1

CHAPTER 1

INTRODUCTION

1.1 General

Ship hull structure is a very important part of ship design as it gives strength to the ship and

accounts for 20% of the total ship are cost. The most important duty of the hull structure design

is to supply a strong enough structure against the internal and external loads.

Motion of ships is a complex hydrodynamics problem that must be analyzed by experimental and

numerical techniques.

Computational fluid dynamics (CFD) are becoming increasingly popular in analyzing flow

problems in almost all branches of engineering, especially in resistance prediction of ships where

complex fluid flow exists.

A ship is mainly divided into three parts:

Hull

Machinery

Superstructure

Fig No. 1.1: Parts of a Ship

The Hull is the outer shell of the ship which is built up by wrapping steel plates around a rolled

steel framed structure. Steel plates may be lapped and riveted or jointed by a fusion welded

process. For structural strength and stiffness the ship is constructed like a girder (a fabricated

beam) which will have enough longitudinal strength to withstand the force of gravity and

buoyancy.

2

The machinery includes the propulsion system, propeller, rudder, anchor etc.

The superstructure consists of deck, bridge and accommodation area.

The performance of the ship of the ship is most influenced by the shape and structure of the Hull.

Types of Hull:

The two general types of hulls are displacement and planing. Other types of hull construction

combine features of the displacement and planing hulls and are called semi-displacement or

semi-planing.

Displacement Hull

Displacement hulls push through the water as they have no hydrodynamic lift, or the boat does

not rise out of the water as speed increases. Some general characteristics of a displacement hull

are:

Rugged construction

Easy to propel through the water at low speeds

Large interior spaces

Fig No.1.2: Displacement Hull

Planing Hull

Planing hulls are designed to run on top of the water at high speeds. To achieve this they

typically have a very flat stern. The hull design (shape) does not limit the maximum attainable

speed but does affect the power required for it to get on plane (on top of the water). Some

general characteristics of a planing hull are:

At high speeds in rough water, the vessel will have a jarring ride as it pounds into waves

and swells

At high speeds, has a tendency to slide sideways in a turn

Tends to roll at rest

Inefficient at low speeds (takes more power to push through the water)

3

Fig No. 1.3: Planing Hull

The displacement hull is a very common hull form and is used for the majority of large shipping

vessels such as freighters, tankers, and cargo carriers. The design of displacement hulls allows

for the most efficient, long distance, safe travel. These vessels move through the water rather

than on top of it. As a displacement hull vessel moves through the water in a plowing motion, it

is the actual hull design doing most of the work. The engines in displacement hull vessels are

quite small compared to the size and weight of the ship. The amount of power being provided by

the engine has no significant effect on the speed of the ship. In fact, the determining factor in the

maximum hull speed of a displacement hull vessel is determined by the square root of the

waterline length. Also the waterlines, or drafts, must indicate the ships loading condition.

1.2 Objective:

It is vital to compute the hydrodynamic performance of the hull, to calculate the engine power,

capable to overcome the hydrodynamic resistance produced by the interaction of the hull with

the flow. Strength analysis of ship makes sure that the ship will be robust in transverse and

longitudinal bending, racking stresses, and stresses due to water pressure. CFD allows ship

designers to create a computer-generated model of a ship and then test the ship at various speeds

in a simulated environment. The result from the CFD simulations is necessary to understand the

complicated flow characteristics for an optimal hull design, which includes a low drag and high

propulsive efficiency. The interest and demand of the industry to implement new methods is one

of the most important reasons that influence the development of CFD.

1.3 Scope of Project:

While it is possible to develop fairly accurate analyses of ship loads and responses by hand, or

using minimal computer help such as spreadsheets, modern CAD computer programs are usually

used today to generate much more detailed and powerful computer models of the structure.

Finite element analysis tools are used to measure the behavior in detail when loads are applied.

These programs can handle much more complex bending and point load calculations than human

engineers are able to do in reasonable amounts of time. However, it is still important to be able to

manually calculate rough behavior of ship hulls. Engineers do not trust the output of computer

programs without some general reality checking that the results are within the expected order of

magnitude. And preliminary designs may be started before enough information on a structure is

available to perform a computer analysis.

4

The integration of computational fluid dynamics (CFD) methods into a wide range of

engineering disciplines is rising sharply, mainly due to the positive trends in computational

power and affordability. One advantage of these methods, when used in the ship industry, is the

large amount of information provided by the solution. The data can be viewed, investigated, and

analysed over and over, after the experiment ends. Furthermore, such virtual solutions can be

created before an actual ship is built and can provide information on hydrodynamic loads on

various areas, flow visualization etc. However, CFD techniques are not sufficiently

comprehensive, and the complementary use of other methods like model tests is the safest

avenue. One of the most important question is how close the equations to be solved simulate the

actual physical conditions. Once the equations (e.g., Euler, full Navier-Stokes, etc.) are selected,

the next question is how well various algorithms approximate these equations and, of course,

which type of solution is affordable from the computational power point of view. Another area of

weakness is the prediction of separation lines, particularly for smooth, moderately curved

surfaces. With sharp edges (as on the side of a rectangular box), flow separation is obvious and

base pressure predictions are better. Also, separated flows and wakes at this Reynolds number

range are time dependent and unsteady models are needed to capture the larger-scale flow

structures.

CFD has become an important tool for studying the flow over complex configuration such as a

ship. It can be used as a preliminary design tool or to complement experimental methods. In

conclusion, CFD is very useful in the preliminary design phase. It is a powerful tool for

providing valuable flow visualizations. Its advantage also lies in the fact that the results can be

viewed over and over again and new aspects of the solution can be investigated. We are going to

perform CFD analysis on Wigley Parabolic Hull and Series 60 (Cargo) Hull. These are the most

extensively used Hulls in the Ship Industry. The comparison of these two Hull forms will be

based on criterias like hydrodynamic lift, wave drag, viscous drag and Froude number.

This project provides a study of following topics:

1. Strength analysis of ship hull (Using FEA and analytical methods)

2. Flow analysis using Fluent for different hull forms (Series 60 and Wigley Hull).

3. Design Optimization of Series 60 Cargo ship hull using CFD techniques.

4. Identifying effects of variables on performance of ships

5

CHAPTER 2

LITERATURE REVIEW

Ship Flow Co-ordinate System:

The coordinate system (x, y, z) for calculating the viscous drag and the wave making drag is

defined to represent the flow patterns around hull form as positive x in the opposite flow

direction, positive y in port side and positive z upward where the origin at the aft perpendicular

of the hull form, as shown in fig.

Fig No. 2.1: Ship Co-ordinate system

The greatest stresses set up in the ship as a whole are due to the distribution of loads along the

ship, causing longitudinal bending which is further divided into still water bending and wave

bending.

Transverse bending occurs as a result of the forces due to the weights of the ship structure,

machinery, fuel, water and cargo, water pressure.

Water Pressure is exerted on the bottom and side shell by the water surrounding the ship, thus

thicker double bottom and side shell plating and frames are designed to withstand these forces.

Fig No. 2.2: Hogging and Sagging

6

Fig No. 2.3: Racking Stresses Fig No. 2.4: Water Pressure Stresses

Fig No. 2.5: Buoyancy, Weight, Bending Moment and Shear curves along length of ship

7

Excluding inertia loads due to ship motion, the loading on a ship derives from only two sources,

gravity and water pressure. It is impossible to conceive a state of the sea whereby the loads due

to gravity and water pressure exactly cancel each other out along the ship’s length. Even in still

water, it is exceedingly unlikely and in a seaway where the loading changes continuously, it is

inconceivable. There is therefore an uneven loading along the ship, and because it is an elastic

structure, it bends as a whole unit.

In still water, the loading due to gravity and water pressure are weight and buoyancy. The net

force decides whether the ship will hog or sag. The hog and sag of a ship can be much increased

by waves. A long wave with crest amidships would increase the forward upward force at the

expense of the ends and hogging will be increased. If there were a hollow amidships, and crest

towards the ends, sagging will be increased.

8

CHAPTER 3

STRENGTH ANALYSIS

3.1 Concepts

The purpose of this analysis is to present the fundamentals of direct ship structure analysis based

on mechanics and strength of materials. Such analysis allows a rationally based design that is

practical, efficient, and versatile, and that has already been implemented in a computer program,

tested, and proven.

Analysis refers to stress and strength assessment of the structure. Analysis requires information

on loads and needs an initial structural scantling design. Output of the structural analysis is the

structural response defined in terms of stresses, deflections and strength. Then, the estimated

response is compared to the design criteria. Results of this comparison as well as the objective

functions (weight, cost, etc.) will show if updated (improved) scantlings are required.

Ship structural design is a challenging activity. The complexities of modern ships and the

demand for greater reliability, efficiency, and economy require a scientific, powerful, and

versatile method for their structural design.

Ship structural analysis and design is a matter of compromises:

Compromise between accuracy and the available time to perform the design. This is

particularly challenging at the preliminary design stage. A 3D Finite Element Method (FEM)

analysis would be welcome but the time is not available. For that reason, rule-based design or

simplified numerical analysis has to be performed.

To limit uncertainty and reduce conservatism in design, it is important that the design

methods are accurate. On the other hand, simplicity is necessary to make repeated design

analyses efficient. The results from complex analyses should be verified by simplified

methods to avoid errors and misinterpretation of results (checks and balances).

Compromise between weight and cost or compromise between least construction cost, and

global owner live cycle cost (including operational cost, maintenance, etc.)

Builder optimum design may be different from the owner optimum design.

Rationally Based Structural Design versus Rules-Based Design:

There are basically two schools to perform analysis and design of ship structure. The first one,

the oldest, is called rule-based design. It is mainly based on the rules defined by the

classification societies.

In the past, ship structural design has been largely empirical, based on accumulated experience

and ship performance, and expressed in the form of structural design codes or rules published by

the various ship classification societies. These rules concern the loads, the strength and the

design criteria and provide simplified and easy-to-use formulas for the structural dimensions, or

“scantlings” of a ship. This approach saves time in the design office and, since the ship must

obtain the approval of a classification society, it also saves time in the approval process.

9

The second school is the Rationally Based Structural Design; it is based on direct analysis.

There are several disadvantages to a completely “rulebook” approach to design. First, the modes

of structural failure are numerous, complex, and interdependent. With such simplified formulas

the margin against failure remains unknown; thus one cannot distinguish between structural

adequacy and over-adequacy. Second, and most important, these formulas involve a number of

simplifying assumptions and can be used only within certain limits. Outside of this range they

may be inaccurate. For these reasons there is a general trend toward direct structural analysis.

Even if direct calculation has always been performed, design based on direct analysis only

became popular when numerical analysis methods became available and were certified.

Direct analysis has become the standard procedure in aerospace, civil engineering and partly in

offshore industries.

Ships are very complex structures compared to other structures. They are subject to a very wide

range of loads in the harsh environment of the sea. Progress in technologies related to ship

design and construction is being made daily, at an unprecedented pace. The efforts of a majority

of specialists together with rapid advances in computer and software technology have now made

it possible to analyze complex ship structures in a practical manner using structural analysis

techniques centering on FEM analysis. The majority of ship designers strive to develop rational

and optimal designs based on direct strength analysis methods using the latest technologies in

order to realize the ship owner’s requirements in the best possible way.

When carrying out direct strength analysis in order to verify the equivalence of structural

strength with rule requirements, it is necessary for the classification society to clarify the strength

that a hull structure should have with respect to each of the various steps taken in the analysis

process, from load estimation through to strength evaluation. In addition, in order to make this a

practical and effective method of analysis, it is necessary to give careful consideration to more

rational and accurate methods of direct strength analysis. Based on recognition of this need,

extensive research has been conducted and a careful examination made, regarding the strength

evaluation of hull structures.

Modeling and Analysis

General guidance on the modeling necessary for the structural analysis is that the structural

model shall provide results suitable for performing buckling, yield, fatigue and vibration

assessment of the relevant parts of the vessel. This is done by using a 3D model of the whole

ship, supported by one or more levels of sub models. Several approaches may be applied such as

a detailed 3D model of the entire ship or coarse meshed 3D model supported by finer meshed

sub models. Coarse mesh can be used for determining stress results suited for yielding and

buckling control but also to obtain the displacements to apply as boundary conditions for models

with the purpose of determining the stress level in more detail. Strength analysis covers yield

(allowable stress), buckling strength and ultimate strength checks of the ship.

10

The hydrodynamic load model must give a good representation of the wetted surface of the ship,

both with respect to geometry description and with respect to hydrodynamic requirements.

The mass model, which is part of the hydrodynamic load model, must ensure a proper

description of local and global moments of inertia around the global ship axes. Ultimate

hydrodynamic loads from the hydrodynamic analysis should be combined with static loads in

order to form the basis for the yield, buckling and ultimate strength checks. All the relevant load

conditions should be examined to ensure that all dimensioning loads are correctly included.

Fig No. 3.1: Flow chart of strength analysis of global model and sub models

Loads

Loads acting on a ship structure are quite varied and peculiar, in comparison to those of static

structures and also of other vehicles. In the following an attempt will be made to review the main

typologies of loads: physical origins, general interpretation schemes, available quantification

procedures and practical methods for their evaluation will be summarized.

11

Classification of Loads

a. Based on Time Duration

Static loads: These are the loads experienced by the ship in still water. They act with time

duration well above the range of sea wave periods. Being related to a specific load condition,

they have little and very slow variations during a voyage (mainly due to changes in the

distribution of consumables on board) and they vary significantly only during loading and

unloading operations.

Quasi-static loads: A second class of loads includes those with a period corresponding to wave

actions (~ 3 to15 seconds). Falling in this category are loads directly induced by waves, but also

those generated in the same frequency range by motions of the ship (inertial forces). These loads

can be termed quasi-static because the structural response is studied with static models.

Dynamic loads: When studying responses with frequency components close to the first structural

resonance modes, the dynamic properties of the structure have to be considered. This applies to a

few types of periodic loads, generated by wave actions in particular situations (springing) or by

mechanical excitation (main engine, propeller). Also transient impulsive loads that excite free

structural vibrations (slamming, and in some cases sloshing loads) can be classified in the same

category.

High frequency loads: Loads at frequencies higher than the first resonance modes (> 10-20 Hz)

also are present on ships: this kind of excitation, however, involves more the study of noise

propagation on board than structural design.

Other loads: All other loads that do not fall in the above mentioned categories and need specific

models can be generally grouped in this class. Among them are thermal and accidental loads.

A large part of ship design is performed on the basis of static and quasi-static loads, whose

prediction procedures are quite well established, having been investigated for a long time.

However, specific and imposing requirements can arise for particular ships due to the other load

categories.

Fig No. 3.2: Static Forces acting on ship

b. Based on Local and Global loads

Another traditional classification of loads is based on the structural scheme adopted to study the

response. Loads acting on the ship as a whole, considered as a beam (hull girder), are named

global or primary loads and the ship structural response is accordingly termed global or primary

response.

12

Loads, defined in order to be applied to limited structural models (stiffened panels, single beams,

plate panels), generally are termed local loads. The distinction is purely formal, as the same

external forces can in fact be interpreted as global or local loads. For instance, wave dynamic

actions on a portion of the hull, if described in terms of a bi-dimensional distribution of pressures

over the wet surface, represent a local load for the hull panel, while, if integrated over the same

surface, represent a contribution to the bending moment acting on the hull girder. This

terminology is typical of simplified structural analyses, in which responses of the two classes of

components are evaluated separately and later summed up to provide the total stress in selected

positions of the structure. In a complete 3D model of the whole ship, forces on the structure are

applied directly in their actual position and the result is a total stress distribution, which does not

need to be decomposed.

Fig No. 3.3: Concept of Buoyancy

13

The most important consideration is the longitudinal strength of the hull girder. The hull girder

feels vertical forces due to weight and buoyancy. For any floating body the total weight must

equal the total buoyancy, and both forces must act along the same line of action. However, at

each location along the ship, the weight will not normally equal the buoyancy. The weights are

set by the combination of lightship and cargo weights. The locations of the weights are fixed

(more or less). The buoyancy forces are determined by the shape of the hull and the location of

the vessel in the water (draft and trim). The net buoyancy will adjust itself until it exactly

counteracts the net weight force. However, this does not mean that each part of the vessel has a

balance of weight and buoyancy. Local segments of the vessel may have more or less weight

than the local buoyancy. The difference will be made up by a transfer of shear forces along the

vessel.

3.2 Model Analysis using FEA

Problem Setup:

• Ship specifications: Cargo Ship with Length = 159m, Breadth = 16.8m, Height = 14.4 m

• Ship carrying capacity: 20,000 tonne

• Bending moment: 7742 tonne m

The Strength Analysis was performed on Ansys Workbench.

The following is the procedure:

1. CAD model generation

Fig No. 3.4: CAD model of cargo ship

14

2. Mesh generation in Ansys

Nodes: 12848

Elements: 6741

Fig No. 3.5: Mesh generated in ANSYS

3. Set up of Loads, Moments and Fixed Supports

Load: 20000 tonne of cargo load acting on ship.

Moment: Forces of 1.19e6 N applied at two ends to model the bending moment of

7742 tonne m acting on ship.

Fixed Support: Edge faces at the two ends of ship fixed.

Fig No. 3.6: Application of Forces

4. Results

Max. stress generated: 87 MPa at the keel

15

Fig No. 3.7: Equivalent Stress(Von-Mises)

3.3 Analytical Strength Analysis

Fig No. 3.8: General arrangement of sections along the ship hull section

16

For performing the analytical strength analysis, the following model was used:

Fig No. 3.9: Analytical Strength Analysis Model

Lin proposed the dynamic relaxation method to derive the reduction factor of the ultimate

strength of a plate with stiffeners and adopted the beam column element to analyze the strength

of ship structure. Among them, the width of a plate was considered effective along with the

section of the plate with stiffeners. The numerical calculation results are obtained by two

parameters, the slender ratios of a stiffener, λs, and of a plate, β, respectively. By using the least

square method, the reduction factor containing the two parameters can be formulated by:

Lin’s reduction formula:

where

Specification of plate used:

Thickness of

plate

(t mm)

Yielding stress

(σy)

Kg/mm2

Young’s modulus

E (Kg/mm2)

Poisson’s ratio

v

3.05 29.3 2.11 X 104 0.277

Table No. 1: Plate Specification

17

For the problem at hand:

a = 540 mm, b = 180 mm, t = 3.05 mm

λs = 0.64

β = 2.199

and c1 = 0.960, c2 = 0.765, c3 = 0.176, c4 = 0.131, c5 = 1.046 (defined constants)

φu = 0.625

Lin’s empirical formula:

Where MVUS - Ultimate vertical bending moment

MP - Total Vertical bending moment of all I-sections used

Thus,

MVUS/ MP = 0.605175

Now, the I-section considered is:

Fig No. 3.10: I – Section implemented

Moment of inertia = 435861 mm4

MP (for one section) = 12.77 tonne m

MP (total for eight sections) = 102 tonne m

MVUS = 61.2 tonne m

18

Result Validation:

A comparison of the experimental data values and Lin’s empirical formula for ultimate vertical

bending moment is as shown:

Experimental data

(ton-m)

Lin’s empirical formula

(ton-m)

% Deviation

58.8 61.2 4 %

Table No. 2: Strength model result validation

The percentage deviation of the values = (61.2-58.8)/58.8 X 100 = 4 %

Hence, this method is suitable for preliminary strength analysis of ship structure due to its accuracy and

simplicity.

3.4 Strength Improvement Example:

In this topic, we have improved the strength of an existing ship hull structure.

Fig No. 3.11: Initial Model

Problem setup:

I = 2.3970 X 108

cm4

Deck: 5 m

Keel: 6 m

E steel: 207 GPa

Bending Moment: 7742 ton m

Added Structure:

• Side Plating: 3.4 m X 10 mm stiffened by one 26 cm2 girder

• Deck plating: 16.8 m X 10 mm stiffened by five 26 cm2 girders

Fig No. 3.12: Improved Model

19

Item A (cm2) h (m) Ah (cm

2 m) Ah

2 (cm

2 m

2) k

2 (m

2) Ak

2 (cm

2 m

2)

Two sides 680 1.7 1156 1965 0.44 202

Two side

girders

52 1.7 88 150 0 0

Deck 1680 3.4 5712 19421 0 0

Five deck

girders

130 3.32 431 1433 0 0

2542 h = Ah/A

= 2.9

7387 22969 0 202

Table No. 3: Area of sections used

New effective area: 4520 + 2542/3 = 5367 cm2

Movement of N.A = 2542 X (5+2.9) / 3 / 5367 = 1.25 m

I old N.A = 77450 cm2 m2

I new N.A = 69063 cm2 m2

Initial Design Stresses:

σkeel = 7742 X 100 X 600/ (2.3970 X 108) = 190 MPa

σdeck = 7742 X 100 X 500/ (2.3970 X 108) = 161 MPa

Improved design stresses:

σkeel = 7742 X 100 X 725/ (6.9063 X 108) = 82 MPa

σdeck = 7742 X 100 X 375/ (6.9063 X 108) = 42 MPa

3.5 Strength Limits specified by IACS

The International Association of Classification Societies (IACS) is a technically based

organization consisting of thirteen marine classification societies headquartered in London.

Marine classification is a system for promoting the safety of life, property and the environment

primarily through the establishment and verification of compliance with technical and

engineering standards for the design, construction and life-cycle maintenance of ships, offshore

units and other marine-related facilities. These standards are contained in rules established by

each Society. IACS provides a forum within which the member societies can discuss, research

and adopt technical criteria that enhance maritime safety.

20

The minimum midship section modulus at deck and keel for ships 90 m < L < 500 m

and made of hull structural steel is

Block coefficient Cb :

The block coefficient Cb is the moulded block coefficient at draught d corresponding to

waterline, based on rule length L and moulded breadth B:

Cb = moulded displacement [m3 ] at draught

LBd

Longitudinal Strength Standard:

This requirement applies only to steel ships of length 90 m and greater in unrestricted service.

1.Loads

1. a Still water bending moment and shear force

Still water bending moments, Ms (kN-m), and still water shear forces, Fs (kN), are to be

calculated at each section along the ship length for design cargo and ballast loading

conditions.

21

For these calculations, downward loads are assumed to be taken as positive values, and are

to be integrated in the forward direction from the aft end of L.

Fig No. 3.13: The sign conventions of Ms and Fs

Design loading conditions:

In general, the following design cargo and ballast loading conditions, based on amount of

bunker, fresh water and stores at departure and arrival, are to be considered for the Ms and

Fs calculations. Where the amount and disposition of consumables at any intermediate stage

of the voyage are considered more severe, calculations for such intermediate conditions are

to be submitted in addition to those for departure and arrival conditions. Also, where any

ballasting and/or deballasting is intended during voyage, calculations of the intermediate

condition just before and just after ballasting and/or deballasting any ballast tank are to be

calculated.

1. b Wave loads

1. b.i Wave bending moments

The wave bending moments, Mw, at each section along the ship length are given by the

following formulae:

Mw (+) = +190MCL2BCb x 10

-3 ( kN - m) For positive moment

Mw (+) = −110 MCL2B(Cb+0.7) x 10

-3 (kN - m) For negative moment

Where,

M = Distribution factor

C = 10.75 – [ 300 – L ]1.5

for 90 ≤ L ≤ 300

100

or 10.75 for 300 ≤ L ≤ 350

L = Length of the ships in metres

B = Greatest moulded breadth in metres

Cb = Block coefficient

22

Fig No. 3.14: Distribution Factor vs Length along ship

1. b.ii Wave shear force

The wave shear forces, Fw, at each section along the length of the ship are given by the

following formulae:

Fw (+) = +30F1CLB (Cb+ 0.7) x 10-2

(kN) For positive shear force

Fw (+) = -30F2CLB (Cb+ 0.7) x 10-2

(kN) For negative shear force

Where, F1, F2 – Distribution factors given in following fig.

Fig No. 3.15: F1 vs Length along ship

23

Fig No. 3.16: F2 vs Length along ship

2. Bending Strength

2. a Section modulus

Hull section modulus, Z, calculated, is not to be less than the values given by the following

formula in way of 0.4 L midships for the still water bending moments Ms and the wave bending

moments Mw given, respectively:

IMs + Mw I x 10-3 (cm3) σ Where,

σ = permissible bending stress = 175/k (N/mm2)

k = 1.0 for ordinary hull structural steel

2. b Moment of inertia

Moment of inertia of hull section at the midship point is not to be less than

Imin = 3CL 3B (Cb+ 0.7) (cm

4)

The main loads applied on the hull structure are buoyancy and weight which are forces in the

vertical direction. Against these vertical loads, the vertical members such as side shell plates,

transverse bulkheads and longitudinal bulkheads form the strength of hull structure. In other

words it can be said that the strength of the hull structure as a whole is maintained principally by

the shearing strength of the side shell plates, transverse bulkheads and longitudinal bulkheads.

Accordingly, for the larger ships, to increase the number of transverse bulkheads as well as

increasing the thickness of side shell plates, transverse and longitudinal bulkheads plates are

desirable. Also, construction of a double hull structure is considered to be very effective.

24

CHAPTER 4

FLOW ANALYSIS

4.1 Introduction to ANSYS FLUENT

ANSYS FLUENT is a comprehensive computer program for modeling fluid flow, heat transfer,

and chemical reactions in complex geometries.

ANSYS FLUENT is written in the C computer language and makes full use of the flexibility and

power offered by the language. Consequently, true dynamic memory allocation, efficient data

structures, and flexible solver control are all possible. In addition, ANSYS FLUENT uses a

client/server architecture, which allows it to run as separate simultaneous processes on client

desktop workstations and powerful computer servers. This architecture allows for efficient

execution, interactive control, and complete flexibility between different types of machines or

operating systems.

ANSYS FLUENT provides complete mesh flexibility, including the ability to solve flow

problems using unstructured meshes that can be generated about complex geometries with

relative ease. Supported mesh types include 2D triangular/quadrilateral, 3D

tetrahedral/hexahedral/pyramid/wedge/polyhedral, and mixed (hybrid) meshes.

ANSYS FLUENT also allows you to refine or coarsen your mesh based on the flow solution.

After a mesh has been read into ANSYS FLUENT, all remaining operations are performed

within ANSYS FLUENT. These include setting boundary conditions, defining fluid properties,

executing the solution, refining the mesh, and post processing and viewing the results.

The ANSYS FLUENT serial solver manages file input and output, data storage, and flow field

calculations using a single solver process on a single computer. ANSYS FLUENT also uses a

utility called cortex that manages ANSYS FLUENT’s user interface and basic graphical

functions. ANSYS FLUENT’s parallel solver allows you to compute a solution using multiple

processes that may be executing on the same computer, or on different computers in a network.

Parallel processing in ANSYS FLUENT involves an interaction between ANSYS FLUENT, a

host process, and a set of compute-node processes. ANSYS FLUENT interacts with the host

process and the collection of compute nodes using the cortex user interface utility.

Fig No. 4.1: Interaction between cortex, solver and disk

25

Program Capabilities

The ANSYS FLUENT solver has the following modeling capabilities:

• 2D planar, 2D axisymmetric, 2D axisymmetric with swirl (rotationally symmetric), and 3D

flows

• Quadrilateral, triangular, hexahedral (brick), tetrahedral, prism (wedge), pyramid, polyhedral,

and mixed element meshes

• Steady-state or transient flows

• Incompressible or compressible flows, including all speed regimes (low subsonic,

transonic, supersonic, and hypersonic flows)

• Inviscid, laminar, and turbulent flows

• Newtonian or non-Newtonian flows

• Ideal or real gases

• Heat transfer, including forced, natural, and mixed convection, conjugate (solid/fluid)

heat transfer, and radiation

• Free surface and multiphase models for gas-liquid, gas-solid, and liquid-solid flows

• Phase change model for melting/solidification applications

• Porous media with non-isotropic permeability, inertial resistance, solid heat conduction,

and porous-face pressure jump conditions

• Lumped parameter models for fans, pumps, radiators, and heat exchangers

• Inertial (stationary) or non-inertial (rotating or accelerating) reference frames

• Multiple reference frame (MRF) and sliding mesh options for modeling multiple moving

frames

• Mixing-plane model for modeling rotor-stator interactions, torque converters, and similar

turbomachinery applications with options for mass conservation and swirl conservation

• Dynamic mesh model for modeling domains with moving and deforming mesh

• Volumetric sources of mass, momentum, heat, and chemical species

• Material property database

• Extensive customization capability via user-defined functions

ANSYS FLUENT is ideally suited for incompressible and compressible fluid-flow simulations

in complex geometries. ANSYS FLUENT’s parallel solver allows to compute solutions for cases

with very large meshes on multiple processors, either on the same computer or on different

computers in a network. ANSYS, Inc. also offers other solvers that address different flow

regimes and incorporate alternative physical models. Additional CFD programs from ANSYS,

Inc. include ANSYS CFX, Airpak, ANSYS Icepak, and ANSYS POLYFLOW.

26

All CFD codes contain three main elements: (1) A pre-processor, which is used to input the

problem geometry, generate the grid, define the flow parameter and the boundary conditions to

the code. (2) A flow solver, which is used to solve the governing equations of the flow subject to

the conditions provided. There are four different methods used as a flow solver: (i) finite

difference method; (ii) finite element method, (iii) finite volume method, and (iv) spectral

method. (3) A post-processor, which is used to massage the data and show the results in

graphical and easy to read format.

Element Form:

Various forms of elements can be used. However, the most common type in CFD programs is a

hexahedron with eight nodes, one at each corner, and this is known as a brick element or volume.

For two-dimensional applications the equivalent element is a four-noded quadrilateral. Some

finite volume programs have now been released which have the ability to use tetrahedral in three

dimensions or triangles in two dimensions. Most finite element CFD codes will allow these

elements to be used together with a small range of other element types. The figure below shows

some of the commonly used sub-domains. Before generating the mesh, we should know

something about the flow behavior. For instance, where in the flow field we have boundary

layers, vortices, large gradients in pressure or velocity, etc. The mesh size and shape should be

such that it can capture the proper physical conditions that occur in the flow. For regions where

large gradients exist,

Fig No. 4.2: Typical computational elements

The ANSYS FLUENT- based fluid flow analysis system, is composed of various cells

(Geometry, Mesh, etc.) that represent the work flow for performing the analysis. ANSYS

Workbench is composed of multiple data-integrated (e.g., ANSYS FLUENT) and native

applications into a single, seamless project flow, where individual cells can obtain data from and

provide data to other cells. As a result of this constant flow of data, a cell's state can quickly

change. ANSYS Workbench provides visual indications of a cell's state at any given time via

icons on the right side of each cell.

27

4.2 Analysis of Series-60 cargo ship Hull (Without bulb)

Drag analysis based on CFD (computational Fluid Dynamics) simulation has become a decisive

factor in the development of new, economically efficient and environment friendly ship hull

forms. In this analysis 3D Finite Volume Method has been applied to determine the drag

coefficient. The numerical solutions of the governing equations have been obtained using

commercial CFD software package FLUENT 6.3.

Basic Flow Chart for CFD Analysis on ship hull

Fig No. 4.3: Flow Chart for CFD Analysis

3D model Generation using CATIA

Grid Generation

Basic Design of Ship Hull

Problem Setup

Calculation through iterations

Performance evaluation

Design Validation

Prototype Design

28

Steps Performed:

3D Model Generation:

3D Model was generated in CATIA V5

Fig No. 4.4: CAD model of Cargo Ship

Control Volume generation using boolean operation:

Dimensions: Length-70m Breadth-40m Height-10m

Fig No. 4.5: Enclosure

Mesh Generation:

Type of mesh- Cutcell

The Cutcell meshing algorithm due to the large fraction of hex cells in the mesh, produces better

results than tetrahedral methods. The Cutcell method uses a patch independent volume meshing

approach (surface mesh automatically created from boundary of volume mesh) without the need

for manual geometry cleanup or decomposition, thereby reducing the turnaround time required

for meshing.

29

Number of nodes: 274818, Number of elements: 226920

In CFD applications, the difficulty in mesh generation is a serious complication for utilizing

maximum efficiency. In case of mesh generation around a ship hull special care and experience

was required, because of the delicate and rapidly changing surfaces. In the present study, we

extended the application further and executed resistance and ship hull interaction tests using

structured meshing.

Fig No. 4.6: Intel, Outlet & Iso-surface

Problem setup

Pressure based, Transient, and gravity effect have been included in the setup.

Multiphase Model (VOF): The VOF model is a surface-tracking technique applied to a fixed

Eulerian mesh. It is designed for two or more immiscible fluids where the position of the

interface between the fluids is of interest. In the VOF model, a single set of momentum equations

is shared by the fluids, and the volume fraction of each of the fluids in each computational cell is

tracked throughout the domain.

Fig No. 4.7: Dialog Boxes in Setup for selecting Model

30

Boundary Conditions:

Inlet: Mass flow inlet

Outlet: Pressure outlet

Ship surface: Wall

Top, bottom and sides of enclosure: Symmetry

Mass flow rate for air = density x velocity x area = 1.225 x 4 x 212 = 1033 kg/s

Mass flow rate for water = density x velocity x area = 998 x 4 x 188 = 750429 kg/s

Fig No. 4.8: Dialog Box for Boundary Condition

31

Solution Methods:

The following solution methods were incorporated:

Scheme: Coupled

Gradient: Least Squares Cell based

Pressure: Body force weighted

Momentum: Second Order upwind

Volume fraction: BGM

Turbulent Kinetic Energy: First order upwind

Pseudo transient: ON

High order term relaxation: ON

Fig No. 4.9: Dialog Box for Solution Method to be used

32

Monitors:

Drag: Plot and Write to file

Lift: Plot and Write to file

Iso-surface was created at water free surface level for better flow visualization

At the end of each solver iteration, the residual sum for each of the conserved variables is

computed and stored, thus recording the convergence history. This history is also saved in the

data file. The residual sum is defined below.

On a computer with infinite precision, these residuals will go to zero as the solution converges.

On an actual computer, the residuals decay to some small value ("round-off'') and then stop

changing ("level out''). For single-precision computations (the default for workstations and most

computers), residuals can drop as many as six orders of magnitude before hitting round-off.

Double-precision residuals can drop up to twelve orders of magnitude.

Fig No. 4.10: Dialog Box of Monitors

33

Solution Initialization:

The Standard Initialization Method was selected and the Relative to Cell Zone reference frame

was implemented.

For flat open channel initialization from the pressure outlet boundary, the hydrostatic pressure

profile based on the Free Surface Level is patched in the domain. The volume fraction in the

domain is patched based on Free Surface Level provided at the pressure outlet boundary. The

pressure which is patched is the hydrostatic pressure based on the free surface level specified in

the selected zone.

Fig No. 4.11: Dialog Box for Solution Initialization

34

Run Calculation:

The time step method used was user specified and the pseudo time step of 0.01 s was selected for

better accuracy.

The total number of iterations required for our model was 3000 for the solution to converge.

Reporting interval of one iteration was chosen for good awareness of change of variables.

Fig No. 4.12: Run Calculation Dialog Box

35

Reports:

Residual history can be displayed using an XY plot. The abscissa of the plot corresponds to the

number of iterations and the ordinate corresponds to the log-scaled residual values.

Fig No. 4.13: Dialog Box for selecting reports to display

Fig No.4.14: GUI of ANSYS WORKBENCH (Fluent)

36

3.3 Analysis of Tug Boat (Wigley Hull):

Wigley Hull is a simplified form of Hull which can be defined mathematically. It is use in

hydrodynamic studies and in optimization processes.

A Tug Boat is an example of Wigley Hull.

3D Model Generation:

3D Model was generated in CATIA V5

Fig No. 4.15: CAD model Tugboat

Control Volume generation using boolean operation:

Dimensions: Length-100m, Breadth-60m, Height-30m

Fig No. 4.16: Enclosure

Mesh generation:

Type of mesh- Cutcell

Number of nodes: 534107, Number of elements: 475180

37

Fig No. 4.17: Mesh

Boundary Conditions:

Inlet: Mass flow inlet

Outlet:

Ship surface: Wall

Upper, Lower, and sides: symmetry

Mass flow rate for air: 4410 kg/s

Mass flow rate for water: 3592800 kg/s

Solution Methods:

Scheme: Coupled

Gradient: Least Squares Cell based

Pressure: Body force weighted

Momentum: Second Order upwind

Volume fraction: BGM

Turbulent Kinetic Energy: First order upwind

Monitors:

Drag: Plot and Write to file

Lift: Plot and Write to file

Iso-surface created at water free surface level created for better flow visualization

38

CHAPTER 5

DESIGN OPTIMIZATION OF SHIP HULL SHAPE

5.1 Importance of Bulbous Bow

A bulbous bow is a protruding bulb at the bow (or front) of a ship just below the waterline. The

bulb modifies the way the water flows around the hull, reducing drag and thus increasing speed,

range, fuel efficiency, and stability. Large ships with bulbous bows generally have a twelve to

fifteen percent better fuel efficiency than similar vessels without them.Thus large vessels that

cross large bodies of water near their best speed will benefit from a bulbous bow. This would

include naval vessels, cargo ships, passenger ships, tankers and supertankers.

In a conventionally shaped bow, a bow wave forms immediately before the bow. When a bulb is

placed below the water ahead of this wave, water is forced to flow up over the bulb. If the trough

formed by water flowing off the bulb coincides with the bow wave, the two partially cancel out

and reduce the vessel's wake. While another inducing wave stream saps energy from the ship,

canceling out the second wave stream at the bow changes the pressure distribution along the hull,

thereby reducing wave resistance. The effect that pressure distribution has on a surface is known

as the form effect.

The water flowing over the bulb depresses the ship's bow and keeps it trimmed better. Since

many of the bulbous bows are symmetrical or even angled upwards which would tend to raise

the bow further, the improved trim is likely a by-product of the reduced wave action as the vessel

approaches hull speed, rather than direct action of water flow over the bulb.

The addition of a bulb to a ship's hull increases its overall wetted area. As wetted area increases,

so does drag. At greater speeds and in larger vessels it is the bow wave that is the greatest force

impeding the vessel's forward motion through the water. For a vessel that is small or spends a

great deal of its time at a slow speed, the increase in drag will not be offset by the benefit in

damping bow wave generation. As the wave counter effects are only significant at the vessel's

higher range of speed, bulbous bows are not energy efficient when the vessel cruises outside of

these ranges, specifically at lower speeds.

Fig No. 5.1: Wave Interaction with Bulbous Bow

39

5.2 Analysis on Series 60 cargo ship hull with bulb and improved geometry:

To enable comparison to the earlier Series 60 model analyzed, the 3D model was modified to

include the bulb and the geometry at the front was improved

3D model Generation:

Fig No. 5.2: CAD model with Bulbous Bow

Mesh Generation

Number of nodes: 526299, Number of elements: 457347

Fig No. 5.3: Mesh

The entire problem setup including Boundary Conditions, Solution Methods and Monitors

remain same as the one used in Series-60 cargo ship Hull (Without bulb).

40

CHAPTER 6

RESULTS AND DISCUSSION

6.1 Series 60 cargo ship hull without bulb :-

Drag Coefficient obtained: Cd = 0.569

Fig No. 6.1: Graph – Drag Co-efficient

Elevation plot in vertical axis along Water Surface:

Fig No. 6.2: Elevation Plot

41

Elevation profile at Fore:

Fig No. 6.3: Elevation Plot at Fore

Elevation profile at Bottom:

Fig No. 6.4: Elevation Plot Bottom

42

Streamlines at the Fore:

Fig No. 6.5: Streamlines at front

Streamlines at the Rear:

Fig No. 6.6: Streamlines at rear

43

Streamline is a tool used in CFD to visualize the velocity field. Knowledge of the streamlines

can be useful in fluid dynamics. The curvature of a streamline is related to the pressure gradient

acting perpendicular to the streamline. The center of curvature of the streamline lies in the

direction of decreasing radial pressure.

Streamlines help designers to identify areas where the curvature of model can be changed to

reduce drag.

6.2 Tug Boat (Wigley Hull):-

Drag Coefficient obtained: Cd = 0.348

Fig No. 6.7: Graph – Drag Co-efficient

Elevation plot in vertical axis along Water Surface:

Fig No. 6.8: Elevation

44

Elevation profile at Fore:

Fig No. 6.9: Elevation at Fore

Frictional Resistance force obtained: 21.43 kN

Streamlines at the Fore:

Fig No. 6.10: Streamlines at fore

45

Streamlines at the Rear:

Fig No. 6.11: Streamlines at rear

Pressure Contours:

Fig No. 6.12: Pressure Contours

46

6.3 Optimized Design

Fig No. 6.13: Iso-Surface

Pressure Contours:

Fig No. 6.14: Pressure Contours

47

Streamlines:

Fig No. 6.15: Streamlines

6.4 Comparisons

Fig No. 6.16 & 6.17: Graph – Drag Co-efficient comparison

Drag Coefficient reduced from 0.569 to 0.392

Initial Design Improved Design

48

Fig No. 6.18: Comparison of Wave Formation and Ship Wake Formation for Initial & Final Design

Frictional force: 54700.68 N Frictional force: 38050.14 N

Forces required to sail reduced by 16650.54 N

Percentage Reduction in Force = 30.4%

6.5 Conclusions

In this project, strength analysis and flow analysis of ship hull was performed.

Strength analysis using analytical methods as well as using FEA software was performed. The

deviation in the results of analytical strength analysis was around four percent from the

experimental values. Hence, this approach is suitable for the preliminary design of ship

structures due to its simplicity and accuracy.

Further, a strength improvement example was taken up in which stresses acting on ship were

reduced due to re-inforcements.

Flow analysis using CFD was performed on two types of hull – Series 60 Cargo ship hull and

Wigley hull. The parameters which affect ship hull performance were identified and design

optimization of shape of Cargo ship hull was carried out.

The drag coefficient was reduced from 0.7 to 0.3 which will lead to savings in running cost of

ship. Also, the forces required to sail were reduced by thirty percent.

49

6.6 Scope for future work

Strength Analysis considering fatigue and vibrations

Modeling of time period of waves which strike the ship surface

Use of CSF(Continuum surface force) model to include surface tension and wall adhesion

effects of water

Methods to decrease CFD computation time

50

Glossary

computational fluid dynamics (CFD)

The science of predicting fluid flow, heat transfer, mass transfer (as in perspiration or

dissolution), phase change (as in freezing or boiling), chemical reaction (e.g., combustion),

mechanical movement (e.g., fan rotation), stress or deformation of related solid structures (such

as a mast bending in the wind), and related phenomena by solving the mathematical

equations that govern these processes using a numerical algorithm on a computer.

convergence

The point at which the solution is no longer changing with each successive iteration.

Convergence criteria, along with a reduction in residuals, also help in determining when

a solution is complete. Convergence criteria are pre-set conditions on the residuals that

indicate that a certain level of convergence has been achieved. If the residuals for all

problem variables fall below the convergence criteria but are still in decline, the solution

is still changing to a greater or lesser degree. A better indicator occurs when the residuals

flatten in a traditional residual plot (of residual value vs. iteration). This point,

sometimes referred to as convergence at the level of machine accuracy, takes time to

reach, however, and may be beyond your needs. For this reason, alternative tools such

as reports of forces, heat balances, or mass balances can be used instead.

discretization

The act of replacing the differential equations that govern fluid flow with a set of algebraic

equations that are solved at distinct points.

mesh

A collection of points representing the flow field, where the equations of fluid motion

(and temperature, if relevant) are calculated.

models

Numerical algorithms that approximate physical phenomenon (e.g., turbulence).

node

The distinct points of a mesh at which the equations of fluid motion are solved.

post processing

The act of analyzing the numerical results of your CFD simulation using reports, integrals,

and graphical analysis tools such as contour plots, animations, etc.

residuals

The small imbalance that is created during the course of the iterative solution algorithm.

This imbalance in each cell is a small, non-zero value that, under normal circumstances,

decreases as the solution progresses.

51

skewness

The difference between the shape of the cell and the shape of an equilateral cell of

equivalent volume. Highly skewed cells can decrease accuracy and destabilize the solution.

solvers

ANSYS FLUENT has two distinct solvers, based on numerical precision (single-precision

vs. double-precision). Within each of these categories, there are solver formulations:

pressure based; density based explicit; and density based implicit.

discretization schemes

(1) Upwind Schemes:

In an upwind (UW) scheme the convection term is formed using a first-order accurate

difference equation equating the velocity derivative to the values at the reference point

and its nearest neighbor taken in the upstream direction. This can give very inaccurate

solutions but they are easy to obtain as they converge readily. For compressible flows,

UW is viewed in a different light. Here, instead of the primitive variables, a set of

characteristic variables is often used. The governing equations for the characteristic

variables are locally hyperbolic. Hence, their solutions are wavelike and upwind

differences are the correct treatment. UW here appears under designations such as flux

splitting, flux difference splitting, fluctuation splitting etc.

(2) Hybrid Schemes:

A hybrid scheme, where the upwind scheme is used if the Reynolds number is greater

than two, and central differences are used if the Reynolds number is two or less. This is

more accurate than the upwind scheme but does not converge on some grids of points.

(3) QUICK Upwind Schemes:

The quadratic upstream interpolation for convective kinetics (QUICK) scheme31 is a

quadratic upwind scheme used mainly in the finite volume formulation and is more

accurate than the two schemes described above. This scheme uses a three-point

upstream-weighted quadratic interpolation for cell face values. In the QUICK scheme,

one adds one point in each direction and calculates the derivative using the cubic

polynomial drawn through the four involved points. Local truncation error analysis shows

third order accuracy. The QUICK scheme is unconditionally bounded up to cell Reynold

numbers of 5. Beyond this limit, it may become unbounded. The QUICK scheme is

normally applied as a correction to the donor cell scheme. In situations with

unboundedness, the correction may locally be limited, thus reverting to the donor cell

scheme. The QUICK scheme has a somewhat different form in finite volume contexts,

since here the differences rather than the derivatives are of interest.

(4) Power-Law Schemes:

Power-law schemes are derivatives of QUICK but are more accurate.

52

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