Ship Hull Resistance Calculations Using CFD Methods
by
ARCHIVES
Petros Voxakis
Bachelor of Science in Marine Engineering
Hellenic Naval Academy, 2003
MASSACHUSETTS INS
OF TECHNOLOGY
JUN 2 8 2012
LIBRARIES
Submitted to the Department of Mechanical Engineering in Partial Fulfillment
of the Requirements for the Degrees of
Naval Engineer
and
Master of Science in Mechanical Engineering
at the
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
May 2012
02012 Petros Voxakis. All Rights Reserved.
The author hereby grants to MIT permission to reproduce and to distribute publicly paper
and electronic copies of this thesis document in whole or in part in any medium now known
or hereafter created.
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Certified by
I
,jv
Department of Mechanical Engineering
May 23, 2012
A
I
Chryssostomos Chryssostomidis
Doherty Professor of Ocean Science and Engineering
Professor of Ocean and Mechanical Engineering
Thesis Supervisor
Accepted by
David E. Hardt
Professor of Mechanical Engineering
Chairman, Departmental Committee on Graduate Students
1
E
Page Intentionally Left Blank
2
Ship Hull Resistance Calculations Using CFD Methods
by
Petros Voxakis
Submitted to the Department of Mechanical Engineering in Partial Fulfillment of the
Requirements for the Degrees of
Naval Engineer
and
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 power
available to designers, in addition to more efficient codes, have made CFD a valuable tool for early
stage 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 and
pitch, thus allowing the simulation to achieve steady dynamic attitude for each speed run. The effect of
dynamic attitude on the resistance is considered to be significant and requires accurate prediction. The
results 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 of
CFD as an effective tool in design space exploration. This will significantly reduce the time and cost of
studies that previously depended solely on physical model testing during preliminary ship design efforts.
Thesis Supervisor: Chryssostomos Chryssostomidis
Title: Doherty Professor of Ocean Science and Engineering
Professor of Ocean and Mechanical Engineering
3
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.
4
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 ....................................
26
3.3. 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 Work ....................................................................
75
References ...........................................................................................................-...-
77
Appendix A - Model 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). .......................................................................
23
Table 3 - Physics models utilized by each simulation type, with or without a free
surface . ...........................................................................................................................
27
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 different
m esh ................................................................................................................................
49
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 simulations .......................................................................................
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
3
simu lation s......................................................................................................................6
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
computation s ..................................................................................................................
84
Table 16 - Frictional resistance coefficient for the hull and each appendage as derived
from the frictional resistance computations in the CFD simulations .............
7
85
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 Without the Stem Wedge [10]....................................................................
16
Figure 6 - STAR-CCM+ Pictures of the Fully Appended Stem of Model 5415..........17
20
Figure 7 - Bilge keel geom etry ....................................................................................
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 ..............................................................................................................
31
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
blo ck...............................................................................................................................
34
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. .................
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
38
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.......................................................................................
Figure 25 - Total resistance experimental data plotted with the CFD results. .............
45
Figure 26 - Trim angle experimental data plotted with the CFD results ............
Figure 27 - Sinkage experimental data plotted with the CFD results ...........................
50
49
50
Figure 28 - Time histories of resistance, trim, and sinkage as generated in CFD code
STA 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 ...........................................................................................................................
Figure 33 - DTMB 5415 hull model with appendages ..................................................
55
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 ........................................................................................................................
Figure 38 - Percentage subdivision of the total resistance in frictional and pressure,
or residuary, drag for the model and full scale hull....................................................66
9
65
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 .....
10
90
CHAPTER
1
INTRODUCTION
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 (Highly
Maneuverable Aircraft Technology) was an experimental NASA aircraft designed to test concepts of
high 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 wing
was 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 highspeed 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 STARCCM+ where the simulations were generated.
12
CHAPTER
2
EXISTING 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 by
the 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. They
are 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 around
1980 [8]. It was constructed at the DTMB model workshop from a blank of laminated wood using a
computerized 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 present
experimental 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 was
designated Model 5415-1 to distinguish it from 5415, which had controllable pitch shafts and struts. In
addition, 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 both
configurations. In this report, from Borda (1984) [10], several experiments were made with different
appendage 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 the
present study. For experiment 33 the DTMB 5415 hull is fully appended but with dummy hubs in place
of propellers, the position of the rudders is at 0 degrees, and the resistance characteristics, with still air
drag not included, are given in terms of effective horse power converted to the full scale ship with a
correlation 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 DTMB
5415 model are given in Table 1. A picture of the fully appended model 5415-1 stem is shown in Figure
5. If the propellers in this picture were replaced with dummy hubs it would show the appendage
configuration used for experiment 33. Figure 6 shows the appended hull of DTMB 5415 as modeled and
used in the relevant CFD simulations presented in this study. Figure 3 shows model DTMB 5512 which
is another geosym of DTMB 5415, this time at a scale of 1/46.6, which was used by the IIHR. The
DTMB 5512 model has contributed significantly in the generation of benchmark information for
validation of CFD results.
Figure 1: Geometry and photo of model INSEAN 2340.
Figure 2: Geometry and photo of model DTMB 5415.
14
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
Scale factor
M odel
24.824
Length between perpendiculars
L,, (M)
142.0
5.720
Length 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
0.248
Trim angle (Initially)
(deg)
0.0
0.0
Displacement
A (t)
8636.0
0.549
Volume
V (m3)
8425.4
0.549
Wetted surface
Sw (m2)
2949.5
4.786
Wetted 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
15
AEu:IG
0
Figure 5: Photographs of the Fully Appended Stern of Model 5415-1 Representing DDG-51
Without the Stern Wedge [10].
16
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 of
resistance 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 and
waves, 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 difference
between 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. This
is 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:
18
(i)
During the model tests the appendages are tested into a much smaller Reynolds number than
at full scale. This means that while the appendages, in the model tests, are intersected by a
laminar 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 in
separated flow decreases.
(iii)
The relative thickness of the model boundary layers, when allowing for scale, is about double
that of the full scale layers for usual model / full scale sizes. As a result, velocity gradient
effects 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 the
boundary layers.
(iv)
Each appendage, attached to the hull, runs at its own Reynolds number, thus, when
measuring its drag at the model size, the procedure to scale to the full size ship will be
different.
Some equations and data that can provide detailed estimates of the appendage drag at the appropriate
Reynolds number in the absence of hull model tests are given in [12], [13], [14], [15], [16] and
presented below.
(i)
Bilge keels
The two sources of drag for the bilge keels are skin friction due to the added water surface
and interference drag at the connection with the hull. A procedure recommended by ITTC to
account for bilge keel drag is to multiply the total resistance with (S + SBK)/S, where S is the
wetted 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 =pSBKV2CF
2
[
2-
+Y
(1
When Z is large interference drag tends to zero, and when Z tends to zero interference drag
can be assumed to be equal to skin friction drag. L is the average length of the bilge keel to
be used when calculating CF.
19
L
Figure 7: Bilge keel geometry.
(ii)
Rudders, shaft brackets and stabilizer fins
Here 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:
t31
S
CM
1 pS
F
X 10-1, (3)
+ 40
1.25 -+
Dcs =-P
2
Cf
A
Ca
where 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
20
(4)
where c is the chord length used for the calculation of CFHoerner [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:
1
Dsp = 0.24-p
2 t,
(5)
1
Dp = 0. 7 5CDpalm h
DINT =
Whp 1 pV 2 , (6)
t 0.00031
1
2
3
0.75-t-
P2tz
C
(t)2
203
(7)
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 bossings
Propeller 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, CDE
According to Hoerner [13], for Reynolds number Re < 5
x
105 (based
on shaft diameter), the
shaft drag is given by:
1
2
2
DSH = -pLSHDSV (1.1sin'a + WcCF),
(8)
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
V
Figure 9: Shaft and bracket geometry.
The equations for the cylindrical portion drags as offered by Kirkman and Kloetzi [15] are:
3
CDP = 1.sin
a, Re < 1 x 10 5
(9)
-0.7154logioRe + 4.677, 1 x 10 5 < Re < 5 x 105, a >
CDP =
CDP =
#
(10)
(-0.7154logioRe + 4.677) [sin 3 (1.7883logioRe - 7.9415)a],
1 x 10s < Re < 5 x 10s,a < fl
CDP
= 0.6sin 3 (2.25a),
(11)
Re > 5 x 10s, 0 < a < 400
(12)
CDP = 0.6, Re > 5 x 105, 400 < a < 900 (13)
where Re = VDc/v,
projected area (L
x
P
= -71.54logioRe + 447.7 and the reference area is the cylinder
Dc).
CF = 1.327Re- 0os, Re < 5 x 10s
1
1700
(3.461logioRe - 5.6)2
Re
CF =7,
(14)
Re > 5 x 10s
(15)
where 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 +
where Vs is the ship speed,
ITTC 1957 line and
SAp
CF
SAPP +
k2)E
RBT,
(18)
is the friction coefficient for the ship determined from the
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,
where
dT
(20)
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
1.5-2.0
Rudder behind stem
1.3-1.5
Twin-screw balanced rudders
Shaft brackets
2.8
3.0
Skeg
1.5-2.0
Strut bossings
Hull bossings
Shafts
Stabiliser fins
Dome
Bilge keels
3.0
2.0
2.0-4.0
2.8
27
1.4
For the current study the appendages of the twin screw DTMB 5415 model consisted of the twin
rudders and rudder shoes, the twin shafting, the shafting brackets or struts, and the bilge keels. CFD
simulations were run for the model with and without the appendages. The total appendage drag, as well
as the drag of each appendage separately, was calculated from these simulations. As part of the analysis
of the results the percentage of each of the appendage drags to the total bare hull drag was found. A
comparison of the CFD findings with results derived from some of the empirical equations previously
mentioned was also made.
23
CHAPTER
3
THE 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. Background
Three 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 be
expressed 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 equations
with 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
Dt
Conservation form
Dt
(21)
+ V - (pV) = 0 (22)
Momentum equations
Nonconservation form
x component
p Du
Dt =
y component
pD
Dt
+
a
x ++
p+ax
ax
ay
+ pfX (23a)
y + az
TY+az
Oz
ay
24
+ pfy (23b)
z component
+
+
+Zpf
(23c)
2(puV)=)
+
+
+a23
a(PV)+ V - (pV) =
+
+
+
+
+
Dw = -
+
Conservation form
+
x component
y component
z component
a(Pw + V - (pwV) =
az ax
at
ay
+
pf
+ pf
az
+ pf
z
(24a)
(24b)
(24c)
Energy equation
Nonconservation form
D
Dt
K(
a(vp)
ay
e +
V2
2)-
a
+
.
pq
T)
a
a aT+
aT
+ ay k-ayl +z(kz
k
( ax)
++
+ pf - V (25)
)v=pi+
a[p(e+Y ]+V -p(e +Y
a-(k aT+
ay \ay
a(uTyx) +
ay
a(up)
-(k aT
z \az
az
a
ax
_(vyy_
___(vxy
az
ay
a(up)
86~x
aUZ + av~)+ av~)+
ay
ax
az
a6u~xx) a(uryx)
a(wp)
a(PVP+a(TX)++
ay
ax
az
(zy + (z
ax
az
Conservation form
p
ax
vxy)++
ax
a(vp)
ay
ay
+
+
Uk
a wp) + a(UTXX) +
ax
-az
az
+
ax
+
+awTxz)
a(WTZ) + awTzz) + pf -V (26)
ay
az
The conservation form of the governing equations derives from the control volume (finite or
infinitesimal) fixed in space with the fluid moving through it, while the nonconservation form
corresponds 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
3.2. The Reynolds Averaged Navier-Stokes (RANS) Solver
The 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, SM
is 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:
(28)
vof + U - VVof = 0
The Finite Volume commercial code STAR-CCM+ [19] was used for the solution of RANS
equations on trimmed unstructured meshes as presented in Chapter 4.
26
3.3. The Physics Models
Table 3: Physics models utilized by each simulation type, with or without a free surface.
Eulerian Multiphase (water, air)
Constant Density Fluid (water)
Implicit Unsteady
Steady
K-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-LSQ
Volume of Fluid (VOF)
No Free Surface
K-Epsilon turbulence model
The 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 for
the turbulent kinetic energy k and its dissipation rate E in order to enable the derivation of the turbulent
viscosity itTwo-Layer All y+ Wall Treatment
To 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 the
turbulent 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 the
wall 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 Flow
The 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 Unsteady
The 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-Dimensional
The 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 Multiphase
The 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 required
for 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
Gravity
The 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) is
taken 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-LSQ
The 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 GreenGauss method.
29
CHAPTER
4
THE 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 Mesh
The 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 code
STAR-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 the
origin of the axes. Finally, the hull was meshed to a stereolithography (STL) file format. STL files
describe 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 the
right-hand rule) of the triangles using a three-dimensional Cartesian coordinate system. The STL format
specifies 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 free
surface, 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 without
free 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 also
contained 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 by
one 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 not
required 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 Description
After 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 simulations
without 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 multiplied
by the scale factor 24.824.
The dimensions of the block that defines the volume mesh region, for the simulations with and
without 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 the
mesh 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 used
to 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 a
more 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 mesh
has a specific and discrete density. The volume meshes of the simulations without free surface, with and
without appendages, are quite similar, but the volume mesh of the simulations with the appendages is
somewhat 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 free
surface 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 to
the full scale, the turbulent boundary layer on a flat plate thickness formula, based on the 1/7-power
approximation for the velocity distribution, was used, 8 = 0.373xRx-
1/,
Rx = Ux/v , where 6 is the
boundary 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 distance
downstream at a rate proportional to
x/.
Table 4: Details on the prismatic near wall layers generated in the simulations.
Yes
No
No
No
No
No
Yes
Yes
Model
Model
Full Scale
Model
Full Scale
-
-
-
Hull
Appendages
Hull
Appendages
5
8
8
8
8
8
8
0.010
0.035
0.347
0.035
0.010
0.347
0.0993
-
0.612%
0.244%
0.612%
-
0.244%
-
No
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 full
scale simulations (right).
The full scale simulations were generated from the model scale simulations using the DTMB
5415 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 the
simulations without free surface, are given in Chapter 6.
4.3. Mesh Evaluation
Two 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 be
used with the implicit unsteady model, thus it was only used to validate the simulations with the free
surface.
Resolving the boundary layer demands a high mesh resolution in the near-wall region. The
normalized 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, it
is generally prudent to aim for y+ values between 30 and 50. Some cells will inevitably have a small
value of y+. That is acceptable. In general, values of y+ below 100 are considered acceptable. The lowy+ 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 to
be below 100.
The convective Courant number = V
dx'
, is a means to evaluate the mesh in conjunction with
the chosen time step. It depends on the velocity V, the time step dt, and the interval length dx, which, in
this case, is the length of the cells. It is the ratio of the time step and the time required for a fluid particle
to travel the cell length with its local speed. It is typically calculated for each cell, and it gives an
indication of how fast the fluid is moving through the computational cells. A finer mesh drives the
Courant number at higher values, a smaller time step drives it at lower values, and a higher velocity
drives it up. Implicit solvers are usually stable at maximum values in the range 10-100 locally, but with
a mean value of about 1. The Courant-Friedrich-Lewy condition states that the Courant number should
be less than or equal to unity. In general, Courant numbers set to values less than 1 are expected to give
models that run faster and with greater stability.
Figure 22 shows the wall y+ parameter values on the ship hull, for the simulations with the
free surface and those with the appendages, while Figure 23 shows the values of the convective Courant
number. The wall y+ parameter receives larger values at the forward part of the bulbous bow in the
appended hull simulations, but all values, for both y+ and Courant number, are within acceptable limits.
woofY*
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
0
OM
02000
O00X0X.600M
Convecnve Couront Number
040YY
0.80)
L.00
Figure 23: The convective Courant number parameter values on the DTMB 5415 hull at Fr=0.41.
4.4. Boundary Conditions
As 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 flow
equations must give a compelling numerical representation of the proper boundary conditions. The
boundary conditions applied at each boundary of the two types of simulations, with and without a free
surface, 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 simulations
without 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 Plane
Block side plane
Velocity Inlet
Symmetry Plane
Block bottom plane
Velocity Inlet
Symmetry Plane
Block top plane
Velocity Inlet
Symmetry Plane
Block inlet plane
Velocity Inlet
Velocity Inlet
Block outlet plane
Pressure Outlet
Pressure Outlet
44
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 viscous
flow, where the relative velocity between the boundary surface and the fluid immediatelyat the surface
is assumed to be zero. If the surface is stationary with the flow moving past it as in this case, then the
velocity of the flow at the surface is zero.
At the inlet we prescribe a constant velocity which corresponds to the Froude number at
which we run the simulation. The direction of the velocity, i.e., the direction at which the flow moves, is
that of the x-axis. In other words, it moves perpendicular to the inlet boundary surface and toward the
outlet. The velocity inlet boundary condition is suitable for incompressible flows. It may be used in
combination with a pressure outlet boundary at the outlet, as was done with these simulations. The
pressure outlet boundary is a flow outlet boundary at which the pressure is specified. The pressure was
specified to be the hydrostatic pressure of the flow with the reference pressure at the free surface being
the atmospheric pressure at sea level.
A symmetry plane boundary condition is better used when the physical geometry of interest
and the expected pattern of the flow have mirror symmetry. Thus, a surface is defined as a symmetry
plane boundary if it is the imaginary plane of symmetry in a simulation that would be physically
symmetrical if modeled in its entirety. The solution obtained with a symmetry plane boundary is
identical to the solution that would be obtained if the mesh was mirrored about the symmetry plane but
in half the domain. The simulations presented in this paper had an imaginary plane of symmetry where
this type of boundary condition was appropriate and utilized.
The symmetry boundary condition can also be used to model zero-shear slip walls in viscous
flows. It was found to work well and was also used at the side, bottom, and top boundaries of the
simulations 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 Model
The 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 moment
acting 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
5
THE DTMB 5415 BARE HULL MODEL WITH A FREE SURFACE
This chapter presents the results from the simulations with a free surface.
5.1. Introduction
The 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 and
the wave profile along the hull.
5.2. Trim, Sinkage, and Resistance Results
In Gothenberg in 2010 at the Workshop on Numerical Ship Hydrodynamics [20] many
researchers 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 from
Gothenberg. The error percentage is given by: (Exp.-CFD)/Exp. x 100. The negative values of the trim
angle 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 of
the 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
23.94
26.11
27.56
29.74
m/s
12.31
13.43
14.18
15.30
m/s
2.471
2.695
2.847
3.071
Fr
0.33
0.36
0.38
0.41
Exp.
0.097
0.047
-0.06
-0.421
CFD
0.070
0.068
-0.0603
-0.260
E%Exp.
27.8
-44.7
-0.50
38.2
CFD
0.014
0.0162
0.0199
0.0265
Exp.
0.0164
0.0198
0.0217
0.0269
E%Exp.
14.7
17.9
8.5
1.4
Exp.
69.2
88.2
108.9
152.6
CFD
67
81.7
100
160
E%Exp.
3.2
7.4
8.2
-4.8
CFD
44
157
E%Exp.
2.6
-2.8
Table 7: Experimental vs. CFD resistance, trim, and sinkage data using a different mesh.
knots
20.31
29.74
m/s
10.45
15.30
m/s
2.097
3.071
Fr
0.28
0.41
250
Exp.
0.108
-0.421
CFD
0.07
-0.37
E%Exp.
35.2
12.1
Exp.
0.0104
0.0269
CFD
0.0085
0.038
E%Exp.
18.3
-41.3
Exp.
45.1
152.6
Total Resistance Experimental vs CFD results
4
200
150
IGO
100
n Experimental Results (INSEAN)
0 CFD results
* CFD results (newer mesh)
-Poly.
(Experimental Results (INSEAN))
50
0
4,)
qzo
4)
Q,
IV
4,
Model Speed (m/s)
Figure 25: Total resistance experimental data from Olivieri et al. [91 plotted with the CFD results.
49
Trim Angle Experimental vs CFD results
0.2
0
il
-0.2
U Experimental Results (INSEAN)
-0.4
CFD Results
CFD Results (newer mesh)
M
-0.6
Poly. (Experimental Results (INSEAN))
-0.8
-1.2
0
0.05
0.1
0.15
0.2
0.35
0.3
0.25
0.4
0.45
0.5
Froude Number (Fr)
Figure 26: Trim angle experimental data from Olivieri et al. [91 plotted with the CFD results.
0.04
Sinkage Experimental vs CFD Results
0.035
0.03
mExperimental
Results (INSEAN)
* CFD Results
0.025
a
+ CFD Results (newer mesh)
-Poly.
a
(Experimental Results (INSEAN))
0
0.02
no
0
0.015
0
0.01
U
U
0.005
0 0
0
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
Froude Number (Fr)
-0.005
Figure 27: Sinkage experimental data from Olivieri et al. [91 plotted with the CFD results.
50
0.5
Rt Plot
20
30
40
50
Time (sec)
-
60
70
80
Rt
Y Rotation Plot
0. 11-
0.1
0. 09
0. 05
so. 07-
0.
05
0.
04
03
\
0.02
0.0 1
0
20
30
40
50
60
Time (sec)
-Trim
Angle
51
70
80
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
53
Time (sec)
60
70
80
Rp -Rf-Rt
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=0.41
Olivieri 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 waterline
length 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
I
0.2
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 little
after the forward perpendicular, and the wave rising again at towards the stem but not as much as at the
bow. The main difference is that the wave at the bow in the CFD code rises considerably less than in the
towing tank tests, with the CFD giving a maximum value of about 0.022 and the experimental result
with the lowest of the highest wave height values being 0.028. As previously mentioned the values for
the 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 wave
length and crest height. The light refraction at the water surface, in the experiment, creates a deformed
underwater 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 measured
quantities (trim angle, sinkage, and resistance) in the 5 percent range when compared to the
experimental data. A lot of different meshes, different time steps, different volume mesh domain
dimensions, and even some different boundary conditions were tried. While it was possible to get two of
these quantities in the 5 percent range (see results previously presented in this Chapter) there was always
one value that would deviate from this range. In this study the resistance computations were the most
consistently accurate even in cases where the trim and sinkage were very different from the
experimental data.
While the focus in the present study was at higher speeds (Fr-0.38 and 0.41) some efforts
were 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 speeds
more accurate numerical predictions relative to the higher speeds are required to achieve 5 percent
accuracy compared to the experimental data. Another reason is that the exact same simulations that were
used 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 and
maybe 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
6
THE DTMB 5415 HULL MODEL WITH APPENDAGES
The results from the simulations without a free surface are presented. The appendage
resistance is analyzed at model scale and full scale simulations of the DTMB 5415 hull.
6.1. Introduction
In 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 prepared
that attempted to examine the effect of the appendages on the resistance and to evaluate the numerical
results with respect to available experimental data [10], as has already been seen in Chapter 2. The
appended 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 the
appended hull at various speeds. He then extrapolated the results to the full scale using the ITTC 1957
correlation frictional line in combination with a correlation allowance (CA) of 0.0004. The full scale
values of the effective power, the frictional power, and the residuary resistance coefficient are the ones
that he gave in his paper. For the full scale predictions the ship (at the full scale) was assumed to be
operating in calm, deep, salt water at 590 F (15
C). During his experiments the model was free to trim
and heave, but restrained in yaw.
Instead of running the simulations with the modeled hull free to trim and heave, as we did in
the first set of simulations, the hull was now fixed in space (with the flow moving around it). Only the
submerged 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 be
converted 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 free
surface 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 move in heave
and pitch. The last approach, though, would be, computationally, the most expensive.
These simulations were run at three velocities and with corresponding Froude numbers.
6.2. Simulations at Model Scale
As already mentioned, the appendage resistance derived from CFD formulations was added
to bare hull resistance experimental data [9]. The appended model hull resistance was found and
converted to full scale using standard towing tank procedures (ITTC 1978 prediction method) similar to
the procedure used by Borda. This procedure assumes the division of the total resistance to a frictional
and a residuary, or pressure, part similar to what was previously described in Chapter 2, section 2.2. An
example of this procedure at Fr-0.41 is given in Appendix A. Table 8 summarizes the CFD numerical
results at three different speeds and gives a comparison with the experimental data. The percentage
difference between the two is given by Diff =
Exp-CFD X
Exp
100. Figures 34 and 35 give a graphical
representation of the agreement between numerical and experimental results for the effective and
frictional power, and for the residuary resistance coefficient respectively.
58
Table 8: Numerical vs. experimental appended hull resistance data.
(knots)
29.74
23.94
11.61
(m/s)
15.3
12.31
5.97
(m/s)
3.071
2.471
1.197
Exp.
35190
12963
1186
-
0.41
0.33
0.16
CFD
35653
12687
1190
-
5 --------------- -
Diff.
-1.3%
2.1%
-0.35%
Exp.
4.135
2.357
1.369
CFD
4.228
2.269
1.401
-
re kexpenmentj
- -
Pf (experiment)
20
Voloc~ty [Knotj
CFD
10735
5715
699
Exp.
10746
5717
703
*------------------pe-(CFD)-
--
*
15
Diff.
-2.25%
3.73%
-2.34%
Diff.
0.11%
0.04%
0.5%
------
Pf(CFD)
25
3
30
Figure 34: Lines of the experimental effective and frictional power at the range of 10-32 knots vs. the numerical
results at three speeds.
Curve of reitac data from~ experiment233
[Borda (1984)]
vs CFD results -----------------------------------...------3-----5 ---
-
----------------
Experiment
-----
15--------------
CFD
3 --
----
15
-
20
- --
25
---
30
35
VelocRy [Knot]
Figure 35: Lines of the experimental residuary resistance coefficient at the range of 10-32 knots vs. the numerical
results at three speeds.
59
6.3. Simulations at Full Scale
In addition to the model scale, these simulations were run at the full scale. As has been
discussed in Chapter 4, the procedure to get from the model scale simulations to the full scale was
simply scaling the dimensions using the proper scale factor, adjusting the prism layer thickness, and
using the proper full scale flow velocity. Results for the full scale simulations could then be compared to
the model scale results. Some evaluation of and conclusions about their differences could also be made.
Subtracting the results of the full scale CFD simulations with appendages from those without
appendages we could get the full scale appendage total resistance at each speed. Using standard towing
tank procedures, as described in Appendix A, the bare hull model resistance experimental data [9] were
converted to the full scale. Then the full scale total resistance of the bare hull was added to the full scale
appendage total resistance from the simulations and, in this way, we could get the full scale total
resistance to tow the appended vessel hull in calm water. This last result was multiplied by the vessel
speed; the effective power was found and compared with what was found from the model scale
simulations and the existing experimental data [10]. All these effective power data are given in Table 9.
Table 9: Numerical vs. experimental appended hull resistance data including the values
from the full scale simulations.
Vsipl
V'ship
(knots)
29.74
23.94
11.61
(m/s)
15.3
12.31
5.97
Vmlodel
(m/s)
3.071
2.471
1.197
Fr
0.41
0.33
0.16
Exp.
35190
12963
1186
CFD (Model)
35653
12687
1190
Effective Power Pe I NN]
CFD (Full scale)
Diff. (Model)
34344
-1.32%
12026
2.13%
1105
-0.35%
Diff. (F. Scale)
2.4%
7.2%
6.8%
Looking at the data in Table 9, one observes that the results from the use of the full scale
simulations do not agree as well with the experimental data as those from the model scale simulations.
This is expected because the procedure to derive the effective power from the full scale simulations is
less compatible with the procedure to obtain the experimental data than the procedure used for the model
scale simulations. More importantly, the effective power estimated from the full scale simulations is
consistently smaller in magnitude than that of both the experimental tests and the model scale
simulations. This also was expected.
As the ship moves through the water the Reynolds number that its hull encounters is different
from the Reynolds number that its appendages encounter. This is primarily due to the fact that the
characteristic length of each appendage changes and then due to the fact that the local fluid velocity at
each appendage varies which can be considered a second order effect. The method used in the present
study and by Borda to convert the appended hull drag to the full scale did not account for this variation
60
in the Reynolds number of each appendage; as a result, it tends to overestimate the full scale ship
resistance. Using directly computed full scale appendage resistance values helps "circumvent" this
overestimation to some extent, and it would be expected that smaller resistance values would be
obtained.
To demonstrate how this different Reynolds number that each of the appendages comes
across affects the total resistance outcome when extrapolated to the full scale with the ITTC 1978
method Figure 36 shows the ITTC 1957 frictional line with five points drawn on it. Each of the points
corresponds to one of the appendages or the bare hull when the characteristic length of each of them is
used to calculate the Reynolds number at Fr=0.41. It can be seen that as the Reynolds number gets
smaller values the frictional coefficient gets larger values. Given that the appendages operate at smaller
Reynolds numbers, when the extrapolation to the full scale is made, the residuary coefficient will get a
smaller value which leads to a smaller total resistance prediction at the full scale compared to using the
bare hull Reynolds number for all of the appendages as well. A logarithmic scale was used on the
horizontal axis of the diagram in Figure 36.
Calculations of the full scale ship resistance were made with each appendage accounted for
separately, with its Reynolds number adjusted to its specific characteristic length during the drag
conversion from model scale. The results of these calculations are given in Table 10. As expected these
values are smaller than the values given in Table 8; but they are also significantly smaller than the
values taken when the full scale appendages were used. This could be explained, to some extent, by the
fact that when extrapolating to the full scale the change in local velocity for each appendage was not
accounted for.
Table 10: Full scale effective power calculations when the Reynolds number of each appendage
was accounted for.
(knots)
(m/s)
(m/s)
-
CFD
29.74
23.94
11.61
15.3
12.31
5.97
3.071
2.471
1.197
0.41
0.33
0.16
31569
10954
991
61
2.OOE+01
-
ITTC'57
-U-Bare Hull
1.80E+01
-*-
Bilge Keels
-4-Shafts
1.60E+01
-U-Struts
-0-
1.40E+01
Rudders
1.20E+01
1.OOE+01
8.00E+00
'4
'4
6.OOE+00
*41
4b
4.OOE+00
2.OOE+00
O.OOE+00
1.OOE+04
1.OOE+05
1.OOE+06
1.00E+07
.OOE+08
1.OOE+09
1.OOE+10
1.00E+11
RnL
Figure 36: Difference in the frictional resistance coefficient value of each appendage when its Reynolds number is
calculated separately at Fr=0.41.
6.4. Other Results
In what follows some further results and results analysis from this set of simulations without
free surface are presented. These contain further evaluation of the simulation results, and also highlight
the possibilities of using CFD for the analysis of the flow around and the drag exerted on a ship hull. All
computation results are presented at both model and full ship scale for the three evaluated velocities.
Table 11 shows the total (frictional and residuary) resistance results of the appended hull
simulations analytically. Results are given separately for each appendage; the sum of the appendages or
total appendage resistance; the hull with the appendages; and the hull without the appendages. Table 12,
on the other hand, gives the bare hull total resistance results from the bare hull simulations. It also gives
the result of the subtraction of the bare hull resistance, from the simulations without appendages, from
62
the appended hull resistance, from the simulations with the appendages. This is the standard way of
estimating the appendage added resistance to the bare hull.
Figure 37 shows the total resistance of each appendage and of all the appendages together,
calculated either from the difference between appended and bare hull resistance (Table 12) or directly
from the appended hull simulations (Table 11), as a percentage of the bare hull total resistance (Table
12). Figure 38 shows how the total resistance, for each model or full scale ship wetted surface
component, is distributed between frictional and residuary (or pressure) resistance at 0.41 Froude
number. The distribution is similar for the other Froude numbers. The hull without appendages
corresponds to the "Appended Hull - Appendages" total resistance values in Table 11, while the hull
with appendages corresponds to the "Appended Hull" total resistance values in Table 11. Appendix B
contains the charts of the total resistance distribution for the other Froude numbers, and a table with the
analytical values of the frictional and residuary components of the total resistance. It is pointed out that
all these values of the resistance and resistance percentages correspond to CFD simulations without a
free surface. If a free surface existed then the pressure resistance, especially for the bare hull, would be
larger. The frictional resistance would not be significantly affected. To demonstrate this Figure 39 shows
what percentage of the total resistance is frictional drag and what is pressure drag when values from the
CFD simulations with a free surface are used at Fr-0.41. The pressure drag is now larger than the
frictional drag but this is because of the large speed; at lower speeds the frictional drag is larger than the
pressure drag but the pressure drag with the effect of the free surface has significantly larger values than
when a free surface does not exist. Table 13 gives the values of the frictional and pressure drag from the
simulations with and without a free surface at Fr-0.41 to show that the frictional drag does not change
much when a free surface exists whereas the pressure drag gets a much larger value.
Table 11: Drag distribution among the hull and its appendages from the appended hull simulations.
Model
1.197/
UJ.1O
U.545b
Model
2.471
0.33
3.162
2.742
2.976
3.04
11.92
60.16
48.24
Model
3.071
0.41
4.764
4.112
4.422
4.552
17.85
90.7
72.84
Ship
5.971
0.16
8668
5898
6584
7256
28406
141394
112988
Ship
12.315
0.33
35362
23476
25928
29032
113800
564776
450978
Ship
15.3
0.41
53860
35540
39120
44040
172560
855800
683240
63
Table 12: Total resistance results from the bare hull simulations. The difference between appended and bare hull drag
is also given.
Total Resistanc9e (N)
Scale
V (m1/s)
Fr-
Model
1.197
0.16
12
3.08
Model
2.471
0.33
48.23
11.93
Model
3.071
0.41
72.42
18.28
Ship
5.971
0.16
105691
35702
Ship
12.315
0.33
417722
147054
Ship
15.3
0.41
631068
224732
BareC Hull
64
Apene-BHll
25%
t-
- -
- - ---
20%
15%
10%
5%
15%
10%
5%
0#%
0%
15%____
15%
0%
0;--1
10%
5%
0%
-
2501
c-<~
10~
10%
5%
tI
04
10/
40%
_______________
for the
hull total resistance. The percentage
bare
the
of
percentage
a
as
given
Figure 37: Appendage total resistance
and from the difference
computations directly on the appendages
from
both
given
is
full set of the appendages
total resistance.
between appended and bare hull
65
120%
Model Fr=0.41
100%
80%
60%
40%
* Pressure/Total
Frictional/Total
20% 0%
0%;
120%
*
Full Scale Fr=0.41
100% 80%
60%
40% -
"
Pressure/Total
" Frictional/Total
20%
0%
Figure 38: Percentage subdivision of the total resistance in frictional and pressure, or residuary, drag for the model
and full scale hull.
66
120%
Model Fr=0.41 with Free Surface
100% i
80% 60% -
Pressure/Total
_---a
U Frictional/Total
40%
-
20%
0%
Bare Hull
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.
Fr=0.41Resistanice
(N)
Free Surface
Frictional
Pressure
Total
No
64.58
7.84
72.42
Yes
65.2
91.8
157
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.
So me comments on the above graphs and tables are:
1. The bare hull total resistance (Table 12) has, with the exception of the model scale result at
Fr--O. 16, smaller values than the result of the difference between appended hull and appendages
resistance in the simulations with appendages (Table 11). The difference can be attributed to
interaction effects between the bare hull and the appendages. This is especially important in the
full scale simulations.
2. In accordance with comment (1), the appendages total resistance is found to be greater when
calculated from the difference between appended and bare hull (Table 12) rather than directly
from the simulations with appendages (Table 11). Again, the difference between the two is the
resistance due to interaction effects between the appendages and the bare hull. These effects
become more important as the flow velocity increases.
3. The struts consistently give the smallest total resistance, while the rudders, which include the
rudder shoes, give the largest. The shafting gives the second largest total resistance with the
67
exception, again, of the model scale result at Fr-0. 16 where the bilge keels give the second
largest total resistance. The struts have the smaller wetted surface area whereas the shafting has
the largest. The rudders are thicker than the struts.
4. The rudders and especially the struts demonstrate larger pressure resistance than frictional
resistance. This could be due to not being perfectly aligned with the local flow. The thickness of
the rudders could also be a factor in its increased pressure resistance. Figure 40 shows the
streamlines at the struts and the rudder on a horizontal section somewhat below the water surface
at Fr-0.33. From this figure it is obvious that the struts are not well aligned not only from the
form of the streamlines but also from the velocity distribution around the struts which is not
symmetric. Figure 42 shows that the pressure coefficient has large values at the leading edges of
the rudders and especially the struts, in agreement with the large percentage of pressure
resistance.
5. In contrast to the rudders and struts, the total resistance of the bilge keels is almost completely
frictional resistance. The bare hull also demonstrates a far larger frictional resistance component,
but as has been shown this is due to the lack of a free surface.
6. The appendage resistance, when the bare hull resistance is subtracted from the appended hull
resistance, demonstrates a larger pressure resistance component. This is more obvious at the full
scale; it is due to the relatively large value of the frictional resistance for the bare hull, in
combination with the relatively large value of the pressure resistance for the appended hull.
When the appendage resistance is estimated directly from the computations in the simulations
with the appendages it is found that the frictional resistance is larger than the pressure resistance.
68
.A.4
U
Figure 40: Streamlines around the struts and at the rudder at Fr=0.33. The velocity magnitude on a horizontal section
of the flow is also shown.
Figure 41 shows the frictional resistance coefficient of each appendage and the bare hull, as
computed from the simulations, drawn against the Reynolds number and compared with the ITTC 1957
frictional line. The dotted line on the left is the Blasius solution for laminar flow. At a given velocity as
the characteristic length of each appendage changes so does the Reynolds number that it encounters. The
larger the velocity and the characteristic length of an appendage, the larger the Reynolds number
becomes. Subsequently, the results at the Full Scale (FS) are located at the right side of the diagram. The
ITTC 1957 frictional line is given by Cf =
Cf =
1 328
-
.
0.075
0
2
(logi 0 Rn-2)
.
The Blasius solution for laminar flow is
To get the frictional resistance coefficient from the CFD simulations we used the computed
frictional resistance Rf and the formula Cf =
Rf
1
2,
where p is the density of the water, Sw is the
-pSwV2
wetter area and V is the velocity. The CFD results are expected to be bounded between the ITTC and
Blasius lines and to follow the slope of these lines. A logarithmic scale was used on the horizontal axis
of the diagram in Figure 41. The frictional resistance coefficients calculated through the CFD
simulations are given in Appendix B along with the corresponding Reynolds numbers.
69
2.OOE+01
-
1.80E+01
-ITTC'57
-U-Bare Hull
-- r-Bilge Keels
1.60E+01
-)*-Shafts
-*K-Struts
1.40E+01
0
0
0 1.00E+01
'-I
-
-
1.20E+01
--
Rudders with Shoes
-
Bare Hull FS
-Bilge
Keels FS
-
*
44~
U
--
8.00E+00
-
Shafts FS
-
Struts FS
-Rudders
6.OOE+00
--
--
with Shoes FS
Blasius
4.OOE+00
2.OE+00
O.OOE+00
1.OOE+04
1.OOE+05
1.OOE+06
1.OOE+07
1.OOE+08
~-~-.-
_
1.OOE+09
1.OOE+10
1.OOE+11
RnL
Figure 41: Matching of the frictional resistance coefficient for each appendage and the bare hull, at the corresponding
Reynolds number, calculated from the CFD simulations with the ITTC 1957 frictional line and the Blasius solution for
laminar flow.
There is, in general, a good agreement between the slopes of the lines formed from the
results of the CFD simulations at three speeds and the ITTC and Blasius lines. The agreement is better
for the bare hull, the bilge keels, and the shafting, all of which have a predominant frictional resistance
component. The struts and rudders, with the large pressure resistance components, are to the left of the
diagram, due to their smaller characteristic lengths and corresponding Reynolds number values. The
struts, for the model scale simulations, are even transcending a bit to the left side of the Blasius line. The
bare hull model scale CFD results are also transcending both sides of the ITTC line.
The results of the simulations at Fr-0.16, especially at the model scale, seem to be the
cause of some inconsistencies for the final resistance results and analysis. As has already been seen at
the model scale Fr-0.16, not only does the bare hull have a greater total resistance than the appended
hull without the appendages in the simulations with the appendages and the bilge keels have a larger
total resistance than the shafting, but also the results for the frictional resistance coefficient at model
70
scale Fr=0. 16 seem to be causing the slopes of the lines formed by the CFD results to deviate from the
slopes of the Blasius and ITTC lines and even cross them in two instances. It may be that a finer mesh
was required to more precisely capture the flow effects at this low speed or that a different wall function
would be more suitable at this low Reynold number to effectively capture the effect of the boundary
layer.
Figure 42 below shows the skin friction and pressure coefficients drawn on the appended
DTMB 5415 hull at model scale and at Fr-0.41. The areas with larger values of the coefficients (drawn
with a red or closer to red color) have a greater contribution to the frictional and pressure resistance
respectively. It can be seen that the pressure coefficient at the leading edges of the struts and rudders
receives large values as has previously been described. Table 14 shows some values of the appendage
resistance estimated with the use of empirical methods which have been described in Chapter 2. The
values estimated by the CFD simulations are also given for the purpose of comparison. Appendage
resistance results are given from the use of two different empirical methods, the Holtrop and Mennen
method and one other as seen in Table 14. The only exception is the shafting full scale drag which was
not estimated empirically with a second method since the Hoerner equation for estimating the shaft drag
described in Chapter 2 is not valid for the Reynolds number at which it operates.
71
0.00000
Skin Friction Coefficient
40.000
60.000
20000
O.00rw
0
20 O0
X0
2.GO
SktnFrction Coefficient
40.000
60,000
Skin Friction Coefficent
40,00
60.U
80.000
80000
100.00
10.00
800L
1X0.0
rV
-0.60000
-0.36000
-0. 60X
-0.60
-0.36000
Pressure Coefficient
-0. 120M
0 12000
Pressure Coefficient
-0.120
0. 12w
0.3600
0.36X
0.60000
0.6X0
Pressure Coefficient
-0.3600
-0.12X
0 1200
0.36000
0.6000
Figure 42: The skin friction and pressure coefficients depicted on the appended hull model at Fr=0.41.
72
Table 14: Some appendage resistance predictions with empirical methods compared to the CFD computations.
Type
Append.
Fr
Appendages
Meth
Bilge
FS
Keels
FS
Rudders
FS
Shafting
Struts
Rudders
B. Keels
Struts
FS
Shafting
FS
Holtrop
0.16
3.714
28956
0.922
7186
0.813
6341
0.388
3025
1.591
12403
and
0.33
13.948
112609
3.461
27947
3.054
24659
1.457
11766
5.974
48237
Mennen
0.41
20.770
169343
5.155
42027
4.549
37083
2.17
17694
8.898
72539
Peck
0.16
-
-
1.473
10780
-
-
-
-
-
-
0.33
-
-
5.459
41656
-
-
-
-
-
-
0.41
-
-
8.101
62529
-
-
-
-
-
-
Peck and
0.16
-
-
-
-
1.460
11350
0.712
3640
-
-
Hoerner
0.33
-
-
-
-
5.362
45004
2.436
13612
-
-
0.41
-
-
-
-
7.952
68112
3.536
20248
-
-
Hoerner,
0.16
-
-
-
-
-
-
-
-
0.772
-
Kirkman
0.33
-
-
-
-
-
-
-
-
2.730
-
and
0.41
-
-
-
-
-
-
-
-
4
-
0.16
3.140
28406
0.812
6584
0.828
8668
0.71
5898
0.796
7256
0.33
11.92
113800
2.976
25928
3.162
35362
2.742
23476
3.040
29032
0.41
17.85
172560
4.422
39120
4.764
53860
4.112
35540
4.552
44040
Kloetzi
CFD
The appendages resistance CFD values in Table 14 are given as a result of the computations
in the simulations with the appendages directly. If the difference with the bare hull simulations was used
we would see significantly larger values at the full scale results. The values for the bilge keels predicted
by the empirical methods are larger than those predicted by the CFD code, with the Peck method giving
significantly larger values than both the CFD code and the other empirical method by Holtrop and
Mennen. The predictions given by the empirical methods for the rudder drag contradict each other as
one gives smaller values and the other significantly larger than the CFD values; the predictions at the
model scale from the Holtrop and Mennen method are very close to the values from the CFD code. The
values for the struts from the CFD code are significantly larger than both empirical methods, with the
exception of the model scale results using Peck and Hoerner empirical equations which are fairly close
to the CFD values. As previously described the bad alignment of the struts in the CFD simulations can
explain the relatively large values of the strut resistance given by the CFD code. The shafting resistance
values given by the Holtrop and Mennen method are much larger than the CFD code calculations; on the
contrary other empirical method gives smaller predictions at the model scale which are quite close to the
CFD values. The CFD values of the appendage drag, given in Table 14, do not capture the effect of the
73
interaction between appendage and hull due to their connection. This can explain, to some extent, the
cases where the empirical methods predict larger values.
From the results of the few calculations of the appendage drag that were made using
empirical methods in Table 14 there is a visible large scatter between the values given by different
empirical formulations as well as with those estimated by the CFD simulations. Using CFD simulations
at the full scale to estimate the appendage resistance there is no need for any extrapolations, as it would
be necessary if model scale simulations were used, and the effects of particular design features and
surface characteristics of each appendage can better be captured compared to using general and
approximate empirical formulations. As a result CFD simulations at the full scale are recommended to
be the method with the best potential to accurately predict the appendage resistance of a ship.
74
CHAPTER
7
CONCLUSIONS / RECOMMENDATIONS
7.1. Conclusions
The present study shows how it is possible to numerically simulate the fully turbulent free
surface flow around a destroyer-like hull form. The overall accuracy of the resistance results obtained
with the free running model is satisfactory for design purposes, showing an average difference of about
6% with peaks up to 8% at some speeds, while for the two runs using a finer mesh at the region close to
the hull combined with a smaller volume mesh domain the difference was kept below 3%. Some major
advantages over model test techniques come from the possibility to accurately estimate the added drag
of the appendages in both model and full scale, overcoming the historic problem of the error associated
with extrapolating the model scale measurements to full scale. Another interesting possibility offered by
CFD simulations is the appendage alignment study which can be done by the designer in a more
effective way in respect to model test practice.
7.2. Recommendations for Future Work
This study focused on predicting the bare hull resistance of a ship's model; then
simulations without a free surface were used to estimate the resistance of the appendages with a
minimized computational cost. The next step would be to simulate the hull with the appendages with a
free surface and free attitude. It is then possible to estimate the appended hull resistance directly from
these simulations without the need to add separate calculations for the appendages and the bare hull. The
results could be compared with the ones presented in this study. Future work may also focus on
modeling the ship to be self-propelled. Running self-propelled simulations of the ship at the full scale
predictions of the thrust deduction could be made and the effect of the propulsor on the flow and the
drag of the ship could be studied. Continuation of this study is also encouraged in order to investigate
75
the effect of different mesh types and different numerical solver techniques on the accuracy of the
obtained results.
76
REFERENCES
[1]
Rouse, Hunter, and Simon Ince: History of Hydraulics, Iowa Institute of Hydraulic Research,
Ames, Iowa 1957.
[2]
Tokaty, G.A.: A History and Philosophy of Fluid Mechanics, G. T. Foulis, Henly-on-Thames,
England, 1971.
[3]
Anderson, J. D., Jr.: ComputationalFluid Dynamics: The Basics with Applications, McGrawHill, New York, 1995.
[4]
Ceruzzi, P. E.: Beyond the Limits, The MIT Press, 1989.
[5]
Sahoo, P.K., Doctors L.J., and Renilson M.R.: Theoretical and experimental investigation of
resistance of high-speed round-bilge hullforms, Fifth International Conference on High-Speed
Sea
Transportation
(FAST
http://academic.amc.edu.au/~psahoo/Research/FAST99
[6]
'99),
1-12,
1999,
paper.pdf.
ITTC, 1999, "Report of the Resistance Committee," Proceedings International Towing Tank
Conference, Seoul, Korea & Shanghai, China, 5-11 September.
[7]
G2K, 2000, http://www.iihr.uiowa.edu/gothenburg2000.
[8]
Stern, F., Longo, J., Penna, R., Olivieri, A., Ratcliffe, T., and Coleman H.: International
Collaborationon Benchmark CFD Validation Datafor Surface Combatant DTMB Model 5415,
Twenty-third Symposium on Naval Hydrodynamics, 401-420, Val de Reuil 2000.
[9]
Olivieri, A., Pistani, F., Avanzini, A., Stern, F., and Penna, R.: Towing tank experiments of
resistance, sinkage and trim, boundary layer, wake, and free surface flow around a naval
combatant INSEAN 2340 model, IIHR Technical Report No. 421, 2001.
[10] Borda, G.: Resistance, Powering and Optimum Rudder Angle Experiments on a 465.9 foot (142
m) Guided Missile Destroyer (DDG-51) Represented by Model 5415-1 and Fixed Pitch
Propellers4876 and 4877, David Taylor Naval Ship R&D Center, 1984.
[11] I.T.T.C.: Final report of The Specialist Committee on Model Tests of High Speed Marine
Vehicles. Proceedings of the 22nd InternationalTowing Tank Conference, Seoul and Shanghai,
1999.
77
[12] Molland, A. F., Turnock S. R., and Dominic A. H.: Ship Resistance and Propulsion,Cambridge
University Press, New York, 2011.
[13] Hoerner, S.F.: Fluid-DynamicDrag,Published by the Author, Washington, DC, 1965.
[14] Peck, R.W.: The determination of appendage resistance of surface ships, AEW Technical
Memorandum, 76020, 1976.
[15] Kirkman, K.L. and Kloetzli, J.N.: Scaling problems of model appendages, Proceedings of the
19th ATTC, Ann Arbor, Michigan, 1981.
[16] Holtrop, J. and Mennen, G.G.J.: An approximate power prediction method. International
Shipbuilding Progress, Vol. 29, No. 335, July 1982, pp. 166-170.
[17] Edward V Lewis. Principles of Naval Architecture (Second Revision), Volume II - Resistance,
Propulsion and Vibration, SNAME (1988).
[18] Ferziger, J. H., and Perid M.: ComputationalMethods for FluidDynamics, Springer, New York,
2002.
[19] STAR-CCM+ v. 7.02.008 User's Manual, CD-Adapco, 2012.
[20] Gothenburg, 2010, "Gothenburg 2010, A Workshop on Numerical Ship Hydrodynamics",
Chalmers
University
of
Technology,
http://publications. Iib.chalmers.se/cpl/record/index.xsql?pubid= 131971.
[21] Batchelor, G.K.: An Introduction to Fluid Dynamics. Cambridge University Press, Cambridge,
UK, 1967.
[22] Wilcox, D.C.: Turbulence Modelingfor CFD. 2nd Edition, DCW Industries, La Canada, CA,
1998.
[23] Hess, J.L.: Panel methods in computationalfluiddynamics. Annual Review of Fluid Mechanics,
Vol. 22, 1990, pp. 255-274.
[24] Godderidge, B., Turnock, S.R., Tan, M. and Earl, C.: An investigation of multiphase CFD
modelling of a lateralsloshing tank. Computers and Fluids, Vol. 38, No. 2, 2009, pp. 18 3 [25] Newman, J.: Marine Hydrodynamics. MIT Press, Cambridge, MA, 1977.
78
19 3 .
APPENDIX
A
MODEL TO FULL SCALE
The conversion of the appended model hull resistance to the full scale ship followed standard
towing tank procedures as given below at Froude number 0.41. The appendages were not considered
separately and were assumed to come across the same Reynolds number as the hull.
model wetted surface
Sm:= 5.21m2
pm
998.424-
Scal:=24.824
ship length
S:=3208 mz
full scale ship wetted surface
fresh water density and kinematic viscosity at 18.9 C
2
-6 m
1.0311910
s
p
1025.87-
3
salt water density and kinematic viscosity at 150C
m
2
v
1.1843110 6
s
m
Vm :=3.071-
model speed
Fn := 0.41
Froude number
5
gravitational acceleration
g = 9.80665m
:
2
~=
V := En.,gAW
scale factor
3
m
vm
L:=142 m
model length
Lm := 5.72m
m
15.299892-
Rtm:=170.936 N
ship speed
5
appended model total resistance
79
7
Lm
Rnm:=Vm-= 1.70348x 10
vm
Cfm:=
model Reynolds number
0.075
20.002741
2)2
(log(Rnm) Rtm
Ctm
=
0.006969
model frictional resistance coefficient (ITTC 1957 line)
model total resistance coefficient
0.5.pm.Vm 2Sm
Crm :=Ctm - Cf m= 0.004228
Rn := V-
1.834473< 109
model residuary resistance coefficient
ship Reynolds number
V
ship residuary resistance coefficient set equal to that of the model
Crs := Crn
0.075
Cfs:=
= 0.001422
ship frictional resistance coefficient (ITTC 1957 line)
(log(Rn) - 2)2
Ca:=0.0004
correlation allowance coefficient
Cts := Crs + Cf s+ Ca = 0.00605
Rfs:= Cfs-0.5p-V 2 .
ship total resistance coefficient
ship frictional resistance
5.475723< 105 N
Rfst
(Cfs + Ca)-0.5p-V 2 . S = 7.016477x 1 N
Rrs
Crs -0.5p.V2-S = 1.628636< 10 N
Rts := Cts-0.5p-V2 .
2.330284< 10 N
ship total frictional resistance including
the correlation allowance
ship residuary resistance
ship total resistance
Pf := Rfst-V = 1.073513< 107 W
frictional power
Pe :=Rts -V = 3.565309x 1 7 W
effective power
80
APPENDIX
B
RESISTANCE DISTRIBUTION AND FRICTIONAL RESISTANCE COEFFICIENTS
The charts below give a picture of the total resistance distribution between frictional resistance
and pressure, or residuary, resistance for Froude numbers 0.16 and 0.33 at model and full size ship. This
information is given separately for each of the appendages, for the appendages altogether, calculated
from both the simulations ran with appendages and from the subtraction between the simulations with
and without appendages, for the hull with appendages, and for the bare hull computed directly from the
bare hull simulations and from the appended hull simulations by neglecting the computations made on
the appendages (hull without appendages). Table 13 gives all these values, for the total, frictional and
pressure resistance as computed from the simulations. Table 14 gives the values for the frictional
resistance coefficients at the three Froude numbers at which simulations were run.
81
120%
Model Fr=0.16
100%
80%
60%
" Pressure/Total
40%
* Frictional/Total
20%
0%
VIE
I I
III
~,
.~,
I
120%
Model Fr=O.33-
100%
80%
60%
. Pressure/Total
40%
* Frictional/Total
20%
0%
41~
82
Full Scale Fr= 0.16
1--120%
100%
80%
60%
" Pressure/Total
40%
* Frictional/Total
20%
0%
bol.
.4
120%
100%
80%
60%
Nl
Full Scale Fr=0.33
I
U
" Pressure/Total
40%
" Frictional/Total
20%
0%
Figure 43: Distribution of total resistance among frictional and pressure resistance. Results presented are from the
CFD simulations without free surface.
83
Table 15: Total, frictional, and residuary resistance values from the CFD computations.
Total
Fr=0.41
Fr=0.33
Fr=0.16
Frictional IfResiduary
Total
Frictional IResiduary
Total
Frictional j Residuary
Bare Hull
12
10.707
1.293
48.23
43.055
5.175
72.42
64.58
7.84
Appended Hull
15.08
12.32
2.76
60.16
48.626
11.534
90.7
73.02
17.68
11.94
10.324
1.616
48.24
41.256
6.984
72.84
62.06
10.78
3.08
1.613
1.467
11.93
5.571
6.359
18.28
8.44
9.84
3.14
1.99
1.15
11.92
7.37
4.55
17.85
10.966
6.884
Rudders
0.828
0.372
0.456
3.162
1.386
1.776
4.764
2.066
2.698
Struts
0.71
0.202
0.508
2.742
0.754
1.988
4.112
1.12
2.992
Bilge Keels
0.812
0.8
0.012
2.976
2.93
0.046
4.422
4.35
0.072
Shafting
0.796
0.62
0.176
3.04
2.302
0.738
4.552
3.4328
1.1192
Total
Frictional
Residuary
Total
Frictional
Residuary
Total
Frictional
Residuary
Bare Hull
105691
91019
14672
417722
356491
61231
631068
537081
93987
Appended Hull
141394
104996.8
36397.2
564776
411770
153006
855800
620566
235234
112988
88739
24249
450978
347950
103028
683240
524368
158872
35703
13978
21725
147054
55279
91775
224732
83485
141247
28406
16258
12148
113800
63820
49980
172560
96204
76356
Rudders
8668
3267
5401
35362
12946
22416
53860
19556
34304
Struts
5898
1503
4395
23476
5788
17688
35540
8690
26850
Bilge Keels
6584
6395
189
25928
25106
822
39120
37846
1274
Shafting
7256
5093
2163
29032
19980
9052
44040
30110
13930
App. HullAppendages
App. HullBare Hull
Appendages
Total
App. HullAppendages
App. HullBare Hull
Appendages
Total
84
Table 16: Frictional resistance coefficient for the hull and each appendage as derived from the frictional resistance
computations in the CFD simulations. The Reynolds number corresponding to the characteristic length of each
appendage at the different Froude numbers is also given.
Rn
Cf (x1000)
Rn
Cf (x1000)
Rn
Cf (x1000)
Bare Hull
6.64E+06
3.087
1.37E+07
2.913
1.70E+07
2.828
Rudders
170056
4.131
351052
3.611
436293
3.485
Struts
47128
5.037
97288
4.412
120911
4.243
Bilge Keels
2242655
3.919
4629575
3.368
5753713
3.237
Shafting
1232764
3.771
2544828
3.285
3162755
3.172
Rn
Cf(x1000)
Rn
Cf(x1000)
Rn
Cf(x1000)
Bare Hull
8.22E+08
1.711
1.70E+09
1.576
2.11E+09
1.538
Rudders
2.11E+07
2.366
4.34E+07
2.204
5.40E+07
2.157
Struts
5.84E+06
2.445
1.20E+07
2.213
1.50E+07
2.152
Bilge Keels
2.78E+08
2.043
5.73E+08
1.886
7.12E+08
1.841
Shafting
1.53E+08
2.02
3.15E+08
1.863
3.91E+08
1.819
85
APPENDIX
C
TIME HISTORIES OF RESISTANCE, TRIM, AND SINKAGE
In this appendix some further resistance, trim, and sinkage plots from the simulations with and
without a free surface are given. Resistance, trim, and sinkage for the simulations with a free surface are
plotted against time, whereas for the simulations without a free surface, where the flow was steady,
resistance is plotted against solution process iterations. The resistance values given in these plots have to
be doubled to get the full ship resistance as, due to symmetry, only have of it was simulated in the CFD
code. Negative values of the trim angle translate to a trim by the stem. It can be seen that the plots from
the simulations without a free surface lack the oscillations that the free surface causes to the simulations
with a free surface. The plots for the simulations with a free surface given in this appendix took about 48
hours to generate on 124 processors while those for the simulations without a free surface about 24
hours on 15 processors. All plots were generated by the CFD code STAR-CCM+.
Resistance Plot Fr-0.41
150
___________
-
___________
___________
__________
_
__________
_
130
110
-
--
90
________
70
0 50LL
30
____________
-
10-10-30
-50
10
20
40
30
Time (sec)
Rp--Rf
86
Rt
50
Z Translation Plot Fr-0. 41
E
-0,03
-0. 04
-0
20
40
30
6
50
Time (sed
-Sinkage
Y Rotation Plot Fr-0.41
0 7
0. 2
0.
0
40
20
50
Time (sec)
-Tnm Angle
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
Resistance Plot at Fr=0.41 for the Bare Hull, Without a Free Surface
40
30
10
0-
1000
2000
3000
5000
4000
6000
7000
9000
B000
iteration
-Rf -- Rp -Rt
Figure 45: Frictional, pressure, and total resistance plot from the bare hull simulations without a free surface at
Fr=0.41.
Resistance Plot at Fr-0.41 for the Appended Hull, Without a Free Surface
60
50
40
30
20
10
0
-10
1C00
200
3C000
400
5000
iteration
-Rf
-Rp
88
-Rt
600
7C00
8030
9000
Resistance Plot at Fr-0 41 of the Bilge Keel
3
0
-1
1000
2000
3000
5000
Iteration
4000
6000
7000
8000
9000
Rf -- Rp - Rt
Resistance Plot at Fr-O 41 of the Rudder
5
4-.
3-
2-
-1
-
1C00
1C060070000090
2000
3000v
4000
Iteration
-Rt
-Rp
-Rf
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 without a free surface at Fr=0.41.
89
Pesistance Plot at Fr-0.41 for the Hull xith the Appendages at Full Scale
500000
400000
300000-
200000
100000
1000
2000
3000
4000
iteration
-Rf
5000
6000
7000
000
-Rp -Rt
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