It is known from the wave basin test and field measurement that RAOs of certain type of floating structures are susceptible to viscous effects. The viscous loading mechanism is usually captured in a mixed modeling frequency domain solver, or a coupled time domain analysis. However, the 2nd order diffraction quantities such as drift force and QTF are also affected by motion RAOs. In this paper the drift force coefficients and QTF calculation are based on the RAO where a Morison drag formula is included, and two cases are studied to investigate the effects of viscous loading on vertical motions and wave drift forces.
The offshore floater design mainly relies on a potential flow solver to calculate linear quantities for frequency analysis, and oftentimes to provide inputs for subsequent time domain simulations. In either approach the second order drift forces are important to properly predict the floater motions.
The second order quantities are relatively small and extend to frequencies below (difference frequency) or higher (sum frequency) than the base wave frequencies. The mean drift forces contribute to platform mean offset, and more importantly, the slowly varying 2nd order force can cause significant resonant responses for motions have long natural periods such as offset and yaw motions, and in certain cases even roll/pitch. Drift force is also imperative to mooring design, whose response is strongly coupled with floater lateral motions.
The simplest form of the second order quantity is the mean drift force in horizontal directions, calculated during linear diffraction analysis with a ‘far field’ method (Newman, 1964). Through Newman's approximation (1974) the mean wave drift loads can approximate the slowly varying wave drift loads, which is generally valid in deep water and long motion period conditions. The mid-field approach (Chen, 2005 & Lee, 2007) provides an improved numerical method for solving mean drift forces. A full QTF (Quadratic Transfer Function) matrix including bi-chromatic 2nd order wave load coefficients are a more complete representation of nonlinear forces in potential flow, which is usually provided to the time domain analysis where the responses are captured for all the base wave frequency combinations. It is noted the full QTF can be approximated by Pinkster method (Pinkster, 1980) without solving the second order velocity potential. This method greatly reduces computational efforts, while provides sufficient results for most problems, and opted by the code implementation in this study for QTF calculations.
