Ship Hull Resistance Calculations Using CFD Methodsby ARCHIVES

MASSACHUSETTS INS EPetros Voxakis OF TECHNOLOGY

Bachelor of Science in Marine Engineering JUN 2 8 2012Hellenic Naval Academy, 2003

LIBRARIESSubmitted to the Department of Mechanical Engineering in Partial Fulfillment

of the Requirements for the Degrees of

Naval Engineerand

Master of Science in Mechanical Engineering

at theMASSACHUSETTS INSTITUTE OF TECHNOLOGY

May 2012

02012 Petros Voxakis. All Rights Reserved.

The author hereby grants to MIT permission to reproduce and to distribute publicly paperand electronic copies of this thesis document in whole or in part in any medium now known

or hereafter created.

Signature of author

,jv Department of Mechanical EngineeringI A May 23, 2012Certified by

I

Accepted by

Chryssostomos ChryssostomidisDoherty Professor of Ocean Science and Engineering

Professor of Ocean and Mechanical EngineeringThesis Supervisor

David E. HardtProfessor of Mechanical Engineering

Chairman, Departmental Committee on Graduate Students

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Page Intentionally Left Blank

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Ship Hull Resistance Calculations Using CFD Methodsby

Petros Voxakis

Submitted to the Department of Mechanical Engineering in Partial Fulfillment of theRequirements for the Degrees of

Naval Engineerand

Master of Science in Mechanical Engineering

ABSTRACT

In past years, the computational power and run-time required by Computational Fluid Dynamics(CFD) codes restricted their use in ship design space exploration. Increases in computational poweravailable to designers, in addition to more efficient codes, have made CFD a valuable tool for earlystage ship design and trade studies.

In this work an existing physical model (DTMB #5415, similar to the US Navy DDG-51 combatant)was replicated in STAR-CCM+, initially without appendages, then with the addition of the appendages.Towed resistance was calculated at various speeds. The bare hull model was unconstrained in heave andpitch, thus allowing the simulation to achieve steady dynamic attitude for each speed run. The effect ofdynamic attitude on the resistance is considered to be significant and requires accurate prediction. Theresults were validated by comparison to available data from tow tank tests of the physical model.

The results demonstrate the accuracy of the CFD package and the potential for increasing the use ofCFD as an effective tool in design space exploration. This will significantly reduce the time and cost ofstudies that previously depended solely on physical model testing during preliminary ship design efforts.

Thesis Supervisor: Chryssostomos ChryssostomidisTitle: Doherty Professor of Ocean Science and Engineering

Professor of Ocean and Mechanical Engineering

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ACKNOWLEDGEMENTS

I would like to express my gratitude to my thesis advisor, Professor Chryssostomos Chryssostomidis, for

supporting me at a difficult point in the course of my studies at MIT and giving me the opportunity to

work on a very interesting subject.

To Professor Stefano Brizzolara without whose support and guidance at every step of the way this work

would not have been possible.

For their mentoring and support during the time of my studies I would like to thank:

Captain Mark S. Welsh, USN

Captain Mark Thomas, USN

Commander Pete R. Small, USN

I would like to thank the Hellenic Navy for giving me the great opportunity to attend MIT and for

financially supporting my studies.

Last, but not least, I would like to express my sincere appreciation and thanks to my family and all the

people whose friendship, love, and faith in me gave me the strength to be where I am today and give me

the strength to move forward.

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TABLE OF CONTENTS

Abstract .............................................................................................................................. 3

Acknowledgem ents...................................................................................................... 4

Table of Contents......................................................................................................... 5

List of Tables......................................................................................................................7

List of Figures .................................................................................................................... 8

Chapter 1 - Introduction............................................................................................. 11

Chapter 2 - Existing D ata and M ethods .................................................................... 13

2.1. The DTM B 5415 Hull - Experim ental D ata ...................................................... 13

2.2. Appendage Resistance Prediction M ethods ........................................................ 18

Chapter 3 - The CFD Solver ....................................................................................... 24

3.1. Background ........................................................................................................ 24

3.2. The Reynolds Averaged Navier-Stokes (RANS) Solver .................................... 263.3. The Physics M odels........................................................................................... 27

Chapter 4 - The CFD M odel..........................................................................................30

4.1. Surface M esh....................................................................................................... 30

4.2. Volum e M esh ...................................................................................................... 36

4.2.1. Volum e M esh Generation and Description.................................................. 36

4.2.2. The Prism Layers............................................................................................. 40

4.3. M esh Evaluation.................................................................................................. 42

4.4. Boundary Conditions......................................................................................... 44

4.5. The 6-DOF M odel............................................................................................. 46

Chapter 5 - The DTMB 5415 Bare Hull Model with a Free Surface ............... 47

5.1. Introduction ............................................................................................................ 47

5.2. Trim , Sinkage, and Resistance Results ............................................................... 47

5.3. W ave Pattern and W ave Profile at Fr-0.41......................................................... 53

5.4. Rem arks .................................................................................................................. 55

5

Chapter 6 - The DTMB 5415 Hull Model with Appendages .................................. 57

6.1. Introduction ........................................................................................................ 57

6.2. Simulations at M odel Scale................................................................................ 58

6.3. Simulations at Full Scale.................................................................................... 60

6.4. Other Results ...................................................................................................... 62

Chapter 7 - Conclusions / Recommendations ........................................................... 75

7.1. Conclusions ........................................................................................................ 75

7.2. Recommendations for Future W ork .................................................................... 75

References ...........................................................................................................-...- 77

Appendix A - M odel to Full Scale ................................................................................. 79

Appendix B - Resistance Distribution And Frictional Resistance Coefficients ........ 81

Appendix C - Time Histories of Resistance, Trim, and Sinkage.............................86

6

LIST OF TABLES

Table 1 - Geometrical data and Experiment 33 particulars for DTMB model 5415 and

full-scale sh ip . ................................................................................................................ 15

Table 2 - Appendage form factors (1+k2). ....................................................................... 23Table 3 - Physics models utilized by each simulation type, with or without a free

su rface . ........................................................................................................................... 2 7

Table 4 - Details on the prismatic near wall layers generated in the simulations. ........... 41

Table 5 - Boundary conditions defined for each simulation.........................................44

Table 6 - Experimental vs. CFD resistance, trim, and sinkage data.............................49

Table 7 - Experimental vs. CFD resistance, trim, and sinkage data using a differentm esh ................................................................................................................................ 4 9

Table 8 - Numerical vs. experimental appended hull resistance data...........................59

Table 9 - Numerical vs. experimental appended hull resistance data including the values

from the full scale sim ulations ....................................................................................... 60

Table 10 - Full scale effective power calculations when the Reynolds number of each

appendage w as accounted for.................................................................................... 61

Table 11 - Drag distribution among the hull and its appendages from the appended hull

sim u lation s......................................................................................................................6 3

Table 12 - Total resistance results from the bare hull simulations. The difference

between appended and bare hull drag is also given. ................................................... 64

Table 13 - Subdivision of the total resistance in frictional and pressure drag for the

model scale hull with and without a free surface at Fr-0.41 ..................................... 67

Table 14 - Some appendage resistance predictions with empirical methods compared to

the C FD com putations................................................................................................ 73

Table 15 - Total, frictional, and residuary resistance values from the CFD

com p u tation s .................................................................................................................. 84

Table 16 - Frictional resistance coefficient for the hull and each appendage as derived

from the frictional resistance computations in the CFD simulations ............. 85

7

LIST OF FIGURES

Figure 1 - Geometry and photo of model INSEAN 2340. ............................................ 14

Figure 2 - Geometry and photo of model DTMB 5415. ................................................ 14

Figure 3 - Geometry and photo of model IHR 5512. ................................................... 15

Figure 4 - Geometry and photo of model DTMB 5415 as used in the CFD simulations.. 15

Figure 5 - Photographs of the Fully Appended Stem of Model 5415-1 Representing

DDG-51 W ithout the Stem W edge [10].................................................................... 16Figure 6 - STAR-CCM+ Pictures of the Fully Appended Stem of Model 5415..........17

Figure 7 - Bilge keel geom etry .................................................................................... 20

Figure 8 - Strut or control surface geometry. .............................................................. 20

Figure 9 - Shaft and bracket geom etry. ....................................................................... 22

Figure 10 - DTMB 5415 hull meshed to an STL file format with a close-up

tow ards the bow .............................................................................................................. 3 1

Figure 11 -: DTMB 5415 hull with appendages meshed to an STL file format with

close-ups towards the bow and stem ........................................................... 32

Figure 12 - DTMB 5415 hull meshed to an STL file format with a close up to the bow.

This is the bare hull model used in the simulations without a free surface..................33

Figure 13 - The calculation domain obtained by the subtraction of the hull from a solid

b lo ck ............................................................................................................................... 3 4

Figure 14 - DTMB 5415 hull remeshed in STAR-CCM+ with a close up to the bow.... 35

Figure 15 - Remeshed DTMB 5415 hull with appendages below the waterline, as used

in the simulations, and close ups towards the bow and towards the stem. ................ 35

Figure 16 - Bare hull model simulations with a free surface volume mesh dimensions.. .36

Figure 17 - Appended hull model scale simulations volume mesh dimensions.............37

Figure 18 - Examples of volume shapes used to control the mesh density. ................. 38

Figure 19 - From top to bottom, profile views of the volume meshes generated

for the simulations with free surface and free motions, the simulations without

free surface with appendages and without appendages.............................................39

8

Figure 20 - The boundary layer of the bare hull was modeled with 5 prism layers,

in the simulations with the free surface, and 8 prism layers, in the simulations without

free surface. ........................................................................................... ... ----- .......... 4 1

Figure 21 - The prism layers of the model size simulations were defined relatively

thicker than those of the full scale simulations .......................................................... 42

Figure 22 - The wall y+ parameter values on the DTMB 5415 hull at Fr-0.41...........43

Figure 23 - The convective Courant number parameter values on the DTMB 5415

hull at Fr-0.4 1 ................................................................................................. . ....-- 44

Figure 24 - Boundary surfaces....................................................................................... 45

Figure 25 - Total resistance experimental data plotted with the CFD results. ............. 49

Figure 26 - Trim angle experimental data plotted with the CFD results ............ 50

Figure 27 - Sinkage experimental data plotted with the CFD results ........................... 50

Figure 28 - Time histories of resistance, trim, and sinkage as generated in CFD code

ST A R -C C M . ................................................................................................................ 52

Figure 29 - The CFD code also calculated the frictional and pressure resistances ..... 52

Figure 30 - Experimental and CFD wave pattern at Fr-0.41 ........................................ 53

Figure 31 - Experimental and CFD wave profile along the hull at Fr-0.41.................54

Figure 32 - Bow wave from the towing tank report and from the CFD simulation at

F r- 0 .2 8 ........................................................................................................................... 5 5

Figure 33 - DTMB 5415 hull model with appendages .................................................. 57

Figure 34 - Lines of the experimental effective and frictional power at the range of

10-32 knots vs. the numerical results at three speeds................................................59

Figure 35 - Lines of the experimental residuary resistance coefficient at the range of

10-32 knots vs the numerical results at three speeds..................................................59

Figure 36 - Difference in the frictional resistance coefficient value of each appendage

when its Reynolds number is calculated separately at Fr-0.41 ................................. 62

Figure 37 - Appendage total resistance given as a percentage of the bare hull total

resistan ce ........................................................................................................................ 6 5

Figure 38 - Percentage subdivision of the total resistance in frictional and pressure,

or residuary, drag for the model and full scale hull....................................................66

9

Figure 39 - Percentage subdivision of the total resistance in frictional and pressure drag

for the model scale hull when a free surface exists at Fr-0.41 .................................. 67

Figure 40 - Streamlines around the struts and at the rudder at Fr-0.33 ....................... 69

Figure 41 - Matching of the frictional resistance coefficient for each appendage and the

bare hull with the ITTC 1957 frictional line and the Blasius solution for laminar flow 70

Figure 42 - The skin friction and pressure coefficients depicted on the appended hull

m odel at Fr-0.4 1 ....................................................................................................... 72

Figure 43 - Distribution of total resistance among frictional and pressure resistance......83

Figure 44 - Time histories of resistance, trim, and sinkage from the simulations with a

free surface using a newer mesh at Fr-0.41............................................................... 87

Figure 45 - Frictional, pressure, and total resistance plot from the bare hull simulations

w ithout a free surface at Fr-0.41............................................................................... 88

Figure 46 - Frictional, pressure, and total resistance plots of the hull with the

appendages, the bilge keel, and the rudder from the appended hull simulations

w ithout a free surface at Fr-0.41............................................................................... 89

Figure 47 - Frictional, pressure, and total resistance plot of the hull with the appendages

from the full scale appended hull simulations without a free surface at Fr-0.41 ..... 90

10

CHAPTER

1INTRODUCTION

Starting in the seventeenth century experimental fluid dynamics appeared in France and England.

Subsequently, theoretical fluid dynamics developed. Until about 1960, fluid dynamics were only studied

using an experimental or theoretical approach. The rapid development of high-speed digital computers,along with precise numerical algorithms for solving problems using these computers, has introduced an

important third dimension in fluid dynamics called Computational Fluid Dynamics, commonly referred

to as CFD, and revolutionized the way we study and practice fluid dynamics today.

In the late 1970s supercomputers were used to solve aerodynamic problems. HiMAT (HighlyManeuverable Aircraft Technology) was an experimental NASA aircraft designed to test concepts ofhigh maneuverability for the next generation of fighter planes. Wind tunnel tests of a preliminary design

for HiMAT showed that it would have unacceptable drag at speeds around the speed of sound.

Redesigning and retesting it would have cost $150,000 and delayed the project unacceptably. The wingwas redesigned by a computer at a $6,000 cost [4].

While the early development of CFD was driven by the needs of the aerospace community it is

now used in all disciplines where the flow of a fluid is important. Some examples are the performance

improvement of cars and their engines, the examination and better understanding of the real flow

behavior of liquid metal during mold filling to help design improved casting techniques, and the

calculation of the flow from an air conditioner.

CFD can also be applied to examine the hydrodynamics of high-speed hull forms. While a large

number of theoretical and experimental investigations into the hydrodynamics of ships have been carried

out there are areas that require further research. The steady free surface flow and related forces

prediction by numerical calculations is one example. The prediction of the flow field for high-speed

hulls is complicated by the dynamic trim and sinkage which have a remarkable effect on ship generated

11

waves. The existence of a transom stem, used on most high-speed vessels, further complicates the

problem as the large low-pressure area behind it generates waves, wave-breaking, and spray.

CFD techniques are especially useful in analyzing flow problems in resistance prediction where

complex fluid flow is present. While towing tank tests provide better absolute accuracy, CFD techniques

can give results that are comparable to the towing tank results at a smaller cost in money and time. In

addition, they have the advantage of allowing modifications to hull forms to be undertaken so that a

comparative study of results can be made in a relatively short time and at relatively small cost [5].

In this study CFD computations are used to predict the resistance, trim, and sinkage of a high-

speed hull with transom stem DTMB 5415. The results are compared to existing experimental ones and

a good agreement is found. Computations are then made to predict the resistance of the same hull adding

the appendages. The resistance characteristics of each appendage and how they affect-the total resistance

of the ship are examined. The surfaces of the hull and its appendages were pre-processed, prepared, and

meshed in CAD Software Rhinoceros 3D. Subsequently they were imported into CFD software STAR-

CCM+ where the simulations were generated.

12

CHAPTER

2EXISTING DATA AND METHODS

In this chapter the hull used in the simulations is described, along with the types of simulations

generated, and the experimental data that were used as a benchmark to evaluate the CFD results. In the

second part of the chapter there is some talk about the existing empirical methods of estimating the

appendage resistance of a ship.

2.1. The DTMB 5415 Hull - Experimental Data

There is-an extensive benchmark database for resistance and propulsion CFD validation.

Detailed tests done to create this database were reported on by the Resistance Committee of the 22nd

International Towing Tank Conference [6]. The focus is on modem hull forms. Tanker (KVLCC2),container ship (KCS), and surface combatant (DTMB 5415) hull forms were recommended for use bythe Resistance Committee and were used as test cases. The results were presented at the Gothenburg

2000 Workshop on CFD for Ship Hydrodynamics [7] and subsequent workshops and conferences. Theyare still used.

The DTMB 5415 hull form was conceived as a preliminary design for a surface combatant with a

sonar dome bow and a transom stem at the David Taylor Model Basin (DTMB) by the US Navy around1980 [8]. It was constructed at the DTMB model workshop from a blank of laminated wood using acomputerized numerical-cutting machine (Figure 2).

The DTMB model 5415 is the hull used for all computations reported in this work. All the

benchmark experimental data used to validate the CFD results were also gathered using the same hull or

an exact geosym (INSEAN 2340).The bare hull resistance, trim, and sinkage results were compared with the results from Olivieri

et al. [9] a combined effort from the Istituto Nazionale per Studi ed Esperienze di Architettura Navale(INSEAN, Italian ship model basin) and the Iowa Institute of Hydraulic Research (IIHR) to presentexperimental towing tank results for the purpose of CFD validation. The model used in this report was

INSEAN 2340 (Figure 1). The CFD resistance computation results for the appended model were

13

compared to existing towing tank results performed at the David Taylor Naval Ship Research and

Development Center [10]. The model used in these tests had fixed pitch shafts and struts and wasdesignated Model 5415-1 to distinguish it from 5415, which had controllable pitch shafts and struts. Inaddition, the propellers, fairwaters, and twin rudders with rudder shoes were all redesigned for the fixed

pitch configuration, while the bow sonar dome, the bilge keels, and the skeg were identical in bothconfigurations. In this report, from Borda (1984) [10], several experiments were made with differentappendage configurations, varying displacements, and measured quantities. From these experiments,experiment 33 was the one that corresponds to the conditions of the simulations prepared and run in thepresent study. For experiment 33 the DTMB 5415 hull is fully appended but with dummy hubs in placeof propellers, the position of the rudders is at 0 degrees, and the resistance characteristics, with still airdrag not included, are given in terms of effective horse power converted to the full scale ship with acorrelation allowance CA=0.0004. The model is ballasted to represent the ship at the design

displacement. Further details of the experimental set-up and the geometric characteristics of the DTMB5415 model are given in Table 1. A picture of the fully appended model 5415-1 stem is shown in Figure5. If the propellers in this picture were replaced with dummy hubs it would show the appendageconfiguration used for experiment 33. Figure 6 shows the appended hull of DTMB 5415 as modeled andused in the relevant CFD simulations presented in this study. Figure 3 shows model DTMB 5512 whichis another geosym of DTMB 5415, this time at a scale of 1/46.6, which was used by the IIHR. TheDTMB 5512 model has contributed significantly in the generation of benchmark information forvalidation of CFD results.

Figure 1: Geometry and photo of model INSEAN 2340.

Figure 2: Geometry and photo of model DTMB 5415.

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Figure 3: Geometry and photo of model IIHR 5512.

Figure 4: Geometry and photo of model DTMB 5415 as used in the CFD simulations.

Table 1: Geometrical data and Experiment 33 particulars for DTMB model 5415 and full-scale ship.

D)escr-iption Sy m1bol Shlip M odelScale factor 24.824

15

Length between perpendiculars L,, (M) 142.0 5.720Length at water level Lw (m) 142.0 5.720

Overall length Los (m)Breadth B (m) 18.9 0.76

Draft T (m) 6.16 0.248Trim angle (Initially) (deg) 0.0 0.0

Displacement A (t) 8636.0 0.549Volume V (m3) 8425.4 0.549

Wetted surface Sw (m2) 2949.5 4.786Wetted surface with appendages SWA (m2) 3208 5.205

Water (1) Temperature T (degrees Celsius) 18.9 15(2) Fresh, Salt Water FW, SW FW SW

AEu:IG

Figure 5: Photographs of the Fully Appended Stern of Model 5415-1 Representing DDG-51Without the Stern Wedge [10].

16

0

Figure 6: 3D Model of the Fully Appended Stern of DTMB 5415 used in the CFD simulations.

17

2.2. Appendage Resistance Prediction Methods

The total resistance of a ship can be physically broken down into two components: frictional

resistance and pressure resistance. The frictional resistance is the sum of the tangential shear forces

acting on each element of the hull surface, and is solely caused by viscosity. The pressure resistance is

the sum of the pressure normal forces acting on each element of the hull surface, and is partly a result of

viscous effects and hull wave making.Towing tank tests to predict the resistance of a ship are initially performed on a bare hull

model of the ship. The measurements of the model are then converted to the full scale ship following an

extrapolation procedure. One such common procedure (Froude's method) assumes the division ofresistance into skin friction and residuary resistance, where the residuary part consists of wave making

and pressure form resistance. Other drag components have to be accounted for separately. These are: (i)appendage drag, (ii) air resistance of hull and superstructure, (iii) roughness and fouling, (iv) wind andwaves, and (v) service power margins [12].

The appendages, in particular, can account for a significant amount of the total ship

resistance. The main appendages of a twin-screw vessel are the twin rudders, the bilge keels, the twin

shafting and shaft brackets, or bossings.The following methods are usually used to estimate the appendage drag:

(i) Separate towing tank tests of the model with and without appendages. The differencebetween the two measured resistances should give the appendage drag which can then be

scaled to full size.(ii) Tests are performed on a geosym set of appended models of varying scales. A form factor

(1+k) is then derived which is used to predict the appendage drag of the full scale ship. Thisis an expensive and time consuming approach but provides a more accurate extrapolation

procedure.(iii) Tests on separate models of the appendages. In this case, with high flow speeds and a larger

model of the appendage, Reynolds numbers closer to full-scale values can be achieved. The

hull influence on the appendage resistance is neglected.

(iv) Empirical data and equations that come from model, and limited full scale, tests.The extrapolation of model test appendage resistance to full scale is not the same as with

the naked hull. Some factors to take into account that complicate the task are:

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(i) During the model tests the appendages are tested into a much smaller Reynolds number thanat full scale. This means that while the appendages, in the model tests, are intersected by alaminar flow, at full scale they are likely to come across turbulent flow.

(ii) Skin friction increases as the flow turns from laminar to turbulent, while the resistance inseparated flow decreases.

(iii) The relative thickness of the model boundary layers, when allowing for scale, is about doublethat of the full scale layers for usual model / full scale sizes. As a result, velocity gradienteffects are greater on the model, and while the model scale appendages may be operating

fully into the boundary layers, the full scale appendages may be projecting outside theboundary layers.

(iv) Each appendage, attached to the hull, runs at its own Reynolds number, thus, whenmeasuring its drag at the model size, the procedure to scale to the full size ship will bedifferent.

Some equations and data that can provide detailed estimates of the appendage drag at the appropriateReynolds number in the absence of hull model tests are given in [12], [13], [14], [15], [16] andpresented below.(i) Bilge keels

The two sources of drag for the bilge keels are skin friction due to the added water surfaceand interference drag at the connection with the hull. A procedure recommended by ITTC toaccount for bilge keel drag is to multiply the total resistance with (S + SBK)/S, where S is thewetted area of the hull and SBK is the wetted area of the bilge keels.A formula to estimate bilge keel drag given by Peck [14] and referring to Figure 7 is:

DB =pSBK V2CF 2- (12 [ +YWhen Z is large interference drag tends to zero, and when Z tends to zero interference dragcan be assumed to be equal to skin friction drag. L is the average length of the bilge keel tobe used when calculating CF.

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LFigure 7: Bilge keel geometry.

(ii) Rudders, shaft brackets and stabilizer finsHere the drag can be broken down to:

(a) Control surface or strut drag, Dcs(b) Palm drag, De(c) Spray drag, in the case that the rudder or strut penetrates the free surface, DSP(d) Interference drag due to the connection of the appendage with the hull, DINT-The total drag, DAY, can then be written: DAP= Dcs + Dp + DSP + DNT (2)A formula proposed by Peck [14] for the control surface drag is:

1 pS F CM S t31Dcs =-P 1.25 -+ + 40 X 10-1, (3)

2 Cf A Cawhere S is the wetted area, A is the frontal area of the maximum section, t is the maximum

thickness, V is the ship speed, and Cm is the mean chord length which equals (Cf + Ca)(Figure 8) and is used for the calculation of CF.

Cm

Ca Cf

Figure 8: Strut or control surface geometry.

A control surface drag formula proposed by Hoerner [13] for 2D sections is:

CD=CF[1+2()+60()]1 (4)

20

where c is the chord length used for the calculation of CF-Hoerner [13] also proposed formulas for the estimation of the spray drag, DSP, the palm drag,Dp, and the interference drag, DINT. These formulas respectively are:

1Dsp = 0.24-p 2t, (5)

1

Dp = 0. 7 5CDpalm h 3 Whp 1 pV 2, (6)

1 t 0.00031DINT = P2tz 0.75-t- 20 3 (7)

2 C (t)2

where tw is the maximum section thickness at the water surface, hp is the height of the palm

above surface, 6 is the boundary layer thickness, W is the palm frontal width, CDPaIm is 0.65

for a rectangular palm with rounded edges, t is the appendage maximum thickness at the hull,and c the appendage chord length at the hull.

(iii) Shafts and bossingsPropeller shafts are generally inclined to the flow. As a consequence lift and drag forces are

induced on the shaft and the shaft bracket. Careful alignment of the shaft bracket strut is

required to avoid cross flow.

The components of the resistance in this case are:

(a) The shaft drag, DsH(b) Skin friction drag of cylindrical portion, CF(c) Pressure drag of cylindrical portion, CDP(d) Forward and after cylinder ends drag, CDEAccording to Hoerner [13], for Reynolds number Re < 5 x 105 (based on shaft diameter), theshaft drag is given by:

1DSH = -pLSHDSV 2 (1.1sin'a + WcCF), (8)2

where LSH is the total length of shaft and bossing, Ds is the diameter of shaft and bossing,

and a is the flow angle relative to the shaft axis in degrees (Figure 9).

21

VFigure 9: Shaft and bracket geometry.

The equations for the cylindrical portion drags as offered by Kirkman and Kloetzi [15] are:CDP = 1.sin 3 a, Re < 1 x 105 (9)

CDP = -0.7154logioRe + 4.677, 1 x 105 < Re < 5 x 105, a > # (10)CDP = (-0.7154logioRe + 4.677) [sin3 (1.7883logioRe - 7.9415)a],

1 x 10s < Re < 5 x 10s,a < fl (11)CDP = 0.6sin3 (2.25a), Re > 5 x 10s, 0 < a < 400 (12)

CDP = 0.6, Re > 5 x 105, 400 < a < 900 (13)where Re = VDc/v, P = -71.54logioRe + 447.7 and the reference area is the cylinderprojected area (L x Dc).

CF = 1.327Re- 0os, Re < 5 x 10s (14)1 1700

CF =7, Re > 5 x 10s (15)(3.461logioRe - 5.6)2 Rewhere Re = VLc/v, Lc = L/tana, Lc > L and the reference area is the wetted surface area 71 x

length x diameter.

For the drag of the cylinder ends, if applicable, we have [15]:

CDE = 0.9CoS 3 a, for support cylinder with sharp edges (16)CDE = 0.01CoS 3 a, for support cylinder with faired edges (17)

Some other empirical equations to estimate the drag of a wide range of appendages are given

by Holtrop and Mennen [16]:

22

RAPP = 1 pVsCF(l + k2)E SAPP + RBT, (18)

where Vs is the ship speed, CF is the friction coefficient for the ship determined from theITTC 1957 line and SAp is the wetted area of the appendage(s). (1 + k2)E is the equivalent (1+ k2) value for the appendages given by:

( (1 + k2)SAPP) SAPP

The appendage resistance factors (1 + k2) as defined by Holtrop are shown in Table 2 [16].RBT in equation (18) is there to account for bow thrusters, if fitted, and is determined by:

RBT = WTPVsdTCBTO, (20)where dT is the diameter of the thruster and the coefficient CBTO lies in the range 0.003->0.012.

Table 2: Appendage form factors (1+k 2)-

Appendage type (0 + k2)

Rudder behind skeg 1.5-2.0Rudder behind stem 1.3-1.5Twin-screw balanced rudders 2.8Shaft brackets 3.0Skeg 1.5-2.0Strut bossings 3.0Hull bossings 2.0Shafts 2.0-4.0Stabiliser fins 2.8Dome 27Bilge keels 1.4

For the current study the appendages of the twin screw DTMB 5415 model consisted of the twinrudders and rudder shoes, the twin shafting, the shafting brackets or struts, and the bilge keels. CFDsimulations were run for the model with and without the appendages. The total appendage drag, as wellas the drag of each appendage separately, was calculated from these simulations. As part of the analysisof the results the percentage of each of the appendage drags to the total bare hull drag was found. Acomparison of the CFD findings with results derived from some of the empirical equations previouslymentioned was also made.

23

CHAPTER

3THE CFD SOLVER

A brief description of the CFD method for solving a fluid flow, with regard to the current study,

follows. The physics models used in the CFD simulations are also briefly described in the last part of the

chapter.

3.1. BackgroundThree fundamental principles govern the physical aspects of any fluid flow: (i) the conservation

of mass, (ii) the conservation of energy, and (iii) Newton's second law. These principles can beexpressed in the form of mathematical equations, which, in their most general form, are integral or

partial differential equations. In many cases these equations cannot be solved analytically.

Computational Fluid Dynamics (CFD) replaces the integrals or partial derivatives in these equationswith appropriate discretized algebraic forms that can be solved. The outcome of the CFD solution is

numbers that in some way describe the flow field at discrete points in time and/or space.

In modern CFD literature the Navier-Stokes equations refer to the complete system of flow

equations, which solves for not only momentum, but continuity and energy as well. The complete

system of flow equations for the solution of an unsteady, three-dimensional, compressible, viscous flow

is:

Continuity Equation

Nonconservation form + pV - V = 0 (21)DtConservation form + V - (pV) = 0 (22)DtMomentum equationsNonconservation form

x component p Du - + + + + pfX (23a)Dt = a x + y az

y component p D p+ax TY+az + pfy (23b)Dt ay ax ay Oz

24

z component

Conservation form

x component

y component

z component

Dw = - + + + +Zpf (23c)

+ 2- (puV)=) + + + pf a23

a(PV) + V - (pV) = + + + + pf

a(Pw + V - (pwV) = + + + + pfat az ax ay az z

Energy equationD V2 . + a aT a aT+ a T) a(up)Nonconservation form e + p k + k-Dt K( 2)- pq ( ax) ay ayl +z(kz ax

a(vp) a(wp) a6u~xx) a(uryx) 86~x ___(vxy _(vyy_a VP (P +a(TX)++ aUZ + av~)+ av~)+ay az ax ay az ax ay

(zy + (z ++ + pf -V (25)az ax ay az

Conservation form a[p(e+Y ]+V -p(e +Y )v=pi+ Uk +

a-(k aT+ -(k aT a(up) a(vp) a wp) + a(UTXX) +ay \ay z \az ax ay -az ax

a(uTyx) + a vxy)+ + + + +awTxz) +ay az ax ay az ax

a (WTZ) + awTzz) + pf -V (26)ay az

The conservation form of the governing equations derives from the control volume (finite orinfinitesimal) fixed in space with the fluid moving through it, while the nonconservation formcorresponds to the control volume moving with the fluid such that the same fluid particles are always in

the same control volume. It is worth noting that this distinction between conservation and

nonconservation form was triggered by the development of CFD and the question of which form of the

equations was more suitable to use for any given CFD application. The conservation form of the

equations is more convenient from a numerical and computer programming perspective.

If we take the Navier-Stokes equations given above and drop all the terms associated with

friction and thermal conduction we would have the equations for an inviscid flow which are called the

Euler equations.The same (Navier-Stokes) equations describe any fluid flow, but not all flow fields are the same.

The boundary conditions, and sometimes the initial conditions, determine the particular solution of the

general governing equations for a specific problem.25

(24a)

(24b)

(24c)

3.2. The Reynolds Averaged Navier-Stokes (RANS) SolverThe Navier-Stokes equations can only be solved analytically for a very small number of cases;

as a result, a numerical solution is required. A numerical solution involves discretization of the

governing equations of motion. When the partial differential equations are discretized then we have

what is called finite differences, while when the integral form of the equations is discretized we have

finite volumes.

In practice, there are a few simplifying assumptions that can be made to allow an analytical

solution to be obtained or to significantly reduce the computational effort demanded by the numerical

solution. Such is the case with the incompressible RANS equations.

By considering the flow as incompressible, which is a good assumption for most fluid flows,the continuity and momentum equations are simplified and the solution of the energy equation is no

longer required. The Reynolds averaging process represents the three velocity components as a slowly

varying mean velocity with a rapidly fluctuating turbulent velocity around it. It also introduces six new

terms, known as Reynolds stresses. These new terms represent the increase in effective fluid velocity

due to the existence of turbulent eddies in the flow. The introduction of turbulence models serves to

represent the interaction between the Reynolds stresses and the underlying mean flow and to close the

system of RANS equations.In the present study the hull flow was computed using RANS equations that are becoming a

standard for the numerical prediction and analysis of the viscous free surface flow around ship hulls.

Continuity and momentum equations, for an incompressible flow, are expressed by:

pU = -Vp + yV2U + V - TRe + SM (27)where U is the averaged velocity vector, p is the averaged pressure field, [i is the dynamic viscosity, SMis the momentum sources vector and TRe is the tensor of Reynolds stresses, computed in agreement

with the k-epsilon (or k - E) turbulence model.The free surface was captured using the Volume of Fluid approach that requires the solution of

another transport equation for a variable that represents the percentage of fluid for each cell:

vof + U - VVof = 0 (28)

The Finite Volume commercial code STAR-CCM+ [19] was used for the solution of RANSequations on trimmed unstructured meshes as presented in Chapter 4.

26

3.3. The Physics ModelsTable 3: Physics models utilized by each simulation type, with or without a free surface.

Eulerian Multiphase (water, air) Constant Density Fluid (water)Implicit Unsteady SteadyK-Epsilon Turbulence K-Epsilon Turbulence

Three-Dimensional Three-Dimensional

Segregated Flow Segregated Flow

Reynolds-Averaged Navier-Stokes Reynolds-Averaged Navier-Stokes

Two-Layer All y+ Wall Treatment Two-Layer All y+ Wall Treatment

Gravity No body forces

Gradient Method: Hybrid Gauss-LSQ Gradient Method: Hybrid Gauss-LSQVolume of Fluid (VOF) No Free Surface

K-Epsilon turbulence modelThe K-Epsilon turbulence model is a two-equation model categorized as an eddy viscosity model. Eddy

viscosity models use the concept of a turbulent viscosity pt to model the Reynolds stress tensor as a

function of mean flow quantities. In the K-Epsilon model additional transport equations are solved forthe turbulent kinetic energy k and its dissipation rate E in order to enable the derivation of the turbulentviscosity it-

Two-Layer All y+ Wall TreatmentTo resolve the viscous sublayer, the K-Epsilon turbulence model, with the two layer treatment, divides

the computations into two layers. In the layer adjacent to the wall the turbulent viscosity pt and theturbulent kinetic energy dissipation rate E are defined as functions of wall distance. The values of E in

the layer adjacent to the wall are blended smoothly with those calculated in the layer further from thewall using the transport equations. The turbulent kinetic energy k equation is solved in the entire flow.The all y+ treatment attempts to emulate both the high y+ wall treatment for coarse meshes and the low

y+ treatment for fine meshes while also producing reasonable results for meshes of intermediate

resolution.

Segregated FlowThe segregated flow model derives its name from the fact that it solves the flow equations, one for each

velocity component and one for the pressure, in a segregated or uncoupled manner. The continuity and

momentum equations are linked with a predictor-corrector approach. This model is most suitable for

27

constant density flows. The second order upwind convection scheme was used with this model in the

present study.

Implicit UnsteadyThe implicit unsteady model uses the implicit unsteady solver and, in STAR-CCM+, it is the only

unsteady solver that can be combined with the segregated flow model. The main function of the implicit

unsteady solver is to control the update of the calculation at each physical time, while it also controls the

time step size. In general, the implicit unsteady solver is the alternative to the explicit unsteady solver

with the choice between the two determined by the time scales of the phenomena of interest. The

explicit schemes have the disadvantage of being prone to instabilities if too large a time step is

employed. The simulations without the free surface do not require the usage of this model, and the flow

for those simulations is modeled as steady.

Volume of Fluid (VoF)As already mentioned the Volume of Fluid approach is used in combination with the RANS solver to

determine the location of the free surface. In this method the location is captured implicitly by

determining the boundary between water and air within the computational domain. An extra

conservation variable is introduced that determines the proportion of water in the particular mesh cell

with a value of one assigned for full and zero for empty. For the simulations where there is no free

surface, with the only fluid being the water, this model is not selected.

Three-DimensionalThe space models primarily provide methods for computing and accessing mesh metrics such as cell

volume and centroid, and cell and face indexes. The three-dimensional space model is selected as it is

designed to work on three-dimensional meshes.

Eulerian MultiphaseThe Eulerian multiphase model is required to create and manage the two Eulerian phases of the

simulations with the free surface, where a phase represents a distinct physical substance. The two phases

for these simulations are water and air, each defined to have constant density and dynamic viscosity

adjusted according to the average temperature of the tow tank experiments. This model is not requiredfor the simulations without a free surface where the only fluid is water, which is again defined to have

constant density adjusted to the temperature of the experiments used to validate the CFD simulations.

28

GravityThe selection of the gravity model means the action of gravitational acceleration is included in the

simulations. This model provides two effects for fluids. The reference altitude (defined by the user) istaken into account in the calculation of the pressure, and the body force due to gravity is included in the

momentum equations. This model is also not necessary for the simulations that do not have a free

surface.

Gradient Method: Hybrid Gauss-LSQThe transport equation solution methodology requires the use of gradients. One of the ways that the

gradients are used is in the computation of the values of the reconstructed field variables at the cell

faces. The chosen method for this computation was the hybrid Gauss-Least Squares Method (LSQ),which is considered to be a more accurate approach for the cell gradient calculations than the Green-

Gauss method.

29

CHAPTER

4THE CFD MODEL

In the following chapter the simulation creation process is described starting from the remeshing

of the hull surface, continuing with the "construction" of the region defining blocks and the generation

of the volume mesh, and concluding with the selection of the boundary conditions and the 6-DOF

model. A brief section on mesh evaluating methods is also given.

4.1. Surface MeshThe DTMB 5415 hull that was used for the work presented in this document has already been

described in Chapter 2. The surface of this hull had to be meshed before it was possible to work with it

in the CFD software. The pre-processing of the surface and initial meshing was done in Computer Aided

Design (CAD) software Rhinoceros 3D, and subsequently the surface was imported into the CFD codeSTAR-CCM+.

The surface processing in Rhinoceros 3D for the hull without appendages included the scaling and

waterline positioning so that the size and position of the waterline respectively-matched that of the hull

used for the benchmark towing tank experiments [9], [10]. Also, the midships was positioned at theorigin of the axes. Finally, the hull was meshed to a stereolithography (STL) file format. STL filesdescribe only the surface geometry of a three dimensional object without any representation of color,texture, or other common CAD model attributes. STL files contain polygon mesh objects. In particular,they describe a raw unstructured triangulated surface by the unit normal and vertices (ordered by theright-hand rule) of the triangles using a three-dimensional Cartesian coordinate system. The STL formatspecifies both ASCII and binary representations, but the binary representation is more compact and, for

this reason, more common. A binary STL file format was used for the current work. When creating the

STL files the focus was to maintain a balance between a mesh that describes the complex geometry of

the hull well but is not too fine, so that size of the mesh is as compact as possible and is easier to

"handle" in the CFD software. Furthermore, a surface mesh that is only as fine as necessary would help

create a more efficient volume mesh, and save in computational cost later in the simulation "building"30

process. Figure 10 shows the STL mesh file generated in Rhinoceros 3D for the simulations with a freesurface, while Figures 11 and 12 show the STL meshes for the hull with and without appendages for the

simulations without a free surface. The mesh is finer at the more complex areas of the hull surface in

order to capture the extra details and to more accurately represent them. For the same reason the mesh of

the hull with the appendages needed to be finer to capture the extra, complex surfaces added by the

appendages. Furthermore, the simulations without the free surface could "afford" a better mesh

refinement, leading to more precise results; the lack of free surface leads to great savings in

computational "effort" required for the calculation of the free surface at each time step. The non-free

surface simulations also had a smaller volume mesh domain, compared to the simulations with a free

surface. Since only the part of the hull below the water surface needed to be modeled, the STL file for

the appended hull was created for the part of the hull below the waterline. This method of creating the

non-free surface simulations led to a lot of errors in the surface mesh at the connection between the hull

below the water surface and the new surface created to cover the gap left by the removal of the upper

half of the hull (the CFD code required a closed surface), and this is why, when the simulations withoutfree surface for the non-appended hull were created, the STL mesh file used was that for the full hull.This can be seen in Figure 12 and is explained later in this chapter.

Figure 10: DTMB 5415 hull meshed to an STL file format with a close-up towards the bow.

31

Figure 11: DTMB 5415 hull with appendages meshed to an STL file format with close-ups towards the bow and stern.

In the stern close-up the shafts, struts, rudders, and part of the bilge keels can be seen.

32

Figure 12: DTMB 5415 hull meshed to an STL file format with a close up to the bow. This is the bare hull model used

for the simulations without a free surface.

One laborious part of the pre-processing for the hull with the appendages was the attachment of

the appendages to the hull. This was required as the hull and its appendages were created separately. The

difficulty of this procedure came from the requirements that the final surface matched the surface of the

model hull used in the towing tank experiments as accurately as possible and that it was watertight. The

connections had to be smooth and not cause an alteration in the dimensions of the final surface. The

final surface had to be closed (or watertight) and allow for the generation of an STL file that alsocontained completely closed (watertight) polygon mesh objects with as few errors as possible.

In STAR-CCM+ the first step was to make a diagnostic check on the mesh to assess the validity

of the surface and repair any errors found. This is a necessary step before creating the simulation and,later on, remeshing the surface in STAR-CCM+ and generating the volume mesh. Some common

surface mesh errors that may need to be repaired are: (i) pierced faces, which are faces intersected byone or more edges of other faces, (ii) free edges, which translate to some opening or hole in the surface,and (iii) non-manifold edges, which, in our case, translated to having some extra surfaces that were notrequired and could reduce the efficiency and effectiveness of the mesh.

33

The next step was to "build" a rectangular block around the hull that would later become the

domain of the volume mesh representing the water and air surrounding of the hull. Then the imported

hull surface was subtracted from the block with the block as the base of the subtraction. The simulation

proceeded with the outcome of this subtraction, the subtracted block. This way it was assured that the

volume mesh would not extend to the inside of the hull. The subtracted block for the simulations with a

free surface is shown in Figure 13. In this figure the block can be imagined to be cut in two symmetric

parts along the symmetry plane of the ship. In the left picture we can see one of the two symmetric parts.

In the right picture there is a closer view to the area of the block where the hull has been subtracted.

Figure 13: The calculation domain obtained by the subtraction of the hull from a solid block.

The surface of the hull was remeshed in STAR-CCM+. This way the surface quality was

improved and a more suitable mesh was created to serve as the base for the generation of the volume

mesh. Ideally, the surface mesh is triangulated with near equal sized triangles. The transition between

areas with smaller and areas with larger sized elements should be smooth and gradual. Figures 14 and 15

show the remeshed hull surface for the simulations with the free surface and those with appendages and

no free surface.

34

Figure 14: DTMB 5415 hull remeshed in STAR-CCM+ with a close up to the bow.

Figure 15: Remeshed DTMB 5415 hull with appendages below the waterline, as used in the simulations, and close ups

towards the bow and towards the stern.

35

4.2. Volume Mesh

4.2.1. Volume Mesh Generation and DescriptionAfter the meshed hull was imported in STAR-CCM+ a block was built around it to provide,

along with the hull, the boundaries for the creation of the volume mesh. The symmetry condition

allowed for the block to be built, and the calculations made, on only half the hull. For the simulationswithout a free surface the DTMB 5415 hull was simulated at both model size and full scale. For the full

scale simulations the model scale dimensions of both the hull and the surrounding block were multipliedby the scale factor 24.824.

The dimensions of the block that defines the volume mesh region, for the simulations with andwithout a free surface are presented in Figures 16 and 17.

Figure 16: Bare hull model simulations with a free surface volume mesh dimensions.

36

Figure 17: Appended hull model scale simulations volume mesh dimensions.

The dimensions of the blocks were chosen with regard to the accuracy of the results. The

intension was to limit these dimensions, as much as possible, as larger dimensions translated to more

computational costs. The lengthwise dimension behind the ship stem is longer than that forward from

the bow to capture the waves generated by the hull. The dimensions of the block for the simulations with

a free surface were initially similar in size to the ones of the simulations without a free surface but, as

pressure concentrations were found at the boundaries, they were gradually increased to better represent

the fluid flow and improve the accuracy of the results.After the surface mesh was created and the physics models, described in Chapter 2, were

selected, the next step was to generate the volume mesh. Volumetric controls were utilized to make themesh more efficient and more effective. A volumetric control can be used to specify the mesh density

for both surface and volume type meshes during mesh generation. Volumetric controls in STAR-CCM+work in conjunction with volume shapes. A volume shape is a closed geometric figure that can be usedto specify a volumetric control for surface or volume mesh refinement or coarsening during the meshing

process. Volume shapes were "built" to encompass more computationally demanding and

computationally important spaces of the mesh, e.g., the space around the bow and around the stem(Figure 18), as well as the space around the free surface up to the height of the generated waves.Through the volumetric controls, those spaces, covered by the volume shapes, were specified to have amore refined mesh. The driving factor behind the mesh refinement process was to maintain a balance

between getting satisfactory results and keeping the computational costs as low as possible.The template growth rate controls the stepping from one cell size to the next within the core mesh.

This was set to medium which gave a minimum of two equal sized cell layers per transition.

37

Figure 19 shows profile views of the volume meshes of the three types of simulations created(with free surface, with appendages and no free surface, and with no appendages and no free surface).Looking at these pictures it is easy to notice the regions where, due to the volumetric controls, the meshhas a specific and discrete density. The volume meshes of the simulations without free surface, with andwithout appendages, are quite similar, but the volume mesh of the simulations with the appendages issomewhat finer in order to effectively capture the details of the appendage surfaces.

Figure 18: Examples of volume shapes used to control the mesh density.

38

Figure 19: From top to bottom, profile views of the volume meshes generated for the simulations with free surface and

free motions, the simulations without free surface with appendages and without appendages. In the uppermost picture

the bow of the hull looks to the left while in the other two to the right.

39

One of the attributes of the finite volume method implemented in STAR-CCM+ is that, unlike

the finite difference method, it can be applied to mesh cells of any arbitrary shape. It does not demand a

uniform, rectangular grid for computations. In other words, there is no demand for a structured mesh.

This has given rise to the use of meshes with no regularity known as unstructured meshes. The benefit of

using this type of mesh is that you have a lot of flexibility in shaping the mesh cells the way you like and

putting them where you want in the physical space, thus making it easier to match the mesh cells with

the boundary surfaces. This last characteristic is especially useful if there are complex geometries in a

simulation. For this reason the surface and volume meshes generated for the simulations described in

this work were unstructured.The meshing model used to generate the volume mesh in STAR-CCM+ gave a trimmed

hexahedral cell shape based core mesh. One of the desirable attributes of this meshing model is that it

does curvature and proximity refinement based upon surface cell size. It utilizes a template mesh

constructed from hexahedral cells from which it cuts or trims the core mesh based on the starting input

surface. Areas of curvature and close proximity are refined based upon the surface cell sizes. The

resulting mesh is composed predominantly of hexahedral cells with trimmed cells next to the surface.

Trimmed cells are polyhedral cells that can be described as hexahedral cells with one or more corners

and/or edges cut off.

4.2.2. The Prism Layers

One significant part of the volume meshing process is defining prismatic near wall layers.

This is possible, with the volume meshing model selected, by adding the prism meshing model as part of

the volume meshing process. The prism layer mesh usually resides next to wall boundaries in the

volume mesh and, thus, models the boundary layer. It is required to accurately simulate the turbulent

speed profile and predict the drag. Table 4 shows the number of prism layers and their thicknesses for

the different simulations created. More prism layers were utilized for the simulations without free

surface (Figure 20). When disregarding the appendages, the hull in all the simulations without a freesurface had the same number and thickness of prism layers. The prism layer thickness of the appendages

was defined relatively smaller than that of the hull, in accordance with their decreased boundary layer

thickness. The relative thickness percentages, in the last row of Table 4, represent the percent of the

prism layer thickness when divided by the waterline length. These values give the size of the prism layer

thickness in relation to a main dimension of the hull to show how this thickness relatively decreases for

40

the full scale simulations. The relative thickness of the model boundary layers, when allowing for scale,was estimated to be about two and a half times that of the full scale layers (Figure 21).

To estimate the change in the relative thickness of the boundary layer when transitioning tothe full scale, the turbulent boundary layer on a flat plate thickness formula, based on the 1/7-powerapproximation for the velocity distribution, was used, 8 = 0.373xRx- 1/, Rx = Ux/v , where 6 is theboundary layer thickness, x is a characteristic dimension, and Rx is the Reynolds number of the flow[25]. According to this formula the turbulent boundary layer increases in thickness with distancedownstream at a rate proportional to x/.

Table 4: Details on the prismatic near wall layers generated in the simulations.

Yes No No NoNo No No Yes Yes

Model Model Full Scale Model Full Scale- - - Hull Appendages Hull Appendages

5 8 8 8 8 8 80.010 0.035 0.347 0.035 0.010 0.347 0.0993

- 0.612% 0.244% 0.612% - 0.244% -

Figure 20: The boundary layer of the bare hull was modeled with 5 prism layers, in the simulations with the free

surface (left), and 8 prism layers, in the simulations without free surface (right).

41

Figure 21: The prism layers of the model size simulations (left) were defined relatively thicker than those of the fullscale simulations (right).

The full scale simulations were generated from the model scale simulations using the DTMB5415 hull scale factor 24.824 for the cases without free surface. These simulations are identical to the

model scale simulations with the exception of the relative thickness of the prism layers and the fact that

all dimensions are scaled by 24.824. More information on these simulations, as well as all thesimulations without free surface, are given in Chapter 6.

4.3. Mesh EvaluationTwo parameters were used to evaluate the generated mesh in each case, the wall y+ and the

convective Courant number, both scalar and dimensionless. The convective Courant number can only beused with the implicit unsteady model, thus it was only used to validate the simulations with the freesurface.

Resolving the boundary layer demands a high mesh resolution in the near-wall region. Thenormalized wall distance parameter y+ is used to verify the mesh quality near the wall and within the

boundary layer. It is defined as y+ = , , where Tw is the shear stress at the wall, p is the local

density, y is the normal distance of the cell centroid from the wall, and v is the local kinematic viscosity.Since the potential for errors increases with large values of y+, when using the high-y+ wall treatment, itis generally prudent to aim for y+ values between 30 and 50. Some cells will inevitably have a smallvalue of y+. That is acceptable. In general, values of y+ below 100 are considered acceptable. The low-y+ wall treatment requires the entire mesh to be fine enough for y+ to be approximately 1 or less. In this

42

work the all-y+ wall treatment is used because it is the most general and the values of y+ are intended tobe below 100.

The convective Courant number = V , is a means to evaluate the mesh in conjunction withdx'the chosen time step. It depends on the velocity V, the time step dt, and the interval length dx, which, inthis case, is the length of the cells. It is the ratio of the time step and the time required for a fluid particleto travel the cell length with its local speed. It is typically calculated for each cell, and it gives anindication of how fast the fluid is moving through the computational cells. A finer mesh drives theCourant number at higher values, a smaller time step drives it at lower values, and a higher velocitydrives it up. Implicit solvers are usually stable at maximum values in the range 10-100 locally, but witha mean value of about 1. The Courant-Friedrich-Lewy condition states that the Courant number shouldbe less than or equal to unity. In general, Courant numbers set to values less than 1 are expected to givemodels that run faster and with greater stability.

Figure 22 shows the wall y+ parameter values on the ship hull, for the simulations with thefree surface and those with the appendages, while Figure 23 shows the values of the convective Courantnumber. The wall y+ parameter receives larger values at the forward part of the bulbous bow in theappended hull simulations, but all values, for both y+ and Courant number, are within acceptable limits.

woof Y*

mV.

Wai Y+0.000 20.00 40.00 606W 80.O 100.00

Figure 22: The wall y+ parameter values on the DTMB 5415 hull at Fr=0.41. On top is the hull used in the simulations

with the free surface.

43

Convecnve Couront NumberOM 02000 040YY O00X0X.600M 0.80) L.00

Figure 23: The convective Courant number parameter values on the DTMB 5415 hull at Fr=0.41.

4.4. Boundary ConditionsAs has already been described, the boundary conditions drive the particular solution of the

general equations that govern any flow. Furthermore, any numerical solution of the governing flowequations must give a compelling numerical representation of the proper boundary conditions. Theboundary conditions applied at each boundary of the two types of simulations, with and without a freesurface, are summarized in Table 5, while Figure 24 shows the location of the different boundaries,listed in Table 5, in the simulations with the free surface. The boundary locations for the simulationswithout free surface are analogous; the hull boundary includes the appendages where those exist.

Table 5: Boundary conditions defined for each simulation.

Ship hull Wall (no-slip) Wall (no-slip)Ship deck Wall (no-slip) Wall (no-slip)Block symmetry plane Symmetry Plane Symmetry PlaneBlock side plane Velocity Inlet Symmetry PlaneBlock bottom plane Velocity Inlet Symmetry PlaneBlock top plane Velocity Inlet Symmetry PlaneBlock inlet plane Velocity Inlet Velocity InletBlock outlet plane Pressure Outlet Pressure Outlet

44

0

Region.Side

.OJgSI

,ReO. DRA egmetry

Figure 24: The boundaries are surfaces that completely surround and define the region.

The no-slip wall boundary condition represents the proper physical condition for a viscousflow, where the relative velocity between the boundary surface and the fluid immediatelyat the surfaceis assumed to be zero. If the surface is stationary with the flow moving past it as in this case, then thevelocity of the flow at the surface is zero.

At the inlet we prescribe a constant velocity which corresponds to the Froude number atwhich we run the simulation. The direction of the velocity, i.e., the direction at which the flow moves, isthat of the x-axis. In other words, it moves perpendicular to the inlet boundary surface and toward theoutlet. The velocity inlet boundary condition is suitable for incompressible flows. It may be used incombination with a pressure outlet boundary at the outlet, as was done with these simulations. Thepressure outlet boundary is a flow outlet boundary at which the pressure is specified. The pressure wasspecified to be the hydrostatic pressure of the flow with the reference pressure at the free surface beingthe atmospheric pressure at sea level.

A symmetry plane boundary condition is better used when the physical geometry of interestand the expected pattern of the flow have mirror symmetry. Thus, a surface is defined as a symmetryplane boundary if it is the imaginary plane of symmetry in a simulation that would be physicallysymmetrical if modeled in its entirety. The solution obtained with a symmetry plane boundary isidentical to the solution that would be obtained if the mesh was mirrored about the symmetry plane butin half the domain. The simulations presented in this paper had an imaginary plane of symmetry wherethis type of boundary condition was appropriate and utilized.

The symmetry boundary condition can also be used to model zero-shear slip walls in viscousflows. It was found to work well and was also used at the side, bottom, and top boundaries of thesimulations without a free surface. For the same boundaries in the simulations with a free surface the

45

velocity inlet boundary condition was found to provide better results. The velocity was that of the flow

with the same magnitude and direction as at the inlet.

4.5. The 6-DOF ModelThe DFBI (Dynamic Fluid Body Interaction) module in STAR-CCM+ is used to simulate

the motion of a rigid body in response to pressure and shear forces exerted by the fluid, as well as any

additional forces defined by the user (gravity force in the current work). The resultant force and momentacting on the body due to all influences are calculated, and the governing equations of rigid body motion

are solved to find the new position of the rigid body.

As in the free surface simulations the hull of the ship is modeled free in heave and pitch

motions the DFBI module is activated. The hull (deck included) of the ship is defined as a 6-DOF(Degrees Of Freedom) body on which the rigid body motion equations are solved.

Some properties of the 6-DOF body that are defined in the simulation are its mass, the

initial position of its center of mass, the diagonal components of the moments of inertia tensor, and the

release time, which is the time before calculation of the body motion begins in order to allow some time

for the fluid flow to initialize.The simulations without free surface did not need to use this model, as the hull was not

allowed any free motion.

46

CHAPTER

5THE DTMB 5415 BARE HULL MODEL WITH A FREE SURFACE

This chapter presents the results from the simulations with a free surface.

5.1. IntroductionThe first set of simulations created for this study were those of the bare DTMB 5415 model

hull with a free surface and free heave and pitch motions. This set included two simulations. The only

difference between them was the flow velocity, which corresponded to the Froude numbers 0.38 and

0.41. During the runs the hull trim, sinkage, and drag were recorded and evaluated against the

experimental ones [9]. Other results that were evaluated were the wave pattern on the free surface andthe wave profile along the hull.

5.2. Trim, Sinkage, and Resistance Results

In Gothenberg in 2010 at the Workshop on Numerical Ship Hydrodynamics [20] manyresearchers came together and presented their results on total resistance, sinkage, and trim using various

CFD codes and grid densities. At Froude number Fr-0.41 the average error for the total resistance over

experimental findings was 4.316%, for the sinkage 12.294%, and for the trim 11.472%. All these errors

corresponding to the use of the finer grid density from those for which results were presented.

Table 6 shows the results of the computations made for the present study at Fr-0.41,

Fr=0.38, Fr-0.36, and Fr-0.33 compared with the experimental (Exp.) data from Olivieri et al. (2001)[9]. At Fr-0.41, with the exception of the trim, the results compare very well with those fromGothenberg. The error percentage is given by: (Exp.-CFD)/Exp. x 100. The negative values of the trimangle correspond to the ship trimmed by the stem.

With the exception of the resistance, at lower speeds the agreement of the calculations from

the CFD simulations with the experimental data worsens, and, as we can see from the results in Table 6,

at Fr=0.36 and Fr-0.33 the CFD values for the sinkage and, especially, the trim deviate significantly

from the experimental data.

47

In an effort to improve the CFD results at a wider range of velocities a new mesh was

created. The volume mesh close to the hull was refined, but the volume mesh region transverse and

vertical dimensions were decreased resulting to a number of cells that was somewhat decreased

compared to the original volume mesh. Simulations with this new mesh were run at Fr--0.41 and

Fr--0.28. The results are given in Table 7. The resistance values at both speeds show a very good and

improved, in comparison with the results from the original mesh, agreement with the experimental data.

The agreement of the results for the sinkage and trim is not as good though and a significant deviation of

the CFD values from the experimental data can still be observed.

Figures 25-27 are plots of the towing tank experimental data for total resistance, trim angle,

and sinkage together with the CFD results shown in Tables 6 and 7. They give a graphic representation

of the agreement between the experimental and CFD values. A fourth order polynomial line has been fit

through the experimental data points in all of these graphs. The best match between experimental and

computational values is observed with the total resistance and an outlier is observed in the sinkage graph

with the sinkage value at Fr--0.41 using the newer mesh.

Figure 28 shows the time histories of the total resistance, trim angle, and sinkage as recorded

in STAR-CCM+ at Fr-0.38 for the 84 seconds that the simulation was run. The oscillatory behavior of

the graphs due to the existence of the free surface (i.e. waves) can be observed. Due to this behavior ofthe graphs the values in Tables 6 and 7 are averages of the oscillatory data. The resistance values given

in this figure have to be multiplied by 2 as the symmetry condition was used and only half the ship was

simulated as has previously been described. Further time plots of the resistance, trim, and sinkage at

Fr-0.41, from the simulations with the newer mesh, and from the simulations without the free surface

are given in Appendix C.The CFD code can give not only the total resistance but also the frictional and residuary

resistance to which the total resistance is subdivided. Figure 29 shows all these resistances at Fr-0.38.

The oscillations of the pressure resistance curve can be observed while the frictional resistance is

relatively stable. The oscillations of the pressure resistance values that can be attributed to the effect of

the free surface are transmitted to the values of the total resistance.

48

Table 6: Experimental vs. CFD resistance, trim, and sinkage data.

knots m/s m/s Fr Exp. CFD E%Exp. Exp. CFD E%Exp. Exp. CFD E%Exp.23.94 12.31 2.471 0.33 0.097 0.070 27.8 0.0164 0.014 14.7 69.2 67 3.226.11 13.43 2.695 0.36 0.047 0.068 -44.7 0.0198 0.0162 17.9 88.2 81.7 7.427.56 14.18 2.847 0.38 -0.06 -0.0603 -0.50 0.0217 0.0199 8.5 108.9 100 8.229.74 15.30 3.071 0.41 -0.421 -0.260 38.2 0.0269 0.0265 1.4 152.6 160 -4.8

Table 7: Experimental vs. CFD resistance, trim, and sinkage data using a different mesh.

knots m/s m/s Fr Exp. CFD E%Exp. Exp. CFD E%Exp. Exp. CFD E%Exp.20.31 10.45 2.097 0.28 0.108 0.07 35.2 0.0104 0.0085 18.3 45.1 44 2.629.74 15.30 3.071 0.41 -0.421 -0.37 12.1 0.0269 0.038 -41.3 152.6 157 -2.8

Total Resistance Experimental vs CFD results

n Experimental Results (INSEAN)0 CFD results* CFD results (newer mesh)

-Poly. (Experimental Results (INSEAN))

4)4,)qzoModel Speed (m/s)

Q,IV 4,

Figure 25: Total resistance experimental data from Olivieri et al. [91 plotted with the CFD results.

49

250

200

150

IGO

100

50

0

4

Trim Angle Experimental vs CFD results

U

-0.4

-0.6

Experimental Results (INSEAN)CFD Results

CFD Results (newer mesh)Poly. (Experimental Results (INSEAN))

0 0.05 0.1 0.15 0.2 0.25Froude Number (Fr)

0.3 0.35 0.4 0.45 0.5

Figure 26: Trim angle experimental data from Olivieri et al. [91 plotted with the CFD results.

Sinkage Experimental vs CFD Results

m Experimental Results (INSEAN)* CFD Results+ CFD Results (newer mesh)

-Poly. (Experimental Results (INSEAN))

a

a

0

00

U U

0 0

0 0.05 0.1 0.15 0.2 0.25 0.3

Froude Number (Fr)

Figure 27: Sinkage experimental data from Olivieri et al. [91

0.35 0.4 0.45 0.5

plotted with the CFD results.

50

0.2

0

-0.2

-0.8

il

M

-1.2

0.04

0.035

0.03

0.025

0.02

no

0.015

0.01

0.005

0

-0.005

Rt Plot

20 30 40 50 60 70 80Time (sec)- Rt

Y Rotation Plot

11-

0.1

09

05

07-

05

04

03 \

02

0 1

0

40 50Time (sec)

-Trim Angle

60 70 80

51

0.

so.

0.

0.

0.

0.

0.

0.

20 30

Z Translation Plot

Time (sec)-Sinkage

Figure 28: Time histories of resistance, trim, and sinkage as generated in CFD code STAR-CCM+ at Fr=0.38.

Fridional, Pressure, and Total Resistance Plot

00

30-

20

30 40 53Time (sec)

Rp -Rf-Rt

60 70 80

Figure 29: The CFD code also calculated the frictional and pressure resistances that add up to the total resistance.

52

5.3. Wave Pattern and Wave Profile at Fr=0.41Olivieri et al. [9] provide figures of the wave pattern and the wave profile along the hull at

Fr-0.41 from their towing tank measurements.

The top half of Figure 30 shows the experimental result from Olivieri et al. for the wave pattern

on the free surface at Fr=0.41, while the bottom half is the wave pattern that was derived from the CFD

code at the same Froude number. We notice that there is a good agreement with the CFD code capturing

the general form of the wave pattern from the towing tank tests. Number 1, on Figure 28, represents the

distance of one ship length.Figure 31 shows the experimental wave profile along the hull from Olivieri et al. in comparison

with the CFD wave profile at Fr-0.41. Distances on both axes of the graphs are divided by the waterlinelength of the hull.

Figure 30: Experimental (top) and CFD wave pattern at Fr=0.41.

53

AM3

0.025

402

0.015

OI

-nas

1) 0.1 0.2 03 (4 V.5 Oh Q7 QA Q9

+ Wave Profile DTMB 5415, Fr=0.41 (CFD)

I I I I0.2 03 (CA 0.5

xt.

Figure 31: Experimental (top) and CFD wave profile along the hull at Fr=0.41.In Figure 31 the experimental wave profile curves represent towing tank tests from three

institutes: DTMB (A), INSEAN (B), and IIHR (C).The wave profile from the CFD code follows the same pattern as the experimental profile,

with the lowest point being at about the middle of the ship, the highest point located at the bow a littleafter the forward perpendicular, and the wave rising again at towards the stem but not as much as at thebow. The main difference is that the wave at the bow in the CFD code rises considerably less than in thetowing tank tests, with the CFD giving a maximum value of about 0.022 and the experimental resultwith the lowest of the highest wave height values being 0.028. As previously mentioned the values forthe wave height have been divided by the ship length at waterline.

54

---------------

----------

----------------- ----------------- -------

-----------------------------------

--------------------------

-----------------

-------

In the towing tank report from Olivieri et al. [9] there is a photo of the bow wave at Fr-0.28.The visual comparison between the CFD and towing tank bow waves in Figure 32 shows a similar wavelength and crest height. The light refraction at the water surface, in the experiment, creates a deformedunderwater image of the ship.

Figure 32: Bow wave from the towing tank report (left) and from the CFD simulation at Fr=0.28.

5.4. Remarks

The goal of this study was to find a CFD simulation that would give values for all measuredquantities (trim angle, sinkage, and resistance) in the 5 percent range when compared to theexperimental data. A lot of different meshes, different time steps, different volume mesh domaindimensions, and even some different boundary conditions were tried. While it was possible to get two ofthese quantities in the 5 percent range (see results previously presented in this Chapter) there was alwaysone value that would deviate from this range. In this study the resistance computations were the mostconsistently accurate even in cases where the trim and sinkage were very different from theexperimental data.

While the focus in the present study was at higher speeds (Fr-0.38 and 0.41) some effortswere made at lower speeds as well, e.g. Fr=O. 16 and Fr-0.28. In general the results, at the lower speeds,were not as good. One reason is that for smaller values of resistance, trim, and sinkage at lower speedsmore accurate numerical predictions relative to the higher speeds are required to achieve 5 percentaccuracy compared to the experimental data. Another reason is that the exact same simulations that wereused for the higher speeds were also used for the lower speeds, changing only the flow velocity. This

55

study showed that in order to predict the resistance, trim, and sinkage at the lower speeds with a similar

accuracy as at the higher speeds adjustments would need to be made to at least the volume mesh andmaybe the time step and the wall function. When a newer mesh was created refined at the area

surrounding the hull combined with the use of a smaller time step and a smaller volume mesh domain

the resistance at Fr--0.28 was predicted very well.

56

CHAPTER

6THE DTMB 5415 HULL MODEL WITH APPENDAGES

The results from the simulations without a free surface are presented. The appendageresistance is analyzed at model scale and full scale simulations of the DTMB 5415 hull.

6.1. IntroductionIn addition to the bare hull simulations, where the numerical computations of resistance,

trim, and sinkage were evaluated against experimental data [9], another set of simulations was preparedthat attempted to examine the effect of the appendages on the resistance and to evaluate the numericalresults with respect to available experimental data [10], as has already been seen in Chapter 2. Theappended DTMB 5415 hull model presented in Figure 33 was used.

Figure 33: DTMB 5415 hull model with appendages.

Borda ran towing tank tests using the DTMB 5415-1 model and derived the resistance of theappended hull at various speeds. He then extrapolated the results to the full scale using the ITTC 1957correlation frictional line in combination with a correlation allowance (CA) of 0.0004. The full scalevalues of the effective power, the frictional power, and the residuary resistance coefficient are the onesthat he gave in his paper. For the full scale predictions the ship (at the full scale) was assumed to beoperating in calm, deep, salt water at 590 F (15 C). During his experiments the model was free to trimand heave, but restrained in yaw.

Instead of running the simulations with the modeled hull free to trim and heave, as we did inthe first set of simulations, the hull was now fixed in space (with the flow moving around it). Only thesubmerged part of the hull, below the waterline, was simulated; in other words, there was no free

57

surface. The assumption made was that the appendages were sufficiently below the free surface so that

their resistance was not significantly affected by the wave induced flow field. Nor was the appendage

resistance significantly affected by the hull motions in heave and pitch. Thus, we could achieve

simulations that would run much faster.

By running simulations for the hull with and without appendages the additional resistance of

the appendages could be estimated. The appendage resistance could then be added to existing data for

the bare hull resistance [9] and the total appended hull resistance found. This data could now beconverted to represent the full scale ship, in the same manner that Borda did, and evaluated against the

experimental data [10].In evaluating the results of this set of simulations in this way, the purpose was to see how

well they could give the effect of the appendages to the bare hull resistance. If the aim was a more

comprehensive CFD numerical approach, independent of experimental data, instead of using data from

Olivieri et al. (2001) [9], data from numerical simulations, as those presented in Chapter 5, with freesurface and the bare hull free to heave and pitch, could be used instead, or, even more comprehensively,simulations could be ran with the appended model floating on a free surface allowed to m