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OCR for page 640
Planing Hull Performance Evaluation
Using a General Purpose CFD Code
Eric Thornhill~, Neil Bose~, Brian Veitch~, Pengfei Liu2
(~Memorial University of Newfoundland, National Research
Council - Institute for Marine Dynamics)
ABSTRACT
Model experiments were used to evaluate CFD
simulations of a high-speed planing vessel. Fluent
(vS.3) was used to simulate the flow around a planing
vessel at steady speed through calm water using 3D
unstructured hybrid grids with hanging node
refinement. Force and moment data from the
simulations were used in an iterative scheme to
determine the dynamic equilibrium position of the
model at selected speeds. The numerical results are
compared with experimental data from model tests.
The strengths and weaknesses of the numericd
approach are discussed.
INTRODUCTION
Performance prediction is an important part of vessel
design. Common methods for predicting planing hull
performance include using empirical equations and
model testing. Empirical equations are often only
applicable to similar hull types over a small range of
parameters, while model testing is often prohibitively
expensive, particularly for small craft. Ever
increasing computer power is making the use of
computational fluid dynamics (CFD) as a
performance prediction tool a practical alternative.
This paper presents the results of a study to use CFD
to evaluate the performance of a high-speed planing
vessel moving at steady speed through calm water.
After a review of the state-of-the-art in CFD
methods (Thornhill, 2002), it was decided that an
unstructured, multiphase, finite volume code
employing the volume-of-fluid (VOF) method for
free surface capturing would be used for the study.
The use of a commercial CFD code was found to be
the best alternative as they are publicly available,
generally undergo extensive validation, have a wide
user-base, and receive periodic upgrades and
improvements. The code chosen was Fluent (vS.3~.
Fluent could not, however, be used to directly
simulate the behaviour of a planing vessel. The
performance of a high-speed vessel is intimately
linked to the orientation of the hull at speed, which
cannot be known a priori. Planing hulls rise and
change trim angle in response to the pressure field
generated by the flow. In order to solve for these
changes in hull position, the simulation method had
to ensure that dynamic equilibrium was achieved in
terms of lift and trimming moment. This was
accomplished with an iterative scheme wherein the
flow field was solved for discrete hull orientations
that were then adjusted based on force and moment
results until the conditions of equilibrium were met.
The work began with a set of physical model
experiments to provide the baseline to which the
numerical results could be compared. Three sets of
simulations were then performed to evaluate the
prediction method. The first set fixed the hull
orientation to match the trim and vertical position
measured in the physical experiments. This was
executed to provide a direct comparison of the
numerical results to the physical results. A second set
of simulations was then performed where only the
equilibrium condition of lift was satisfied. Trim
angles remained fixed at the experimental values.
These were used to examine the influence of sinkage
on the results. The last set of simulations solved for
equilibrium in both lift and trimming moment and
represent the results of predictions that would be
produced without the benefit of physical experiments.
A brief description of the physical model
experiments is given, followed by a description of the
numerical approach. Results of the simulations are
then given along with a discussion, and a comparison
with the physical model results.
BACKGROUND
Savitsky (1964) discussed the basic hydrodynamic
characteristics of prismatic planing hulls. Based on
previously published work, empirical equations for
lift, drag, wetted area, center of pressure, and
porpoising limits as functions of speed, trim angle,
OCR for page 641
deadrise angle and loading were given. A procedure
was presented for using these equations to predict the
performance of a prismatic planing hull. This paper,
and the work it was derived from, presents one of the
earliest methods for predicting planing hull
performance and is still widely used today. This
iterative method was based on choosing trim angles,
which were then fed into empirical equations that
produced values for lift and moment. Iterations
continued until these values balanced those produced
by the hull's weight and center of gravity.
Ikeda et al. (1993) addressed the need to include
the effects of trim and sinkage in high speed craft
predictions by performing a set of captive model tests
with systematic variations of the model's position
and attitude. Nine model shapes were tested. The
model was fixed to the tow carriage by a threw
component dynamometer that measured lift, drag and
trimming moment. Sinkage and trim were
incrementally varied to create a database of the
hydrodynamic forces for each model over a range of
Froude numbers. A computer program was also
developed to use this database to estimate the
linkage, trim angle, and resistance of a given model
at speed for a given ballast condition (displacement
and LCG). Hydrodynamic forces could be
determined by interpolation from the datable for a
given vessel attitude in an iterative scheme until they
were in equilibrium with the model's weight and
LCG. Simulations of this type were found to be in
good agreement with results obtained from free
attitude model tests.
Brizzolara et al. (1998) presented comparisons of
wave patterns and wave resistance from both
numerical and experimental results. A high speed
monohull and two catamaran type hulls were used in
model tests at Froude numbers up to 0.9. Their
boundary element code, previous used for slower
speed vessels, was extended for use on high speed
vessels by including calculations of dynamic
equilibrium. Forces and moments were evaluated
after each iteration and the model's position was
updated and re-meshed. The cycle continued until
convergence was achieved (usually under 10
iterations). Results for the Wigley hull in the speed
range from 0.2 to 0.8 were shown to be under-
predicted for linkage, trim, and wave resistance,
though trends in the data were roughly followed.
Yang et al. (2000) extended their unstructured,
free surface, inviscid, finite element based flow
solver (see Lohner et al., 1998) to account for sinkage
and trim effects in steady ship flows. Simulations
began with the model in its "at-rest" position. The
flow solution was then calculated and used to
determine sinkage and heave corrections for the next
iteration. The near field mesh moved with the hull,
far field meshes remained fixed, while intermediate
mesh elements were smoothed for even transition
from the near to far field grids. Iterations continued
until dynamic equilibrium was achieved. Sinkage and
trim corrections at each iteration were based on
current flow results in conjunction with the vessel's
waterplane area and moment of inertia. Tests were
performed for the Wigley and Series 60 hulls over a
range of Froude numbers. Results indicated
significant differences in wave drag between fixed
and free to trim and sink configurations, in agreement
with experimental observations.
Subramani et al. (2000) extended a CFD code
(CFDSHIP-IOWA) for surface-ship boundary layers,
wakes and wave fields to include the capability of
predicting sinkage and trim. Simulations were
performed on hulls of the naval combatant FF1052
and the Series 60. The CFD code uses the finite
volume method for block-structured grids. It
employed the Baldwin-Lomax turbulence model and
accounted for the free surface boundary conditions
with the aid of a body-free-surface conforming grid.
Dynamic trim and sinkage were calculated
iteratively. Forces and moments on the hull were
summed at the end of each iteration. The hull was
then re-positioned and the domain grid regenerated
for the next iteration, or until equilibrium was
achieved. Simulations on the two hulls used mesh
sizes from 216,000 to 906,000 nodes. When
compared with model experimental data, it was found
that although the trends in sinkage and trim were
predicted correctly, the percentage difference in
absolute values varied with Froude number.
The importance of dynamic equilibrium
calculations in vessel performance prediction has
been addressed by all of the above authors. The
procedure was similar in all cases. Different hull
orientations were tested in an iterative scheme until
forces and moments matched the required values.
Planing vessel performance is the most sensitive to
hull orientation making the additional equilibrium
calculations essential. This problem was addressed in
the current work by using a similar iterative
technique. A low dead-rise planing hull was chosen
(more conventional hull shapes were used by Yang et
al. 2000, and Subramani et al. 2000~. Simulations
were performed using a RANS CFD code with a free
surface capturing method.
PHYSICAL MODEL TESTS
The physical model experiments were performed in
the Clearwater Towing Tank at the National Research
Council of Canada's Institute for Marine Dynamics
and consisted of a series of resistance tests with a
planing craft. Tests covered several ballast
2
OCR for page 642
configurations (displacement and longitudinal center
of gravity) over a range of speeds. Measurements
were made of tow force, running trim and linkage,
hull pressures, wetted lengths and surface area, as
well as detailed wave profiles. Additional tests were
done to measure the boundary layer profiles at two
locations along the hull using a laser Doppler
velocimeter.
The planing hull used was a 1:8 scale model of a
full scale vessel currently in operation. The hull
surface, shown in Figure 1, was marked with station
numbers on the bottom and port side. Knife edges
extending lmm from the hull surface were fitted
along the chines to promote flow separation. The hull
was not prismatic but did have a simple shape as
shown in Figure 2. This cross section was constant
from the transom for about 2/3 the length of the hull.
A small flat bottom area at the centerline turns to a
low deadrise of 5.9°. This deadrise then turns sharply
to 40.8° near the chine (see Figure 2~.
Figure 1: Model Hull (LOA = 1.475m).
~ ' 530 ~ ~
1 lSnn ~ I
~ - i 99nn ~ 64nr1 _
Figure 2: Model Hull Cross Section. <, 30
~ 20 -
The model was free to heave, pitch and roll but
was restrained in yaw. The tow point was located
22 cm forward from the transom and 5 cm above the
baseline. Although several ballast conditions were
tested, only the design ballast condition was
examined in the numerical simulations. This
condition consisted of a model displacement of
29.6 kg with a center of gravity located 53.4 cm from
the transom, and 2.6 cm above the baseline. Resting
draft at the tow point measured 6.7 cm with a bow-up
trim angle of 1.1°. The model was tested for speeds at
intervals of 0.5 m/s up to 7.0 m/s.
NUMERICAL APPROACH
The Fluent (vS.3) CFD software is a finite volume
code using the VOF method for free surface
capturing. It includes several turbulence models and
supports fully unstructured hybrid adaptive meshes.
Though later used to solve for the dynamic
equilibrium position of the hull at speed, the code
was first tested to see if it could simulate the flow
around a planing hull in general.
During this testing phase, combinations of
domain sizes, meshing strategies, and solver
parameters were examined, many of which created
divergent solutions. The following are some of the
conclusions from this study:
. Although the problem was of a steady-state flow, a
transient solution scheme was necessary.
Time steps needed to be very small to avoid
divergence (~0.001 seconds).
The solution had to progress for some time in order
for pressure-induced forces to stabilize (~2500
time steps). Figure 3 shows an example of lift force
history of a typical simulation.
Turbulence models such as the Spallart-Allmaras
and k-s models could not be used in their standard
forms as they created excessive turbulence
generation at the air/water interface on the hull
bottom that quickly led to divergence.
When using an unstructured mesh that does not
have element faces that coincide with the calm
water surface (i.e. elements sporadically crossed
the initial air/water boundary), care had to be taken
to ensure these elements were assigned the correct
volume fraction when initializing for the first
iteration.
an -
0.0 0.5 1.0 1.5
Time [see]
Figure 3: Lift Force History
3
2.0 2.5
OCR for page 643
One of the consequences of these conclusions
was that it was necessary to restrict the mesh size as
much as possible in order to keep computation times
reasonable due to the large number of small tine
steps required. The final meshing strategy that was
used, relied on a relatively small domain size initially
given a fairly coarse mesh. The elements within
20 cm of the hull (model scale) were then subject to
hanging node refinement, resulting in increased
resolution in this area. Mesh sizes produced from this
process ranged in size from approximately 125,000 to
150,000 elements. Solution time on a 500au
DIGITAL Personal Workstation took from 2 to 4
days for a single simulation.
The planing model domain, shown in Figure 4,
was defined by a box (referred to as a 'tank') 5.5 m
long, 1.6 m wide and 2.1 m tall. The still waterplane
was defined at approximately 60% of the domain
height. The model and flow field were symmetrical
about the x-z plane at the model's centerline, so only
half the width of the full domain was meshed. A
symmetric boundary condition was then applied at
this location.
Figure 4: Planing Hull Model Domain
Another consequence ofthe small mesh size and
the lack of turbulence modeling was that frictional
resistance could not be predicted accurately. This
problem was addressed by separating forces into
pressure and frictional components. The numerical
simulations provided the pressure forces while the
frictional forces were determined by welLestablished
empirical means (Lewis, 1988) as described below.
The wetted lengths of the numerical model were
used to calculate the Reynolds number using the
mean wetted lengths (Savitsky, 1964) as given by
equations t1] and t23.
L = L, +L~.
[1]
Re = -
v
where,
Lm is the mean wetted length
Lk is the wetted length along the centerline
Lc is the wetted length along the chine
Re is the Reynolds number
V is the model speed
is the kinematic viscosity of water
[2]
The Reynolds number was used with the
Schoenherr friction line (1947 ATTC Line), given by
equation t3i, to determine the coefficient of friction.
The frictional force was calculated by equation t43.
0242 =log~O(Re CF)
F
FF = 2 P AW V CF [4]
where,
CF is the coefficient of friction
FF is the frictional force on the hull
Aw is the wetted surface area of the hull
p is the density of water
Though only meant for fixed geometries, the
CFD code was used to solve for the geometry
dependent problem of planing hull flow by
incorporating it into an iterative solution scheme. An
external program was written which ran both the
meshing program (Gambit v1.2) and the solver, and
evaluated the results from simulations. It executed
the meshing program, adjusted the hull orientation,
and then ran the solver. The results from the
simulation were then evaluated and a new hull
orientation chosen. This procedure is shown as a flow
chart in Figure 5. In step (2) a journal file was a text
file of commands for the meshing program Gambit.
In step (3), a scheme file was another text file but
with commands for the Fluent solver.
This method of using an external program to
solve for equilibrium was found to work for the
planing hull case, and can also be modified for a wide
variety of problems in which the geometry of the
domain and the flow field are inter-related.
The requirements for dynamic equilibrium for
the planing hull evaluated in step (7) were that the net
flow-induced vertical force must equal the weight of
the model, and that the net trimming moment (taken
about the tow point) from flowinduced forces must
equal the trimming moment caused by the model's
weight and center of gravity (also taken about the tow
point). These two conditions specify the at-speed
4
OCR for page 644
sinkage and trim of the hull needed to properly
determine resistance.
The behaviour of the forces and moments in
response to changes in hull positions followed fairly
linear trends (over a small range of sinkage and trim
angles). This allowed for some interpolation of
values, thereby saving computation time. Typically
anywhere from 6 to 8 iterations were used to
determine the equilibrium position of the hull per
speed tested.
Savitsky's method (Savitsky, 1964~. The results from
Savitsky's method under predicted the experimental
results, though at higher speeds the results tended to
improve. The CFD results were above the
experimental results, particularly in the 3.0to 4.0 m/s
range. Similar trends are seen in Figure 8, which
shows only the component - of resistance from
pressure forces. Savitsky's method uniformly under
predicts the experimental data, while the CFD results
over predict the experiments. The worst comparison
was at 3.0 m/s.
(A Start A)
—I— 8 0 .
L~tial Hull Onentation | 70 ~ ~ f ~ ~~- ~ -
1 ~ 5.0- if of/
| (2) Create Gambit Joumal File ~ l E 4 0 ~ ~ ' i ~ ~
| (3)Create Fluent Scheme File | 2.0 ~ _: ~ ~ ~ ~ ~~:
0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0
. Model Speed [m/s]
~ (4) Create Mesh (Run Gambit) ~ Figure 6: Experimental Sinkagei & Trim Results
| (5) Run Fluent Solver l
| (6) Evaluate Results |
<' Equilibnum
l Yes
,~,
(8) Determine New Hull
Orientation
.
No
Figure 5: Flowchart for Equilibrium Program
0-DEGREE OF FREEDOM RESULTS
This section presents the results of CFD simulations
where the orientation of the hull was set to match
those determined from the physical experiments for
each speed (shown in Figure 6~. These tests were
used to directly compare the experimental and
computational results for the planing hull model.
In general, the CFD results for the 0-degree of
freedom case were higher than those seen in the
experimental results. Shown in Figure 7 are the total
resistance curves for the experimental results, the
CFD results, and those obtained by applying
- 50
- 40
- 30
- 20 E
- 10 ~
a'
O ~
--10 co
- -20
-so
-40
80 -
.
70 .
60 /- - -— - - -
z ' / ' ' .: '
8 50 - ~ =
~ 40 - ~ if
._ ~ / 1 1 1 ~ ~
30 /
, / , I , , + Expenmental
2 0 ~
' ~. ' I l , —Savitsky
10 - ~ ~ ___ ~CFD: 0-DOF
o
0.0 1.0 2.0 3.0 4.0 5.0
Model Speed [m/s]
Figure 7: Total Resistance: DOE
6.0 7.0 8.0
The frictional resistance results, shown in Figure
9, were well matched between the three sets of data.
This was primarily a consequence of the similarly
compliant wetted surface area results shown inFigure
10. Small deviations in the CFD results were likely
due to experimental error in the determination of
sinkage used to set the vertical position of the
numerical model for these simulations. As these
variations were small, they cannot account for the
high values of total resistance. High values of
l The sinkage values given are the difference between
the vertical positions of the tow point at speed to the
tow point at rest. Positive values mean the tow point
has risen.
s
OCR for page 645
resistance were instead attributed to an over-
prediction of hull pressure forces.
70
60
_ 50
~o 40
.= 30
~ 20
in
~ ice
/ ~
1 / 1 1 \
l
+ Expenmental
—Savitsky
CFD: 0-DOF
0.0 1.0 2.0 3.0 4.0 5.0
Model Speed [m/S1
Figure 8: Pressure Resistance: WOOF
6.0 7.0 8.0
An
an 25
-
~c 20
(o
.~ 15
1n
5
o
0- .
~ .
0.0 1.0 2.0 3.0 4.0 5.0 6.0
Model Speed [m/s]
+ Expenmental l
—Savitsky ,
~ CFD: 0-DOF
it'
- -D-
Figure 9: Frictional Resistance: ODOR
.
0.7 - .
HE 0.6- .
~ 0.5- .
At: 0.4-
— 0.3-
i)
~ 0.2-
0.0 - _
,
_,———1——'^———
~~—,~ ~
'I:
_
7.0 8.0
+ Expenmental '
—Savitsky F
~ CFD: 0-DOF ,
r r
1
. _ _______ _____ ____
1~ ~ 1 ~ 1 1
_ _~ ____________
—Ad_ —~
- - r - - By_ - r - - r - - r
__________ ~ _
T _~
1
T T 1
0.0 1.0 2.0 3.0 4.0 5.0
Model Speed [m/s]
Figure 10: Wetted Area: 0-DOF
.
1 1
6.0 7.0 8.0
Several pressure taps were used in the physical
experiments to determine hull pressures at speed.
Comparing these results to the CFD simulations gave
some indication as to where computed pressures were
being over-predicted. Figure 11 shows the hull
pressures measured during the physical experiments
alongside those from CFD at the same locations. The
four positions are labeled in terms of their distance
from the transom measured parallel to the hull
bottom. The 90mm and 530mm positions were on the
centerline while the 620mm and 275mm positions
were 50mm to the port side.
Experimental hull pressures near the stagnation
region increased with increasing speed whereas the
pressures near the transom showed decreasing trends
with increasing model speed, even becoming
negative at the highest speeds. The CFD results also
followed these trends, although there were
differences in the magnitudes when compared with
the experimental values. The forward pressures seem
to be under-predicted while the aft pressures were
over-predicted. In other words, the pressure profiles
indicated by the experimental results show
considerably larger variation along the hull than
produced by the CFD simulations. Generally, the
region of over-predicted pressure (near the aft of the
hull) was larger than the under-predicted region,
which was isolated to near the leading edge of the
air/water interfaces. The net result of these higher
than expected pressures led to an over-prediction of
both drag and lift on the numerical model, despite a
good correlation for wetted area and frictional
resistance.
3500
3000 -
2500-
2000
1 500
1 000
500
O-
-500 -
0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0
Model Speed [m/s]
620mm (CFD)
~ 530mm (CFD)
hit 275mm (CFD)
~ 90mm (CFD)
- - *--620mm (Exp)
-~---530mm (Exp)
- ~ ~ --275mm (Exp)
· ~ ~ - - 90mm (Exp)
Figure 11: Hull Pressures
The hull pressures along the centerline of the
hull are shown in Figure 12 for the CFD simulations.
Given in terms of pressure coefficient (defined by
equation Hi), several characteristics became apparent
between model speeds. First, the wetted length was
seen to decrease with increasing speed, as given by
the locations of the peak pressures. The peak
pressures, in terms of pressure coefficient, also
decreased with increasing speed, although this was
actually found to be a consequence of trim angle. The
figure also shows the relative contributions to net lift
2 The forward pressures were sensitive to the location
of the leading edge due to a large pressure gradient
near this region. Aft pressures were less sensitive
due to a relatively smaller gradient.
6
OCR for page 646
from hydrostatic and dynamic forces. At the slower
speeds, there was a pronounced hump in the aft
region caused by hydrostatic pressure. As speed
increased this hump gradually dissipated.
The coefficient of pressure, Cal, is defined as:
p
Cp = C.p.V2)
0.0 -
~ 0.4 -
ED ~ 3 ~ _
0 0.2 0.4 0.6 0.8
X-Coordinate [m]
~2.0 m/s 3.0 m/s —4.0 m/s
5.0 m/s 6.0 m/s —7.0 m/s
Figure 12: Pressure Distributions on Hull Centedine
The pressure profile for a CFD simulation of the
model at 5.0 m/s forward speed is shown inFigure 13
as a pressure elevation plot. The pressure on the hull
is represented as a 3D surface shaded by value. These
results were consistent with some experimental data
on prismatic hulls presented by Hirano et al. (1990),
which gave a similar plot but based on physical
model data.
0.3` . . .
_ 0.25 . ~
j3 0~.~........
o 0.15~.
0.1~. -
X O~ ,.
`' 3 ' - , . ~ -
tm ~2 ~~ ~ 0~ ~~
Figure 13. Hull Pressure (Model Speed= 5.0 m/s)
— .
~_.- ~ .5
In order to better understand the differences
between the numerical and experimental free stream
velocities and pressures, their profiles along the
centerline of the hull were examined. Figure 14
t5]
shows the total pressure from a typical CFD
simulation along with experimental values. Also
shown is the CFD velocity profile with experimental
values (measured at two positions on the hull using a
laser Doppler velocimeter). Velocities were taken at a
position 15mm from the hull surface to ensure they
were outside of the boundary layer.
A^n~ 6.5
- 6.0
co
5.5 ~
5 0 >0
· 4.5
- 4.0
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
X-Coordinate [m]
—Total Pressure ~ Experimental Pressure
1.2 1.4 Free Stream Velocity ~ Experimental Free Stream
Figure 14: Pressure Profiles on Hull Centerline
These results were typical for this set of tests.
Pressure was under predicted at the front of the hull
and over predicted at the aft part of the hull. The
apparent shift between the CFD results and LDV
results from the physical experiments could be
explained by a possible bias error in the physical
measurement. However, the simulations significantly
over predicted the net pressure force, suggesting that
velocities were indeed being under predicted in the
aft region.
The results from the zero degree of freedom
simulations were found to follow the trends expected
for a planing hull, although net pressure was over
predicted. As net lift was higher than required for
equilibrium, the next step was to balance net lift to
the model's weight (in isolation of trim angle and
trimming moment). This process is presented in the
next section.
1-DEGREE OF FREEDOM RESULTS
In this set of tests, the model's vertical position
relative to the waterline was altered by the
equilibrium program so that net lift balanced the
model's weight. The trim angle used for each speed
was that measured during the physical experiments.
The goal of these tests was to determine the
sensitivity of the model to linkage, and to establish
whether deviations in the Degree of freedom model
could be attributed to experimental error in this
parameter.
7
OCR for page 647
The resistance curves for the CFD runs, the
experimental tests, and Savitsky's method are
presented in Figure 15. The hump speed, hollow and
resistance increase were all clearly followed by the
CFD predictions, showing some improvement over
the Savitsky results.
~~ —
50
-
z 40
o
~ 30
.cn
07
20
10
50
40
E 30
E 20
0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 0' 10
Model Speed [m/s] ~ O
-10
-20
-30
-4Q
+ Expenmental
—Savitsky
+CFD: 1-DOF
O
Figure 15: Total Resistance: 1-DOF
The frictional resistance, shown in Figure 16,
was lower than the experimental values. This was
primarily a function of the wetted area, which
followed a similar trend. The low wetted area results
were attributed to the fact that the final sinkage
values for the simulations that satisfied the 1-degree
of freedom equilibrium condition were higher than
those measured during the physical experiments.
Shown in Figure 17, the sinkage values for both the
CFD and experimental results are given. The
numerical model was farther out of the water than the
physical model, thereby having less hull submerged
and therefore less wetted area. This confirmed that
the pressure forces calculated by the numerical
method were greater than those produced by the
actual flow.
35
30 -
_ 25- .
of
8 20- .
.~ 15- .
a'
~ 10- .
I + Expenmental
—Savitsky ,
+CFD: 1-DOF ,
5- .
l
l Dlr/l
Do, All].,
off
At,
.
_
0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0
Model Speed [m/s]
Figure 16: Frictional Resistance: 1-DOF
Figure 18 shows the pressure resistance for the
numerical, experimental and Savitsky results. The
pressure resistance was computed for the
experimental results by first calculating the frictional
component, and then subtracting that value from the
total measured resistance. The numerical pressure
resistance was computed by directly integrating the
pressure forces over the hull area. The results for the
1-degree of freedom CFD simulations closely match
those from the experimental results, despite the
differences in linkage, wetted area and fictional
resistance. This match was attributed to a
combination of the nature of the 1-degree of freedom
constraint. and the shade of the hull.
~ , ~
~ ~ 1 / ~
. ~ ~ ~ ' ~ my/ ~ ~ ~ ~' ~ ~ ~ ' ~ ~ + Expenmental
~ _tU]~O,
0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0
Model Speed [m/s]
Figure 17: Sinkage: 1-DOF
50
45
40
z 35
30
' 25
20
Q)
15
10 -
5
o
0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0
Model Speed [m/s]
Figure 18: Pressure Resistance: 1-DOF
The 1-degree of freedom simulations required
that the net lift (vertical force) exerted on the model
was equal to the model's weight. When planing at
high speeds, the portion of the hull in contact with the
water was essentially planar in the longitudinal
direction. This and the fact that the transom was dry
meant that the system could be crudely represented as
a flat plate with a pressure force acting perpendicular
to it. This force can be expressed as a vertical
component (lift) and a horizontal component (drag),
whose magnitudes depend on the size of the pressure
force and the trim angle of the plate (see part A in
Figure 19~. In a 1-degree of freedom simulation, the
trim angle was held constant while the vertical
position of the hull was altered, thus changing the
8
OCR for page 648
location and magnitude of the resultant pressure force
on the hull. As the location of this force was not
relevant to the decomposition of the vector into lift
and drag on a flat plate, altering the vertical position
of the model was therefore equivalent to simply
changing the magnitude of the resultant pressure
force. The end result was that by requiring the lift
component of this pressure force to equal the model
weights, the drag force was inadvertently fixed to a
value dependent only on the trim angle (given by
equation ted).
Dp = WMode~ tan(T) t6]
where,
Dp is the pressure drag
WMode~ is the model weight
is the trim angle
The drag force given by equation t6] is also
shown in Figure 18 (labeled 'Pressure Vector').
There was a close match between both the
experimental and numerical results to the theoretical
values, particularly between 4.0 and 6.0 m/s. There
were, however, discrepancies such as at 3.0 m/s. The
numerical value was near the theoretical curve, but
the experimental value was somewhat larger. The
reason for this difference lies in the hull shape, and
the difference in sinkage values for the numerical and
experimental results.
As discussed, the CFD sinkage values were all
somewhat larger than the experimental values, so that
the CFD hull was relatively higher in the water. The
numerical simulation at 3.0 m/s had a water contact
area that still satisfied the 'flat plate' model and
therefore had a pressure drag matching the theoretical
value. In the physical experiments at this speed, the
model was slightly lower in the water and the contact
area included a region of the hull hat began sloping
upward towards the bow. This changed how the
resultant pressure force was decomposed into lift and
drag components. An illustration of this effect is
shown in Figure 19. Part A) in the figure shows the
flat plate case, while part B) simplifies the curved
hull case with two flat plates at different angles.
Although the net lift for the two cases is identical,
case B) has a slightly larger drag value.
The differences in contact area between the
experimental and numerical simulations are best
described in terms of the length of the wetted
centerline. These lengths denote the maximum
3 The constraint was actually that the net lift on the
hull was equal to model weight; however, the
contribution to net lift from frictional forces was in
all cases less than 1%.
distance that the wetted surface area extended
forward on the hull bottom. Shown in Figure 20, the
wetted lengths for both the CFD and experimental
tests are presented. Also shown in the figure is a line
designating the point at which the hull begins to
curve upward towards the bow. Points below this line
followed the flat plate model and had pressure drag
measurements matching the theoretical values. Points
above this line tended to have higher pressur~drag
values than given by equation t63.
\
A ) I
10,
L, ~ Lo
Q:
0,
O ~F
Figure 19: Lift and Drag Vectors
. . .
~1 .2 - - - r - - ~ - ;
O) 1.0- . , - - ~ W
c . ~
~ 0.6 - . Maximum Length
c Before Longitudinal
0.4 - - Hull Curvature
, , ~ , 1
1
~ ~ , , .
—~ __ ~
° 0.2 ~ ~ ~ |+ Experimental
, , , , , +CFD: WOOF
0.0 - , , I , , , ~
0.0 1.0 2.0 3.0 4.0 5.0 6.0
Model Speed [m/s]
Figure 20: Wetted Centerline Length: 1-DOF
7.0 8.0
The results from this set of simulations led to the
following conclusions. They show that by removing
the frictional drag (calculated by the method
discussed) from the total measured drag,the resulting
pressure drag falls on the curve predicted by simple
theory, thereby validating the force component
9
OCR for page 649
separation procedures. This also supports the use of
the method for the CFD case, which can result in
large savings in mesh size and computation time. The
1-degree of freedom CFD results match the curve
from simple theory, showing that the equilibrium
solving procedure was working properly. The high
values of sinkage and low values of wetted area for
the CFD results compared with the physical
experiments show that net pressure was being over
predicted. Examination of the flow field in the CFD
simulations suggested that the pressures on the hull
were higher in the aft region and lower near the
air/water interface than the experimental
measurements. Free stream velocities followed the
experimental trends, but were offset to lower values.
In general, the computed flow was qualitatively
consistent with experimental observations of planing
hull flow, but actual values tended to deviate from
the physical data.
2-DEGREES OF FREEDOM RESULTS
The last set of simulations involved solving for
dynamic equilibrium of the steady state motion of a
planing hull through calm water. Both sinkage and
trim values were used to determine the model
orientation for which the net vertical force and net
trimming moment on the hull were zero.
The results from this set of simulations generally
under predicted those of the physical experiments,
except for linkage, which was over predicted. These
trends were consistent with excessive surface
pressure forces computed for the planing hull. As
discussed for the 1-degree of freedom case, the CFD
hull was lifted higher than expected to balance the
model's weight at the experimental trim angle. The
resulting decrease in wetted area not only produced
low values of frictional drag, but also shifted the
location of the net pressure force farther aft. Due to a
smaller 'moment arm' the net trimming influence on
the model was also substantially reduced.
As the magnitude of net pressure force was
effectively fixed by the lift equilibrium requirement,
the only alternative left to increase the trimming
moment was to shift its location forward. This was
achieved by lowering the running trim angle. Other
consequences of this move were an increase in
wetted area, and hence frictional drag, a decrease in
linkage, and a decrease in pressure drag.
4 In fact, provided the water contact area is within the
portion of the hull without longitudinal curvature and
the transom is dry, the frictional component of drag
could be determined simply by subtracting the
theoretical pressure drag from the measured total
drag.
The results for running trim and sinkage are
shown in Figure 21 and Figure 22 respectively. The
trends were roughly followed, though there were
shifts in the relative locations of the curves on the
plots. The trim angles were all uniformly lower and
the peak was shifted from approximately 3.2 m/s to
between to 2.0 m/s and 3.0 m/s. Sinkage values were
improved slightly from the 1-degree of freedom
model but were still higher than the experimental
values.
an 1 -
. .
6.0
r._
5.0
~ 4.0
.E 3.0
2.0
1.0
. .
+ Expenmental
— _ ~ — 1 J — — ~ — ~
1 /
- - T -I- ~ - -
0.0 1.0 2.0 3.0 4.0 5.0
Model Speed [m/s]
Figure 21: Running Trim: 2-DOF
60 -
50 -
40 -
30-
20-
10-
~ O-
cn -10 -
-20 -
-30 -
-40 -
6.0 7.0 8.0
- ~ r ~
·_ i /1 ,#~ 1 ~ ~ ~
>~ ~ ~ ~ +Expenmental
' - - T - ~ -~-~-r - - -' - - _, _ +CFD: 1-DOF
CFD: 2-DOF
0.0 1.0 2.0 3.0 4.0 5.0
Model Speed [m/s]
Figure 22: Sinkage: 2-DOF
6.0 7.0 8.0
Figure 23 gives an illustration of typical model
orientations for the three sets of simulations that were
performed. The top hull has a trim and sinkage
corresponding to the experimental measurements, or
the 0-degree of freedom model. The second hull has
the same trim angle but has been lifted higher out of
the water and represents the 1-degree of freedom
model. The last hull shows the 2-degree of freedom
orientation, lower in the water than the second hull
and with a smaller trim angle.
In general, the wetted lengths followed the
pattern shown in the figure. The 2-degree of freedom
orientations had larger wetted lengths than the
experimental values even though they had matching
vertical forces and trimming moments. The increase
in length was attributed to the fact that the net
10
OCR for page 650
pressure force did not shift proportionately with the
wetted length. The pressure distributions changed
with trim angle resulting in lower peak values for
lower trim angles. Shown in Figure 24 is a plot of
peak pressure values against trim angles for various
2-DOF simulations. A clear linear relationship is seen
which was not speed dependent (e.g. runs were
performed at 4.0 m/s and 5.0 m/s at approximately
5.2° trim, both simulations had essentially the same
peak pressures coefficients). Experimental values
presented by Hirano et al. (1998) also fit on this
curve. They tested prismatic hulls at various speeds,
all at a trim angle of 6.0° and measured peak
pressures coefficients between 0.3 and 0.4.
I-DOF O-OOF 2-DOF
Figure 23: Hull Orientations
_
0.4
a)
~ 0.3
a)
o
~ 0.2
u,
0.1
O
. _
0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0
Trim Angle [deg.]
Figure 24: Peak Pressure vs. Trim Angle
The increased wetted lengths illustrated inFigure
23 also led to larger wetted areas. Whereas the 1-
degree of freedom simulations under predicted
wetted area, the 2-degree of freedom showed a slight
over prediction as shown in the frictional drag results
in Figure 25.
Pressure resistance values were lower in the 2-
degree of freedom simulations, a direct consequence
of smaller trim angles. They were, however, still in
agreement with theoretical values calculated with
equation [6] (using the new trim angles), provided the
wetted lengths supported the flat plate assumption
(Figure 19~. The reduction in values, shown in Figure
26, demonstrates the importance of trim angle when
predicting planing vessel performance. The results
for total resistance are shown in Figure 27. The
improvement in frictional resistance was not enough
to counter the reduced pressure drag. The total
resistance curve for the 2-degree of freedom system
was therefore shifted downwards by as much as 10N
from the experimental one. The hump and hollow
portions of the curve were also shifted about lm/s
towards slower speeds.
35
an
J -
___,___,___,__,*___
~ ^
1 ' ~~
—,— <
_ _ _L _ _ _
_ ' _ ~~ '
_ ~____________
~ ~ to I I I I
0.0 1.0 2.0 3.0 4.0 5.0 6.0
Model Speed [m/s]
Figure 25: Frictional Resistance: 2-DOF
60 1 - -
10
o
l
7.0 8.0
+ Experimental
T - - , - - -, - - -, _ _ _ I _
CFD: 0-DOF
~ ~ ~ ~/ ~ ~ ~~~ ~ ~ ~ +CFD: 1-DOF
CFD: 2-DOF
0.0 1.0 2.0 3.0 4.0 5.0
Model Speed [m/s]
Figure 26: Pressure Resistance: 2-DOF
11
6.0 7.0 8.0
OCR for page 651
70 -
60 -
-
Z 50-
co 40 -
07
30-
20 -
10 -
~ 1 1 1 1
/ 1
— —————.r———— —
/ \: 1 1
_ _ _1 ~ _ _ 1 _ _ _ _ _ _ At_ _ 1 _ _ _ i_ _ _
/~
— T — —
~ I
- - - 1 - - - - - - + Experimental
~ l l I ~ ~ CFD: WOOF
;e , I I I _CFD: 1-DOF
~ ~ _ J _ _ _ I _ _ _ I _ _ _ I _ _
~ I ' ~ CFD: 2-DOF
O - — 1 1 1 1 1 1 .
0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0
Model Speed [m/s]
Figure 27: Total Resistance: 2-DOF
CONCLUSIONS
Predicting the performance of a planing hull requires
the solution of dynamic equilibrium. It is through
balancing lift and trimming moment with the model's
weight and center of gravity that the proper trim
angle and sinkage are determined. These parameters
are essential for an accurate prediction of resistance.
The goal of this project was to extend the ability of a
commercial CFD package to handle this type of
calculation, thereby making it a versatile tool for
estimating planing hull performance.
The first step was to evaluate the CFD method in
direct comparison with physical experimental data.
The results of this test shoed that velocities and
pressure profiles were in qualitative agreement with
experimental observations. However, there was an
over prediction of net pressure leading to higher lift
and drag values (by as much as 20 N). The numerical
model was then tested in a 1-degree of freedom (in
vertical position only) system in order to balance the
lift forces with the model's weight. The pressure drag
improved to within 5% of the experimental values,
although this did lead to a smaller wetted area and
hence an under predicted frictional resistance by up
to 10%. In simulations involving full dynamic
equilibrium, trim angle was found to decrease as
much as 2° in order to balance the trimming moment
while simultaneously satisfying the lift requirement.
This increased the wetted area but decreased the
pressure drag, leading to low total resistance results.
All of the CFD results followed trends
characteristic of a planing hull. However, for each set
of tests, the curves were shined or stretched in
reaction to the requirements of each case, in response
to high net computed values of pressure. For both
cases of dynamic equilibrium (1-degree of freedom
and 2-degrees of freedom), these high hull pressures
led to low total resistance values. This result may be
counter-intuitive, but was a consequence of the
model's ability to change its orientation in response
to the flow field.
The cause of the relatively high pressures in the
CFD simulations was not determined. They could be
caused by insufficient grid resolution, a common
problem in numerical approaches. A grid dependence
study was conducted, but did not investigate the
effects of large element count increases (on the order
of 10 times or more than those used here). Another
possible contributing factor was the lack of
turbulence modeling in these tests. Proper turbulence
simulation could alter the character of the pressure
profiles and lower the net pressure. The treatment of
spray was also a possible contributing factor.
Although the VOF free surface capturing method
does allow for fluid to be ejected from the near hull
above the free surface, it was not necessarily
equivalent to the spray produced in the physical
experiments. This phenomena may need to be
modeled in future simulations. Despite the high
pressure values, the results of these predictions were
valuable and the procedure for solving dynamic
equilibrium was proven to be successful.
ACKNOWLEDGEMENTS
These experiments were performed at the National
Research Council of Canada's Institute for Marine
Dynamics (NRC/IMD). In addition to NRC/IMD,
funding and technical assistance was provided by
Memorial University of Newfoundland, Oceanic
Consulting Corporation, and NSERC (Natural
Sciences and Engineering Research Council). Fluent
v5.3 was made available through an educational
research license from Fluent Incorporated.
NRC/ Institute for Marine Dynamics
http ://www.nrc.ca/imd/
Memorial University of Newfoundland
http: //www. engr. mun. c a/
Ocean Engineering Research Centre
http: llwww. engr. mun. c a/O ERC/
Oceanic Consulting Corporation
http://www.oceaniccorp.com/
NSERC
http://www.nserc.ca/
REFERENCES
Brizzolara S., Bruzzone D., Cassella P., Scamardella
A., Zotti I., "Wave Resistance and Wave Patterns for
High-Speed Crafts; Validation of Numerical Results
by Model Test",1998.
Du Cane P., High Speed Small Craft 3rd Ed. Temple
Press Books, London. 1964.
12
OCR for page 652
Hirano S., Uchido S., Himeno Y., "Pressure
Measurement on the Bottom of Prismatic Hulls",
Kansai Soc. Nav. Arch. J., No.213, March 1990.
Ikeda Y., Yokomizo K., Hamasaki J., Umeda N.,
Katayama T., "Simulation of Running Attitude and
Resistance of a High Speed Craft Using a Database
of Hydrodynamic Forces Obtained by Fully Captive
Model Experiments", FAST '93~ 2n~ International
Conference on Fast Sea Transportation 1993.
Lewis E.V (ed.), Principles of Naval Architecture
Second Revision. Society of Naval Architects and
Marine Engineers (SNAME), Jersey City, 1988.
Lohner R., Yang C., Onate E., "Viscous Free Surface
Hydrodynamics Using Unstructured Grids", 22nd
Symp. on Naval Hydrodynamics Washington DC,
pp. 128-142, August 9-14, 1998.
Payne P.R., Design of High Speed Boats Volume 1:
Planing. Fishergate Inc. Annapolis. 1988.
Savitsky D., "Hydrodynamic Design of Planing
Hulls", Marine Technology, vol. 1, no. 1, pp. 71 - 95,
October 1964.
Subramani A.K., Paterson E.G., Stern F., "CFD
Calculation of Sinkage and Trim", J. Ship Research,
vol. 44, no. 1, pp.59-82, March 2000.
Thornhill, E. "Application of a General CFD Code to
Planing Craft Performance", Thesis submitted to
Faculty of Engineering and Applied Science,
Memorial University, 2002.
Thornhill E., Veitch B., Bose N., "Dynamic
Instability of a High Speed Planing Boat Model".
Marine Technology, July 2000.
Yang C., Lohner R., Noblesse F., Huang T.T.,
"Calculation of Ship Sinkage and Trim Using
Unstructured Grids". ECCOMAS 2000, 11-14
September 2000, Barcelona.
13
OCR for page 653
DISCUSSION
L. J. Doctors
The University of New South Wales, Australia
At the leading edge of the wetted surface of a
planning hull (just behind the spray root), one
has a stagnation region. Since the elevation of
this point is very small (relative to the
undisturbed free surface), one should realize a
pressure coefficient of unity at all speeds.
Your results display a pressure coefficient much
less than unity (0.1 to 0.4~. Could you please
comment?
AUTHORS' REPLY
The peak pressure coefficients in the CFD
simulations were indeed well below the
theoretical value of 1.0 predicted by classical
planing theory (e.g. Du Cane 1964~. Peak
pressures were not measured during the physical
experiments of this model for comparison.
However, measurements of the pressure
distribution (including the leading edge) on a
planing hull model were conducted by Hirano et
al. (1990~. The peak pressure coefficients
measured in these experiments were in the range
of 0.3 - 0.4 putting them much closer to our
computed values than the theoretical value of
1.0. It was also determined in our study that the
CFD simulations were over predicting the net
pressure force on the hull, which contradicts the
premise that the computed pressures were too
low.
Another consideration was raised when the
computed peak pressure coefficients, though
independent of speed, were found to be
dependent on trim angle as shown in Figure 24.
In planing theory the peak pressure would be 1.0
regardless of trim angle. This means that the
peak pressure would have to jump
instantaneously from 0.0 (for a hull with zero
trim angle) to 1.0 given even the slightest
increase in trim. Such jumps are difficult for real
flows.
The behaviour of the spray root region also
differed somewhat from the theoretical
predictions. In the CFD model there was no flow
projected forward (relative to the model) as
spray. In the physical experiments, only a small
trickle of water preceded the leading edge, the
vast majority of spray was directed aftwards and
to the side away from the model. Classical
theory suggests that a much more pronounced
forward directed spray should be produced,
particularly at the flat bottom portion of the
hull's cross-section.
It is possible that a region on the hull with a
pressure coefficient of 1.0 did exist, but that it
was so small and that the pressure gradient on
each side was so steep that it could not be
resolved by either physical experiments (for
example, those done by Hirano et al., 1990) or
by the current numerical predictions. However,
the above observations lead to the alternate
conclusion that planing theory based on a 2D flat
plate is insufficient to describe the flow around a
realistic 3D planing hull form.
DISCUSSION
Hoyte C. Raven
MARIN, The Netherlands
From your Figure 1, the hull form appears to be
very flat. Therefore, a smooth bow wave will
not exist, spray/breaking/jet formation will occur
at the intersection, and I suppose your choice for
a VOF method may well be appropriate. To get
an idea of how the method is performing in this
area, can you show us what the computed bow
wave and wave pattern look like?
AUTHORS' REPLY
Thank you for your discussion. As requested,
here are a few examples of the computed free
surface.
Figure 28 shows the free surface on the
centerline plane (symmetry plane) of the model.
The transom was dry as a gently sloping wave
was produced behind the model. Free surface
contours at elevations of +1 5mm at 5mm
increments are shown in Figure 29. The stern
wave is shown as well as the beginnings of the
system of divergent waves. These results are
qualitatively in agreement with the waves
observed during the physical experiments, which
are shown in Figure 30 (coloured by elevation of
the surface, blue represents the lowest levels, red
represents the highest).
The air/water interface on the hull, which
designates the wetted surface area, wetted
centerline length and wetted chine length, is
shown in Figure 31. The shape and contact area
OCR for page 654
closely matched those from the physical
experiments. An image from the underwater
video of the physical model experiments is given
in Figure 32.
Figure 28: Free Surface at Centerline Plane
Figure 29: Free Surface Contours
~ .
Figure 30: Wave Profiles from Physical
Experiments
~ ._
~~ ~~_
, s HIT ~ —
I .. ~ ~ ~ ^ A . ~ ~ ~ _
I. ~ _
~ ~ A_ ~ ~
- .~ _ ~ Aim. mu. I_. ~~1.-
~! 13 ~~
.~ ~
~ _
Figure 31: Wetted Surface Area from CFD
Figure 32: Wetted Surface Area from
Experiments
Representative terms from entire chapter:
planing hull
