Appendix A
DESCRIPTION OF TEST RUNS

WAMIT V7.0 includes 37 standard test runs, including 12 low-order and 25 higher-order applications. These are designed to illustrate various different options and features of WAMIT, and to help users to develop appropriate input files for their own purposes.

The following table gives relevant features of each test run. In this table the first column tst denotes the name of the test run. All of the corresponding input/output files are assigned the filenames TESTtst. (For example, the input POT file for the first test run listed below is TEST01.POT.) The first character of tst is 0 for low-order test runs (ILOWHI=0), and 1 for higher-order test runs (ILOWHI=1). Test runs which are identical except for different input options are assigned the same number with a letter suffix. For example, TEST11 and TEST11a-c describe the same physical problem using different options to represent the geometry (B-splines, exact analytic formulae, MultiSurf, uniform and nonuniform mapping). In TEST14, the ISSC TLP is analysed and the use of the fixed mode option is illustrated. In TEST14a, the same geometry is analysed for a large number of input frequencies including zero and infinite frequencies and the outputs are postprocessed by the F2T utility. In TEST16 a rectangular barge is defined by the subroutine BARGE (IGDEF=-5), and in TEST16a the patches are defined by flat panels (IGDEF=0). Tests 17 and 17a-c illustrate alternative methods for analyzing a body with moonpools, as explained in Section A.17. Tests 01a, 09a, 13a and 22a are examples showing the use of trimmed waterlines (ITRIMWL=1). PICT PICT

        
tstdescription ILOWHIother parameters
01 Circular cylinder 0
01aCircular cylinder 0 ITRIMWL=1
02 Circular cylinder 0 IRR=3
03 Circular cylinder 0 ISOR=1
04 Barge near wall 0 IWALLy0=1
04aBarge in channel 0 CHANNEL_WIDTH=80.0
05 Cylinder & spheroid 0 NBODY=2
05aCylinder & spheroid 0 NBODY=2, ISx=1
06 ISSC TLP (coarse) 0 NPAN=128
07 ISSC TLP (fine) 0 NPAN=1012
08 Elastic column 0 NEWMDS=4
09 Spar with strakes 0 NPDIPOLE=(673 960)
09aSpar with strakes 0 ITRIMWL=1
11 Circular cylinder 1 IGDEF=1
11aCircular cylinder 1 IGDEF=-1
11bCircular cylinder 1 IGDEF=-1, INONUMAP=1
11cCircular cylinder 1 IGDEF=2
12 Circular cylinder 1 IGDEF=-1, INONUMAP=0, IRR=1
13 Cylinder & spheroid 1 NBODY=2
13aCylinder & spheroid 1 NBODY=2, ITRIMWL=1
14 ISSC TLP 1 IGDEF=-9
14a ISSC TLP 1 NPER=101, IPERIN=2
15 Semi-sub 1 IGDEF=-10
16 Elastic barge 1 IGDEF=-5, NEWMDS=8
16aElastic barge 1 IGDEF=0, NEWMDS=8
17 Cylinder & moonpool 1 IGDEF=-7,
17aCylinder & moonpool 1 IGDEF=-7, NEWMDS=2, IDAMP=0
17bCylinder & moonpool 1 IGDEF=-7, NEWMDS=2, IDAMP=1
17cCylinder & moonpool 1 IGDEF=-7, NMODESFSP=1
18 Elastic column 1 IGDEF=-1, NEWMDS=4
19 Catamaran barge 1 IGDEF=0
20 MultiSurf barge 1 IGDEF=2
20aMultiSurf barge in channel 1 IGDEF=2, CHANNEL_WIDTH=100.0
21 Spar with strakes 1 IGDEF=-12, NPDIPOLE = 2 4 6
22 FPSO with 2 tanks 1 IGDEF=-21, NPTANK=(8-11) (12-15)
22aFPSO with 2 tanks 1 ITRIMWL=1, XTRIM=(1.0, 0.0, 15.0)
22bFPSO with 2 tanks 1 ITRIMWL=1, XBODY(3)=-1.2
23 Bank of wavemakers 1 IGDEF=0, ISOLVE=-1, NEWMDS=8
24 Motions of a hinged vessel 1 IGDEF=-32, NEWMDS=4
25 ACV with two pressure chambers 1 IGDEF=0, NMODESFSP=2

In all of the test runs metric units are used, and the gravitational acceleration is set equal to 9.80665 meters-per-second2.

Each test run is described briefly in the following sections. Also included in these sections are perspective illustrations of the complete underwater geometry, including reflections about the indicated planes of symmetry, and abbreviated listings of the input files. For the low-order tests the perspective figures show the subdivisions into panels. For the higher-order tests two perspective figures are included, to show the subdivisions into patches (upper or left) and into panels (lower or right).

All of the required input files for each test run, and the labeled output file (*.out) are included with the WAMIT software provided to licensed users. The same files can be downloaded with the demonstration programs from the web site http:://www.wamit.com. The input files for PICT PICT Test Run tst are named with the filename ‘testtst’ followed by the extensions .gdf, .pot, and .frc. The corresponding files fnames and config are given the same filenames with the extensions .wam and .cfg.

The additional configuration file config.wam is included with the test files, and is intended to supplement the separate .cfg file for each test. The standard version of this file is as shown below: PICT PICT

! generic configuration file:  config.wam  
  RAMGBMAX=0.5  
  NCPU=1  
  USESRID_PATH=c:\wamitv7

The first line is a comment line which is ignored by the program. The parameters on the other lines are explained in Section 4.7.

Before running TESTtst, the user should copy the fnames files as follows:

as explained in Chapter 2. Alternatively, the batch file runtests.bat can be used to run all tests in succession. PICT PICT

A.1 TRUNCATED VERTICAL CYLINDER – TEST01

The added-mass and damping coefficients, exciting forces, motions, wave elevations, field pressures, field velocities and drift forces are evaluated for a freely floating truncated vertical circular cylinder of radius 1 meter and draft 0.5 meters, in infinite water depth for three wave periods and one wave heading.

The origin of the coordinate system is located at the intersection of the vertical axis of the cylinder and the undisturbed position of the free surface. Using two planes of symmetry, only the first quadrant of the surface of the cylinder is discretized with 256 panels. 16, 8, and 8 panels are distributed in the azimuthal, radial, and vertical directions with equal spacing. The characteristic length is set equal to the radius of the cylinder. The cylinder center of gravity is located at the origin of the coordinate system, and the radii of gyration relative to its axes are taken equal to 1 meter.

In TEST01A, the option to trim the waterline is specified with the parameters ITRIMWL and XTRIM included in the TEST01A.CFG file. The other input files are unchanged, but the filenames TEST01A.POT and TEST01A.FRC are used so that the output files will be named accordingly. The cylinder is rotated 15 degrees about the x-axis and elevated 0.27m, as shown in the lower figure below. The vertical elevation is required in this case since the gdf file only extends up to the original waterplane, and trimming in roll or pitch about the center without vertical displacement would submerge half of the waterline with a gap above it.


PICT PICT PICT PICT

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PICT PICT
 Input file:  fnames.wam  
test01.pot  
test01.frc  
test01.cfg  
 
 Input file:  test01.cfg  
! TEST01.CFG -- cylinder R=1, T=0.5, ILOWHI=0, IRR=0  
 ipltdat=5  
 ISOR=1       (omit ISOR in POT file, include source formulation)  
 ISOLVE=0     (use iterative solver)  
 ISCATT=0     (solve for total diffraction potential, not scattering)  
 ILOG=1       (omit ILOG in POT file, integrate log singularity)  
 IRR=0        (omit IRR in POT file, no irregular-frequency removal)  
 MONITR=0     (do not write FORCE output data to monitor)  
 NUMHDR=1     (write headers to numeric output files)  
 
 Input file:  test01.pot  
TEST01.POT -- cylinder R=1, T=0.5, ILOWHI=0, IRR=0  
 -1.       HBOT  
   1   1                          IRAD,IDIFF  
 3                            NPER (array PER follows)  
 8.971402 2.006403 1.003033   PER  
 1                            NBETA (array BETA follows)  
 0.                           BETA  
   1                          NBODY  
 test01.gdf  
 0. 0. 0. 0.                HBOT, XBODY(1-4)  
  1  1  1  1  1  1               IMODE(1-6)  
 
 First 10 lines of input file:  test01.gdf  
TEST01.GDF  --  circular cylinder, R=1, T=0.5, ILOWHI=0  
    1.000000       9.806650     ULEN, GRAV  
            1           1       ISX, ISY  
          256                   NEQN  
   0.0000000E+00  0.0000000E+00 -0.5000000  
   0.0000000E+00  0.0000000E+00 -0.5000000  
   0.1243981      1.2252143E-02 -0.5000000  
   0.1250000      0.0000000E+00 -0.5000000  
   0.1250000      0.0000000E+00 -0.5000000  
   0.1243981      1.2252143E-02 -0.5000000
PICT PICT

PICT PICT

 Input file:  test01.frc  
 TEST01.FRC  Circular cylinder, ILOWHI=0, IRR=0  
   1   1   1   1   0   3   0   2   1  
 0.000000                                    VCG  
 1.000000      .0000000      .0000000  
 .0000000      1.000000      .0000000  
 .0000000      .0000000      1.000000        XPRDCT  
 0                                           NBETAH  
 2                                           NFIELD  
 1.5  0.  0.  
 1.5  0. -0.5                                XFIELD  
  

PICT PICT

 
 Input file:  test01a.cfg  
! TEST01A.CFG -- cylinder R=1, T=0.5, trimmed waterline  
 ilowgdf=1  
 ipltdat=5  
 ISOR=1       (omit ISOR in POT file, include source formulation)  
 ISOLVE=0     (use iterative solver)  
 ISCATT=0     (solve for total diffraction potential, not scattering)  
 ILOG=1       (omit ILOG in POT file, integrate log singularity)  
 IRR=0        (omit IRR in POT file, no irregular-frequency removal)  
 MONITR=0     (do not write FORCE output data to monitor)  
 NUMHDR=1     (write headers to numeric output files)  
 ITRIMWL=1  
 XTRIM= 0.27 0.0 15.  
 
 Input file:  test01a.pot  
TEST01A.POT -- cylinder R=1, T=0.5, trimmed waterline  
 -1.       HBOT  
   1   1                          IRAD,IDIFF  
 3                            NPER (array PER follows)  
 8.971402 2.006403 1.003033   PER  
 1                            NBETA (array BETA follows)  
 0.                           BETA  
   1                          NBODY  
 test01.gdf  
 0. 0. 0. 0.                HBOT, XBODY(1-4)  
  1  1  1  1  1  1               IMODE(1-6)  
 
 Input file:  test01a.frc  
 TEST01A.FRC  Circular cylinder, trimmed waterline  
   1   1   1   1   0   3   0   2   0  
 0.000000                                    VCG  
 1.000000      .0000000      .0000000  
 .0000000      1.000000      .0000000  
 .0000000      .0000000      1.000000        XPRDCT  
 0                                           NBETAH  
 2                                           NFIELD  
 1.5  0.  0.  
 1.5  0. -0.5                                XFIELD  
  
PICT PICT

PICT PICT

A.2 IRREGULAR-FREQUENCY REMOVAL – TEST02

This test run illustrates the use of the irregular-frequency option described in Chapter 10. The geometry and most other inputs are the same as in TEST01. The parameter IRR=3 is set to use automatic panelization of the interior free surface. Wave periods are chosen so that the wave frequencies are near the first and second irregular frequencies of the cylinder. The direct solver (ISOLVE=1) is used since the iterative and block-iterative solvers do not converge reliably for the source formulation (ISOR=1).

The GDF input is the same as TEST01.GDF. The additional panels on the interior free surface, which are generated automatically by the program, are shown in red in the Figure below.


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 Input file:  test02.cfg  
!  TEST02.CFG -- Circular cylinder, ILOWHI=0, IRR=3, direct solver  
 ilowgdf=1  
 ipltdat=5  
 IRR=3  
 ISOR=1  
 ISOLVE=1  
 ILOG=1  
 MONITR=0  
 NUMHDR=1  
 
 Input file:  test02.pot  
 TEST02.POT -- Circular cylinder, ILOWHI=0, IRR=3  
 -1.       HBOT  
   1   1                          IRAD,IDIFF  
 2  
 1.182288    1.003025  
 1  
 0.0  
   1                          NBODY  
 test02.gdf  
  0.0  0.0  0.0  0.0  
  1  1  1  1  1  1  
 
 First 10 lines of input file:  test02.gdf  
TEST02.GDF  circular cylinder, R=1, T=0.5, ILOWHI=0, IRR=3,  
    1.000000       9.806650  
            1           1  
          256  
   0.0000000E+00  0.0000000E+00 -0.5000000  
   0.0000000E+00  0.0000000E+00 -0.5000000  
   0.1243981      1.2252143E-02 -0.5000000  
   0.1250000      0.0000000E+00 -0.5000000  
   0.1250000      0.0000000E+00 -0.5000000  
   0.1243981      1.2252143E-02 -0.5000000

PICT PICT

 
 Input file:  test02.frc  
 TEST02.FRC  -- Circular cylinder, ILOWHI=0, IRR=3  
   1   1   1   1   0   3   0   1   1  
 0.000000  
 1.000000      .0000000      .0000000  
 .0000000      1.000000      .0000000  
 .0000000      .0000000      1.000000  
 0  
 2  
 1.5 0.0  0.0  
 1.5 0.0 -0.5  
  

PICT PICT

A.3 LOCAL PRESSURE DRIFT FORCE – TEST03

This test run is used to illustrate the use of the source formulation (Section 5.2) to determine the mean drift force and moment from local pressure integration. The motions and the drift forces are evaluated for a freely floating truncated vertical circular cylinder of radius 1 meter and draft 1 meter, in a water depth of 7.14 meter for four wave periods and one wave heading.

The origin of the global coordinate system is located at the intersection of the vertical axis of the cylinder and the undisturbed position of the free surface. The origin of the body fixed coordinate system is shifted -0.515 meters under the free-surface. Using two planes of symmetry, the first quadrant of the surface of the cylinder is discretized with 288 panels. 12, 8, and 16 panels are distributed in the azimuthal, radial, and vertical directions with cosine spacing at the free surface and corner. The characteristic length is set equal to the radius of the cylinder. The cylinder center of gravity is located at the origin of the body coordinate system, and the radii of gyration relative to its axes are shown in the FRC file.

All three options (IOPTN 7,8,9) are included in the FRC file. For option 7, where the drift_     force and moment are evaluated from the method described in (Chapter 11), the control surface is a co-axial cylinder with radius and draft 2 meters as specified in the file test03.csf. In option 8 the horizontal drift force and vertical moment are evaluated based on the momentum at infinity, but this method cannot be used for the vertical force or horizontal components of the moment. In option 9 the mean pressure is integrated over the body surface. Generally speaking, the evaluation of mean drift forces is more accurate when one of the momentum conservation methods is used, especially for bodies with sharp corners where the local velocity and second-order pressure are singular. Comparison of the outputs shows that they are in good agreement, except for the second wave period which is close to the heave resonance frequency, where the vertical drift force computed in option 7 is quite accurate but the output in option 9 contains a large error. This is due to cancellation between two large contributions of opposite signs (the second integration in equations (12.47) and (12.48)), when the heave motion amplitude is large. In the FRC file IOPTN(7)=-1 is assigned to use the source formulation (ISOR=1) in option 7.


PICT PICT PICT PICT

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PICT PICT
 
 Input file:  test03.cfg  
! TEST03.CFG  Cylinder, R=T=1, ILOWHI=0, ISOR=1  
 ilowgdf=1  
 ipltdat=5  
 ISOR=1  
 ISOLVE=0  
 ISCATT=0  
 ILOG=0  
 IRR=0  
 MONITR=0  
 NUMHDR=1  
 
 Input file:  test03.pot  
TEST03.POT  Cylinder, R=T=1, ILOWHI=0, ISOR=1  
    7.14       HBOT  
   1   1                          IRAD,IDIFF  
    4  
    2.837491 2.398118 2.006409 1.638226  
    1  
    0.0  
   1                          NBODY  
 test03.gdf  
  0.0  0.0  -0.515 0.0  
     1  1  1  1  1  1

PICT PICT

 First 10 lines of input file:  test03.gdf  
TEST03.GDF  Cylinder, R=T=1, ILOWHI=0, ISOR=1  
    1.000000       9.806650  
            1           1  
          288  
   0.0000000E+00  0.0000000E+00 -0.4850000  
   0.0000000E+00  0.0000000E+00 -0.4850000  
   0.1934213      2.5464399E-02 -0.4850000  
   0.1950903      0.0000000E+00 -0.4850000  
   0.1950903      0.0000000E+00 -0.4850000  
   0.1934213      2.5464399E-02 -0.4850000  
 
 Input file:  test03.frc  
TEST03.FRC  Cylinder, R=T=1, ILOWHI=0, ISOR=1  
  0    0    0    1    0    0    -1     1     1  
  0.000000  
  0.742000      0.000000      0.000000  
  0.000000      0.742000      0.000000  
  0.000000      0.000000      1.000000  
  0  
  0  
 
 Input file:  test03.csf  
test03.csf higher-order csf file, circular outer boundary  
1 ILOWHICSF  
1 1 ISX ISY  
0 0 1. NPATCSF ICDEF PSZCSF cf section 11.5, page 11-12  
2.0 2.0 RADIUS, DEPTH  
0 NPART  
  

PICT PICT

A.4 BODY IN A CHANNEL OR NEAR A WALL – TEST04

_    

The option to analyze bodies near one vertical wall, or two vertical walls which intersect at a right angle, is described in (Section 12.4). The option to analyze bodies in a channel bounded by two parallel vertical walls is described in (Section 12.7). In Test 04 a rectangular barge of length 80m, beam 20m, draft 10m is positioned with its longitudinal axis parallel to one wall, separated by a gap of 2m. In Test 04a the same barge is in a channel of width 80m and depth 20m, with its longitudinal axis 10m off-center from the axis of the channel. Incident head waves are considered, and computations are made of the surge, heave, and pitch coefficients, RAO’s, and drift force and moment in incident waves which propagate parallel to the wall or parallel to the channel axis (BETA=0).

In the GDF file one half of the barge is discretized, forward of the midship section x = 0. Both the port and starboard sides of the barge are included in the GDF file, hence the appropriate symmetry indices for this case are ISX=1, ISY=0.

The case of one wall is considered in Test 04. Since the incident waves propagate parallel to the wall this problem is identical to the ‘barge catamaran’ studied in [6], and in TEST19, when the motion in the transverse direction is not considered. The only modifications required in the latter case are (1) a lateral offset equal to the sum of the half-beam and gap must be added to the y-coordinates of the panels in the GDF file; (2) ISY=1; and (3) the forces and moments calculated for the catamaran are the total acting on both hulls. The definition of the incident-wave amplitude differs between these different problems, however, due to the convention for the wave amplitude in the presence of a wall Section 12.4. In the present case, where the incident-wave angle is zero and the waves propagate parallel to the wall, the wave system in the absence of the body is a progressive wave with total physical amplitude 2A.

It also is possible to replicate the Test 04 results with the NBODY option, specifying two independent hulls in place of the rigid constraint implied by the catamaran. The figure below shows the catamaran configuration or, equivalently, the original hull plus its image with respect to the wall.


PICT PICT PICT PICT

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PICT PICT
 
 Input file:  test04.cfg  
! TEST04.POT -- Barge near wall, ILOWHI=0  
 ilowgdf=1  
 ipltdat=5  
 ISOR=1  
 ISOLVE=0  
 ISCATT=0  
 ILOG=0  
 IRR=0  
 MONITR=0  
 NUMHDR=1  
 IWALLY0=1  
 
 Input file:  test04.pot  
TEST04.POT -- Barge near wall, ILOWHI=0  
 -1.       HBOT  
   0   0                          IRAD,IDIFF  
 3  
 6.  7.  8.  
 1  
 0.0  
   1                          NBODY  
 test04.gdf  
 0. 12. 0. 0.  
  1  0  1  0  1  0  
 
 First 10 lines of input file:  test04.gdf  
TEST04.GDF -- Barge near wall, ILOWHI=0  
    40.00000       9.806650  
     1     0       ISX, ISY  
          640  
    3.920686       10.00000     -0.3806022  
   0.0000000E+00   10.00000     -0.3806022  
   0.0000000E+00   10.00000      0.0000000E+00  
    3.920686       10.00000      0.0000000E+00  
    3.920686       10.00000      -1.464466  
   0.0000000E+00   10.00000      -1.464466  

PICT PICT

 
 Input file:  test04.frc  
TEST04.FRC -- Barge near wall, ILOWHI=0  
 1    1    1    1    0    0    0    0    1  
 3.0  
 20.00000      0.000000      0.000000  
 0.000000      5.000000      0.000000  
 0.000000      0.000000      20.00000  
 0  
 0  
  

PICT PICT

In Test 04a the mean drift force is evaluated by all three options (7,8,9). For option 7 the control surface is a pair of transverse planes across the channel, at X = 100.0. Their vertices are assigned in the file test04.csf. This file is only used for test 04a, but its filename must be the same as the gdf file. Since the data in the csf file is defined in body coordinates, the outer boundaries are offset by 10m from the global position of the channel walls in global coordinates.

The configuration of Test 04a is shown in the figure below. (Note that the tank walls and bottom extend to infinity in both directions, and only a finite segment is shown in the figure.)


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PICT PICT
 Input file:  test04a.cfg  
! TEST04a.cfg -- Barge in channel 80x15m  
 ilowgdf=1  
 ipltdat=5  
 ISOR=1  
 ISOLVE=0  
 ISCATT=0  
 ILOG=0  
 IRR=0  
 MONITR=0  
 NUMHDR=1  
 channel_width=80.0  
 
 Input file:  test04a.pot  
TEST04a.POT -- Barge in channel 80x15m, off-center 10m  
 20.       HBOT  
   0  0                          IRAD,IDIFF  
 3  
 6.  7.  8.  
 1  
 0.0  
   1                          NBODY  
 test04.gdf  
 0. 10. 0. 0.  
  1  0  1  0  1  0  
 
TEST04a.FRC -- Barge in channel 80x15m  
 1    1    1    1    0    0    1    1    1  
 3.0  
 20.00000      0.000000      0.000000  
 0.000000      5.000000      0.000000  
 0.000000      0.000000      20.00000  
 0  
 0  
 
 Input file:  test04.csf  
test04.csf  control surface for test04a in channel  
  1             ILOWHICSF  
  1   0         ISX  ISY  
  1   0  10.0   NPATCH  ICDEF  PSZCSF  
   100.0       -50.0    -15.0 <span class=PICT" > <span class=PICT" >  
   100.0        30.0    -15.0  
   100.0        30.0      0.0  
   100.0       -50.0      0.0  
 
  

PICT PICT

A.5 MULTIPLE BODIES – TEST05

The NBODY option described in Chapter 7 is illustrated in this test run. Body one is a circular cylinder of radius 1 meter and draft 2 meters. Body 2 is a spheroid of length 4 meters and maximum radius 0.25 meters. The gap between these two bodies is set equal to the beam of the spheroid (0.5 meters) and the origin of the global coordinate system is located at the mid-point of this gap. The relative locations of the two bodies and the orientation of the spheroid are specified in the GGDF file. One quadrant of the cylinder is discretized with 112 panels. 8,6 and 8 panels are distributed in the azimuthal, radial, and vertical directions using cosine spacing in radial and vertical directions. One quadrant of the spheroid is discretized with 64 panels. 8 and 8 panels are distributed in the longitudinal, and transverse directions using cosine spacing in the longitudinal direction.

The Alternative 3 input format is used for FORCE. The separate FRC files TEST05C, TEST05S are used with IALTFRC=3. The vector IALTFRCN is included in TEST05.CFG to indicate that IALTFRC=1 in the separate FRC files for each body.

The added-mass and damping coefficients, exciting forces, motions, wave elevations, field pressures and field velocities, and drift forces are evaluated in infinite water depth for two wave periods and one wave heading.

The option is used to evaluate the mean drift force and moment using a control surface, following the instructions in Chapter 11. The control surfaces surrounding the cylinder and spheroid are defined by the input files TEST05c.csf and TEST05s.csf. In order to illustrate the alternatives, the control surface for the cylinder uses low-order panels (ILOWHICSF=0) and the control surface for the spheroid is generated with the higher-order (ILOWHICSF=1) subroutine ELLIPSOID_CS in the GEOMXACT DLL library. The corresponding output for the mean drift force and moment is contained in the file TEST05.9c. It should be noted that the higher-order control surface for the spheroid does not include the intermediate free surface patch, and thus the horizontal drift force is correct whereas the vertical drift force is not complete. The reason for omitting the free surface patch here is that the low-order solution for the body does not give a sufficiently robust evaluation of field velocities and wave elevations at points on the free surface that are very close to the body. The low-order control surface is more suitable for use with low-order body representations, in this respect, provided the panels on the free surface have dimensions similar to the dimensions of the adjacent panels on the body.

In Test05a the relative orientations of the two bodies are the same, but they are positioned such that the 90 degree rotation of the spheroid is not required, and the plane X=0 is a plane of symmetry for both bodies, as explained in Section 8.5. This reduces the number of equations (NEQN) by a factor of one-half, and reduces the run time and storage requirements. The outputs from the two runs are essentially the same, except that the directions of the coordinates are changed with corresponding changes in the definitions of the force coefficients and field velocities. A rectangular array of uniformly-spaced field points are defined on the free surface in the file_     test05a.frc and the parameter IFIELD_ARRAYS=1 is specified in test05a.cfg. Some of PICT PICT these field points are on or inside the body waterlines. These points are identified with zero in column five, in the output file test05a.fpt, and the outputs for the pressure and velocity are equal to zero at these points (see Section 4.3 and Section 4.7).


PICT PICT PICT PICT

PIC PICT PICT


PICT PICT
 
 Input file:  test05.cfg  
! TEST05.CFG -- Cylinder + spheroid, NBODY=2, ILOWHI=0  
 IPLTDAT=1  
 ISOR=1  
 ILOG=0  
 IRR=0  
 NUMHDR=1  
 NOOUT=0 1 1 1 0 1 1 1 1  
 IALTFRC = 3    !  Alternative Form 3 FRC  
 IALTFRCN= 1 1  
 
 Input file:  test05.pot  
 TEST05.POT -- Cylinder + spheroid, ILOWHI=0  
 -1.0       HBOT  
   0   0                          IRAD,IDIFF  
 2  
 1.5 2.0  
 1  
 0.0  
   2                          NBODY  
 test05c.gdf  
  1.25 0.0 0.0 0.0  
  1   1   1   1   1   1  
 test05s.gdf  
  -0.5 0.0 0.0 90.0  
  1   1   1   1   1   1  
 
 First 10 lines of input file:  test05c.gdf  
 Cylinder R=1 T=2 8*(6+8)  
    1.000000       9.806650  
            1           1  
          112  
   0.0000000E+00  0.0000000E+00  -2.000000  
   0.0000000E+00  0.0000000E+00  -2.000000  
   0.2538459      5.0493091E-02  -2.000000  
   0.2588190      0.0000000E+00  -2.000000  
   0.2588190      0.0000000E+00  -2.000000  
   0.2538459      5.0493091E-02  -2.000000  
 
 First 10 lines of input file:  test05s.gdf <span class=PICT" > <span class=PICT" >  
Spheroid, Slendernes =0.125 Halflength=2m 8*8  
    2.000000       9.806650  
            1           1  
           64  
    2.000000     -0.0000000E+00 -0.0000000E+00  
    1.961571     -7.9460625E-09 -4.8772585E-02  
    1.961571      9.5150545E-03 -4.7835436E-02  
    2.000000      0.0000000E+00 -0.0000000E+00  
    2.000000      0.0000000E+00 -0.0000000E+00  
    1.961571      9.5150545E-03 -4.7835436E-02  
 
 Input file:  test05.frc  
 TEST05.FRC -- Cylinder + spheroid, ILOWHI=0  
   1   1   1   1   0   3   1   1   1  
  1.0  
test05c.frc  
test05s.frc  
  0  
  1  
  0. 0. 0.  

PICT PICT

 
 Input file:  test05c.frc  
 CYL.FRC  
 0    0    0    0    0    0    0    0    0  
 0.000000  
 1.000000      .0000000      .0000000  
 .0000000      1.000000      .0000000  
 .0000000      .0000000      1.000000  
 0  
 0  
 
 Input file:  test05s.frc  
 SPD.FRC  
 0    0    0    0    0    0    0    0    0  
 0.000000  
 1.000000      .0000000      .0000000  
 .0000000      1.000000      .0000000  
 .0000000      .0000000      1.000000  
 0  
 0  
 
 First 10 lines of input file:  test05c.csf  
cylinder R=1.2 T=2.2 -- low-order control surface  
    0        ILOWHICSF  
    1     1  ISX ISY  
    160      NPAN  
  0.12000E+01  0.00000E+00  0.00000E+00  
  0.12000E+01  0.00000E+00 -0.27500E+00  
  0.11769E+01  0.23411E+00 -0.27500E+00  
  0.11769E+01  0.23411E+00  0.00000E+00  
  0.11769E+01  0.23411E+00  0.00000E+00  
  0.11769E+01  0.23411E+00 -0.27500E+00  
 
 Input file:  test05s.csf  
ELLIPSOID CONTROL SURFACE defined by subroutine ELLIPSOID_CS  
1   ILOWHICSF  
1  1        ISX  ISY  
1  -1003  0.5 NPATCH  IGDEF PSZCSF  
2           NLINES  
2.2 0.3 0.3    A, B, C  
2.0 0.25 (x and y maximum of ellipsoid GDF) <span class=PICT" > <span class=PICT" >  
  

PICT PICT

 Input file:  test05a.cfg  
! TEST05a.CFG -- array of field points  
 IPLTDAT=1  
 ISOR=1  
 ILOG=0  
 IRR=0  
 NUMHDR=1  
 NOOUT=0 1 1 1 0 1 1 1 1  
 IALTFRC = 3    !  Alternative Form 3 FRC  
 IALTFRCN= 1 1  
 IFIELD_ARRAYS=1  
 
 Input file:  test05a.pot  
 TEST05a.POT -- Cylinder + spheroid, ILOWHI=0  
 -1.0       HBOT  
   0   0                          IRAD,IDIFF  
 2          NPER  
 1.5 2.0    PER  
 1          NBETA  
 90.0       Beta  
   2                          NBODY  
 test05c.gdf  
   0.0 1.25 0.0 0.0  
  1   1   1   1   1   1  
 test05s.gdf  
   0.0 -0.5 0.0 0.0  
  1   1   1   1   1   1  
 
 Input file:  test05a.frc  
 TEST05a.FRC -- array of field points  
   1   1   1   1   0   3   1   1   1     (IOPTN(1-9)  
  1.0                             (RHO -- fluid density)  
test05c.frc                       (frc file for body 1)  
test05s.frc                       (frc file for body 2)  
  0                               (NBETAH)  
 0                                (NFIELD -- no individual field points)  
 1                                (NFIELD_ARRAYS -- number of arrays)  
 0                                (Array is in exterior fluid domain)  
 11 -2.5   0.5                    (NFX, X1, DELX)  
 10 -1.5   0.5                    (NFY, Y1, DELY)  
  1  0.0   0.0                    (NFZ, Z1, DELZ) <span class=PICT" > <span class=PICT" >  
  

PICT PICT

A.6 THE ISSC TENSION-LEG PLATFORM – TEST06

The added-mass, damping coefficients, exciting forces, motions and wave loads are evaluated for the ISSC Tension-Leg-Platform, in a finite water depth of 450 meters, for three wave periods and one wave heading. The TLP consists of four circular cylindrical columns and four rectangular pontoons as shown in the plots of the panel discretization. The radius of each column is 8.435 meters. The width and height of each pontoon are 7.5 meters and 10.5 meters, respectively. The distance between the centers of adjacent columns is 86.25 meters. Further information is given by Eatock Taylor and Jefferys [7].

Two planes of symmetry are used with 128 panels in one quadrant. Thus there are a total of 512 panels on the complete surface. The origin of the coordinate system is located at the intersection of the undisturbed free surface and the two planes of symmetry. The characteristic length is set equal to 43.125 meters, which corresponds to half of the distance between the centers of adjacent columns.

Only head seas are considered, with β = 0 specified in the .pot file. For this reason, only the modes (surge, heave, pitch) are analyzed with IRAD=IDIFF=0, and these modes are specified on line 3. There is a warning message for options 5-9, as explained in Section 10.1, since IDIFF=0.

In the .frc file the horizontal modes (1,2,6) are free and the vertical modes (3,4,5) are fixed, to represent a TLP moored by vertical tendons. The Alternative 1 form is used, with the result that the body mass is evaluated as if the TLP is freely floating (see Section 3.5).

The output shows the conventional response amplitude operator for surge, and the wave loads for heave and pitch.


PICT PICT PICT PICT

PIC PICT PICT


PICT PICT
 
 Input file:  test06.cfg  
! TEST06.CFG -- ISSC TLP, coarse discretization  
 ipltdat=1  
 ISOR=1  
 ISOLVE=4  
 ISCATT=1  
 ILOG=0  
 IRR=0  
 MONITR=0  
 NUMHDR=1  
 IALTFRC=2  
 
 Input file:  test06.pot  
TEST06.POT -- ISSC TLP, coarse discretization  
 450.       HBOT  
   0   0                          IRAD,IDIFF  
 3  
 5. 10. 15.  
 1  
 0.  
   1                          NBODY  
 test06.gdf  
 0. 0. 0. 0.  
  1  0  1  0  1  0  
 
 First 10 lines of input file:  test06.gdf  
TEST06.GDF -- ISSC TLP, coarse discretization  
  43.125     9.80665  
   1          1  
          128  
                 49.09267       37.15733        0.00000  
                 49.09267       37.15733       -5.12567  
                 51.56456       43.12500       -5.12567  
                 51.56456       43.12500        0.00000  
                 49.09267       37.15733       -5.12567  
                 49.09267       37.15733      -17.50013

PICT PICT

 
 Input file:  test06.frc  
 TEST07.FRC  ISSC TLP -- ILOWHI=0, fine discretization -- IALTFRC=2  
 1  1  1 -2  0  0  0  1  1  IOPTN (IOPTN(4)<0 signifies fixed modes)  
 6                          NDFR  
 1 1 0 0 0 1                IMODE  
 1.                         RHO  
 0. 0. 3.0                  XCG  
 1                          IMASS  
    53066.4      0.        0.        0.     159199.2         0.  
        0.   53066.4       0.  -159199.2         0.          0.  
        0.       0.    53066.4       0.          0.          0.  
        0. -159199.2       0.  8.0201552E7       0.          0.  
   159199.2      0.        0.        0.   8.0201552E7        0.  
        0.       0.        0.        0.          0.  9.54906731E7  
 0                          IDAMP  
 0                          ISTIFF  
 0                          NBETAH  
 0                          NFIELD  
  

PICT PICT

A.7 THE ISSC TENSION-LEG PLATFORM – TEST07

This test run is intended to refine the analysis of the ISSC TLP described in TEST06. 1012 panels are used on each quadrant, resulting in 4048 panels for the complete structure. The block iterative solver is used (ISOLVE=4) to provide a relatively fast but robust solution. For the sake of variety in the analysis of the diffraction problem, the solution for the scattered potential is computed (ISCATT=1).

Alternative form 2 of .FRC is used, but the mass is assumed to be equal to the displacement computed by WAMIT. Note that the displacement is about 4% greater than for Test Run 2, due to the more accurate description of the columns. (The panel vertices are defined to lie on the exact circular cylinder surface, hence the flat panels define a surface with less displaced volume than the exact body.)

Comparisons should be made with the output files from TEST06 to judge the convergence of the results with increasing numbers of panels. As explained in Appendix A.6 a warning message is displayed for Options 8 and 9 since IDIFF=0.


PICT PICT PICT PICT

PIC PICT PICT


PICT PICT
 
 Input file:  test07.cfg  
! TEST07.CFG  ISSC TLP -- ILOWHI=0, fine discretization  
 ipltdat=1  
 ISOR=1  
 ISOLVE=4  
 ISCATT=1  
 ILOG=1  
 IRR=0  
 MONITR=0  
 NUMHDR=1  
 IALTFRC=2  
 
 Input file:  test07.pot  
 TEST07.POT  ISSC TLP -- ILOWHI=0, fine discretization  
 450.       HBOT  
   0   0                          IRAD,IDIFF  
 3  
 5. 10. 15.  
 1  
 0.  
   1                          NBODY  
 test07.gdf  
 0. 0. 0. 0.  
  1  0  1  0  1  0  
 
 First 10 lines of input file:  test07.gdf  
 TEST07.GDF  ISSC TLP -- ILOWHI=0, fine discretization  
     43.125   9.806650  
     1       1  
     1012  
     49.09267      37.15733       0.00000  
     49.09267      37.15733      -0.33626  
     50.43388      38.90522      -0.33626  
     50.43388      38.90522       0.00000  
     49.09267      37.15733      -0.33626  
     49.09267      37.15733      -1.33212  

PICT PICT

 
 Input file:  test07.frc  
 TEST07.FRC  ISSC TLP -- ILOWHI=0, fine discretization -- IALTFRC=2  
 1  1  1 -2  0  0  0  1  1  IOPTN (IOPTN(4)<0 signifies fixed modes)  
 6                          NDFR  
 1 1 0 0 0 1                IMODE  
 1.                         RHO  
 0. 0. 3.0                  XCG  
 1                          IMASS  
    53066.4      0.        0.        0.     159199.2         0.  
        0.   53066.4       0.  -159199.2         0.          0.  
        0.       0.    53066.4       0.          0.          0.  
        0. -159199.2       0.  8.0201552E7       0.          0.  
   159199.2      0.        0.        0.   8.0201552E7        0.  
        0.       0.        0.        0.          0.  9.54906731E7  
 0                          IDAMP  
 0                          ISTIFF  
 0                          NBETAH  
 0                          NFIELD  
  

PICT PICT

A.8 ELASTIC COLUMN WITH GENERALIZED MODES – TEST08

This test run evaluates the force coefficients and RAO’s for a bottom-mounted vertical cylinder of circular cross-section, with four bending modes defined by shifted Jacobi polynomials. The hydroelastic analysis of these bending modes is analyzed using the generalized body mode option described in Chapter 8. Further details are given in Reference [13]. The cylinder extends from the free surface, where it is free, down to the bottom, at a depth of 200m, where it is clamped. The cylinder radius is 10m. Since the cylinder is clamped at the bottom the six rigid-body modes are all fixed, and specified by the values MODE(j)=0 in the POT file.

External mass and stiffness matrices are defined in the (Alternative 2) FRC file. The cylinder is considered to have a constant distributed mass equal to half of the displaced mass of fluid, and also a concentrated mass at the free surface equal to the displaced mass. The stiffness factor EI for the beam equation is assumed constant with the value 0.41m0h3, where m 0 is the concentrated mass and h is the fluid depth. No matrix elements are required for the square submatrix (i,j) 6 since the body is fixed in these modes. Further details for this case are given in [13].

The cylinder geometry is defined with two planes of symmetry and 512 panels on one quadrant. The length scale ULEN is specified as 1.0 to simplify the definitions of modes and output quantities. The generalized modes are defined in the subroutine defmod.f, which is distributed to licensed users. The use of DEFMOD is described in Chapter 8. The output file from DEFMOD, TEST08.MOD, is included with the test files so that this test can be run without prior use of DEFMOD. Only one wave period is considered here, which coincides with resonant bending motion of the cylinder. See also TEST18, where the NEWMODES DLL file is used to define the generalized modes.


PICT PICT PICT PICT

PIC PICT PICT


PICT PICT
 
 Input file:  test08.cfg  
! TEST08.CFG -- bending of vertical column with 4 generalized modes  
 ilowgdf=1  
 ipltdat=5  
 NUMHDR=1  
 NUMNAM=0  
 ISOR=0  
 IRR=0  
 MONITR=0  
 NEWMDS=4  
 IALTFRC=2  
 
 Input file:  test08.pot  
TEST08.POT -- bending of vertical column at resonance, 200m depth  
      200.0       HBOT  
   0   0                          IRAD,IDIFF  
           1  
           6.5  
           1  
           0.0  
   1                          NBODY  
 test08.gdf  
  0.0  0.0  0.0  0.0  
        0   0   0   0   0   0  
 
 First 10 lines of input file:  test08.gdf  
TEST08.GDF vertical cylinder, 16*32, cosine spacing at free surface  
     1.0000        9.80665  
           1           1  
         512  
    10.0000       0.000000       -200.000  
    9.95185       0.980171       -200.000  
    9.95185       0.980171       -190.186  
    10.0000       0.000000       -190.186  
    10.0000       0.000000       -190.186  
    9.95185       0.980171       -190.186  

PICT PICT

 
 Input file:  test08.frc  
TEST08.FRC file, vertical column with 4 bending modes  
         1    1    1    1    0    0    0    0   0  
        1.0  
        .0000000      .0000000      1.000000  
    1  
  0.   0.   0.   0.   0.   0.        0.        0.        0.        0.  
  0.   0.   0.   0.   0.   0.        0.        0.        0.        0.  
  0.   0.   0.   0.   0.   0.        0.        0.        0.        0.  
  0.   0.   0.   0.   0.   0.        0.        0.        0.        0.  
  0.   0.   0.   0.   0.   0.        0.        0.        0.        0.  
  0.   0.   0.   0.   0.   0.        0.        0.        0.        0.  
  0.   0.   0.   0.   0.   0.    69115.    62832.    62832.    62832.  
  0.   0.   0.   0.   0.   0.    62832.    67320.    62832.    62832.  
  0.   0.   0.   0.   0.   0.    62832.    62832.    66323.    62832.  
  0.   0.   0.   0.   0.   0.    62832.    62832.    62832.    65688.  
    0  
    1  
  0.   0.   0.   0.   0.   0.        0.        0.        0.         0.  
  0.   0.   0.   0.   0.   0.        0.        0.        0.         0.  
  0.   0.   0.   0.   0.   0.        0.        0.        0.         0.  
  0.   0.   0.   0.   0.   0.        0.        0.        0.         0.  
  0.   0.   0.   0.   0.   0.        0.        0.        0.         0.  
  0.   0.   0.   0.   0.   0.        0.        0.        0.         0.  
  0.   0.   0.   0.   0.   0.   103044.   412177.   824354.   1339575.  
  0.   0.   0.   0.   0.   0.   412177.  4430902.  9789203.  16487078.  
  0.   0.   0.   0.   0.   0.   824354.  9789203. 37899671.  64382041.  
  0.   0.   0.   0.   0.   0.  1339575. 16487078. 64382041. 162406554.  
    0  
    0  
  

PICT PICT

A.9 SPAR WITH THREE STRAKES – TEST09

This test run analyzes a circular cylinder with three spiral strakes. The strakes are modeled as zero-thickness dipole panels, following the method described in Section 5.4. The radius of the cylinder is 18m and the draft is 200m. The strake width is 3.7m. There are no planes of symmetry, due to the twist of the strakes. A total of 960 panels are used, including 672 on the cylinder plus 288 on the strakes. The excerpts from the GDF file include the first body panel and also the first dipole panel.

In TEST09A the trimmed waterline option is used, with the parameters ITRIMWL and XTRIM specified in the file TEST09A.CFG. These parameters specify a vertical trim of 10m and a pitch angle of 10 degrees. The same TEST09.GDF file is used for both tests. Only the filenames are changed in TEST09A.POT and TEST09A.FRC. Perspective views in the untrimmed and trimmed conditions are shown below.

The FORCE run includes all options which can be evaluated without using the source formulation (ISOR=1), since the latter option cannot be used with dipole panels. The body pressure file TEST09.5p includes the pressure on the body panels, and the pressure jump on the dipole panels. The corresponding panel centroids are listed in the output file TEST09.PNL.

The figure below shows the submerged body surfaces for both TEST09 and TEST09a. The dipole panels are red.


PICT PICT PICT PICT

PIC PICT PICT


PICT PICT
 
 Input file:  test09.cfg  
! TEST09.CFG (Spar with three strakes)  
 ilowgdf=1  
 ipltdat=5  
 ISOR=0  
 ISOLVE=0  
 ISCATT=1  
 ILOG=0  
 IRR=0  
 MONITR=0  
 NUMHDR=1  
 IPERIN=3  
 IPEROUT=3  
 NOOUT= 1 1 1 1 0 1 1 1 1  
 NPDIPOLE = ( 673  960 )  
 
 Input file:  test09.pot  
TEST09.POT (Spar with three strakes)  
 -1.       HBOT  
   1   1                          IRAD,IDIFF  
 3                              NPER (array PER follows)  
 0.1 0.5 1.0  
 2                              NBETA (array BETA follows)  
 0.0 45.                        (end of file)  
   1                          NBODY  
 test09.gdf  
 0. 0. 0. 0.                HBOT, XBODY(1-4)  
  1  1  1  1  1  1               IMODE(1-6)  
 
 First 10 lines of input file:  test09.gdf  
 SPAR  R, D, W, T, NS, TWIST=   18.00  200.00    3.70  0.000000    3  1.000  
   18.00000       9.806650  
           0           0  
     960  
   18.00000      0.0000000E+00  0.0000000E+00  
   17.38667       4.658743      -8.333333  
   15.58846       9.000000      -8.333333  
   17.38667       4.658743      0.0000000E+00  
   17.38667       4.658743      -8.333333  
   15.58846       9.000000      -16.66667 <span class=PICT" > <span class=PICT" >  

PICT PICT

 
 Input file:  test09.frc  
TEST09.FRC (Spar with three strakes)  
   1   1   1   1   1   3   0   2   0  
 0.000000                                    VCG  
 1.000000      .0000000      .0000000  
 .0000000      1.000000      .0000000  
 .0000000      .0000000      1.000000        XPRDCT  
 0                                           NBETAH  
 2                                           NFIELD  
 23.  0.  0.  
 15.  15. -0.5                                (end of file)  
  

PICT PICT

 
 Input file:  test09a.cfg  
! TEST09a.CFG -- Spar with trimmed waterline  
 ISOLVE=0  
 ISCATT=1  
 ILOG=0  
 IRR=0  
 MONITR=0  
 NUMHDR=1  
 IPERIN=3  
 IPEROUT=3  
 NOOUT= 1 1 1 1 0 1 1 1 1  
 ITRIMWL=1  
 XTRIM=10. 10. 0.  
 NPDIPOLE = ( 673  960 )  
 
 Input file:  test09a.pot  
TEST09A.POT -- spar - trimmed waterline  
 -1.       HBOT  
   1   1                          IRAD,IDIFF  
 3                              NPER (array PER follows)  
 0.1 0.5 1.0  
 2                              NBETA (array BETA follows)  
 0.0 45.                        (end of file)  
   1                          NBODY  
 test09.gdf  
 0. 0. 0. 0.                HBOT, XBODY(1-4)  
  1  1  1  1  1  1               IMODE(1-6)  
 
 Input file:  test09a.frc  
TEST09A.FRC (Spar with three strakes, trimmed waterline)  
   1   1   1   1   1   3   0   2   0  
 0.000000                                    VCG  
 1.000000      .0000000      .0000000  
 .0000000      1.000000      .0000000  
 .0000000      .0000000      1.000000        XPRDCT  
 0                                           NBETAH  
 2                                           NFIELD  
 23.  0.  0.  
 15.  15. -0.5                                (end of file)  
   <span class=PICT" > <span class=PICT" >

PICT PICT

A.11 CIRCULAR CYLINDER – TEST11

The same cylinder used for the low-order TEST01 is used here with the higher-order option (ILOWHI=1). Two alternatives are used for the geometry.

In TEST11 the geometry is defined by B-splines (IGDEF=1). The parameters, knot vectors, and coefficients for each patch are contained in the file TEST11.GDF. It should be noted that the circular patches and boundaries cannot be fit exactly with B-splines; however the geometric errors are generally much smaller in this case, compared to the flat-panel representation in TEST01. For example the maximum error of any point output in the data file test11.pnl is less than 3E-5, and the maximum error in the computed volume is 1E-5. By comparison, using the flat-panel discretization in TEST01, the maximum error in the computed volume is 3E-3. Thus, when the higher-order method is used, the principal errors in the results should be associated with the approximation of the potential by B-splines, as opposed to the representation of the geometry. This approximation can be systematically refined by increasing the number of panels, or by using the PANEL-SIZE option in the CONFIG.WAM (or CFG) file and reducing the value of this parameter.

In TEST11a the geometry is defined analytically by the GEOMXACT.F subroutine CIRCCYL (IGDEF=-1). The radius and draft of the cylinder are input in TEST11a.GDF. The parameter INONUMAP=0 specifies uniform mapping. Comparison of the output files with TEST01 and TEST11 confirms the statements above regarding accuracy. Most of the output data from TEST11 and TEST11a agree to at least five decimals, except for the third wave period which coincides with an irregular frequency.

In TEST11b the geometry is defined analytically, in the same manner as for TEST11a, except that nonuniform mapping is specified by the parameter INONUMAP=1 as explained in Section 6.8. This modification gives a more accurate solution near the corner and waterline, which is particularly beneficial for the pressure drift force evaluation. Comparison between the outputs for the momentum and pressure drift force shows that the results are more consistent in this case, compared to the use of uniform mapping in TEST11a. More extensive comparisons for the same geometry are included in Reference 24.

TEST11c illustrates the use of the option IGDEF=2, where the geometry is described by MultiSurf (see Section 6.7 and Appendix 2). In this case the same nonuniform mapping is used as in TEST11b, using the relabeling technique in MultiSurf. Comparison of the results with TEST11b indicates that they are practically identical.


PICT PICT PICT PICT

PIC PICT PICT


PICT PICT
 
 Input file:  test11.cfg  
! TEST11.CFG  Cylinder R=1, T=0.5, igdef=1  
 ipltdat=5  
 ilowgdf=5  
 ILOWHI=1  
 IRR=0  
 ISOLVE=2  
 KSPLIN=3  
 IQUADO=3  
 IQUADI=4  
 MONITR=0  
 NOOUT= 1 1 1 1 0 1 1 1 1  
 NUMHDR=1  
 
 Input file:  test11.pot  
TEST11.POT  Cylinder R=1, T=0.5, igdef=1  
 -1.  
 1           1               IRAD, IDIFF  
 3                            NPER (array PER follows)  
8.971402 2.006403 1.003033  
 1                            NBETA (array BETA follows)  
 0.  
 1                            NBODY  
 test11.gdf  
 0. 0. 0. 0.                  XBODY  
 1  1  1  1  1  1             IMODE(1-6)  
 
 First 10 lines of input file:  test11.gdf  
TEST11  cylinder R=1 T=0.5 defined by B-splines (IGDEF=1)  
1. 9.80665  ULEN GRAV  
1  1        ISX  ISY  
2  1        NPATCH, IGDEF  
           4           2  
           4           4  
  -1.00000000000000       -1.00000000000000       -1.00000000000000  
  -1.00000000000000      -0.500000000000000       0.000000000000000E+000  
  0.500000000000000        1.00000000000000        1.00000000000000  
   1.00000000000000        1.00000000000000  
 
 Input file:  test11.spl <span class=PICT" > <span class=PICT" >  
TEST11  cylinder R=1 T=0.5 defined by B-splines (IGDEF=1)  
4  2        NU NV (Patch 1, side   u azimuthal v vertical)  
4  2        NU NV (Parch 2, bottom u azimuthal v radial)  
 
 Input file:  test11.frc  
TEST11.FRC  Cylinder R=1, T=0.5, igdef=1  
   1   1   1   1   3   3   0   2   2  
 0.000000                                    VCG  
 1.000000      .0000000      .0000000  
 .0000000      1.000000      .0000000  
 .0000000      .0000000      1.000000        XPRDCT  
 0                                           NBETAH  
 2                                           NFIELD  
1.5 0.  0.  
1.5 0. -0.5                                  (end of file)  
  

PICT PICT

 
 Input file:  test11a.cfg  
! TEST11a.CFG  Cylinder R=1, T=0.5, igdef=-1  
 ipltdat=5  
 ILOWHI=1  
 IRR=0  
 ISOLVE=2  
 KSPLIN=3  
 IQUADO=3  
 IQUADI=4  
 MONITR=0  
 NUMHDR=1  
 NOOUT= 1 1 1 1 0 1 1 1 1  
 
 Input file:  test11a.pot  
TEST11A.POT  Cylinder R=1, T=0.5, igdef=-1  
 -1.  
 1           1               IRAD, IDIFF  
 2                            NPER (array PER follows)  
8.971402 2.006403  
 1                            NBETA (array BETA follows)  
 0.  
 1                            NBODY  
 test11a.gdf  
 0. 0. 0. 0.                  XBODY  
 1  1  1  1  1  1             IMODE(1-6)  
 
 Input file:  test11a.gdf  
TEST11a cylinder R=1 T=0.5 -- analytic geometry (npatch=2)  
1. 9.80665  ULEN GRAV  
1  1        ISX  ISY  
2  -1       NPATCH  IGDEF  
 2  
1.0 0.5     RADIUS, DRAFT  
0           UNIFORM MAPPING  
 
 Input file:  test11a.spl  
TEST11a.spl - cylinder R=1 T=0.5 -- analytic geometry (npatch=2)  
4  2        NU NV (Patch 1, side   u azimuthal v vertical)  
4  2        NU NV (Parch 2, bottom u azimuthal v radial)  
<span class=PICT" > <span class=PICT" >

PICT PICT

 
 Input file:  test11a.frc  
TEST11a.FRC  Cylinder R=1, T=0.5, igdef=-1  
   1   1   1   1   3   3   0   2   2  
 0.000000                                    VCG  
 1.000000      .0000000      .0000000  
 .0000000      1.000000      .0000000  
 .0000000      .0000000      1.000000        XPRDCT  
 0                                           NBETAH  
 2                                           NFIELD  
1.5 0.  0.  
1.5 0. -0.5                                  (end of file)  
  

PICT PICT

 
 Input file:  test11b.cfg  
! TEST11b.CFG  Cylinder R=1, T=0.5, igdef=1  
 ILOWHI=1  
 IRR=0  
 ISOLVE=2  
 KSPLIN=3  
 IQUADO=3  
 IQUADI=4  
 MONITR=0  
 NUMHDR=1  
 NOOUT= 1 1 1 1 0 1 1 1 1  
 
 Input file:  test11b.pot  
TEST11B.POT  Cylinder R=1, T=0.5, igdef=-1  
 -1.  
 1           1               IRAD, IDIFF  
 2                            NPER (array PER follows)  
8.971402 2.006403  
 2                            NBETA (array BETA follows)  
 0. 45.  
 1                            NBODY  
 test11b.gdf  
 0. 0. 0. 0.                  XBODY  
 1  1  1  1  1  1             IMODE(1-6)  
 
 Input file:  test11b.gdf  
TEST11 cylinder R=1 T=0.5 -- analytic geometry, nonuniform mapping  
1. 9.80665  ULEN GRAV  
1  1        ISX  ISY  
2  -1       NPATCH  IGDEF  
2           NLINES  
1.0 0.5     RADIUS, DRAFT  
1           INONUMAP  (nonuniform mapping)  
 
 Input file:  test11b.spl  
TEST11b.spl - cylinder R=1 T=0.5 -- analytic geometry (npatch=2)  
4  2        NU NV (Patch 1, side   u azimuthal v vertical)  
4  2        NU NV (Parch 2, bottom u azimuthal v radial)  
PICT PICT

PICT PICT

 
 Input file:  test11b.frc  
TEST11B.FRC  Cylinder R=1, T=0.5, igdef=-1  
   1   1   1   1   3   3   0   2   2  
 0.000000                                    VCG  
 1.000000      .0000000      .0000000  
 .0000000      1.000000      .0000000  
 .0000000      .0000000      1.000000        XPRDCT  
 0                                           NBETAH  
 2                                           NFIELD  
1.5 0.  0.  
1.5 0. -0.5                                  (end of file)  
  

PICT PICT

 
 Input file:  test11c.cfg  
! TEST11c.CFG  Cylinder R=1, T=0.5, igdef=2  
 ILOWHI=1  
 IRR=0  
 ISOLVE=2  
 KSPLIN=3  
 IQUADO=3  
 IQUADI=4  
 MONITR=0  
 NUMHDR=1  
 NOOUT= 1 1 1 1 0 1 1 1 1  
 
 Input file:  test11c.pot  
TEST11C.POT  Cylinder R=1, T=0.5, igdef=2  
 -1.  
 1           1               IRAD, IDIFF  
 2                            NPER (array PER follows)  
8.971402 2.006403  
 2                            NBETA (array BETA follows)  
 0. 45.  
 1                            NBODY  
 test11c.gdf  
 0. 0. 0. 0.                  XBODY  
 1  1  1  1  1  1             IMODE(1-6)  
 
 Input file:  test11c.gdf  
TEST11 cylinder R=1 T=0.5 -- MultiSurf .ms2 input, nonuniform mapping  
1. 9.80665  ULEN GRAV  
1  1        ISX  ISY  
0  2        NPATCH  IGDEF  
3           NLINES  
TEST11C.MS2  
wetted_surfs  
0  0  0     default settings: FAST, DivMult, outward normal  
 
 Input file:  test11c.spl  
TEST11c.spl - cylinder R=1 T=0.5 -- MultiSurf geometry (npatch=2)  
 4 2        NU NV (Patch 1, side   u azimuthal v vertical)  
 4 2        NU NV (Parch 2, bottom u azimuthal v radial)  
<span class=PICT" > <span class=PICT" >

PICT PICT

 
 Input file:  test11c.frc  
TEST11C.FRC  Cylinder R=1, T=0.5, igdef=2  
   1   1   1   1   3   3   0   2   2  
 0.000000                                    VCG  
 1.000000      .0000000      .0000000  
 .0000000      1.000000      .0000000  
 .0000000      .0000000      1.000000        XPRDCT  
 0                                           NBETAH  
 2                                           NFIELD  
1.5 0.  0.  
1.5 0. -0.5                                  (end of file)  
  

PICT PICT

A.12 IRREGULAR-FREQUENCY REMOVAL – TEST12

TEST12 is the higher-order analog of TEST02, intended to illustrate the removal of irregular-frequency effects using the higher-order method. As in TEST11a, the geometry is defined analytically (IGDEF=-1) and the dimensions are input in the file TEST12.GDF. In this case NPATCH=3 is specified, where the additional patch corresponds to the interior free surface as required for the irregular-frequency option. In the figures below the patch and panels on the interior free surface are shaded red. One quadrant of the side and interior free surface are omitted to show the bottom surface.


PICT PICT PICT PICT

PIC PICT PICT


PICT PICT
 
 Input file:  test12.cfg  
! TEST12.CFG  Cylinder R=1, T=0.5, igdef=-1, npatch=3 (IRR=1)  
 ILOWHI=1  
 IRR=1  
 ILOG=1  
 ISOLVE=1  
 KSPLIN=3  
 IQUADO=3  
 IQUADI=4  
 MONITR=0  
 NUMHDR=1  
 NOOUT= 1 1 1 1 0 1 1 1 1  
 
 Input file:  test12.pot  
TEST12.POT  Cylinder R=1, T=0.5, igdef=-1, npatch=3 (IRR=1)  
 -1.  
 1           1               IRAD, IDIFF  
 3                            NPER (array PER follows)  
8.971402 2.006403 1.003033  
 2                            NBETA (array BETA follows)  
 0. 45.  
 1                            NBODY  
 test12.gdf  
 0. 0. 0. 0.                  XBODY  
 1  1  1  1  1  1             IMODE(1-6)  
 
 Input file:  test12.gdf  
TEST12 cylinder R=1 T=0.5 -- analytic geometry (npatch=3)  
1. 9.80665  ULEN GRAV  
1  1        ISX  ISY  
3  -1       NPATCH  IGDEF  
2           NLINES  
1.0 0.5     RADIUS, DRAFT  
0           UNIFORM MAPPING  
 
 Input file:  test12.spl  
TEST12.spl - cylinder R=1 T=0.5 -- analytic geometry (npatch=3)  
4  2        NU NV (Patch 1, side   u azimuthal v vertical)  
4  2        NU NV (Parch 2, bottom u azimuthal v radial)  
4  4        NU NV (Parch 3, interior free surface)  RESET NV=2 FOR STANDARD <span class=PICT" > <span class=PICT" >  

PICT PICT

 
 Input file:  test12.frc  
TEST12.FRC  Cylinder R=1, T=0.5, igdef=-1 (irr=1)  
   1   1   1   1   3   3   0   2   2  
 0.000000                                    VCG  
 1.000000      .0000000      .0000000  
 .0000000      1.000000      .0000000  
 .0000000      .0000000      1.000000        XPRDCT  
 0                                           NBETAH  
 2                                           NFIELD  
1.5 0.  0.  
1.5 0. -0.5                                  (end of file)  
  

PICT PICT

A.13 MULTIPLE BODIES – TEST13

This test uses the same cylinder and spheroid as in the low-order TEST05. The geometry is defined by the input files TEST13C.GDF and TEST13S.GDF. TEST13C uses IGDEF=-1 as in TEST11a. TEST13S.GDF uses the ELLIPSOID subroutine (IGDEF=-4) with the semi-axes (2.0, 0.25, 0.25) specified. The same separate FRC files TEST05C, TEST05S are used with IALTFRC=3. The vector IALTFRCN is included in TEST13.CFG to indicate that IALTFRC=1 in the separate FRC files for each body. (Normally it is necessary to duplicate the FRC files for analogous runs, as for example in TEST01 and TEST11, since the output filenames are assigned based on the FRC filename. This is not necessary for individual FRC files for each body when multiple bodies are analyzed, since these do not affect the output filenames.)

The option is used to evaluate the mean drift force and moment using a control surface, following the instructions in Chapter 11. The control surfaces surrounding the cylinder and spheroid are defined by the input files TEST13c.csf and TEST13s.csf. These control surfaces are generated by the subroutines CIRCYL_CS and ELLIPSOID_CS in the GEOMXACT DLL library. The surfaces generated by these subroutines include the portion of the free surface between the body and outer control surface. The corresponding output for the mean drift force and moment is contained in the file TEST13.9c.


PICT PICT PICT PICT

PIC PICT PICT


PICT PICT
 
 Input file:  test13.cfg  
! TEST13.CFG -- Cylinder + spheroid, ILOWHI=1  
 IPLTDAT=4  
 ILOWHI=1  
 IRR=0  
 ISOLVE=2  
 KSPLIN=3  
 IQUADO=3  
 IQUADI=4  
 NUMHDR=1  
 NOOUT=0 1 1 1 0 1 1 1 1  
 IALTFRC = 3    !  Alternative Form 3 FRC  
 IALTFRCN= 1 1  
 
 Input file:  test13.pot  
 TEST13.POT -- Cylinder + spheroid, ILOWHI=1  
 -1.  
 1           1               IRAD, IDIFF  
 2                           NPER (array PER follows)  
 1.5  2.0      PER  
 1                           NBETA (array BETA follows)  
 0.                          BETA  
 2                           NBODY  
 test13c.gdf  
 1.25 0.0 0.0 0.0            XBODY  
 1  1  1  1  1  1            IMODE(1-6)  
 test13s.gdf  
 -0.5 0.0 0.0 90.0           XBODY  
 1  1  1  1  1  1            IMODE(1-6)  
 
 Input file:  test13c.gdf  
TEST13C cylinder R=1 T=2 -- analytic geometry (npatch=2)  
1. 9.80665  ULEN GRAV  
1  1        ISX  ISY  
2  -1       NPATCH  IGDEF  
2           NLINES  
1.0 2.0     RADIUS, DRAFT  
1           UNIFORM MAPPING  
 
 Input file:  test13c.spl <span class=PICT" > <span class=PICT" >  
TEST13C cylinder R=1 T=2 -- analytic geometry (npatch=2)  
 8  8        NU NV (side)  
 8  4        NU NV (bottom)  
 
 Input file:  test13s.gdf  
TEST13S spheroid  a=2, b=c=0.25 -- igdef=-4  
1. 9.80665  ULEN GRAV  
1  1        ISX  ISY  
1  -4       NPATCH  IGDEF  
1           NLINES  
2.0 0.25 0.25    A, B, C  
 
 Input file:  test13s.spl  
TEST13S spheroid A=2 B=C=.25 -- analytic geometry (npatch=1)  
 8  4        NU NV  
 
 Input file:  test13.frc  
 TEST13.FRC -- Cylinder + spheroid, ILOWHI=1  
   1   1   1   1   1   3   1   1   1  
  1.0  
test05c.frc  
test05s.frc  
  0  
  1  
  0. 0. 0.  
 
 Input file:  test13c.csf  
test13c.csf   cylinder control surface  
1   ILOWHICSF  
1  1        ISX  ISY  
3 -1001  1. NPATCH  ICDEF  PSZCSF  
2  
1.2 2.2   1.     RADIUS, DRAFT , Inner radius  
0             uniform mapping  
 
 
 Input file:  test13s.csf  
ELLIPSOID CONTROL SURFACE defined by subroutine ELLIPSOID\_CS  
1   ILOWHICSF  
1  1        ISX  ISY  
2 -1003  1.0  NPATCH  IGDEF PSZCSF  
2           NLINES  
2.2 0.3 0.3    A, B, C  (semi-axes of outer control surface)  
2.0 0.25                (semi-axes of body waterline) <span class=PICT" > <span class=PICT" >  
  

PICT PICT

TEST13A illustrates the use of trimmed waterlines, as specified by the last three lines of the file TEST13A.CFG. The cylinder is raised vertically by 1m, and rotated about the pitch axis by 15 degrees. The options IRR=3 and IRR=1 are used to remove irregular frequency effects, as described in Section 9.4. The interior free surface of the spheroid is defined by the GDF file and subroutine ELLIPSOID, with IRR=1 (See Sections 6.8 and 9.1). The interior free surface of the trimmed cylinder is defined automatically by the program, based on the trimmed waterline, with IRR=3 (See Section 9.4). (Since the cylinder is trimmed the waterplane is elliptical, and the IRR=1 extension of CIRCCYL in GEOMXACT is not valid.) Note that NPATCH=2 is assigned in test13as.gdf, to provide for the interior free surface, and test13as.spl includes the spline parameters NU,NV for this extra patch. Conversely for the cylinder the input files test13ac.gdf and test13ac.spl do not include the extra patch since this is added by the program using IRR=3.


PICT PICT PICT PICT

PIC PICT PICT


PICT PICT
 
 Input file:  test13a.cfg  
! TEST13A.CFG -- Cylinder + spheroid with trim  
 IPLTDAT=4  
 ILOWHI=1  
 IRR(1)=3  
 IRR(2)=1  
 ILOG=1  
 ISOLVE=1  
 KSPLIN=3  
 IQUADO=3  
 IQUADI=4  
 NUMHDR=1  
 NOOUT=0 1 1 1 0 1 1 1 1  
 IALTFRC = 3    !  Alternative Form 3 FRC  
 IALTFRCN= 1 1  
 ITRIMWL=1    trim waterline  
 XTRIM(1)=  1.0 15. 0.  
 XTRIM(2)=  0.0  0. 0.  
 
 Input file:  test13a.pot  
 test13a.POT -- Trimmed Cylinder + spheroid, IRR=3  
 -1.  
 1           1               IRAD, IDIFF  
 2                           NPER (array PER follows)  
  1.00   2.00  
 1                           NBETA (array BETA follows)  
 0.  
 2                            NBODY  
 test13ac.gdf  
 1.25 0.0 0.0 0.0             XBODY  
 1  1  1  1  1  1             IMODE(1-6)  
 test13as.gdf  
 -0.5 0.0 0.0 90.0            XBODY  
 1  1  1  1  1  1             IMODE(1-6)  
 
 Input file:  test13ac.gdf  
test13ac.gdf -- Cylinder, trimmed, no interior fs  
1. 9.80665  ULEN GRAV  
1  1        ISX  ISY  
2  -1       NPATCH  IGDEF <span class=PICT" > <span class=PICT" >  
2           NLINES  
1.0 2.0     RADIUS, DRAFT  
0           UNIFORM MAPPING  
 
 Input file:  test13as.gdf  
test13as.gdf -- untrimmed spheroid with interior fs IRR=1  
1. 9.80665  ULEN GRAV  
1  1        ISX  ISY  
2  -4       NPATCH  IGDEF  
1           NLINES  
2.0 0.25 0.25    A, B, C  
 
 Input file:  test13ac.spl  
TEST13C cylinder R=1 T=2 -- analytic geometry (npatch=2)  
 8  8        NU NV (side)  
 8  4        NU NV (bottom)  
 
 Input file:  test13as.spl  
test13as.spl -- untrimmed spheroid with interior fs for IRR=3  
 4  2     body patch   NU NV  
 4  2     interior fs  NU NV  
 
 Input file:  test13a.frc  
 TEST13a.FRC -- Cylinder + spheroid, trimmed waterlines  
   1   1   1   1   0   3   0   1   1  
  1.0  
test05c.frc  
test05s.frc  
  0  
  1  
  0. 1. 0.  
  

PICT PICT

A.14 ISSC TLP – TEST14

The subroutine TLP (IGDEF=-9) is used to generate the ISSC TLP with the dimensions specified in TEST14.GDF. Except for the geometry, the inputs correspond to the low-order test runs TEST06 and TEST07. As explained in Appendix A.6 a warning message is displayed for Options 8 and 9 since IDIFF=0.

For TEST14a, TEST14a.CFG TEST14a.POT and TEST14a.FRC are used to output data to be used as input to F2T. TEST14.GDF and TEST14.SPL are used without change. TEST14a.POT has zero and infinite frequencies and 99 uniformly spaced additional frequencies. IPERIN=2 is specified in the cfg file. In FRC, IOPTN(4) is set to output the RAOs in all six modes.

Since there are a large number of wave frequencies in TEST14a, it is a good example of the benefit of multiple processors (See Section 14.6). The runtimes in this case using NCPU=1,2,4,8 are almost inversely proportional to NCPU.


PICT PICT PICT PICT

PIC PICT PICT


PICT PICT
 
 Input file:  test14.cfg  
! TEST14.CFG -- ISSC TLP (ILOWHI=1)  
 ipltdat=5  
 ILOWHI=1  
 IRR=0  
 ISOLVE=1  
 IQUADI=4  
 IQUADO=3  
 KSPLIN=3  
 NUMHDR=1  
 IALTFRC=2  
 
 Input file:  test14.pot  
TEST14 -- ISSC TLP (ILOWHI=1)  
 450  
 0         0                  IRAD, IDIFF  
 3                            NPER (array PER follows)  
 5. 10. 15.  
 1                            NBETA (array BETA follows)  
 0.  
 1                            NBODY  
 test14.gdf  
 0. 0. 0. 0.                  XBODY  
 1  0  1  0  1  0             IMODE(1-6)  
 
 Input file:  test14.gdf  
TEST14 -- ISSC TLP (ILOWHI=1)  
43.125  9.80665  ULEN GRAV  
1  1        ISX  ISY  
12 -9     NPATCH, IGDEF  
2           NLINES  
8.435  35.    43.125      RADIUS  DRAFT  HSPACE  
7.5    10.5               WIDTH   HEIGHT  

PICT PICT

 
 Input file:  test14.spl  
TEST14 -- ISSC TLP (ILOWHI=1)  
1  2        NU NV patch 1  
1  2        NU NV patch 2  
1  2        NU NV patch 3  
1  2        NU NV patch 4  
1  2        NU NV patch 5  
1  2        NU NV patch 6  
1  2        NU NV patch 7  
1  2        NU NV patch 8  
4  1        NU NV patch 9  
4  2        NU NV patch 10  
4  1        NU NV patch 11  
1  1        NU NV patch 12  
 
 Input file:  test14.frc  
TEST14 -- ISSC TLP (ILOWHI=1, IALTFRC=2)  
 1  1  1 -2  0  0  0  1  1  IOPTN (IOPTN(4)<0 signifies fixed modes)  
 6                          NDFR  
 1 1 0 0 0 1                IMODE  
 1.                         RHO  
 0. 0. 3.0                  XCG  
 1                          IMASS  
    53066.4      0.        0.        0.     159199.2         0.  
        0.   53066.4       0.  -159199.2         0.          0.  
        0.       0.    53066.4       0.          0.          0.  
        0. -159199.2       0.  8.0201552E7       0.          0.  
   159199.2      0.        0.        0.   8.0201552E7        0.  
        0.       0.        0.        0.          0.  9.54906731E7  
 0                          IDAMP  
 0                          ISTIFF  
 0                          NBETAH  
 0                          NFIELD  
  

PICT PICT

 
 Input file:  test14a.cfg  
 ILOWHI=1  
 IRR=0  
 ISOLVE=1  
 IQUADI=4  
 IQUADO=3  
 KSPLIN=3  
 NUMHDR=1  
 IALTFRC=2  
 IPERIN=2  
 IPEROUT=2  
 
 Input file:  test14a.pot  
TEST14A -- ISSC TLP (ILOWHI=1)  
 450  
 0         0                  IRAD, IDIFF  
 -101                            NPER (array PER follows)  
 -0.05 0.05  
 1                            NBETA (array BETA follows)  
 0.  
 1                            NBODY  
 test14.gdf  
 0. 0. 0. 0.                  XBODY  
 1  0  1  0  1  0             IMODE(1-6)  
 
 Input file:  test14a.frc  
 TEST14A -- ISSC TLP (ILOWHI=1, IALTFRC=2)  
 1  1  1  1  0  0  0  0  0  IOPTN  
 1.                         RHO  
 0. 0. 3.0                  XCG  
 1                          IMASS  
    53066.4      0.        0.        0.     159199.2         0.  
        0.   53066.4       0.  -159199.2         0.          0.  
        0.       0.    53066.4       0.          0.          0.  
        0. -159199.2       0.  8.0201552E7       0.          0.  
   159199.2      0.        0.        0.   8.0201552E7        0.  
        0.       0.        0.        0.          0.  9.54906731E7  
 0                          IDAMP  
 0                          ISTIFF  
 0                          NBETAH <span class=PICT" > <span class=PICT" >  
 0                          NFIELD  
  

A.15 SEMI-SUB – TEST15

The subroutine SEMISUB (IGDEF=-10) is used to generate a Semi-submersible with the dimensions specified in TEST15.GDF. There are five columns on each pontoon, as shown in the figures below. For this structure a total of 10 patches are required. If NPATCH=11, extensions of the pontoons can be included as explained in the subroutine comments.

Option 7 is used to evaluate the drift force and moment from the method described in Chapter 11. The control surface is defined by the program, using the automatic method described in Section 11.4, with the input parameters specified in the CSF file. The outer control surface is a rectangular box, and three inner partitions are defined to separate the columns, as discussed in Example 4 of Section 11.4.


PICT PICT PICT PICT

PIC PICT PICT


PICT PICT
 
 Input file:  test15.cfg  
! TEST15.CFG -- Semi-sub with five columns on each pontoon  
 ipltdat=1  
 ISOLVE=1  
 NUMHDR=1  
 KSPLIN=3  
 IQUADI=4  
 IQUADO=3  
 ILOWHI=1  
 
 Input file:  test15.pot  
TEST15  Semi-sub with five columns on each pontoon  
 -1.  
  0           0               IRAD, IDIFF  
 1                           NPER (array PER follows)  
 18.0  
 1                           NBETA (array BETA follows)  
 180.  
 1                            NBODY  
 test15.gdf  
 0. 0. 0. 0.                  XBODY  
 0  0  1  0  1  0             IMODE(1-6)  
 
 Input file:  test15.gdf  
TEST15  Semi-sub, NCOL=5, IGDEF=-10  
1.  9.80665  ULEN GRAV  
1   1        ISX  ISY  
10 -10       NPATCH IGDEF  
2            NLINES  
260. 20. 40. -30. -20.            XL, Y1, Y2, Z1, Z2  
60. 8. 5                          DCOL, RCOL, NCOL  
 
 Input file:  test15.spl  
TEST15  Semi-sub, NCOL=5, IGDEF=-10  
9  2        NU NV                 (patch 10+32 - pontoon bottom)  
32 1        NU NV                 (patch 9+32 - pontoon side)  
2  2        NU NV                 (patch 1+32 - column 3)  
2  1        NU NV                 (patch 2+32 - annulus 3)  
5  2        NU NV                 (patch 3+32 - between annulus 3&4)  
4  2        NU NV                 (patch 4+32 - column 4) <span class=PICT" > <span class=PICT" >  
4  1        NU NV                 (patch 5+32 - annulus 4)  
5  2        NU NV                 (patch 6+32 - between annulus 4&5)  
4  2        NU NV                 (patch 7+32 - column 5)  
4  1        NU NV                 (patch 8+32 - annulus 5)  
 
 Input file:  test15.frc  
TEST15  Semi-sub with five columns on each pontoon  
   1   1   1   1   0   0   1   1   1  
       0.0000  
       20.0      0.0        0.0  
       0.        60.0        0.0  
       0         0.         60.0  
       0  
       0  
 
 Input file:  test15.csf  
 test15.csf  semi sub, outer box 150*60*40  
1   ILOWHICSF  
1  1        ISX  ISY  
0   0  10. NPATCH  ICDEF  PSZCSF   (1st two indicate this is automatic)  
 0.0  40.0    RADIUS, DRAFT of outer box  
  4   NPART  
  3   nv0  
  150.0   0.0  
  150.0  60.0  
    0.0  60.0   end of partition line 0 (outer boundary of control surface)  
  3   nv1  
   0.0  0.0  
  30.0  0.0  
  30.0  50.0  
  4   nv2  
  30.0  50.0  
  30.0  0.0  
  90.0  0.0  
  90.0  50.0  
  3   nv3  
  90.0  50.0  
  90.0  0.0  
  150.0  0.0   end of partition line column 3  
  

PICT PICT

A.16 BARGE WITH BENDING MODES – TEST16

The test runs TEST16 and TEST16a analyze the structural response of a rectangular barge with total length 80m, beam 10m, and draft 5m. Eight free-free beam modes are included to analyze the elastic deformation of the barge. These mode shapes are defined in the NEWMODES subroutine FREEBEAM_X and the length is input to this subroutine using the file test16_Length.dat, as described in Section 9.3. The response amplitude of each mode is included in the RAO’s.

In TEST16 the subroutine BARGE (IGDEF=-5) is used. The half-length, half-beam and draft are specified in TEST16.GDF. In TEST16a the option IGDEF=0 is used, with the vertices of the patches specified in TEST16a.GDF in the same format as for low-order panels.


PICT PICT PICT PICT

PIC PICT PICT


PICT PICT
 
 Input file:  test16.cfg  
! TEST16.CFG elastic barge with 8 beam modes  
 ipltdat=5  
 ilowgdf=5  
 ILOWHI=1  
 IALTFRC=2  
 ISOLVE=1  
 IQUADI=5  
 IQUADO=4  
 MONITR=0  
 NUMHDR=1  
 IGENMDS=16  
 NEWMDS=8  
 
 Input file:  test16.pot  
TEST16 elastic barge with 8 beam modes  
 -1.  
 0           0               IRAD, IDIFF  
 2                            NPER (array PER follows)  
 7. 8.  
 1                             NBETA (array BETA follows)  
 180.  
 1                            NBODY  
test16.gdf  
 0. 0. 0. 0.                  XBODY  
 1  0  1  0  1  0             IMODE(1-6)  
 
 Input file:  test16.gdf  
TEST16 elastic barge  
1. 9.80665  ULEN GRAV  
1  1        ISX  ISY  
3  -5       NPATCH  IGDEF  
1           NLINES  
40.0   5.0  5.0         half-length, half-beam, draft  
 
 Input file:  test16.spl  
TEST16 elastic barge  
3  3        NU NV   (end)  
4  4        KU KV  
5  2                (side) <span class=PICT" > <span class=PICT" >  
4  4  
5  2                (bottom)  
4  4  
            IQUO IQVO are not specified IQUADO=3 in config.wam  
            IQUI IQVI are not specified IQUADI=4 in config.wam  
 
 Input file:  test16.frc  
TEST16 elastic barge with 8 beam modes  
 1  1  1  1  0  0  0  0  0  
 1000.  
 0. 0. 0.  
 1  
  4.00000E+06 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.  
  0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.  
  0. 0. 4.E+06 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.  
  0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.  
  0. 0. 0. 0. 2.13333E+09 0. 0. 0. 0. 0. 0. 0. 0. 0.  
  0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.  
  0. 0. 0. 0. 0. 0. 1.E+06 0. 0. 0. 0. 0. 0. 0.  
  0. 0. 0. 0. 0. 0. 0. 1.E+06 0. 0. 0. 0. 0. 0.  
  0. 0. 0. 0. 0. 0. 0. 0. 1.E+06 0. 0. 0. 0. 0.  
  0. 0. 0. 0. 0. 0. 0. 0. 0. 1.E+06 0. 0. 0. 0.  
  0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 1.E+06 0. 0. 0.  
  0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 1.E+06 0. 0.  
  0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 1.E+06 0.  
  0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 1.E+06  
 0  
 1  
  0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.  
  0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.  
  0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.  
  0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.  
  0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.  
  0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.  
  0. 0. 0. 0. 0. 0. 6.25705E+06 0. 0. 0. 0. 0. 0. 0.  
  0. 0. 0. 0. 0. 0. 0. 4.75441E+07 0. 0. 0. 0. 0. 0.  
  0. 0. 0. 0. 0. 0. 0. 0. 1.82720E+08 0. 0. 0. 0. 0.  
  0. 0. 0. 0. 0. 0. 0. 0. 0. 4.99297E+08 0. 0. 0. 0.  
  0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 1.11419E+09 0. 0. 0.  
  0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 2.17352E+09 0. 0.  
  0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 3.85260E+09 0.  
  0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 6.35602E+09  
0  
0 <span class=PICT" > <span class=PICT" >  
  

PICT PICT

 
 Input file:  test16a.pot  
TEST16a elastic barge with 8 beam modes - igdef=0  
 -1.  
 0           0               IRAD, IDIFF  
 2                            NPER (array PER follows)  
 7. 8.  
 1                             NBETA (array BETA follows)  
 180.  
 1                            NBODY  
test16a.gdf  
 0. 0. 0. 0.                  XBODY  
 1  0  1  0  1  0             IMODE(1-6)  
 
 First 10 lines of input file:  test16a.gdf  
TEST16a elastic barge with 8 beam modes - igdef=0 (3 flat panels)  
     1.0000        9.80665  
           1           1  
           3           0          NPATCH, IGDEF  
    40.0000       0.000000       -5.00000  
    40.0000        5.00000       -5.00000  
    40.0000        5.00000       0.000000  
    40.0000       0.000000       0.000000   (end)  
    40.0000        5.00000       -5.00000  
   0.000000        5.00000       -5.00000  
 
 Input file:  test16a.spl  
TEST16A elastic barge with igdef=0 (patches defined by flat panels)  
3  3        NU NV       end  
4  4        KU KV  
5  2                    side  
4  4  
5  2                    bottom  
4  4  

PICT PICT

 
 Input file:  test16a.frc  
TEST16a elastic barge with 8 beam modes (igdef=0)  
 1  1  1  1  0  0  0  0  0  
 1000.  
 0. 0. 0.  
 1  
  4.00000E+06 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.  
  0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.  
  0. 0. 4.E+06 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.  
  0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.  
  0. 0. 0. 0. 2.13333E+09 0. 0. 0. 0. 0. 0. 0. 0. 0.  
  0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.  
  0. 0. 0. 0. 0. 0. 1.E+06 0. 0. 0. 0. 0. 0. 0.  
  0. 0. 0. 0. 0. 0. 0. 1.E+06 0. 0. 0. 0. 0. 0.  
  0. 0. 0. 0. 0. 0. 0. 0. 1.E+06 0. 0. 0. 0. 0.  
  0. 0. 0. 0. 0. 0. 0. 0. 0. 1.E+06 0. 0. 0. 0.  
  0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 1.E+06 0. 0. 0.  
  0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 1.E+06 0. 0.  
  0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 1.E+06 0.  
  0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 1.E+06  
 0  
 1  
  0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.  
  0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.  
  0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.  
  0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.  
  0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.  
  0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.  
  0. 0. 0. 0. 0. 0. 6.25705E+06 0. 0. 0. 0. 0. 0. 0.  
  0. 0. 0. 0. 0. 0. 0. 4.75441E+07 0. 0. 0. 0. 0. 0.  
  0. 0. 0. 0. 0. 0. 0. 0. 1.82720E+08 0. 0. 0. 0. 0.  
  0. 0. 0. 0. 0. 0. 0. 0. 0. 4.99297E+08 0. 0. 0. 0.  
  0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 1.11419E+09 0. 0. 0.  
  0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 2.17352E+09 0. 0.  
  0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 3.85260E+09 0.  
  0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 6.35602E+09  
0  
0  
  
PICT PICT

PICT PICT

A.17 CYLINDER WITH MOONPOOL – TEST17

This test run illustrates three alternative methods for analyzing bodies with moonpools. The geometry used is the circular cylinder with a concentric fluid chamber, as shown in the figure. The inner chamber of fluid, referred to as a ‘moonpool’, is open at the bottom of the cylinder to the external fluid domain. The top of the moonpool is a free surface with atmospheric pressure. One of the practical aspects of this problem is the existence of highly tuned resonant frequencies of the motion at the moonpool free surface. If the draft is comparable or large compared to the horizontal dimensions of the moonpool, the principal resonance is a ‘pumping mode’ which occurs when Kd, the product of the wavenumber K and draft d is slightly less than one. Additional resonances occur in ‘sloshing modes’ at higher frequencies, corresponding approximately to standing waves inside the moonpool.

A cylinder with draft 1m is used, with the outer radius 0.5m and the inner radius 0.25m. The geometry is represented analytically by the subroutine CYLMP (IGDEF=-7). In TEST17 three patches are used to represent the outer side r=RADIUS, the annular bottom z =-DRAFT, and the inner side r=RADMP. The free surface inside the moonpool is part of the physical free surface, and the appropriate free-surface boundary condition is satisfied by the Green function as described in Chapter 15. The side of one quadrant is omitted in the figures below, to show more clearly the bottom and the side of the moonpool.

To clarify the behavior near resonance, the wavenumber K is input in the POT file with the corresponding option IPERIN=3 specified in the TEST17.cfg file. 61 values of K are input in the range 0.1 K 1.5 to describe the behavior near resonance. The computed hydrodynamic parameters include the force coefficients, RAO’s, and the elevation of the free surface at the center of the moonpool.


PICT PICT PICT PICT

PIC PICT PICT


When the structure is fixed in heave the resonant pumping mode in the moonpool occurs at Kd = 0.85. The outputs related to the vertical force component display singular features near this point. This includes large amplitudes of the heave damping and exciting force, and negative added mass. The heave RAO has two adjacent resonant peaks as shown in the Figure below, due to coupling between the heave mode and the moonpool pumping mode.


PICT PICT PICT PICT

PIC

Figure A.1: Heave RAO for each of the test17 runs. The results for Test17, Test17a, and Test17c are practically identical. The results for Test17b (lid with damping) include three values of the external damping coefficients. In Test17b b33 = 0.4 and b77 = 0.1, as shown in the test17b.frc file below. In Test17bh these values are reduced by a factor of one-half and in Test17bq they are reduced by a factor of one-quarter.
PICT PICT


These very large responses are non-physical, and their existence in the computations can be attributed primarily to the neglect of viscous damping associated with flow separation at the outer and inner corners of the cylinder. This damping is only important when the vertical motions of the cylinder and/or moonpool are large. Typical resonant amplitudes are likely to be in the range represented by the dashed lines in Figure A.1.

In order to damp the moonpool response and heave motions separately, a different physical problem is considered where a ‘lid’ is placed on the free surface of the moonpool. This lid is considered to be an extension of the body surface, and represented by an additional patch. Thus NPATCH=4 is assigned in test17a.gdf (and used also in Test17b and Test17c). The geomxact subroutine CYLMP assigns the patch number 4 to be the circular disc of radius RADMP in the plane Z=0. However allowance must be made for the motions of the actual free surface relative to the body. This is done by defining appropriate generalized modes, which are nonzero only on patch 4. The most important mode is a vertical translation, assigned here in the subroutine file NEWMODES.F with the index j = 7. In Test17b a pitch rotation of the lid (j = 8) is also included to provide a more general deflection of the free surface. A more complete expansion can be introduced, but at the wavenumbers considered here and for head-sea incidence angle these two modes of motion are sufficient. These two generalized modes, physically analogous to pitch and heave but defined relative to the body, are introduced via the subroutine MOONPOOL_FS in NEWMODES.F.

In test run TEST17a, the lid is assumed to be free with no external force or moment acting on it. The IALTFRC=2 option is employed, and the only external force matrix that is included in TEST17.FRC is the mass matrix of the body. This mass matrix is equivalent to the radii of gyration specified in TEST17.FRC. It can be confirmed by comparison of the outputs that the motions of the body (RAO) are virtually identical to TEST17, as shown in the Figure above, confirming that the representation of the moonpool free surface in this manner is legitimate. A comparison can also be made between the moonpool free surface elevation (numeric output file TEST17.6) and the response of the lid in mode 7 (RAO(7) in the numeric output file TEST17a.4), but in this comparison account must be made for the fact that RAO(7) is relative to the body motions, and thus it is necessary to compare the (complex) sum RAO(3)+RAO(7) in TEST17a with the moonpool free surface elevation in TEST17. The input_     file test17a.pot uses the optional parameter NPERGROUP to define the same array of wavenumbers as in test17.pot in a more compact manner, as described in Section 4.2.

In TEST17b, empirical damping is introduced via the external damping matrix in TEST17b.FRC. Since this is the only difference between TEST17a and TEST17b, it is not necessary to re-run POTEN and the same TEST17a.P2F file is used for TEST17b. Thus TEST17a.pot is specified in FNAMES.17b, and IPOTEN=0 in the TEST17b.cfg file. The only nonzero elements of the external damping matrix are for heave (j = 3) and the lid vertical motion (j = 7). With these empirical damping coefficients added, more appropriate RAO’s are obtained as shown in the Figure. This general approach can be refined based on experimental PICT PICT data. Experience with similar problems suggests that relatively crude estimates based on the observed response at resonance are sufficient to correct the response over a broad range of wave periods.

In TEST17c the same geometry is used with the free-surface pressure option (FSP) described in Section 10.11. The FSP surface is the same as the lid described above, and the same gdf file is used as in TEST17a and 17b. In the CFG file the parameter IMODESFSP=1 is used to select the subroutine PRESSURE_FS in the NEWMODES.DLL file, and NMODESFSP=1. The pressure distribution on the FSP surface is constant. To correspond with the original Test17, the pressure represented by mode 7 is set equal to zero by assigning mode 7 to be fixed in the file test17c.frc. PICT PICT

 
 Input file:  test17.cfg  
! TEST17.CFG file, cylinder with moonpool  
 ipltdat=5  
 ilowgdf=5  
 ILOWHI=1  
 IALTFRC=1  
 ISOLVE=1  
 PANEL_SIZE = 0.2       (use default .spl parameters)  
 IPERIN=3               (input wavenumber)  
 IPEROUT=3              (output wavenumber)  
 NUMHDR=1  
 
 Input file:  test17.pot  
TEST17 cylinder with moonpool, NPATCH=3  
 -1.  
 0           0               IRAD, IDIFF  
          61  
    0.100000    0.150000    0.200000    0.250000    0.300000  
    0.350000    0.400000    0.450000    0.500000    0.550000  
    0.600000    0.610000    0.620000    0.630000    0.640000  
    0.650000    0.660000    0.670000    0.680000    0.690000  
    0.700000    0.710000    0.720000    0.730000    0.740000  
    0.750000    0.760000    0.770000    0.780000    0.790000  
    0.800000    0.810000    0.820000    0.830000    0.840000  
    0.850000    0.860000    0.870000    0.880000    0.890000  
    0.900000    0.910000    0.920000    0.930000    0.940000  
    0.950000    0.960000    0.970000    0.980000    0.990000  
    1.000000    1.050000    1.100000    1.150000    1.200000  
    1.250000    1.300000    1.350000    1.400000    1.450000  
    1.500000  
 1                             NBETA (array BETA follows)  
 180.  
 1                            NBODY  
test17.gdf  
 0. 0. 0. 0.                  XBODY  
 1  0  1  0  1  0             IMODE(1-6)  

PICT PICT

 
 Input file:  test17.gdf  
TEST17 cylinder with moonpool  
1. 9.80665  ULEN GRAV  
1  1        ISX  ISY  
3  -7       NPATCH  IGDEF  
1           NLINES  
0.5 1.0 0.25     radius, draft, moonpool radius  
 
 Input file:  test17.frc  
TEST17.FRC  Cylinder with moonpool  
 1    1    1    1    0    1  0  0 0     IOPTN(1-9)  
 0.000000                                    VCG  
 0.500000      .0000000      .0000000  
 .0000000      0.500000      .0000000  
 .0000000      .0000000      0.500000        XPRDCT  
 0                                           NBETAH  
 1                                           NFIELD  
0.0 0.0 0.0  
  

PICT PICT

 
 Input file:  test17a.cfg  
! TEST17A.CFG file, cylinder with moonpool, free lid  
 ipltdat=5  
 ilowgdf=5  
 ILOWHI=1  
 IALTFRC=2  
 ISOLVE=1  
 PANEL_SIZE = 0.2       (use default .spl parameters)  
 IPERIN=3               (input wavenumber)  
 IPEROUT=3              (output wavenumber)  
 ILOG=1  
 NUMHDR=1  
 IGENMDS=17  
 NEWMDS = 2  
 
Input file:  test17a.pot  
TEST17 cylinder with moonpool, NPATCH=3  
 -1.  
 0           0               IRAD, IDIFF  
  NPERGROUP=3  
   -11  
   0.10 0.05    (end of group 1, K = 0.10 to 0.60)  
   -40  
   0.61 0.01    (end of group 2, K = 0.61 to 1.00)  
   -10  
   1.05 0.05    (end of group 3, K = 1.05 to 1.50)  
 1                             NBETA (array BETA follows)  
 180.  
 1                            NBODY  
test17a.gdf  
 0. 0. 0. 0.                  XBODY  
 1  0  1  0  1  0             IMODE(1-6)  

PICT PICT

 
 Input file:  test17a.gdf  
TEST17a cylinder with moonpool -- undamped patch on free surface  
1. 9.80665  ULEN GRAV  
1  1        ISX  ISY  
4  -7       NPATCH  IGDEF  
1           NLINES  
0.5 1.0 0.25     radius, draft, moonpool radius  
 
 Input file:  test17a.frc  
TEST17a moonpool with generalized modes for free surface - no damping  
 1  1  1  1  0  0  0  0  0  
 1.  
 0. 0. 0.  
    1  imass (mass matrix of body)  
    0.589    0.0      0.0      0.0      0.0      0.0      0.0      0.0  
    0.0      0.589    0.0      0.0      0.0      0.0      0.0      0.0  
    0.0      0.0      0.589    0.0      0.0      0.0      0.0      0.0  
    0.0      0.0      0.0      0.147    0.0      0.0      0.0      0.0  
    0.0      0.0      0.0      0.0      0.147    0.0      0.0      0.0  
    0.0      0.0      0.0      0.0      0.0      0.147    0.0      0.0  
    0.0      0.0      0.0      0.0      0.0      0.0      0.0      0.0  
    0.0      0.0      0.0      0.0      0.0      0.0      0.0      0.0  
    0  idamp  
    0  istif  
 0  
 0  
  

PICT PICT

 
 Input file:  test17b.cfg  
! TEST17B.CFG file, cylinder with moonpool, damped lid  
 ILOWHI=1  
 IPOTEN=0  
 IALTFRC=2  
 ISOLVE=1  
 PANEL_SIZE = 0.2       (use default .spl parameters)  
 IPERIN=3               (input wavenumber)  
 IPEROUT=3              (output wavenumber)  
 ILOG=1  
 NUMHDR=1  
 IGENMDS=17  
 NEWMDS = 2  
 
 Input file:  test17b.frc  
TEST17b cylinder+moonpool, generalized modes, damping b33=.4, b77=.1  
 1  1  1  1  0  0  0  0  0  
 1.  
 0. 0. 0.  
    1  imass (mass matrix of body)  
    0.589    0.0      0.0      0.0      0.0      0.0      0.0      0.0  
    0.0      0.589    0.0      0.0      0.0      0.0      0.0      0.0  
    0.0      0.0      0.589    0.0      0.0      0.0      0.0      0.0  
    0.0      0.0      0.0      0.147    0.0      0.0      0.0      0.0  
    0.0      0.0      0.0      0.0      0.147    0.0      0.0      0.0  
    0.0      0.0      0.0      0.0      0.0      0.147    0.0      0.0  
    0.0      0.0      0.0      0.0      0.0      0.0      0.0      0.0  
    0.0      0.0      0.0      0.0      0.0      0.0      0.0      0.0  
    1  idamp  
    0.0      0.0      0.0      0.0      0.0      0.0      0.0      0.0  
    0.0      0.0      0.0      0.0      0.0      0.0      0.0      0.0  
    0.0      0.0      0.4      0.0      0.0      0.0      0.0      0.0  
    0.0      0.0      0.0      0.0      0.0      0.0      0.0      0.0  
    0.0      0.0      0.0      0.0      0.0      0.0      0.0      0.0  
    0.0      0.0      0.0      0.0      0.0      0.0      0.0      0.0  
    0.0      0.0      0.0      0.0      0.0      0.0      0.1      0.0  
    0.0      0.0      0.0      0.0      0.0      0.0      0.0      0.0  
    0  istif  
 0  
 0 <span class=PICT" > <span class=PICT" >  
  

PICT PICT

 
 Input file:  test17c.cfg  
 ILOWHI=1  
 IALTFRC=1  
 ISOLVE=1  
 PANEL_SIZE = 0.2       (use default .spl parameters)  
 IPERIN=3               (input wavenumber)  
 IPEROUT=3              (output wavenumber)  
 IRR=0  
 ILOG=1  
 NUMHDR=1  
 NPFSP=(4 4)            (free surface pressure on patch 4)  
 IMODESFSP=1            (use NEWMODES subroutine PRESSURE_FS)  
 NMODESFSP=1            (1 pressure mode, same symmetry as heave)  
 
 Input file:  test17c.pot  
TEST17c  cylinder with free-surface pressure in moonpool  
 -1.  
 0       1               IRAD, IDIFF  
          61  
    0.100000    0.150000    0.200000    0.250000    0.300000  
    0.350000    0.400000    0.450000    0.500000    0.550000  
    0.600000    0.610000    0.620000    0.630000    0.640000  
    0.650000    0.660000    0.670000    0.680000    0.690000  
    0.700000    0.710000    0.720000    0.730000    0.740000  
    0.750000    0.760000    0.770000    0.780000    0.790000  
    0.800000    0.810000    0.820000    0.830000    0.840000  
    0.850000    0.860000    0.870000    0.880000    0.890000  
    0.900000    0.910000    0.920000    0.930000    0.940000  
    0.950000    0.960000    0.970000    0.980000    0.990000  
    1.000000    1.050000    1.100000    1.150000    1.200000  
    1.250000    1.300000    1.350000    1.400000    1.450000  
    1.500000  
 1                             NBETA (array BETA follows)  
 180.  
 1                            NBODY  
test17a.gdf  
 0. 0. 0. 0.                  XBODY  
 1  0  1  0  1  0             IMODE(1-6)  
 
   <span class=PICT" > <span class=PICT" >

PICT PICT

 
 Input file:  test17c.frc  
TEST17c.FRC cylinder with surface pressure in moonpool, fixed mode 7  
 1    1    1    -1    0    0  0  0 0     IOPTN(1-9)  
 7  
 1    1    1   1    1    1   0  
 0.000000                                    VCG  
 0.500000      .0000000      .0000000  
 .0000000      0.500000      .0000000  
 .0000000      .0000000      0.500000        XPRDCT  
 0                                           NBETAH  
 0                                           NFIELD  
 
  

PICT PICT

A.18 ELASTIC COLUMN – TEST18

The same inputs are used as in the low-order test run TEST08, except for the GDF file. The circular column is represented by the subroutine CIRCCYL (IGDEF=-1). Since the cylinder is bottom-mounted, NPATCH=1 and the patch on the bottom of the cylinder is omitted. The draft is set equal to the fluid depth. IGENMDS=18 is assigned in CFG file, and in NEWMODES this results in a call to subroutine JACOBI for the four shifted Jacobi polynomials, as described in Section 9.3.


PICT PICT PICT PICT

PIC PICT PICT


PICT PICT
 
 Input file:  test18.cfg  
! TEST18.CFG -- bending of vertical column with 4 generalized modes  
 ipltdat=5  
 ilowgdf=5  
 ISOLVE=1  
 NUMHDR=1  
 NUMNAM=0  
 NEWMDS=4  
 ILOWHI=1  
 IALTFRC=2  
 KSPLIN=3  
 IQUADO=3  
 IQUADI=4  
 IGENMDS=18  
 
 Input file:  test18.pot  
TEST18.POT -- bending of vertical column at resonance, 200m depth  
      200.0       HBOT  
   0   0                          IRAD,IDIFF  
           1  
           6.5  
           1  
           0.0  
   1                          NBODY  
 test18.gdf  
  0.0  0.0  0.0  0.0  
        0   0   0   0   0   0  
 
 Input file:  test18.gdf  
TEST18.GDF vertical cylinder, bottom mounted  
     1.0000        9.80665     ulen, grav  
    1   1               isx,isy  
    1  -1               npatch, igdef  
    2           NLINES  
    10.0000  200.000    radius, draft  
    0                   uniform mapping  
 
 Input file:  test18.spl  
TEST18.spl - bottom-mounted cylinder R=10 T=200 -- (npatch=1)  
4  8        NU NV (Patch 1, side   u azimuthal v vertical) <span class=PICT" > <span class=PICT" >  

PICT PICT

 
 Input file:  test18.frc  
TEST08.FRC file, vertical column with 4 bending modes  
         1    1    1    1    0    0    0    0   0  
        1.0  
        .0000000      .0000000      1.000000  
    1  
  0.   0.   0.   0.   0.   0.        0.        0.        0.        0.  
  0.   0.   0.   0.   0.   0.        0.        0.        0.        0.  
  0.   0.   0.   0.   0.   0.        0.        0.        0.        0.  
  0.   0.   0.   0.   0.   0.        0.        0.        0.        0.  
  0.   0.   0.   0.   0.   0.        0.        0.        0.        0.  
  0.   0.   0.   0.   0.   0.        0.        0.        0.        0.  
  0.   0.   0.   0.   0.   0.    69115.    62832.    62832.    62832.  
  0.   0.   0.   0.   0.   0.    62832.    67320.    62832.    62832.  
  0.   0.   0.   0.   0.   0.    62832.    62832.    66323.    62832.  
  0.   0.   0.   0.   0.   0.    62832.    62832.    62832.    65688.  
    0  
    1  
  0.   0.   0.   0.   0.   0.        0.        0.        0.         0.  
  0.   0.   0.   0.   0.   0.        0.        0.        0.         0.  
  0.   0.   0.   0.   0.   0.        0.        0.        0.         0.  
  0.   0.   0.   0.   0.   0.        0.        0.        0.         0.  
  0.   0.   0.   0.   0.   0.        0.        0.        0.         0.  
  0.   0.   0.   0.   0.   0.        0.        0.        0.         0.  
  0.   0.   0.   0.   0.   0.   103044.   412177.   824354.   1339575.  
  0.   0.   0.   0.   0.   0.   412177.  4430902.  9789203.  16487078.  
  0.   0.   0.   0.   0.   0.   824354.  9789203. 37899671.  64382041.  
  0.   0.   0.   0.   0.   0.  1339575. 16487078. 64382041. 162406554.  
    0  
    0  
  

PICT PICT

A.19 CATAMARAN BARGE – TEST19

The geometrical configuration is the same as the barge near a wall (TEST04). Since only head seas are considered, the hydrodynamic outputs correspond to TEST04 except for the different definition of the incident wave amplitude which applies for a body near a wall. In TEST19 IGDEF=0 is used, with four patches specified in the GDF file corresponding to one quadrant of the catamaran configuration. Since there are two hulls in this case, the forces acting on both hulls are two times the corresponding forces in TEST04, but since the incident wave amplitude in TEST04 is increased by a factor of two, the exciting force coefficients and RAO’s are the same in both test runs, except for small differences in accuracy. Note that in TEST19 two planes of symmetry can be utilized, unlike TEST04 where reflection about the plane x = 0 is required by the program. The comparisons of cross-coupling coefficients and Haskind/Diffraction exciting forces implies that the results of TEST19 are more accurate, with less computational cost.

Generalized modes can be used to extend the analysis of this configuration to include two independent bodies. In this case each of the rigid-body modes of the catamaran must be supplemented by a corresponding generalized mode which has the same normal velocity on one barge, and the opposite phase on the other. The separate modes of each independent body are then evaluated by combining the corresponding symmetric and antisymmetric modes for the catamaran. It is simpler to use the option NBODY=2 for this purpose, but the number of unknowns is increased by a factor of four, resulting in a substantial increase of the run time. For the more efficient approach used in TEST19 it is necessary to represent the entire forward half of one barge, as shown in the patch figure. The subroutine BARGE (IGDEF=-5) is not suitable, since this only represents one quadrant of one barge. On the other hand, BARGE can be used in the alternative NBODY=2 approach.


PICT PICT PICT PICT

PIC PICT PICT


PICT PICT
 
 Input file:  test19.cfg  
! TEST19.CFG -- Catamaran barge  
 ipltdat=5  
 ILOWHI=1  
 IALTFRC=1  
 ISOLVE=1  
 IQUADI=5  
 IQUADO=4  
 MONITR=0  
 NUMHDR=1  
 
 Input file:  test19.pot  
TEST19.POT -- Catamaran barge, same geometry as TEST04  
 -1.       HBOT  
   0   0                          IRAD,IDIFF  
 3  
 6.  7.  8.  
 1  
 0.0  
   1                          NBODY  
 test19.gdf  
 0. 0. 0. 0.  
  1  0  1  0  1  0  
 
 First 10 lines of input file:  test19.gdf  
TEST19 one quadrant of catamaran barge configuration  
40. 9.80665  ULEN GRAV  
1  1        ISX  ISY  
4  0        NPATCH  IGDEF  
    40.0000       2.000000      -10.00000  
    40.0000       22.00000      -10.00000  
    40.0000       22.00000       0.000000  
    40.0000       2.000000       0.000000   (end)  
    40.0000       22.00000      -10.00000  
   0.000000       22.00000      -10.00000  

PICT PICT

 
 Input file:  test19.spl  
TEST19 catamaran barge  
2  2        NU NV   (end)  
4  4        KU KV  
5  2                (outside)  
4  4  
5  2                (bottom)  
4  4  
5  2                (inside)  
4  4  
            IQUO IQVO are not specified IQUADO=3 in config.wam  
            IQUI IQVI are not specified IQUADI=4 in config.wam  
 
 Input file:  test19.frc  
TEST19.FRC -- Catamaran barge, ILOWHI=1 (same as TEST04.FRC)  
 1    1    1    1    1    0    0    1    1  
 3.0  
 20.00000      0.000000      0.000000  
 0.000000      5.000000      0.000000  
 0.000000      0.000000      20.00000  
 0  
 0  
  

PICT PICT

A.20 MULTISURF BARGE – TEST20

This example illustrates the use of a MultiSurf geometry representation with IGDEF=2. The barge has a length of 100m, beam 20m, and draft 4.8m with one plane of symmetry (y = 0). The origin of the body coordinate system is at the intersection of the waterplane and midship section. The format of the GDF file is as explained in ?? and ??. Four patches are used on one side of the body to represent the forebody, parallel middlebody, afterbody, and transom. Reference 24 includes results for a multiple-body configuration including two barge hulls identical to this model.

The body pressure is evaluated at the points specified in the input file test20.bpi, as explained in Section 4.11. The parameter IPNLBPT=1 in the .cfg file is used to specify this option with the input points specified in the body coordinate system.

Test 20a illustrates the use of the channel option described in Section 12.7. In this case the_     barge is on the centerline of a channel of width w =100m and depth 15m. Results for the heave and pitch RAO’s are shown in Figure A.2. (In order to reproduce all of the curves in this figure, the input files test20a.cfg and test20a.pot must be modified as noted below.)


PICT PICT PICT PICT

PIC PICT PICT


PICT PICT
 
 Input file:  test20.cfg  
! TEST20.CFG - MultiSurf barge  
 ipltdat=4  
 ILOWHI=1  
 IALTFRC=1  
 ISOLVE=1  
 NUMHDR=1  
 panel_size= 10.  
 IPNLBPT=1  
 
 Input file:  test20.pot  
single barge based on MultiSurf model (igdef=2)  
 -1.  
  1     1                     IRAD, IDIFF  
   3                          NPER (array PER follows)  
 6. 9. 12.  
 3                            NBETA (array BETA follows)  
 180. 135. 90.  
 1                            NBODY  
  test20.gdf  
 0.0  0.0  0.0  0.0              XBODY  
 1  1  1  1  1  1             IMODE(1-6)  
 
 Input file:  test20.gdf  
Test run for barge modelled with MultiSurf  
 1.000000  9.80665  ULEN, GRAV  
  0  1  ISX, ISY  
  0   2  NPATCH, IGDEF  
  3  NLINES  
test20.ms2  
wetted_surfs  
0  0  0 FAST,DivMult, outward normals  
 
 Input file:  test20.frc  
test20.frc igdef=2  
 1    1    1    1    1    0  0  1 1     IOPTN(1-9)  
   0.0                                        VCG  
 10.00000      .0000000      .0000000  
 .0000000      25.00000      .0000000  
 .0000000      .0000000      25.00000        XPRDCT <span class=PICT" > <span class=PICT" >  
 0                                           NBETAH  
 0                                           NFIELD  
 
 First 10 lines of input file:  test20.bpi  
 bpi input file for test20, body pressure points for MultiSurf barge  
         556  
    -44.7760      0.0000     -1.0074  
    -42.9240      0.0001     -1.8961  
    -45.0680      0.2891     -0.8477  
    -43.5610      0.6874     -1.6131  
    -45.3540      0.5549     -0.6847  
    -44.1780      1.2902     -1.3169  
    -40.8950      0.0006     -2.6665  
    -38.6880      0.0006     -3.3185


PICT PICT PICT PICT

PIC

Figure A.2: Heave and pitch RAO’s of the MultiSurf Barge as computed in TEST20a. The black lines are the RAO’s in a fluid domain of infinite width. The red lines are the RAO’s in a channel of width w = 100m and depth 15m. Resonant standing waves occur near kw = 2π and kw = 4π, where k = 2π∕λ is the finite-depth wavenumber and λ is the wavelength. The blue lines show the results when the parameter CHANNEL_REFLECT = 0.5 is used, to reduce the effect of the wall reflections near resonance.
PICT PICT


The input files for TEST20a are shown below. The wavenumber k is designated instead of the wave period, using the options IPERIN=4 and IPEROUT=4, to give a more physical understanding of the wall effects. A large number of closely-spaced wavenumbers are required to reproduce the curves shown in Figure A.2. These can be input by modifying test20a.pot to use the last group of lines of data in place of the two lines starting with NPER. The NPERGROUP option described in Section 4.2 is used in this case, to provide more closely-spaced wavenumbers where the curves in Figure A.2 change more rapidly.

The blue curve in Figure A.2 can be reproduced using the parameter CHANNEL_REFLECT in the cfg file, and the black curve for unbounded width can be reproduced by commenting out or removing the line with the parameter CHANNEL_WIDTH, or assigning this parameter with a value less than or equal to zero. It is not necessary to use such a large number of closely-spaced wavenumbers in the latter case. PICT PICT

 Input file:  test20a.cfg  
! TEST20a.CFG - MultiSurf barge in channel  
 ipltdat=4  
 ILOWHI=1  
 IALTFRC=1  
 ISOLVE=1  
 NUMHDR=1  
 panel_size= 10.  
 iperin=4  
 iperout=4  
 channel_width=100.0  
! channel_reflect=0.5  (used for the blue line in Figure 12.2)  
 
 Input file:  test20a.pot  
 MultiSurf barge in channel  
  15.0  
  0     0                     IRAD, IDIFF  
  -7                          NPER  
  0.02 0.02                   Coarse array of wavenumbers  
  1                           NBETA (array BETA follows)  
  180.  
  1                           NBODY  
  test20.gdf  
  0.0  0.0  0.0  0.0          XBODY  
  1  0  1  0  1  0            IMODE(1-6)  
 
 npergroup=5  !  group of wavenumbers used in Figure 12.2  
     -60  
     .001   .001  
     -50  
     .0601  .0001  
     -35  
     .066   .001  
     -190  
     .1010  .0001  
     -20  
     .121   .001  
 
 Input file:  test20a.frc  
MultiSurf barge in channel  
 1    1    1    1    0    0  0  0 0     IOPTN(1-9) <span class=PICT" > <span class=PICT" >  
   0.0                                        VCG  
 10.00000      .0000000      .0000000  
 .0000000      25.00000      .0000000  
 .0000000      .0000000      25.00000        XPRDCT  
 0                                           NBETAH  
 0                                           NFIELD  }

A.21 SPAR WITH THREE STRAKES – TEST21

The subroutine SPAR (IGDEF=-12) is used to generate the SPAR with three strakes with the dimensions specified in TEST21.GDF. Except for the geometry, the inputs correspond to the low-order test runs TEST09.


PICT PICT PICT PICT

PIC PICT PICT


PICT PICT
 
 Input file:  test21.cfg  
! TEST21.CFG -- SPAR with three strakes  
 ipltdat=4  
 ilowgdf=4  
 ILOWHI=1  
 ISOLVE=1  
 KSPLIN=3  
 IQUADO=3  
 IQUADI=4  
 IPERIN=3               (input wavenumber)  
 IPEROUT=3              (output wavenumber)  
 MONITR=0  
 NUMHDR=1  
 NOOUT= 1 1 1 1 0 1 1 1 1  
 PANEL_SIZE=18  
 ILOG=1  
 NPDIPOLE = 2 4 6  
 
 Input file:  test21.pot  
TEST21.POT  SPAR with three strakes igdef=-12 (TEST21.GDF)  
 -1.  
 1           1               IRAD, IDIFF  
 3                            NPER (array PER follows)  
 0.1 0.5 1.  
 2                            NBETA (array BETA follows)  
 0. 120.  
 1                            NBODY  
 test21.gdf  
 0. 0. 0. 0.                  XBODY  
 1  1  1  1  1  1             IMODE(1-6)  
 
 Input file:  test21.gdf  
TEST21 SPAR2 with three strakes IGDEF=-12  
18. 9.80665  ULEN GRAV  
0  0        ISX  ISY  
7  -12       NPATCH  IGDEF  
5  
18. 200.              RADIUS, DRAFT  
3.7 0. 1. 3           WIDTH, THICKNESS, TWIST, NSTRAKE  
0                     IRRFRQ <span class=PICT" > <span class=PICT" >  
0  0.                 IMOONPOOL, RADIUSMP  
0                     IMPGEN  
 
 Input file:  test21.frc  
TEST21.FRC  SPAR with three strakes igdef=-12  
   1   1   1   1   0   3   0   2   0  
 0.000000                                    VCG  
 100.000000      .0000000      .0000000  
 .0000000      100.000000      .0000000  
 .0000000      .0000000      10.000000        XPRDCT  
 0                                           NBETAH  
 2                                           NFIELD  
23. 0.  0.  
15. 15. -0.5                                 (end of file)  
  

PICT PICT

A.22 FPSO WITH TWO INTERNAL TANKS – TEST22

The subroutine FPSOINT (IGDEF=-21) is used to generate the FPSO with two internal tanks with the dimensions specified in TEST22.GDF. One plane of symmetry is specified, about y = 0. The tanks are rectangular, and the vertices of each patch are specified in TEST22.GDF. Both tanks have the same length (2m), breadth (4.2m), and depth (1.1m). The aft side of tank 1 and the forward side of tank 2 are in the same plane x = 0.0. The free surface of tank 1 is at z = 1, 1m above the plane of the exterior free surface. The free surface of tank 2 is at z = 0.0. The first and last patches of each tank are assigned by the parameter NPTANK. Both tanks contain fluid of relative density 1.0, as specified in TEST22.CFG. The parameter ITANKFPT=1 is used so that the field points can be assigned in each tank, on the last two lines of TEST22.FRC.

Option 7 is used to evaluate the mean drift force and moment using a control surface. The control surface surrounding the FPSO is automatic, defined by the input file test22.csf. The parameter PSZCSF is negative, indicating that the subdivision of the control surface is determined by the parameters in the file TEST22.CSP. A second CSF file is contained in the file test22.csf for illustration, but it is not read by the program unless it is moved to the top of the file. In the second case the outer boundary is circular, and PSZCSF is positive, indicating that automatic subdivision of the control surface is performed as described in Section 11.4.

The corresponding output for the mean drift force and moment is contained in the file TEST13.7. Comparison of the results for the mean drift force in the sway direction from the files TEST22.9 (direct pressure integration) and TEST22.7 (control surface), with the far-field momentum drift force data in TEST22.8, confirms that the control surface gives a more accurate result compared to direct pressure integration for this body.


PICT PICT PICT PICT

PIC PICT PICT


PICT PICT
 
 Input file:  test22.cfg  
! TEST22.CFG  fpso with 2 interior tanks  
 ipltdat=4  
 ILOWHI=1  
 ILOG=1  
 ISOLVE=1  
 KSPLIN=3  
 IQUADO=3  
 IQUADI=4  
 MONITR=0  
 NUMHDR=1  
 NOOUT= 1 1 1 1 0 1 1 1 1  
 NPTANK=(8-11)  (12-15)  
 RHOTANK= 1.0  1.0       (relative densities of tank fluids)  
 ITANKFPT=1              (tank field points are in .frc file)  
 
 Input file:  test22.pot  
TEST22.POT  fpso with 2 interior tanks  
 -1.0  
   1         1               IRAD, IDIFF  
     3  
 2.0 2.5 3.0  
 1                           NBETA (array BETA follows)  
 90.  
 1                            NBODY  
 test22.gdf  
 0. 0. 0. 0.                  XBODY  
 1  1  1  1  1  1             IMODE(1-6)  
 
 Input file:  test22.gdf  
TEST22.GDF -- fpso with 2 tanks, one raised, joined at x=0  
1. 9.80665  ULEN GRAV  
0  1        ISX  ISY  
 15 -21      NPATCH  IGDEF  
36          NLINES  4+16*2  
 3.   15.   2.     XBOW, XMID, XAFT  
 2.2   1.2    HBEAM, HTRANSOM  
 1.2  0.6   DRAFT, DTRANSOM  
 0    0.0        INONUMAP, XBODY(3)  
   2.000000       0.000000       1.000000 <span class=PICT" > <span class=PICT" >  
   2.000000       2.100000       1.000000  
   2.000000       2.100000      -0.100000  
   2.000000       0.000000      -0.100000   patch8  tank1 fwd  
   2.000000       2.100000       1.000000  
   0.000000       2.100000       1.000000  
   0.000000       2.100000      -0.100000  
   2.000000       2.100000      -0.100000   patch9  tank1 side  
   0.000000       0.000000      -0.100000  
   2.000000       0.000000      -0.100000  
   2.000000       2.100000      -0.100000  
  -0.000000       2.100000      -0.100000   patch10  tank1 bot  
  -0.000000       0.000000      -0.100000  
  -0.000000       2.100000      -0.100000  
  -0.000000       2.100000       1.000000  
  -0.000000       0.000000       1.000000   patch11  tank1 aft  
   0.000000       0.000000       0.000000  
   0.000000       2.100000       0.000000  
   0.000000       2.100000      -1.100000  
   0.000000       0.000000      -1.100000   patch12  tank2 fwd  
   0.000000       2.100000       0.000000  
  -2.000000       2.100000       0.000000  
  -2.000000       2.100000      -1.100000  
   0.000000       2.100000      -1.100000   patch13  tank2 side  
  -2.000000       0.000000      -1.100000  
   0.000000       0.000000      -1.100000  
   0.000000       2.100000      -1.100000  
  -2.000000       2.100000      -1.100000   patch14  tank2 bot  
  -2.000000       0.000000      -1.100000  
  -2.000000       2.100000      -1.100000  
  -2.000000       2.100000       0.000000  
  -2.000000       0.000000       0.000000   patch15  tank2 aft  
 
 Input file:  test22.spl  
 TEST22.SPL  FPSO with two tanks  
      4   3  
      4   2  
      8   3  
      8   2  
      2   1  
      3   3  
      3   2  
      3   2  
      3   2  
      3   3 <span class=PICT" > <span class=PICT" >  
      3   2  
      3   2  
      3   2  
      3   3  
      3   2  
 
 Input file:  test22.frc  
TEST22.FRC fpso with 2 tanks, one field point on free surface in each tank  
   1   1   1   1   0   3   1   1   1  
 0.000000                                    VCG  
 1.000000      .0000000      .0000000  
 .0000000      1.000000      .0000000  
 .0000000      .0000000      1.000000        XPRDCT  
 0                                           NBETAH  
 2                                           NFIELD  
1  1.0 1.0 1.0  
2 -1.0 1.0 0.0  
 
 Input file:  test22.csf  
 test22.csf  FPSO, rectangular outer boundary  
1   ILOWHICSF  
0  1        ISX  ISY  
0   0  -2. NPATCH  ICDEF  PSZCSF   (1st two indicate this is automatic)  
  0.0  2.0   RADIUS, DRAFT of outer box (0.0 signifies outer bdry defined below  
  1   NPART  
  4   nv0  
  12.0   0.0  
  12.0   3.0  
 -12.0   3.0  
 -12.0   0.0  
 
THE FOLLOWING IS AN ALTERNATIVE CSF FILE WHICH IS NOT READ BY THE PROGRAM  
 UNLESS IT IS INTERCHANGED WITH THE FILE ABOVE.  
 
 test22.csf  FPSO, circular outer boundary  
1   ILOWHICSF  
0  1        ISX  ISY  
0   0  2. NPATCH  ICDEF  PSZCSF   (1st two indicate this is automatic)  
  12.0  2.0    RADIUS, DRAFT of outer box  
  0   NPART  
 
  

PICT PICT

In test22a the waterline is trimmed with a bow-up pitch angle of 6 degrees and a roll_     angle of 10 degrees, as shown in the figures. The draft is increased by 2m in the GDF file, and a vertical trim XTRIM(1)=2.0 is specified in the CFG file, giving a mean depth that is approximately the same as in test22. In this manner one ensures that the entire submerged portion of the hull surface is correctly defined. Since the draft is increased in the GDF file it is necessary to lower the tank bottoms by the same amount; thus the lower edges of the tank patches in test22a.gdf are 2m lower than in test22.gdf. With these inputs the waterline at the bow intersects both the vertical curved patch on the side of the bow and the flat bottom patch, with both end points on the curved side. The chine which connects these two patches in the untrimmed condition is submerged at the two ends, but above the free surface in the middle. For this reason it is necessary to assign the parameter ITRIMWL=2 in the cfg file. If ITRIMWL=1 is used the program will stop with an error message stating that part of patch 2 is above the free surface.


PICT PICT PICT PICT

PIC PICT PICT


PICT PICT
 
 Input file:  test22a.cfg  
! TEST22a.CFG  fpso with 2 interior tanks, trimmed waterline  
 ipltdat=4  
 ILOWHI=1  
 ILOG=1  
 ISOLVE=1  
 KSPLIN=3  
 IQUADO=3  
 IQUADI=4  
 MONITR=0  
 NUMHDR=1  
 NOOUT= 1 1 1 1 0 1 1 1 1  
 NPTANK=(8-11)  (12-15)  
 RHOTANK= 1.0  1.0       (relative densities of tank fluids)  
 ITANKFPT=1              (tank field points are in .frc file)  
 ztankFS= 1.0   0.0  
 ITRIMWL=2  
 XTRIM=2.0  -6.  10.0  
 
 Input file:  test22a.pot  
TEST22a.POT  fpso with 2 interior tanks, trimmed waterline  
 -1.0  
   1         1               IRAD, IDIFF  
     3  
 2.0 2.5 3.0  
 1                            NBETA (array BETA follows)  
 90.  
 1                            NBODY  
 test22a.gdf  
 0. 0. 0. 0.                  XBODY  
 1  1  1  1  1  1             IMODE(1-6)  
 
 Input file:  test22a.gdf  
TEST22.GDF -- fpso with 2 tanks, trimmed waterline  
1. 9.80665  ULEN GRAV  
0  1        ISX  ISY  
 15 -21      NPATCH  IGDEF  
36          NLINES  4+16*2  
 3.   15.   2.     XBOW, XMID, XAFT  
 2.2   1.2    HBEAM, HTRANSOM <span class=PICT" > <span class=PICT" >  
 3.2  2 .6   DRAFT, DTRANSOM  
 0    0.0        INONUMAP, XBODY(3)  
   2.000000       0.000000       1.000000  
   2.000000       2.100000       1.000000  
   2.000000       2.100000      -2.100000  
   2.000000       0.000000      -2.100000   patch8  tank1 fwd  
   2.000000       2.100000       1.000000  
   0.000000       2.100000       1.000000  
   0.000000       2.100000      -2.100000  
   2.000000       2.100000      -2.100000   patch9  tank1 side  
   0.000000       0.000000      -2.100000  
   2.000000       0.000000      -2.100000  
   2.000000       2.100000      -2.100000  
  -0.000000       2.100000      -2.100000   patch10  tank1 bot  
  -0.000000       0.000000      -2.100000  
  -0.000000       2.100000      -2.100000  
  -0.000000       2.100000       1.000000  
  -0.000000       0.000000       1.000000   patch11  tank1 aft  
   0.000000       0.000000       0.000000  
   0.000000       2.100000       0.000000  
   0.000000       2.100000      -3.10000  
   0.000000       0.000000      -3.10000   patch12  tank2 fwd  
   0.000000       2.100000       0.000000  
  -2.000000       2.100000       0.000000  
  -2.000000       2.100000      -3.10000  
   0.000000       2.100000      -3.10000   patch13  tank2 side  
  -2.000000       0.000000      -3.10000  
   0.000000       0.000000      -3.10000  
   0.000000       2.100000      -3.10000  
  -2.000000       2.100000      -3.10000   patch14  tank2 bot  
  -2.000000       0.000000      -3.10000  
  -2.000000       2.100000      -3.10000  
  -2.000000       2.100000       0.000000  
  -2.000000       0.000000       0.000000   patch15  tank2 aft  
 
 Input file:  test22a.spl  
 TEST22a.SPL  FPSO with two tanks, trimmed waterline  
      4   3  
      4   2  
      8   3  
      8   2  
      2   1  
      3   3  
      3   2 <span class=PICT" > <span class=PICT" >  
      3   2  
      3   2  
      3   3  
      3   2  
      3   2  
      3   2  
      3   3  
      3   2  
 
 Input file:  test22a.frc  
TEST22A.FRC fpso with 2 tanks, one field point on free surface in each tank  
   1   1   1   1   0   3   0   1   1  
 0.000000                                    VCG  
 1.000000      .0000000      .0000000  
 .0000000      1.000000      .0000000  
 .0000000      .0000000      1.000000        XPRDCT  
 0                                           NBETAH  
 2                                           NFIELD  
1  1.0 1.0 1.0  
2 -1.0 1.0 0.0  
  

PICT PICT

In test22b the origin of the coordinate system is shifted to the bottom of the_     keel, with XBODY(3)=-1.2 assigned in the POT file and also in the GDF file. The geometry is unchanged from TEST22, except that the tops of the tanks are defined by two extra patches and the free surface elevations in the tanks are defined by the parameters ZTANKFS(1)=0.99 and ZTANKFS(2)=-0.01 in the CFG file. Thus the height filling ratios of the tanks are about 99%. Except for the roll and pitch moments and corresponding cross-coupling coefficients, which are affected by the coordinate shift, the hydrostatic and hydrodynamic outputs are close to the corresponding values in test22. Since XBODY(3) is nonzero the values of ZTANKFS in body coordinates, shown in the header of the output file test22b.out, differ from the inputs in global coordinates in the CFG file.

If the assignments of ZTANKFS and/or ITRIMWL are removed from the CFG file the tanks will be full, including the rigid tops, and there will be no free surface effects in the tanks. In that case the exciting forces and damping coefficients are unchanged, but the added-mass coefficients are different. PICT PICT

 
 Input file:  test22b.cfg  
! TEST22b.CFG  fpso with 2 interior tanks, trimmed to 99%  
 ipltdat=4  
 ILOWHI=1  
 ILOG=1  
 ISOLVE=1  
 KSPLIN=3  
 IQUADO=3  
 IQUADI=4  
 MONITR=0  
 NUMHDR=1  
 NOOUT= 1 1 1 1 0 1 1 1 1  
 NPTANK=(8-12)  (13-17)  
 RHOTANK= 1.0  1.0       (relative densities of tank fluids)  
 ztankFS=  0.99   -0.01  
 ITRIMWL=1  
 
 Input file:  test22b.pot  
test22b.pot  fpso with 2 interior tanks, rigid tops, xbody(3)=-1.2  
 -1.0  
   1         1               IRAD, IDIFF  
     3  
 2.0 2.5 3.0  
 1                           NBETA (array BETA follows)  
 90.  
 1                            NBODY  
 test22b.gdf  
 0. 0.0 -1.2 0.                  XBODY  
 1  1  1  1  1  1             IMODE(1-6)  
 
 Input file:  test22b.gdf  
test22b.GDF -- fpso with 2 tanks, with rigid tops, xbody(3)=-1.2  
1. 9.80665  ULEN GRAV  
0  1        ISX  ISY  
 17 -21      NPATCH  IGDEF  npatch=7+2*5  
44          NLINES  4+5*4*2  
 3.   15.   2.     XBOW, XMID, XAFT  
 2.2   1.2    HBEAM, HTRANSOM  
 1.2  0.6   DRAFT, DTRANSOM  
 0 -1.2        INONUMAP, xbody(3) <span class=PICT" > <span class=PICT" >  
   2.000000       0.000000       1.000000  
   2.000000       2.100000       1.000000  
   2.000000       2.100000      -0.100000  
   2.000000       0.000000      -0.100000   patch8  tank1 fwd  
   2.000000       2.100000       1.000000  
   0.000000       2.100000       1.000000  
   0.000000       2.100000      -0.100000  
   2.000000       2.100000      -0.100000   patch9  tank1 side  
   0.000000       0.000000      -0.100000  
   2.000000       0.000000      -0.100000  
   2.000000       2.100000      -0.100000  
  -0.000000       2.100000      -0.100000   patch10  tank1 bot  
  -0.000000       0.000000      -0.100000  
  -0.000000       2.100000      -0.100000  
  -0.000000       2.100000       1.000000  
  -0.000000       0.000000       1.000000   patch11  tank1 aft  
  -0.000000       2.100000       1.000000  
   2.000000       2.100000       1.000000  
   2.000000       0.000000       1.000000  
   0.000000       0.000000       1.000000   patch12  tank1 top  
   0.000000       0.000000       0.000000  
   0.000000       2.100000       0.000000  
   0.000000       2.100000      -1.100000  
   0.000000       0.000000      -1.100000   patch13  tank2 fwd  
   0.000000       2.100000       0.000000  
  -2.000000       2.100000       0.000000  
  -2.000000       2.100000      -1.100000  
   0.000000       2.100000      -1.100000   patch14  tank2 side  
  -2.000000       0.000000      -1.100000  
   0.000000       0.000000      -1.100000  
   0.000000       2.100000      -1.100000  
  -2.000000       2.100000      -1.100000   patch15  tank2 bot  
  -2.000000       0.000000      -1.100000  
  -2.000000       2.100000      -1.100000  
  -2.000000       2.100000       0.000000  
  -2.000000       0.000000       0.000000   patch16  tank2 aft  
  -2.000000       2.100000       0.000000  
   0.000000       2.100000       0.000000  
   0.000000       0.000000       0.000000  
  -2.000000       0.000000       0.000000   patch17  tank2 top  
 
 Input file:  test22b.spl  
 TEST22b.SPL  FPSO with two tanks, rigid tops  
      4   3 <span class=PICT" > <span class=PICT" >  
      4   2  
      8   3  
      8   2  
      2   1  
      3   3  
      3   2  
      3   2  
      3   2  
      3   3  
      3   2  
      3   3  
      3   2  
      3   2  
      3   3  
      3   2  
      3   3  
 
 Input file:  test22b.frc  
test22b.frc fpso with 2 tanks, xbody3=-1.2  
   1   1   1   1   0   0   1   1   1  
 0.000000                                    VCG  
 1.000000      .0000000      .0000000  
 .0000000      1.000000      .0000000  
 .0000000      .0000000      1.000000        XPRDCT  
 0                                           NBETAH  
 0                                           NFIELD  
  

PICT PICT

A.23 RADIATED WAVE FIELD FROM A BANK OF WAVEMAKERS – TEST23

Several variants are considered to illustrate the analysis of wavemakers in a wave tank.

In TEST23, following the procedure in Section 12.3, the option ISOLVE=-1 is used to compute the radiated waves from a bank of ‘paddle’ wavemakers. The wavemakers are in the plane x = 0 of a rectangular tank, as shown below. The tank has a reflecting wall at y = 0. The tank depth is 4m. Each wavemaker is represented by one rectangular patch, using IGDEF=0, with the vertices listed in TEST23.GDF. The motion of each wavemaker is rotational about its lower edge, at the same depth below the free surface, represented by a generalized mode with the same distribution of normal velocity and with symmetry prescribed about the walls x = 0 and y = 0. These generalized modes are defined in the subroutine WAVEMAKER, in the DLL file NEWMODES.F, designated by the parameter IGENMDS=21 in TEST23.CFG. This subroutine reads the depth of the lower edge of the wavemaker, ZHINGE=-2m, from the file WAVEMAKER_DEPTH.DAT. Wave elevations are evaluated at a square array of 64 field points defined in TEST23.FRC, using the uniform field point array option in Section 3.10.


PICT PICT PICT PICT

PIC PICT PICT


PICT PICT
 
 Input file:  test23.cfg  
! TEST23.CFG -- 8 wavemaker segments in wall x=0  
 ILOWHI=1  
 IALTFRC=2  
 ISOLVE=-1              (skip POTEN solutions for wavemakers in walls)  
 MONITR=0  
 NUMHDR=1  
 IGENMDS=21             (use NEWMODES subroutine WAVEMAKER)  
 PANEL_SIZE=1.          (use default .spl parameters)  
 INUMOPT6=1             (output separate radiation modes in .6 file)  
 IFIELD_ARRAYS=1        (field points input in array format in .frc file)  
 ipltdat=4  
 NEWMDS = 8  
 
 Input file:  test23.pot  
TEST23.POT -- 8 wavemaker segments in wall x=0  
 4. fluid depth  
 0           -1               IRAD, IDIFF  
 2                            NPER (array PER follows)  
 2. 4.  
 1                            NBETA (array BETA follows)  
 0.0  
  1                            NBODY  
test23.gdf  
 0. 0. 0. 0.                  XBODY  
 0  0  0  0  0  0             IMODE(1-6)  
 
 First 10 lines of input file:  test23.gdf  
TEST23.GDF wavemaker, 8 segments in wall x=0 2<y<10m, ISY=1  
 1. 9.80665  ULEN GRAV  
 1  1        ISX  ISY  
 8  0        NPATCH  IGDEF  
     0.0000      2.000000      -2.00000  
     0.0000       3.00000      -2.00000  
     0.0000       3.00000       0.000000  
     0.0000      2.000000       0.000000   (end of Patch 1)  
     0.0000      3.000000      -2.00000  
     0.0000       4.00000      -2.00000  
PICT PICT

PICT PICT

 
 Input file:  test23.frc  
TEST23.FRC (field point wave elevations, IALTFRC=2, no external forces)  
 0  0  0  0  0  1  0  0  0        (IOPTN(1-9)  
 1.                               (RHO -- fluid density)  
 0. 0. 0.                         (XCG)  
 0                                (IMASS)  
 0                                (IDAMP)  
 0                                (ISTIF)  
 0                                (NBETAH)  
 0                                (NFIELD -- no individual field points)  
 1                                (NFIELD_ARRAYS -- number of arrays)  
 0                                (Array is in exterior fluid domain)  
 8   2.5   1.0                    (NFX, X1, DELX)  
 8   2.5   1.0                    (NFY, Y1, DELY)  
 1   0.0   0.0                    (NFZ, Z1, DELZ)  
  

PICT PICT

A.24 MOTIONS OF A HINGED VESSEL – TEST24

The subroutine CCYLHSP (IGDEF=-32) is used to generate a horizontal circular cylinder, with spheroidal ends, as shown below. The dimensions are specified in TEST24.GDF. Two planes of symmetry are specified. The cylinder is subdivided into five segments, to permit the analysis of a vessel with transverse hinges between the segments. Half of the middle segment and two others are in the domain x > 0. Four patches are required for these three elements plus the spheroidal end. The total number of segments, specified in TEST24.GDF, is used to read the x-coordinates of the boundaries between adjacent segments and also the end of the vessel. The total number of segments is equal to seven, including five cylinders plus two spheroids. Only the boundaries with coordinates x>0 are included in the last line of the GDF file, since ISX=1.

The generalized modes which represent the deflection of the hinges are defined in the subroutine HINGE_MODES in the DLL file NEWMODES.F, designated by the parameter IGENMDS=22 in TEST24.CFG. This subroutine reads the appropriate input data from the file test24_xhinge.dat, as described in Section 9.3. This input file specifies the symmetry index ISX=1, number of segments, and the x-coordinates of the hinges. The last cylinder and the spheroidal end are considered to be rigidly joined. Thus there are five ‘active’ segments corresponding to the parameter NSEG in the file, and NEWMDS=4 is assigned in the TEST24.POT file.

In the TEST24.FRC file, the 10×10 matrix of inertia coefficients is specified. No external damping or stiffness matrices are input, corresponding to the situation where the hinges are ideal without friction or other mechanical constraints.

Further information can be found in the headers and comments of the subroutines which are used to generate the geometry and to represent the hinge modes.


PICT PICT PICT PICT

PIC

Figure A.3: Generalized modes used for the hinged barge with four hinges. The modes on the left are ‘tent functions’, suitable for use when ISX=0. When ISX=1 each mode must be either symmetric or antisymmetric, as shown in the right column. The latter modes are used for TEST24. The conventional rigid-body modes in heave and pitch represent the nonzero vertical motions at the two ends.
PICT PICT



PICT PICT PICT PICT

PIC PICT PICT


PICT PICT
 
 Input file:  test24.cfg  
! TEST24.CFG -- segmented vessel with 7 segments and 4 hinge modes  
 ipltdat=5  
 ILOWHI=1  
 IALTFRC=2  
 ISOLVE=1  
 IQUADI=4  
 IQUADO=3  
 KSPLIN=3  
 MONITR=0  
 NUMHDR=1  
 IGENMDS=22  
 NEWMDS = 4  
 
 Input file:  test24.pot  
TEST24 segmented vessel with 7 segments and 4 hinge modes  
 -1.  
 0           0               IRAD, IDIFF  
 2                            NPER (array PER follows)  
 3. 5.  
  1                             NBETA (array BETA follows)  
 180.  
 1                            NBODY  
test24.gdf  
 0. 0. 0. 0.                  XBODY  
 1  0  1  0  1  0             IMODE(1-6)  
 
 Input file:  test24.gdf  
TEST24 segmented vessel with 7 segments  
1. 9.80665  ULEN GRAV  
1  1        ISX  ISY  
4  -32       NPATCH  IGDEF  
3           NLINES  
7     Nsegments  
1.    Radius  
 2. 6. 8. 10.   xseg  
 
 Input file:  test24.spl  
TEST24 segmented vessel with 7 segments  
 4 2      NU NV   mid cylinder <span class=PICT" > <span class=PICT" >  
 4 4              next cylinder  
 4 2              outer cylinder  
 4 4              spheroidal end  
 
 Input file:  test24.frc  
TEST24 segmented vessel with 7 segments and 4 hinge modes  
 1  1  1  1  0  0  0  0  0  
 1000.  
 0. 0. 0.  
 1  
  29321.5     0.      0.    0.     0.      0.     0.     0.     0.     0.  
  0.      29321.5     0.    0.     0.      0.     0.     0.     0.     0.  
  0.          0.  29321.5   0.     0.      0. 12000.     0. 12000.     0.  
  0.          0.      0. 1.5E4     0.      0.     0.     0.     0.     0.  
  0.          0.      0.    0. 7.33E5      0.     0. -24000.    0. -72000.  
  0.          0.      0.    0.     0.  7.33E5     0.     0.     0.     0.  
  0.          0.  12000.    0.     0.      0. 10000.     0.  2000.     0.  
  0.          0.      0.    0. -24000.     0.     0.  6000.     0.  2000.  
  0.          0.  12000.    0.     0.      0.  2000.     0.  8000.     0.  
  0.          0.      0.    0. -72000.     0.     0.  2000.     0.  8000.  
 0  
 0  
 0  
 0  
  

PICT PICT

A.25 AIR-CUSHION VESSEL WITH PRESSURE CHAMBERS – TEST25

The vessel consists of two air chambers surrounded by rectangular skirts. The length is 20m, beam 10m and draft 2m. The width of the skirts is 1m. The free surface in the chambers, shown by red shading in the figures below, is 1m below the exterior free surface. One quadrant of these surfaces is represented by flat quadrilateral patches in the GDF file, with two planes of symmetry. Two pressure modes are used to represent anti-symmetric and symmetric pressure distributions with constant pressure in each chamber, denoted by Modes 7 and 8 respectively. These pressure modes are defined by the NEWMODES subroutine PRESSURE_FS. The configuration parameter ICCFSP=1 is used to include the external_     restoring coefficients due to the pressure acting on the upper surface of the air chambers (see Section 12.5).


PICT PICT PICT PICT

PIC PICT PICT


PICT PICT
 
 Input file:  test25.cfg  
! TEST25.CFG -- ACV (air-cushion vehicle) with 2 air chambers  
 ipltdat=1  
 ILOWHI=1  
 IALTFRC=1  
 ISOLVE=1  
 PANEL_SIZE = 1.0       (use default .spl parameters)  
 NUMHDR=1  
 IMODESFSP=1            (use NEWMODES subroutine PRESSURE_FS)  
 NMODESFSP=2            (2 pressure modes, sym & antisym about x=0)  
 NPFSP=(9 9)            (free surface pressure on patch 9)  
 ICCFSP=1               (include external restoring coefficients)  
 
 Input file:  test25.pot  
TEST25 ACV (air-cushion vehicle) with 2 air chambers  
 -1.  
 0       1               IRAD, IDIFF  
 6                            NPER (array PER follows)  
 5.0 6.0 7.0 8.0 9.0 10.0  
 1                             NBETA (array BETA follows)  
 180.  
 1                            NBODY  
test25.gdf  
 0. 0. 0. 0.                  XBODY  
 1  0  1  0  1  0             IMODE(1-6)  
 
 First 10 lines of input file:  test25.gdf  
TEST25 ACV (air-cushion vehicle) with 2 air chambers - igdef=0  
     1.00        9.80665  
           1           1  
           9           0          NPATCH, IGDEF  
     9.00        0.00       -2.00  
     9.00        5.00       -2.00  
    10.00        5.00        0.00  
    10.00        0.00        0.00   (end)  
     9.00        5.00       -2.00  
     0.00        5.00       -2.00  

PICT PICT

 
 Input file:  test25.frc  
TEST25.FRC  ACV (air-cushion vehicle) with 2 air chambers  
 1    1    1    1    0    0  0  0 0     IOPTN(1-9)  
 0.000000                                    VCG  
 2.500000      .0000000      .0000000  
 .0000000      5.000000      .0000000  
 .0000000      .0000000      5.000000        XPRDCT  
 0                                           NBETAH  
 0                                           NFIELD  
 
  

PICT PICT PICT PICT PICT PICT


Examples of structures analyzed by WAMIT

(for more details click on one of the structures)
Cylinder NavExp Test09 Test 22 Test 25 TLP2ndOrder WitFig6