hydrodynamic_modelling_of_hulls_using_ranse_codes.ortin-montesinos_2015_mye.pdf

7/21/2019 Hydrodynamic_modelling_of_hulls_using_RANSE_codes.Ortin-Montesinos_2015_MYE.pdf

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[email protected] [email protected]

Hydrodynamic modelling of hulls using RANSE codes

Jos Luis Ortn Montesinos

Supervisor:

Dr. Stuart E. Norris

Master of Engineering Studies in Yacht Engineering

MechEng 776 Yacht Engineering Project

Department of Mechanical Engineering

The University of Auckland

Auckland, New Zealand

June, 2015


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Abstract

This report describes the modelling of an appended yacht hull that is free to heave and

pitch with CFX v15.0, a finite volume Reynolds Averaged Navier-Stokes (RANS) code

developed by ANSYS. The model is validated against experimental towing tank data, and

is compared with predictions made using the Delft Systematic Yacht Hull Series (DSYHS)

regression equations, and the results of a panel code.

Although hydrodynamic CFD applications have been successfully applied in recent

years, limited public information has been publicly available in regards to sailing yachts.

Nowadays, these methods have been commonly used in performance-yacht design

offices; however as it involves a large amount of research and development, these

companies keep their CFD measurements private, and little information is made public

in the open literature.

As with every software tool predicting real physical behaviour, the validation of theresults is a key aspect to the process. Again, there is limited literature for doing reliable

research in order to contrast the data obtained with the software. The towing tank tests

are very expensive and, as previously stated, it is very valuable information for most

design offices. However, the Delft Systematic Yacht Hull Series (DSYHS) is now openly

available, which provides hull geometries, force data from towing tank experiments and

hydrostatics data. Aside from upright resistance, data is available for yacht hulls that are

heeled with leeway.


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Jos Luis Ortn-Montesinos iii

Acknowledgments

The development of this study has been possible thanks to the inestimable help and

support of the project supervisor Dr. Stuart Norris.

I would like to express my gratitude to the University of Auckland and the Yacht

Research Unit for giving me the opportunity of using the computer Cluster to perform

the numerical analysis.

I would also like to thank Delft University of Technology for making publicly available

the experimental towing tank data from the Delft Systematic Yacht Hull Series, vital for

validating the numerical analysis, and to Jean-Baptiste Souppez for sharing some of the

numerical results obtained in his yacht research project.

Last but not least I would like to thank my family and colleagues for their support and

encouragement through the course.


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Jos Luis Ortn-Montesinos iv

Table of contents

1. Introduction............................................................................................................................. 1

2. Methodology............................................................................................................................. 2

2.1 Experimental...................................................................................................................... 2

2.2 Numerical Modelling......................................................................................................... 4

2.2.1 Overall approach....................................................................................................... 4

2.2.2 Geometry and Computational Domain.................................................................... 4

2.2.3 Mesh generation........................................................................................................ 6

2.2.3.1 Mesh convergence study............................................................................ 10

2.2.3.2 Artificial ventilation.................................................................................... 13

2.2.4 Set-up and boundary conditions............................................................................ 16

2.2.4.1 Set-up........................................................................................................... 16

2.2.4.2 Boundaries................................................................................................... 22

2.2.5 Considerations about the available data................................................................ 24

2.2.5.1 Longitudinal centre of gravity and Displacement..................................... 24

2.2.5.2 Appendages considerations........................................................................ 26

3. Results and Discussion.......................................................................................................... 28

3.1 Bare hull........................................................................................................................... 28

3.2. Upright with appendages............................................................................................... 30

3.3 Yawed and heeled geometry........................................................................................... 33

3.3.1. Upright with leeway.............................................................................................. 33

3.3.2 Yawed case for 10 degrees of heel........................................................................ 35

3.3.3 Yawed case for 20 degrees of heel........................................................................ 38

3.4 Comparison with FS Flow and Delft empirical formulas.............................................. 40

3.4.1 Model heeled 10 and 20 degrees for 3 degrees of leeway.................................. 41

3.4.2 Model heeled 10 and 20 degrees for 6 degrees of leeway.................................. 43

3.4.3. Discussion.............................................................................................................. 453.4.4. Waves and body movement plots........................................................................ 46

4. Conclusions............................................................................................................................ 52

5. Further work.......................................................................................................................... 53

6. References.............................................................................................................................. 54

Appendix A. Wigley geometry.................................................................................................. 56

A.1. Experimental data.......................................................................................................... 56

A.2. Numerical methodology................................................................................................. 58

A.3. Unstructured mesh......................................................................................................... 59

A.4. Structured mesh............................................................................................................. 63

A.5. Results............................................................................................................................. 63

A.6 Conclusions...................................................................................................................... 67


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List of figures

FIGURE 1.EXPERIMENTAL SETUP OF THE DSYHS,FROM [1] ............................................................... ....................... 2

FIGURE 2.SYSSER 62LINESPLAN. ......................................................................................................................... 5

FIGURE 3.HORIZONTAL POSITION OF THE APPENDAGES (DISTANCES IN MM). ............................................................... . 5

FIGURE 4.DIMENSIONS OF THE COMPUTATIONAL DOMAIN FOR THE SYSSER62HULL,HEELED AND YAWED. ......................... 6

FIGURE 5.MESH DETAILS OF THE BARE HULL (LONGITUDINAL VIEW). ............................................................... ............ 7

FIGURE 6. TRANSVERSAL VIEW OF THE DEFORMED MESH AND WAVE GENERATED FOR THE BARE HULL, UPRIGHT

CASE,FR=0.40, (LEFT) AND APPENDED, HEELED 10 DEGREES AND YAWED 6 DEGREES, FR=0.40

(RIGHT).. ........................................................ ................................................................. ............ 8

FIGURE 7.DETAILS OF THE DEFORMED MESH AND FREE SURFACE AT BOW AND STERN. .................................................... 8

FIGURE 8.LONGITUDINAL VIEW OF THE MESH GENERATED FOR THE APPENDED CASE. ..................................................... 9

FIGURE 9.MESH ORTHOGONALITY ANGLE (20DEGREES OF HEEL AND 6DEGREES OF LEEWAY . ................... 10

FIGURE 10.CONVERGENCE STUDY AT FR=0.45 .................................................................................................... 11

FIGURE 11.DETAIL OF THE MESH REFINEMENT AND THE AIR ENTRAINMENT AT THE STERN FOR FR=0.35. ......................... 13

FIGURE 12.AIR ENTRAINMENT UNDER THE HULL FOR A COARSE MESH (ABOVE) AND A FINE MESH (BELOW) FORFR =0.35. ................................................................................................................................ 14

FIGURE 13.EVOLUTION OF THE AIR ENTRAINMENT ALONG THE SIMULATION OF THE SYSSER 62HULL AT FR 0.40,WITH

10DEGREES OF HEEL AND 9DEGREES OF LEEWAY. ........................................................ ..................... 15

FIGURE 14. Y PLUS VALUES AND DEFORMED FREE SURFACE (WATER VOLUME FRACTION OF 0.5) FOR FR=0.325

(ABOVE)AND FR=0.6(BELOW). .......................................................................................... .......... 19

FIGURE 15.RMSVALUES OF THE UPRIGHT SIMULATION FOR FR=0.50. ........................................................... .......... 20

FIGURE 16.DRAG FORCE EVOLUTION FOR FR=0.25,(UPRIGHT,APPENDED CASE). ..................................................... .. 20

FIGURE 17.DRAG FORCE CONVERGENCE FOR FR=0.6.UPRIGHT AND APPENDED CASE. ................................................. 21

FIGURE 18.DRAG AND SIDE FORCE CONVERGENCE FOR FR=0.4,20DEGREES OF HEEL AND 6DEGREES OF LEEWAY. ........... 21

FIGURE 19. WATER TURBULENT KINETIC ENERGY OF THE HEELED AND YAWED CASE OVER THE FREE SURFACE FOR

FR=0.35. ....................................................... ................................................................. .......... 22

FIGURE 20.FORCES AND DISTANCES CONSIDERED DURING THE DSYHSEXPERIMENTAL TESTS. ........................................ 24

FIGURE 21.PITCH ANGLE CONVERGENCE FOR BOTH CORRECTED AND ORIGINAL LCGPOSITION,FR=0.55. ........................ 25

FIGURE 22. FINAL TRIM POSITION REACHED BY THE MODEL WITH LCG CORRECTION (ABOVE) AND WITHOUT LCG

CORRECTION (BELOW). ............................................................ ..................................................... 26

FIGURE 23.SYSSER 62BARE HULL UPRIGHT RESISTANCE FOR FREE CASE (GREEN)AND FIXED CASE (RED). .......................... 28

FIGURE 24. EXPERIMENTAL AND NUMERICAL HEAVE OF THE SYSSER 62 BARE HULL, MEASURED AT THE RESPECTIVE

CENTRES OF GRAVITY (POSITIVE DOWN) ........................................................... ................................ 29

FIGURE 25.EXPERIMENTAL AND NUMERICAL PITCH ANGLES OF THE SYSSER 62BARE HULL BOW UP POSITIVE.................... 29

FIGURE 26.SYSSER 62UPRIGHT RESISTANCE (APPENDED CASE),WITH ORIGINAL AND CORRECTED LCG. ........................... 30

FIGURE 27. LOGARITHMIC PLOT OF THE SYSSER 62 UPRIGHT RESISTANCE (APPENDED CASE), WITH ORIGINAL ANDCORRECTED LCG. ........................................................ .............................................................. .. 31

FIGURE 28.EXPERIMENTAL AND NUMERICAL HEAVE OF THE SYSSER 62UPRIGHT AND APPENDED HULL,MEASURED AT

THE RESPECTIVE CENTRES OF GRAVITY,FOR BOTH ORIGINAL AND CORRECTED LCG(POSITIVE DOWN). ........ 311

FIGURE 29. EXPERIMENTAL AND NUMERICAL PITCH ANGLES OF THE SYSSER 62 UPRIGHT AND APPENDED HULL, FOR

BOTH ORIGINAL AND CORRECTED LCG(BOW UP POSITIVE). ................................................................. 32

FIGURE 30.RESISTANCE FOR 3,6AND 9DEGREES OF LEEWAY;EXPERIMENTAL DATA REPRESENTED BY THE CONTINUOUS

LINE AND NUMERICAL RESULTS BY CROSSES. ................................................................ ...................... 33

FIGURE 31. LATERAL FORCE FOR 3, 6 AND 9 DEGREES OF LEEWAY; EXPERIMENTAL DATA REPRESENTED BY THE

CONTINUOUS LINE AND NUMERICAL RESULTS BY CROSSES. ................................................................... 34

FIGURE 32.PITCH ANGLE FOR 3,6AND 9LEEWAY ANGLES;EXPERIMENTAL DATA REPRESENTED BY THE CONTINUOUS

LINE AND NUMERICAL RESULTS BY CROSSES (BOW DOWN POSITIVE). ...................................................... 34


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FIGURE 33.HEAVE FOR 3,6AND 9LEEWAY ANGLES;EXPERIMENTAL DATA REPRESENTED BY THE CONTINUOUS LINE AND

NUMERICAL RESULTS BY CROSSES (DOWN POSITIVE). .......................................................................... 35

FIGURE 34.RESISTANCE VALUES FOR 3,6AND 9DEGREES OF LEEWAY AND 10DEGREES OF HEEL;EXPERIMENTAL DATA

REPRESENTED BY THE CONTINUOUS LINE AND NUMERICAL RESULTS BY CROSSES. ...................................... 36

FIGURE 35.LATERAL FORCE VALUES FOR 3,6AND 9DEGREES OF LEEWAY AND 10DEGREES OF HEEL; EXPERIMENTAL

DATA REPRESENTED BY THE CONTINUOUS LINE AND NUMERICAL RESULTS BY CROSSES. .............................. 36FIGURE 36. PITCH ANGLE FOR 3, 6 AND 9 LEEWAY ANGLES AND 10 DEGREES OF HEEL; EXPERIMENTAL DATA

REPRESENTED BY THE CONTINUOUS LINE AND NUMERICAL RESULTS BY CROSSES (BOW DOWN POSITIVE). ....... 37

FIGURE 37.HEAVE FOR 3,6AND 9LEEWAY ANGLES AND 10DEGREES OF HEEL;EXPERIMENTAL DATA REPRESENTED BY

THE CONTINUOUS LINE AND NUMERICAL RESULTS BY CROSSES (DOWN POSITIVE). ................................... 388

FIGURE 38. RESISTANCE FOR 3, 6 AND 9 LEEWAY ANGLES AND 20 DEGREES OF HEEL; EXPERIMENTAL DATA

REPRESENTED BY THE CONTINUOUS LINE AND NUMERICAL RESULTS BY CROSSES. ...................................... 38

FIGURE 39.LATERAL FORCE VALUES FOR 3,6AND 9DEGREES OF LEEWAY AND 20DEGREES OF HEEL; EXPERIMENTAL

DATA REPRESENTED BY THE CONTINUOUS LINE AND NUMERICAL RESULTS BY CROSSES. .............................. 39

FIGURE 40. PITCH ANGLE FOR 3, 6 AND 9 LEEWAY ANGLES AND 20 DEGREES OF HEEL; EXPERIMENTAL DATA

REPRESENTED BY THE CONTINUOUS LINE AND NUMERICAL RESULTS BY CROSSES (BOW DOWN POSITIVE). ....... 39

FIGURE 41.HEAVE FOR 3,6AND 9LEEWAY ANGLES AND 20DEGREES OF HEEL;EXPERIMENTAL DATA REPRESENTED BY

THE CONTINUOUS LINE AND NUMERICAL RESULTS BY CROSSES (DOWN POSITIVE). ..................................... 40

FIGURE 42.TOTAL RESISTANCE COMPARISON BETWEEN THE EXPERIMENTAL DSYHSRESULTS,ANSYS CFXNUMERICAL

RESULTS CALCULATED IN THE PRESENT STUDY AND THE NUMERICAL RESULTS OF FS-FLOW AND DSYHS

EMPIRICAL FORMULA PROVIDED IN [13](3DEGREES OF LEEWAY AND 10DEGREES OF HEEL). ................... 411

FIGURE 43. LATERAL FORCE COMPARISON BETWEEN THE EXPERIMENTAL DSYHS RESULTS,ANSYS CFX NUMERICAL


EMPIRICAL FORMULA PROVIDED IN [13](3DEGREES OF LEEWAY AND 10DEGREES OF HEEL). ..................... 41



EMPIRICAL FORMULA PROVIDED IN [13](3DEGREES OF LEEWAY AND 20DEGREES OF HEEL). ..................... 42FIGURE 45. LATERAL FORCE COMPARISON BETWEEN THE EXPERIMENTAL DSYHS RESULTS,ANSYS CFX NUMERICAL














EMPIRICAL FORMULA PROVIDED IN [13](6DEGREES OF LEEWAY AND 20DEG). ...................................... 44

FIGURE 50.TOP VIEW OF THE WAVES GENERATED BY THE UPRIGHT AND APPENDED HULL FOR FR=0.40........................... 46

FIGURE 51.TOP VIEW OF THE WAVES GENERATED BY THE APPENDED HULL WITH A LEEWAY OF 6DEGREES........................ 46

FIGURE 52.TOP VIEW OF THE WAVES GENERATED BY THE APPENDED HULL WITH A LEEWAY OF 6DEGREES AND A HEEL

ANGLE OF 20DEGREES FOR A FR=0.4 ............................................................................................. 47

FIGURE 53.HULL POSITION FOR FR=0.25 ........................................................................................................... 47




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FIGURE 61.WINDWARD VIEW OF THE KEEL INCLUDING THE WATER WALL SHEAR STREAMLINES FOR 20DEGREES OF HEEL

AND 6DEGREES OF LEEWAY. ......................................................................................................... 50

FIGURE 63.BACK VIEW OF THE HULL HEELED 20DEGREES AND YAWED 6DEGREES. ..................................................... 51

FIGURE 62.FRONT VIEW OF THE HULL HEELED 20DEGREES WITH 6DEGREES OF LEEWAY.............................................. 51

FIGUREA1.WIGLEY HULL................................................................................................................................. 56

FIGUREA2.COMPARISON OF CF FOR THE MODEL OF 2.5AND 3.048M. ......................................................... .......... 57

FIGUREA3.UNSTRUCTURED MESH WITH NO INFLATION LAYERS.......................................................... ..................... 60

FIGUREA4.FREE SURFACE GENERATED WITH THE UNSTRUCTURED MESH................................................................... 60

FIGUREA5.INFLATION LAYERS AND BLOCK AROUND THE HULL................................................................................. 60

FIGUREA6.CROSS AND LONGITUDINAL VIEW OF THE UNSTRUCTURED MESH............................................................... 61FIGUREA7.DISCONTINUITY OF THE WATER VOLUME FRACTION AT THE FREE SURFACE.................................................. 61

FIGUREA8.CROSS SECTION OF THE SELECTED UNSTRUCTURED MESH........................................................................ 62

FIGUREA9.WATER VOLUME FRACTION AT THE HULL SURFACE............................................................ ..................... 62

FIGUREA10.STRUCTURED MESH................................................................. ...................................................... 62

FIGUREA11.DIMENSIONLESS WAVE PROFILE ON THE HULL AT FR=0.25 .......................................................... .......... 64

FIGUREA12.ISOSURFACE WAVE PROFILE ON THE HULL AT FR=0.25(STRUCTURED MESH) ............................................ 64

FIGUREA13.DIMENSIONLESS WAVE PROFILE ON THE HULL AT FR=0.267.................................................................. 64





FIGUREA18.ISOSURFACE WAVE PROFILE ON THE HULL AT FR=0.408(UNSTRUCTURED MESH) ...................................... 66

FIGUREA19.EXPERIMENTAL AND NUMERICAL RESISTANCE COEFFICIENTS.................................................................. 67

List of tables

TABLE 1.SYSSER 62MAIN DIMENSIONS......................................................... ....................................................... 3

TABLE 2.MESHES GENERATED FOR THE DIFFERENT CASES.......................................................................................... 9

TABLE 3.MESHES USED FOR THE MESH REFINEMENT STUDY,FR=0.45...................................................................... 11TABLE 4.RICHARDSON EXTRAPOLATION PARAMETERS............................................................................................ 12

TABLE 5.DENSITY AND KINEMATIC VISCOSITY OF THE WATER FOR THE SIMULATIONS.................................................... 23

TABLE 6.APPENDAGES AND CANOE BODY CHARACTERISTICS............................................................... ..................... 27


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Notation list

B Beam

D Depth

CAD Computer Aided-DesignCEL CFX expression languageCf Friction resistance coefficient

CFD Computational Fluid DynamicsCFX Ansys CFD module

CPU Central Processing UnitCt Total resistance coefficient

Cv Viscous resistance coefficient

Cw Wave resistance coefficient

DSYHS Delft Systematic Yacht Hull SeriesFr Froude number

ICEM Mesh generation softwareIGES Initial Graphics Exchange SpecificationIHI Ishikawajima-Harima Heavy Industries Co. Ltd.

IOR International Offshore RuleITTC International Towing Tank Conference

L Length

LCG Longitudinal position of the Centre of Gravity

RAM Random Access MemoryRe Reynolds number

RMS Root Mean Square Values

SRI Ship Research Institute

SST Shear Stress Transport turbulence model

SYSSER 62 Systematic Series, model 62UT University of Tokyo

VOF Volume of fluidVPP Velocity Prediction Program

YNU Yokohama National University


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Jos Luis Ortn-Montesinos 1

1. Introduction

The hydrodynamic modelling of hulls using RANSE codes has becoming increasingly

used in recent years, reducing the time need for access to towing tanks that was

common practice for many naval architectural offices. Nowadays it may just be used to

validate the numerical simulations.

The simulation of the hydrodynamic problem of hulls implies the simulation of two

different fluids and therefore it is necessary to correctly model the free surface. In this

regard, the most common approaches of modelling free surface problems can be

classified as interface-tracking methods or Lagrangian methods and interface-capturing

or Eularian methods. The former have the advantage that the interface is specifically

delineated and precisely followed and the disadvantage of suffering instability and

internal inaccuracy. In the latter, the fluid travels between cells in fixed mesh and

adaptive grid techniques can be used. The volume of fluid method is integrated in this

interface capturing technique and it has been selected in the present study.

The very well-known DSYHS were developed at Delft University of Technology,

generating seventy different models and forty publications over 39 years. The series

were started by Gerritsma, in cooperation with Newman and Kerwin at the

Massachusetts Institute of Technology (MIT) and it is one the major public investigation

of yachts. Since 2010 all the generated data has been made public, allowing the

possibility to be used for further investigations and validations worldwide. The series

began back in 1973 and it has been a reference to predict yachts resistance since then.Hull shapes during all this time have changed radically, going from the IOR forms of the

eighties and nineties to a wider, lighter and faster hulls of the present day; being

normally out of the boundary of the formulas developed from these series. Nonethelessit is very useful for CFD validation projects, where the methods developed can be

extrapolated to the actual shapes; hence its interest and relevance for these type of

projects.


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2. Methodology

In order to explain the development process it is necessary to explain not just the

numerical but also the experimental methodologies, both are linked and its

comprehension is basic to achieve good agreement in the numerical results.

2.1 Experimental

When comparing numerical simulations with experimental data it is important to

understand how the experimental setting up was done in order to repeat it as close as

possible to achieve good results. Needless to say that even with the most precise code if

the experimental setting up has not been taken into account precisely the simulated

results are going to be different than the experimental ones. In this regard the data

provided by Delft University of Technology contain not just the experimental results but

also a manual describing the main aspects of the experimental setting up.

Along the years the DSYHS was developed as a way to investigate and research the most

common shapes in sailing yachts, generating a systematic series able to predict the

hydrodynamic performance of similar hulls. The models were tested in the towing tank

of the Delft Ship-hydrodynamics Laboratory, having a total length of 145 m, width of 4.5

m and a depth of 2.5 m

The model was linked to the carriage with two balance arms at even positions from the

centre of gravity, designed to avoid adding any extra forces or moments to the model

caused by its weight and restraining it in sway and yaw motions. The model was towed

from the carriage with a towing line attached at one end to the pivot point near the bow

of the model, at deck level, and at the other end to the carriage where the force wasmeasured with a force transducer. The attachment system is represented in figure 1,

taken from the experimental description [1].

Figure 1. Experimental setup of the DSYHS, from [1]


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Where:

- 1 and 2 are the balance arms fore and aft

-

3 is a shifting weight on deck to adjust pitch and roll angles

- 4 is the force transducer mounted to the carriage to measure resistance

-

5 and 6 are force transducers to measure the fore and aft side forces, with pivotpoints mounted underneath.

- 7 and 8 are the pivot points of the balance arm fore.

The model was tested for Froude numbers from 0.1 up to 0.6, generating Reynolds

numbers from to . The upright resistance tests were carried out twice,using one stimulation strip and double stimulation strips in order to ensure that the

boundary layer of the model was turbulent.

The main dimensions of the model are:

Loa 2.431 m

Lpp 2.078 m

Lwl 2.078 m

Bmax 0.656 m

Bwl 0.506 m

Tc 0.107 m

Volc 0.041 m3

Table 1. Sysser 62 main dimensions.

The sequence of testing was kept the same for the different models tested over the

years. Firstly the upright resistance tests were carried out; being the longitudinal centre

of gravity equal to the longitudinal centre of buoyancy, without any trimming moment

applied and without any heel or leeway angles. The model was then towed to the

corresponding Froude number, obtaining the result as a time-average of the recorded

signal during the run. The process was repeated for the different speeds generating the

speed-resistance curve of the upright model with and without appendages. Secondly the

tests are repeated applying a trimming moment to account for the sails propulsive force

of the full scale yacht. This trimming moment was exerted by shifting longitudinally the

centre of gravity. Finally a series of tests are carried out for various heel and leeway

angles and for different speeds, always with appendages. Sailing trim correction and a

correction to account for the vertical forces of the sails is added by means of adding a

weight to the model, without exerting a heeling moment on it. These corrections are

deeply explained further in the project, in the considerations about the available data

(2.2.5.1).

The forces were measured with strain gauge force transducers and the motions with

potentiometers and spring-loaded strings. It was measured the relative displacement ofdifferent points of the model, from which the rotations could be derived.


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2.2 Numerical Modelling

The numerical modelling was performed using the CFD code Ansys CFX. An initial study

was made modelling the flow around a Wigley hull, in order to test meshing techniques

and simulation (Appendix A). Based on the findings of this study, the flow around theSysser 62 was modelled, with fixed pitch and heave, and then allowing the hull to heave

and pitch as it was done during the real towing tank testing as a second stage.

For the free to heave and pitch simulations, four series of cases were tested and

compared; upright without appendages, upright with appendages, yawed with

appendages and heeled and yawed with appendages for different heel and yaw angles.

Each series was run for a range of Froude numbers, giving a large data set for the

validation of the numerical model.

2.2.1 Overall approach

It can be found different publications about CFD modelling of hulls which are free to

heave and pitch. The approaches vary widely depending on the particular purpose of

each study. In this study, the considered method has consisted on applying the rigid

body solver available in Ansys CFX, along with mesh deformation aiming natural

equilibrium between the different forces acting over the hull as in the real case. The

general approach has consisted of placing the hull in the upright equilibrium and then

accelerates the fluid until a new static equilibrium is reached. Then the process is

repeated for different fixed velocities corresponding to each of the Froude numbers and

for each of the conditions considered.

2.2.2 Geometry and Computational Domain

The Sysser 62 geometry was downloaded from the Delft University website as an IGES

file, which allowed it to be easily imported into a CAD software package. The keel and

ruder geometries are also provided, together with their locations during the

experiments. A bare hull lines plan is shown below in figure 2.

It is important to have the correct draught and submerged volume, and this is possible

since the hydrostatic data is available from the Delft University website [2]. The model

was initially set without pitch, yaw or heel angle, with the centre of gravity located

longitudinally at the same position as the centre of buoyancy. This is not important for

the fixed condition but it is essential for the free model simulations since it will affect the

final pitch and resistance.


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Figure 2. Sysser 62 linesplan.

The location of the appendages is given specified in the DSYHS database and manual [1]

and [2], and their position for the Sysser 62 hull is shown in figure 3.

Figure 3. Horizontal position of the appendages (distances in mm).

Whilst the longitudinal position of the appendages was provided, their vertical positions

were not. The positions were estimated by moving them vertically until their wetted

surface areas matched those specified in the hydrostatic data sheet provided by Delft

University of Technology.

The final geometry was imported as an IGES file into Ansys design modeller. The choice

of the domain geometry in design modeller must account for the meshing process and

the interaction that the size can have in terms of blockage of the fluid. The best meshing

procedure required the domain to be divided into two sub domains, allowing the

generation of inflation layers around the free surface which accurately captured the

waves generated by the hull. The size of the domain size is also important; it will

determine the total mesh size and therefore the number of nodes, having a direct impact

in the total computational time. It has to be big enough to avoid blockage problems and

small enough to avoid excessive computational time therefore a balance must be found.

Perez et al [3] verified and validated the effects that grids, domain sizes and turbulencemodels had in the resistance and wave profiles of a Wigley hull for six different Froude


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numbers. They found that the domain size had different effects in the resistance

depending on the turbulence model used, showing that accurate data can be obtained

even for a small lengths between the stern and the outlet. For the Shear Stress Transport

(SST) turbulence model it was found that a domain of 1.2 L downstream, 0.5 L upstream,

width of L and a depth of L/2+T gave good results. In the current study, slightly largerdimensions were used for the Wigley model (Appendix A), achieving a good agreement

with the experimental data.For the Sysser 62 similar domain dimensions to the Wigley

model have been used. The domain dimensions were 0.75L upstream, 2L downstream,

2L width, 0.40L deep and 0.25L high, as shown below in figure 4.

Figure 4. Dimensions of the computational domain for the Sysser62 hull, heeled and yawed.

For the upright cases with zero yaw the domain was split down the centreline of the

hull, taking advantage of symmetry to half the computational domain and the

computational effort.

For the free to heave and pitch cases it was important to have space between the deck

and the top boundary to allow free movement of the hull. In the fixed case this boundary

can be adjusted to the deck, saving nodes and computational time.

2.2.3 Mesh generation

Good mesh generation is critical to achieving good results in CFD simulations. The mesh

must be fine enough near the hull in order to resolve the boundary layer as well as

around the free surface to model it properly; this is essential to accurately predict the

resistance.

In this project it was decided to generate an unstructured mesh in order to simplify the

meshing process for appendages and irregular surfaces. A fuller study of different

meshing creation is summarized in Appendix A, where a comparison between

structured and unstructured approaches was performed. Here we will restrict ourselves


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to discussing the meshing procedure that was found to be the most successful in the

previous study.

In the mesh generation process it is important to differentiate the fixed and dynamic

cases. For the fixed test the objective is to generate enough inflation layers around the

hull to correctly simulate the turbulent boundary layer and around the free surface todevelop with enough precision the wave pattern generated by the hull. In order to

achieve that it is very important to get a smooth transition between free surface and the

hull surface, which is easy for curved surfaces like the sides of the hull, but more difficult

for the bow and transom where the angle between the free surface and the hull can be

close to ninety degrees. In the dynamic test it is important to have these considerations

into account but it is also necessary to consider that the bow is going to rise whereas the

transom is going to sink considerably for high Froude numbers. To this regard it is

necessary to create a different mesh around the bow and stern which also will help to

reduce the overall number of nodes and elements.

Details about the mesh around bow and stern are shown in figure 5 for the free cases;

the union between the two different domains is adjusted to the transom not to the free

surface, allowing good geometrical adjustment of the inflation layers at the stern. The

free surface lies below than the boundary between the two domains and therefore this

technique requires sufficient inflation layers around the free surface.

Figure 5. Mesh details of the bare hull (longitudinal view).

The transversal section is affected in a positive way by this elevation of the two domainslimit; the inflation layers around the hull are a bit higher, allowing enough nodes for the

inflation layer not only in the submerged body but also at the parts that are dry at the

start of the simulation but will be submerged at the end.


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Figure 6. Transversal view of the deformed mesh and wave generated for the bare hull, upright case, Fr=0.40, (left) and

appended, heeled 10 degrees and yawed 6 degrees, Fr=0.40 (right).

Figure 7 shows the deformed mesh where it can be seen how near the hull the inflation

layers do not suffer deformation.

The set-up has been done in a way that the mesh keep practically constant near the hull,allowing more freedom on the rest parts of the domain, this is important in order to

keep constant the number of nodes where the boundary layer has to be resolved.

Figure 7. Details of the deformed mesh and free surface at bow and stern.

For the appended case the same parameters were used as for the bare hull and no extra

time was needed to generate a different mesh:


17/75



Figure 8. Longitudinal view of the mesh generated for the appended case.

The same sets of variables were applied for the cases with leeway and heel, obtaining

very similar meshes. The number of elements and nodes vary from the upright cases

because these can be simulated by applying symmetry whereas for the cases with

leeway and heel the whole model must be meshed since the flow is no longer symmetric.

New meshes were generated for the different heel and leeway angles, requiring around

15 minutes to generate each of them. The number of nodes for each mesh is summarised

in table 2.

Nodes Elements

Bare Hull 706144 1925421

Appended upright 733659 2015536

Appended upright 3 deg leeway 1139655 3460465



Appended 10 deg heel 3 deg leeway 1108910 3242845

Appended 10 deg heel 6 deg leeway 943885 2546956Appended 10 deg heel 9 deg leeway 1113355 2905784




Table 2. Meshes generated for the different cases.

It can be seen how with the selected domain and meshing method a good quality mesh

can be generated without an excessive number of nodes. It can be seen in table 2 how for

the 10 degrees of heel and 6 degrees of leeway there is a discernible lower quantity of

points; this was noticed when comparing the numerical results and after investigating


18/75



the mesh it was noticed that the surface mesh selection did not include one of the top

lateral surfaces of the hull, nonetheless the variation in the results was not significant.

A way of measuring the mesh quality is with the orthogonality property, which

quantifies how close adjacent element faces and edges are to 60 degrees in tetrahedral

elements; large deviations from 60 degrees may adversely affect accuracy androbustness. Values above 20 degrees are recommended in the Ansys CFX manual [4].

Figure 9. Mesh orthogonality angle (20 degrees of heel and 6 degrees of leeway).

Figure 9 shows the mesh orthogonality angle for the heeled hull with leeway case. It can

be seen how the submerged part is mostly around 80 degrees, ensuring a good mesh

quality and therefore a good estimation of the forces acting on the hull. The green line

indicating elements of 40 degrees are placed where the two domains are joined, above

the free surface level.

The computational time is directly proportional to the number of nodes. Half of the

domain is required for the upright cases due to the symmetry of the problem, however

for the cases with heel and leeway the symmetry condition is no longer valid and higher

quantity of nodes is required.

2.2.3.1 Mesh convergence study

The mesh convergence study has been performed by keeping certain mesh parameters

constant and refining others. In a structured mesh the general step to do a mesh

refinement is to reduce equally the mesh size, however with an unstructured mesh this

is an issue due to its irregular nature. The mesh refinement study was made for the first

simulations with the bare hull geometry in order to validate the mesh before attempting

the appendage hull with heel and leeway.


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The mesh refinement was made by reducing the mesh elements in both hull surface and

inflation layers. The inflation layers were defined by specifying the first layer thickness

and then the maximum layers with the growth rate, the way the refinement was made

was by keeping the same growth rate and reducing the first layer thickness to half of the

one used for the previous mesh. In CFD simulations the hull surface is normally definedwith mesh elements; this elements must be small enough in order to reproduce the

smooth surface of the real model. However when more inflation layers are placed

around the hull surface, the boundary layer might capture this artificial roughness giving

an increase in the viscous resistance; therefore the elements defining the hull surface

must be refined as well. The mesh size at the hull surface was specified by using the face

sizing selection available in the Ansys meshing tool. For each of the refinements the hull

surface mesh size was reduced too in order to avoid this artificial roughness.

Figure 10. Convergence study at Fr=0.45

Figure 10 shows the resistance values obtained with three different meshes. It can be

seen how the more nodes are placed around the hull the best results are achieved;

approaching the experimental result.

Table 3 presents the number of nodes, the resistance and the relative error for each of

the meshes used in the refinement study.

Coarse Medium Fine

Nodes 706144 1110727 1453646

(1/N)1/3

4.72047E-07 3E-07 2.29308E-07

Resistance 20.870 20.838 20.420

Relative error % -3.127 -2.969 -0.904Table 3. Meshes used for the mesh refinement study, Fr=0.45

19.20

19.40

19.60

19.80

20.00

20.20

20.40

20.60

20.80

21.00

0.0E+00 1.0E-07 2.0E-07 3.0E-07 4.0E-07 5.0E-07

Numerical

Experimental

(1/N)1/3

Resistance(N)

Fn=0


20/75



The Richardson extrapolation has been used to calculate discretization error and the

Roache and Celik error estimation for calculating the grid convergence index (GCI), both

methods detailed in [5].

Table 4 show the results of the extrapolation and convergence index study, showing a

numerical uncertainty solution of 1.4 %.

Volume of the domain (m^3) 35.857

Resistance value for the fines mesh f1 20.420

Resistance value for the medium mesh f2 20.838

Resistance value for the normal mesh f3 20.870

e21=f2-f1 4.18E-01

e32

= f3-f

1 3.20E-02

Number of nodes N1(Finer mesh) 1453646

Number of nodes N2(medium mesh) 1110727

Number of nodes N3(Normal mesh) 706144

Representative mesh size h1= [V/N1]1/3

8.22E-06


1.08E-05


1.69E-05

Grid refinement factor r21 1.309

Grid refinement factor r32 1.573

Apparent order p 5.673

Extrapolated value of the resistance f21extrap 20.136

Grid convergence index CGI1 0.145

Grid convergence index CGI2 0.668

Approximate relative error % 2.047

Extrapolated relative error % 1.408

Table 4. Richardson extrapolation parameters


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2.2.3.2 Artificial ventilation

A common problem identified by a number of authors [6] [7] is the artificial ventilation,

where air is entrained below the waterline, reducing the shear forces over the wetted

surfaces and therefore reducing the viscous resistance. This problem was initially

encountered for Froude numbers greater than 0.35. However, means for overcoming theproblem were found through careful mesh generation, and the correct selection of the

solver options.

The mesh morphology developed to avoid artificial ventilation begins with mesh

refinement at the hull surface; it was noted that the cells used to define the hull surface

had to be small enough in both tangentially and perpendicularly directions in order to

avoid the first evidences of air entrainment; this was measure by keeping the Yplus

values around 50 for Froude numbers around 0.4.

After reducing the mesh size at the hull surface it was noticed that the air entrainmentwas initiated at the transom, where the hull surface is normal to the free surface. Figure

11 compares a coarse mesh with the air entrainment issue and then a finer mesh that

avoids it. Different methods were attempted to reduce this artificial air entrainment,

however it was eliminated by reducing the size of the elements that define the edge

where the transom join the bottom of the hull. This was done using the edge sizing tool

implemented in the Ansys mesh module; defining the elements size to 3 mm. Figure 11

shows this refinement.

Figure 11. Detail of the mesh refinement and the air entrainment at the stern for Fr=0.35.

With small enough elements the air entrainment was eliminated and it was possible to

achieve a good agreement with the viscous resistance. Figure 12 shows a global view of

the water volume of fraction before and after the mesh refinement shown in figure 11.


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Figure 12. Air entrainment under the hull for a coarse mesh (above) and a fine mesh (below) for Fr=0.35.

The refinement of the edge was proven to be enough up to Froude number of 0.55,

further attempts showed that for higher speeds further refinements were needed in this

particular edge, eliminating completely the air entrainment after about 250 iterations.

Once the results were obtained for the new mesh, it was noted some additional air

entrainment when the model was tested for a Froude number of 0.6; the highest of the

experimental tests. Further mesh refinements would be necessary in order to avoid it;

nonetheless this requires running all the simulations again in order to have consistencyin the simulations. Being the problem identified and resolved it was decided to continue

with the same mesh parameters for the yawed and heeled cases where the highest

Froude number was 0.4; nonetheless this means that for Froude numbers in the range of

0.6 further mesh refinements are needed.

The entrainment was also reduced by the use of the mixture model to represent the

flow. With the mixture model even though at early iterations there was a considerable

amount of air entrainment, it was eliminated after around 250 iterations. The process of

elimination of entrained air is shown in Figure 13, for representative iterations in the

solution of flow about a yawed heeled hull. The combination of small mesh elementstogether with the mixture model was found to be the best means to avoiding air

entrainment.

Figure 13 shows the dynamic behaviour; during the first 100 iterations the bow rises

and then drops, trapping an inhomogeneous volume of fluid below the hull. This

oscillating behavior is damped until equilibrium is reached. It is also interesting to note

how the free surface on the upper part of each image (windward) is affected by the low

pressure generated by the appendages due to the leeway angle.


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Figure 13. Evolution of the air entrainment during the simulation of the Sysser 62 hull at Fr 0.40, with 10 degrees of heeland 9 degrees of leeway.


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2.2.4 Set-up and boundary conditions

The set-up of any CFD simulation is along with the mesh methodology the most

important points; a good study of them is essential to get good agreement with

experimental results.

2.2.4.1 Set-up

The model had to reach its own equilibrium, it is an inherent unsteady simulation and

therefore a transient simulation was selected. Nonetheless the final equilibrium has a

static behaviour; once the equilibrium is reached the final position and rotation of the

hull are constant.

In order to simulate the free movement it was used the rigid body solver available in

Ansys CFX. The body is defined by selecting its meshed faces; mesh motion is then used

to move the mesh around the selected faces in agreement with the rigid body equationsof motion. Ansys CFX allows up to 6 degrees of freedom, three rotations and three

motions, using equations of motion. This equations describe the physical behaviour of a

rigid body undergoing translation and rotation, in which the rate of change of linear and

angular momentum and , respectively, is equal to the applied force Fand torque m,acting on the body [4].

(2.1)

(2.2)

F represents the sum of all forces including aero/hydrodynamic, weight of the rigid

body, spring and/or explicit external force. Similarly m represents the total moment

from all the separate contributors. In these simulations no external force, apart from

gravity, has been applied allowing the equilibrium between the dynamic forces

produced by the water and the motion of the hull.

In the solver there were specified to update the body forces and moments every time

step adding coefficient loops to reach the equilibrium between the forces and the

motions. These coefficient loops update the position of the rigid body at the beginning ofeach coefficient loop within each time step, and gets to the next iteration either when the

applied forces/moments reach the equilibrium or when the maximum number of loops

are reached. It was selected a maximum of 10 coefficient loops for each time step.

Two different schemes are needed to solve the iterations of the linear and angular

momentum equations. Ansys CFX has implemented the Newmark integration scheme for

the linear momentum solver [8], resulting in a second order scheme with the

parameters applied in CFX, and two schemes for the rotational motions; a First Order

Backward Euler algorithm and a second order Simo Wong [9] time stepping algorithm.

The later was selected allowing an exactly conservation of energy and enforcing

conservation o total angular momentum [4].


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The degrees of freedom selected in the simulations were the translation about the z axis

(heave), and the rotation around the y axis (pitch), being fixed the different leeway and

heel angles.

Being the canoe body draft constant for all the simulations the submerged volume

changes from bare to appended hull situations, therefore the mass of the hull was variedaccordingly. It was also taken into account the weight added during the towing tank

sessions to account for the vertical force of the sails in the full scale yacht, varying it for

each heel and leeway angles accordingly to the experimental tests. This is very

important if a good agreement with the results has to be achieved and it will be further

discussed in the following sections.

It also had to be specified the mass moment of inertia of the body, this is important for

this kind of simulation where the body is free to move, nonetheless without waves or

external forces acting on the body this variables state just how fast or slow the semi

static state is going to be reached; without waves or external forces acting on the body,

the final pitch and heave are going to be governed by the dynamic forces generated by

the movement of the body, being constant for each Froude number. This fact allows

changing artificially these in order to get a faster simulation. It was noticed that for

lower moments if inertia the forces converged faster but they ended up being cyclic,

showing a less stiff body, however for higher moments of inertia the forces neededmore time to converge, reaching a more stable final state.

The mesh deformation is an important variable where there are rigid bodies moving in

the domain. For the simulation it was chosen the option Region of Motion Specified,which basically enables to select in each domain different mesh deformation options.

With this model the displacements applied on domain boundaries or in sub domains arediffused to other mesh points by solving the equation 2.3, [4]:

(2.3)Where is the displacement relative to the previous mesh location and is the meshstiffness, specifying how the different regions of nodes move together. This equation is

solved at the start of each iteration during the simulations. The way of how the mesh is

deformed is essential for a correct simulation, if the mesh deforms significantly in high

refinement regions then the boundary layer can be incorrectly resolved due to the

inhomogeneous distribution of the nodes around the surface. Another problem that canbe presented is when the mesh is folded due to the high mesh refinement in these

regions, resulting in a negative volume element and crashing the simulation. These

behaviours are basically defined by the mesh stiffness, which can be defined by different

options in Ansys CFX. In this case it was chosen to simulate it in a dynamic way, entering

the following equation as a CEL expression (CFX Expression Language):

(2.4)

In this equation (volume of finite volumes) is a predefined variable related tothe local mesh element volume. Being the stiffness inversely proportional to this


26/75



variable allows increasing the mesh stiffness for the smaller elements. This equation

keeps the mesh almost constant in the inflation layers, decreasing the possibility of

experience mesh folding and allowing the bigger elements outside of the sensitive areas

to absorb the rigid body movements. Pictures of the deformed mesh are shown in the

mesh generation section (2.2.3).

For the multiphase simulation it was chosen the homogeneous model. Here is important

to differentiate between fluid models and fluid pair models tabs in the setup

configuration. If a homogeneous model is selected in the fluid models tab then a

common flow field is shared by all the fluids, as well as other relevant fluids such as

temperature and turbulence. In a homogeneous model a free surface model appears as a

way of modelling the inter phase between both fluids. When these are continuous, the

fluid pair model allows additionally simulating the inter phase transfer between both

fluids by selecting the free surface or the mixture models. When the free surface model

is selected to model the inter phase transfer it resulted in the well-known problem of the

air entrainment. Nevertheless it is recommended to use the mixture model when this

problem appears [4], so this was the final option for all the simulations, with an interface

length scale of 1 mm. The evolution of the air entrainment when a mixture model is

selected was previously shown and discussed in section 2.2.3.2.

The flow past the model had a Reynolds number and and so wasconsidered turbulent. As such, the flow was modelled using the Reynolds Averaged

Navier-Stokes equations (RANS), using the SST two equation turbulence model. Ansys

CFX uses an automatic near-wall treatment for the SST model, which switches from the

use of wall functions to a low-Re wall formulation with the mesh refinement.

The boundary layer must be resolved in order to accurately predict the skin friction, andthis requires a fine mesh at the hulls surface. The fineness of the mesh near the surface

can be measured by the cells high, non-dimensionalised by the skin friction as a y+

value, defined as:

(2.5)

Where is the distance between the wall and the first grid points off the wall, is thewall shear stress, and

and

are the density and kinematic viscosity of the fluid

respectively. If the value of y+ is too large then the wall function will simulate the

boundary layer thicker than would normally be physically appropriate.


27/75



Figure 14. Y plus values and deformed free surface (water volume fraction of 0.5) for Fr=0.325 (above) and Fr=0.6

(below).

Figure 14 shows contours of y+ values for a hull at a Froude number of 0.325 (above)

and 0.6 (below). The y+ lies in the range 30 < y+ < 50 for Fr=0.325 and 50 < y+ < 80 for

Fr=0.6. Ansys manual suggests that y+ values above 1000 might be enough for modelling

large ships where the Reynolds number is on the order of 109, whereas for smaller

Reynolds numbers, y+ values of 300 might be enough to capture the entire boundary

layer [4]. At model scale however, the Sysser 62 model reaches Reynolds number in the

order of 106and therefore lower values must be expected. Azcueta [10], Viola [11], and

Wilcox [12], who investigated the effect of y+ on frictional resistance, achieved similar

y+ values to the ones shown in Figure 14. The values are also in the range of y+ values

used by Blake [6] and Nava [7] for modelling similar problems.

The Ansys CFX "High Resolution" scheme was used for the advection scheme to calculate

the advection terms in the discrete finite volumes. The solver calculates a transient

solution, using bounded Second Order Backward Euler time stepping as a transientscheme for momentum and volume fraction.

Tests were made to determine suitable the convergence criteria. Following the

recommendations of Blake [6] and Nava [7], a time step of 0.02 s was used, with a RMS

residual convergence target of 1E-06 and a maximum of 10 iterations per time step. The

simulations converged to RMS values around in the upright cases and in the heeled and yawed cases. The forces showed a different behaviour for different

Froude numbers, for low Froude numbers (0.1-0.3) the resistance showed an oscillating

behaviour after around 200 iterations whereas for high Froude numbers (0.5- 0.6) the

oscillation reduced significantly, being practically constant after 200 iterations (see

figures 16 and 17). For moderate Froude numbers the convergence behaviour was in

between the two extreme cases.


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Figure 15. RMS values of the upright simulation for Fr=0.50.

Figure 15 shows the convergence of the RMS values of the upright and appended case

for a Froude number of 0.5.

The variation of the resistance in the simulation follows the same trend than the RMS

values depending on the Froude numbers. Figure 15 shows the oscillating evolution of

the hull resistance for a Froude number of 0.25.

Figure 16. Drag force evolution for Fr=0.25, (upright, appended case).

In cases like the one shown in Figure 16, where it was not reached a steady value, the

average between the last maximum and minimum values was taken as the predicted

force. For higher Froude numbers the resistance remains constant after around 200

iterations, showing a less oscillation behaviour as it can be seen in Figure 17.

1.0E-07

1.0E-06

1.0E-05

1.0E-04

1.0E-03

1.0E-02

1.0E-01

1.0E+00

0 200 400 600 800 1000 1200 1400

RMS P-Vol

RMS U-Mom (Bulk)

RMS V-Mom (Bulk)

RMS W-Mom (Bulk)

Variablevalue

Accumulated Timestep

0

1

2

3

4

5

6

7

8

9

10

0 200 400 600 800 1000 1200 1400

Numerical

Experimental


Resistance(N)


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Figure 17. Drag force convergence for Fr=0.6. Upright and appended case.

The cases with heel and leeway also show this behaviour in both resistance and lift

forces. Reaching more damped values for medium Froude number values as it can be

seen in Figure 18.

Figure 18. Drag and side force convergence for Fr=0.4, 20 degrees of heel and 6 degrees of leeway.

In the advanced options tab of the solver it was chosen the initial volume fraction

smoothing option, with a volume-weighted smoothing for start-up robustness.

As any RANS simulation the computational time is an important factor to have into

account. The simulations were performed in the Yacht Research Unit Cluster, where

different points were calculated at the same time using parallel CPUs. The simulations

were carried out in Super Micro 827-14 models, having 12 cores and a CPU of Intel Xeon

X5650 2.67GHz .The computational time varied depending on different factors like the

number of mesh nodes and the type of simulation; thereby the shorter runs wereachieved for the fixed cases, with symmetry conditions and steady simulation type, and

0

10

20

30

40

50

60

70

80

0 200 400 600 800 1000 1200 1400

Numerical

Experimental


Resistance

(N)

-20

0

20

40

60

80

100

120

0 100 200 300 400 500 600 700 800 900 1000 1100

Drag Force (Numerical)

Drag Force (Experimental)

Side Force (Numerical)

Side Force (Experimental)

Force(N)



30/75



the longest were performed for the heeled and leeway cases where it was not possible to

apply symmetry conditions and where transient simulation time and rigid body solver

were used. The shorter time for the fixed cases was around 8 hours for each point. The

free to pitch and heave required around 40 hours in the upright cases and 90 hours for

the heeled and yawed simulations.

2.2.4.2 Boundaries

The boundary conditions are another important aspect of the simulation and must be

carefully chosen in order to achieve good results. The upstream boundary was defined

as an inlet, with a constant velocity and a volume fraction that varied with height, with a

sharp change in the volume fraction at the free surface. Turbulence was set as medium,meaning a turbulence intensity of 5%. The calculation was relatively insensitive to this

since the turbulent kinetic energy is largely dissipated by the time it reaches the hull

(see figure 19). There was not available turbulence data of the towing tank tests but itwas specified that the time between runs was around 15 minutes, allowing the free

surface to stabilise after each run; fairly low levels of turbulence are therefore expected.

Figure 19. Water turbulent kinetic energy of the heeled and yawed case over the free surface for Fr=0.35.

After some attempts and comparisons opening condition was proven to be more robust

for a wider range of velocities for the lateral walls, top boundaries and outlet; coinciding

with the observations noted by Blake [6] and Nava [7]. Within this condition the flow is

able to flow in and out of the domain, it avoids reflections on the walls and it is useful for

domains where a rigid object is going to move; this movement in and out of the flow is

expected due to the motion of the water and the interaction between the air and water

in the fluid region [4].


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The entrainment option was selected for the mass and momentum equations, and the

static pressure set to hydrostatic which varied with height for lateral and outlet

boundaries. For the cases where inflow occurs at these boundaries, a zero gradient

option was selected for turbulence scalars, and the volume fraction was set to that at the

inlet. The top surface was set as an opening, with both pressure and direction specified,

with the volume fraction being set to 1 for air. The bottom boundary was specified as afree slip wall and the hull was set as a smooth no-slip wall. For the mesh deformation,

only the hull was allowed to move, with all other boundaries being constrained to being

stationary.

The first iterations are the most sensitive to fail if the initial conditions are not well

defined. These initial conditions were the same as the ones used for the inlet; constant

velocity set to the corresponding Froude number, volume fraction defined with the step

function to define the free surface and the pressure set to hydrostatic type. This was

sufficient for the upright cases at low Froude numbers. For higher Froude numbers it

was necessary to use solutions from lower speed runs to initialise the solution. It is

recommended to use a fully converged simulation for the global initialization however it

was proven enough to import the solution generated just after around 10 iterations of a

lower Froude number. This improves considerably the robustness at the beginning of

the simulation, where it is more likely to fail.

For the domain it is important to correctly define the fluids properties; these are very

sensitive data that will have an important effect in the final resistance. The data

provided by the Delft University of Technology contained the density and viscosity of the

water for the different tests so it could be reproduced on the CFD simulations. One can

image that this data is hardly to be constant for a whole range of Froude numbers,

moreover having into account that the tests were carried out twice, with two differentturbulence stripe configurations and waiting sometime between runs. The provided

water properties are different for bare and appended hull, being the same for the

appended cases; heeled, yawed and upright. These properties are shown in table 3.

T [C] [kg/m3] [m

2/s]

Bare Hull 17.7 998.947 1.07E-06

Appended 16 999.222 1.11E-06

Table 5. Density and kinematic viscosity of the water for the simulations


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2.2.5

Considerations about the available data

2.2.5.1 Longitudinal centre of gravity and Displacement

The free condition implies that the model is free to heave and pitch, therefore the massand centre of gravity must be determined in order to correctly reproduce the real

conditions. The data provided by Delft University of Technology has the possibility of

selecting both model and full scales and it also gives the possibility to get the data

corrected with a trim moment correction in order to simulate the full scale yacht

propulsive force acting on the sails. When the model is upright the data can be selected

with or without correction, nevertheless the correction is always applied when the

model is heeled, as well as a variation in the displacement due to the vertical force

induced by the sails (see figure 20). This is very important to note in the numerical

simulations since it will change quite significantly the resistance and behaviour of the

model in the free mode.

Another important fact is that the model is towed from the bow at deck level instead of

doing it from the inside of the hull; near the centre of gravity. This is a restrain that

affects slightly the completely free movement of the hull when is towed through the

towing tank; generating a small trimming moment that is basically the resistance force

times the distance between the towing point and the centre of gravity of the model. This

restrain is not significant at low Froude numbers however it does make a difference in

the pitch angle for higher Froude numbers.

Figure 20. Forces and distances considered during the DSYHS experimental tests.

Figure 20 shows the forces taken into account during the experimental set up; the

trimming moment correction is applied by shifting a weight longitudinally at deck level.

The vertical force is added as a means of a weight the longitudinal position H1, showed

in Figure 20; it varies for each of the Froude numbers as is shown in the provided data

[1]. In order to reproduce the towing tank conditions in the numerical simulations theoverall trimming moment introduced during the tests has to be taken into account.


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This is done by increasing the original longitudinal centre of gravity a distance that

corresponds to the trimming moment applied during the towing tank tests, , plus the moment generated by the vertical component and anadditional trimming moment generated by towing the model at the deck level

.

Formula 2.6 shows this increment.

(2.6)

is the distance between the towing point and the vertical centre of gravity; takenat waterline level during the experiments. is the model resistance and so it seemsquite obvious that an increase in resistance will generate also an increase in the

trimming moment and vice versa since both depends on each other. The towing tank

test must be repeated more than once to find a convergence point in order to know whatthe correct trimming moment is, nonetheless during the experimental tests the

resistance used to calculate this trimming moment was the upright resistance. The same

procedure has been followed during the numerical simulations to account for the

trimming moment generated by towing the model at deck level.

The global increase of the longitudinal centre of gravity has only been taken into account

for the heeled and yawed cases; however the quantity corresponding to towing the

model from the deck was tested for a few Froude numbers in the upright case to see how

this affected the resistance and the pitch angles. Figure 21 compares the experimental

pitch angle with the numerical convergence, with and without LCG correction.

Figure 21. Pitch angle convergence for both corrected and original LCG position, Fr=0.55.

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

0 200 400 600 800 1000 1200 1400

Numerical (original LCG)

Numerical (corrected LCG)

Experimental


Pitchangle(deg)


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It can be seen how the pitch angle is better predicted when the change of the centre of

gravity is applied. It also produces a small variation in the predicted resistance; it

increases from 6 % to 8 % the error with respect to the experimental data. This

difference in the final trim is also noticeable when comparing both cases in the final trimposition.

Figure 22. Final trim position reached by the model with LCG correction (above) and without LCG correction (below).

Figure 22 shows the final trim position reached by the model when applied the LCG

correction (above) and without applying it (below). It can be seen how the model with

the correction has a lower trim angle, increasing the wet surface and therefore

increasing the viscous resistance.

2.2.5.2 Appendages considerations

The hydrostatics provided by Delft University of Technology divide the values of the

appendages and hull volumes and set the draught of the canoe body so in order to

calculate the correct displacement these conditions must coincide. The appendages were

the same for all the models tested in Delft and therefore it is comprehensible that they

had to adjust the joint between hull and appendages [1]. Nonetheless, the volume and

wetted surfaces of the provided IGES files of the appendages do not coincide with thehydrostatics and so they had to be adjusted by introducing them slightly into the hull.


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During the experimental tests the process was different, they filled the gap between hull

and appendages, however due to the discrepancy between measured wetted surface and

the real surface of the appendage in the IGES files it was decided to adjust to the

measured values provided in the hydrostatics data sheet. The upper part of the

appendages is straight and therefore some part of them will be inside of the hull in order

to follow the curved shape of the bottom.

DescriptionExperimental Numerical

Wetted surface (m2) Volume (m

3) Wetted surface (m

2) Volume (m

3)

DSYHS Standard Keel 0.1539 0.002620 0.1586 0.002600

DSYHS Standard Rudder 0.0550 0.000230 0.0546 0.000229

Sysser 62 canoe body 0.8041 0.041339 0.8005 0.041110

Total 1.0130 0.044189 1.0137 0.043939

Error % -0.060 0.566

Table 6. Appendages and canoe body characteristics

It was iterated until the respective values of the submerged volume and wetted surface

were close enough to the experimental data. The description provided in the manual

about the appendages position was closely followed however it was not possible to get

closer to the experimental values, as it is shown in table 4. There seems to be some

inconsistency in the experimental data because when the wetted surfaces were exact the

volume suffered some deviation and vice versa. Due to this fact it had to be decided

which variable approximate more when placing the appendages. It was decided to get as

close as possible to the wetted measured area in order to accurately reproduce the

viscous resistance. The final deviations between the experimental and numerical data

are 0.06% for the wetted area and 0.57 % for the submerged volume.


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3. Results and Discussion

Presented in this section are the hydrodynamic resistance, heave and trim for the

upright cases, including the lateral forces for the cases where the leeway and heel are

integrated. The forces results have good agreement with the experimental data, havingan approximate relative error of 6 % for the resistance, and 1% for the lateral forces;

being fairly constant for all the simulations. However there is significant error in the

predictions of heave and trim in some cases.

Each of these cases is going to be showed and commented in the following sub sections;

where the presented results correspond to model scale of the Sysser 62.

3.1 Bare hull

Initial calculations were made of a bare hull both fixed and free to trim and heave. This

showed that the fixed geometry case gave good results up to a Froude number of 0.4.

Figure 23. Sysser 62 bare hull upright resistance for free case (green) and fixed case (red).

The variation of resistance with Froude number is shown in Figure 23. It can be seen

that the fixed geometry shows good agreement with experiment for Froude numbers up

to 0.4, where the dynamic forces are high enough to vary the vertical position and the

trim significantly. This is important due to the different computational times required

for this type of simulation; the fixed case was able to perform the run in about 8 hours

meanwhile the free case runs for the upright cases lasted for about 40 hours.

The heave has proven to be the hardest value to agree with the experimental results.

This is not strange when thinking about how this distance varies along the hull length.

During the DSYHS the heave displacement was the vertical displacement of the centre of

gravity; however this point is defined differently for the bare hull and the rest of the

cases. The initial vertical position of the centre of gravity was taken at the waterline, sothe measured heave was relative to this point. For the numerical simulations the initial

0

5

10

15

20

25

30

35

40

45

50

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

Experimental

Numerical fixed

Numerical free

Resistance[N]

Fr


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height of the centre of gravity was taken at the same height however the results differ

greatly from the ones shown in the experimental data sheet.

Figure 24. Experimental and numerical heave of the Sysser 62 bare hull, measured at the respective centres of gravity

(positive down)

Figure 24 compares both experimental and numerical heave at the centre of gravity; it

can clearly be seen the difference between both. It has been hard to find a reason for this

divergence; the resistance and the pitch angles coincide relatively well with the

experimental results and therefore this difference seems to be due to a different

measured position of the initial centre of gravity. The obtained numerical results are

similar to the same case with appendages shown in Figure 28; where both experimental

and numerical results have the same type of slope than the numerical results shown inFigure 24.

Unlike the heave motion, the pitch angle of the hull is going to be the same; regardless of

where it is measured and therefore a good agreement is more representative of the

quality achieved by the simulation.

Figure 25. Experimental and numerical pitch angles of the Sysser 62 bare hull (bow up positive).

-5

0

5

10

15

20

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

Heave (experimental)

Heave (numerical)

Heave(mm)

Fr

-0.5

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70

Pitch (experimental)

Pitch (numerical)

Pitchangle(deg)


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Figure 25 shows the numerical and experimental pitch angles. It can be seen how the

points follow the same trend, increasing after Froude number of 0.40, where the hull

enters the pre-planing zone. The biggest differences are obtained for the higher Froude

numbers. This may be a consequence of adding an artificial restrain when towing it at

deck level as it was explained in section 2.2.5.1 where a deeper investigation is done to

this regard. The longitudinal position of the centre of gravity was not corrected to havethis factor into account and therefore this difference was expected. A comparison of the

different behaviours of the numerical simulations with and without this LCG shift is

hydrodynamic_modelling_of_hulls_using_ranse_codes.ortin-montesinos_2015_mye.pdf

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