Self-Propulsion CFD calculations · 2018-11-23 · Self-propulsion CFD calculations using the...

Self-propulsion CFD calculations using theContinental Method

Thales Augusto Damasceno MachadoMaster Thesis

Presented in partial fulfillment

of the requirements for the double degree:

“Advanced Master in Naval Architecture” conferred by University of Liege

”Master of Sciences in Applied Mechanics, specialization in Hydrodynamics,

Energetics and Propulsion” conferred by Ecole Centrale de Nantes

developed at University of Rostock

in the framework of the

“EMSHIP”

Erasmus Mundus Master Coursein “Integrated Advanced Ship Design”

EMJMD 159652 – Grant Agreement 2015-1687

Supervisor: Dr.-Ing. Nikolai Kornev, University of Rostock

Reviewer: Prof. Florin Pacuraru, University of Galati

January 15, 2018

Self-propulsion CFD calculations using the Continental Method I

DECLARATION OF AUTHORSHIP

I, Thales Augusto Damasceno Machado declare that this thesis and the work pre-

sented in it are my own and has been generated by me as the result of my own original

research.

Self-propulsion CFD calculations using the Continental Method .

I confirm that:

1. This work was done wholly or mainly while in candidature for a research degree

at this University;

2. Where any part of this thesis has previously been submitted for a degree or

any other qualification at this University or any other institution, this has been clearly

stated;

3. Where I have consulted the published work of others, this is always clearly

attributed;

4. Where I have quoted from the work of others, the source is always given. With

the exception of such quotations, this thesis is entirely my own work;

5. I have acknowledged all main sources of help;

6. Where the thesis is based on work done by myself jointly with others, I have

made clear exactly what was done by others and what I have contributed myself;

7. None of this work has been published before submission.

8. I cede copyright of the thesis in favour of the University of Rostock.

Signed:

Date:

”EMSHIP” Erasmus Mundus Master Course, period of study September 2016 - February 2018

II Thales Augusto Damasceno Machado

Master Thesis developed at University of Rostock

Self-propulsion CFD calculations using the Continental Method III

Contents

1 Introduction 1

2 Literature Review 4

2.1 British Method - Experimental Approach . . . . . . . . . . . . . . . . . . 4

2.2 Continental Method - Experimental Approach . . . . . . . . . . . . . . . 5

2.2.1 Skin-friction correction- Introducing the deduction force (FD) . 5

2.3 Comparison - British x Continental method . . . . . . . . . . . . . . . . 7

2.4 CFD Research . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

2.5 Reynolds Averaged Navier-Stokes Equations (RANSE) . . . . . . . . . . 12

2.6 Turbulence models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

2.6.1 k-ω Wilcox model . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

2.6.2 k-ω -The Base Line Model (BSL) . . . . . . . . . . . . . . . . . . . 15

2.6.3 k-ω Shear Stress Transport (SST) . . . . . . . . . . . . . . . . . . 17

2.7 Numerical Discretization of the Governing Equations . . . . . . . . . . 17

2.7.1 Finite Volume Method . . . . . . . . . . . . . . . . . . . . . . . . 17

2.7.2 Shape Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

2.7.3 Control Volume Gradients . . . . . . . . . . . . . . . . . . . . . . 21

2.7.4 Advection Term . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

3 Description of CFD model 23

3.1 Hull Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

3.2 Propeller Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

3.3 Domain Creation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

3.3.1 Ship Domain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

3.3.2 Propeller Domain . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

3.3.3 Interface Domain Modelling . . . . . . . . . . . . . . . . . . . . . 27

3.4 Boundary Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

3.5 Mesh Generation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

3.6 Mesh Quality Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

3.6.1 Skewness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

3.6.2 Orthogonal Quality . . . . . . . . . . . . . . . . . . . . . . . . . . 32

3.7 Mesh Characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

4 Description of Speed Controller 35

4.1 Background Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

4.2 Proposed Controller . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

4.3 JcbInitControl.F . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

4.4 UserSetAVOmega.F . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41


IV Thales Augusto Damasceno Machado

4.5 UserSetOmega.F . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

5 Body of Revolution - Convergence Study 435.1 Geometry and Mesh Characteristics . . . . . . . . . . . . . . . . . . . . . 43

5.2 Runs definition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

5.2.1 Convergence Criteria . . . . . . . . . . . . . . . . . . . . . . . . . 48

5.3 Self-Propulsion of Body of Revolution . . . . . . . . . . . . . . . . . . . 49

5.4 RUNS Post-Processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

5.5 Finding Optimum setup . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

6 KVLCC 2 - British Method 556.1 Post-Processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

7 KVLCC2 - Continental Method 587.1 Determining Initial Setup for the Controller . . . . . . . . . . . . . . . . 58

7.2 Continental Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

8 Results 638.1 Post-Processing - Continental Setup . . . . . . . . . . . . . . . . . . . . . 63

8.2 Comparison - British x Continental x Model Basin . . . . . . . . . . . . 65

9 Conclusion 67


Self-propulsion CFD calculations using the Continental Method V

List of Figures

1 Components of ship powering - main considerations [1] . . . . . . . . . 1

2 Global Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

3 Test set-up for British method [9] . . . . . . . . . . . . . . . . . . . . . . 4

4 Test set-up for Continental method [3] . . . . . . . . . . . . . . . . . . . 5

5 Resistance curves for ship and model [12] . . . . . . . . . . . . . . . . . 6

6 Guidelines for the dimensions of studs and their location as turbulence

stimulators on a raked stem of conventional type [13] . . . . . . . . . . 7

7 Numerical methods for modelling propellers Adapted from [1] . . . . . 9

8 Blade element and momentum representations of propeller action [1] . 10

9 Propeller generation process for a surface panel code [1] . . . . . . . . 11

10 Control Volume Definition [15] . . . . . . . . . . . . . . . . . . . . . . . 18

11 Mesh Element [15] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

12 Tetrahedron Element [15] . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

13 Typical triangle mesh [19] . . . . . . . . . . . . . . . . . . . . . . . . . . 22

14 CFD Workflow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

15 Imported Surfaces - KVLCC2 . . . . . . . . . . . . . . . . . . . . . . . . 23

16 Propeller representation . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

17 Reflected hull - Double body approach [3] . . . . . . . . . . . . . . . . . 25

18 Ship Domain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

19 Propeller representation . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

20 Ship boundary conditions . . . . . . . . . . . . . . . . . . . . . . . . . . 28

21 Propeller boundary conditions . . . . . . . . . . . . . . . . . . . . . . . . 28

22 Cell types [22] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

23 Ideal and skewed triangle[21] . . . . . . . . . . . . . . . . . . . . . . . . 31

24 Vectors used to compute orthogonal quality of cell [21] . . . . . . . . . . 32

25 Rudder detail mesh . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

26 Ship detail mesh . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

27 Propeller detail mesh . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

28 The two-step approach to find the self-propulsion operating point [6] . 36

29 Diagram of ship + controller system [6] . . . . . . . . . . . . . . . . . . . 36

30 Time evolution of ε [6] . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

31 Time evolution of the propeller rotational speed: a) during the whole

computation and b) when the small time step is applied [6] . . . . . . . 37

32 Forces acting on KVLCC2 . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

33 User Function work-flow . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

34 Junction box routines possible locations [20] . . . . . . . . . . . . . . . . 40

35 Check condition for recalculation of rotational propeller speed . . . . . 42


VI Thales Augusto Damasceno Machado

36 Body of Revolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

37 Mesh of Body and Domain . . . . . . . . . . . . . . . . . . . . . . . . . . 44

38 Detail of Mesh . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

39 Propeller mesh . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

40 Detail of propeller mesh . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

41 Forces acting on the Body . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

42 Residuals (Diverged simulation) . . . . . . . . . . . . . . . . . . . . . . . 51

43 Relative Convergence Speed Variation . . . . . . . . . . . . . . . . . . . 54

44 RUN 1 - Forces and Torque for the last 216 time steps . . . . . . . . . . 56

45 RUN 1 - Torque for the last 216 time steps and Residuals . . . . . . . . 56

46 RUN 2 - Forces for the last 216 time steps . . . . . . . . . . . . . . . . . 56

47 RUN 2 - Torque for the last 216 time steps and Residuals . . . . . . . . 57

48 RUN 1: Post-Processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

49 RUN 1: Asymptotic behavior of forces and propeller rotational speed

nupdated . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

50 Continental Setup - Methodology . . . . . . . . . . . . . . . . . . . . . . 62

51 Continental RUN - PART I . . . . . . . . . . . . . . . . . . . . . . . . . . 63

52 Continental RUN - PART II - Fpropm and Qm . . . . . . . . . . . . . . . . 64

53 Continental RUN - PART II - Fxm [N] ; Asymptotic behavior of forces . . 64

54 Continental RUN - PART II - Propeller rotational speed nupdated ; DeltaF

normalized by Fxm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64

55 Zoom at DeltaF normalized - PART II . . . . . . . . . . . . . . . . . . . 65


Self-propulsion CFD calculations using the Continental Method VII

List of Tables

1 Main dimensions of the ship . . . . . . . . . . . . . . . . . . . . . . . . . 24

2 Propeller main characteristics . . . . . . . . . . . . . . . . . . . . . . . . 24

3 Domain dimensions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

4 Boundary Conditions - Ship . . . . . . . . . . . . . . . . . . . . . . . . . 29

5 Boundary Conditions - Propeller . . . . . . . . . . . . . . . . . . . . . . 29

6 Advantages and Disadvantages of cell types [22] . . . . . . . . . . . . . 30

7 Skewness quality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

8 Body of Revolution dimensions . . . . . . . . . . . . . . . . . . . . . . . 43

9 Parameters’ label . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

10 Factors’ label . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

11 Run definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

12 Self-propulsion RUNS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

13 Converged Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

14 Parameters’ entries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

15 Error % . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

16 Number of Iterations versus Error (ε) . . . . . . . . . . . . . . . . . . . . 53

17 Relative Convergence Speed . . . . . . . . . . . . . . . . . . . . . . . . . 53

18 Measured values from SVA mode-basin . . . . . . . . . . . . . . . . . . . 55

19 British simulation results . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

20 CFD and Model Basin comparison . . . . . . . . . . . . . . . . . . . . . 57

21 Runs Definition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

22 KVLCC2 - Converged simulations . . . . . . . . . . . . . . . . . . . . . . 61

23 Continental Method - Results . . . . . . . . . . . . . . . . . . . . . . . . 65

24 British x Model Basin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

25 Continental x Model Basin . . . . . . . . . . . . . . . . . . . . . . . . . . 66

26 British x Continental . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66

27 Computational Time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66

28 Accuracy x Computational time . . . . . . . . . . . . . . . . . . . . . . . 67


VIII Thales Augusto Damasceno Machado

Abstract

The growing need for high efficient propulsion systems allied to the demand for

accurate power predictions with lower costs, justify the usage of numerical simulations

by companies in order to achieve strategic advantages over their competitors.

There are two approaches which can be used to find the self-propulsion point of a

vessel, either experimentally or numerically, those are the load varying method, also

known as British method and the constant loading method, commonly called as Con-

tinental method.

The British method requires at least two runs for each speed to determine the self-

propulsion point, a run with an under-loaded propeller and one with an over-loaded

propeller, thereafter the propulsion point may be estimated.

Experimentally, the Continental method requires only one run to determine the

propulsion point for each speed, this is possible due to the presence of a RPM cor-

rector attached to the model which can adjust the propeller velocity during the run.

Numerically, this feature may bring advantage over the British method by reducing

computational time.

The main objective of this work is to propose and implement a suitable numerical

model to estimate the self-propulsion parameters of the KVLCC2 using the Continen-

tal method, ANSYS CFD Package will be used for analyses.

A RPM controller is firstly implemented on a simpler body and a convergence study

is performed in order to determine an initial setup for the KVLCC2. Self-propulsion

simulations are performed using the British and Continental methods, therefore com-

parison regarding accuracy and computational time between the two numerical meth-

ods are made. Finally, the report ends with conclusions and suggestions for further

investigations.

Key words: CFD, self-propulsion, continental-method, british-method, numerical

simulation.


Self-propulsion CFD calculations using the Continental Method IX


Self-propulsion CFD calculations using the Continental Method 1

1 Introduction

On the last few decades, environmental awareness has raised significantly all over

the world, when it comes to designing a ship, the propulsion system plays an important

role in order to comply with fuel consumption imposed by official regulators .

Therefore, estimating the parameters involved in propulsion efficiency is crucial,

one significant parameter to be estimated is the self-propulsion point of the ship,

meaning the point where the thrust provided by the propeller is able to overcome

the total resistance imposed by the ship and propels the vessel.

The three main components considered to establish the ship power comprise the

ship resistance to motion, the open water efficiency ant the hull-propeller interaction

efficiency and these are shown in Figure 1.

Figure 1: Components of ship powering - main considerations [1]

The self-propulsion analysis models as closely as possible the ship operating condi-

tion, i.e appendages are in place and the propeller is operating in a non-uniform flow

due to the model wake [2]. When full-scale prognosis are performed, both resistance

and open water test are required to evaluate the self-propulsion test.

• Resistance test: it aims to measure the model resistance, form factor and skin-

friction deduction force (FD);

• Open water test: it aims to measure the propeller characteristics by itself, consid-

ering uniform flow conditions, the output are η0, KT , KQ1 for different advanced

coefficients (J) ;

1η0 is open water efficiency, KT is thrust coefficient and KQ is torque coefficient


2 Thales Augusto Damasceno Machado

There are mainly two approaches which can be used to find the self-propulsion

point of a vessel, either experimentally or numerically, those are the load varying

method, also known as British method and the constant loading method, commonly

called as Continental method.

The British method requires at least two runs for calculating the self-propulsion

parameters for a single velocity, a run with an under-loaded propeller and one with an

over-loaded propeller, afterwards the propulsion parameters may be estimated.

The Continental method requires only one run to determine the propulsion point

for each speed, this is possible due to the presence of a RPM corrector attached to the

model which can adjust the propeller velocity during the run.

Experimental tests may be performed with the idea to extract information from a

model and then scale to real ships, however there is some empiricism required to use

this method, also these tests may be expensive and time-consuming.

Numerical approaches on the other hand have showed themselves as a good alter-

native on the design process. For ship resistance and powering, CFD has become es-

sential to the design process, since hull-propeller interaction, powering performance

and propulsion parameters are possible to be estimated [3].

Many authors [4], [5], [6], [7] have used CFD to investigate self-propulsion param-

eters of different vessels.

Master Thesis

Within this context, the present Master’s thesis focuses on developing a numerical

model to find the self-propulsion parameters (thrust, torque and propeller rotational

speed) by adding a RPM controller to the CFD setup considering the KVLCC2 in model

scale only. The main objective is to investigate the difference in accuracy and compu-

tational time between the British and Continental methods.

All numerical simulations will be performed with Ansys CFX Solver, Ansys Work-

bench will be used for pre-processing. Fortran subroutines will be used to change the

rotational propeller velocity.

Firstly, a convergence study will be performed with a simpler geometry (Body of

Revolution) in order to investigate the behaviour of the RPM controller, on this study, a

Perl script will be developed in order to run several simulations in sequence (BoRev.pl).

From the convergence study, a initial setup will be proposed for the KVLCC2. The



Continental Setup for the KVLCC2 will be divided in 2 parts. Part I will be running at

steady state with the RPM controller active for 2000 time steps, therefore the propeller

rotational speed (nm) will be estimated . Part II will run at unsteady state for 510 time

steps. The global methodology is presented on Figure 2.

Figure 2: Global Methodology



2 Literature Review

2.1 British Method - Experimental Approach

The International Towing Tank Conference describes in detail the steps to be fol-

lowed regarding model installation, measurement systems, calibration, test procedure,

analysis and validation related to propulsion tests, the setup for the British propulsion

test should follow the same guidelines [8].

In this towing test, the ship model is connected to the towing carriage through a

force transducer, normally called resistance dynamometer, which in this test measures

the force required to make the ship model move at a constant speed with the propeller

running [9].

Figure 3: Test set-up for British method [9]

The towing carriage should be accelerated from rest and simultaneously the pro-

peller rate of revolutions increased also from rest so that the estimated thrust is reached

as soon as possible after steady carriage speed is attained, the model should then be

released so that it is towed by the resistance dynamometer and running conditions al-

lowed to settle [10]. The input for the test are nm (propeller speed) and Vm (velocity),

during the test, the quantities of interest are measured:

• Tm (thrust);

• Qm (torque);

• Fx (carriage force).

It is also possible to record trim and sinkage if desired. The measurement of data starts

when the running conditions have settled. On this method, at least two values of nm,

consequently two runs should be performed for each value of Vm, one with an under-

loaded propeller and the other with an over-loaded propeller, thereafter the values of

Tm and Qm may be estimated by interpolation.



2.2 Continental Method - Experimental Approach

The set-up for this test is different than the one used for the British method. This

method introduces a tow force on the model (FD) which should be computed for each

run, and tuned such that it corresponds to the skin friction difference between model

and full scale [11].

The test starts with the model being accelerated simultaneously as the propeller

rate of revolutions are increased, when the model has reached the target speed, the

propulsion system should (together with the applied tow force) propel the model

freely at the same speed as the towing carriage. Measurements start when a steady

state is achieved [11]. Similarly as in the British test, the quantities of interest are

measured.

Figure 4: Test set-up for Continental method [3]

On this method, one value of nm, consequently one run is required for each value

of Vm, once the tow force is considered imposing the skin friction difference, thereafter

the values of Tm and Qm are directly obtained.

2.2.1 Skin-friction correction- Introducing the deduction force (FD)

While the propulsion test is performed, the speed of the towing tank carriage is

constant and the propeller speed varies until the equilibrium of forces is reached. The

Propulsion tests mentioned on Sections 2.1 and 2.2 follows ITTC recommendations

which is lead by Froude’s similarity, therefore the total resistance is composed by fric-

tional and residual components where the frictional coefficient follows the ITTC-57:

CF =0.075

(logRe − 2)2 (1)

There are two resistance components which can be separately calculated in order



to compute the total resistance. The viscous term which is calculated from the fric-

tional component, and the wave making or residuary term RW which is calculated by

subtracting the frictional component RF from the total resistance RT .

CV = (1 + k).CF (2)

CT = (1 + k).CF +CW (3)

Where the coefficients are: CV is the viscous, CF the frictional, CW the wave-making

and CT the total one. The form factor k is a constant which may be calculated from

experimental test or empirical formulas, ITTC procedures recommend the Prohaska

method for evaluation of the form factor [8] .

The resistance curves for model and ship present similar behaviour, although the

model curve is greater. This is due to the fact that Reynolds number is considerably

larger at full scale which leads into a decrease on CFs as shown by Equation 1, therefore

CT s is smaller than CTm2.

Figure 5: Resistance curves for ship and model [12]

Clearly, there is an over-estimation of the total resistance coefficient when consid-

ering the model-scale which can not be neglected, therefore the frictional deduction

force FD is introduced to counter-balance this difference.

FD =12ρ.V 2

m.Sm.((1 + k)(CFm −CFs)−CA −CAA) (4)

Then, the propeller should provide thrust to overcome not the model total resis-

tance, but the difference between the model resistance and deduction force (RTm−FD).

Where CA3 is the correlation allowance, its formula is recommended by the ITTC [8]

2 The subscript (s) stands for the full scale ship while (m) stands for model.3 This is the modified formula for CA which excludes roughness allowance.



as it follows:

CA = (5.68− 0.6logRe)x10−3 (5)

The air resistance coefficient CAA is calculated as it is shown:

CAA = 0.001ATS

(6)

Where AT is the frontal area of the ship above the waterline and S is the wetted

surface. During the self-propulsion test, some turbulence stimulation is achieved on

the model by gluing a sand strip or placing studs on the hull, these should be clearly

described in the model documentation.

Figure 6: Guidelines for the dimensions of studs and their location as turbulence stim-ulators on a raked stem of conventional type [13]

Finally, it is possible to conclude that the self-propulsion test is carried out to find

torque and thrust corresponding to the point where the force carriage equals the fric-

tion deduction force FD .

2.3 Comparison - British x Continental method

Both tests have their advantages and disadvantages. The British method requires

several load varied tests for each speed, which is more time-consuming than the Con-

tinental method, once this one needs only one run for each speed. Therefore, the con-

stant loading method is cheaper to perform, and this is the reason why the constant



loading method is the most used method nowadays [9].

Although it seems not attractive to use more time and money on performing the

British method, it also has an advantage over the Continental method when it comes

to using the results afterwards. As it has recordings for several loading conditions

at each speed, it is easy to re-scale the results to different scaling ratios and different

powering performance methods later [11].



2.4 CFD Research

There are different approaches when it comes to ship resistance and powering pre-

dictions, CFD has become increasingly and is considered one important part of the

design process.

Molland, Turnock & Hudson (2011) present a table that classifies several approaches

in increasing order of physical and temporal accuracy regarding to propeller mod-

elling (Figure 7). A simplified computational cost measure is included, this represents

an estimate of the relative cost of each technique normalised to the baseline blade

element-momentum theory (BEMT) which has a cost of one.

As can be seen, the hierarchy reflects the historical development, as well as the pro-

gressively more expensive computational cost as shown on Figure 7 [1]. The methods

are briefly explained on this section, and the selected method for this work (RANS) is

detailed on next section.

Figure 7: Numerical methods for modelling propellers Adapted from [1]



Blade Element-Momentum Theory

It can be understood as the combination of axial momentum theory and analysis of

blade element performance. Figure 8(a) shows that the blade element approach pro-

vides information on the action of the blade, however it does not show the momentum

changes (induced velocities a,a’), on the other hand, the momentum approach pre-

sented on Figure 8(b) provides information on the momentum changes (a,a’) but not

the action of the blade moment.

In order to solve that problem, both theories can be combined in a way that part of

the propeller between radius r and (r + δr) is analysed by matching forces generated

by the blade elements, as two-dimensional lifting foils, to the momentum changes

occurring in the fluid flowing through the propeller disc between these radii [1].

Although the analysis is straightforward, there are assumptions and associated er-

rors related to it. One assumption worth to mention is that there is no interaction

between the analyses of each blade element, and the forces exerted on the blade el-

ements by the flow stream are estimated only by the two-dimensional lift and drag

characteristics of the blade element airfoil shape. This assumption may be valid at

most places on the propeller, but it over predicts the lift near the propeller tips.This

method is still popular due to its low cost, however when accurate results are expected,

other techniques should be used.

(a) (b)

Figure 8: Blade element and momentum representations of propeller action [1]

Lifting-Line Theory

This theory was developed by Prandtl on the 20’s and it was first applied to aero-

nautics. Prandtl’s lifting line theory is a method used to describe the circulation at

different span-wise locations of the blade.

Differently from the Blade-Element Theory, in this method each blade section is

represented by a single-line vortex whose strength varies from section to section. This



theory has some limitations, it assumes inviscid flow, it assumes that there is no flow

separation as stated by Prandtl.

This approach is successful for high-aspect ratio blades more suited to aircraft. For

the low-aspect ratio blades widely used for marine propellers, this assumption is not

valid [1].

Panel-Method

Commonly called as surface panel method, this one requires a series of steps to

model the full surface geometry.

This method consists on processing a table of propeller characteristics sections such

as offsets, chord, pitch, rake, skew and thickness in order to generate a series of sec-

tions, each consisting of a set of Cartesian coordinate nodes as shown on Figure 9.

Figure 9: Propeller generation process for a surface panel code [1]

Differently from the previous discussed methods, this one allowed the full geome-

try of the propeller to be modelled, providing more information on the section flow.

Large Eddy Simulation (LES)

In order to investigate particular characteristics such as induced vibrations and

noise, RANS is limited once it is based on the average flow field. The operating envi-

ronment for the propeller is instantaneously very different from the average condition,



then, LES may be considered as a potential solution, once it can consider the full tran-

sient flow instantaneously.

Using LES, it is possible to study the time resolved quantities related to the flow,

their origin and their implications on operation of the propulsor system [14].

2.5 Reynolds Averaged Navier-Stokes Equations (RANSE)

When numerical simulation for ship and propeller is performed, the flow in many

cases is mainly turbulent because of the viscosity, therefore the RANS CFD approach

with a turbulence model is chosen for this work, once this one is able to capture the

necessary characteristics of the flow without spending as much computational time as

LES. The main aspects of the selected approach will be discussed on this Section.

The main reason why RANS equations are used, it is because the majority of the

industrial problems are in turbulent regime and it is not possible to perform direct

simulation of Navier-Stokes equations for complex cases, thus a Reynolds decomposi-

tion with a turbulence model is a possible solution.

The CFD codes will require the definition of surface geometry of the propeller and

hub, in addition a suitably mesh that will fulfill the solution domain should be created.

It is important to care about the quality of the mesh and whether it captures all the

necessary flow features, once this will determine the accuracy of the solution.

Ship flows are governed by the three conservation laws : mass, momentum and

energy. Normally referred to as the Navier–Stokes equations. The mass conservation

law, also known as the continuity equation states that the rate of change of mass in an

infinitesimally small control volume equals the rate of mass flux through its bounding

surface [1]. Being U = (u,v,w) and ρ is density.

∂ρ

∂t+∇.(ρU) = 0 (7)

The momentum equation states that the rate of change of momentum for the in-

finitesimally small control volume is equal to the rate at which momentum is entering

or leaving through the surface of the control volume, plus the sum of the forces acting

on the volume itself [1] .

∂(ρu)∂x

+∇. (ρuU ) = −∂p

∂x+∂τxx∂x

+∂τyx∂y

+∂τzx∂z

+ ρfx (8)

∂(ρv)∂x

+∇. (ρvU ) = −∂p

∂x+∂τxy∂x

+∂τyy∂y

+∂τzy∂z

+ρfy (9)



∂(ρw)∂x

+∇. (ρwU ) = −∂p

∂x+∂τxz∂x

+∂τyz∂y

+∂τzz∂z

+ρfz (10)

The energy equation states that the rate of change in internal energy in the control

volume is equal to the rate at which enthalpy is entering, plus work done on the control

volume by viscous stresses [1]. Where U2 = U.U, p is pressure, τij is viscous stress and

fi is body force.

∂∂x

[ρ(e+ U2

2

)]+∇.

[ρ(e+ U2

2

)U

]= ρq+ ∂

∂x

(k ∂T∂x

)+ ∂∂y

(k ∂T∂y

)+ ∂∂z

(k ∂T∂z

)−∂(up)

∂x −∂(vp)∂y −

∂(wp)∂z + ∂(uτxx)

∂x +∂(uτyx)∂y + ∂(uτzx)

∂z +∂(vτxy )∂x

+∂(vτyy )∂y +

∂(vτzy )∂z + ∂(wτxz)

∂x +∂(wτyz)∂y + ∂(wτzz)

∂z + ρf .V

(11)

In order to simplify the Equations (7), (8), (9), (10) and remove the need of solving

Equation (11), the flow may be assumed as incompressible. The Reynolds Averaging

process considers that a velocity may be represented as a fluctuating turbulent velocity

around a mean velocity. The mean velocity may be calculated as it follows.

U =1∆t

∫ t+∆t

tu (12)

Being u = U + u′, v = V + v′ and w = W +w′, the terms with a bar represent the

mean velocities and the ones with the quote, the fluctuating velocities, these may be

substituted on Equation (8), (9) and (10):

∂U∂t

+U(∂U∂x

+∂V∂x

+∂W∂x

)= −1

ρ∂P∂x

+ v(∂2U

∂x2 +∂2U

∂y2 +∂2U

∂z2

)−∂2u′

∂x2 +∂u′v′

∂x∂y+∂u′w′

∂x∂z

(13)

∂V∂t

+V(∂U∂y

+∂V∂y

+∂W∂y

)= −1

ρ∂P∂y

+ v(∂2V

∂x2 +∂2V

∂y2 +∂2V

∂z2

)− ∂2u′

∂x∂y+∂2v′

∂y2 +∂v′w′

∂y∂z

(14)

∂W∂t

+W(∂U∂z

+∂V∂z

+∂W∂z

)= −1

ρ∂P∂z

+v(∂2W

∂x2 +∂2W

∂y2 +∂2W

∂z2

)−∂u′w′∂x∂z

+∂v′w′

∂y∂z+∂2w′

∂z2

(15)

This averaging process introduces six new terms, the so-called Reynolds stresses,

on the Equations above, these are the terms with the quotes. These terms arise from

the nonlinear convective term in the un-averaged equations. They reflect the fact that

convective transport due to turbulent velocity fluctuations will act to enhance mixing

over and above that caused by thermal fluctuations at the molecular level [15] .

In order to close this system of equations a turbulence model has to be introduced

that can be used to represent the interaction between these Reynolds stresses and the



underlying mean flow [1].

2.6 Turbulence models

Turbulence may be interpreted as fluctuations in the flow field regarding time and

space. It is a complicated process, mainly because it is not only three dimensional,

but also unsteady and consists of many scales. It can have a significant effect on the

characteristics of the flow.

Turbulence occurs when the inertial forces in the fluid become significant com-

pared to viscous forces, and is characterized by a high Reynolds Number [15]. There

are many turbulence models, which are normally classified accordingly to the number

of transport equations that are resolved together with RANS. On this thesis the well

known two-equation Shear Stress Transport (SST) k-ω model is applied, therefore it

will be further discussed.

k-ω based models

These models are an adaptation of the k-εmodel, which has been largely used when

it comes to numerical modeling of propellers . The k-ω turbulence model represents a

group of two-equation turbulence models in which the transport equation are solved

for the turbulent kinetic energy k and its specific dissipation rate ω.

One of the advantages of the k-ω formulation is the near wall treatment for low-

Reynolds number computations. The model does not involve the complex nonlinear

damping functions required for the k-εmodel and is therefore more accurate and more

robust.

The k-ω different models assume the turbulence viscosity(µt) linked to the turbu-

lence kinetic energy (k) and turbulence frequency (ω) by the Equation below:

µt = ρkω

(16)

2.6.1 k-ω Wilcox model

The starting point to explain the model used by Ansys was developed by Wilcox

[16]. It solves the transport equations for turbulent kinetic energy (k) and turbulent

frequency (ω). Equation 17 (k − equation) and Equation 18 (ω − equation).

∂ρk

∂t+∂∂xj

(ρUj)k

)=

∂∂xj

[(µ+

µtσk

)∂k∂xj

]+ Pk − β

′ρkω+ Pkb (17)



∂ρω

∂t+∂∂xj

(ρUj)ω

)=

∂∂xj

[(µ+

µtσω

)∂ω∂xj

]+α

ωkPk − β

′ρω2 + Pωb (18)

Density and velocity vector U are treated as known quantities from the Navier-

Stokes method. The formulation for Pk is the same used by the k − ε model and it

represents the production rate of turbulence due to viscous forces, one is calculated as

it follows:

Pk = µt

(∂Ui∂xj

+∂Uj∂xi

)∂Ui∂xj− 2

3∂Uk∂xk

(3µt

∂Uk∂xk

+ ρk)

(19)

If the full buoyancy model is applied, the buoyancy production term (Pkb) is calcu-

lated as it follows:

Pkb = −µtρσρ

gi∂ρ

∂xi(20)

Where the turbulence Schmidt number σρ = 1. Finally the additional buoyancy

term for the ω based models Pωb may be read as :

Pωb =ωk

((α + 1)C3max(Pkb,0)− Pkb) (21)

Where the dissipation coefficient C3 = 1 . The constants 4 in the model are β′ = 0.09,

α = 59 , β = 0.075, σk = 2 and σω = 2.

The unknown Reynolds stress tensor, ρuiuj , is calculated as it follows.

− ρuiuj = µt

(∂Ui∂xj

+∂Uj∂xi

)− 2

3δij

(ρk +µt

∂Uk∂xk

)(22)

2.6.2 k-ω -The Base Line Model (BSL)

Menter [17] developed a model in order to overcome a problem arisen by the Wilcox

model. The main problem with the Wilcox model is its strong sensitivity to freestream

conditions [15]. The results of the numerical model may vary abruptly depending

on the value of value of the specific dissipation rate (ω) specified at inlet, in order to

trespass this problem, Menter [17] proposed a blending between the k-ε model in the

outer region and the k-ω developed by Wilcox near the surface.

The model per itself consists in transforming the k-ε model to a k-ω formulation

by the relation ε = β′ωk. Subsequently, the Wilcox model is multiplied by a blending

function (F1) and the transformed k-ε model by a function (1− F1), F1 is 1 near by the

4 For more information about the constants refer to [15]



surface and decreases to a value of zero outside the boundary layer (that is, a function

of the wall distance) [15].

F1 = tanh(arg41 ) (23)

With :

arg1 =min(max

( √k

β′ωy,500νy2ω

),

4ρkCDkωσω2y2

)(24)

Where y is the distance to the nearest wall, ν is the kinematic viscosity, σω2 =1

0.856and:

CDkω =max(2ρ

1σω2ω

∂k∂xj

∂ω∂xj

,1.0x10−10)

(25)

Therefore the transformed k-ε model reads:

∂ρk

∂t+∂∂xj

(ρUj)k

)=

∂∂xj

[(µ+

µtσk2

)∂k∂xj

]+ Pk − β

′ρkω (26)

∂ρω

∂t+∂∂xj

(ρUj)ω

)=

∂∂xj

[(µ+

µtσω2

)](2ρ

1σω2ω

∂k∂xj

∂ω∂xj

)+α2

ωkPk − β2ρω

2 (27)

Regarding the next step, the Equations 17 and 18 of the Wilcox model are multi-

plied by F1, the transformed k-ε Equations by (1 − F1) and the corresponding k− and

ω− equations are added to give the BSL model. Including buoyancy effects the BSL

model reads:

∂ρk

∂t+∂∂xj

(ρUjk

)=

∂∂xj

[(µ+

µtσk3

)∂k∂xj

]+ Pk − β

′ρkω+ Pkb (28)

∂ρω

∂t+∂∂xj

(ρUjω

)=

∂∂xj

[(µ+

µtσω3

)]+ (1 +F1)

(2ρ

1σω2ω

∂k∂xj

∂ω∂xj

)+α3

ωkPk −β3ρω

2 + Pωb

(29)

The coefficients of the new BSL model are a linear combination of the correspond-

ing coefficients of the underlying models:

φ3 = F1φ1 + (1−F1)φ2 (30)

Being β2 = 0.0828, α2 = 0.44, σk2 = 1 and σω2 = 1/0.856 . The BSL model com-

bines the advantages of the Wilcox and the k-ε model, however it still fails to correctly

predict the amount of flow separation from smooth surfaces, which is relevant regard-



ing propulsion simulation. This problem is discussed in detail by [17], but primarily

arises because these models overpredict the eddy-viscosity, once they do not take into

account the transport of the turbulent shear stress.

2.6.3 k-ω Shear Stress Transport (SST)

The k-ω based SST model overcomes the problem of BSL method, therefore it takes

the transport of the turbulent shear stress into account and gives highly accurate pre-

dictions of the onset and the amount of flow separation under adverse pressure gradi-

ents which is why this model was selected for this work. The problem may be solved

by considering a limiter to the formulation of the eddy-viscosity such as :

νt =a1k

max(a1ω,SF2)(31)

Where νt = µt/ρ, S is an invariant of the strain rate, F2 is a blending function which

restricts the limiter to the wall boundary layer.

The blending function F2 is calculated as:

F2 = tanh(arg22 ) (32)

Where:

arg2 =max(

2√k

β′ωy,500νy2ω

)(33)

2.7 Numerical Discretization of the Governing Equations

The three most frequent discretization methods (in the percent of the available

commercial CFD codes) are the finite difference (FDM) (' 2%), finite element (FEM)

(' 15%) and finite volume (FVM) (' 80%) methods [18]. This section aims to explain

the most relevant aspects of numerics used by Ansys CFX.

2.7.1 Finite Volume Method

Ansys CFX uses an element-based finite volume method, which first involves the

discretization of the spatial domain using a mesh, thereafter the mesh is used to con-

struct finite volumes, which are used to conserve relevant quantities such as mass, mo-

mentum, and energy. The mesh is three dimensional, but for simplicity this process

will be illustrated for two dimensions. The description of the control-volume(shaded-

area) is shown on Figure 10 .



All solution variables are stored at the nodes. In order to illustrate the finite volume

methodology, one consider the conservation equations for mass, momentum, and a

passive scalar (ϕ), expressed in Cartesian coordinates:

∂ρ

∂t+∂∂xj

(ρUj) = 0 (34)

∂∂t

(ρU i)+∂∂xj

(ρU jU i

)= −

∂p

∂xi+∂∂xj

(µef f

(∂U i

∂xj+∂U j

∂xi

))(35)

∂(ρϕ)∂t

+∂∂xj

(ρU jϕ

)=

∂∂xj

(Γef f

(∂ϕ

∂xj

))+Sϕ (36)

Figure 10: Control Volume Definition [15]

The equations then are integrated over each control-volume. Gauss’ Divergence

Theorem is applied in order to convert the volume integrals involving divergence and

gradient operators to surface integrals and the integrated equations become:

ddt

∫VρdV +

∫SρU j dnj = 0 (37)

ddt

∫VρU i dV (ρU i)dV+

∫VρU jU i dnj = −

∫Sp dnj+

∫Sµef f

(∂U i

∂xj+∂U j

∂xi

)dnj

∫VSUi dV

(38)

ddt

∫Vρϕ dV+

∫SρU jϕdnj =

∫SΓef f

(∂ϕ

∂xj

)dnj +

∫VSϕdV (39)

Where V and S respectively denote volume and surface regions of integration, and



dnj are the differential Cartesian components of the outward normal surface vector.

The volume integrals represent source or accumulation terms, and the surface inte-

grals represent the summation of the fluxes.

The next step in the numerical algorithm is to discretize the volume and surface

integrals. To illustrate this step, consider a single element like the one shown on Figure

11.

Volume integrals are discretized within each element sector and accumulated to

the control volume to which the sector belongs. Surface integrals are discretized at the

integration points (ipn) located at the center of each surface segment within an element

and then distributed to the adjacent control volumes. Due to the fact that the surface

integrals are equal and opposite for control volumes adjacent to the integration points,

the surface integrals are guaranteed to be locally conservative. After discretizing the

volume and surface integrals, the integral equations become:

Figure 11: Mesh Element [15]

V

(ρ − ρ◦

∆t

)+∑ip

mip = 0 (40)

V

(ρUi − ρ◦Ui◦

∆t

)+∑ip

mip(Ui)ip =∑ip

p(∆ni)ip +∑ip

(µef f

(∂U i

∂xj+∂U j

∂xi

)∆nj

)ip

+ SUiV

(41)

V

(ρϕ − ρ◦ϕ◦

∆t

)+∑ip

mipϕip =∑ip

(Γef f

∂ϕ

∂xj∆nj

)ip

+ SϕV (42)

Where (◦) is the superscript for the past time level, mip = (ρU j∆nj)ip, V is the

control volume, ∆t is the timestep, ∆nj is the discrete surface outward vector, the sub-

script (ip) denotes evaluation at an integration point, Sϕ and SUi stands for momentum

source terms, Γef f is the effective diffusivity, µef f is the effective viscosity, summations



are over all the integration points of the control volume. On this example, first order

backward scheme was assumed.

2.7.2 Shape Functions

As aforementioned, all the solution variables are stored at the nodes, nonetheless,

to evaluate many of the terms, the solution field or gradients should be approximated

at integration points, therefore finite element shape functions are used to perform

these approximations. A finite element shape function describes the variation of a

variable ϕ within an element as it follows:

ϕ =Nnode∑i=1

Niϕi (43)

Where Ni is the shape function for node i and ϕi is the value of ϕ at node i. The

summation is over all nodes of an element. Key properties of shape function include :

Nnode∑i=1

Ni = 1 (44)

At node j, Ni = 1 if i = j, or Ni = 0 if i , j.

The shape functions used in Ansys CFX are linear in terms of parametric coordi-

nates. They are used to calculate various geometric quantities as well, including (ip)

coordinates and surface area vectors. This is possible because Equation 43 also holds

for the coordinates:

y =Nnode∑i=1

Niyi (45)

As the mesh element chosen for this work is tetrahedron, the tri-linear shape func-

tions supported for the nodes are shown below.

Figure 12: Tetrahedron Element [15]



N1(s, t,u) = 1− s − t −uN2(s, t,u) = s

N3(s, t,u) = t

N4(s, t,u) = u

(46)

2.7.3 Control Volume Gradients

On situations where the gradients are required at the nodes, the Gauss’ divergence

theorem is applied to evaluate these gradients.

∇ϕ =1v

∑ip

ϕ∆−→n ip (47)

The above formula is used after the evaluation of ϕ at integration points, which is

done by using the shape functions.

2.7.4 Advection Term

The advection term requires the integration point values of ϕ to be approximated

in terms of the nodal values of ϕ. The advection schemes implemented in Ansys CFX

can be cast in the form [15]:

ϕip = ϕup + β∇ϕ.∆−→r (48)

Where ϕup is the value at upwind node, and −→r is the vector from upwind node

to the ip. The choice of a particular β (Flux Limitting) and ∇ϕ yields to different

schemes. Ansys CFX has several schemes, such as upwind, specified blend factor,

central difference, bounded central difference and high resolution. The high resolution

scheme was chosen to be used on this work, therefore this one will be further discussed.

High Resolution Scheme

The high resolution scheme uses a special nonlinear recipe for β at each node, com-

puted to be as close to 1 as possible without introducing new extrema, this one was

first developed by Barth and Jespersen [19] [15]. The advective flux is then evaluated

using the values of β and ∇ϕ from the upwind node.

On the triangle A presented on Figure 13, the idea is to find a linear representation

of the state variables about the origin which coincides to be the centroid of triangle A

[19].

The methodology for this method first computes ϕmin and ϕmax at each node using

a stencil involving adjacent nodes and the node itself. Subsequently, for each integra-



Figure 13: Typical triangle mesh [19]

tion point around the node, the Equation 48 is solved for β to ensure that it does not

undershoot ϕmin neither overshoot ϕmax [19].

The nodal value for β taken to be the minimum value of all integration point values

surrounding the node. The value of β is restrained to the maximum value of 1 . This

algorithm can be shown to be Total Variation Diminishing (TVD) when applied to one-

dimensional situations [15].



3 Description of CFD model

The aim of this section is to introduce a detailed description of the CFD model

created with Ansys. The basic CFD Workflow is shown as it follows.

Figure 14: CFD Workflow

3.1 Hull Geometry

The chosen hull for the study is the tanker known as KVLCC2, this one was con-

ceived by Korean Institute of Ships and Ocean Engineering (KRISO) to provide data

for both explication of flow physics and CFD validation, which is the first reason to

justify the choice of this object of study. The second reason was the fact that the com-

pany where this work was conducted had also experimental results from the Potsdam

Model Basin (SVA) for self-propulsion. Therefore direct comparison can be made be-

tween CFD model and experimental test.

The simulations will be performed at model-scale in order to save computation

time, the following table shows the dimensions of the vessel at full-scale and the

model-scale used by SVA. The considered scale factor (λ) is 53.953.

Figure 15: Imported Surfaces - KVLCC2



Table 1: Main dimensions of the ship

Parameter Model Full

LOS [m] 6.18 333.58LWL [m] 6.03 325.50Lpp [m] 5.93 320.0BWL [m] 1.08 58.0TA [m] 0.39 20.8TF [m] 0.39 20.8S [m2] 9.47 27573.5∇ [m3] 1.99 312635tW [°C] 17.20 15.0ρ [kg/m³] 998.72 1025.83ν [m²/s] 1.08E-06 1.19E-06

Where S is the wetted surface, LOS is the overall length, LWL is the waterline length,

LP P is the length between perpendiculars, TA is the draft at aft and TF is the draft at

fore, ∇ is the displacement, tW is the water temperature, ν is the kinematic viscosity .

The hull was imported with the rudder, afterwards the hull-geometry and the rudder

were closed and the volume body was created.

3.2 Propeller Geometry

The propeller model M1493S001 VP1133 was tested by SVA, therefore the geome-

try was imported to Ansys Design Modeler.

Table 2: Propeller main characteristics

Parameter Model

D [m] 0.18Ae/Ao [-] 0.55c0.7 [m] 0.05306Z [-] 4

Rake ε 8.0P0.7/D [-] 0.721dh/D [-] 0.25

One blade was imported and then the propeller was generated as it follows. After-

wards, a trapezoidal geometry is revolved in order to generate a volume which will be

the interface between ship and propeller mesh.



(a) Propeller Volume (b) Propeller Geometry

Figure 16: Propeller representation

3.3 Domain Creation

The propeller is the main component regarding self-propulsion analyses, therefore

two different domains were created in order to better represent this problem, the ship

and propeller domain.

The approach used on this work is the so called double-body. Accordingly to

Bertram [3], the double-body approach comes from an interpretation that the ship’s

hull is reflected at the waterline at rest, therefore the wavemaking at the free surface

and the effects of viscosity are neglected.

Figure 17: Reflected hull - Double body approach [3]

3.3.1 Ship Domain

The ship domain was defined by a parallelepiped as it follows. This one is defined

in a stationary frame. Where:

• X coordinate = 3 ∗Lpp backwards and 1.5 ∗Lpp onwards ;

• Y Coordinate = 1.5 ∗Lpp starboard and 1.5 ∗Lpp portboard ;

• Z Coordinate = 1.5 ∗Lpp below the draft of the ship.



Figure 18: Ship Domain

3.3.2 Propeller Domain

The propeller domain has a conical shape and its dimensions are highlighted on

Table 3.

(a) Dimensions

(b) Propeller domain

Figure 19: Propeller representation

Table 3: Domain dimensions

Parameter Model

L1 [m] 0.60*DL2 [m] 0.30*DL3 [m] 0.43*D



3.3.3 Interface Domain Modelling

Two different interface domains models were used on this work. For all the un-

steady simulations performed on this work, the frame change/mixing model selected

was Transient Rotor Stator, since it is the one which better represents transient phe-

nomenon, while Frozen Rotor was chosen for all steady simulations.

A general connection is necessary when one side is in a stationary frame of reference

and the other side is in a rotating frame of reference [20], which is the case between

propeller and ship domains.

Frozen Rotor

On this model, the frame of reference is changed but the relative orientation of the

components across the interface is fixed. The two frames of reference connect in a way

that they each have a fixed relative position throughout the calculation. If the frame

changes, the appropriate equation transformations are performed.

According to Ansys Solver Modelling Guide [20], this model produces a steady-

state solution to the multiple frame of reference problem, with some account of the

interaction between the two frames.

This model requires the least amount of computational effort of the three frame

change/mixing models available in CFX, however this one presents the disadvantage

of not modeling the transient effects at the frame change interface. Also, modeling

errors are generated when the quasi-steady assumption does not apply. Lastly, the

losses which happens in the real (transient) situation as the flow is mixed between

stationary and rotating components are not modeled [20].

Transient Rotor Stator

This model is recommended when it is important to account for transient interac-

tion effects at a sliding (frame change) interface, which is the case between propeller

and ship domains. One is capable of predicting the true transient interaction of the

flow between two different domains. In this approach the transient relative motion

between the components on each side of the general grid interface connection is truly

simulated. The interface position is updated each time step, as the relative position of

the grids on each side of the interface changes [20].

In despite of being more accurate, the main disadvantage of this method is that the

computer resources required may be large, in terms of simulation time and disk space.



When periodic-in-time quasi-steady-state simulation is sought, it may be helpful to

first obtain a steady-state solution using Frozen Rotor interfaces between components,

once this solution will contain most of the overall flow features, therefore it should

converge to the desired transient simulations in the fewest transient cycles.

3.4 Boundary Conditions

The choice of boundary conditions may define the quality of the results of any

numerical method, therefore the CFX Ansys user guide was consulted in order to find

the most suitable conditions for this work.

Regarding the ship domain, the following boundary conditions showed on Table 4

were created. The boundary called Sides is highlighted in green on Figure 20.

Figure 20: Ship boundary conditions

(a) (b)

Figure 21: Propeller boundary conditions



Table 4: Boundary Conditions - Ship

Name Type

Inlet Velocity inlet

Outlet Average static pressure outlet

Sides Free slip wall

Hull No slip wall

Prop inlet Conservative interface flux

Prop outlet Conservative interface flux

Prop side Conservative interface flux

Table 5: Boundary Conditions - Propeller

Name Type

Prop blades No slip wall

Prop hub No slip wall

Prop inlet Conservative interface flux

Prop outlet Conservative interface flux

Prop side Conservative interface flux

3.5 Mesh Generation

Mesh generation is an important step to work with CFD, once the quality of mesh

has direct impact on accuracy of the simulation. Ansys Meshing package has two main

different types of meshing : meshing by algorithm and meshing by element shape.

• Meshing by algorithm: two algorithms can be used to mesh, patch- conformingor patch-independent.

• Meshing by element shape: applicable mesh control options for each element

shape such as Tetrahedron, Hex or Prism .

Patch-Conforming

Patch conforming meshing is a technique in which all faces and their boundaries

(edges and vertices) [patches] within a small tolerance are respected for a given part.

Mesh based defeaturing is used to overcome difficulties with small features and dirty

geometry. Virtual Topology can lift restrictions on the patches, however the mesher

must still respect the boundaries of the Virtual Cells [21].



Patch-Independent

Differently from Patch-Conforming algorithm, this one is a meshing technique in

which the faces and their boundaries (edges and vertices) [patches] are not necessarily

respected unless there is a load, boundary condition, or other object scoped to the

faces or edges or vertices (topology). Patch independent meshing is useful when gross

defeaturing is needed in the model or when a very uniformly sized mesh is needed

[21].

Zhao [22], developed a table in which the advantages and disadvantages of each

cell type is presented (Table 6).

Table 6: Advantages and Disadvantages of cell types [22]

Cell type Advantages Disadvantages

Hexahedral

1. Low numerical diffusion when a meshaligned with low can be built.2. Suited for boundary layersbecause of little sensitivity to stretching.

1. For complex geometries,get poor cell quality.

Tetrahedral1. Well suitable for automatic mesh generation.2. Good cell quality for complex geometries.

1. Having only 4 neighboursmakes it insufficient toachieve the accuracyoffered by a mesh cellwith 6 faces.

WedgePrismPyramids

1. Use in ”transition” mesh layers betweenboundaries and main core mesh, and betweenmesh blocks featuring different cell types.

1. In comparison with hexa-hedralcells, it is more nume-rically diffusive.

Polyhedral

1. Greater automatic meshing benefitsthan tetrahedral cells.2. Variable gradients can be much betterapproximated because of many neighbourcells.3. Cells can easily be joined, split or modifiedby introducing additional points or edges.4. More accurate results

1. Memory usage for poly-hedral mesh is approxi-mately four times morecompared to a tetrahedralmesh of similar cell count.2. General polyhedral meshtakes longer time for oneiteration, compared to atetrahedral mesh of similarcell count.

The chosen meshing type for this work was the meshing by algorithm patch-conformingusing tetrahedral cells, in despite of not being so accurate as a structured mesh, this

one is able to better deal with complex geometries.

In order to analyze the fluid flow, the computational domains are split into subdo-

mains and the discretized Navier-Stokes equations are solved inside of each cell.



Figure 22: Cell types [22]

3.6 Mesh Quality Control

The quality of the mesh will be assessed using two of the global mesh controls

provided by Ansys : skewness and orthogonal quality.

3.6.1 Skewness

It determines how close to ideal (i.e., equilateral or equiangular) a face or a cell is.

Figure 23: Ideal and skewed triangle[21]

Table 7: Skewness quality

Value of Skewness Cell Quality

1 degenerate0.9 — <1 bad (sliver)

0.75 — 0.9 poor0.5 — 0.75 fair0.25 — 0.5 good>0 — 0.25 excellent

0 equilateral

The disadvantage of highly skewed faces and cells are due to the fact that the equa-

tions solved assume that cells are relatively equilateral.



There are two method for measuring skewness:

• Based on equilateral volume, applies to triangles and tetrahedron;

• Based on deviation from normalized equilateral angle, applies to all cell and face

shapes

Equilateral-Volume-Based Skewness

The definition is as it follows:

Skewness =OptimalCellSize −CellSize

OptimalCellSize(49)

Where the optimal cell size is the size of an equilateral cell with the same circum-

radius [21].

Normalized Equiangular Skewness

In the normalized angle deviation method, skewness is calculated as it follows:

max

[θmax −θe180−θe

,θe −θmin

θe

](50)

Where θmax is the largest angle in the face or cell, θmin is the smallest one, θe is the

angle for an equiangular face/cell (e.g, 60 for a triangle).

3.6.2 Orthogonal Quality

The orthogonal quality for a cell is computed as the minimum of the following

quantities computed for each face i:

min

−→A i .−→f i

|−→A i |.|−→f i |

,

−→A i .−→c i

|−→A i |.|−→c i |

(51)

Figure 24: Vectors used to compute orthogonal quality of cell [21]



Where−→A i is the face normal vector for each face, −→c i is the vector from the cell

centroid to the centroid of adjacent cells and−→f i is the vector from the cell centroid to

each of the faces as shown on Figure 24 . The range of orthogonal quality varies from

0 (worst) to 1 (best).

3.7 Mesh Characteristics

There were defined different mesh patches for hull, rudder, rudder’s trailing edge,

stern of Hull, water domain, propeller’s interface domain, hub, blades, blades’ trail-

ing edge and propeller domain, the chosen algorithm for meshing is patch-conformingusing tetrahedral cells, this one is well described on Section 3.5.

The generated propeller mesh had 1.9 million elements, with an averaged skewness

of 0.298 (good cell quality according Table 7) and orthogonal quality of 0.807 with the

best value being 1. Regarding the ship, its generated mesh had 1.9 million elements,

with an averaged skewness of 0.241 (excellent cell quality according Table 7) and or-

thogonal quality of 0.850, therefore the complete mesh had approximately 3.8 million

cells.

Figure 25: Rudder detail mesh

Figure 26: Ship detail mesh



Figure 27: Propeller detail mesh



4 Description of Speed Controller

4.1 Background Theory

The biggest challenge involved in directly modeling a self-propelled ship is the

difference in timescale between the propeller and the ship itself. Since the propeller

typically rotates 20–40 times for each ship length advanced, the resolution of the flow

around the propeller necessitates a very small time step in terms of what is needed to

compute the flow around the ship. To overcome this problem, most self-propulsion

simulations are performed using a body force model of the propeller [5].

Lubke (2005) computed the KCS container ship under self-propelled conditions

using the commercial code CFX, the author used a body force approach for the pro-

peller and his results presented deviations to experimental test results, nonetheless

his computations showed that the direct calculation of a rotating propeller on a ship

is feasible. The ship speed and propeller RPS were imposed, not predicted, and the

propulsion parameters rather than the self-propulsion point were predicted.

Carrica, Castro & Stern (2010) performed self-propulsion computations using CFD

Ship-Iowa v4, a speed controller and a discretized propeller with dynamic overset

grids were used, the authors imposed a velocity by a speed controller until the ship

reaches the desired Froude number in a single transient simulation. The controller

acts on the rotational speed of fully discretized propeller, thus it captures the effects of

the ship wake on the propeller performance. Moreover, during the computation, the

controller aims at cancelling the difference ε(t) = Vship(t)−Vshiptarget. A total of 20.000

time steps with ∆t = 0.0005 for the KVLCC1 were necessary.

Krasilnikov (2013) computed fully unsteady RANS analysis where the free surface

effects are accounted approximately for the MOERI KCS, the author used the CFD code

STAR CCM+ as the main viscous platform and the panel method code APKA devel-

oped at MARINTEK as the propeller solver in the coupled viscous/potential approach.

The total value of ship resistance (Ctsp) was defined as the resistance value obtained

directly from the calculation (Ct) plus the additional components due to wave making

(CtFS) calculated as the difference in towing resistance with and without free surface

effects included [4]. The author defined as the criterion for finding the self-propulsion

point, the minimization of the imbalance between the propeller thrust behind hull,

hull resistance and deduction force.

Schrooyen, Randle, Herry & Malllol (2014) observed that the time step used by

Carrica et al., (2010) was rather small and this may not be necessary during the ac-



celeration phase where the flow does not need to be very precisely solved, therefore

the authors developed a dynamic controller to automatically modify the RPM of the

propeller during the simulation divided in a two step approach carried by the software

FINETM/Marine .

Figure 28: The two-step approach to find the self-propulsion operating point [6]

During step 1, the time step is based on the vessel’s characteristics and may be

large (timestep = 0.03s), while during step 2 the time step is continuously reduced us-

ing a tangent hyperbolic law during 10 propeller rotations, thus the timestep reaches

0.000526 s where about 200 time steps per propeller period are used (assuming n=9.5rps)

[7].

Figure 29: Diagram of ship + controller system [6]

During both steps, the controller is active and the controller adjusts the propeller

rotational speed in order to make the sum of forces acting on the vessel to be equals to

0 as shown on Equation 52.

limt→∞ε(t) = limt→∞Fship(t) +Fprop(t) +Fext = 0 (52)

Where Fship is the hull drag, Fprop is the propeller thrust, both are time dependent,

while Fext is an external force which may be tug force, deduction force during towing

tank test or any other external force, moreover this force is constant in time. The model

was validated on MOERI KCS container ship for model scale.



Figure 30: Time evolution of ε [6]

Figure 31: Time evolution of the propeller rotational speed: a) during the whole com-putation and b) when the small time step is applied [6]

When the small timestep is applied, after 11 propeller revolutions, the propeller

rotational speed converges towards an asymptotic value of 9.56 RPS as shown on Fig-

ure 31. This is a 0.6% difference with the experimental value of 9.50 RPS [7].

4.2 Proposed Controller

On this work, it is proposed the implementation of a numerical model within a

speed controller capable to adjust the propeller rotational speed according to the dif-

ference of forces acting on the hull which characterizes the Continental method.

The controller will be represented by Fortran subroutines which will update the

rotational propeller speed during the simulation. The software chosen for this work

has a limitation regarding the implementation of subroutines for unsteady state con-



dition, the subroutine is not able to deal with variable time steps, for this reason the

subroutines can only be implemented for steady state condition.

A steady state simulation is the one which characteristics do not change with time,

while a transient simulation requires real time information in order to determine the

time intervals at which the solver calculates the flow field. When a steady state solution

is sought, one does not take into account cross terms and higher order terms from

Navier-Stokes equations solution dealing with time.

Regarding the propulsion analysis, the phenomenon is unsteady, since the pro-

peller is rotating, the passing flow varies according to the rotational offset of the blades.

Thence the engineering solution proposed by this work to develop the Continental

model is to divide the method in two parts.

PART I has the controller active and the rotational propeller speed will be sought

for a steady state condition, while PART II has the controller inactive for an unsteady

state condition and the propeller angular frequency will be set as the one found by

PART I . Afterwards, thrust and torque convergence will be analyzed and comparison

will be made against model basin results and British simulations.

Controller’s Functionality

Figure 32: Forces acting on KVLCC2

When the sum of forces acting on the ship equals 0 (∆F = 0), one is able to self-

propels. Where Fprop is the thrust provided by the propeller, FD is the deduction force,

Frudder , Fhub and Fhull are the resistance forces imposed by rudder, hub and hull re-

spectively.

∆F = Fprop +FD +Fhull +Frudder +Fhub (53)

Otherwise:

∆F =

∆F ≤ 0 : Fprop should increase

∆F ≥ 0 : Fprop should decrease(54)

In order to adjust the propeller rotational speed, two User CEL Functions5 together

5 CEL stands for CFX Expression Language



with three subroutines will be used : JcbInitControl.F, UserAVOmega.F and UserSe-tOmega.F, these are further discussed on next sub-sections.

User CEL functions enable the user to create his own functions in addition to the

predefined CEL functions in Ansys CFX. The advantage of using a CEL Function is the

customization which one can apply to any CEL expression.

The user CEL function passes one or several arguments to a subroutine which had

to be previously compiled , and then uses the returned values from the subroutine to

set values for the quantity of interest while the simulation still running. The quantity

of interest on this work is the propeller rotational speed. The Flowchart (Figure 33)

demonstrates the user function work-flow.

Figure 33: User Function work-flow

The first user function defined was called UserSetOmega, this one has the goal of

triggering the UserSetOmega.F subroutine which calculates a new value of propeller

frequency, secondlyUserSetAVOmegawas created in order to triggerUserSetAVOmega.F

subroutine that reads the new value of propeller frequency and store it in an additional

variable created on the CFD model called AVOmega.

4.3 JcbInitControl.F

Junction box routines are used to call Fortran subroutines during execution of the

CFX-Solver, it is necessary to create a junction box routine object so that the CFX-Solver



knows the location of the subroutine, the location of the shared libraries associated

with the subroutine, and when to call the subroutine as stated by [23]. The junction

box Routine can be called at different locations as shown on Figure 34 , on this work ,

JcbInitControl will be called at three different locations : Start of Coefficient Loop, End

of Linear Solution and User Start.

Figure 34: Junction box routines possible locations [20]

JcbInitControl objectives

• Compute the value of the acting forces on the body at a given iteration number

and store this value to MMS (CFX Memory Management System).

• Initialize a new value of rotational propeller speed to all partitions.

The location user start was chosen to guarantee that the mesh has been read in all

partitions. It is also relevant to call the routine at Start of Coefficient Loop, since it is

when the distribution of the latest value of rotational propeller speed to the domains



is done. Lastly, the routine is called at the End of Linear Solution, since it is necessary

to store the new computed value of forces.

4.4 UserSetAVOmega.F

This subroutine has the task of reading the value of rotational propeller speed

stored at CFX MMS and assigning it to an additional variable called AVOmega de-

fined in CFX-Pre, therefore this variable will be distributed to all domains and the

simulation continues.

4.5 UserSetOmega.F

UserSetOmega.F is responsible for updating the rotational propeller speed. The

subroutine is activated by the CEL expression OmegaUser shown below.

OmegaUser =UserSetOmega(citern,aitern,FirstUpdate,UpdateFreq,

nP ROPmodel,Sollwert,Factor)(55)

Where:

• citern : current iteration number.

• aitern : accumulated iteration number.

• FirstUpdate : the starting point of updating rotational propeller speed.

• UpdateFreq : the number of iterations required until a new update of rotational

propeller speed is performed .

• nPROPmodel: initial rotational propeller speed.

• Sollwert : target value used to calculate the adjustment value on rotational pro-

peller speed.

• Factor : a multiplier which will be used to tune the adjustment value of the new

rotational propeller speed.

The first practical feature performed inside this routine is the iteration check for

updating the rotational propeller speed. In order to check, the remainder function

(MOD) is used.

From the code transcription (Figure 35), it is possible to see that the rotational

propeller speed will only be updated when the aitern is larger or equal FirstUpdate

and if the remainder between aitern and UpdateFreq is equal to 0 .



Figure 35: Check condition for recalculation of rotational propeller speed

The second feature of this subroutine is altering the value of the rotational propeller

speed. Inside the subroutine, the following operations are performed.

∆ = Sollwert −RCURRENT∆O = Factor.∆

ωprop =ωprop +∆O

(56)

Where RCURRENT represents the sum of forces calculated by the JcbInitControl

and ωprop stands for rotational propeller speed.

RCURRENT = Fhull +Fhub +Fprop +Frudder (57)

Bringing it back to the KVLCC2 problem, Sollwert will be the deduction force (FD)

previously explained. Due to the negative sign on Equation 56, FD is defined with a

negative value in order to keep the same sign as Fprop, therefore substituting Equation

57 on Equation 56 :

∆ = −FD − (+Fhull +Fhub +Fprop +Frudder)

∆ = −FD −Fhull −Fhub −Fprop −Frudder(58)

On the first scenario, if ∆ > 0, therefore:

|Fhull |+ |Fhub|+ |Frudder | > |Fprop|+ |FD | (59)

Thus, Fprop should increase. On the second scenario, if ∆ < 0:

|Fhull |+ |Fhub|+ |Frudder | < |Fprop|+ |FD | (60)

Thus, Fprop should decrease.

Once the controller behavior is explained, a convergence study will be performed

in order to find an initial setup regarding the controller’s parameters FirstUpdate,

UpdateFreq, Factor and nm .



5 Body of Revolution - Convergence Study

5.1 Geometry and Mesh Characteristics

The controller is based on the difference of forces, therefore a study is proposed

in order to seek an optimal configuration to start the simulation. In order to do so, a

simpler geometry was adopted, a submerged body of revolution was chosen as shown

on the Figure 36. The choice of this geometry is justified by the necessity of a smaller

mesh when compared to the KVLCC2, therefore a larger number of simulations could

be performed to establish an optimal set of parameters.

Figure 36: Body of Revolution

Table 8: Body of Revolution dimensions

Parameter Model Full

LOS [m] 4.26 51.17B [m] 0.39 4.73TA [m] 0.39 4.73S [m2] 4.40 645.23∇ [m3] 0.39 674.02ρ [kg/m3] 998.72 1025.83ν [m2/s] 1.08E-06 1.19E-06

The chosen method for meshing was Tetrahedrons with the algorithm patch- con-

forming, leading to an average mesh skewness of 0.230 (excellent cell quality accord-

ing Table 7) and an orthogonal quality of 0.861 being the best value 1 (Section 3.6.2) .

The final mesh for the body has 0.64 million elements.

Regarding the propeller, the same method and algorithm were adopted, it led to

an average mesh skewness of 0.291 and an orthogonal quality of 0.804. The final

propeller mesh has 0.46 million elements, bringing the setup to a final mesh of 1.1

million cells.



Figure 37: Mesh of Body and Domain

Figure 38: Detail of Mesh

Figure 39: Propeller mesh



Figure 40: Detail of propeller mesh

5.2 Runs definition

There were defined 121 runs in a Perl script (BoRev.pl) varying the parameters of

the controller (Factor, FirstUpdate, UpdateFreq) and the initial rotational propeller

speed (nm). The parameters’ labels are shown on Tables 9 and 10 .

Table 9: Parameters’ label

nm UpdateFreq FirstUpdate

n1=1 UpdateFreq1=20 FirstUpdate1=100n2=3 UpdateFreq2=50 FirstUpdate2=200n3=5 UpdateFreq3=100 FirstUpdate3=300

Table 10: Factors’ label

Factor (rad/sN)

ID 1 2 3 4 5 6 7 8 9 10 11Value 1.5 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1

The runs were defined changing one parameter and fixing the others, once this

methodology makes it possible to investigate the influence of each parameter on the

convergence speed, they are shown on Table 11.



Table 11: Run definitions

Run Factor FirstUpdate UpdateFreq n1 1 1 1 12 2 1 1 13 3 1 1 14 4 1 1 15 5 1 1 16 6 1 1 17 7 1 1 18 8 1 1 19 9 1 1 1

10 10 1 1 111 11 1 1 112 1 1 1 213 2 1 1 214 3 1 1 215 4 1 1 216 5 1 1 217 6 1 1 218 7 1 1 219 8 1 1 220 9 1 1 221 10 1 1 222 11 1 1 223 1 1 1 324 2 1 1 325 3 1 1 326 4 1 1 327 5 1 1 328 6 1 1 329 7 1 1 330 8 1 1 331 9 1 1 332 10 1 1 333 11 1 1 334 1 1 2 335 1 1 3 336 2 1 2 337 2 1 3 338 3 1 2 339 3 1 3 340 4 1 2 341 4 1 3 342 5 1 2 343 5 1 3 344 6 1 2 345 6 1 3 346 7 1 2 347 7 1 3 348 8 1 2 349 8 1 3 350 9 1 2 351 9 1 3 352 10 1 2 353 10 1 3 354 11 1 2 355 11 1 3 356 1 2 2 357 1 3 2 358 2 2 2 3



Table 11 – continued from previous pageRun Factor FirstUpdate UpdateFreq n59 2 3 2 360 3 2 2 361 3 3 2 362 4 2 2 363 4 3 2 364 5 2 2 365 5 3 2 366 6 2 2 367 6 3 2 368 7 2 2 369 7 3 2 370 8 2 2 371 8 3 2 372 9 2 2 373 9 3 2 374 10 2 2 375 10 3 2 376 11 2 2 377 11 3 2 378 1 2 2 279 1 3 2 280 2 2 2 281 2 3 2 282 3 2 2 283 3 3 2 284 4 2 2 285 4 3 2 286 5 2 2 287 5 3 2 288 6 2 2 289 6 3 2 290 7 2 2 291 7 3 2 292 8 2 2 293 8 3 2 294 9 2 2 295 9 3 2 296 10 2 2 297 10 3 2 298 11 2 2 299 11 3 2 2

100 1 2 2 1101 1 3 2 1102 2 2 2 1103 2 3 2 1104 3 2 2 1105 3 3 2 1106 4 2 2 1107 4 3 2 1108 5 2 2 1109 5 3 2 1110 6 2 2 1111 6 3 2 1112 7 2 2 1113 7 3 2 1114 8 2 2 1115 8 3 2 1116 9 2 2 1117 9 3 2 1



Table 11 – continued from previous pageRun Factor FirstUpdate UpdateFreq n118 10 2 2 1119 10 3 2 1120 11 2 2 1121 11 3 2 1

RUNS Description

• RUN 1 to 11 : Varying Factors, other parameters fixed for $n1;

• RUN 12 to 22: Varying Factors, other parameters fixed for $n2;

• RUN 23 to 33: Varying Factors, other parameters fixed for $n3;

• RUN 34 to 55: VaryingUpdateFreq for all Factors for fixed $n3 and FirstUpdate1;

• RUN 56 to 77: Varying FirstUpdate for all Factors for fixed $n3;



5.2.1 Convergence Criteria

The convergence criteria was defined in a way to assure the equilibrium of forces of

the body, ideally that would happen when the sum of forces equals 0, however due to

uncertainties associated to any CFD-Solver, it was decided to establish the convergence

criteria for a sufficiently small sum of forces at the interval between 0 and 0.1 N, hence

the DeltaF monitor was created in CFX-Pre (Equation 62).

Another control variable was added in order to assure that the simulation would

not stop when DeltaF first reaches 0, in the consideration of the foregoing, the stan-

dard deviation of the last 50 iterations (STDev) was implemented, the second reason

behind this control monitor is to make sure that the forces are not varying abruptly

when the convergence is met. The standard deviation criteria should respect the same

rule as DeltaF, thus the convergence criteria implemented on CFX-Pre is shown on

Equation 61 as it follows:

aitern > FirstUpdate&&DeltaF <= 0.1[N ]&&DeltaF >= 0[N ]

&&probe(ExpressionV alue.StandardDeviation)@STDdev <= 0.1[N ](61)

DeltaF = f orce x()@REGION : prop blades+ f orce x()@REGION : BoRev

+f orce x()@REGION : prop hub − Sollwert(62)



NOTE: Sollwert receives negative FD .

The maximum number of iterations was set to 2000.

5.3 Self-Propulsion of Body of Revolution

The self-propulsion of the Body of Revolution was computed by the British-method

in order to have a reference to compare the further results found using the imple-

mented controller.

There are four forces acting on the body including the deduction force (FD), they

are represented on Figure 41.

Figure 41: Forces acting on the Body

The deduction force was computed by the ITTC recomendations (Section 2.2.1),

FD = 9.294 [N] .

Two different runs were necessary in order to interpolate FD at the carriage force

(Fcarriage) and to find the self-propulsion point, being Fx = Fhub +FxBoRev .

Table 12: Self-propulsion RUNS

RUN Vm n Fx Fpropm Qm FCarriage

[m/s] [rps] [N] [N] [N.m] [N]

1 3.75 8 -45.63 14.59 2.3364 31.04

2 3.75 10 -58.75 100.2 7.539 -41.45

SelfProp 3.75 8.600 -49.567 40.277 3.897 9.29

Fcarriage = |Fx| − |Fpropm | (63)

5.4 RUNS Post-Processing

The runs were performed, thereafter a verification on the forces, torque (Qm) and

propeller frequency was made in order to see the behavior of the controller for each

setup. The simulations were performed on 42 cores and each simulation took from 45

to 80 minutes. In total, 24 simulations converged and those are shown on Table 13.



Table 13: Converged Simulations

RUN N. Iterations nupdated STDdev DeltaF Qm Fpropm Fx

55 1568 8.594 0.0985 0.0996 3.925 41.388 -50.58254 1515 8.587 0.0682 0.0098 3.957 42.067 -51.26133 1506 8.584 0.027 0.095 3.970 42.335 -51.3677 1357 8.594 0.026 0.0947 3.978 42.403 -51.60276 1418 8.592 0.0795 0.099 3.978 42.431 -51.62653 1508 8.581 0.0614 0.0732 3.997 42.464 -51.68522 1390 8.592 0.026 0.094 4.007 42.988 -52.18850 1457 8.578 0.085 0.006 4.012 43.117 -52.40498 1209 8.609 0.031 0.098 4.041 43.521 -52.71574 1358 8.592 0.084 0.084 4.055 43.914 -53.12352 1406 8.594 0.0997 0.0988 4.091 44.591 -53.78775 1258 8.598 0.09 0.093 4.093 44.601 -53.80299 1012 8.625 0.05 0.099 4.103 44.614 -53.80996 1158 8.608 0.078 0.076 4.116 44.974 -54.19097 958 8.625 0.094 0.09 4.185 46.195 -55.39832 1351 8.601 0.025 0.097 4.19 46.420 -55.62011 949 8.677 0.0454 0.094 4.344 48.879 -58.07821 1165 8.635 0.037 0.22 4.340 49.160 -58.24010 909 8.682 0.0356 0.0996 4.403 50.018 -59.21294 1765 8.939 0.08 0.0006 4.578 51.446 -60.74095 1607 8.936 0.057 0.021 4.587 51.656 -60.928

118 913 8.865 0.0805 0.0068 4.573 51.95 -61.237120 1161 8.875 0.004 0.0004 4.585 52.059 -61.353116 1656 8.869 0.082 0.056 4.596 52.266 -61.503

The percentage of converged simulations (19.8%) is considered low, to clarify the

reason behind that, the number of entries of each parameter was summarized on Table

14.

Table 14: Parameters’ entries

Factor UpdateFreq

0.1 0.2 0.3 100 50 20

No 10 10 4 2 16 6

% 41.67 41.67 16.67 8.33 66.67 25

FirstUpdate n

100 200 300 5 3 1

No 11 8 5 11 8 5

% 45.83 33.33 20.83 45.83 33.33 20.83



Conclusions

1. Factor is the critical parameter on the analysis, once it is always multiplying the

difference of Forces, in the case of this object of study, the difference of Forces was con-

siderably large when the updates started, therefore it lead mostly of the simulations to

divergence, whether taking propeller rotational speed to negative values or to extreme

positive, this would generate extreme high values of Residuals (Figure 42) and then

the simulation would diverge;

2. Among the converged simulations, UpdateFreq = 50 appeared to be dominant

over the others;

3. As expected, n=5 is dominant over the other propeller frequencies, once it is

closer to the sought velocity;

4. Factor 0.1 and 0.2 had the same number of entries;

5. Soonest the updates started, most likely the simulations converged.

Figure 42: Residuals (Diverged simulation)

5.5 Finding Optimum setup

A comparison between the results (Table 13) and the reference values for the self-

propulsion (Table 12) point was performed and it is presented on Table 15 .

Table 15 shows that the updated propeller frequency error vary in a range from

−0.07% to 3.94% which is considered satisfactory, nonetheless thrust deviations may

reach up to 29.77%, torque reaches 17.92% difference while Fx has 24.08% difference

as its maximum. In order to better analyze the results, an averaged accumulated error

(ε) will be calculated:

ε =nupdated +Qm +Fpropm +Fx

4(64)



Table 15: Error %

RUN nupdated Qm Fpropm Fx

55 -0.07% 0.71% 2.76% 2.05%54 -0.16% 1.54% 4.45% 3.42%33 -0.18% 1.86% 5.11% 3.62%77 -0.07% 2.07% 5.28% 4.11%76 -0.10% 2.07% 5.35% 4.15%53 -0.22% 2.56% 5.43% 4.27%22 -0.09% 2.83% 6.73% 5.29%50 -0.26% 2.94% 7.05% 5.72%98 0.10% 3.68% 8.06% 6.35%74 -0.10% 4.04% 9.03% 7.18%52 -0.08% 4.97% 10.71% 8.51%75 -0.03% 5.02% 10.74% 8.54%99 0.29% 5.28% 10.77% 8.56%96 0.09% 5.61% 11.66% 9.33%97 0.29% 7.38% 14.69% 11.76%32 0.01% 7.51% 15.25% 12.21%11 0.90% 11.47% 21.36% 17.17%21 0.41% 11.36% 22.06% 17.50%10 0.95% 12.99% 24.19% 19.46%94 3.94% 17.46% 27.73% 22.54%95 3.90% 17.69% 28.25% 22.92%

118 3.08% 17.33% 28.98% 23.55%120 3.20% 17.64% 29.25% 23.78%116 3.13% 17.92% 29.77% 24.08%

Thereafter, a table containing the averaged accumulated error versus number of

iterations was created in order to analyze an optimum setup regarding convergence

speed (Table 16).

By analyzing Table 16, RUN 55 presented the setup with the smallest averaged

accumulated error (ε) 1.36%, however its number of iterations is fourth highest on the

list, in the consideration of the following, RUN 55 will be taken as a reference and a

relative convergence speed (CSRel) will be calculated from it in order to find the best

compromise between accuracy and convergence speed .

CSReli =N.Iterationsi −N.IterationsRUN55

N.IterationsRUN55(65)

From Table 17, it is noticeable the possibility to reduce the convergence speed in

22.9% and keep an accumulated error lower than 5% (RUN 98), therefore this run is

taken as the most suitable setup.



Table 16: Number of Iterations versus Error (ε)

RUN N. Iterations ε Factor FirstUpdate UpdateFreq n55 1568 1.36% 0.1 100 100 554 1515 2.31% 0.1 100 50 533 1506 2.60% 0.1 100 20 577 1357 2.85% 0.1 300 50 576 1418 2.87% 0.1 200 50 553 1508 3.01% 0.2 100 100 522 1390 3.69% 0.1 100 20 350 1457 3.87% 0.3 100 50 598 1209 4.55% 0.1 200 50 374 1358 5.04% 0.2 200 50 552 1406 6.03% 0.2 100 50 575 1258 6.07% 0.2 300 50 599 1012 6.22% 0.1 300 50 396 1158 6.67% 0.2 200 50 397 958 8.53% 0.2 300 50 332 1351 8.74% 0.2 100 20 511 949 12.72% 0.1 100 20 121 1165 12.83% 0.2 100 20 310 909 14.40% 0.2 100 20 194 1765 17.92% 0.3 200 50 395 1607 18.19% 0.3 300 50 3

118 913 18.24% 0.2 200 50 1120 1161 18.47% 0.1 200 50 1116 1656 18.73% 0.3 200 50 1

Table 17: Relative Convergence Speed

RUN N. Iterations ε CSRel55 1568 1.36% -54 1515 2.31% -3.38%33 1506 2.60% -3.95%77 1357 2.85% -13.46%76 1418 2.87% -9.57%53 1508 3.01% -3.83%22 1390 3.69% -11.35%50 1457 3.87% -7.08%98 1209 4.55% -22.90%74 1358 5.04% -13.39%52 1406 6.03% -10.33%75 1258 6.07% -19.77%99 1012 6.22% -35.46%96 1158 6.67% -26.15%97 958 8.53% -38.90%32 1351 8.74% -13.84%11 949 12.72% -39.48%21 1165 12.83% -25.70%10 909 14.40% -42.03%94 1765 17.92% 12.56%95 1607 18.19% 2.49%

118 913 18.24% -41.77%120 1161 18.47% -25.96%116 1656 18.73% 5.61%



Figure 43: Relative Convergence Speed Variation

NOTE: Although a lot of simulations were performed, only a few reached conver-

gence, therefore this study is on a preliminary level, and the found setup will be a

starting point for the simulations with the KVLCC2, nonetheless changes on the setup

can be made along the study.



6 KVLCC 2 - British Method

Before running the controller for the KVLCC2, the self-propulsion parameters will

be estimated by the British method.

The speed of the run was chosen based on the model basin measured values, (Vm =

1.069m/s, nm = 8.743rps). The advection scheme used was High Resolution (Section

2.7.4) for a second order backward euler transient scheme, the frame change/mixing

interface domain model was chosen as transient rotor stator (Section 3.3.3 , once this

setup is running on unsteady state. The turbulence model selected was the k −ω SST

model (Section 2.6.3).

Table 18: Measured values from SVA mode-basin

Vm nm Fpropm Qm FD Fxm

[m/s] [rps] [N] [N.m] [N] [N]

1.069 8.743 13.730 0.332 10.045 -23.775

6.1 Post-Processing

In order to find the self-propulsion point for the rotational propeller speed speci-

fied on Table 18, two runs were performed, firstly considering the propeller on under-

loaded condition (nprop=8.543 rps), afterwards considering an over-loaded condition

(nprop=8.943 rps), the deduction force (FD=10.05 N) was provided by the model basin.

Results of the simulations are summarized on Table 19. NOTE: Fxm = Fxhull + Fxhub +

Fxrudder .

Table 19: British simulation results

RUN Vm nm Qm Fxm Fpropm DeltaWave FCarriage

[m/s] [rps] [N.m] [N] [N] [N] [N]1 1.069 8.543 0.315 -23.698 13.045 0.295 10.9472 1.069 8.943 0.359 -24.050 15.203 0.295 9.143

Result 8.743 0.337 -23.874 14.123 10.05

The simulations ran taking the double-body approach into account, therefore the

wave contribution is added through the term DeltaWave, this term represents not only

the wave resistance but also, all the double model approximations (e.g. variation of

the hull wettted surface). Torque and forces were computed taking the average values

of the 3 last propeller’s revolution considering 5 ◦ rotation/timestep. In total, 24 cores

were used for 1000 time steps, each run took roughly 18h .



(a) Fpropm [N] (b) Fxm [N]

Figure 44: RUN 1 - Forces and Torque for the last 216 time steps

(a) Residuals (b) Qm [N.m]

Figure 45: RUN 1 - Torque for the last 216 time steps and Residuals

(a) Fpropm [N] (b) Fxm [N]

Figure 46: RUN 2 - Forces for the last 216 time steps



(a) Residuals (b) Qm [N.m]

Figure 47: RUN 2 - Torque for the last 216 time steps and Residuals

All the residuals are below 1E−4 which is a good indicator of convergence [15].

Nonetheless, the measured quantities presented on Figures 44(a) and 45(b) for RUN 1

are not completely converged, once Torque6 and Thrust are slightly increasing along

time steps periodically.

Indeed, the quantities are well converged for RUN 2 as shown on Figures 46(a) and

47(b), they present only the periodical variation which is expected by the rotation of

the 4 blades.

The values obtained were compared to the model basin values (Table 18) and are

summarized on Table 20.

Table 20: CFD and Model Basin comparison

nm Fpropm Qm Fxm

[rps] [N] [N.m] [N]

Model Basin 8.743 13.730 0.332 -23.775

CFD 8.743 14.123 0.337 -23.874

DELTA - 2.87% 1.44% 0.41%

6Negative sign of Torque comes from a definition on the setup.



7 KVLCC2 - Continental Method

7.1 Determining Initial Setup for the Controller

The aim of this section is to determine the initial setup for the controller capable

of meeting the convergence criteria for the KVLCC2. During this phase, steady state

simulations are performed for the KVLCC2 with the RPM controller active. Firstly,

the parameters found for the controller on Section 5.5 will be implemented for the

KVLCC2 (RUN 1 on Table 21).

Regarding the convergence criteria, DeltaF had to be modified in order to take the

rudder force into account (Equation 66). The results of this simulation are shown on

Figure 48 and Figure 49 .

DeltaF = f orce x()@REGION : prop blades+ f orce x()@REGION : hull

+f orce x()@REGION : prop hub+ f orce x()@REGION : rudder − Sollwert(66)

(a) Fpropm [N] (b) Fx [N]

(c) DeltaF [N] (d) Standard Deviation of DeltaF

Figure 48: RUN 1: Post-Processing



(a) Fpropm and Fxm [N] (b) nupdated [rev/s]

Figure 49: RUN 1: Asymptotic behavior of forces and propeller rotational speednupdated

Conclusions

• Forces present an asymptotic behavior;

• DeltaF did not reach the interval between 0 and 0.1 [N], therefore the convergence

criteria was not met;

• Standard deviation is sufficiently small, which means the forces are varying slowly;

• On the KVLCC2, the difference of forces are not so high as in the Body of Revolu-

tion, therefore the small Factor of 0.1[rad/sN ] used for the controller to update

the rotational propeller speed, could not lead the simulation to meet the conver-

gence criteria within 2000 iterations.

Runs Definition

Other runs were defined for the KVLCC2. From the previous study, it is under-

stood that sooner the updates start, better chance the simulation has to converge, as

closer the rotational propeller speed is to the point we are analyzing, better chances the

simulation has to converge. The new runs defined were based on these observations.

The parameters have the same labels as previously defined on Tables 9 and 10,

although a fourth propeller frequency was added ($n4 = 7 rps), this one is closer to the

speed sought by the controller.



Table 21: Runs Definition

Run Factor FirstUpdate UpdateFreq n1 11 2 2 22 10 1 2 33 9 1 2 34 8 1 2 35 7 1 2 36 6 1 2 37 5 1 2 38 4 1 2 39 3 1 2 3

10 2 1 2 311 10 1 1 312 9 1 1 313 8 1 1 314 7 1 1 315 6 1 1 316 5 1 1 317 4 1 1 318 3 1 1 319 2 1 1 320 10 1 2 421 9 1 2 422 8 1 2 423 7 1 2 424 6 1 2 425 5 1 2 426 4 1 2 427 3 1 2 428 2 1 2 429 10 1 1 430 9 1 1 431 8 1 1 432 7 1 1 433 6 1 1 434 5 1 1 435 4 1 1 436 3 1 1 437 2 1 1 438 9 1 3 439 8 1 3 440 7 1 3 441 6 1 3 442 5 1 3 443 4 1 3 444 3 1 3 445 2 1 3 4



Table 22: KVLCC2 - Converged simulations

RUN N. Iterations nupdated

2 1522 9.4013 1139 9.5584 943 9.6395 822 9.6866 730 9.7167 669 9.7368 622 9.7519 583 9.760

10 548 9.76511 794 9.69112 601 9.75313 509 9.77814 465 9.78515 453 9.78516 374 9.77017 367 9.74818 461 9.75319 611 9.79620 1363 9.51021 1076 9.62122 919 9.67823 805 9.71124 732 9.73425 681 9.74926 638 9.75927 605 9.76528 586 9.77129 778 9.72230 626 9.76331 551 9.77832 516 9.78133 500 9.78134 479 9.78035 456 9.77936 432 9.78637 462 9.74338 1793 9.30139 1408 9.44640 1155 9.54941 1010 9.61242 876 9.66243 763 9.69944 703 9.72645 629 9.754

Simulations ran in 62 cores and took from 50 min to 150 min. All the simulations

but the first, met the convergence criteria (DeltaF), although the forces were not com-

pletely converged.

Based on the results shown on Figure 22, the fastest setup (RUN17) was chosen

for the Continental Setup, since this one can meet the convergence criteria in a shorter

period of time, it is most likely to find a more accurate solution if it runs for more

iterations.



7.2 Continental Setup

After the selection of the initial setup, the self-propulsion simulation using the

Continental method is initialized. The aim of this section is to find the self-propulsion

point of the KVLCC2 .

Figure 50: Continental Setup - Methodology

Firstly, a Perl script (Continental.pl) starts the first part of the simulation (Steady)

with the fastest setup (RUN 17) implemented and the controller active. On this part,

the controller seeks the self-propulsion point of the KVLCC2 which is represented by

an unsteady phenomenon, however the setup is defined for a steady condition.

Hence, in order to account for the unsteadiness an assumption was made. The

controller should seek for a rotational propeller speed considering an additional force

(Fadd) of the same order of magnitude as the thrust fluctuations for the three last pro-

peller revolutions showed on Figures 44(a) and 46(a) was added to Sollwert. This

additional force (Fadd) has the value of 1.1 N acting on the same direction as FD .

Sollwert = FD +DeltaWave+Fadd (67)

After 2000 iterations, the second part begins when Continental.pl calls a Python

script (GetSpeed.py) in order to collect the updated propeller rotational speed (nupdated).

This value is returned to Continental.pl and sent as an input to the second part (Un-

steady), this one performs 510 time steps considering 5◦ rotation/timestep.



8 Results

8.1 Post-Processing - Continental Setup

The results of the Continental method are presented on this Section, further on,

comparison between the different methods will be made. For the PART I, it is notice-

able that the convergence criteria was met, once DeltaF reaches 0.044 [N] while the

Standard Deviation is 0.0013 by analyzing Figure 51(b), although Thrust and Torque

still present some variation (Figures 51(c) and 51(d)).

(a) nupdated [rev/s] (b) DeltaF and STDDev of DeltaF [N]

(c) Fpropm [N](d) Qm [N.m]

Figure 51: Continental RUN - PART I

Regarding PART II, Torque and Thrust were plotted against the three last propeller

revolutions as previously done for the British case to check convergence of the forces.

From Figures 52(a) and 52(b), it is noted that the solution found is not fully converged,

once Thrust and Torque7 are slightly increasing periodically.

DeltaF is normalized by the total hull drag, from Figure 54(b), it is possible to see

a peak of force variation at 2000th time step, this is due to the change of steady to un-

7Negative sign of Torque comes from a definition on the setup.



(a) Fpropm [N] (3 last propeller revolutions) (b) Qm [N.m] (3 last propeller revolutions)

Figure 52: Continental RUN - PART II - Fpropm and Qm

(a) Fx [N](b) Fpropm and Fxm [N]

Figure 53: Continental RUN - PART II - Fxm [N] ; Asymptotic behavior of forces

(a) nupdated [rev/s] (b) DeltaF/Fxm

Figure 54: Continental RUN - PART II - Propeller rotational speed nupdated ; DeltaFnormalized by Fxm

steady state , nonetheless DeltaF normalized quickly goes down and keeps its ampli-



tude oscillation in 0.04% of the final hull drag as presented by Figure 55. Oscillations

can not be avoided, once the propeller thrust is unsteady, therefore the value found for

DeltaF normalized being 0.04% of the total hull drag is considered acceptable.

Figure 55: Zoom at DeltaF normalized - PART II

Table 23: Continental Method - Results

Vm nm Fpropm Qm

[m/s] [rps] [N] [N.m]Continental 1.069 9.05 15.2 0.361

8.2 Comparison - British x Continental x Model Basin

The following Tables aimed to summarize the self-propulsion parameters found by

the different methods analyzed. Regarding thrust and torque, the comparison is made

considering the last three propeller revolutions for a 5 ◦rotation/time step .

Table 24: British x Model Basin

Vm nm Fpropm Qm

[m/s] [rps] [N] [N.m]Model Basin 1.069 8.743 13.730 0.332

British 1.069 8.743 14.123 0.337Delta 2.87% 1.44%

From Table 24, thrust and torque deviations are found to be below 3%, while the



rotational speed is the same on both cases. That is due to the interpolation performed

after the computation of the 2 runs in the British method.

Table 25: Continental x Model Basin

Vm nm Fpropm Qm

[m/s] [rps] [N] [N.m]Model Basin 1.069 8.743 13.730 0.332Continental 1.069 9.050 15.200 0.361

Delta 3.51% 10.71% 8.83%

When the Continental self-propulsion simulation is compared to model basin, torque

reaches 8.83% difference, while thrust is 10.71% higher than the one found by model

basin (Table 25).

Table 26: British x Continental

Vm nm Fpropm Qm

[m/s] [rps] [N] [N.m]British 1.069 8.743 14.123 0.337

Continental 1.069 9.05 15.200 0.361Delta 3.51% 7.62% 7.28%

By analyzing Table 26, torque and thrust are less than 8% different, while propeller

rotational speed is 3.51% higher for the Continental method.

Table 27: Computational Time

Setup No Type time steps N.Cores Time (h) Total Time (h)

British 2 Unsteady 1000 24 18 36

Continental1 Steady 2000 24 5.09

14.091 Unsteady 510 24 9

Delta (%) -60.87%

The British setup took 36 hours in total to find the self-propulsion parameters for

1 velocity, while the Continental method needed 14.09 hours (Table 27).



9 Conclusion

Marine industry is in constant evolution, the need for high efficient propulsion

systems allied to the demand for accurate power predictions with lower costs is one of

the reasons why CFD has increasingly being used for self-propulsion calculations. On

this work, a commercial CFD package was used in order to implement an alternative

numerical method to estimate the self-propulsion parameters of a scaled vessel.

The methodology adopted consisted on performing a convergence study on a sim-

pler geometry, where 121 simulations were performed in order to understand the be-

havior of a RPM controller based on the difference of forces acting on the body. This

analysis provided a starting setup to the KVLCC2. However, the setup found for the

simpler geometry did not lead the KVLCC2 to meet the convergence criteria. That

was due to the considerably lower difference of forces acting on the KVLCC2, there-

fore the Factor used by the controller for the simpler geometry was unable to lead the

simulation of the KVLCC2 to convergence.

Afterwards, new runs combining the controller’s parameters were defined and 45

simulations were performed in order to find the initial configuration of the controller

for the KVLCC2.

Further on, the Continental method starts, in which the configuration previously

found is used for 2000 time steps in a steady setup (PART I) followed by 510 time steps

in a unsteady setup (PART II).

The Continental method was unable to find a fully converged solution for the

KVLCC2, two hypothesis may be raised to justify this fact.

1. Due to software limitations, the controller could not be active during the un-

steady part of the simulation, therefore it was not possible to update the propeller

rotational speed during this phase.

2. The controller could not take the unsteadiness of the phenomenon completely

only by the addition of the force Fadd .

Table 28: Accuracy x Computational time

Setup n Thrust Torque Cores Time (h)

British - 2.87% 1.44% 24 36

Continental 3.5% 10.7% 8.8% 24 14



The methods were compared to the model basin results and their accuracy, devia-

tion and computational time are displayed on Table 28. The Continental method took

39% of the required computational effort by the British method to estimate thrust,

torque and propeller frequency, nonetheless the British simulation found the parame-

ters more accurately. The Continental method presented 3.73 and 6.11 times less ac-

curacy in Thrust and Torque respectively, while the difference in propeller frequency

is 3.5%.

In despite of being computationally expensive, it is possible to conclude that the

British method is more efficient than the Continental method implemented on this

work.

It is relevant to mention that the self-propulsion parameters (Thrust, Torque and

propeller rotational speed) are only found for model-scale on this study, therefore it is

not possible to determine how these would affect the full-scale prognosis of the vessel.

In order to do so, open-water and resistance simulations would be required.

Finally, the model implemented showed itself as a potential tool to reduce com-

putational time, and the results found here provide initial insights on the time steps

needed for convergence regarding the KVLCC2, however the Continental model re-

quires further development to overcome the accuracy of the British method and to

find a final fully converged solution.

FURTHERWORK SUGGESTIONS

1. It was demonstrated throughout this research that it is difficult to successfully

find fully converged Thrust and Torque using a RPM controller, thus, one could de-

velop a more complex subroutine based on UserSetOmega.F in order to change how

the controller is updating the propeller rotational speed, therefore changes could be

expected for Torque and Thrust.

2. One possible continuation of this work may be achieved by performing open-

water and resistance simulations in order to investigate how the parameters found

would affect the full-scale prognosis of the ship.

3. On this study, the controller is active only during the steady part of the Continen-

tal setup, in order to increase accuracy of the model on finding the rotational propeller

speed, one could use another CFD package which has the capability of implementing

subroutines for unsteady state condition able to deal with variable time-steps.



ACKNOWLEDGMENTS

Firstly, I would like to thank my supervisor M.Sc. Tom Goedicke whose constant

support was essential throughout the period of my internship providing interesting

discussions and unconditional help to develop this CFD model.

I would also like to express my sincere gratitude toM.Sc.Rodrigo dos Santos Correa

for his collaboration with several programming tips and valuable insights to develop

this topic.

I thank all the Professors from Universite de Liege, Ecole Centrale de Nantes and

Universitat Rostock for kindly sharing their knowledge. Moreover, I express my grat-

itude to Dr. − Ing. Nikolai Kornev and P rof . Florin Pacuraru for supervising and re-

viewing this thesis.

I am truly thankful to P rof . Philippe Rigo for the opportunity to participate of

EMSHIP program.

This thesis was developed in the frame of the European Master Course in “In-

tegrated Advanced Ship Design” named “EMSHIP” for “European Education in Ad-

vanced Ship Design”, Ref.: 159652-1-2009-1-BE-ERA MUNDUS-EMMC.

Thales Augusto Damasceno Machado



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