Hydrodynamics on Vertical Cylinder (Spar): Potential flow theory or Morison’s equation?

Spar type floating offshore wind turbine.

Hydrodynamic loads–those associated with excitation from incident waves and radiation of outgoing waves from cylinder motion–depend on whether flow separation occurs. Flow separation occurs when the Keulegan-Carpenter number, which is defined as  $ KC=VT/D$ where  $D$ is the cylinder diameter,  $T$ the wave period, and  $V$ the amplitude of the fluid velocity normal to the cylinder, exceeds 2. The diameter to wavelength ratio,  $D/\lambda$ , is also an important factor that determines the proper formulation for hydrodynamic loads. Diffraction effects are important when  $D/\lambda$ exceeds 0.2 and unimportant for smaller ratios.

For  $KC$ values lower than 2, potential flow theory applies. For  $KC$ values exceed 2 and  $D/\lambda$ lower than 0.2, Morison’s formulation is applicable. In practical situation, there is another condition for the use of Morison’s formulation that the radiation damping is negligible. For the vertical cylinder, the radiation damping in most modes of motion is small.

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