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| Introduction |
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The
HSVA test case involves the flow around the submerged
hull of a single-propeller ship. Initially, the ship
model is tested without the propeller, during which
many aspects of the hull performance are measured.
One such aspect is the flow through the propeller
plane. The propeller is located behind the ship hull
and hence it rotates in water that has been already
disturbed by the passage of the hull. The velocity
in the wake of the ship is not uniform but changes
with radial and angular positions of the propeller.
The wake velocity consists of axial, radial, tangential
components.
The propeller rotates at a constant speed, and the
blades are fixed-pitch propellers. Through a single
revolution, the blades pass through regions of differing
flow velocities. This results in varying angles of
attack for any given propeller section, and consequently,
a cyclic, oscillating propeller thrust is generated.
Minimizing this oscillation is critical. Vibration
and noise can be intolerable to crew and passengers.
They may also reduce propulsion efficiency, leading
to higher fuel costs, or even cause structural damage
to the ship in extreme cases.
HSVA performs both numerical computations and model
testing to measure this flow disruption. These measurements
serve as a baseline, against which the effects of
a propeller are compared. The results can be used
to verify a propeller performance, and to indicate
areas of improvement during the design phase. For
the computations, it is of importance to the HSVA
and the client to obtain these results quickly, accurately,
and reliably.
FlowGrid will be tested not only to verify and benchmark
against currently used methods, but also demonstrate
its use with extreme computing methods. In this test
case, two methods for computation will be computed
and evaluated. The first method, using wall functions,
is the commonly used computational method at the HSVA.
It uses a moderately sized grid, and provides acceptable
results in a short computing time. FlowGrid is to
be used to compare with experimental model measurements
and other CFD software for wall function computing
method. The second, a non-wall function computing
method, provides higher accuracy compared to the more
commonly used method. However, due to the large grid
and long computing times necessary, it is not practical
to use this computing method with conventional computing
software and hardware configurations. FlowGrid will
demonstrate its superiority for the application of
this more complex, unconventional computing method.
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| Detailed
descriptions |
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The
computations are based on the Napa geometry description
of the model (HSVA model-2962) for the containership
“Sydney Express”. An experimental model
was constructed according to this geometry description.
From the Napa description, an IGES file was generated,
to be used as the basis for grid generation using
the commercial grid generation software ICEM-CFD.
The ship profile is shown in the figure below.
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Profile view of “Sidney Express”
The ship is symmetrically shaped, and uses a single
propeller for propulsion. The test case simulates
full ahead travel, thus the flow is parallel to the
ship’s length. Under these conditions, it is
only necessary to compute one half of the ship, with
the plane of symmetry along the longitudinal centerline
of the ship. The actual ship is 210.00 meters long,
but the computational grid was scaled to match the
7.50 meter length of the experimental model, in order
to conduct a direct comparison with experiment measurements.
The table below gives the main ship characteristics.
Full
Scale Ship Dimensions |
| Lpp |
210.00 |
Length between
perpendiculars (m) |
| B |
30.50 |
Breadth (m) |
| T |
11.00 |
Design draught
(m) |
| Vs |
10.5 |
Ship speed (m/s) |
| Rn |
1.859*109 |
Reynolds number
based on Lpp and Vs |
| Fn |
0.231 |
Froude number
based on Lpp and Vs |
| |
Model
measurement |
| lambda |
28.0 |
Model scale
factor |
| Vm |
1.97 |
Model speed
(m/s) |
| Rn |
1.246*107 |
Reynolds number
based on Lm and Vm |
| Fn |
0.230 |
Froude number
based on Lm and Vm |
With
the model testing, similarity laws come into conflict.
Reynolds scaling is based on the viscous effects,
and dictates the speed of the model should increase
inversely as the model size decreases. Froude scaling,
however, is based on gravity effects, and dictates
that the model speed should decrease as the model
size decreases. In model testing, the gravity effects
at the free surface are dominant, and the model
speed is defined according to Froude’s Law
for similarity as
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This test case uses two frames of reference: a global
frame and a propeller-based frame of reference.
The global frame of reference is right-handed Cartesian
coordinate system. Typical to shipbuilding practices,
the origin of the global reference frame is along
the longitudinal plane of symmetry at the rudder
shaft centerline. The x-axis is centered at the
ruder shaft centerline and points forward. From
this frame of reference, the free-stream fluid flow
is defined as flowing in the negative x-direction.
The z-axis is centered at the baseline of the ship,
pointing positive upward. By default, the y-axis
points in the port direction.
The secondary frame of reference is a cylindrical
coordinate system, coinciding with the rotation
of the ship propeller. Most of the plots depicting
computation results are in this frame of reference.
Computational domain bounding edges
The computational domain is often either cylindrical
or rectangular shaped; in this test case it is cylindrical,
as shown in the figure above It is important, that
the side and bottom boundaries are far enough from
the ship hull as to avoid shallow water and channel
wall effects; ½ ship length is sufficient
in this case. The inlet is at ½ ship length
ahead of the ship, and the outlet is placed 1 ship
length behind the ship. The top of the computational
domain is at the design waterline of the ship, 0.393
meters (11.00 meters, full scale). This type of
computation does not take the free surface into
account, and thus the top of the computation domain
is a solid surface. These are generally known as
„double body“ computations. The focus
of the computations is the flow through the propeller
plane, as indicated in tne figure below.
Propeller
plane location
Based on the ship hull geometry and the computational
domain bounding surfaces, two grids were generated
using ICEM-CFD. The first grid had 868,465 cells
and the second had 1,302,966 cells. Mainly, the
cell height in the region at and near the hull surface
changed the most from the first grid to the second.
The initial cell height at the hull surface in the
second grid was set to 2.86*10-3 m. For the second
grid, the initial cell height at the hull was reduced
to 1.79*10-4 m. Subsequently, to keep the aspect
ratios in these cells within reason, the cell sizes
in the other two directions, i.e. tangential to
the hull surface, were also reduced. Further, the
cell heights in the next several surrounding layers
were also reduced, to maintain smooth continuity
of cell sizes. Outside a 1 meter (full scale) region,
the cell spacing for both grids were very similar.
A cross-sectional slice from the same location of
both grids is shown in the next figure.
These two grids were generated for application of
two computational methods for resolving the boundary
layer at and near the hull surface. At the hull
surface, a no-slip boundary condition was applied.
The no-slip condition implies that the velocity
of the fluid is equal to that of the adjacent solid
surface. However, if the flow is turbulent and the
grid elements are too coarse to resolve this large
velocity variation in the region near the wall,
then a special interpolation of the velocity and
shear stress is necessary. This interpolation is
based on so-called “wall functions”.
For finer grids, the cell height in the region near
the hull is sufficiently small that wall functions
are not necessary to represent the distributions
of velocity, temperature, turbulence, energy, etc.
within the boundary layer that forms adjacent to
the hull surface. With the size of the ships computed,
a grid fine enough to fulfill this criterion is
impractical for computing on the current HSVA hardware/software
configuration. Using FlowGrid would provide the
opportunity to perform such computations effectively
and competitively.
Grid comparison: wall function coarse grid,
left; non-wall function fine grid, right
Description
of relevant parameters to be observed
In
this test case, the relevant parameters to be observed
are as follows:
• Pressure along the hull surface
• Shear stress along the hull surface
• Flow velocity near the hull surface
• Flow velocity components on the propeller
plane
• y+ values along the hull surface
• k and e values for the turbulence model
The pressure and shear stress are integrated along
the hull surface to compute the resistance of the
hull. The flow velocity near the hull surface gives
an indication of where flow problems may occur.
The flow velocity components- u,v,w- on the propeller
plane are used extensively for propeller design
and evaluation.
The y+ values provide information to whether wall
functions are used or not. Comet sets a limit; for
y+ <11, non-wall function method is applied,
otherwise wall functions are used for resolving
the boundary layer.
The turbulence values k and e affect nearly all
of the parameters mentioned above.
Available
experimental data
Experimental
data was gathered from model tests in the HSVA’s
300 meter towing tank. The model tests used force
gauges to measure the longitudinal force required
to tow the model, and 5-hole pitot tubes to measure
the flow velocity in the propeller plane. The pitot
tubes were arranged on a small armature, spaced
from 30% propeller radius to 110% propeller radius,
in 10% increments. The armature could be rotated
through the entire propeller revolution in 10º
increments. See figure for details.
Pitot
tube arrangement for measuring flow
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| FlowGrid
evaluation |
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The
HSVA has identified several comparison characteristics,
with which the FlowGrid system is to be evaluated.
This consists of visual comparison of the computation
results, as well as numerical evaluation. The following
table summarizes these characteristics and corresponding
values:
Complete
“turn-around” time |
1-1
½ days |
Computation convergence times |
1-2
hours |
| Global
Ship hull resistance (CFD
computations only) |
Within
10% of Comet computations |
Nominal
wake fraction value |
Appx.
5% of Comet and model values |
Axial
velocity component error |
Under
10% of model values |
Flow
velocity distribution |
Visual
survey |
The term “turn-around” time describes
the time needed to deliver results to the customer
for a given problem. This includes preparation time
for the solver, as well as post-processing of the
results. Since this is still the developmental phase
of FlowGrid, this turn-around time is not expected
to be comparable to the process currently in use
at the HSVA. However, it will become an important
factor, once the process has been established, and
the learning curve has been passed. Currently, turn-around
times in the order of 1 to 1 ½ days is acceptable
for the coarse grid computation using Comet. FlowGrid
should meet or exceed this once the learning curve
has passed. For the finer grid computation, an acceptable
turn-around time is difficulty to determine, as
the Comet calculations are impractical with HSVA’s
current computing power.
The computation convergence time shows how quickly
the calculations can arrive at a solution. Unlike
the aforementioned turn-around time, the computational
convergence time is not so strongly dependent of
user experience and, therefore, can be compared
against the computations performed on the HSVA’s
parallel cluster. The computing times for the coarse
grid computation using FlowGrid should be comparable
to within 1 to 2 hours, comparable to those for
Comet.
The global ship hull resistance compares the representation
of the no-slip boundary condition of the ship hull.
It is the sum of the integrated pressure component
of the ship surface and the integrated shear stress
acting on the hull surface. The resulting longitudinal,
x-direction, forces should be comparable to Comet
computations and experimental results by 5 to 10%.
The
nominal wake fraction is the average deficiency
in the axial flow through the propeller plane, caused
by the wake of the ship hull. This value is calculated
by the integration of the normalized axial velocity
component over area enclosed by the propeller-bounding
circle. The equation is in the form of a summation,
based on the integral:
where
ux is the normalized computed
axial component of velocity.
The HSVA propeller expert uses the following formula
to compute the velocity axial component error,
where Vi A_measured is the measured axial component,
Vi A_computed is the computed axial component, and
V0 is the free stream velocity (1.97 m/s). This
formula may be applied to a single radius, or to
the entire set of measurement points in the propeller
disk.
Other aspects for evaluation of FlowGrid performance
are not specific to this test case. These are the
characteristics of FlowGrid that cannot be quantified.
FlowGrid should be easy to use; learning to use
FlowGrid should not be laborious. The HSVA has experience
with at least three other RANSE solvers, and expects
similar features to be found in FlowGrid as in the
other solvers. Of course, not all features can be
available initially. This is not a primary concern
for HSVA, as it is understood that FlowGrid will
be further improved beyond this developmental stage.
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