Offshore Technology

Linearization of Quadratic Drag to Estimate CALM Buoy Pitch Motion in Frequency-Domain and Experimental Validation

[+] Author and Article Information
Amir G. Salem, Sam Ryu, Arun S. Duggal

 SOFEC, Inc., 14741 Yorktown Plaza Drive, Houston, TX 77040

Raju V. Datla

 Stevens Institute of Technology, 711 Hudson Street, Hoboken, NJ 07030

J. Offshore Mech. Arct. Eng 134(1), 011305 (Oct 17, 2011) (6 pages) doi:10.1115/1.4003645 History: Received June 23, 2009; Revised September 07, 2010; Published October 17, 2011; Online October 17, 2011

The dynamics of an oil offloading catenary anchor leg mooring (CALM) buoy coupled with mooring and flow lines are directly related to the fatigue life of a mooring system, necessitating an accurate estimate of the buoy hydrodynamic response. Linear wave theory is used for modeling the surface boundary value problem, and the boundary element method is used to solve the fluid-structure interaction between the buoy hull and the incident waves in the frequency-domain. The radiation problem is solved to estimate the added mass and radiation damping coefficients, and the diffraction problem is solved to determine the linear wave exciting loading. The buoy pitch motion is investigated, and linearizations of the quadratic drag/damping term are performed in the frequency-domain. The pitch motion response is calculated by considering an equivalent linearized drag/damping. Quadratic, cubic, and stochastic linearizations of the nonlinear drag term are employed to derive the equivalent drag/damping. Comparisons between the linear and nonlinear damping effects are presented. Time-domain simulations of the buoy motions are performed in conjunction with Morison’s equation to validate the floating buoy response. The time- and frequency-domain results are finally compared with the experimental model test results for validations. The linearization methods applied result in good estimates for the peak pitch response. However, only the stochastic linearization method shows a good agreement for the period range of the incident wave where typical pitch response estimate has not been correctly estimated.

Copyright © 2012 by American Society of Mechanical Engineers
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Figure 1

Steps to calculate the buoy pitch motion response

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Figure 2

Photo of buoy model in preparations for testing

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Figure 3

Plan view of the experimental configuration of buoy

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Figure 4

Random wave spectrum using JONSWAP

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Figure 5

Schematic model representation of mass-spring-damper system

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Figure 6

Schematic of the panel model used in WAMIT

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Figure 7

(a) Frequency dependent added-mass coefficients and (b) frequency dependent added-mass coefficients

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Figure 8

(a) Frequency dependent radiation damping coefficients and (b) frequency dependent radiation damping coefficients

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Figure 9

Pitch added mass from the radiation solution

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Figure 10

Pitch radiation damping from the radiation solution

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Figure 11

Pitch exciting load from the diffraction solution

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Figure 12

Pitch free decay comparison among experimental result, analytical solution, and time-domain simulation

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Figure 13

Phase comparison for buoy motion and wave exciting moment

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Figure 14

Pitch motion RAO comparison: model test, frequency-domain, and time-domain




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