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OCR for page 682
24th Symposium on Naval Hydrodynamics
Fukuoka, JAPAN, 8-13 July 2002
Viscous Roll Predictions of a Circular Cylinder with
Bilge Keels
Ronald W. Miller, Joseph J. Gorski, David J. Fly
(Naval Surface Warfare Center, Carderock Division)
Abstract
The roll motion of a ship is largely
influenced by viscous effects. This includes the drag
on the hull form as it rolls and the flow separation
from the bilge and keel where subsequent vortex
formation accounts for a large amount of the roll
damping. Bilge keels will significantly increase the
damping of roll motions as well as generate a lift
force if any forward motion of the ship is present.
Predicting roll effects analytically has been
problematic because of the significant viscous
effects. Roll motions are an ideal area to pursue
viscous calculations methods including the Navier-
Stokes equations. Yeung et al (2000) showed results
recently in this regard, though limited to two-
dimensions. The current effort demonstrates some
RANS calculations to simulate roll motions of a
These are three-
dimensional calculations, which will provide an
assessment of the accuracy that can be obtained with
RANS codes for predicting viscous roll damping
effects. This assessment is performed by comparing
RANS solution data with measurement data obtained
from the experiment recently carried out in the
Circulating Water Channel at the Naval Surface
Warfare Center, Carderock Division.
cylinder with bilge keels.
Introduction
The roll response of a ship is an important
consideration in its design. Roll motion limits ship
operability, affects crew performance and ship
habitability, and affects dynamic stability and ship
capsize. Viscous related effects have a large influence
on the roll motion of a ship. These include the drag
on the hull form as it rolls and the flow separation
from the bilge and keel where subsequent vortex
formation accounts for a large amount of the roll
damping. Bilge keels will significantly increase the
damping of roll motions as well as generate a lift
force if any forward motion of the ship is present.
The prediction of ship roll motions has been difficult
because of its nonlinear nature as well as the strong
dependence on forward speed. Current ship motion
prediction methods rely primarily on strip-theory
potential-flow based methods. Roll effects have
largely been included in such predictions based on
empirical results, flat plate lift and other simple
theories. Such techniques can provide aspects of roll
motion, but are not adequate for correctly predicting
roll effects because of the viscous effects, even with
bilge keels present, and dependence on specific hull
geometry.
As demonstrated by Sarpkaya and O'Keefe
(1996) bilge keel damping is affected by the vortices
shedding from the edge of the bilge keel and the use
of damping coefficients from flat plate tests in a free
stream are not necessarily accurate for wall bounded
bilge keels. Consequently, these methods must be
supplemented with empirical information and much
effort has been directed at developing coefficient-
based approaches for roll prediction. Himeno (1981)
summarized much of the development of these
coefficient-based methods and it is not clear that they
have changed substantially to the present. These
approaches have been used successfully when
applied to hull forms for which they were developed.
However, these methods required new data when
applied to new hull forms as demonstrated by Blok
and Aalbers (1991) for a high-speed displacement
hull form. Additionally Liut, et al (2001), needed to
tune the viscous model used in the motion prediction
program LAMP to match roll-damping characteristics
of CG47 based on experimental roll data. To remedy
such deficiencies modifications to the basic model
may be needed as well as new test data requiring
numerous forced roll or roll extinction tests at model-
scale to define coefficients that describe the roll
motion. Additionally, model-scale coefficients may
not relate well to full-scale behavior due to the
differences in Reynolds number. As revolutionary
new naval combatants are considered, where existing
databases do not provide the necessary design
OCR for page 683
information in general (Rood, 2000), there is a strong
desire to have better computational capability for ship
roll motions as the Navy progresses to a more
computational based design paradigm in general.
Viscous flow computations can provide roll
motion information. However, due to the need to
evaluate ship motions in a variety of sea states under
a large number of headings viscous flow calculations
will not replace traditional strip-theory in the
foreseeable future. However, viscous flow
calculations, in particular Reynolds Averaged
Navier-Stokes (RANS) codes, do have a role to play
as considerable advancements have been made in the
prediction of ship flows with them (Gorski a&b,
20011. RANS predictions have already been
demonstrated for a destroyer model with propeller
shafts, struts, rudders, and propellers for straight
ahead and a restricted maneuver in the horizontal
plane (Kim, 20014. This prediction demonstration,
provided the complete flow field around the hull
showing the ship motion predicted as a result of the
propeller induced thrust and turning rudder. Such
calculations can be run for a few conditions to help
understand the flow field that may be causing a
particular force distribution on the hull and
appendages during a maneuver or other ship motion.
Another area where RANS codes can contribute is in
supplementing conventional strip-theory approaches,
which rely on empirical databases for the damping
coefficients. As already mentioned when calculating
nonconventional hull forms, traditional roll damping
coefficients may be inadequate requiring new model
tests to replace them. Rather than model tests RANS
predictions may be able to fulfill the same role.
Viscous computations of roll motions have been
reported in the past. Yeung, et al. (1998) presented
two-dimensional computational results for a
rectangular cylinder. Later, Yeung et al (2000) added
bilge keels and demonstrated that viscous flow
calculations could adequately be used for obtaining
coefficients. These methods consisted of a Free-
Surface Random Vortex Method and a Boundary-
Fitted Finite Difference Method, but were only
applied in two-dimensions. Korpus and Falzarano
(1997) applied a finite analytic RANS calculation to
a rotating square, demonstrating that the RANS code
could be used to obtain roll motion coefficients, but
again only in two-dimensions. Full three-
dimensional RANS results have also been
demonstrated for ship hull forms undergoing roll
(Kim, 2001), but without data comparisons or the
free-surface present. These calculations demonstrate
that RANS may fulfill the role of traditional forced
roll tests if adequate accuracy can be demonstrated.
The current effort demonstrates some RANS
calculations to simulate roll motions of a 3-D
cylinder with bilge keels. Measurement data from
experiments performed at Naval Surface Warfare
Center, Carderock Division (NSWCCD) is used to
validate the RANS solutions. The experiment
provides data for a large set of test conditions
available for numerical simulations, including the
actual roll motion of the body. These conditions
include a range of frequencies and amplitudes of
forced roll motion, model sizes, forward speeds, and
ballast conditions. Case-by-case comparisons of
calculations with measurements for a set of these
conditions are shown to be good. Additionally, the
use of the RANS solver with the body undergoing an
ideal sinusoidal roll motion demonstrates the effects
of forward motion and scale on the bilge keel force.
Experiment
Experiments were recently carried out in the
Circulating Water Channel (CWC) at NSWCCD.
This recirculating water channel has a 9.1 x 6.7 x 2.7
m. (30 x 22 x 9 ft) test section with a free surface.
Figure 1 shows the test section with the largest
cylinder in place. Flow velocities into the CWC test
section ranged from O to 2.0 m/s (4 knots). The
cylinder mount allowed immersed and various
emerged elevations. Under conditions of zero flow at
partial submergence, keel generated waves reflect
back from the test section sides. Wave absorbers and
multiple short duration experiments prevented
contamination from reflected waves.
Figure 1 Test section with the largest cylinder
Four different cylinder configurations are
tested. These consist of a smaller, 0.48 m (19 in)
diameter cylinder was tested with 0.025 m (1 in) and
2
OCR for page 684
OS9 ~ IS rr
`34.9 rl. 1 l20.~ i: -
q~ ~ - it
Figure 2 Roll Cylinder Dimensions (Large Cylinder)
0.051 m (2 in) wide bilge keels and a large 0.897 m
(35.3 in) diameter cylinder with 0.051 m (2 in) and
0.102 m (4 in) wide bilge keels. The basic cylinder
dimensions appear in Figure 2 for the larger cylinder.
The twin bilge keels (located 90 degrees apart on the
circumference) run along the cylinder's constant
diameter section.
The model is forced to roll about its longitudinal
axis at various frequencies (0.08 - 0.64 Hz) and
amplitudes (15 - 60 degrees). The actual motion
varies from an ideal sinusoidal variation of roll angle
because of friction, asymmetrical force loads, and
control system limitations. Roll position is measured
by resolver sensors that are sampled at 100 Hz. The
position at any time is quite close to a sinusoidal
variation (Figure 31. However the angular velocity is
far from ideal for the slowest roll oscillations (Figure
4~. There is also significant cycle to cycle variation.
At higher amplitudes and frequencies, the angular
velocity is closer to the sinusoidal ideal with
variations consistent cycle to cycle(Figure 5~.
RMS Error / Amnlitr~rt~ = n Oo/^
to in
1
Oscillation Cycles (12.5 see period)
Figure 3 Slow Roll Displacement
Force measurements are taken on a central
0.61 m (2 ft.) section of both the port and starboard
bilge keels (Figure 2~. They are instrumented with
strain gauge flexures which are sampled at 100 Hz..
O04,] Do.
_ ,
j5 2 in
__. i_,_
0.2 r
0.15
~ 0.1
Oh
C 0.05
Ct o
~5
4,
~ -0.05
00
0 4) 1
-0.15
-1
RMS Error / Amplitude = 20.8%
L2EO-A3F1~132
A, Measured
, Sinusoid
Van ', I, I
· 1 1.2 1.4 1.6 1.8 2 22 2.4 2 6 2.8 3
Oscillation Cycles (12.5 see period
Figure 4 Slow Roll rate
RMS Error/Amplitude = 6.1%
Oscillation Cycles (3.12 see periods
Figure 5 Faster Roll Rate
The two dimensional, flow field near the
port bilge keel is measured using Particle Image
Velocimetry (PIV). Camera and light sheet
generating components are attached to the exterior of
the rolling cylinder (Figure 6~. The support geometry
and fairings are designed to have minimal impact on
the sampled flow field and port keel force
measurement. A fiber optic cable brings light from
two stationary Dye Lasers out to the cylinder.
Electrical cables connect the camera to power
supplies and an image acquisition computer.
3
OCR for page 685
Autocorrelated images (2048 x 2048 pixels) are
recorded at a rate of 4 Hz. Approximately 300 are
collected for each cylinder/roll condition. The PIV
images (Figure 7) also provide free surface
deformation and air ingestion information for
conditions when the keel interaction with the free
surface is strong.
CYLINDER ROLLING AT FREE SURFACE
Figure 6 Particle Image Velocimetry (PIV)
Camera and Light Sheet Components
The small cylinder was tested under 55
different conditions. This included variations in
cylinder elevation. freestream current. keel width
motion amplitude and frequency. The large cylinder
was tested under 70 different conditions.
Figure 7 PIV Image showing bilge keel interaction
with free surface
Governing Equations and
Numerical Implementation
Math Mode/ and UNCLE
To compute the viscous flow field the
incompressible Reynolds Averaged Navier-Stokes
equations are solved using the Mississippi State
University code UNCLE, (Taylor et al 1991, 1995~.
The UNCLE code is one of two RANS codes used
for the ONR Surface Combatant Accelerated Hydro
S&T Initiative to provide documented computational
solutions for innovative propulsor/hull concepts of
interest for DD-2 1 and beyond, e.g. Gorski et.
al.~2002~. The equations are solved using the
pseudo-compressibility approach of Chorin (1967)
where an artificial time term is added to the
continuity equation and all of the equations are
marched in this artificial time to convergence. The
UNCLE version used is 1St order accurate in time.
Subiterations are necessary for convergence of the
continuity equation at each time step. For the present
calculations a third-order upwind biased
discretization, based on the MUSCL approach of Van
Leer et al. (1987), is used for the convective terms.
The equations are solved implicitly using a
discretized Newton-relaxation method (Whitfield and
Taylor, 1991) with multigrid techniques implemented
for faster convergence due to Sheng et al (1995~. The
turbulence model used for the present calculations is
a k-c model. The RANS equations are solved in an
absolute frame of reference with a rotating body and
deforming volume grid. An important factor in being
able to compute and evaluate the operating conditions
of interest is the implementation of a parallel version
of the UNCLE code. The code uses MPI for message
passing due to its portability. To run in parallel the
computational grid is decomposed into various
blocks, which are sent to different processors. Load
balancing is obtained by making the blocks as
equally sized as possible. More details of the solver
can be found in the various references provided.
Boundary conditions - surfaces
Surfaces bounding the computational fluid
volume require boundary conditions. For the RAN S
calculations, the CWC entrance, exit, and side walls
are replaced by farfield surfaces at least one body
length forward and at least two to the sides and aft.
On these surfaces characteristic boundary conditions
are applied. Shown in Figure 8 is the port side of the
extent of the immersed body configuration, but the
grid wraps around the starboard side for the 3D
4
OCR for page 686
calculation. For the emerged cases, the fluid only
extends to the mean free-surface level, where either a
zero Froude number or linearized free surface
boundary condition has been used. The last surface
bounding the domain is the test model, where the
noslip boundary condition is applied. This surface
rotates at a specified angular velocity. The angular
velocity, d'0 is specified from actual experimental
dt
data or from the ideal sinusoidal function
Amcos(mt). Figures 4 and 5 show the actual
experimental angular velocity versus the smooth
analytic velocity. At each time step the body is
,1as
rotated the amount ^0B = "v ~ about its
dt
longitudinal axis, where At is the computational
time step. The calculated wall velocity required by
the noslip boundary condition is then imposed. The
cylindrical emerged body has been extended
downstream to the outflow boundary because of
difficulties with the free surface boundary conditions
for the actual flat back of the cylinder.
Flow region - volume grids
Structured grids are used for the present
calculations. Figure 8 shows the point clustering at
body walls and at the bilge keels. Because the
angular velocity of the test body is time dependent,
the discretization of the computational fluid volume
changes with time. However the basic grid topology
for each configuration, in an immersed or emerged
ballast condition, will remain the same for all time.
The initial grids were created using GRIDGEN.
The flow region is decomposed into equal
sized blocks, i.e. an equal number of cell volumes per
block, for load balancing on a parallel processor. For
the immersed body cases the fluid domain is
decomposed into 84 blocks each with dimensions
33x33x33. This region consists of about 3 million
grid points. There are 193 points in the axial
direction and 65 in the radial direction.
Circumferentially there are 193 points. At every time
step all grid points rotate about the longitudinal axis
an amount AB = ABB SO that the entire region
rotates as a solid body. In this region all volumes
remain constant for all time although their location in
the absolute frame is changing.
Figure 8 Grid and extent of computational domain
for immersed body
For the emerged configuration the domain is
decomposed into 56 blocks each with dimensions
33x33x33. This region contains about 2 million grid
points. Circumferentially there are 129 points. The
tree surface must always be located on the
computational parameter j = jmax surface. Since the
constant j-surface at the free surface does not rotate,
computational blocks containing this surface must
deform in time and must be modified differently. For
each of these blocks a dummy block has been created
whose j-varying lines extend above the free surface
level for any amount of specified rotation. These
dummy blocks, shown as blue grids in Figure 9, are
rotated an amount, /~0 = /~eB, at every time step as
before and the cell volumes remain constant. The
computational blocks are then created from these
blocks. The j-varying curves in the dummy blocks
are cut at the free surface. The points remaining
below the free surface makeup the curves used to
interpolate a new set of points with a hyperbolic
tangent distribution with specified arclengths at the
ends. The coefficients for the distribution are
calculated according to the algorithm found in
Thompson (1985). In this region, /~0 charges in
space resulting in expanding and contracting cell
volumes. Figure 9 shows this process. The upper
figures show the computational grid and the dummy
grid at some time. The lower two figures show the
resulting rotated grids at a later time. The rotation
amount used here has been exaggerated for purposes
of illustration. Blocks not bounded by the free
surface are modified as in the immersed case. At
every time step, UNCLE calculates grid velocities
and updates all volume quantities.
s
OCR for page 687
if
Test Cases (Actual Roll Motion)
For each experimental configuration,
measured time histories of both roll motion (angle
and angular velocity) and flow quantities are
recorded. This data is time averaged to eliminate
some of the noise over small intervals and then
ensemble averaged to create one period of data. The
one period of measured angular velocity,—, is
dt
used for input to the RANS solver for all time and the
Figure 9 Grid rotation for the emerged body
same one period of measured flow results is used for
validating the RANS solver solutions.
Force comparisons are made of the
measured normal force on the individual bilge keels
with the RANS force for one period of roll. The
RANS force is found by integrating the calculated
pressures and viscous stresses along the
corresponding section of the port bilge keel
computational surface. For some experimental cases
data for only one bilge keel is available. For all
cases, differences (sometimes large) between the port
and starboard measurements occur. For the small
amplitude submerged cases, one would expect the
forces on the port and starboard bilge keels to be the
6
OCR for page 688
same. For the larger amplitude cases, where
interference between the keels could be present, the
force magnitudes should only be 180° out of phase.
Similarly for the emerged cases, the force differences
between the two keels, should only be evident in the
phase.
Flow field comparisons are also made of the
RANS velocity vectors with experimental velocities
created from PIV data. The calculated velocities are
interpolated to match the time and position of the
measured velocities. Overlaid or side-by-side
animations or still pictures at constant times can be
created from this data.
The large cylinder (D = 0.897 m), small
bilge keel (w = 0.051 m) configuration is used for all
of the calculations. From the large set of
experimental configurations a subset is chosen to
simulate using the RANS code. Calculations are
done for the immersed and emerged body
configurations with zero and forward speeds. Two
amplitude-frequency combinations are chosen from
the available data for comparison purposes. Both low
and high-speed amplitude roll velocity cases with
good experimental roll motion and force
measurements are desired as well as a combination
that spans the range of ballast conditions and forward
speeds tested. The lowest frequency tested in all of
the configurations for comparisons in the calculations
is .32 Hz. Experiments with this frequency and the
relatively small 15° amplitude provide a good set of
low speed data for all speeds and ballast conditions.
Experiments for a immersed body with amplitude 40°
and frequency 40 Hz. are used for higher speed
compansons.
Computational time steps are chosen so that
360 time steps per period results. Six subiterations
are used to get a converged solution at each time step.
Using 30 subiterations does not change the calculated
force results. The roll motion starts abruptly with its
maximum velocity, at the position of zero roll angle.
At this time the port side bilge keel is moving
upward. At a quarter of a period, the bilge keel is at
its maximum roll angle where the velocity is zero.
The roll accelerates down past the zero roll angle
position at a half of a period. The motion continues
downward to its lowest point at three quarters of
period and then returns to its starting position at the
end of the period. For forward motion cases, the
forward speed solution is converged, to set up the
boundary layers on the cylinder, before the roll
motion started. The force generally becomes
periodic after about 5 or 6 periods. The calculation
takes approximately 24 hours for 10 periods of roll
on an IBM SP3.
immersed Body Comparisons
Figures 10-13 show comparisons for the immersed
body. Each figure shows the calculated and
measured normal force on the bilge keels versus time
for one period of roll motion. The different angular
roll velocities at which the model is forced to roll is
also shown in the figures. Figures 10 and 12 show the
results for zero forward speed, basically a 2D flow,
and Figures 11 and 13 show the results for 1.0 m/s (2
kts.) forward speed. The figures show that the RAN S
calculations predict both the magnitude and phase of
the measured data accurately and the significantly
larger forces of the high amplitude roll as compared
to the low amplitude. Also predicted are the highly
oscillating variations in the force data. The rapid
acceleration and deceleration of the actual roll motion
causes the sharp peaks in the force data. Comparing
the motion of these two cases shows that the higher
speed roll case has smaller oscillations. Because of
the sharp peaks, case to case comparisons are
difficult, but given accurate roll motion data to use in
the RANS solver, very good validation comparisons
can be made.
20
10
He
Go' o
IL
-10
_ _ 1
~ Experiment - Port
_ RXPNesment-Staboald
—~ ~ r
20 1 1 1 1 -1
0 0.25 0.5 0.75 1
AT
Figure 10 f = .32 Hz., A = 15°, U = 0 m/s.,
Immersed
7
o
OCR for page 689
~1
10
At
- o
o
-10
- Experiment Starboard |
RANS |
deeds I
_~: it\ _~
As- ~~W -0.S
=~ ~= -1
0.75 1
0.25 0.5
AT
0.5
US
In
O ~
Figure 11 f = .32 Hz., A = 15° U = 1.0 m/s (2kts),
Immersed
7OI
35
-
z
-
~ 0
o
u"
-35
-70 0
Experiment - Polt
it- Add'- ~ _
/ ~e
0.75 1
0.25 t).5
AT
2
-
u,
-
u
Figure 12 f = .40 Hz., A = 40°, U = 0 kts.,
Immersed
7OI
35
z
o o
IL
-35
_ _ 4
== Expenme~t-Starboard
RANS
Lab
~ 0.: !5 0 5 0.75 .
VT
7
O
Figure 13 f = .40 Hz., A = 40°, U = 1.0 m/s (2 kts),
Immersed
Figure 14 shows a comparison of the
calculated velocity vectors with the velocities
obtained from PIV data, looking aft at the port bilge
keel, for the zero forward speed case where the roll
motion amplitude is approximately 15° and its
frequency is .32 Hz. The calculated velocity was
interpolated to the PIV point locations. The left
column shows the experimental data and the right
column shows the RANS solution data. The time
sequence begins at (a) t/T = -0.125 where the body is
accelerating in the counterclockwise direction. At
this time, we see large flow velocity passing over and
around the keel, from top to bottom, creating the
large separated zone behind it. The next row shows
the results at (b) t/T = 0.0 where the maximum
counterclockwise velocity of the body occurs. At this
time the flow at the bilge keel tip has reduced and the
vortex center has moved down as the vortex is
elongating. At (c) t/T = 0.125 the body is slowing
down. Here the flow on the top and the tip of the
bilge keel continues to reduce, but the trailing vortex
center position remains approximately the same. As
the counterclockwise motion stops ~ (d) t/T = 0.250)
we see that the cross flow impinging on the bilge keel
starts to reverse. This creates an upflow on the bilge
keel. Although the large separated flow above the
bilge keel is still present, the upflow around the keel
creates a counter rotating vortex on the topside of the
keel.
Overall the predicted and measured
flowfields have very similar behaviors with similar
magnitudes for the velocities. The calculations
predict the location of the trailing vortex fairly well,
but the predicted location of the new counterrotating
vortex appears to be somewhat off as shown Figure
14d. Some of the differences are because of the
difficulty in obtaining accurate ensemble averaging
of the PIV data at the flowhield locations in time,
particularly because of the unsmooth motion.
Because of this it is unrealistic to expect that the
experiment and the computations should compare
one-to-one. However, this demonstrates significant
progress in using unsteady PIV data in a time
dependent manor for comparing with RANS
solutions.
8
OCR for page 690
Experiment
_ _ _ _ _ ~~ItIJIt~ fIll ~
J ~ I ~ ~ I I J I
dlJItlIIIJI
l I I I I ~ I ~ ~ ~ I I I
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till t1
I l I l l 1
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!!'~i!l!i
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~:
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'.3iiii,,iTiT~
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(a)t/T= 0.125
(b) t/T = 0.0
9
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, , , , , , , ~ ~ 1
i, l ., . . I ~ ~ I
t I ~ t t t I ~ ~ 1
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OCR for page 691
I ~ 1
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(c) t/T = ~ 125
(d) t/T = 0.250
1~,:
Figure 14 Velocity vectors: Actual roll motion, PIV measurements vs. RANS solution (experiment on left)
Emerged Body Comparisons
Figures 15-17 show the results for the
emerged body moving forward at 0, 1.0 m/s (2 kts),
and 1.5 rn/s (3 kts.) The amplitude of the roll motion
is 15° and the frequency is 0.32 Hz. The water level
is approximately 0.108 m (4.25 in.) below the
longitudinal axis of the cylinder. The linearized free
surface boundary condition is used in these
calculations. For the O forward speed case there is a
significant difference between the measured port and
starboard bilge keel forces. The starboard force data
is suspect in Figure 15, since it should be more
symmetric. Physically they should be the same,
albeit out of phase with each other. The computation
predicts the port force very well, but this is a
significantly lower then the measured starboard force.
For the nonzero forward speed cases only starboard
10
OCR for page 692
data is available for comparison and at 1.0 m/s (2.0
kts.) the prediction is less than the measured
starboard force, but at 1.5 m/s (3.0 kts.) it compares
well. In these forward speed cases the starboard
force data appears more symmetric as physically
expected. There does appear to be a drop in the force
from 0 to 1.5 m/s (3 Its.), but with the port-starboard
difference in the data as well as the oscillating
variation, it is hard to draw definitive conclusions.
Figure 18 shows the computed free surface elevations
at the time t/T = 0.0 for the 1.5 m/s (3kts) case. Only
very small port-starboard differences in the wave
elevations are seen over a roll period at this
amplitude. High amplitudes could not be run with
this RANS code due to difficulties associated with
the bilge keels nearing the free surface.
10
,,,
s c
Figure 15 f = 32 Hz., A = 15° U = 0 kts. Emerged
on
1n
__ _ l 1
_~_:
ZocL:N
-20 ,
0 0.25 0.5 0.75 1
AT
Figure 16 f = 32 Hz., A = 15°, U = 1.0 m/s (2 kts),
Emerged
20 ~
Expelunenl - Starboard
RANS
dew
1 ~` ~ ~ ._. f O
~-10 ~ ~: ~ ~
-20 1 1 1 ,
0 0.2fi 0.5 0.75 1
AT
no
V
no
Figure 17 f = 32 Hz., A = 15° U = 1.5 m/s (3kts),
Emerged
~ I / Hi '''I'd il.// 1,,
~ `; J ~ ~ Hi
Figure 18 FS contours, f = .32 Hz., A = 15° U = 1.5
m/s (3kts),
Test Cases (Ideal Roll Motion)
Once convinced of the good performance of
the RANS code for predicting bilge keel forces for
forced roll body tests, the solutions are used to
compare differences in force data due to varying roll
test parameters. These tests use an ideal sinusoidal
roll motion, resulting in smooth force results. Figure
19 shows the comparison of the normal force on the
port bilge keel for an immersed body rolling at .32
Hz. and amplitude 15° for a range of forward speeds.
The results show the maximum force decreasing as
the forward speed increases. The shape is also
changing. At low speeds the force curves show
narrower and steeper peaks.
11
OCR for page 693
10
5
~ _ l
U = 0.0 misdo 0}
- - - U = 1.0 miss dial
U-~.5~s(3~5.\
~ZD~ ~ ~
0.: 25 0 5 0. 5
AT
indicated by very small mean value, aO, in the
decomposition.
0.5
-
O -
3
_0.5
Figure 19 RUNS Solution: f = .32 Hz., A = 15°,
Fwd. Speed Comparison (Smooth Roll)
Traditionally the bilge keel force is
decomposed into an inertial term proportional to the
acceleration (IS' sine harmonic) and into drag terms
proportional to the rotational speed and speed
squared (dominated by 1St and 3r~ cosine harmonics).
The Fourier decomposition of the force histories
shown in Figure 20, shows that the first harmonic sin
and cos terms have about equal contributions at a
particular speed, but reduce as the forward speed
increases. At zero forward speed, a significant
contribution from the third harmonic cos term is seen.
As the forward speed is increased to 2.0 m/s (4 kts.)
this harmonic disappears as the force curve
approaches a purer sine wave with lower amplitude.
1
, i i I , i ,
' . . ~ ~ · Is a,, cosco'~b~nlo'
a 0 ~~ bh dill conlrib~nion5
! ~ ! . ~ 4 Is ~ Is corm anion
! ~ a 4 - As b - ' oot~lbutia~s
~ ~ ~ I—- —t ~ ~ ~ , i
_ _ I ~ ~ . ~ L
__ ~ . ail_., .. - i. ~~ ..
......... ...... .. . ~ , . ~ .
o
1
k 5
Figure 20 Fourier coefficients
10
Figure 19 also shows that magnitude of the
force does not depend on the direction of rotation,
which indicates that for these conditions there is little
or no influence on the port bilge keel force due to the
starboard bilge keel and vice versa. This is also
Figures 21 and 22 show the calculated
vorticity for the O and 2.0 m/s (4 kts.) forward speed
cases at different times in a partial period of
counterclockwise rotation. The vorticity being
created at the bilge keel tip rotates in a clockwise
direction (indicated by red contours), opposite to the
rotation of the bilge keel. This vortex is also shown
in Figure 14. The counterclockwise vorticity
(indicated by blue contours) is the disturbance
remaining from the previous clockwise motion of the
bilge keel.
Figures 21a and 22a show the bilge keel at
the tlT = -0.125 (t/T = 0.875~. Since the body is
accelerating at this time, the inertial force (first sin
harmonic) adds to the drag force (first cos harmonic)
resulting in a peak in the total bilge keel damping
force. These dominating contributions produce a
maximum force somewhere in the period between the
maximum acceleration and maximum velocity.
Additional drag occurs in the zero forward speed case
where the left over "interference" vorticity (third cos
harmonic) is present. This vorticity could possibly be
contributing to the large velocity vectors at the bilge
keel tip as shown in Figure 14a. This vorticity (drag
contribution) is not seen in the 2.0 m/s (4 kts.) case,
most likely because the forward speed has swept it
downstream out of the way by the time the bilge keel
rotates back.
12
OCR for page 694
'1
(a) t/T = -0.125
it'
(c) t/T = 0.125
~ :
(b) t/T = 0.0
/
(d) t/T = 0.250
Figure 21 RANS Vorticity: Ideal Roll Motion f = .32 Hz., A = 15°, U = 0.0 m/s
(a) t/T = -0.125
fit
( c) t/T = 0.125
hi.... <{I
..
(
,__
I..
At'
(b) t/T = 0.0
hi"
(d) t/T = 0.250
Figure 22 RANS Vorticity: Ideal Roll Motion f = .32 Hz., A = 15°, U = 2.0 m/s (4 Its.)
13
OCR for page 695
Figures 21b and 22b show the bilge keel at
t/T = 0.0 (tlT = 1.0). At this time, the acceleration is
zero and the velocity has obtained its maximum
value. The inertial forces are zero here so that the
bilge keel force is entirely due to the drag terms.
Figures 21c and 22c show the bilge keel at
t/T = 0.125. At this time the body is slowing down
so that the inertial force subtracts from the drag
forces resulting in a small total bilge keel force.
The last figures, 21d and 22d show the bilge
keel at t/T = 0.25 where the roll velocity is zero and
the acceleration is maximum. Here the total bilge
keel force is mostly due to the inertial contribution.
Also seen in these figures is the counterclockwise
vorticity created by fluid catching up with and
passing the bilge keel tip, also demonstrated in Figure
14d.
Figures 23 and 24 show the calculated axial
velocity for two different times of a period roll
motion. The roll velocity is at its maximum in the
first and zero in the second. Both figures show the
thickening of the boundary layer and the growth of
the vorticity in the downstream direction. Also seen
is the depression of the boundary layer in the region
behind the bilge keels due to the vertical motion over
them. When the roll is at its maximum velocity,
Figure 23, we see the vortex roll up over the length of
the keel much like a wing tip vortex. At zero roll
velocity, Figure 24, the vortex behavior is much
different with no tip vortex like flow present.
Axial Velocity
0.90
0.80
Q.70
0.60
0.50
0.40
0.30
0.20
o1n
Figure 23 RANS: f = .32 Hz., A = 15°, U = 2.0 m/s
(4 Its.), t/T = 0.0
Figure 25 shows the comparison of the
normal force on the port bilge keel for the immersed
body rolling at .32 Hz and amplitude 60° for zero and
2.0 m/s (4 kts.) forward speed. At this amplitude the
bilge keel rotates 15° beyond the centerline of the
body into the wake of the opposite bilge keel. The
dashed curves are the forces plotted 180° out of phase
and opposite sign. At zero forward speed this
illustrates that the force magnitude is different when
the body is rolling counterclockwise then when
rolling clockwise.
axial Velocity
1 o.9o
Q.8O
i o.7o
; 0.60
0.50
OAO
0.30
0.20
~ O1D
Figure 24 RANS: f = .32 Hz., A = 15°, U = 2.0 m/s
(4 kts.), t/T = 0.25
This indicates an influence on the port bilge keel
force due the starboard bilge keel and vice versa.
The interference is not seen at 2.0 m/s (4 kts.), again
because the forward speed has swept the vortices,
created by each bilge keel, downstream out of the
way by the time the opposite keel sweeps past the
centerline of the body.
14
OCR for page 696
70
35
o o
-35
/\
/f' \
~ ~ \
-- ~ - -
0.' 25 0 5
VT
U · 0.0 ants (A fits.) - Pot BK
. _ — — — U · G.0 m/s tO Ids.) - Sta,rbo, rdi BK
U ~ 2.0 m/5 (4 ~as.) - Pod BK
— - — U ~ ~0 ~S (4 - .) - ~i~i7i~ BK
dell
I/
. _ \\~~
_
0.75 1
u,
O '-
_
.'
Figure 25 f = .32 Hz,., A = 60°, Fwd. Speed
Comparison (Smooth Roll)
The Fourier decomposition of the port bilge
force histories is shown in Figure 26. As in the 15°
case the magnitude of the force decreases and the 3r~
cosine harmonic disappears as the forward speed
increases. Also shown is the nonzero mean value in
the decomposition for the zero forward speed case,
indicating the interference of the opposite bilge keel.
9
t
8
3 r
O
:
-6
~-
== I.~-~.........
_ . ~ .
=_ = ~.._..~._...
=1 =1
_,
=
o
| O - US. is - e phi - him
a 0 H~ be shy co~un~ns
~ 4 54s a,, ads Henry, tio,-?s
0 4 - 54s b,, Tiff U - - liens
~-1
1-
·f~l-~-.L~ l-~--l
j . _.~ __ I.... .~
EMU ! in ' ~ I
-t---'i~--'-'-'!~---'t"~ '--"-- 1
t i . t ~ |
I . 1 . T I
t , , t ~ I
t ' .
Fi-~ ~.. ,~Ui .
it t t
I I ! !
, 1 1
s
k
Figure 26 Fourier Coefficients
10
One advantage of having reliable
computational capabilities is the ability to quantify
scaling effects when moving from small to large
geometries. These effects can be used to justify the
use of a smaller model versus a larger model or
extrapolating small model data to full-scale data.
Calculations have been performed using the same
computational geometry, with smooth motion as
before but with half of the Reynolds number. No
noticeable effects were seen in the force data.
Conclusions
Comparisons of RANS calculated force data
with measured data and calculated velocity vectors
with PIV data have been made using the actual roll
motion of the cylinder for a range of test conditions.
Overall, these demonstrate that the RANS solver
can be used to accurately simulate forced roll motion.
Particularly, the solver provides excellent bilge keel
force data for the submerged, forward speed cases.
Emerged case calculations also compared well to
experimental data, but are limited due to numerical
stablility problems when the bilge keels approach the
free surface. Comparisons with PIV data also
demonstrate that the calculations are predicting the
correct flow physics.
Calculations performed using an ideal
sinusoidal roll motion allowed trends to be
investigated by enforcing the same roll motion for a
number of forward speeds and simplified (somewhat)
the harmonic content of the total bilge keel force. The
results showed that the magnitude of the total bilge
keel force decreased as the forward speed was
increased.
Acknowledgements
This effort was sponsored by NAVSEA
PMS 500. The authors would like to thank Mr.
James Webster for his direction and encouragement
during this effort. Partial support for this effort from
ONR under Dr.
_
Pat Purtell is gratefully
acknowledged. The authors would also like to
acknowledge Mr. Martin Donnelly for providing the
processed experimental bilge keel force data. The
computations were performed using facilities at Maui
and ARSC under DOD HPCMO.
15
OCR for page 697
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16
Representative terms from entire chapter:
roll motion
