidence were measured in a water channel. Experimentally determined force coefficients and phase angles were compared to calculated coefficients determined using the "unsteady airfoil theory" and the "quasi-steady theory". The results showed that calculation of the time-dependent lift force coefficient according to the quasi-steady theory can only be used at low oscillation frequencies. While the quasi-steady theory does not account for fluid inertia, the unsteady airfoil theory models the forces resulting from the cylinder acceleration and modifies the lift force with a circulation function. Accordingly, unsteady airfoil theory may be applied to a broader frequency range. One advantage of the unsteady airfoil theory is that, in addition to the lift force, the phase angle between the lift force and cylinder displacement can be calculated. By virtue of knowing this phase angle, the ranges of positive energy transfer from the fluid to the cylinder can be determined and thereby the ranges of possible self-excited cylinder oscillations. The limits to the applications of both the unsteady airfoil theory and the quasi-steady theory were examined in detail and discussed with respect to oscillation frequency and amplitude. Neither theory is capable of encompassing the instability-induced phenomena such as resonance due to vortex shedding or phase jump. For rectangular and octagonal cylinders (prisms), the influence of the oscillation amplitude was investigated in detail, through both experiments and calculation, for several excitation frequencies of interest. One important result is that for the rectangular cylinder oscillating at a constant frequency, the direction of energy transfer between the fluid and the cylinder appeared to change as a function of oscillation amplitude. (C) 1998 Academic Press.