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Hydrodynamics of Unconventional SWATH Vessels in Waves by

MASSACHUSETTS INSTrTuTE OF TECHNOLOLGY

Abiodun Timothy Olaoye

JUL 3 0 2015

B.S., Petroleum & Gas Engineering University of Lagos (2010)

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Submitted to the Department of Mechanical Engineering in partial fulfillment of the requirements for the degree of Master of Science in Mechanical Engineering at the MASSACHUSETTS INSTITUTE OF TECHNOLOGY June 2015

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Signature redacted -- --....................---- -- -- -- -- -Abiodun Timothy Olaoye Department of Mechanical Engineering May 7, 2015

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Stefano Brizzolara Research Scientist and Lecturer irector for Research at MIT Sea Grant 4 T0hesis Supervisor

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. ........................ David E. Hardt Chairman, Committee on Graduate Students Department of Mechanical Engineering

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Hydrodynamics of Unconventional SWATH Vessels in Waves by Abiodun Timothy Olaoye Submitted to the Department of Mechanical Engineering on May 7, 2015, in partial fulfillment of the requirements for the degree of Master of Science in Mechanical Engineering

Abstract The motion responses of unconventional Small Water-plane Area Twin Hull (SWATH) vessels are unique in the sense that viscosity has significant non-linear effects on their hydrodynamic parameters. The parametric optimization of the hull shape of these vessels to reduce the total resistance in waves yields an interesting hull form where viscous effects become significant and this kind of problem is generally more difficult to solve. This study aims to investigate the motion response of these special kind of ships in waves using both numerical and experimental approach with some theoretical simplifications to better understand the hydrodynamics of the ship. The two modes of motion of interest in this study are heave and pitch motions which were chosen in order to focus on the degrees of freedom which significantly contributes to the resistance of the ship in head waves. The vessel under investigation is an unmanned surface vessel (USV) proposed to be used to monitor a team of autonomous underwater vehicles. A scaled version of this model is built and some experiments were conducted at the MIT towing tank at zero speed. Additionally, the numerical methods are implemented using 2D and 3D potential flow solvers. As this is an ongoing project, the results obtained so far including the study of the effects of the inertial characteristics of the ship on the response amplitude operator (RAO) are presented. Thesis Supervisor: Stefano Brizzolara Title: Research Scientist and Lecturer Assistant Director for Research at MIT Sea Grant

2

Acknowledgement To almighty God be all the glory for the good health and sound mind that sustained me through this Masters program. With a feeling of accomplishment, I would like to express my sincere gratitude and appreciation to the Federal government of Nigeria and particularly to the President and Commander-in-Chief of the Nigerian Armed forces, President Goodluck Ebele Jonathan (GCFR) for initiating the Presidential Scholarship Scheme for Innovation and Development (PRESSID) under which I was fully funded to pursue a Master of Science degree in Mechanical Engineering at MIT. I would also like to thank the PRESSID implementation committee at the National Universities Commission, Abuja for every support that I have received through out this Masters program. Additionally, this thesis was actualized with the academic support provided by my Advisor, Professor Stefano -Brizzolara and other members of the MIT i-Ship group including Luca Bonfigilo and Guliano Vernengo. The experimental part of the thesis carried out at the MIT towing tank was aided by the following research students: Jacob Israelevitz, Jeff Dusek, Amy Gao, and Stephanie Steele. Also, I would like to thank Giovani Diniz, and Heather Beem for their friendliness which really helped me through out the program. Finally, I would like to thank my family especially my parents, Mr. Joel Adebisi Olaoye and Mrs. Oluyemisi Beatrice Olaoye for their moral support in the course of this program.

3

Contents

Title Page

1

Abstract

2

Acknowledgement

3

Table of Contents

4

List of Figures

6

List of Tables

7

List of Symbols

8

1 Introduction

13

1.1

Literature Review ........

.............................

14

1.2

Thesis Objectives ........

.............................

17

2 Theoretical study of Motion of a Floating Body in Waves 2.1

Theory of Ship Motions in Regular Waves

. . . . . . . . . . . . . . .

19

2.1.1

Ship-Motion Strip Theory . . . . . . . . . . . . . . . . . . . .

21

2.1.2

Equations of Motion of a SWATH . . . . . . . . . . . . . . . .

25

2.1.3

Radiation and Diffraction Problems of SWATH Vessels in Regular Waves . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2.1.4

2.2

19

26

Wave Excitation Forces and Moments on SWATH Ships: Strip Theory M ethod . . . . . . . . . . . . . . . . . . . . . . . . . .

28

Second-order Non-linear Forces Acting on Floating Bodies in Waves .

30

4

2.2.1

Added Resistance of Ships in Waves . . . . . . . . . . . . . . .

31

2.2.2

Salvesen's Method for Predicting Added resistance in Waves .

32

2.2.3

Other Methods of Predicting Added Resistance of a Ship in Waves 35

2.2.4

Comparison between the Integrated Pressure Method and Salvesen's M ethod

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2.2.5

Results of Added Resistance Computation for a Series 60 hull

2.2.6

Viscosity effects on the hydrodynamics of an unconventional

SWATH ........ 2.2.7

...

.. .. ..

..

.. ..

..

..

3

Analytical Investigation of the effects of inertial characteristics

Sum m ary

40

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

43

Computational Study of the Motion of a Floating Body in Waves

45

3.1

2D Strip Theory Method (PDSTRIP and CAT 5D) . . . . . . . . . .

46

3.2

3D Potential Flow Solver (WAMIT) . . . . . . . . . . . . . . . . . . .

47

3.3

Numerical Investigation of the Effects of Inertial Characteristics on

3.4

4

37

.. ... ...39

on SWATH RAOs . . . . . . . . . . . . . . . . . . . . . . . . . 2.3

36

motion RAOs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

49

3.3.1

Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

53

Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

54

Experimental Study of the Responses of SWATH USV in Regular Head Waves

55

4.1

The SWATH Model . . . . . . . . . . . . . . . . . . . . . . . . . . . .

55

4.1.1

. . . . . . . . . . . . . . . . . . . . . .

55

4.2

Experimental Set-up . . . . . . . . . . . . . . . . . . . . . . . . . . .

56

4.3

Instrumentation and Procedure

. . . . . . . . . . . . . . . . . . . . .

60

4.3.1

Laser Sensors . . . . . . . . . . . . . . . . . . . . . . . . . . .

60

4.3.2

Data Processing . . . . . . . . . . . . . . . . . . . . . . . . . .

60

Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . .

74

4.4.1

76

4.4

Assembling the Model

D iscussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

5 Conclusion

77

5.1

Summary of Results ........

5.2

Recommendations. . . . . . . . . . . . . . . . . . . . . . . . . . . . .

...........................

78 78

Biblography

79

Appendices

81

List of Figures 2-1

Transverse Section of a Theoretical SWATH Vessel

2-2

Added Drag Versus Encounter Frequency for Series60 with Cb=0.6 at

. . . . . . . . . .

F,=0.283 in Head Waves . . . . . . . . . . . . . . . . . . . . . . . . . 2-3

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

38

Comparison of WAMIT and PDSTRIP Heave RAOs for Series 60 ship with Cb=0.7 at Zero Speed

3-2

38

Added Drag Versus Wavelength for Series60 with Cb=0.7 at Zero Speed in Head Waves

3-1

26

. . . . . . . . . . . . . . . . . . . . . . .

50

Comparison of WAMIT and PDSTRIP Pitch RAOs for Series 60 ship with Cb=0.7 at Zero Speed

. . . . . . . . . . . . . . . . . . . . . . .

50

3-3

Effect of Varying the pitch Gyradius on Heave RAO at Constant VCG

51

3-4

Effect of Varying the pitch Gyradius on Pitch RAO at Constant VCG

51

3-5

Effect of Varying the VCG on Heave RAO at Constant Pitch Gyradius

52

3-6

Effect of Varying the VCG on Pitch RAO at Constant Pitch Gyradius

52

4-1

Profile View of Model during Experiment . . . . . . . . . . . . . . . .

56

4-2

Frontal view of model during experiment . . . . . . . . . . . . . . . .

57

4-3

Plan view of Model during experiment

. . . . . . . . . . . . . . . . .

57

4-4

Heave and Pitch Motion Time History for Wave Test No. 1 . . . . . .

62

4-5


63

6

4-6


64

4-7


65

4-8


66

4-9


67

4-10 Heave and Pitch Motion Time History for Wave Test No. 7 . . . . . .

68


69


70

4-13 Heave and Pitch Motion Time History for Wave Test No. 10 . . . . .

71

4-14 Heave and Pitch Motion Time History for Wave Test No. 11 . . . . .

72

4-15 Cut Heave and Pitch Responses of SWATH USV

73

. . . . . . . . . . .

4-16 Comparison of Experimental and Computational Predictions of Heave Motions of SWATH USV . . . . . . . . . . . . . . . . . . . . . . . . .

74

4-17 Comparison of Experimental and Computational Predictions of Pitch Motions of SWATH USV . . . . . . . . . . . . . . . . . . . . . . . . .

75

List of Tables 4.1

Main Model Parameters

. . . . . . . . . . . . . . . . . . . . . . . . .

58

4.2

Tank Dimensions and Model Test Factors . . . . . . . . . . . . . . . .

58

4.3

Wave Parameters for Different Cases of Model Test . . . . . . . . . .

59

7

THIS PAGE INTENTIONALLY LEFT BLANK

8

List of Symbols aij

- Sectional added mass coefficient

A

- Wave amplitude

Aij

- Added mass coefficient

AW

- Water plane area

bij

- Sectional damping coefficient

Bij (w)

- Damping coefficient

Cb

- Block coefficient

cij

- Sectional restoring coefficient

Cij

- Restoring coefficient

da

- Stern displacement

df

- Bow displacement

F(t)

- Excitation force due to waves

Fi

- Complex amplitude of excitation force

F

- Froude-Krylov force on port side due to waves

FP

- Froude-Krylov force on starboard side due to waves

TFf"

- Hydromechanic force acting in ith direction

(Fji)*

- Complex conjugate of the Froude-Krylov part of the exciting force

Fn

- Froude number

Fs

- Second-order mean steady force

g

- Acceleration of gravity

GML

- Metacentric height

hj (t)

- Harmonic motion of ship in the jth mode of motion

Hij

- Complex analytical function of added mass and damping coefficients

Iij

- Ship's mass moment of inertial for rotational modes of motion

9

k

- Wave number

(Kv)

- Pitch gyradius

11

- Distance between bow sensor and LCG

12

- Distance between stern sensor and LCG

13

- Longitudinal distance between stern sensor and aftmost point of the ship

L

- Length overall of ship

LS

- Distance between sensors

M

- Mass of ship

Paw

- Energy dissipated by the ship during one encountering period

Pi

- Linear hydrodynamic pressure obtained from Bernoulli's equation

R

- Added resistance

RAOmax

- RAO at resonance

R,

- Incident wave contribution to the added drag.

Rf

- Diffraction contribution to the added drag.

R7

- A function of the sectional damping coefficients in heave and sway.

t

- time co-ordinate

UP3

- Wave particle orbital velocity

g3

- Wave orbital acceleration

V

- Velocity vector in two or three dimensions

Vz

- Relative vertical velocity

VCG

- Distance from waterline to center of gravity. Positive above the waterline

w

- Circular wave frequency

we

- Wave encountering frequency

Wn

- Natural Frequency

x

- Longitudinal axis of ship

Xb

- X-coordinate of a given section

y

- Transverse axis of ship

Yb

- Y-coordinate of a given section

10

YO

- Half the distance between center planes

z

- Vertical axis of ship

Zb

- Z-coordinate of a given section

Zb

- Vertical distance between top of bow and CG in deflected position

Zh

- Heave displacement

OP

- Pitch angle

ZS

- Vertical distance between top of stern and CG in deflected position

0

- Angle between direction of wave propagation and ship heading

'Ei

- Phase difference

r1

- Regular wave elevation

7

- Damping ratio

A

- Wavelength

P

- Dynamic viscosity

V

- Spatial derivative

#j

- Radiated wave potential

#0

- Incident wave potential

#7

- Diffraction potential

IT

- 2D time domain linear potential

p

- Density of water

0

- Angular displacement of body

0

- Total fluid potential

OB

- Potential due to body disturbance

0*

- conjugate of the incident wave potential

(j

- Response of ship(in the jth mode of motion) to sinusoidal waves

(j (w)

- Complex amplitude of ship motion in the jth degree of freedom - Ship acceleration

- Ship velocity

11


12

Chapter 1 Introduction The hydrodynamics of floating structures in waves is unique because of the frequency dependence of hydrodynamic parameters such as added mass, damping and the wave exciting force. For a SWATH, the effect of viscosity on the added mass and damping is non-negligible and must be taken into consideration when predicting the motion response of this kind vessels in waves. This paper presents the theoretical, numerical and experimental study of the motion responses of floating bodies in waves with focus on an unconventional SWATH USV proposed to be used to monitor a team of autonomous underwater vehicles (Brizzolara, 2011).

The use of this watercraft is expected to reduce maintenance

costs associated with manned ships and fixed platforms. Additionally, using remotely operated surface vessels such as this would guarantee safety and make very remote areas more readily accessible. The design operations of this vessel involves recharging batteries of AUVs and retrieving the AUVs back to onshore locations. A small version of this vessel can retrieve at least one autonomous vehicle per trip. A literature review of the advancement made in the optimization of this class of water crafts is presented as a basis on which future research is being carried out to study the hydrodynamics of this vessel. The objectives of this thesis are to compute the motion responses of the SWATH USV using 2D and 3D potential flow solvers, report experimental results obtained so far and attempt to validate the numerical results. The importance of this work

13

extends to other classes of multi-hull ships as there exists only few available data in this range of crafts relative to well established mono-hull ships. Additionally, the effect of the inertial characteristics of the model, vertical position of the center of gravity (VCG) and gyradius in pitch (K.) on the RAO is investigated both analytically and numerically.

1.1

Literature Review

Strip theory originally developed by Korvin-Krokowsky and Jacobs (1957) formed the basis of most numerical methods for computing the motions of various kinds of ships in waves. This was further extended to account for wave-induced vertical shear forces and bending moments according to Jacobs (1958). The original strip theory gave very good agreement with experiments especially for regular cruiser stern ships operating at moderate speeds in head waves (Salvesen et. al., 1970). Gerritsma and Beukelman (1967) further extended the method by proposing a modified strip theory which predicts the motions of high speed destroyer hull in head seas very well with respect to experiments. The strip theory method for heave and pitch motions in head waves in which the forward speed terms satisfy the symmetry relationship proved by Timman and Newman (1962) was properly derived independently by Soding (1969), Netsvetayev (1969) and Tasai and Takaki (1969). Following the significant improvements made in the computation of the sectional added mass and damping coefficients using closed-fit methods, Smith and Salvesen (1970) showed that this method can be used to predict the motions of high speed hulls with large bulbous bows in head seas with satisfactory accuracy. Major advancements in the computation of ship hydrodynamics using the strip theory method were proposed in the famous work of Salvesen, Tuck and Faltinsen (1970). Their method can predict satisfactorily the heave, pitch, sway, roll and yaw motions as well as wave-induced vertical and horizontal shear forces and bending moments and torsional moments for a ship advancing at constant forward speed with 14

III

I

I

Pi"op"1111IT IIIP1,11II, I"'I"11 II

I-IIIIIII III II

arbitrary heading in regular sinusoidal waves.

The lateral symmetry of the ship

guarantees that the equations of motion in the six degrees of freedom can be written into two sets of coupled equations of motion as follows: one set of three coupled equations for surge, heave and pitch as well as another set of three coupled equations for sway, roll and yaw. It was proved that in the first set of coupled equations, the surge motion may be neglected if the ship is a slender body in addition to having lateral symmetry.

Hence, the equations of motion in the first set reduces to two

coupled equations for heave and pitch. Of course, the strip method defined assumes that viscous effects are negligible and the assumption is credible because viscous damping is insignificant for vertical ship motions. Soding (1987) further improved the strip theory but the predictions were still limited to linear equations of motion, rigid-body responses to periodic exciting forces and moments due to free surface waves with small slopes. This method also assumes that the ship maintains mean forward speed in infinite water and a straight mean course. The strip theory method offers an immediate insight into the hydrodynamics of a ship saving computational costs at the preliminary design stage. The Numerical implementation of this method has been carried out using two-dimensional and threedimensional approaches. Both approaches give reasonably accurate predictions for the response amplitude operator of the ship motions; however, the latter is more efficient for predicting hydrodynamic pressures and forces. SWATHs are special types of watercrafts which are designed basically to reduce their motions in waves by reducing the water plane area of the sections interacting with surface waves. Hence, SWATHs are generally expected to have better seakeeping performance in waves than equivalent mono-hulls and catamarans. Earlier works on determining the motions and wave loads of SWATHs showed that analytical methods need to account for the effects of wave interaction between the two hulls. Soding (1988) developed a strip theory method that takes this interaction into account and the obtained results are more accurate than those obtained by solving merely the boundary value problem involving two-dimensional twin cylinders. This is because it 15

considers the speed effects on the radiated and diffracted waves between the hulls. Dallinga et. al. (1989) developed a seakeeping program to gain a physical understanding of SWATH motions and described improved prediction methods. Their approach utilizes the 3D diffraction theory as well as empirical information on the associated loads and this was compared with traditional strip theory method. Hullfins interaction and free surface effects was found to be significant and are difficult to estimate using simple methods. In addition, they posited that accurate predictions of the seakeeping of SWATHs will require a more detailed description of the dynamics of the flow around the vessel. A frequency domain based strip theory method developed by Papanikolaou and Schellin (1991) accounts for the effects of forward speed on the hydrodynamic interaction between the hulls. This method gives motion predictions which agrees well the model test measurements and three-dimensional diffraction theory calculations. Brizzolara (2004) used an efficient differential evolution algorithm to implement a parametric design of a SWATH vessel which is optimized for total resistance. The optimized vessel is a variant of the original base vessel characterized by two humps at the bow and stern area and an intermediate hollow shape. This method automatically picks the optimized dimensions SWATH vessel with minimal total resistance. It was demonstrated that the operation profile of a watercraft should play a major role in shaping its hull during design. More advancements in design of SWATHs have focused on reducing wave pattern and added resistance. A major contribution to this development is achieved using the parametric optimization method as demonstrated by Brizzolara and Chryssostomidis (2012).

This approach involves the modification of the submerged hull shape to

maximize wave cancellation effects between both hulls.

Such optimization of the

SWATH ship hulls results in the reduction of total resistance by more than 25 percent at high speeds with respect to a conventional design. The computation of the hydrodynamics of multi-hull ships may or may not include the interaction between objects piercing through the free surface at different locations depending on the sophistication of the method employed. Although, it is important 16

11FOOPm-

to consider this hull interaction effects in SWATHs, its usually good practice to use simple and computationally cheap methods which gives reasonably accurate results at preliminary stages of design (Patrikalakis and Chryssostomidis, 1986).

1.2

Thesis Objectives

The aim of this thesis is to predict the motion of an unconventional SWATH USV in waves using numerical and experimental approaches. There exist three dimensional fully viscous time domain simulations to account for non-linear free surface and viscosity effects but they can be computationally expensive. Hence, it's more efficient to develop quicker hybrid methods which account for these effects especially at early design stages. However, these new methods require sufficient experimental data for validation purposes and to boost the confidence in their applications. Only a few experimental data on the hydrodynamics of SWATHs are available in literature while some substantial numerical results can be found for existing SWATH designs. Moreover, in order to further progress with this work, the computationally predicted better performance of unconventional SWATHs in waves must be validated using experiments. Hence, the need for more experimental results such as those reported in this thesis.

17


18

Chapter 2 Theoretical study of Motion of a Floating Body in Waves The motion of a body in random seas may be computed by the superposition of the responses of the body to each of the constituent elementary waves.

Hence, it

is very useful to study this problem using regular exciting waves which are easy to understand and apply the Wiener-Khinchin theorem to obtain the response of the ship in irregular waves. Another very important simplification is the assumption of potential flow and also the linearization of the free surface boundary condition in terms of the velocity potential. The solution to this problem is achieved by solving the diffraction and the radiation problems as would be discussed in following sections.

2.1

Theory of Ship Motions in Regular Waves

This section discusses the theory of ship motions in the context of input and output into a linear time-invariant (LTI) system as assumed in studying small motions of a ship in the six degrees of freedom. Furthermore, this guarantees that if the input, that is- the exciting wave is sinusoidal, the response of the ship is also sinusoidal with the same frequency but in general, a different amplitude and phase. The magnification factor is otherwise known as the Response Amplitude Operator (RAO). Here, the RAO is a function of frequency but independent of the wave amplitude. This

19

concept as described is known as the linear theory of ship motions and it proves to be accurate for estimating the responses of ships in regular waves and irregular waves of considerable height. The regular wave elevation, q is given as follows:

q(x, y, z, t) = Re{Aew t - kx}

(2.1)

The response of the ship to sinusoidal exciting waves, (j can be expressed as:

(j(t) = Re{y (w)ewt}

(2.2)

The RAO which is the transfer function of the LTI system described above is the ratio of the complex amplitude of the ship motion to the wave amplitude, A. Hence,

RAO =

A

(2.3)

In model testing, the complex amplitude of the ship response is the measured amplitude of oscillation for a given frequency which can be measured using displacement sensors or derived from readings obtained using an accelerometer. Theoretically, the RAO is obtained from the solution of the equation of motion of the ship-water system using the strip theory method described in the next section. The equation of motion of a simple mass-spring system with a dashpot is a linear second-order differential equation and is given as:

M

+ B

+C( = F (t) 20

(2.4)

2.1.1

Ship-Motion Strip Theory

The strip theory is a relatively simple method of computing the forces acting on a submerged slender body by direct integration of the net pressure acting on a piece of length, dx over the entire length of the body. This tranche is generated by "tearing up" the body of the ship into sections also known as stations. Generally, viscous effects are neglected and the flow is assumed to be irrotational. Hence, the linear-ship motion strip theory is framed in the context of the potential flow theory. Also, the ship is considered to be very long compared to its beam, that is, the slender body theory is applied which allows surge motion to be ignored. The slender body theory applied in strip theory makes it possible to compute the exciting force and moment, hydrodynamic coefficients namely added mass and damping of the entire ship from two-dimensional potential flow solution for oscillating cylinders. Also, it is assumed that the disturbance of the free surface is due to the incident wave only. Hence, radiated waves can be ignored. For a ship with forward speed, the encounter frequency is assumed to be high. However, the strip theory gives good prediction for the heave and pitch motions even at low encounter frequencies because the Froude-Krylov force is dominated by the restoring force at low frequencies and is independent of the wave frequency. The strip theory calculations yield the hydrodynamic coefficients, that is, added mass and damping coefficient and the heave and pitch motion values with their corresponding phase relationship. These results are used as input to the formulation for predicting the added drag and must be accurate to ensure reasonable prediction of

the added drag. The hydrodynamic coefficients may be determined using close-fit conformal mapping methods or by considering time harmonic motions of small amplitude for ship motions with the complex factor ei

applied to the periodic quantities as described

below. The total fluid potential around a ship hull using strip theory method is given as:

21

6