,.;yc0
1-'sI.
DiVISION OF ORT AND OCEAN ENGINEERING
THE UNIVERS1TY OF TRONDHEIM Lab.
v. ScheepsbouwIctjnd
THE NORWEGIAN !NSTITUTE OF TECHNOLOGechnische
Hogeschooi
N-7034 TRONDHE!M - NTH. NORWAY
Dr. P. Kaplan Oceanics, Inc
Technical. Industrial Park
Plainview New York 11803 U.S.A. SI 0 ¼_ : Dear Paul, ISSC - REPORT 76
According to your letter dated August 2, 1974 I should write about loads on offshore units and on internal loads.
I have written about loads on offshore units, primarily on floating
units. My plan was to use my ONR-paper in Boston to write about
internal loads. This paper gives a survey over the subject . But two of my coautbors on that paper are members of committee 11.3 Slamming and Impacts. That is dr. Abramson and Mr. Olsen.
I have just seen their contribution to the report of Committee 11.3 and it is very much extracted from the ONR-paper. I see no meaning in duplicating their work and a compeUn with another group. So I
suggest we drop the business about internal load in our Committee. With regard to model experiments in Norway most of the work is
con-fidential. I may mention the work I did together with Michelsen, which I have ref erzwto in my report.
I will be in USA to the end of May so it will be difficult for me to attend any meeting in Europe before that time.
Bes regards
Odd Faltinsen
P.S. I have enclosed a comment to S3dings contribution
cc: Members of ISSC Committe I 2
Associate Professor 0. Faltinsen
Deift
PHONE (075) 30100
EXT. 150 - 453
- El I March 11, 1975
0. FALTINSEN
WAVE LOADS ON OFFSHORE UNITS
It is usual to catagorize the offshore units as large-volume
structures and small-volume structures..
With large-volume structures we mean structures. with character-istic dimensions large compared with a charactercharacter-istic length of
the waves. For a vertical circular cylinder in indident regular waves, standing on a horizontal sea floor and penetrating the free surface, it is common to say that the structure is large when the wave length A of the incident waves is smaller than five times the diametre D of the cylinder. For a large-volume structure the wave-field will be significantly changed due to ths structure and the calculation
cannot
be based on a simpleMorison equation type calculation (Morison et al (1)).
Examples on large-volume structures are ships, gravity platforms and floating harbors. The calculation of wave loads in regular waves on offshore Units of the ship type, for instance
pipe-laying barges and driliships, can be performed by strip theory. The strip theory seems to give quite good results even for
small length CL) to beam (B) ratios. Gerritsma, Béukelman and Glansdorp (2) have presented comparisons for L/B - ratios down
to 4. But to our knowledge there exists no systematic
examina-tion for how small L/B- ratios the strip theory can be used. However, it should be mentioned that Kim and Chou (3) have got satisfactory results for the heave and pitch motions for a L/B- ratio equal to 1.5 by arranging the strips in the length-wise direction. Faltinsen and Michelsen (4) show that strip-theory and a three-dimensional strip-theory are not in agreement for a L/B- ratio equal to 1.0. Their theoretical results are
Faltinsen and Michelsen is a generalization of the Frank Closef it method (Frank (5)) which is wellknown in 2-dimensional problems.
The method consists in finding a Green's function satisfying the three-dimensional Laplace equation, harmonic oscillations, the classical linear free surface condition, radiation condition and bottom condition. Green's functions with singularities at the wetted surface of the body are then distributed over the wetted
surface so that the body boundary condition is satisfied.
Garison (6) has also used the same kind of method for floating
structures. One drawback of the method is the possibility of irregular frequencies, which mean frequencies where the method give no solution. This, kind of phenomena is well-known for
2-Dimensional problems (Frank (5)). But usually the irregular. frequencies are above the frequency range of interest. The method and a similar kind of method which consists in placing the singularities inside the body, have been and are extensively used in connection with calculation of wave loads on fixed
large-volume structures and give very good results compared with experiments. See for instance Garison and Rao (7), van Oortmersen (8) and Hogben and Standing (9).
Bai and Young (10) have presented two other. methods which may be used to solve the wave load problem. It is a finite element
variation method and a fundamental-singularity distribution method where Green's theorem is applied using merely the source.
function for an unbounded fluid. K. Kokkinowrackos and
H. Wilchens (11) have presented a theoretical method to. calcu-late wave loads and motions of objects composite of large verti-cal cylindriverti-cal members. The method is based on the theory
-3-a method to c-3-alcul-3-ate hydrodyn-3-amic forces on horizont-3-al -3-and vertical multiple cylinders.
To predict responses of large-volume structures in irregular waves the common approach applied for ships can usually be
applied. But resonance oscillations can be excited due to nonlinearities in the wave-structure interaction, which render the linear superposition principle invalid.
This may for instance be the case for surge, sway and yaw oscil-lations of a moored structure (Remery and Hermans (13)), and for the heave, pitch and roll oscillations of a
low-waterplane-area 1arge-V3ltzme structure. This kind of phenomena is most likely to be explained by a complete second order theory.
Further research in this area is highly needed. The oscillat-ions are slow so even if the excursoscillat-ions are large the accelera-tions need not be large. So there is a hope that the intergrat-ed horizontal loads might be reasonably printergrat-edictintergrat-ed by 1. order
-theory even if the slow resonance oscillations occur.
The calculation of wave loads on small-volume structures are
in principle much more simple than the calculation of wave loads on large-volume structures. One may use the Morison's equation and/or the more general formula derived for instance by Hooft (14). Hoof t's expression is based on potential theory
and for the very small structures dragforces have to be
consid-ered. A semisubmersible is considered to be a small-volume
structure. The reason is that the cross-dimensions of the structural members are.smal]. compared with the wave lengths of
interest. Usually dragforces are not important in the calcula-tion of wave loads on semisubmersibles. The rather simple formulas used in the wave force calculation are based on strip
theory for each submerged member and Hoof t's expression (14)
together with a straight-forward correction for the
Froude-Kriloff force at joints between submerged structural
members. But this kind of calculation give often good agree-ment with experiagree-mental values of motions. For recent surveys see Hooft (15) and St. Denis (16).
Paulling (17) and Pedersen, Langfeldt and Egeland (18) have shown two different ways how to use the wave loads in a struc-tural model for a semisubmersible. Both methods are based on the linear superposition principle Paulling finds transfer functions for, stresses while Pedersen, Langfeldt and Egeland
response simulate the wave load distribution and find the .structura]Yfor consecutive time instants and then perform a statistical analysis.
For structure members and structures like jackets where dragforces are important the linear superposition principle
become invalid. The drag force calculation are based on empiri-cal data and as average drag coefficient corresponding data for cylinders in uniform stream are usually applied. To our knowledge no analytical method exist. When dragforces are important one should be aware of the vortex-shedding, which
-5-REFERENCES
Morison, J.R., O'Brien, M.P., Johnson, J.W. and Shaaf, S.A.:
"The Forces Exerted by Surface
Waves on Piles"; Transactions
American Petroleum Institute, Vol. 189,
No. 2846, 1950.
Gerrjtsrna, J, Beukelman, W. and Glansdorp,
C.C.:
"The Effects of Beam
on the Hydrodynamic Characteristics of
Ship Hulls", Tenth Naval Hydrodynamics
Syinposituzn,ONR,
Boston, 1974.
Kim, Ch. and Chou, P.: "Hydrodynamic
Characteristics of barges",
Offshore Technology Conference,
Houston 1971.
Faltinsen, 0. og Michelsen, F.C.: "Motion of Large Structures in
Waves at Zero Froude Number", International Symposium on The
Dynamics of Marine Vehicles and Structures
in Waves,
University College
London 1974.
Frank,W.: "Oscillation of Cylinders in
or below the Free Surface
of Deep Fluid", Naval Ship Research
and Developtment Center,
Washington D.C., Report 7375, 1967.
Garrison, C.J.: "Dynamic Response of Floating Bodies", OTC 2067,
Offshore Technology Conference,
Houston, 1974.
Garrison, C.J. og Rao,
:"Interactions of waves with submerged
objects", J. Waterways, Harbours, Coastal Engineering Div.,
ASCE, 97, 1971
Van Oortmersen, G.: "Some Aspects of
very large Offshore
Structures", Proc. ONR Ninth Symposium
on Naval Hydrodynamics,
Hogben, N. and Standing, R.G.: "Wave Loads on Large Bodies", International Symposium on The Dynamics of Marine Vehicles
and Structures in Waves,.tiniversity College London 1974.
Bai, K.J. and Young, R.W.: "Numerical Solutions to
Free-Surface Flow Problems". Tenth Naval Hydrodynamics Symposium, ONR, Boston, 1974.
Kokkinowrachos, K. and Wilckens, H.: "Hydrodynamic Analysis of Cylindrical Offshore Oil Storage Tanks". OTC 1944,
Offshore Technàlogy Conference 1974,
Garrett, C.J.R.: "Wave Forces on a Circular Dock", Journal of Fluid Mechanics, 1971, Vol. 46, Part 1, pp 129-139.
Remery, G.F.M. and Hermans, A.S.: "The slow drift oscillations of a moored object in random seas". Soc. Petroleum Engs. J., 1972, 12, No. 3.
Hoof t, Y.P.: "Hydrodynamic Aspects of Semi-submersible Platforms", Doctoral Thesis at The University of Deift,
H. Veenman en zonen N.y. - Wageningen, 1972.
Hoof t, J.P: "Motions of Stationary Structures", International.
Symposium on The Dynamics of Marine Vehicles and Structures in Waves, University College London 1974.
.6. M.St. Denis: "On the Motions of Oceanic Platforms",
International Symposium on The Dynamics of Marine Vehicles and Structures in Waves, University College London 1974.
-7-Paulling, J.R.: "Elastic.Response of Stable Platform Structures", International Symposium on The Dynamics of Marine Vehicles and Structures in Waves, University College London 1974.
Pedersen, B., Egeland, 0. og Langfeldt, J.N.: "Calculation of long-term values for motions and structural response of mobile drilling rigs". Offshore Tech. Conf. 1973.
Wiegel, R.L.: "Ocean Wave Spectra, Eddies and Structural Response", Symposium on Flow-Induced Structural Vibrations, Karlsruhe, Germany, 1972.
Okhusu, M.: "Hydrodynamic Forces on Multiple Cylinders in Waves",
International
Symposium on The Dynamics of Marine Vehicles andCOMMENTS TO SöDING'S CONTRIBUTION
S3ding says in his chapter about calculation of the 2-dimensional added mass and damping coefficients that the Frank Closefit
method requires much more computing effort than the Lewis form
technique. This is not completely true. If we compare the computer time by the two methods for the calculation of both the added mass and damping and the pressure then there is not any significant difference in computer time (See KolbjØrn
Johannesen: "A Study of.Two-Dimensional Added Mass and Damping", Report No. 74-14-S. Det norske Veritas, Oslo, 1974).
S3ding also states that the Frank Closeft method does not always give reliable results. I assume he means the difficulty with the irregular frequencies. But I have very good experience using the fairing technique described in 0. Faltinsen, "A study of the two-dimensional added-mass and damping cOefficients by the Frank Closefit method". Det norske Veritas, Oslo, Norway. Report No 69-43-S. 1969. This fairing technique increases the computer time, but I do not consider the computer time to be any problem for a 2-Dimensional problem. To apply the same kind of fairing technique to a 3-DImensional problem might be a problem from a computer time point of view.
SZding refers to the second order method by Potash, who uses
a similar approach as the FrankC1osefit method. But in this second
order problem the irregular frequencies seem to be a problem because they might be more in the frequensy range of interest than is the case for the 1 order problem.If it is possible to make a fairing of the result for the second order problem has
to be examined more closely.
Söding favours the Ogilvie and Tuch method. I agree in his argument that it is based on a sounder theoretical basis then the other methods. But it should be mentioned that it is for forced heave and pitch motions only.. It does not present a
rational method to calculate exciting force and moment, and it does not calculate loads and the other fundamental motions. The same approach can in some cases be used for the forced
motion of the other fundamental motions. But it should be kept in mind that the rational basis for the theory is a high.
frequency assumption. I think it should be stressed that
the
Ogilvie and Tuch method is basically a three-dimensional
method where two-dimensional results are used.
I have tried to use the same rational approach as Ogilvie and Tuch to calculate exciting force and moments in head sea
(0. Faltinsen "Wave Forces on a Restrained Ship in Head-Sea
Waves", Proceedings of the Ninth Symposium on Naval Hydrodynamics,
Paris, 1972). The theory is still not complete, but it predicts quite good values of the pressure distribution away from the bow and in the high frequency range. Ogilvie is presently
working with fixing up the solution in the bow region and it is
planned that Ogilvie, tjrsell and I shall continue working on
this problem next year. This work is especially important for the springing. i think this approach should be mentioned in
the ISSC report.
S6ding says that large differences between calculations and model experiments are encountered for loads associated with swaying and yawing motions. This should be documented.
10
-It should be mentioned that there is difficulties with surging motion in following sea when the frequency of encounter go to
zero.
Söding. says that the inclusion of nonlinear terms in strip
theories seems to be no problem. I am not sure that this is the case for irregular sea and any wave, direction.
