RD-Ri148 030 MOTION ANALYSIS OF A SEMII-SUBMIERSIBLE PLATFORM(U ) DAVID i/iW TAYLOR NAVAL SHIP RESEARCH AND DEVELOPMIENT CENTERBETHESDA MID SHIP PERFORMANCE DEPT Y S HONG OCT 84
UCASIFIED DTNSRDC/SPD-ii 2-81 F/6 26./4EEEEE son h2 EmmohiEsouuuuu..rn..rn
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MICROCOPY RESOLUTION TEST CHARTNATIOAL BUREAU OF STANDUM-S1963-A
DAVID W. TAYLOR NAVAL SHIP 'J"/\
RESEARCH AND DEVELOPMENT CENTERBethesda, Mawyland 20064
MOTION ANALYSIS OF A SEMI-SUBMERSIBLE PLATFORM
o by0 YOUNG S. HONG
APPROVED FOR PUBLIC RELEASE: DISTRIBUTION UNLIMITED
SHIP PERFORMANCE DEPARTMENT
id*J
_jOCTOBER 1984 DTNSRDC/SPD-1122-01
WW-TWRC m aM)84 11 29 027bupwwds 39MMV
MAJOR DTNSRDC ORGANIZATIONAL COMPONENTS
DTN8RDC
COMMANDER 0TECHNICAL DIRECTOR
01 1
OFFICER-IN-CHARGE IFIE-NCAGCARDE ROCK ANNAPOLIS
06 04
SYSTEMSDEVELOPMENTDEPARTMENT
SHIP ERFORANCEAVIATION AND
SHIPARFOMANCE SURFACE EFFECTS
iEAsMN DEPARTMENT 6
STRUCTURES] f COMPUTATION,DEPARTMENT MATHEMATICS AND
17 J LOGISTICS DEPARTMENT_____17_______ is
SHIP ACOUSTICS 1 ___ ___I PROPULSION ANDDEPARTMENT AUXILIARY SYSTEMS
19 DEATET27
SHIP MATERIALS I__ _ _CENTRALENGINEERING I INSTRUMENTATIONDEPARTMENT 28 DEPARTMENT 2
NDW-OThURDC mWMi (240
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DTNSRDC/SPDi 122-01 #4k6 004. TITLE (4nd SubtItle) S. TYPE OF REPORT & PERIOD COVERED
Motion Analysis of A Semi-Submersible PlatformS. PERFORMING ORG. REPORT NUMBER
S 7. AurmOR(a) S. CONTRACT OR GRANT NUMBER(@)
Young S. Hong
9. PERFORMING ORGANIZATION NAME AND ADDRESS 10. PROGRAM ELEMENT, PROJECT. TASKCAREA & WORK UW4IT NUMBERS
David Taylor Naval Ship Research and Development Work Unit 1500-001Center (Code 1562) Bethesda, ED 20084
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19. KEY WORDS (Continue an reverse aide f neceeal, &Wd Identify by block nmmber)
-Semi-Submersible; Motion Analysis;
20. ABSTRACT (Continue an reverse aide it necessary and Idenify by block numbe)
The Motions of a semi-submersible platform are computed for three differentheadings relative to the waves. This was done as part of a study establishedto compare various methods of semi-submersible platform motion predictionorganized by the ITTC Ocean Engineering Committee. A strip met'hod is appliedin the numerical analysis. The results of this analysis are presented alone,that is, no comparisions are made with other theoretical methods or experi-mental data. This can be done when the ITTC Committee publishes the results
DD I OR7 1473 EDITION OF I NOV 5U1S OGOLETC UNCLASSIFIEDSIN 002.L-0146601SECURITY CLASSIFICATION OP THIS PAGE (When Date Entered)
SICURITY CLASSIFICATION OF THIS PACM (When Date Entoiod)
of all participants of this study. The results of-heave motion show a
*resonance when the wave period is about 3.335 seconds.
A cCeSs'iO jor
I-TlS GRA&I1-,ic TAB
3ustif icatio
IDiStributi~/-
* '7iv~abilty Codes
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UNCLASSIFIEDsaCuRIVV CLASSIFICATION OFVMHIS PA~GI~rmo Doma amQ
TABLE OF CONTENTSmae
ADMINISTRATIVEIORMA TIO .. . .. .. . .. . . ... 1
I NTRODUCTION e * o * e . . . . . . . * * * * * * * 1
EQUATIONS OF MOTION .. . ... .. . .. .*. . .. . . 1
NUMERICA METODAD RESULSLT. .. .. .. . . . . ... 4
REFERENCES e e e . a e * . s e e a 5
LIST OF TABLES
1- Principal Dimenns......... 6
2 -Locations of ections ........ 7
LIST OF FIGURES
I Cordinate System ..........
2-Plan Vw f Ptform......... 9
3-Starboard Viewvof Platform...... ~~ 10
4 -Forward View of Platform . 11
5-Amplitude of Surge Motion .e e.e e*e12
6 - Amplitude of SwayMotion ..... .~. 13
7 7-Amplitude of Heave Motion a.... & .&...... 0a 14
8 - Amplitude of Roll Motion 9e e *9eeae *.*e a.*.e e *17
9 -Amplitude of Pitch Notion 9e *e aeae*e@ e e e 18
10- Amplitude of Yaw Motion e....eec. 20
11 - Phase Angle of Surge Notion * 21
12- Phase Angle of Say ottoe ae~ 23
LNPLSi
* ~13 -Phase Angle of Heave motion *s** 25
14 -Phase Agle of RollNotion. ... e . 28
15 -Phase Angle of Pitch Mtion *.e4 e.*see@*.. 30
16-Phase Angle of Yawotion ........ 32
" W ll II I
NOTATION
A Amplitude of incoming wave
Awp Waterplane area
Ajk Added mass coefficients
Bjk Damping coefficients
Cjk Hydrostatic coefficients
fj Exciting force
g Gravitational acceleration
i = (-1)1/2 Imaginary unit
Ij Moments of inertia (roll, pitch and yaw)
GML Longitudinal metacentric height
GMT Transverse metacentric height
K = wo2/g Wave number of incoming wave
mjk Mass matrix
M Mass of the platform
Mwp Moment of waterplane area
nj Components of unit vector directed into the fluid
xc Longitudinal location of center of flotation
Xg Longitudinal location of center of gravity
Zg Vertical location of center of gravity
P Water density
A Displacement of platform
B Angle of incoming wave in the xy-plane positive clockwise(present computer program notation)
X Angle of incoming wave in the xy-plane positive counterclockwise(ITTC notation)
Frequency of wave encounter
Wo Wave frequency
tiI
* Total velocity potential
Potential of incoming wave
*B Disturbance velocity potential due to the presence of theplatform
*j Velocity potential due to motion of the platform with unitamplitude in each of six degrees of freedom
Ej Amplitude of motion in each of six degrees of freedom(surge, away, heave, roll, pitch, and yaw)
'7 Diffraction potential
A In Figures 5 through 16, the following notation is used:
T Wave period
CA Free-surface wave elevation
XA Surge amplitude of motion
YA Sway amplitude of motion
ZA Heave amplitude of motion
bA Roll amplitude of motion
8A Pitch amplitude of motion
*A Yaw amplitude of motion
Phase angle of motion (erO: maximum positive motion occurs
when wave crest is amidship.)
II'OL
ABSTRACT
The notions of a semi-submeruible platform are computed for threedifferent headings relative to the waves. This was done as partof a study established to compare various methods of semi-submersible platform notion prediction organized by the ITTCOcean Engineering Committee. A strip method is applied in thenumerical analysis. The results of this analysis are presentedalone, that is, no comparisions are made with other theoreticalmethods or experimental data. This can be done when the ITTCCommittee publishes the results of all participants of thisstudy. The results of heave motion show a resonance when thewave period is about 3.35 seconds.F,
ADININSTRATIVE INFORMATION
This study was performed under the Department Overhead Function.The Work Unit number is 1500-001.
INTRODUCTION
The 17th ITTC Ocean Engineering Committee, which met in the Autumn 1982 atTokyo, decided to sponsor a comparative study oi the motions of a semi-submersible. The primary purpose of this study is to compare existing com-putational methods and to validate their results. An opportunity was thusprovided to further validate the computer program currently used by the SpecialShips and Ocean Systems Dynamics Branch at the David Taylor Naval Ship Researchand Development center.
The platform configuration to be used for the study was selected bythe ITTC Committee, and its description is given later in this report.The existing computer program was developed for semi-submersible platforms,with strip theory being applied as described in Reference 1.*
EQUATIONS OF MOTION
The coordinate system, oxyz, is fixed at the midship section of the semi-submersible platform (see Figure 1). The oz-axis is directed verticallyupward, and the oxy-plane is in the plane of the undisturbed free surface.
The total velocity potential of the fluid in the presence of the platformis expressed as
*(x,y,z,t) - Re[(¢ 1 + ¢B)eiwt()
*References are listed on page 6.
where *1 is the potential of the incoming wave and is given asigA
- -- exp[Kz + iMxcosO - iKysinO] (2)WO
and *B is the disturbance velocity potential due to the presence of theplatform. In Equation (2), A is the amplitude of the incoming wave, wo is itsfrequency, g the gravitational acceleration, 0 the angle of the incomingwave relative to the ox-axis (0 - 0 deg is following seas and 0 - 180 deg ishead seas), and K - wo2/g is the wave number. The disturbance potentialconsists of the following velocity potentials
¢B - 17 + EEJ J (3)
where *j (j - 1, 2, ... , 6) is the velocity potential arising from unitamplitude of platform in each of the six degrees of freedom, andEj (j - 1, 2, ... , 6) is the amplitude of motion in each of the six degrees offree tom. The diffraction potential is represented by *7.
The potential *j is determined as the solution of the Laplace equationwith appropriate boundary conditions. To avoid the difficulty in solving athree-dimensional numerical problem, a strip theory or two-dimensionalmethod is applied to obtain *j. The fundamental assumptions of strip theoryare discussed in Reference 2.
Using strip theory, *j is solved for j - 2,.3, 4, and 7 (sway, heave,roll motion and diffraction potential) at each section, and potentials forpitch and yaw are computed by simply multiplying the longitudinal distance ofeach section from the origin by the heave and sway potentials respectively.The surge potential, *1, is assumed to be zero.
In applying potential theory, it is assumed that the fluid is incQmpres-sible and inviscid, and that the flow is irrotational. The potential, *j(j - 2, 3, 4, and 7) is determined as the solution of the following equationwith the conditions specified.
1. Laplace equation in the fluid domain
a2*j1. a2*j- + - - 0, for j - 2, 3, 4, 7 (4)
ay 2 8z2
2. the body boundary condition
-P -iwnj, forj - 2, 3,4 (5)an
a01-_ for j - 7
an
2
*. & -- . a 4 - = -,- JT= =
. 3. the linearized free-surface condition
ajSjl j-- -0 , on z - 0 for J-2, 3, 4, 7 (6)
3z
The right hand side of Equation (5) is the normal velocity component at thebody and the unit vector is directed into the fluid domain. All potentialfunctions, *1, must satisfy the radiation condition for outgoing progeessivewaves at infinity, and become zero as z becomes negative infinity.
The solution of Equation (4) with the boundary conditions, Equations (5)and (6), is given in Reference 3. The hydrodynamic forces and moments areobtained by integrating the pressure on the wetted surface of the' body. Thedetails of the derivation of these forces and moments for heave and pitchmotions are given in Reference 4. The forces and moments for other motions canbe easily derived using a procedure similar to that described in Reference 4.
If we let a - e- i dt and equate the inertia force with the hydrodynamicforce, the equation ol motion can be expressed as
Z[(mjk + Ajk)aj + Bjkaj + CJkaJ] - fj (7)
where !Jk is the mass matrix, A k the added mass, Bjk the damping force, Cjkthe hydrostatic coefficients ani fj the exciting force. The equations for Ajk,Bjk, and fj are given in Reference 4. The mass matrix, mjk, is expressed as
mjk - M, for J - k - 1, 2, 3
m44 - 14
m5 5 - 15
=66 16 (8)
m24 - m42 - -Mzg
m15 - 251 - MZg
all other =Jk - 0
where M is the mass of the platform; 14, 15, and -16 roll, pitch and yaw momentsof inertia, and Zg is the vertical location of the center of the gravity withrespect to free surface. The hydrostatic coefficent, Cjk, is given as
C33 - pgAp
C3 5 - C5 3 - -Pg(Mwp - xgAwp)
C4 4 - AGMT (9)
C5 5 - AGML + PgAwp(xg - xc)2
all other Cjk - 0
3
I' where AWp is the waterplane area, M,1 its moment, xg the longitudinal centerof gravity, xc the longitudinal center of flotation, GMT the transversemetacentric height, QHL the longitudinal metacentric height, and A thedisplacement of the platform.
NUMERICAL METHOD AND RESULTS
The model description is given in Figures 2, 3, and 4, and its principaldimensions are given in Table 1. In the numerical analysis, only 8 verticalcolumns and lower hulls are included in the computation. The transverse,longitudinal and diagonal columns are small compared to the vertical columns,and therefore, are excluded from the computation.
The platform is divided into 29 sections in the longitudinal direction.At each section, the hydrodynamic forces (added mass, damping force and excitingforce) are computed, and later these sectional forces are integrated along thelength. There are 17 sections with lower hulls only and 12 sections with lowerhulls and columns. The sections with lower hull only are treated as completely
'S. submerged sections and those with hull and column are treated as floating
sections. The locations and types of sections are given in Table 2.The computations have been carried out for three different headings: 8 - 0
(following), 8 - 315 (x - 45), and 8 - 270 (X - 90). The heading angle of theincoming wave in the oxy-plane is taken positive counterclockwise by theITTC Committee, while this angle is taken positive clockwise in the existingcomputer program. Therefore, the relationship between X and 8 is: X + 0 - 360.A step increment of wave period of 0.2 seconds was used for periods between0.5 and 10 seconds. Wherever there is resonance in the motion, smaller timetime increments were used. Furthermore, it has been assumed that the waterdepth is infinite even though it was given as 3 m by the ITTC Committee.This assumption is necessary because the present computer program is applicableonly for the deep water. The computer program can be easily extended to treatthe case of finite water depth.
The results are plotted in Figures 5 through 16. Since the experimentalor numerical results produced by the other participants are not available atthe present time, only the results computed by the author are shown in the figures.
ACKNOWLEDGEMENT
The author thanks Dr. W. B. Morgan, the Head of the Ship PerformanceDepartment, for his support in carrying out this project. The author alsowishes to thank Mr. A. Gersten for his editorial advice.
4
4i
REFERENCES
1. Paulling, J.R., Hong, Y.S., Chen, H.H., and Stiansen, S.G., "Analysis of'C Semi-submersible Catamaran-type Platforms," OTC 2975, Offshore Technology
Conference, Houston, Texas 1977.2. Salvesen, N., Tuck, E.O., and FaltInsen, 0., "Ship Motions and Sea Loads,"
SNAME Trans., vol. 78, 1970.3. Frank, W., "Oscillation of a Cylinder In or Below the Free Surface of Deep
Fluids," DTNSRDC Report No. 2375, Oct. 1967.4. Hong, Y.S., "Prediction of Motions of SWATH Ships in Following Seas,"
DTNSRDC Report No. DTNSRDC-81/039, Nov. 1981.
A53'.'
Table 1 : Principal Dimensions
Length of lower hull, L 1.797 aBeam (total) 1.172 mBeam (one hull) 0.234 mHull spacing between centerlines 0.938 aDraft 0.313 aCenter of gravity LCG at the midship
TOG at the center lineKG 0.281 a
Metacentric height GHL 0.037 mGMT 0.046 a
Radius of gyration Roll 0.536 aPitch 0.556 aYaw 0.634 u
Displacement in fresh water 230.3 NWater depth infiniteWave direction 0 360, 313, 270
x 0, 45, 90
1 6
V! V Ii ~. .- ~ ' *
Table 2: Locations of Sections
x (meter) Section Type NO. of Input Points
1 (AP) -0.8975 0 02 -0.8400 Lower Hull 193 -0.7815 194 -0.6665 195 -0.6145 Lower Hull + Column 276 -0.5625 257 -0.5105 278 -0.4585 Lower Hull 199 -0.3650 19
10 -0.2715 1911 -0.2285 Lower Hull + Column 2712 -0.1875 2713 -0.1465 2714 -0.1035 Lower Hull 1915 0.0 1916 0.1035 1917 0.1465 Lower Hull + Column 2718 .0.1875 2719 0.2285 2720 0.2715 Lower Hull 1921 0.3650 1922 0.4585 1923 0.5105 Lower Hull + Column 2724 0.5625 2525 0.6145 2726 0.6665 Lower Hull 1927 0.7815 1928 0.8400 1929 (FP) 0.8985 0 0
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DTNSRDC ISSUES THREE TYPES OF REPORTS
1. DTNSRDC REPORTS, A FORMAL SERIES, CONTAIN INFORMATION OF PERMANENT TECH-NICAL VALUE. THEY CARRY A CONSECUTIVE NUMERICAL IDENTIFICATION REGARDLESS OFTHEIR CLASSIFICATION OR THE ORIGINATING DEPARTMENT.
2. DEPARTMENTAL REPORTS, A SEMIFORMAL SERIES, CONTAIN INFORMATION OF A PRELIM-INARY, TEMPORARY, OR PROPRIETARY NATURE OR OF LIMITED INTEREST OR SIGNIFICANCE.THEY CARRY A DEPARTMENTAL ALPHANUMERICAL IDENTIFICATION.
3. TECHNICAL MEMORANDA, AN INFORMAL SERIES, CONTAIN TECHNICAL DOCUMENTATIONOF LIMITED USE AND INIEREST. THEY ARE PRIMARILY WORKING PAPERS INTENDED FOR IN-TERNAL USE. THEY CARRY AN IDENTIFYING NUMBER WHICH INDICATES THEIR TYPE AND THENUMERICAL CODE OF THE ORIGINATING DEPARTMENT. ANY DISTRIBUTION OUTSIDE DTNSRDCMUST BE APPROVED BY THE HEAD OF THE ORIGINATING DEPARTMENT ON A CASE-BY-CASEBASIS.
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FIGURE 10 AMPLITUDE OF YAW MOTION AT )C-45 0 m m ----------------20
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