Small-amplitude oscillations of perforated disks

Dynamic stability of deep-water floating structures, such as off-shore wind turbines or oil and gas platforms, is essential for their optimum performance and for minimizing downtime. To this end, these structures are usually appended by submerged flat objects known as heave plates. The plates are designed to dampen unwanted environmental disturbances and, thereby, maintain the oscillations of the platforms within an acceptable range. Despite their widespread use, whether impermeable plates qualify as optimal dampers still remains an open question. To provide practical insights into this inquiry, we examine the hydrodynamic response of perforated disks, as characterized by their added mass and damping coefficients, under small-amplitude oscillations. Numerical simulations are used to solve for the flow field and to calculate the force coefficients for disks of various porosity and thickness. Our calculations reveal that permeable disks behave as their impermeable counterparts at small and intermediate values of the oscillatory Reynolds number Re_ω, with the effect of thickness being relatively insignificant. As Re_ω transitions to higher values (O(10²) and beyond), the added mass coefficient decreases monotonically with increasing the porosity, whereas the damping coefficient initially rises with the porosity, then reaches a maximum, and finally declines with further increasing the degree of perforation. In this regime, we observe modest improvements of both added mass and damping coefficients for thicker disks. Overall, our findings provide new insights into (i) the role of porosity in the dynamic response of perforated disks and (ii) the advantages offered by the porosity for performance optimizations in practical settings.