Proceedings of the Thirty-second (2022) International Ocean and Polar Engineering ConferenceShanghai, China, June 5–10, 2022
Copyright © 2022 by the International Society of Offshore and Polar Engineers (ISOPE)
ISBN 978-1-880653-81-4; ISSN 1098-6189

www.isope.org

Viscous Loading Effects on Large Floater Vertical Motions and Wave Drift Forces
Da Li1,3, Cong Yi1, Yongjun Chen 2
CNOOC Research Institute, Beijing, China
2
DMAR Engineering, Inc., Houston, Texas, USA
1

3

College of Shipbuilding Engineering, Harbin Engineering University, Harbin, Heilongjiang, China

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 isusually provided to the time domain analysis where the responses arecaptured for all the base wave frequency combinations. It is noted thefull 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 studyfor QTF calculations.

ABSTRACT
It is known from the wave basin test and field measurement that RAOsof 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 andQTF are also affected by motion RAOs. In this paper the drift force
coefficients and QTF calculation are based on the RAO where aMorison drag formula is included, and two cases are studied toinvestigate the effects of viscous loading on vertical motions and wave
drift forces.

A practical procedure usually used in offshore industry design practiceis to linearize the quadratic/viscous damping (Malta,2010), together
with the assessed damping from mooring and risers, in the first orderdiffraction calculation, such that the motion RAO (Response AmplitudeOperator) is close to the basin tests (Rogne, 2016), or the preliminary
fully coupled time domain analysis. Most of the diffraction codes
available in the market today allow defining a damping matrix, which isestimated for the specific analysis condition (e.g., with increasing
damping levels for higher sea-states and larger motions). There aresome disadvantages for this approach: The first problem is that thedamping level has to be based on same type of existing floaters, andsame level of analysis environment; this can be mitigated by iterations
and referring to motion RAOs from previous design data. The second
issue, which can be more important is that this method neglects theviscous exciting forces which in some frequency range can bedominant, and will completely change the response curve, such as in
the cancellation frequencies for a column / pontoon floater. For
cylindrical FPSO structure, due to its large volume and special skirt
design, the impact of viscous damping on platform motion response iseven more significant (Ji, 2019, Jiang, 2020 & Cui, 2021). Thisphenomenon cannot be properly represented by introducing equivalentlinear damping matrix alone.

KEY WORDS: Morison Drag, RAO, Mean Drift Force, QTF
INTRODUCTION
The offshore floater design mainly relies on a potential flow solver tocalculate linear quantities for frequency analysis, and oftentimes toprovide 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 tofrequencies below (difference frequency) or higher (sum frequency)
than the base wave frequencies. The mean drift forces contribute toplatform mean offset, and more importantly, the slowly varying 2 ndorder force can cause significant resonant responses for motions havelong 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'sapproximation (1974) the mean wave drift loads can approximate theslowly varying wave drift loads, which is generally valid in deep waterand long motion period conditions. The mid-field approach (Chen,2005 & Lee, 2007) provides an improved numerical method for solving

Since most of the commercial codes usually calculate the 2 nd orderforce with the RAO internally calculated using only linearized damping
matrix, in this study the drag element modeling and Morison formula isincluded in the diffraction code which is being developed. The motion
RAO is solved iteratively for a specific, nominal wave height. The
RAO is subsequently used to calculate the 2nd order forces, i.e., mean779