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OCR for page 820
Submarine manoeuvrability assessment using
Computational Fluid Dynamic tools
D. Bellevre, A. Diaz de Tuesta, P. Perdon
(Bassrn d' Essais des Carenes, France)
ABSTRACT
Tha ks to tha constant increasa in computing
power, it is now bacoming possibB to aim at mora
and mora ambitious rasults in using Computational
Pluid Dy amic. Tha objact of this papar is tha
dascription of tha impBmentation of a calc~lahon
tool, which should aventually conhibuta to tha
sathug up of a quasi-axhaustiva data bank of
hydrody amic coafficients of my submarina, for
any m mauvars likaly t ba studiad.
A mash ganeration tool davalopad in ordar to
facilitata tha pra-procassing staga of CPD
calculation is prasantad. Than different casas of
calculation performad ara dascribad, tha rasults ara
comparad to thosa obtainad with towing ta k modal
tasts. Tha validity of aach typa of calc~lahon is
discussad, with an ovarvi w on tha actual prog ass.
A mathamatical m mauvarability modal has baen
identifiad f om tha rasults obtainad through
calculation. Simulations parfo mad with this modal
ara comparad to rasults obtainad at saa.
INTRODI CTION
It is now possibB to expact rapid rasults for a
wida rmga of calculations. CPD (Computational
Pluid Machanic) is considarad hara as a'`numarical
towing tank", which allows to compara tha rasults
with modal tast data.
Although tha diract simulahons of manauvars
using an unsteady RANSB coda is possibB, it is
very tima cons ming md tha usa of a mathamatical
modal basad on coafficiants in a quasi steady
approach is practically instantanaous and allows a
very wida ranga of simulations in a short tima.
In order to facilitata tha pra-procassing staga of
CPD calculation, a mash ganaration t ol has baen
davalopad at Bassin d'assais das carinas. This t ol
automatically providas a 3D mash whan cinamatic
paramaters (d if t angB, angB of attack, rata of turn
in horizontalha tical pi ma) ara given or whan
changas in tha gaomat y of tha submarina (L D
ratio, m mbar, siza or location of tha appendagas,
shapa of dack, ) ara proposad. This avoids tha
long and laborious task which consists in ra-mash
tha submarsibB for my minor changa in its
gaomat y. Purtha mora, using this tool tha grid
topology is idanhcal f om ona casa to another so
that tha numarical rasults ara mora raliabB, at Bast
for comparison pu posas.
This study has bean perfo mad on an axisting
submarina for which modal tast rasults wera
availabB, and calc~lahons hava baen dona on tha
basis of usual captiva modal tast: r~ddar
affactivanass tasts, obliqua towing tasts, and
rotating arm tast in both vertical md horizontal
pimas. Tha solver usad was a commercially
availabB Raynolds Avaraga Navier-Stokas coda
(Nawtonim homogenaous md incomprassibB
duid).
MESH GENERATION
Tha philosophy of tha numaric tool usad to
conduct this study is basad on a '`modular"
concaption of tha submarina, so that tha shapa,
position, or aven a datail m tha mash of aach part of
tha ship can aasily ba ch mgad, and ra-inco poratad
int tha mash of tha whoB ship. Tha following
parag aphs dascriba briady tha chronology of
manipulations carriad out to obtain this adaptabB
mash.
Bodv and deck
Tha shapas of tha dack and of tha body of tha
submarina ara obtainad f om a CAD fiB. At this
staga, tha number, siza md rapartition of tha calls
corrasponding to thosa two pa ts of tha submarina
ara sat up.
Anuend~
Va mean by'`appandagas" tha diraction and diva
r~ddars, md tha sail. Tha gaomahic data nacassa y
ara, on tha ona h md, tha ganeral charact ristics of
tha appendaga (wingspread, chord, ralativa
thicknass), and on tha othar h md tha fiBs of Bazier
poBs dafining tha thick ass laws at tha basa and in
haad of tha appandaga.
OCR for page 821
The number of cells in thickness and in chord is
now fixed. The number of cells in wingspread will
adapt at best the revolution mesh of the mother hull.
Combination
The principle for the mesh of the submarine for
the purpose of maneuverability calculation is the
following: the 2D mesh of the body is reproduced
by symmetry of revolution around the axis of the
ship. The different appendages are afterwards
incorporated in the mesh, by locally distorting it.
The deck is finally taken into account, by a
deformation of the mesh in the concerned areas.
Maneuvering
To satisfy to the limit conditions of calculation,
which are of"Neumann" type, it is necessary to
maintain the flow perpendicular to the outlet of the
mesh. So the mesh used for calculation in
maneuvering (rotation, incidence) is deformed to
adapt to this necessity. This operation is fairly
quick (one or two minutes).
: ~
Hi,
Fig 1: deformation of the mesh for a rotation
calculation
NUMERICAL TESTS
Different mesh
The size of the mesh is a preponderant factor in
the time required and in the quality of calculations.
In order to determine a satisfying compromise
between those two necessities, tests have been
performed with three different mesh sizes.
The smallest one, quite coarse, comprises
400.000 cells for the whole submarine. The
intermediate one, 800.000 cells, and the finest one,
1.400.000 cells. These numbers correspond to the
case where the symmetry related to the vertical
plane cannot be used (typically the cases of
maneuvering in the horizontal plane). For the other
cases, the number of cells is of course reduced by
one half.
It is obvious that the more the number of cells is
important, the longer the calculations are. First,
because each iteration takes more time, and then
because the calculation needs more iterations to
converge. That is why the size of the mesh is a
parameter that has to be carefully chosen, before
starting of a wide range of calculations.
A mesh that includes the forward dive planes
requires the use of the finest mesh resulting in a
large number of cells. Therefore the impact of fins
on the quality of the results has to be evaluated.
:
Fig 2: coarsest mesh
Fig 3: intermediate mesh
OCR for page 822
o
2
3
4
6
8
+/-2.5
+1-3
+1-4
+/-5
+1-6
+1-8
The two cases s=0 and 6=0 correspond to the
same calculation. In the same way, the negative
values of ~ correspond to the same cases as the
positive ones, because of the symmetry of the
submarine.
Rotation (vertical and horizontal planes!
Fig 4: finest mesh
Fig 5: "forward dive planes" mesh
Pure incidence/pure drift
Calculation cases have been chosen to coincide
with the results of captive model tests available.
The following table enumerates the different
cases of incidence (vertical plane: s) and drift
(horizontal plane: 6) performed during this study.
~ 1 ~
values in degrees(°)
-8 1 0
-6 +/-0 5
-4 +/-1
-3 +/-1.5
-2 +1-2
As in previous section, the calculations with
yaw and pitch rate have been modeled based on
rotating arm test which results were available.
During these tests, the radii of rotation were chosen
in a geometrical progression between the two
extreme positions of the rotating arm carriage.
Were retained:
R=_1 lm; _13 .83m; _1 7.39m; _21 .97m; _27.50
Since the model length was 4.33m, we obtained
the following non dimensional rates of turn:
For r)=L/R=_0.39; _0.31; _0.25; _0.16
By convention, we use q to design the rate of
turn in the vertical plane, and r for the horizontal
one. The following table, exposing the calculation
performed, was obtained by combining those values
with different incidence (or drift) angle.
q (or r) -0.39 -0.31
-12 (g) (g)
-10 (D (D
-8
5
-4
-2
O
2
4
5
8
10
12
.
.
-0.2s -0.20
(53 ~
.
.
.
.
_ O
,53
,53
,53
,53
,53
,53
=
1
1
1
1
1
1
1
T4:
1 ~ 1
1 ~
OCR for page 823
Some of these calculations were performed with
different mesh, in order to determine the best
compromise in term of mesh size between precision
and rapidity.
Rudder effectiveness
The rudder effectiveness is estimated by
studying the hydrodynamic coefficients in a straight
line, with no incidence, for different plane
deflection (or flap angles, if the rudder doesn't
move entirely around its axes, as in this case). In
the following table, Q~ represents the angle of flap
of the stern dive planes, and or the rudder angle.
of +
5
CONVERGENCE
p~ or or (degrees)
10 1 15 1 20 1 25 1 30
The following graphs show the convergence of
a calculation: the curve representing the evolution
of the computed values of physical data, like the
forces along the x-axis must present a zero gradient
at the end of the calculations. The curve "residual"
represents the evolution of the difference between
the solution computed at stage n, and the one at
stage n+1. Depending on the quality of convergence
expected, a maximum value is fixed for those
"residual", above which the calculation is not
considered as being converged.
A..,..,
I.
5$~t
~ :~.~i;
i''' ,...
~55
$5: I:
3..
~~$f..5)
I'.:
Ski ::: -$ ~
on >...k
- ..~ .. :.~
~ it ,,. .. ~ ~ - - ~ . ,, ,,,, ~
~ , .. . ... . . . . . .
~ :. ..~ ~,~ a:'. 5 ,.~,.:.5i5 '5~:5,:~ :55i:' ~ .~, ~ ~ .$v,,.5~ ~ 5~5 ^:
in_
~ ...........
::~1 ·:..
:,
·: I.
5
.,
Some calculations required more attention than
others before they converge in a satisfactory way.
Among the main parameters we modified are
the values of the relaxation factor used for the
calculations. This relaxation factor represents the
proportion of the result of the iteration "n" re-used
as a base to compute the iteration "n+1". The larger
the factor is, the faster the solution converges, if
everything is going all right, but also the higher is
the risk of divergence. Indeed, if the first solution
computed is radically false, and if the second one is
based in a large extent on the precedent, it is very
likely to obtain a result even worse.
The majority of the problems of this type were
met for rotation/incidence cases. They were
countered by reducing the relaxation for the first
100 iterations, before setting them back to their
usual (default) values.
The missing points on the following graphs,
showing the calculations results, correspond to the
cases where calculation did not converge, despite
changes in relaxation factors. Most of them have
been encountered for rotations in horizontal plane.
EFFECT OF MEStI SIZE
Horizontal plane
For manoeuvring in horizontal plane, the
forward dive planes theoretically do not play a
leading role. On the other hand, a very clear
difference was observed between the coarsest mesh
and the middle one.
The comparison with model test results showed
that the middle mesh gives results closer to the
reality. Tests with the finest mesh still have to be
performed. Since it is not possible to use any
symmetry in the horizontal plane (which was not
the case for vertical plane motions), the size ofthe
OCR for page 824
required mesh is at least doubled and therefore,
still poses memory capacity problems.
e
id 0,80
c,
0,60
0,40
+coarsest meshing
middle meshing
<<,,~,~,<~r model tests ~ /
-0,20
Drift (degrees)
Fig 6: Pure drift: comparison between two
meshes
The accuracy of the results seems therefore to
be directly related to the size of mesh, and in all
likelihood, it will not be judicious to merely
compute using the coarsest mesh, even if this would
have represented a considerable economy in
calculation time.
Vertical plane
Pure incidence.
It appears that the mesh density has a lesser
effect on the result accuracy than in horizontal
plane.
The presence or the absence of the front rudders
leads to a difference of 18% on the gradient of the
curve of heave force versus incidence, for the pure
incidence maneuvering. This results are presented
further, in the paragraph "comparison with model
test results"(f~g 104.
The following graph shows the curves related
the drag coefficient as a function of the incidence
angle for different meshes.
0,00
-6 -4 -2 - 0 2 4 6
:, Drift (degrees)
° Coarse meshing
Middle meshing
ED ~ Bme meshing
~0 TO ^~"1 orward planes" meshing
,
-0,20-
Fig 7: drag coefficient in pure incidence
manoeuvring
The results of the coarsest mesh are quite
different from those obtained with the three finer
meshes. It is more difficult to obtain precise results
for the drag coefficient calculations, because of its
nature: the whole drag is the algebraic sum of
different drag forces of great absolute value, and of
comparable magnitude, but of different signs. A
low relative variation of these great values has a
very sensible effect on the whole sum, which
absolute value is very low.
The drag induced by incidence which is more of
concern for manoeuvrability purposes does not
seem to be much dependent on the refinement of
the mesh.
Low rotation rates.
The difference between the heave force
coefficient calculated with the coarse mesh and the
finer one is less important when a rotation is
introduced in the manoeuvre.
The following graph shows that even for a low
rotation rate, the difference between the two curves
related respectively with the coarse and the
"forward plane" mesh is only 10%, against the 18%
observed in pure incidence. We do not have yet any
satisfying explanation for this difference, but this
will allow us to consider that the coarse mesh is
sufficient as long as the rotation rate remains
inferior or equal to 0,2. It must be noted that during
usual situation the non-dimensional rate of turn of a
submarine in the vertical plane does not exceed 0,2.
0,2
Incidence (degrees)
4 ~ ~ 12
Coarse meshing; q=0,16
"forward planes" meshing; q=0,16
<~ Coarse meshing; q=0,20
Am "forward planes" meshing; q=0,20
Fig 8: Heave force for rotation in vertical
plane (low rotation rates)
Higher rotation rates.
This good agreement between results
corresponding to the two mesh remains valid as
long as the rotation rates are not too high. Actually,
OCR for page 825
as soon as q>0.25, the curve related to the
coarse mesh collapses for the highest incidence
angles.
o
-4 0
?~
~~ \
4}
=
1 ' ~
4 ~
In_
+coarsest meshing; q=0,25 Fry.
} "forward planes" meshing; q=0,25 ~ I
-0,8
~ coarsest meshing; q=0,39
-1,2 fffffffff "forward planes" meshing; q=0,39
Fig 9: Pitching moment for rotation in
vertical plane (higher rotation rates)
4 0 4 y Incidence (degrees)
e 0,04+
e=,
=t
0,08~ Ail
.^^f~'ffff Coarsest meshing; q=0,16
~-0,12 "forward planes" meshing; q=0,16
.. (/ off coarsest meshing; q=0,20
~'ffffff "forward planes" meshing; q=0,20
-0,16
Fig 10: pitching moment for rotation in
vertical plane (two different mesh)
On the other hand, a very clear improvement is
obtained by refining the mesh if we compare the
curves related to the pitching moment, even for low
rotation rates. For largest incidences, we observe a
notable reduction of the values obtained with the
small mesh which does not exist for model tests,
and which reveals a bad repartition of forces due to
the insufficient precision of the cells.
COMPARISON WITH MODEL TESTS DATA
Pure incidence (without rotations
The slope of the curves resulting of calculation,
representing the lift coefficient present a satisfying
concordance with those of model tests in vertical
plane.
It is clear that due to the presence of the sail and
the deck a submarine is not symmetrical in the
vertical plane and therefore a non zero value is
expected for heave force and pitching moment at
zero incidence angle. This offset is much bigger
when for model tests results but is to a great extend
related to the experimental set-up (presence of
struts) and to the precision limit of strain gauges
calibrated for much bigger forces.
0,40
e
..
—8
-u,~u
Fig 11: Heave force coefficient in incidence
~ _ _ A
-0,20
~ ~.~
+coarse meshing
}intermediate meshing
~ Bme meshing
Am "forward planes" meshing
Model tests
Drift (degrees)
manocuvring (vertical plane!
Pure drift (without rotation)
As seen in the section "comparison between
meshes", the concordance between model tests and
calculation results is very good, as soon as a
sufficient refinement of the mesh is adopted.
The following graphs show the evolution of the
yaw moment as a function of drift angle, for the
two meshes already performed, and for the model
tests. We see that the slope of the curves is very
similar. The shift of values observed is probably
due to errors related to test operating. Actually,
since the submarine (without propeller) is
symmetrical to the horizontal plane, it is logical to
obtain a zero value of the yaw coefficient for a zero
drift angle, as observed for calculation results,
unlike for model test results.
non
e
o
e -0,20
E
-0,10
-2 ~~>,,, 2
_O,10 \ it,
6
Coarse meshing
}middle meshing
off model tests
Fig 12: yaw moment versus drift angle
Dim (d~,~,
1--
10
OCR for page 826
Rotation/drift (horizontal plane)
Rotation/incidence (vertical plane)
The rotation/drift cases posed most of the
We present here the comparison between the convergence problems (that is why some of
results of model tests and calculations with the calculation points are missing on the graph above).
finest mesh ("forward planes" mesh), since we saw The calculations are more time consuming in the
before that they are sensibly better than the ones horizontal plane, because of the lack of symmetry,
with a coarser mesh. but this cannot be the only reason for those
difficulties. We can suppose that the rotation of the
05 .' sail in horizontal plane disrupts strongly the flow,
~ : and therefore the calculations. More precisely, the
calculation *~0~ chord of the sail can not be considered as small in
-1 5 -10 -0 5 ~;~' 0. 0 0 '5 relation to the radius of rotation and therefore the
~ q=031 .~: OS sail acts as a lifting surface in a curved flow.
, ~ ~ , ~ _ ~ c ~ ~ cud ~ lion ~
-15 -2 0 -15 ~ -1 0 -0 5 ~ F ~ ~ O. .0 ~ 0 .5
~ r=039 ~ -05
Fig 13: Heave force coefficient for combination I. ~0:21 ~ ~ I
of pitching rate and incidence ~ r 16 ~ ~ ~]
,.---'', Is j
Despite the presence of an offset already -2
addressed, it can be seen that the overall prediction
of heave force is quite correct for all combination
of rate of turn and incidence. For largest incidence Fig 15: Sway force coefficient (combination
angles (where forces are the highest), we can notice of drift and yaw rate)
a slight under estimation of heave forces by
calculation.
The results obtained in the horizontal plane are
Amp
03calculation -02 -01 ~ ~ '.' 00 not as good as they were in the vertical plane.
- ' Independently from the offset, it can be observed
~~ ~~ that the points do not follow the ideal line. Forces
;. ~ - -01 are under estimated for large drift angle.
~ ~ ~ .. Looking at the yaw moment coefficient we can
· ~a- . q=0~39 observe that the overall tendency is well respected.
· .' ..' ~~ q-025 -02 However, a small variation of the gradient can be
. ~ ~ q=031 ~ detected between the different rates of turn.
.' ~~ q-0 16 0
-0~3
Fig 14. Pitch moment coefficient for ~839 ~ a:
combination of pitching rate and incidence ;~ I:,
The same comments can apply to the pitching calculation ~ ~ - ~
moment coefficient (figure 14). The higher O 3 -0 2 o 1 ~ 0. 0 ~ 1 0 2 ~ 0. 3 0. 4
discrepancy for points at large turning rates can be .- ~ .,
explained by the fact that the influence of incidence
on pitching moment becomes lower as turning rate L ~ ~-02~ ~ ~
increases (at least for combination of incidence and 1 -03-
pitch rate close to the natural situation of a free
· Fig 16 Pitching moment coefficient
running submarine).
(combination of drift and yaw rate)
OCR for page 827
Some options have been thought of to improve
these results, such as a local refinement of the mesh
in "strategic areas" (connection between rudders
and body of the submarine, for example), but they
have not been performed yet.
Rudder effectiveness
A:
..~..~
The gap between test and calculation results
lead us to try to have the mesh to coincide better
with the real geometry of the submarine.
Indeed, we observe an overestimation of almost
50 TO of the lift coefficient related to the rudder
orientation.
The pressure distribution on both sides of the
starboard stern plane for the original mesh is
presented on the following figure corresponding to
25 degrees deflection ofthe plane (by.
On this picture, it can be seen that the pressure
distribution over the flap (responsible for the lifting
effect) is regularly spread over the span and is also
present in the vicinity of the root of the plane.
Fig 17: calculated pressure on suction side (high)
and on pressure side (low) of the right dive
rudder, with the finest mesh.
But the real geometry of those rudders is so that
when the rudder's flap is inclined, a gap appears
between it and the submarine's body, letting the
fluid balance in a certain measure this pressure
difference observed in calculation results.
The easiest way of remedying this problem was
to modify a small part of the mesh and transforming
the cells corresponding to the gap into "live" cells,
which means that they let the fluid go through. The
mesh with live cells corresponds to the mesh with
forward planes with this slight modification.
The following figure shows the results obtained
in this way: the depression surface on the suction
side is less wide than the one calculated with the
former mesh, like the overpressure surface on the
pressure side. The heave coefficient resulting in the
difference of pressure repartition between the two
faces will therefore be less important. This effect
can be assimilated to a reduction of the effective
span.
,~.,.
..~..
., ~~..~ ~~.,..~..
,,.. it.... ~
- - ~ ~ ~ .. ..
... :~.~ ~
|~ :,. ..;.;
,.~...~. ~~ .....
Fig 18: calculated pressure on suction side
5~ ~~ ~~ (high) and on pressure side (low) of the right
dive rudder, with the "alive cells" mesh
The results obtained with the new mesh ("live
cells" mesh) show a remarkable improvement of
the concordance between calculation and test
(approximately 30°/O), even if the results are not
perfect yet, as you can see on the following graph.
Those types of calculations have not been
performed yet for rudders (because of the mesh size
problem for horizontal plane manoeuvring we have
already mentioned).
OCR for page 828
r r
\
050
~middle meshing
"forward planes" meshing
0 25 "alive cells" meshing
~ ~ ^~ model tests
-30 ~" ' :~ _ _
-0.25
1
-I.. -11, ~,
t ~
-0 50
Fig 19: Rudders effectiveness
PREDICTION OF SUBMARINE BEHAVIOUR
In order to evaluate the benefit of numerical
calculation in the prediction of submarine
manoeuvrability, a mathematical model has been
derived from the results of the calculation.
All the derivatives usually obtained through
captive model tests have been identified from the
results of calculations, except for rudder and stern
plane effectiveness derivatives, for which
prediction appeared to be poor. Fins effectiveness
derivatives used in the following simulations have
been derived from captive model tests.
In the horizontal plane, the lack of accuracy of
yaw rate influence on the sway forces lead to a bad
estimation of the stability indices. In this particular
case, the submarine is predicted as being course
stable though sea trials (and model tests) indicated
slight course instability.
L/R
'''
/~
5
In
15
20
7~
30
Fig 20: Non dimensional yaw rate versus rudder
deflection
On the same figure it can be seen that the
estimation of non-dimensional rate of turn for
intermediate rudder deflection is quite correct while
greater discrepancy arise for larger deflection
angles. In addition to the under estimation of sway
forces for large drift angles, the relatively simple
mathematical model used in this case can also
explain those latter discrepancies. More precisely
non-linear derivatives used to describe the coupling
effect between planes deviation and local incidence
were voluntary omitted.
In the vertical plane, the prediction of the
submarine behaviour is globally better. The figure
21 display the maximum non-dimensional pitch rate
obtained during stern plane deflection trials (stern
plane angle being average between deflection to
dive and deflection to rise). It can be observed that
the behaviour of the submarine is well represented.
The non-symmetry of the behaviour of the
submarine in the vertical plane is more important
for the simulation, but sea trials results show some
discrepancy
Kiss simulation - dive
simulation - rise
sea trials - dive
.....
.,., ~
,i~ A,.
.. ~.i
.~
0 5 10 15 20 25
Fig 21: Non dimensional maximum pitch rate vs.
mean stern plane angle deflection
A step further was the simulation of six degrees
of freedom manoeuvres. For this purpose, a reduced
set of out of plane derivatives has been identified
from NS calculation.
.^r~
—simulations
~ sea trials 0.08
006
petit mai Ilage
mailIage moyen
captive mode' tests
004
0.02
0004 ~
000 200
, .
.
./
At/
400 600 800
Fig 22: Pitching moment induced by yaw
OCR for page 829
The simulation is performed using time histories
of actuator positions measured at sea as inputs. The
maneuver considered consists in a stern plane
deviation, followed 30 seconds later by a rudder
deviation in conjunction with forward plane
deviation.
In addition to rudder and stern plane motion, the
propeller is stopped. Such a maneuver, which can
be considered as a recovery maneuver for dive
plane jam, emphasizes the well known coupling
effects between yaw and pitch.
Fig 23: Simulation inputs (planes deviation)
Motions predicted by the simulation are
compared in the time domain to full scale tests. For
this complex maneuver, the dynamic of the
submarine is qualitatively well predicted as shown
on figure 24 where the rates of turn simulated are
compared to measurements.
By_
~~ roll rate - sea trials
Troll rate - simulation
pitch rate - sea trials
pitch rate - simulation
c' yaw rate - sea trials
—yaw rate - simulation
Fig 24: Rates of turn
It is clear that for time domain simulation, the
small errors encountered during the prediction of
forces and consequently on components of
acceleration is magnified by the integration.
Therefore, motions calculated during simulation
differ significantly from those measured at sea. On
figure 25, a factor two is observed on the pitch
angle and also on the depth changing between
simulation and sea trials.
~ roll - sea trials
—roll - simulation
pitch -sea trials
simulation
>> depth sea trials
Depth simulation
CONCLUSIONS
. ~, .....
: ::
.....
Fig 25: Motions
...
NS calculations have shown their ability to
provide relevant results in terms of efforts acting on
. .
a maneuvering su Marine.
Pure drift and incidence forces are very well
predicted by NS calculations even with a relatively
simple mesh.
As soon as a rotation is introduced, the quality
of the results becomes more dependent on the
parameters of the calculation. This study showed
that the use of a finer mesh was absolutely
necessary. Vertical plane rotation prediction is quite
satisfying on the basis of the calculations already
performed. Horizontal plane rotation would require
an even finer mesh than the vertical plane in order
to simulate more accurately the details of the
appendages. Indeed, an oversimplified geometrical
description of the planes led to bad results in terms
of rudder efficacy prediction. Results have already
been improved thanks to an easy manipulation of
the existing mesh. Some more efforts are to be
made in this direction.
Relevant comparisons (on a relative basis)
between different alternative shapes are already
being made and very interesting results have been
obtained which enable the evaluation of novel
appendage configurations without having to engage
in costly systematic experimental tests.
In the end, this study should allow us to obtain
accurate absolute values of the hydrodynamic
coefficients of the submarines as well as a
description of the mechanism of the generation of
these forces on the different elements of the
submarine. Indeed, one of the great advantages of
using computational fluid dynamic tools is that in
addition to an estimation of global forces, it
provides a precise evaluation of local consequences
of some geometrical modifications, which would
OCR for page 830
bring to light phenomena which arc so far
poorly understood.
To gain eonfidenoe in this n w tool, calculations
arc now systematically perfo mad in parallel with
captive model tests. At this stage, the math matinal
models used for the pu pose of m meuvering
simulations arc the same as those developed for
captive model tests analysis.
M!e do think that a earef I analysis of the huge
quantity of data provided by each NS calculation
will be of help to improve existing empirical
prediction methods, and fiom a more general point
of view to improve the understanding of physics
involved in submarine m mew en hi in.
11 11 RE DEVELOPMENT
The present study showed some difficulties for
prediction of rudder efficacy derivatives and for
y w induced forces.
To overcome those problems, we plan to
perform calculations of a single dapped rudder to
date mme the neeessa y mo mt of refinement in
the mesh to allow for m accept bie prediction. This
calculation will be based on m existing set of test
data for which geometrical details such as root gap
were explored.
M!e arc confident that horizontal plane forces
associated with y w motions will be correctly
calculated once sufficient mesh sizes will be
m mageabie.
Once the overall prediction of hyd odynamie
forces will be considered as being correct, specific
aspects arc to be studied. Among those aspects, the
induenoe of test inshumeutation (stings, suppo on-v
struts, etc..) on towing tank md rotating a m tests
will be considered. Calculations will be performed
with md without shut and for different strut
an my ment.
Also, specific effort will be devoted to
emphasize the induenoe of propulsion on
m meuverability.
One additional perspective for further studies in
m meuverability is the direct simulations of
m meuvers using the unsteady low capabilities of
the RANSE codes.
OCR for page 831
DISCUSSION
U. Bulgarelli
Instituto Ncziorule per St di ed E perienze di
A chitetturc Nacelle, Italy
To apply CFD to study of m meuverability you
should already developed unstecdy Na vier states
code, bee mse the phenomenon under
m- e n anon is completely unstecdy is f is
true?
AUTHOR'S REPLY
The quasi steady approach we used to investigate
the capacity of RANS code for submarine
m moeuvrability studies hr. two cdv Stages:
Using CFD cclcubtions es c mom ert al towing
tmkgavetheopport nitytouse mexistingset
of tools to quickly derive time domain
simulations of m uloeu.~ et fi om cclcubtion of
forces
Results of calculation were du ectly c mparable
to existing model tests data Ed could therefore
lead, to c certain extend, to validation
Although unstecdy ph nom ffk~ ar he during
m moeuvres, the quasi steady cpproachhcs
demon trcted for c long time its capacity to
provide pertinent simulations of He behaviour of
submarines ion conventional m Hoed n et For
most cases, the dynamic of the submarine is
relatively slow compared to the dynamic of
unstecdy phenomena concerned Ed the see trials
don't really show some major i fluency of
unsteadiness
A other problem of unsteadiness, which is not
solved, is that the solution of steady flow
cclculationc moot fheoreticcllybe consideredas
the me m force acting on He body on which
separation c mses un te tdiness in She flow (es it
would be me tech d in c towing t mk or m c
rotating arm facility) The calculations
performedhehe show d how ver some
concord mce with measurements
DISCUSSION
IK H Kim
Naval Surface Warfare C nter, Carderock
Division, USA
When simulating the deflection of fin/control
surface, how do you h mdle She gap betw en the
body cod fins?
AUTHOR'S REPLY
During simulations of rudder effectiveness for c
fl mped rudder, we discovered large discrepancy
betw en calculation Ed model te ts Previous
cclcubtions for all movable surfaces did 't show
such problems Ed w w nt to the conclusion
that the mesh of the geometry of the su face Ed
especially She root (including gaps) should be
improved To solve His problems, w considered
that the cells located et the ro ot are active The
difference betw en the two meshes is show on
figme 17 Ed I g of our paper Although
encouraging, the results obtained are not
completely satisfactory Ed m me work ht. to be
done in fi is field We plarmed to do more
extensive cclcubtion of isolated fins m order to
comparetocavitationtum Itests Theobjective
is to define what is She "minimum acceptable"
degree of refinement of She mesh for rudder
effectiveness prediction bearing in m Ed that in
our meshing method, the refinement of the mesh
in the vicinity of planes ht. c greet impact on She
overall size of She mesh for the whole submarine
DISCUSSION
I-Y tioh
Naval Surface Warfare C nter, Carderock
Division, USA
How do you pl m to do unstecdy maneuvering
predictionusmg CFD?
AUTHOR'S REPLY
It is the Id feasible to perform unstecdy
m moeuvrmg prediction using CFD For this
purpose, it is possible to use the "deforming
mesh" option of unstecdy RANS codes for
which unstecdy ~ Ice ht i on are performed et
each time step, c new mesh being t tom tti tlly
generated taking into account the dynamic of the
submarine es w ll es the ch m e. in control
su face deflection Bcssin ht. already used this
kind of approach in c simplified way (without
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solving the equation of the d. cmic of the body)
for c cycloidal f uster AD) or for c
c on- em Oral propeller on c inclined shaft (3 D)
How ver, it is clear Nat At the moment, the 3D
case of c m moeuvring submarine would requite
too much computation time to be of c practical
use On the of her, h Ed He possibility for
validation are reduced for such m approach Ed
co fidence hr. still
Representative terms from entire chapter:
vertical plane
