CNA wave pump platform design concept evaluation : numerical modelling of floating moored bodies in regular sea states

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CNA wave pump platform design concept evaluation : numerical

modelling of floating moored bodies in regular sea states

Boileau, Renee; Raman-Nair, Wayne

https://publications-cnrc.canada.ca/fra/droits

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OCRE-TR-2013-043

NATIONAL RESEARCH COUNCIL CANADA OCEAN, COASTAL AND RIVER ENGINEERING

CNA wave pump platform design concept

evaluation: numerical modelling of floating

moored bodies in regular sea states

Technical Report

Renee Boileau and Wayne Raman-Nair November 1, 2013

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DATE ◆♦✈❡♠❜❡r ✶✱ ✷✵✶✸

REPORT NUMBER PROJECT NUMBER SECURITY CLASSIFICATION DISTRIBUTION

❖❈❘❊✲❚❘✲✷✵✶✸✲✵✹✸ ❆✶✲✵✵✸✻✼✻ ❯♥❝❧❛ss✐✜❡❞ ❯♥❧✐♠✐t❡❞

TITLE

❈◆❆ ✇❛✈❡ ♣✉♠♣ ♣❧❛t❢♦r♠ ❞❡s✐❣♥ ❝♦♥❝❡♣t ❡✈❛❧✉❛t✐♦♥✿ ♥✉♠❡r✐❝❛❧ ♠♦❞❡❧❧✐♥❣ ♦❢ ✢♦❛t✐♥❣ ♠♦♦r❡❞ ❜♦❞✐❡s ✐♥ r❡❣✉❧❛r s❡❛ st❛t❡s

AUTHOR(S)

❘❡♥❡❡ ❇♦✐❧❡❛✉ ❛♥❞ ❲❛②♥❡ ❘❛♠❛♥✲◆❛✐r

CORPORATE AUTHOR(S)/PERFORMING AGENCY(S) PUBLICATION(Journal or Conference name)

SPONSORING AGENCY(S)

❈♦❧❧❡❣❡ ♦❢ t❤❡ ◆♦rt❤ ❆t❧❛♥t✐❝

RAW DATA STORAGE LOCATION(S) MODEL# PROP#

❚❡st❞❛t❛✿❭❚❡st❴❆✶✵✵✸✻✼✻❭❈❲❚

PROJECT✭NPArC✮ PEER REVIEWED EMBARGO PERIOD GROUP(NPARC)

◆♦ ✵ ❘❡s❡❛r❝❤

PROGRAM✭NPArC✮ FACILITY✭NPArC✮

▼■❊❲❘ ❙t✳❏♦❤♥✬s✿ P✳❖✳ ❇♦① ✶✷✵✾✸✱ ❆r❝t✐❝ ❆✈❡✱ ❙t✳ ❏♦❤♥✬s✱ ◆▲ ❆✶❇ ✸❚✺

KEYWORDS PAGES TABLES FIGS.

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National Research Council Canada Ocean, Coastal and River Engineering Conseil national de recherches Canada Génie océanique, côtier et fluvial UNCLASSIFIED

CNA wave pump platform design concept evaluation:

numerical modelling of floating moored bodies in regular sea

states

OCRE-TR-2013-043

Renee Boileau and Wayne Raman-Nair

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OCRE-TR-2013-043

Abstract

This report presents the results of numerical simulations for the purpose of assessing the survivability of a moored platform in the Lord’s cove environment. A time domain numerical model was used to predict platform motions and line tensions under both typical operating conditions and in extreme conditions (hurri-cane). Inputs to the numerical model were provided by the results of model tests, computations by ANSYS AQWA and published data for the mooring lines. Re-sults indicate that, for the parameters investigated, the line tensions are well within acceptable safety margins. It is recommended that mooring lines be chosen stiff enough to minimise motions under operating conditions without breaking under extreme environmental conditions.

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OCRE-TR-2013-043 Contents

List of Figures

1 CNA wave pump platform concepts . . . 1

2 Platform models at the Clear Water Towing Tank (CWTT) . . . 4

3 Initial mooring configuration . . . 6

4 Platform response with wire rope . . . 9

5 Model animation . . . 10

6 Model #1 with Qualisys target balls . . . 16

7 Model and coordinate axes . . . 17

8 Trimmed models in CWTT trim tank . . . 19

9 Simplified model geometry . . . 28

10 Meshed models . . . 28

11 Platform response with synthetic Aramid rope . . . 71

12 Platform response with 20:80 synthetic/wire rope . . . 72

13 Platform #1 response by wave height . . . 73

14 Platform #1 response by wave period . . . 74

16 Platform #2 response by wave period . . . 76

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OCRE-TR-2013-043 List of Tables

List of Tables

1 Hydrodynamic coefficient comparison . . . 4

2 Dimensions and mass properties at model and prototype scale . . . 5

3 Mooring line configurations . . . 6

4 Wave parameters . . . 7

5 Completed numerical test matrix . . . 8

6 Data channel list . . . 17

7 Completed physical test matrix . . . 20

8 Tank test log . . . 21

9 Model scale hydrostatics check . . . 29

10 ANSYS AQWA/Workbench reported issues . . . 31

11 Numerical model results for test program . . . 79

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OCRE-TR-2013-043 Acronyms

Glossary

significant wave height mean height (trough to crest) of the one-third highest waves significant wave period mean of the periods corresponding to the significant waves

Acronyms

CAD computer-aided drawing CNA College of the North Atlantic CWTT Clear Water Towing Tank DOF degree of freedom SI System International

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OCRE-TR-2013-043 1 Introduction

1 Introduction

The College of the North Atlantic (CNA) has engaged the NRC in the design of a wave pump to supply water to an onshore aquaculture centre at Lord’s Cove, Newfoundland. The pump must supply a minimum continuous flow requirement based on typical sea states and remain on station in sea states as high as hurricane conditions. In previous work, the sea states at Lord’s Cove have been characterized over a year of observa-tions [1] and a numerical model of a double-acting positive displacement pump has been developed [2].

The next stage in wave pump development is to compare platform and mooring designs. To that end, a numerical mooring model based on lumped mass theory has been applied; the numerical model can simulate the two-dimensional motions and line loads of a floating body with elastic catenary moorings in waves and current, given certain mass properties, hydrodynamic coefficients and external loads as inputs. This numerical model has been applied to floating bodies representing three different wave pump platform concepts developed in meetings between CNA and NRC.

To provide inputs for the numerical model, simple geometric (non-functioning) mod-els have been drafted in a computer-aided drawing (CAD) program for the three plat-form concepts. (Figure 1 shows views from the fabrication drawings.) The mass prop-erties are estimated directly from the CAD models.

15 14 5 7 7 11 4 7 14 11 6 8 13 7 7 8 8 9 8 13 10 12 2 12 1 2 3 6 7 7 8 11 11 02 02 NOTES:

REVISIONS HISTORY /HISTORIQUE DES RÉVISIONS

ZONE REV. DESCRIPTION DATE BY/PAR C4, B3 02 ADDED PIPE CAPS 13AUG2013 JS

ITEM

NO. PART NUMBER DECSRIPTION QTY. 1 A1-003676-00003 STEEL PLATE .75m x .75m 1 2 A1-003676-00010 FOAM .75m x .75m 2 3 A1-003676-00005 PLYWOOD .75m x .75m 4 Holes 1 4 A1-003676-00012 PIPE 1 MODEL 1 4 5 A1-003676-00013 PIPE 2 MODEL 1 1 6 A1-003676-00019 BALLAST PLUG 10 7 HNUT 0.5000-13-D-N HEX NUT 1/2"-13 UNC 20 8 FW 0.5 FLAT WASHER 1/2" 15 9 A1-003676-00016 THREADED ROD 1/2"-13 UNC x 24.5 Long 4 10 A1-003676-00017 THREADED ROD 1/2"-13 UNC x 21.75 Long 1 11 A1-003676-00020 PIPE CAP 4" 10 12 A1-003676-00006 PLYWOOD .75m x .75m 5 Holes 2

D C B A B C D 8 7 6 5 4 3 2 1

DO NOT SCALE DRAWING NE PAS MESURER SUR LE DESSIN REPORT ALL ERRORS TO THE DESIGN OFFICE SIGNALER TOUTES ERREURS AU BUREAU DE CONCEPTION

RETURN ALL DRAWINGS TO THE DESSIGN OFFICE RETOURNER TOUS LES DESSINS AU BUREAU DE CONCEPTION

TOLERANCES/TOLÉRANCES UNLESS OTHERWISE NOTED SAUF INDICATION CONTRAIRE

ALL DIMENSIONS IN INCHES DIMENSIONS EN P0UCES .X .020 .XX .010 .XXX .002 ALL FRACTIONS 1/32 ANGULAR .50 A1-003676-95 SEE NOTES Conseil national de recherches Canada  National Research Council Canada DES. /CONCEPT. DFS/SCF FAB No. HEAT TREAT./TRAITMENT THERM. MATERIAL/MATÉRIEL

A FINISH/FINI

SEE NOTES SEE NOTES

Design and Fabrication Services Service de Conception et de Fabrication

ASSY, WAVE PUMP MODEL 1 (a) #1 14 9 13 12 2 5 14 3 5 6 3 1 5 5 6 12 11 13 10 5 6 5 8 6 7 5 6 7 3 12 12 4 4 NOTES:

REVISIONS HISTORY /HISTORIQUE DES RÉVISIONS

ZONE REV. DESCRIPTION DATE BY/PAR

ITEM NO. PART NUMBER DESCRIPTION QTY.

1 A1-003676-00004 STEEL PLATE .75m Dia. 1

2 A1-003676-00007 PLYWOOD .75m Dia. 1 Hole 1

3 A1-003676-00011 FOAM .75m Dia. 4

4 A1-003676-00018 BALLAST PLUG 6

5 HNUT 0.5000-13-D-N HEX NUT 1/2"-13 UNC 20

6 FW 0.5 FLAT WASHER 1/2" 15

7 A1-OO3676-00021 LARGE DIAMETER FLAT WASHER 2

8 A1-003676-00017 THREADED ROD 1/2"-13 UNC x 21.75 Long 1

9 A1-003676-00016 THREADED ROD 1/2"-13 UNC x 24.5 Long 4

D C B A B C D 8 7 6 5 4 3 2 1

DO NOT SCALE DRAWING NE PAS MESURER SUR LE DESSIN REPORT ALL ERRORS TO THE DESIGN OFFICE SIGNALER TOUTES ERREURS AU BUREAU DE CONCEPTION

RETURN ALL DRAWINGS TO THE DESSIGN OFFICE RETOURNER TOUS LES DESSINS AU BUREAU DE CONCEPTION

TOLERANCES/TOLÉRANCES UNLESS OTHERWISE NOTED SAUF INDICATION CONTRAIRE ALL DIMENSIONS IN INCHES DIMENSIONS EN P0UCES SEE NOTES Conseil national de recherches Canada  National Research Council Canada HEAT TREAT./TRAITMENT THERM.

MATERIAL/MATÉRIEL

A

FINISH/FINI

SEE NOTES

Design and Fabrication Services Service de Conception et de Fabrication

(b) #2 (c) #3

Figure 1: CNA wave pump platform concepts

External (wave) loads are estimated for regular waves based on wave heights and periods representative of typical measured sea states at Lord’s Cove.

The hydrodynamic coefficients for each sea state are predicted using a potential code (ANSYS AQWATM).

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OCRE-TR-2013-043 2 Numerical model development

tests in surge, heave and roll in the CWTT at NRC (St. John’s). Analysis of the test data provides validation data for hydrodynamic coefficients at the natural frequency in each mode. This aids in developing an independent, purely numerical method to predict platform performance without the need for physical model fabrication and testing.

The numerical model has been applied to predict maximum mooring line loads for the three platform concepts on two-dimensional taut catenary multi-point moorings recommended for point-absorber wave energy devices[3] with three material config-urations: wire rope, synthetic lines and lines with a combination of stiff and stretchy sections.

This report describes the work flow from design and fabrication of the platform models through comparison of hydrodynamic inputs predicted by potential code and physical test data to numerical simulation of the platforms on different moorings in a series of regular waves and comparison of the motion of the platforms and the robust-ness of the moorings. Details on a method for predicting hydrodynamic coefficients and validation with physical tank testing and AQWA are included in Appendices A and B; more detailed results are in Appendix C.

2 Numerical model development

The numerical mooring model used in this study is based on previous work[4] funded through the ecoENERGY Innovation Initiative (ecoEII) federal program. The numerical model uses mooring algorithms to simulate time-domain motion of a moored floating body with applied wave and/or current loads in typical and extreme wave environments. The model allows for touchdown on the seabed. This is a two-dimensional model that predicts surge, roll and heave motions.

The floating platform is modelled as a cylinder that is assigned mass properties from CAD that represent the platform’s more complex shape. The mooring lines are modelled as a series of lumped masses with mass properties from published sources. The numerical model includes scripts to check the hydostatics of the mooring line, which are useful for determining initial line length. The model is described in detail in the ecoEII report[4].

For this project, Matlab R _{scripts were developed to run the model in various}

plat-form and line configurations in a series of wave conditions.

While mass properties can be extracted from CAD and lines and sea states can be defined from published data, the model requires hydrodynamic inputs from physical model tests or numerical simulation.

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OCRE-TR-2013-043 3 Determination of hydrodynamic inputs for numerical model

3 Determination of hydrodynamic inputs for numerical model

The hydrodynamic inputs needed for the numerical model are added surge and heave mass, added roll inertia and damping coefficients, all of which depend on wave fre-quency. A method for determining these inputs for a variety of platform concepts without costly, time-consuming physical tests is desirable. Certain assumptions and limitations affect both the numerical and physical methods.

3.1 Assumptions

The comparisons between numerical and physical model data are based on the follow-ing assumptions:

◦ no coupling between modes

◦ “irregular frequencies” do not represent real responses

◦ shifts in natural frequency with and without added mass are negligible ◦ difference in test conditions between fresh and sea water are negligible

3.2 Known limitations

Limitations in the results from physical testing and AQWA simulations are known to include the following:

◦ tank test coupling occurs between channels but is at least an order of magnitude below the mode of interest

◦ tank testing is only representative at the natural frequency in each mode ◦ AQWA frequencies are limited by mesh size

3.3 Potential code validation with test data at natural frequencies

The potential code method was evaluated by comparing AQWA outputs at the natural frequency determined by test data for surge, heave and roll. Physical models were fabricated and trimmed to the design waterline in fresh water. Each model was excited in surge, heave and roll in the CWTT and the motion data were analysed in Matlab. To demonstrate independence from physical testing, all AQWA runs used inputs from the CAD models only. Figure 2 shows the three physical models used to estimate added mass and inertia and damping coefficients for each mode.

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OCRE-TR-2013-043 3 Determination of hydrodynamic inputs for numerical model

Figure 2: Platform models at the CWTT

surge data could not be evaluated (negative added mass). Some disagreement is due to running the AQWA model in 30-♠-deep salt water (vs 5 ♠ fresh water in the CWTT). However, the damping coefficients are a factor of 3–5 lower than calculations from test data (not including surge, which is 5 orders of magnitude lower).

Table 1: Hydrodynamic inputs from physical test data and AQWA at natural periods, Tn

data AQWA data AQWA data AQWA

added mass/inertia

model T_n(s) m_a,surge (❦❣) T_n(s) m_a,heave(❦❣) T_n(s) I_a,roll (❦❣·♠2₎

#1 15.0 -25.0 57.8* 2.2 368.3 369.1⋄ _1.8 _22.2 _20.3⋄

#2 14.0 -21.6 51.4 2.0 297.7 293.3 1.9 7.3 16.3⋄

#3 7.6 -1.2 17.3⋄ 1.2 85.0 89.5 1.5 7.3 7.0†

damping coefficients

c_surge(◆·s✴♠) c_heave (◆·s✴♠) c_roll(◆·♠·s✴r❛❞)

#1 15.0 5.3 8E-05* 2.2 80.0 29.6⋄ _1.8 _10.3 _2.04⋄

#2 14.0 4.1 8E-05 2.0 142.2 53.1 1.9 3.1 1.6⋄

#3 7.6 3.6 1.E-04⋄ 1.2 indet. 97.1† 1.5 5.5 0.7†

* interpolated ⋄ _nearest †_{extrapolated period} The AQWA results were considered more reliable in this case, and so are used exclusively for mooring model inputs. In addition to hydrodynamic inputs, the model requires mass properties, line configuration and external loads (waves).

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OCRE-TR-2013-043 4 Application of numerical model

4 Application of numerical model

The two-dimensional numerical model has been used to predict line tensions and roll under a set of regular waves based on typical wave buoy data from Lord’s Cove in 2012. In total, the numerical test program spanned 45 configurations (3 platforms on 3 moorings in 5 regular waves) and numerous repeated runs to check model sensitivity and consistency.

4.1 Platform concepts

The three preliminary platform concepts (Figure 1) arose out of meetings between NRC and CNA in spring 2013. Two concepts are new and have been drafted in CAD; the third is based on a prototype from a previous joint project. Mass properties for the platforms are extracted from the CAD models. Table 2 lists the primary dimensions and mass properties for each physical model and numerical scale used in this study.

4.2 Scale

Since the physical models are presumably not large enough to provide the specified flow rate, all static and hydrodynamic inputs were arbitrarily scaled in length by 1.5 using Froude scaling.

Table 2: Dimensions and mass properties at model and prototype scale

platform #1 platform #2 platform #3

scale: model 1:1.5 model 1:1.5 model 1:1.5

height (♠) 1.00 1.50 1.00 1.50 1.13 1.70 mass (❦❣) 152.90 516.04 133.54 450.70 36.61 123.57 roll inertia (❦❣·♠2 ) 20.25 153.77 20.36 154.59 8.16 62.00 draft (♠) 0.07 0.11 0.07 0.11 0.08 0.12 metacentric height (♠) 0.35 0.52 0.29 0.44 0.76 1.14 waterplane area (♠2 ) 0.44 0.99 0.44 0.99 0.35 0.79 added mass/inertia: surge (❦❣) 58.28 196.70 51.84 174.98 17.39 58.71 heave (❦❣) 389.08 1,313.16 315.09 1,063.44 100.58 339.44 roll (❦❣·♠2 ) 18.95 143.91 14.94 113.47 6.20 47.11 damping coefficients:

surge (◆·s✴♠) 1.5E-02 4.0E-02 1.1E-02 3.0E-02 1.0E-03 2.7E-03

heave (◆·s✴♠) 8.9 24.5 9.4 25.8 6.7 18.5

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4.3 Mooring concepts

Three mooring line configurations were selected based on recommended moorings for point-absorber wave energy devices[3], which is similar in function to this wave pump application. The moorings are modelled in two dimensions: each mooring system consists of two identical catenary lines, fixed to anchor points 10 metres on either side of the platform and attached to points on either side of the platform centre of gravity (±0.6 ♠).

All moorings are pre-tensioned (taut) with the initial position above the wave peak, as shown in Figure 3. Each line was represented using 6 to 10 lumped masses.

Three line types were modelled: wire rope (steel), synthetic (AramidTM) lines and lines with a combination of stiff and elastic sections (20% synthetic: 80% wire rope).

Figure 3: Initial mooring configuration with lumped masses (×)

Table 3: Mooring line configurations

Aramid 6-strand wire rope 20:80 Aramid /wire rope

diameter (♠♠) 10 10 [10, 10]

lumped masses (count) 7 6-7 [10, 10]

unit density (❦❣✴♠) 0.14 0.43 [0.14, 0.43]

elastic modulus (●P❛) 57.3 19.1 [57.3, 19.1]

drag coefficient 1.5* 1.5* [1.5, 1.5]*

inertia coefficient 1.2* 1.2* [1.2, 1.2]*

* assumed based on similar study in [5]

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4.4 Wave definitions

A set of regular waves was defined by the significant wave height and significant wave period from a set of wave buoy data at a site approximately 1❦♠ from the harbour en-trance defined each regular wave. Five sea states typical of Lord’s Cove were selected from observations made in 2012[6], ranging from a light chop (“calm”) to hurricane force seas.

Table 4: Wave parameters

description wave height (♠) period (s) wave buoy date/time

calm 0.2 6.0 2012-05-31 03:15

low 1.0 5.5 2012-08-09 04:16

moderate 2.4 8.0 2012-05-12 03:14

storm 4.0 10.0 2012-02-12 22:44

hurricane 6.6 14.0 2012-09-11 13:13

4.5 Numerical test matrix

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OCRE-TR-2013-043 5 Results

Table 5: Completed numerical test matrix

Wave response

calm low moderate storm hurricane

0.2♠ @ 6 s 1♠ @ 5.5 s 2.4♠ @ 8 s 4 ♠ @ 10 s 6.6 ♠ @ 14 s platform

#1 L1, L2, L3 L1, L2, L3 L1, L2, L3 L1, L2, L3 L1*, L2, L3 #2 L1, L2, L3 L1, L2, L3 L1, L2, L3 L1, L2, L3 L1, L2, L3* #3 L1, L2, L3 L1*, L2, L3 L1, L2, L3 L1, L2, L3 L1, L2, L3

L1 = 10-mm 6-strand wire rope L2 = 10 mm synthetic Aramid rope L3 = 20:80 synthetic:wire

* reduced lumped mass count

Sensitivity study

# comparisons effect noted

transient filtering 3 major (3%–70%)

c_roll_correction ₁₇ _{negligible (<2%)}

lumped mass count 3 negligible (<3%)

total runs: 109

5 Results

The completed numerical test program provides results from 109 runs, covering 45 test configurations and repeats (due to incorrect inputs or intentional variations). For each run, the test configuration and model response were exported to a ✳❝s✈ file and the complete Matlab workspace was saved including animations.

Figure 4 summarizes the model responses for one line type (wire rope). Com-plete results, including similar plots for the other two moorings and maximum line ten-sions and roll angle for each model compared by sea state and mooring appear in Appendix C.

Maximum line tension is very similar for all three platforms. Platform #1 and #2 behave similarly in roll - #1 is slightly more stable than #2; #3 has a much lower roll response, possibly due to less wetted surface interacting with the wave.

A script is available to convert an animation to a real-time movie file (.avi). (Figure 5 shows a sample movie frame.)

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OCRE-TR-2013-043 5 Results

5 10 15 20 25 30 35 40 45 50 55 sea state maximum tension (N) platform #1 platform #2 platform #3

0 5 10 15 20 25 30 35 40 sea state maximum roll ( ° ) platform #1 platform #2 platform #3

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OCRE-TR-2013-043 6 Discussion

Figure 5: Sample frame from a numerical model animation

6 Discussion

Each phase of the test program was sensitive to potential sources of error due the variety of inputs (physical and numerical) and the complexity of transferring information between the CAD models, Qualisys data, Matlab results, potential code and numerical model with correct axes and units. Each step presented new challenges.

6.1 Coupled effects in physical testing

The results from physical model testing were sensible except for surge added mass, which was negative for all three models in most runs. Pull tests were conducted on both springs, with good agreement (22.3◆♠ and 22.7 ◆♠). It is thought that the spring mode may be more complex than expected. The source of negative added mass was not explored fully.

Fits to decay curves for heave and roll damping are imperfect due to coupling with other modes. This was minimized as much as practicable by careful excitation of the models, repeating tests in like and opposite initial displacements and using the least coupled runs for comparison with AQWA.

Results were also compared with GEDAP code written specifically for handling decay curves. Details on physical testing and analysis methods are provided in Ap-pendix A.

Due to the unreliable and limited physical results, the added mass and inertia and damping coefficients predicted by ANSYS AQWA were used as mooring model inputs.

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OCRE-TR-2013-043 6 Discussion

6.2 Evaluation of ANSYS AQWA for predicting hydrodynamic coefficients

Physical testing only yields coefficients at the natural modes, unless the model is driven at other frequencies. Potential code, i.e., ANSYS AQWA, can provide results at any fre-quency above a limit imposed by the mesh size (in turn limited by number of elements allowed by the license). Exceptions are certain “irregular frequencies” noted, possibly due to sharp edges on Model #3.

Typical hazards were default settings such as sea depth (default 1 ❦♠) and units (default angles in degrees). AQWA output files were double-checked for each model.

Damping coefficients for surge are orders of magnitude less than the physical re-sults (which are arguable), but ultimately have little effect on the numerical model.

Some issues with rounding errors and/or blunt bodies may have affected the stabil-ity of the AQWA results.

These issues and methods for overcoming them are described in Appendix B.

6.3 Numerical mooring model sensitivities

The numerical mooring model is sensitive to starting position and number of lumped masses. However, steady state results show good agreement, so the methods used to ensure solution were effective.

The model will fail unless the body is above the wave peak to start; the input file automatically sets the initial point at one wave amplitude (2 · hm0) above water depth for each wave definition. Data is collected after the first two periods to eliminate transient effects due to this initial displacement.

The model will also fail when a light line is represented by too many lumped masses. Multiple runs were checked at different lumped mass counts to verify convergence in maximum line tensions and roll angles. Typically 7 lumped masses were used for simple, homogeneous lines and 10 for the composite line. The number of lumped masses for three runs was reduced to 6 to ensure a solution. Those results did not differ significantly (< 1%) from the case with 5 lumped masses.

Repeatability was checked by running the model with different inputs. Changing roll damping had negligible effect on maximum roll angle. Changing the number of lumped masses for mooring lines had minor effects. Less than 1% in variation were unaccounted for between repeated runs. (See Table 5 for a record of the repeatability check.)

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OCRE-TR-2013-043 8 Recommendations for future work

7 Conclusions

The goal of this application of the numerical model was to aid in the selection of a platform design among three concepts and to demonstrate the effects of mooring on survivability. The response of these three models and three line configurations were largely indistinguishable: all three moorings survived hurricane conditions with less than 10% difference in maximum line load between platforms. The line tensions re-mained well below catalogue breaking strength for the materials selected (factor of safety = 10). The corners of Platform #1 reduce yaw coupling compared to Model #2. Model #3 shows more roll.

The three platform concepts behave comparably in regular waves; mooring design is relatively light with respect to line size and weight in these conditions.

8 Recommendations for future work

The following work is required to develop the numerical model so it can predict a power transfer function for the Lord’s Cove wave resource:

1. create inputs for complete wave spectra

2. translate wave conditions into time-series forces on pump piston(s)

If the mooring is designed to be stiff enough so that the platform can be assumed to have minimal motion under operating conditions, future predictions of flow rate can be made, eliminating the complexity of coupling the pump motion to the platform motion

This has demonstrated what can be done with a given set of design ideas. New inputs for different shapes can be extracted from AQWA with approximately 2–3 days effort and the numerical model can be re-run easily to generate wave responses in 10– 15 minutes per configuration. Future design choices can be readily evaluated using the method with significantly less effort, now that a robust work flow has been developed.

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OCRE-TR-2013-043 References

References

[1] R. Boileau, “Wave resource assessment for Lord’s Cove, Newfoundland – 2012 survey,” National Research Council Canada, Technical Report OCRE-TR-2013-008, Jan. 2013.

[2] R. Boileau and W. Raman-Nair, “NRC wave pump tests for numerical model devel-opment,” NATIONAL RESEARCH COUNCIL CANADA, Technical Report OCRE-TR-2013-030, May 2013.

[3] R. E. Harris, L. Johanning, and J. Wolfram, “Mooring systems for wave energy converters: a review of design issues and choices,” in 3rd Intl. Conference on Marine Renewable Energy (MAREC 2004), Blythe, UK, 2004.

[4] W. Raman-Nair and R. Boileau, “Two-dimensional mooring dynamics for wave en-ergy converters,” National Research Council Canada, Technical Report TR-2012-04, Jan. 2012.

[5] L. Johanning, G. H. Smith, and J. Wolfram, “Mooring design approach for wave energy converters,” in J. Engineering for the MarItime Environment, vol. 220 Part M, 2006, pp. 159–174.

[6] R. Boileau and E. Baddour, “Wave resource assessment for Lord’s Cove, New-foundland – winter/spring 2012 survey,” National Research Council Canada, Tech-nical Report OCRE-TR-2012-19, Jul. 2012.

[7] K. Ogata, System Dynamics, 3rd ed. Prentice Hall, 1998, §6–3.

[8] S. C. Chapra and R. P. Canale, Numerical Methods for Engineers, 6th ed., D. B. Hash, Ed. McGraw-Hill, 2010.

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OCRE-TR-2013-043

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OCRE-TR-2013-043 A Physical test method for hydrodynamic inputs

A

Physical test method for hydrodynamic inputs

Hydrodynamic inputs, including added mass and inertia and damping coefficients were determined experimentally for the natural frequency in each mode by exciting the model and observing the period and decay rate of its oscillations. The three CNA models were characterized in surge, heave and roll. The method used for surge is based on the mass-spring parameter identification method in [7, §6.3]; the methods for heave and roll are described in [8, §17.3–17.4].

A.1 Model test apparatus

Two models were fabricated from NRC drawings by CNA. An existing pump platform model was modified to make the third model. Model #1 is square in cross-section, Model #2 is circular and Model #3 has a rectangular float with a spar-like submerged body.

Position and motion are measured relative to an arbitrary point in space by a isys motion capture camera system installed on the CWTT tow carriage. Three Qual-isys target balls are mounted on rods attached to the model, as shown in Figure 6.

Figure 6: Model #1 with Qualisys target balls (circled in red)

A.2 Coordinate definition

By naval architecture convention, the positive z-axis is down. The “bow” of each model is marked on the upper surface of the float with an arrow pointing forward; this defines the direction of the positive x-axis (”forward”). The positive y-axis (”starboard”) is de-fined using the right hand rule. This convention is followed in the CAD drawings and in data channel names.

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OCRE-TR-2013-043 A Physical test method for hydrodynamic inputs x y z Global origin x y z Model origin

Figure 7: Model and coordinate axes

A.3 Data acquisition and pre-processing

Data was sampled from the Qualisys system using the towing tank data acquisition system. Eight channels were recorded for 6 degree of freedom (DOF) position, as listed in Table 6. Data were sampled at 50 ❍③; however, Qualisys was only set to provide data at 26❍③ for the first day of testing (this is noted in the test log).

Table 6: Data channel list

channel # name units note

1 X (Body 1) ♠ surge

2 Y (Body 1) ♠ sway

3 Z (Body 1) ♠ heave

4 Yaw (Body 1) ❞❡❣ rotation about z

5 Pitch (Body 1) ❞❡❣ rotation about y

6 Roll (Body 1) ❞❡❣ rotation about x

7 Residual (Body 1) - measurement error

A.4 Calibrations

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A.5 Test program

The test program included manually-initiated surge, heave and roll damping tests. (Pitch and sway damping tests were also conducted, although not needed for the nu-merical mooring model.)

A.5.1 Surge (sway) damping

Surge oscillation is generated by pushing the model with a long pole either forward or aft (abeam for sway) parallel to the long side of the tow tank to create an initial displacement and then releasing it suddenly. The test is repeated multiple times from different directions and by pushing on different points (upper or middle body section).

A.5.2 Heave damping

Heave oscillation is generated by suspending the model a few centimetres above the draft waterline by a single line and releasing it suddenly by cutting the line.

A.5.3 Roll (pitch) damping

Roll oscillation is generated by pushing the model with a long pole either down or up to create an initial angle about the x (or y for pitch) axis and then releasing it suddenly. The test is repeated multiple times from different directions and by pushing on different points (upper or middle body).

A.5.4 Test procedure

The following steps were followed for each of the three models.

1. The waterline is checked against the fabrication drawing in the CWTT trim tank and the ballast adjusted to level it, as shown in Figure 8.

2. The model is towed to a position under the towing carriage and attached to two horizontal (submerged) springs, fore and aft, which are fixed to a point on the carriage via pulleys and steel cable.

3. Surge damping tests are performed at least twice with the model in each of the following orientations:

◦ bow pointing down the tank, springs attached fore and aft

◦ bow pointing 45◦from the tank wall, springs attached to diagonal points ◦ bow pointing toward the tank side, springs attached port and starboard

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(a) model #1 (b) model #2 (c) model #3

Figure 8: Trimmed models in CWTT trim tank

4. Roll damping tests are performed at least twice with the model in each of the following orientations:

◦ bow pointing down the tank, springs attached fore and aft ◦ bow pointing down the tank, free floating (no springs)

◦ bow pointing 45◦from the tank wall, springs attached to diagonal points ◦ bow pointing 45◦from the tank wall, free floating

◦ bow pointing toward the tank side, springs attached port and starboard ◦ bow pointing toward the tank side, free floating

5. Heave damping tests are performed twice.

6. After testing, the model is inclined in the CWTT trim tank to verify mass properties from Solidworks.

A.5.5 Completed tests

The completed test matrix is given in Table 7. In total, 142 tests were completed (in 37 data runs) for 31 different test conditions.

A.6 Calculation of hydrodynamic inputs

Added mass and inertia and damping coefficients were calculated using Matlab scripts and functions based on [7] and [8]. Several results were checked against damping

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Table 7: Completed physical test matrix

surge sway heave captive pitch free pitch

yaw angle 0◦ ₄₅◦ ₀◦ _n/a ₉₀◦ ₉₀◦ ₉₀◦

tank orientation long. long. long. n/a long. long. lat. excitation count

#1 7x 9x 2x 1x

platform #2 8x 8x 2x 2x

#3 6x 5x 6x 2x 6x 8x 6x

captive roll free roll

yaw angle 0◦ ₄₅◦ ₀◦ ₀◦ ₄₅◦ ₄₅◦

tank orientation long. long. long. lat. long. lat. excitation count

#1 5x 7x 3x 2x 2x 2x

platform #2 6x 6x 3x 2x 4x 4x

#3 6x 6x 3x 3x

A.7 Sources of error

In this experiment, systematic errors include measurement error, variation between springs and differences in sampling rates. The estimated accuracy for Qualisys posi-tion is better than ±1 ♠♠ and ±0.1◦; the three tracking balls are arranged in a plane nearly parallel to the model yz-plane, so measurements in that plane will have the low-est accuracy (i.e., sway and roll). Spring constants were averaged between the two springs (22.5 ± 0.2 ◆✴♠). For runs in which Qualisys data were sampled at 26 ❍③ (vs data acquisition at 50❍③), data were interpolated linearly.

The largest source of error is coupling between modes (e.g., yaw response during roll damping tests), especially when the model is unrestrained: coupled amplitudes were generally an order of magnitude below the main mode. Tank wall and bottom re-flections also interacted with the model after a certain time, although this was mitigated by manually selecting data before any apparent effect.

A.8 Test log

The following table is a log of tank testing including in situ notes, taken verbatim from the file❆✶❴✵✵✸✻✼✻❴t❡st ❧♦❣✳①❧s.

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OCRE-TR-2013-043 A Ph ysical test met hod for h ydrodynamic

Table 8: Tank test log (excitation count added in green)

DATE START WAIT FILENAME(.DAQ) excit. RUN Video COMMENTS TIME TIME count DESCRIPTION Track #

27-Aug-13 Begin Tank Setup

" 12:11 00:04 SURGE_DAMPING_M1_001 2 Surge Decay, Model 1, 0deg heading " 12:15 01:34 ROLL_DAMPING_M1_001 1 Roll Decay,

Model 1, 0deg heading

" Springs were too stiff. Replaced

them with longer softer springs. " 13:49 00:13 SURGE_DAMPING_M1_002 2 Surge Decay,

1 model was pushed from cable at-tachment point.

" 14:02 00:14 SURGE_DAMPING_M1_003 3 Surge Decay, Model 1, 0deg heading

1 model was pushed from top deck

" 14:16 00:26 ROLL_DAMPING_M1_002 4 Roll Decay, Model 1, 0deg heading

2 1st two segmants were pushed down unto top deck, 3rd segment was pulled up from mid deck, 4th segment was pushed down unto mid deck.

" rotate model 45deg

" 14:42 00:13 SURGE_DAMPING_H45_M1_001 3 Surge Decay, Model 1, 45deg heading

3 three segments were pushed from the mid deck(aft to fwd)

" 14:55 00:14 SURGE_DAMPING_H45_M1_002 3 Surge Decay, Model 1, 45deg

4 three segments were pushed from the top deck(aft to fwd)

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OCRE-TR-2013-043 A Ph ysical test met hod for h ydrodynamic inputs

DATE START WAIT FILENAME(.DAQ) excit. RUN Video COMMENTS

TIME TIME count DESCRIPTION Track #

" 15:09 00:11 ROLL_DAMPING_H45_M1_001 4 Roll Decay, Model 1, 45deg heading

5 1st two segmants were pushed down unto mid deck, 3rd & 4th segments were pulled up from mid deck.

6 1st segment was puched from the aft to fwd, 2nd & 3rd segments were pushed from the fwd to aft. All seg-ments were at the mid deck. " 15:34 ROLL_DAMPING_H45_M1_002 3 Roll Decay,

7 1seg - large amp, 2nd small amp, 3rd seg normal amp. (resaved as ROLL_DAMPING_H45_M1_003

28-Aug-13 Disconnected model from mooring.

Repeat roll decay at 0 & 45deg heading

" 08:33 00:14 ROLL_DAMPING_M1_FREE_001 5 Roll Decay, Model 1, 0deg heading, free (unmoored)

8 The first 3 seg were roll, the forth was pitch, the 5th & 6th were with the model rotated 90deg so that the roll was orietated up the tank in-stead across the tank.

" 08:47 00:28 ROLL_DAMPING_H45_M1_FREE_001 6 Roll Decay, Model 1, 45deg heading, free (unmoored)

9 The first 2 seg were roll, the 3rd & 4th were junk, the 5th & 6th were with the model rotated 90deg so that the roll was orientated up the tank instead across the tank.

" 09:15 00:21 HEAVE_DAMPING_M1_FREE_001 1 Heave Decay, Model 1, free (unmoored)

10 lifted by crane til bottom of float just submerged

continued. . .

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" removed Model 1 and prepared

Model 2.

" 10:00 00:18 Installed Model 2

12 1st three segments were pushed from the mid deck(aft to fwd), 4th segment from top deck(aft to fwd) " 10:35 00:27 SURGE_DAMPING_M2_002 4 Surge Decay,

13 1st three segments were pushed from the mid deck(fwd to aft), 4th segment from top deck(fwd to aft), resaved as SURGE_DAMPING_M2_003 WAIT TIME = 14:36

" 11:02 00:19 ROLL_DAMPING_M2_001 6 Roll Decay, Model 2, 0deg heading

14 1st three segments were pushed from the top deck, the last three segments were from mid deck.

toprule " rotate model 45deg

15 1st three segments were pushed from the mid deck(aft to fwd), 4th segment from top deck(aft to fwd) " 11:36 00:15 SURGE_DAMPING_H45_M2_002 4 Surge Decay,

16 1st three segments were pushed from the mid deck(fwd to aft), 4th segment from top deck(fwd to aft) " 11:51 01:18 ROLL_DAMPING_H45_M2_001 6 Roll Decay,

17 1st three segments were pushed from the top deck, the last three segments were from mid deck.

toprule " Disconnected model from mooring.

Repeat roll decay at 0 & 45deg heading

" 13:09 00:12 ROLL_DAMPING_M2_FREE_001 5 Roll Decay, Model 2, 0deg

18 The first 3 seg were roll, the 4th & 5th was pitch, the 5th & 6th were

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" 13:21 00:15 ROLL_DAMPING_H45_M2_FREE_001 5 Roll Decay, Model 2, 45deg heading, free (unmoored)

n/a The first 2 seg were roll, the 3rd & 4th were with the model rotated 90deg so that the roll was orientated up the tank instead across the tank. Video missed.

" removed Model 2 and prepared

Model 3

" 14:30 00:37 Installed Model 3

21 1st three segments were pushed from inside bottom of top tank(aft to fwd), segments 4 to 6 were pushed from inside bottom of top tank(fwd to aft).

" 15:20 ROLL_DAMPING_M3_001 6 Roll Decay, Model 3, 0deg heading

22 The first 4 segments were pushed down, the last segments were pulled up.

29-Aug-13 08:16 00:17 Sway_DAMPING_M3_001 6 Surge Decay, Model 3, 90deg heading

23 1st four segments were pushed from inside bottom of top tank(aft to fwd), segments 5 & 6 were pushed from inside bottom of top tank(fwd to aft). Video Annotation says surge & H90, should be same as filename.

continued. . .

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" 08:33 00:18 PITCH_DAMPING_M3_001 6 Roll Decay, Model 3, 90deg heading

24 The first 3 segments were pushed down, the last 3 segments were pulled up.

25 1st three segments were pushed from inside corner of top tank(aft to fwd), segments 4 & 5 were pushed from inside corner of top tank(fwd to aft).

" 09:04 00:19 ROLL_DAMPING_H45_M3_001 6 Roll Decay, Model 3, 45deg heading

26 The first 3 segments were pushed down, the last 3 segments were pulled up from flange.

Remove model from mooring and setup for free tests.

" 09:23 00:11 ROLL_DAMPING_M3_FREE_001 6 Roll Decay, Model 3, free (unmoored)

27 The first 3 seg were transverse roll, the last 3 were longitudinal roll - with the model rotated 90deg so that the roll was orientated up the tank in-stead across the tank.

" 09:34 00:10 PITCH_DAMPING_M3_FREE_001 5 Pitch Decay, Model 3, free (unmoored)

28 The first 3 seg were transverse roll, the last 3 were longitudinal roll - with the model rotated 90deg so that the roll was orientated up the tank in-stead across the tank.

Qualisys body cooridinates went off during run. Reset Qualisys and re-peat run.

" 09:44 00:25 PITCH_DAMPING_M3_FREE_002 8 Pitch Decay, Model 3, free (unmoored)

29 The first 3 seg were longitudinal roll - with the model rotated 90deg so that the roll was orientated up the

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30

" 10:20 HEAVE_DAMPING_M3_FREE_002 1 Heave Decay, Model 3, free (unmoored)

31

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OCRE-TR-2013-043 B Potential code method for Hydrodynamic inputs

B

Potential code method for Hydrodynamic inputs

The hydrodynamic inputs for the numerical mooring model were estimated for a range of wave periods using the AQWATM Hydrodynamic Diffraction module in ANSYS Work-bench (v14.5). AQWA needs a geometry, mass properties, wave directions and fre-quencies to run. The workflow for AQWA includes the following steps:

1. define the geometry 2. set mass properties 3. mesh the model 4. check hydrostatics

5. set up analysis and wave environments 6. choose outputs and solve

7. check results

B.1 Geometry

The geometry for each platform is generated in ANSYS Design ModelerTM. The plat-form is drawn from the top down, starting on a plane offset from the XY-plane (a.k.a. the water plane) by the design draft. The dimensions are specified in metres so that outputs are SI.

B.2 Point mass

The mass properties are defined in a Point Mass element added to the geometry, including position of centre of gravity and moments of inertia extracted from the CAD models.

B.3 Mesh

Each model is meshed using automatic mesh generation in Workbench.

B.4 Analysis settings

Water density is set to 1025 ❦❣·♠2

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con-OCRE-TR-2013-043 B Potential code method for Hydrodynamic inputs

(a) #1 (b) #2 (c) #3

Figure 9: Simplified model geometry in ANSYS Design Modeler

(a) #1 (b) #2 (c) #3

Figure 10: Meshed models in ANSYS Workbench

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CWTT depth 5♠) – it is assumed that disagreement in results due to these settings is negligible, so the runs were not repeated due to time constraints.

Wave directions are aligned forward, aft and diagonal with respect to the model “bow” as defined in physical testing; model #3 runs also include sway. The range of wave frequencies (specified as periods ins) included each sea state of interest for this study.

The complete analysis settings for each model are included in tables 1–16 in the AQWA reports in §B.9

B.5 Solve hydrostatics

The depth of the centre of gravity, principle moments of inertia and the wetted surface (specified by the draft dimension) determine the program-controlled mass calculation in AQWA.

Table 9 compares the results from AQWA based on CAD inputs with the expected values from Solidworks and measured mass from the physical models on a crane scale.

Table 9: Model scale hydrostatics check

property z_cg_* _draft _{metacentric height} _mass

♠ (flooded) ♠ ♠ ❦❣ (dry) (flooded)

Model #1 Solidworks −0.730 0.070 0.345 141.89 152.90 crane scale† _143.4 AQWA _−0.730 0.070 Model #2 Solidworks _−0.631 0.070 0.293 123.56 133.54 crane scale† 119.9 AQWA −0.631 0.070 Model #3 Solidworks −0.460 0.082 0.760 36.61 crane scale† _34.1 AQWA _−0.460 0.082

*vertical centre of gravity measured from waterline †_{TCI model LPC-4-AC ± 0.2 ❧❜s = 0.1 ❦❣}

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B.6 Solve

Each run with 10 wave periods from 3 or 4 directions typically took 1.5–2 hours to solve. Solutions included added surge and heave mass, added roll inertia and damping coefficients for each surge, heave and roll. For Platform #3, motion was checked to ensure rigid body motion, since fine rods connecting the float and heave plate were neglected.

B.7 Comparison with natural frequency results from test data

Hydrodynamic inputs from AQWA were compared with results calculated from test data by selecting added mass/inertia and damping coefficient for one mode (i.e., surge, heave or roll) at the natural period observed in the physical model tests for that mode and the nearest (or interpolated) AQWA period.

B.8 Common problems

Several issues arose that caused solutions to fail to run or to abort or that resulted in corrupted files. Some workarounds are listed in Table 10

Paul Schofield at ANSYS Technical Support confirmed known issues and has sub-mitted defects, some of which will be addressed in v15. He could not replicate ◆❛◆ results, although his results included extremely large and/or negative added mass at some frequencies.

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Table 10: ANSYS AQWA/Workbench reported issues

Issue Workaround

Failure to run

frequency order AQWA fails to start with

added frequencies. Frequency high-lighted in yellow, no error (irrespective of initial range).

Select frequencies in ascending order.

Aborted run

abort with error unspecified error message

after running all frequencies:

Hydrodynamic Diffraction (B4): COMPLETED SUCCESSFULLY

Hydrodynamic Diffraction (B4):

TERMI-NATED WITH ERRORS

Hydrodynamic Diffraction (B4): Solve

aborted!

Possible irregular frequency. Check ❆◆❆▲❨❙■❙✳▲■❙ for ◆❛◆ re-sults. Conduct separate sensitivity study around trouble frequency to confirm anomaly. Re-run main study replacing❬NaN] frequencies with nearby solved frequencies. Unexpected results

wrong frequencies Results are for

frequen-cies other than original specification. (Fre-quencies change after any change to model or mesh; interval and count do not recalculate reliably.)

Always check frequencies, interval and number of intermediate fre-quencies LAST. Toggle selection method from period to frequency and back to clear impossible recal-culations.

Corrupted database

disappearing geometry when launching AQWA in Workbench after changing geometry.

Known issue with multi-threaded database (tree) check. Delete AQWA element and start again. Archive frequently. Upgrade to v15 when released.

error opening file Use of multiple parameters

or loss of network drive connection may trigger database corruption.

File cannot be recovered. Archive frequently. Upgrade to v15 when released.

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B.9 AQWA results

ANSYS Workbench produces complete reports for each run — the reports on the CNA platforms at model scale follow this page.

B.10 Workflow options

While this workflow worked for this set of models, several options may be considered for future work.

Imported geometry from CAD Geometry can be imported directly from CAD, e.g.,

as a parasolid file; Design Modeler has a Simplify tool to eliminate small parts. However, the each pump platform fabrication drawings included up to 130 parts, which would have taken more time to simplify than drawing from scratch.

Mesh refinement To reduce the total number of elements while accurately modelling

small details, a model with a small feature can be meshed locally with finer el-ements by splitting the body (Slice or Freeze) before joining as a part. Add a Mesh Control to the body in the Mesh tool. While AQWA requires a slice at the waterline (XY plane), it will also accept multiple bodies broken on other planes.

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Project

Name Project

Data Folder Root C:\Users\BoileauR.IOTPC\Documents\ANSYS working files\CNA model 1_files\dp0\AQW\AQW Date of Creation 2013-10-03 17:21:42

Last Modified 2013-10-08 12:57:18

Product Version 14.5 RELEASE

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Contents z Units z Model (B3) { Geometry CNA CNA Axes Point Mass Topsides Submerged { Connections Catenary Data { Mesh { Hydrodynamic Diffraction (B4) Analysis Settings Gravity Structure Selection Wave Directions Wave Frequencies Solution (B5) Hydrostatic

Added Mass, Global X (Force/Moment vs Frequency) Added Mass, Global Z (Force/Moment vs Frequency) Added Inertia, Global RX (Force/Moment vs Frequency) Radiation Damping, Global X (Force/Moment vs Frequency) Radiation Damping, Global Z (Force/Moment vs Frequency) Radiation Damping, Global RX (Force/Moment vs Frequency) Units

TABLE 1

Model (B3)

Length Meter Mass Kilograms Rotational Velocity Degrees Force Newton Frequency Hertz Time Second Geometry TABLE 2 Model (B3) > Geometry

Object Name Geometry

State Fully Defined

Details of Geometry

Attached Assembly Name M:\My Documents\2530 CNA\platform coefficients (Aqwa)\CNA model 1_files\dp0\Geom\DM\Geom.agdb

Sea Geometry Water Level 0 m Water Depth 30 m Water Density 1025 kg/m³ Water Size X 1000 m Water Size Y 1000 m Import Preferences

Import Solid Bodies No

Import Surface Bodies Yes

Import Line Bodies Yes

CNA

TABLE 3 Model (B3) > Geometry > Part

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TABLE 4

Model (B3) > Geometry > CNA > Axes

TABLE 5

Model (B3) > Geometry > CNA > Point Mass

TABLE 6

Model (B3) > Geometry > CNA > Body

Object Name CNA State Fully Defined

Details of CNA

Part Visibility Visible Suppressed Not Suppressed Total Structural Mass 153.130795434117 kg

X Position of COG 2.38403679020394E-08 m Y Position of COG -1.15647068810176E-07 m Z Position of COG -0.73 m Generate Internal Lid No Current Calculation Depth 0 m

Fixity Options

Structure Fixity Structure is Free to Move

Force Factors

Drag Factor 1 Mass Factor 1 Slam Factor 0

Advanced Options

Submerged Structure Detection Program Controlled Override Calculated GMX No Override Calculated GMY No

Non-Linear Roll Damping

Non-Linear Roll Damping Excluded from Calculations

Object Name CNA Axes State Fully Defined

Details of CNA Axes

Visibility Visible Alignment Method Global Axes Rotation About Global Z 0 °

Rotation About Local Y 0 ° Rotation About Local X 0 ° Unit Vector X [1, 0, 0] Unit Vector Y [0, 1, 0] Unit Vector Z [0, 0, 1]

Object Name Point Mass State Fully Defined

Details of Point Mass

Visibility Not Visible Suppressed Not Suppressed

X 2.38403679020394E-08 m Y -1.15647068810176E-07 m Z -0.73 m Mass definition Program Controlled

Mass 153.130795434117 kg Define inertia values by Direct input of Inertia

Kxx 0.36363905540238 m Kyy 0.36363905540238 m Kzz 0.315109823907887 m Ixx 20.249 kg.m² Ixy 0 kg.m² Ixz 0 kg.m² Iyy 20.249 kg.m² Iyz 0 kg.m² Izz 15.205 kg.m²

Object Name Topsides State Fully Defined

Details of Topsides

Body Visibility Visible

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TABLE 7

Model (B3) > Geometry > CNA > Body

Suppressed Not Suppressed Structure Type Physical Geometry

Surface Type Program Controlled

Object Name Submerged State Fully Defined

Details of Submerged

Body Visibility Visible Suppressed Not Suppressed Structure Type Physical Geometry

Surface Type Program Controlled

Connections

TABLE 8 Model (B3) > Connections

TABLE 9

Model (B3) > Connections > Catenary Data

Object NameConnections State Fully Defined

Details of Connections

Object NameCatenary Data State Fully Defined

Details of Catenary Data

Mesh TABLE 10 Model (B3) > Mesh Hydrodynamic Diffraction (B4) TABLE 11 Model (B3) > Analysis TABLE 12

Model (B3) > Hydrodynamic Diffraction (B4) > Analysis Settings

Object Name Mesh State Meshed

Details of Mesh

Defeaturing Tolerance 0.002 m Max Element Size 0.04 m Max Allowed Frequency 2.55 Hz

Meshing Type Program Controlled

Generated Mesh Information

Number of Nodes 8868 Number of Elements 8930 Number of Nodes (Diffracting Bodies) 7699 Number of Elements (Diffracting Bodies) 7712

Object Name Hydrodynamic Diffraction (B4) State Solved

Details of Hydrodynamic Diffraction

Analysis Type Hydrodynamic Diffraction/Radiation

Object NameAnalysis Settings State Fully Defined

Details of Analysis Settings

Sea Grid Size Factor 2

Output File Options

Output Full QTF Matrix Yes Do Not Output .LIS Banner Page No No Wave Elevation at Field Points No Output Source Strengths No Output Potentials No

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TABLE 13

Model (B3) > Hydrodynamic Diffraction (B4) > Gravity

TABLE 14

Model (B3) > Hydrodynamic Diffraction (B4) > Structure Selection

TABLE 15

Model (B3) > Hydrodynamic Diffraction (B4) > Wave Direction

TABLE 16

Model (B3) > Hydrodynamic Diffraction (B4) > Wave Frequency

Output Centroid Pressures No Output Element Properties No Output ASCII Hydrodynamic Database No Output Example of Hydrodynamic Database No

QTF Options

Calculate Full QTF Matrix Yes

Common Analysis Options

Ignore Modelling Rule Violations Yes No Drift Coefficients No No Pressure Post-Processing No Near Field Solution No Linearized Tube Drag No

Object Name Gravity State Fully Defined

Details of Gravity

Gravity, g 9.80665 m/s²

Object NameStructure Selection State Fully Defined

Details of Structure Selection

Structures to Exclude None

Group Of Structures

Interacting Structure Groups None

Structure Ordering

Structure 1 CNA

Object Name Wave Directions State Fully Defined

Details of Wave Directions

Type Range of Directions, No Forward Speed

Required Wave Input

Wave Range -180° to 180° (-PI to PI) Interval 180 ° Number of Intermediate Directions 1

Optional Wave Directions A

Additional Range Single Start Angle 45 °

Optional Wave Directions B

Additional Range None

Optional Wave Directions C

Optional Wave Directions D

Object NameWave Frequencies State Fully Defined

Details of Wave Frequencies Frequency / Period definition

Range Manual Definition Definition Type Range Lowest Frequency 0.063 Hz

Longest Period 16 s Highest Frequency 0.5 Hz

Shortest Period 2 s Interval Type Period Interval Period 2 s Number of Intermediate Values 6

Additional Frequencies A

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Solution (B5)

TABLE 17

Model (B3) > Hydrodynamic Diffraction (B4) > Solution (B5) > Hydrostatic Results

Additional Range Single Lowest Frequency 2 Hz

Longest Period 0.5 s

Additional Frequencies B

Additional Range Single Lowest Frequency 0.182 Hz

Longest Period 5.5 s

Additional Frequencies C

Additional Frequencies D

Object Name Hydrostatic State Solved

Details of Hydrostatic

Structure CNA

Graphical Representation

Show Centre of Gravity Yes Show Centre of Buoyancy Yes Show Centre of Floatation Yes

Results

Actual Displaced Volume 0.1493959 m³ Metacentric Height GMX 0.3389662 m Out of Balance Force/Weight, Fz 2.0728e-5

Aqwa Hydrostatic Results

Structure CNA

Hydrostatic Stiffness

Centre of Gravity Position: X: 2.384e-8 m Y: -1.1565e-7 m Z: -0.73 m

Z RX RY

Heave(Z): 4437.8301 N/m -5.0587e-6 N/° -1.4073e-6 N/° Roll(RX): -2.8984e-4 N.m/m 8.8841715 N.m/° 1.3898e-7 N.m/° Pitch(RZ): -8.0633e-5 N.m/m 1.3898e-7 N.m/° 8.8841572 N.m/°

Hydrostatic Displacement Properties

Actual Volumetric Displacement: 0.1493959 m³ Equivalent Volumetric

Displacement: 0.1493959 m³

Centre of Buoyancy Position: X: 2.9295e-8 m Y: 3.1898e-7 m Z: -0.49486 m

Out of Balance Forces/Weight: FX: -9.0253e-8 FY: -3.325e-8 FZ: 2.0728e-5

Out of Balance Moments/Weight: MX: 2.4265e-7 m MY: 6.8369e-8 m MZ: 1.4793e-8 m

Cut Water Plane Properties

Cut Water Plane Area: 0.4414954 m²

Centre of Floatation: X: 4.2009e-8 m Y: -1.8096e-7 m Principal 2nd Moment of Area: X: 1.5511e-2 m^4 Y: 1.5511e-2 m^4 Angle Principal Axis makes with X

(FRA): 0. °

Small Angle Stability Parameters

C.O.G. to C.O.B.(BG): -0.23514 m

Metacentric Heights (GMX/GMY): 0.3389662 m 0.3389656 m COB to Metacentre (BMX/BMY): 0.1038261 m 0.1038256 m

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TABLE 18

Model (B3) > Hydrodynamic Diffraction (B4) > Solution (B5) > Hydrodynamic Graph Results

FIGURE 1

Model (B3) > Hydrodynamic Diffraction (B4) > Solution (B5) > Added Mass, Global X (Force/Moment vs Frequency)

TABLE 19

Model (B3) > Hydrodynamic Diffraction (B4) > Solution (B5) > Added Mass, Global X (Force/Moment vs Frequency)

TABLE 20

Model (B3) > Hydrodynamic Diffraction (B4) > Solution (B5) > Hydrodynamic Graph Results

Restoring Moments/Degree

Rotations (MX/MY): 0.155058 N.m/° 0.1550578 N.m/°

Object NameAdded Mass, Global X (Force/Moment vs Frequency)

State Solved

Details of Added Mass, Global X (Force/Moment vs Frequency)

Presentation Method Line Axes Selection Force/Moment vs Frequency Frequency or Period Scale Frequency

Line A

Structure CNA

Type Added Mass

SubType Global X Component Global X Position of Min in X 2 Position of Max in X 0.5 Minimum Value 42.507 Maximum Value 63.607 Line B

Structure Not Defined...

Frequency (Hz) Line 1 0.063 57.808136 0.071 57.82975 0.083 57.863487 0.1 57.920486 0.125 58.029034 0.167 58.280231 0.182 58.396114 0.25 59.106441 0.5 63.607437 2 42.506611

Object NameAdded Mass, Global Z (Force/Moment vs Frequency)