0
Research Papers: Ocean Engineering

Suppression of Irregular Frequency Effect in Hydrodynamic Problems and Free-Surface Singularity Treatment

[+] Author and Article Information
Yujie Liu

Marine Dynamics Laboratory,
Department of Ocean Engineering,
Texas A&M University,
College Station, TX 77843
e-mail: yjliu2012@tamu.edu

Jeffrey M. Falzarano

Marine Dynamics Laboratory,
Department of Ocean Engineering,
Texas A&M University,
College Station, TX 77843
e-mail: jfalzarano@civil.tamu.edu

1Corresponding author.

Contributed by the Ocean, Offshore, and Arctic Engineering Division of ASME for publication in the JOURNAL OF OFFSHORE MECHANICS AND ARCTIC ENGINEERING. Manuscript received September 9, 2016; final manuscript received May 26, 2017; published online July 6, 2017. Assoc. Editor: Lance Manuel.

J. Offshore Mech. Arct. Eng 139(5), 051101 (Jul 06, 2017) (16 pages) Paper No: OMAE-16-1113; doi: 10.1115/1.4036950 History: Received September 09, 2016; Revised May 26, 2017

Multibody operations are routinely performed in offshore activities, for example, the floating liquefied natural gas (FLNG) and liquefied natural gas carrier (LNGC) side-by-side offloading case. To understand the phenomenon occurring inside the gap is of growing interest to the offshore industry. One important issue is the existence of the irregular frequency effect. The effect can be confused with the physical resonance. Thus, it needs to be removed. An extensive survey of the previous approaches to the irregular frequency problem has been undertaken. The matrix formulated in the boundary integral equations will become nearly singular for some frequencies. The existence of numerical round-off errors will make the matrix still solvable by a direct solver, however, it will result in unreasonably large values in some aspects of the solution, namely, the irregular frequency effect. The removal of the irregular effect is important especially for multibody hydrodynamic analysis in identifying the physical resonances caused by the configuration of floaters. This paper will mainly discuss the lid method on the internal free surface. To reach a higher accuracy, the singularity resulting from the Green function needs special care. Each term in the wave Green function will be evaluated using the corresponding analysis methods. Specifically, an analytical integral method is proposed to treat the log singularity. Finally, results with and without irregular frequency removal will be shown to demonstrate the effectiveness of our proposed method.

Copyright © 2017 by ASME
Your Session has timed out. Please sign back in to continue.

References

John, F. , 1950, “ On the Motion of Floating Bodies II,” Commun. Pure Appl. Math., 3(1), pp. 45–101. [CrossRef]
Frank, W. , 1967, “ Oscillation of Cylinders in or Below the Free Surface of Deep Fluids,” Naval Ship Research and Development Center, Bethesda, MD, Technical Report No. 2375. http://www.dtic.mil/dtic/tr/fulltext/u2/668338.pdf
Ursell, F. , 1953, “ Short Surface Waves Due to an Oscillating Immersed Body,” Proc. R. Soc. A: Math., Phys. Eng. Sci., 220(1140), pp. 90–103. [CrossRef]
Schenck, H. A. , 1968, “ Improved Integral Formulation for Acoustic Radiation Problems,” J. Acoust. Soc. Am., 44(1), pp. 41–58. [CrossRef]
Burton, A. J. , and Miller, G. F. , 1971, “ The Application of Integral Equation Methods to the Numerical Solution of Some Exterior Boundary-Value Problems,” Proc. R. Soc. A: Math., Phys. Eng. Sci., 323(1553), pp. 201–210. [CrossRef]
Jones, D. , 1974, “ Integral Equations for the Exterior Acoustic Problem,” Q. J. Mech. Appl. Math., 27(1), pp. 129–142. [CrossRef]
Ogilvie, T. F. , and Shin, Y. S. , 1978, “ Integral Equation Solutions for Time Dependent Free Surface Problems,” J. Soc. Nav. Arch. Jpn., 1978(143), pp. 41–51. [CrossRef]
Sayer, P. , 1980, “ An Integral-Equation Method for Determining the Fluid Motion Due to a Cylinder Heaving on Water of Finite Depth,” Proc. R. Soc. London, Ser. A, 372(1748), pp. 93–110. [CrossRef]
Ursell, F. , 1981, “ Irregular Frequencies and the Motion of Floating Bodies,” J. Fluid Mech., 105, pp. 143–156. [CrossRef]
Wu, X.-J. , and Price, W. , 1987, “ A Multiple Green's Function Expression for the Hydrodynamic Analysis of Multi-Hull Structures,” Appl. Ocean Res., 9(2), pp. 58–66. [CrossRef]
Lau, S. M. , and Hearn, G. E. , 1989, “ Suppression of Irregular Frequency Effects in Fluid-Structure Interaction Problems Using a Combined Boundary Integral Equation Method,” Int. J. Numer. Methods Fluids, 9(7), pp. 763–782. [CrossRef]
Lee, C.-H. , and Sclavounos, P. D. , 1989, “ Removing the Irregular Frequencies From Integral Equations in Wave-Body Interactions,” J. Fluid Mech., 207, pp. 393–418. [CrossRef]
Lee, C.-H. , 1988, “ Numerical Methods for Boundary Integral Equations in Wave Body Interactions,” Ph.D. thesis, Massachusetts Institute of Technology, Cambridge, MA.
Kress, R. , 1985, “ Minimizing the Condition Number of Boundary Integral Operators in Acoustic and Electromagnetic Scattering,” Q. J. Mech. Appl. Math., 38(2), pp. 323–341. [CrossRef]
Zhu, X. , 1994, “ Irregular Frequency Removal From the Boundary Integral Equation for the Wave-Body Problem,” Ph.D. thesis, Massachusetts Institute of Technology, Cambridge, MA. https://dspace.mit.edu/bitstream/handle/1721.1/11691/32279180-MIT.pdf?sequence=2
Martin, P. , 1981, “ On the Null-Field Equations for Water-Wave Radiation Problems,” J. Fluid Mech, 113, pp. 315–332. [CrossRef]
Liapis, S. , 1993, “ A Method for Suppressing the Irregular Frequencies From Integral Equations in Water Wave-Structure Interaction Problems,” Comput. Mech., 12(1), pp. 59–68. [CrossRef]
Paulling, J. , 1970, “ Stability and Ship Motion in a Seaway,” Defense Technical Information Center, Fort Belvoir, VA, Report No. AD0714078. http://www.dtic.mil/docs/citations/AD0714078
Ohmatsu, S. , 1975, “ On the Irregular Frequencies in the Theory of Oscillating Bodies in a Free Surface,” Ship Research Institute, Tokyo, Japan, Paper No. 48. http://mararchief.tudelft.nl/catalogue/entries/12180/
Kleinman, R. E. , 1982, “ On the Mathematical Theory of the Motion of Floating Bodies: An Update,” David W. Taylor Naval Ship Research and Development Center, Bethesda, MD, Report No. DTNSRDC-82/074. http://www.dtic.mil/dtic/tr/fulltext/u2/a121433.pdf
Rezayat, M. , Shippy, D. , and Rizzo, F. , 1986, “ On Time-Harmonic Elastic-Wave Analysis by the Boundary Element Method for Moderate to High Frequencies,” Comput. Methods Appl. Mech. Eng., 55(3), pp. 349–367. [CrossRef]
Lee, C. , Newman, J. N. , and Zhu, X. , 1996, “ An Extended Boundary Integral Equation Method for the Removal of Irregular Frequency Effects,” Int. J. Numer. Methods Fluids, 23(7), pp. 637–660. [CrossRef]
Newman, J. N. , 1985, “ Algorithms for the Free-Surface Green Function,” J. Eng. Math., 19(1), pp. 57–67. [CrossRef]
Telste, J. , and Noblesse, F. , 1986, “ Numerical Evaluation of the Green Function of Water-Wave Radiation and Diffraction,” J. Ship Res., 30(2), pp. 69–84.
Newman, J. , and Sclavounos, P. , 1988, “ The Computation of Wave Loads on Large Offshore Structures,” International Conference on Behaviour of Offshore Structures (BOSS), Trondheim, Norway, June, pp. 1–18. http://salsahpc.indiana.edu/dlib/articles/00000714/3/
Noblesse, F. , 1982, “ The Green Function in the Theory of Radiation and Diffraction of Regular Water Waves by a Body,” J. Eng. Math., 16(2), pp. 137–169. [CrossRef]
Liu, Y. , and Falzarano, J. M. , 2017, “ Irregular Frequency Removal Methods: Theory and Applications in Hydrodynamics,” J. Mar. Syst. Ocean Technol., 12(2), pp. 49–64. [CrossRef]
Liu, Y. , and Falzarano, J. M. , 2017, “ A Method to Remove Irregular Frequencies and Log Singularity Evaluation in Wave-Body Interaction Problems,” J. Ocean Eng. Mar. Energy, 3(2), pp. 161–189. [CrossRef]
Guha, A. , 2012, “ Development of a Computer Program for Three Dimensional Frequency Domain Analysis of Zero Speed First Order Wave Body Interaction,” Ph.D. thesis, Texas A&M University, College Station, TX. https://www.researchgate.net/profile/Amitava_Guha2/publication/272682470_Development_Of_A_Computer_Program_For_Three_Dimensional_Frequency_Domain_Analysis_of_Zero_Speed_First_Order_Wave_Body_Interaction/links/55e4e9bc08aede0b57358484.pdf
Liu, Y. , and Falzarano, J. M. , 2016, “ Suppression of Irregular Frequency in Multi-Body Problem and Free-Surface Singularity Treatment,” ASME Paper No. OMAE2016-54957.
Liu, Y. , and Falzarano, J. M. , 2017, “ Frequency Domain Analysis of the Interactions Between Multiple Ships With Nonzero Speed in Waves or Current-Wave Interactions,” ASME Paper No. OMAE2017-62322.
Liu, Y. , and Falzarano, J. M. , 2017, “ A Note on the Conclusion Based on the Generalized Stokes Theorem,” J. Offshore Eng. Technol., in press.
Liu, Y. , and Falzarano, J. M. , 2017, “ Improvement on the Accuracy of Mean Drift Force Calculation,” ASME Paper No. OMAE2017-62321.
Lee, C. , 1995, “ WAMIT Theory Manual,” Department of Ocean Engineering, Massachusetts Institute of Technology, Cambridge, MA.

Figures

Grahic Jump Location
Fig. 1

Coordinate setting

Grahic Jump Location
Fig. 2

Coordinate setting for log singularity

Grahic Jump Location
Fig. 4

Shape of R0−ln(d−v) for 5 × 5 panel

Grahic Jump Location
Fig. 5

Shape of R0−ln(d−v) for 10 × 10 panel

Grahic Jump Location
Fig. 6

Shape of R0−ln(d−v) for 20 × 20 panel

Grahic Jump Location
Fig. 7

Added mass A15 versus frequency ωL/g

Grahic Jump Location
Fig. 8

Added mass A33 versus frequency ωL/g

Grahic Jump Location
Fig. 9

Added mass A55 versus frequency ωL/g

Grahic Jump Location
Fig. 3

Shape of R0−ln(d−v) for 2 × 2 panel

Grahic Jump Location
Fig. 26

Added mass A55 versus frequency ωL/g

Grahic Jump Location
Fig. 27

Perspective view of boxbarge

Grahic Jump Location
Fig. 28

Added mass A11 versus frequency ωL/g

Grahic Jump Location
Fig. 10

Damping B11 versus frequency ωL/g

Grahic Jump Location
Fig. 11

Damping B33 versus frequency ωL/g

Grahic Jump Location
Fig. 12

Damping B55 versus frequency ωL/g

Grahic Jump Location
Fig. 13

Surge drift force versus frequency ωL/g

Grahic Jump Location
Fig. 14

Pitch drift force versus frequency ωL/g

Grahic Jump Location
Fig. 15

Perspective view of miniboxbarge

Grahic Jump Location
Fig. 16

Added mass A51 versus frequency ωL/g

Grahic Jump Location
Fig. 17

Added mass A75 versus frequency ωL/g

Grahic Jump Location
Fig. 18

Added mass A11-7 versus frequency ωL/g

Grahic Jump Location
Fig. 24

Added mass A15 versus frequency ωL/g

Grahic Jump Location
Fig. 25

Added mass A33 versus frequency ωL/g

Grahic Jump Location
Fig. 19

Damping B57 versus frequency ωL/g

Grahic Jump Location
Fig. 20

Damping B33 versus frequency ωL/g

Grahic Jump Location
Fig. 21

Damping B55 versus frequency ωL/g

Grahic Jump Location
Fig. 22

Perspective view of two miniboxbarges (separation 10 m)

Grahic Jump Location
Fig. 23

Added mass A11 versus frequency ωL/g

Grahic Jump Location
Fig. 49

Sway FKD force versus frequency ωL/g

Grahic Jump Location
Fig. 50

Pitch FKD force versus frequency ωL/g

Grahic Jump Location
Fig. 51

Perspective view of BOB hope–BOBO (separation 3 m)

Grahic Jump Location
Fig. 29

Added mass A15 versus frequency ωL/g

Grahic Jump Location
Fig. 30

Added mass A22 versus frequency ωL/g

Grahic Jump Location
Fig. 31

Added mass A24 versus frequency ωL/g

Grahic Jump Location
Fig. 32

Perspective view of cylinder dock

Grahic Jump Location
Fig. 33

Added mass A11 versus frequency ωL/g

Grahic Jump Location
Fig. 34

Added mass A51 versus frequency ωL/g

Grahic Jump Location
Fig. 35

Damping B11 versus frequency ωL/g

Grahic Jump Location
Fig. 36

Damping B15 versus frequency ωL/g

Grahic Jump Location
Fig. 37

Perspective view of BOB hope

Grahic Jump Location
Fig. 38

Added mass A11 versus frequency ωL/g

Grahic Jump Location
Fig. 39

Added mass A13 versus frequency ωL/g

Grahic Jump Location
Fig. 40

Added mass A33 versus frequency ωL/g

Grahic Jump Location
Fig. 41

Added mass A55 versus frequency ωL/g

Grahic Jump Location
Fig. 42

Heave drift force versus frequency ωL/g

Grahic Jump Location
Fig. 43

Pitch drift force versus frequency ωL/g

Grahic Jump Location
Fig. 44

Perspective view of BOBO

Grahic Jump Location
Fig. 45

Added mass A11 versus frequency ωL/g

Grahic Jump Location
Fig. 46

Added mass A33 versus frequency ωL/g

Grahic Jump Location
Fig. 47

Added mass A55 versus frequency ωL/g

Grahic Jump Location
Fig. 48

Damping B11 versus frequency ωL/g

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In