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OCR for page 624
24th Symposium on Naval Hydrodynamics
Fukuoka, JAPAN, 8-13, July 2002
Validation of Control-Surface Induced Submarine
Maneuvering Simulations using UNCLE
R. Parkajaksharl, M.G. Remoiigue, L.K. Taylor, M. Jiang, W.R. Briley, D.L.
Whitfield
(Computational Simulation and Design Center' Mississippi State University USA)
ABSTRACT
Physics based simulations of control surface
induced maneuvers of a model submarine are compared
with experimental results. The forces and moments
acting on the body are computed using an UnRANS
code (UN(~`F,) capable of handling moving control
surfaces and rotating propulsors. A six degree of
freedom code is used to calculate the trajectory and
orientation of the model. Essential steady validations of
drag and lateral force coefficients for the appended
SUBOFF body and thrust and torque for the 5168
propeller show excellent agreement. Computed
trajectories, orientations, velocities, force and moments
are compared with experimental measurements for a
vertical overshoot maneuver and three horizontal
overshoot maneuvers of the ONR Body 1 Radio
Controlled Model (RCM), a free running model
submarine. As carefully as can be determined, the level
of agreement with experiment is regarded as extremely
good.
INTRODUCTION
Submarine maneuvering simulations are of great
interest to the naval community from the standpoints of
design, analysis and operational safety. The key
requirement for maneuvering simulations is accurate
prediction of the forces acting on the hull, propeller and
control surfaces. Current techniques treat the forces and
moments as functions of the motion state variables and
their derivatives md approximate them using truncated
Taylor series expansions often containing second, third
and cross derivative terms (Boger, 1997~. The
derivatives are determined using a combination of
empirical and theoretical correlations with the empirical
coefficients being computed from captive model tests
or tests on individual components. Maneuvering codes
based on scale models are not only expensive but also
suffer from a serious limitation in that some of the
phenomena of interest do not scale well to full scale
Reynolds numbers. The current methodology also has
major difficulties in dealing with extreme maneuvers,
propeller effects and even small changes to the design
(Boger, 19971. Thus a validated unsteady RANS based
maneuvering code could lead to improved
understanding of the complex physics that govern these
problems and would be a valuable addition to extant
techniques. Some of the thinking that went into the
genesis of this effort to do full physics-based
maneuvering simulations are detailed in McDonald
(1991) and Boger (1997~.
FLOW SOLVER
The basic flow solver of Taylor (1991) and
Whitfield (1991) is comprised of an iterative implicit
finite-volume scheme, Roe/MUSCL fluxes, numerically
computed state-vector flux linearizations, and an
approximate-Newton iteration solved using LU/SGS
relaxation. The cell-centered finite-volume scheme
using artificial compressibility and time-dependent
curvilinear coordinates can be written as
aq = _[ditf -fv) +dj (g -gv )+ dk (h - ha)] = it(q)
(1)
Here q = J(p, u, v,w) is the solution vector, J is the
Jacobian of the inverse coordinate transformation, p is
pressure, u, v, and w are Cartesian velocity components,
and ~ is time. The steady residual vector is R(q), the
inviscid and viscous flux vectors are denoted fg,h and
fv' gv ~ hv respectively. The central difference operators
~i ~ ~ j ~ ~k apply to the respective curvilinear ;, ~ and
coordinate directions.
The inviscid fluxes are approximated by Roe's
(1981) scheme, with a third-order MUSCL
extrapolation of left and right state vectors, qR and
OCR for page 625
A, as implemented by Anderson, Thomas and van A+ afi+l~2 A- ~i-l/2
Leer(1986). The flux approximation for the idirection Ai = a ~ ~ i = ~ R (7)
f. 1 =f(q )+A (qR,qL).(qR_qL) (2)
1 1
2
Here, A_3f lOq is the inviscid flux Jacobian, A-is
defined by A- = SASSY, where S is the matrix of
right eigenvectors of A, A- is a diagonal matrix
containing the negative eigenvalues of A as nonzero
elements, and the overbar denotes a Roe average.
Analogous definitions apply to the j and k directions,
with B _ Og I ~q and C _ Oh I aq . Details and
nonsingular eigensystems that use metric information
from only one direction are given in Taylor (1991).
An iterative implicit nonlinear scheme for solving
(1) is given by
i~qn,S+l /~ =—R(qn+i,S+~ ) (3)
where /~( On = (.)n+~ _(.)n, and s = 0,1,... is an iteration
index. The spatial residual is linearized as
R(qn+l,s+l ~ = R(qn+l,s )+~3 n+l,s(? qn+l,s ~ (4)
where /\s(~) _ Ads+ _~)s, and Fin+ s(~) is a linear
spatial difference operator made up of flux derivatives
to be defined subsequently. This leads to the following
iterative linearized implicit scheme:
t?t -I] +5n+l,s ( )] (a? qn+l~s )=RU (qn+l,s ~ (I)
The physical unsteady residual R u is defined as
R u (qn+i ~ = LAt-iIzZ76(qn+l _ qn' + R`< no+ '] (6)
where Ip _ [O. l, l,l lT .
The flux linearization matrices are computed using
numerical state-vector flux linearizations, as proposed
by Whitfield et al. (1994). These are defined as in
A A
Analogous definitions apply to B j and Ck . The
linearized flux derivative operator i3n~ ~ can now be
defined as
3n() =
- Ai_l ( )i-l + (Ai - Ai ~ ( )i + Ai+l ( )i+l
BJ-I()j-l +(`Bj -BJ ~ ()j+BJ+I()j+l
Ck-l ( )k-1 + (`Ck Ck ~ ( )k + Ck +1 ( )k+l
(8,
The solution of (5) for /\sqn+~'s is obtained by Lower-
Upper Symmetric Gauss-Seidel (LU/SGS) relaxation.
Introducing a second subiteration index m and
appropriate definitions for the matrix D and operators
i, and ~ 2 ~ the LU/SGS scheme can be written as
tDn+l~s + :3ln+l,s (.) Jo? qn+l,s )8
+ :32n+l'S (?sqn+l~s )m =Ru (qn+l,s )
[LDn+l~ + 32n+l's ( ) ]( ~sQn+l'S In
+ :3ln+l~s (?sqn+l~s )* =Rii (qn+l,s ~
(9)
The definitions of D, At, andS2 for the LU/SGS
scheme are
Do)=? I+(Ai-A~
+ (,Bj—BJ \~+ j(`C k—Ck i)] ( )i, j, k
31() =
A`-I ( )i-l BJ-I ( )j-l Ck-l ( )k-l
52() =
Ai+1 ( )i+1 BJ+I ( )j+l Ck+l ( )k+1
OCR for page 626
The right hand side of (5) contains additional terms
(Janus, 1989) to ensure that the Geometric
Conservation Law (Thomas, et al, 1978) is satisfied in
the regions with deforming grids. Further discussion of
this algorithm can be found in Briley (2000~.
PARALLEL SOLVER
The parallel solution process consists of a scalable
solution algorithm implemented to run efficiently on
sub-domains distributed across multiple processes and
communicating through MPI. The solution algorithm
has multiple nested kernels viz. time step, FAS
multigrid iteration, LU/SGS iteration etc. and the block-
to-block coupling is at the innermost level i.e. in the
solution of the linear system. A block-Jacobi type
updating of the subdomain boundaries ensures efficient
parallelization with a small incremental cost incurred in
terms of sub-iterations required to recover the
convergence rate of the sequential algorithm. Details
about the parallel algorithm can be found in
Pankajakshan (2002~.
TURBIlLENCE MODELS
Turbulence is modeled in UNCLE using one of
two available 2-equation models viz. the modified Shih
and Lumley he model (ShTh et al. 1993, Yang ~ al,
1995 and Liou et al., 1994) and the q-co model
(Coakley, 19831. The convective terms and dissipative
terms are computed in a manner analogous to the
corresponding terms in the mean flow solver. The
turbulence model is loosely coupled, implying that the
mean flow and two-equation model are solved in
sequence with each using the latest available flow or
turbulence quantities. The parallel solution algorithm
and the associated message passing routines used in the
turbulence models are directly derived from the main
solver. Typically the thin layer approximation is used
and integration is performed up to the wall using tightly
packed grids with off the wall spacings chosen to give
yF values less than 1 for the first cell.
CONTROL SURFACE DEFLECTIONS
One of the basic requirements for this study was
the ability to generate valid grids around 25 degree
control surfaces deflections within the context of a
parallel multi-block simulation. The first approach
(Jiang, 2000) could be termed "deform and regenerate"
and involved deforming the grid and then regenerating
when the deformations became too large. The
regeneration was done using reference surfaces
corresponding to various intermediate deflection angles.
The reference surfaces were generated and tested a
priori and then read in during the actual simulation.
Each block which contained any portion of the
deforming sections of the grid read in these surfaces
and used them for regeneration as and when required.
Thus the grid regeneration scheme was scalable with
only a small increase in memory required to store the
reference surfaces. This method was used successfully
for a number of simulation involving deflections of the
sailplane and rudder (Pankajakshan, 2000~. However
several deficiencies in this method were identified
which precluded it from being used productively on a
regular basis. Specifically, the generation and
placement of the reference surfaces was ad hoc and the
success of the method relied heavily on the knowledge
of an experienced grid generator. This made it
cumbersome and error-prone when used without this
expertise. It was also found that there were minute
variations in the geometry during the deformation phase
and that the method could fail without extensive pre-
simulation testing.
Drawing on the experiences from the first method,
a second control surface deflection module (Remotigue
et al., 2002) was developed using a more flexible and
general approach. The grids in the deformation zones
are generated by interpolating between a sequence of
volume grids that span the maximum deflection angle.
A minimum of three grids is required, but more may be
needed for larger deflection angles. The interpolation is
performed in an appropriately chosen cylindrical
coordinate system and yields grids that preserve the
quality and relative spacings from the original volume
grids. To prevent loss of geometry, faces of the
deforming blocks which constitute the hull are formed
to the hull surface assuming that it is a body of
revolution.
The volume grids which are the inputs to the
interpolation routine must satisfy certain requirements
in order to be used in the deflection module. The outer
boundaries of the grids must be identical and must
exactly mesh with the corresponding faces of the full
grid. The generation of the volume grids can be done
using any structured grid generation package and the
restrictions are not onerous enough to exclude any of
the commonly used packages. USS_UNCLE
(Remotigue, 2002), which is a preprocessor for setting
up UNCLE simulations, has a module for testing of the
interpolation grids and then writing out the grids and
other inputs in the format required by the flow solver.
The interpolation can also be tested for the full range of
deflection in successively decreasing increments. Since
USS_UNCLE and UNCLE use the same interpolation
routines, a successful test in the pre-processing phase
guarantees that valid grids shall be generated during the
actual simulation.
OCR for page 627
PROBLEM SETUP
USS_UNCLE is a general-purpose tool with a GUI
for setting up flow simulations using the UNCLE code.
It is used for partitioning the grid, applying boundary
conditions, checking the load balancing efficiency and
also automatically determining the block connectivities.
It is also a grid manipulation tool capable of simple
operations such as rotation, translation and mirroring as
well as extraction, smoothing, reversal and swapping of
physical and computational space axes. It can be used
to specify moving control surfaces as well as the blocks
and faces that make up a sliding interface. During the
application of boundary conditions, surfaces can be
individually tagged in order to obtain the force and
moment histories on particular components such as
rudders, stern-planes or individual propeller blades.
USS_UNCLE checks for a host of common setup errors
such as undefined or over-defined boundaries, block
boundaries with gaps, negative volumes etc. A snapshot
of the RCM surface grid within the USS_UNCLE user
interface is shown in Figure 1
Figure 1 Snapshot of USS-UNCLE with RCM
geometry showing tagged components
6-DEGREE OF FREEDOM CODE
The forces and moments computed by the RANS
solver are used by the 6 Degree of Freedom (6-DOF)
code to compute the instantaneous linear and angular
velocities. A body-fitted non-inertial reference frame
and a fixed inertial coordinate system are used for the
angular and linear components of the computation
respectively. In the body-fitted reference frame, the
moments of inertia of the model are constants and this
greatly simplifies the solution process. The use of a
four-variable attitude propagation (Stevens et al., 1992)
or quaternion representation eliminates the so-called
"wraparound" problems that arise from singularities at
certain orientations in a formulation based on Euler
angles. The quaternion formulation has the added
advantage that the quaternion rate equations are linked
to the angular rates by a set of linear differential
equations.
The linear velocities and displacements are
obtained by directly integrating the accelerations after
addition of the buoyancy and gravity terms in the
inertial reference frame. The angular rates and the
attitude quaternion satisfy the relations
= J QB Jo) + J T (11)
O -R Q
R O —P and
-Q P O
O P Q R
_p o -R Q
-Q R O _p
-R -Q P O
P. Q and R are the three components of the angular
rate ~ J is the moments of inertia matrix, T is the total
moment acting on the model while q is the attitude
quaternion of the body-fixed reference system. The
quaternion rate equation is solved using a Stage
Runge-Kutta-Merson integration scheme with built in
error estimation. The linear displacements and the
attitude quaternion computed at each time step are used
to translate and rotate the grid into position for the next
time step.
Verification and validation of the WOOF modules
were carried out using simple problems from celestial
mechanics and spinning tops involving elliptical orbits,
. .
nutat~on and precession.
The GOOF module also allows simulations where
the vehicle follows a prescribed path specified in the
form of a time history of displacements and attitudes.
The primary reason for the development of this module
was to approximate to the degree possible, the initial
OCR for page 628
conditions of a vehicle prior to initiation of a maneuver
simulation under 6-DOF control.
The WOOF module also allows the automatic
computation and addition of a "body force" term for
allowing self-propulsion in simplified models without
the actual rotating propulsors. The term is made equal
to the total drag of the vehicle during a straight and
level simulation and is appropriately vectored during
the maneuvering simulation. A similarly computed
moment term can be used to compensate for the rolling
effects of the propeller without resorting to small
deflections of the control surfaces to achieve the same
effect.
ROTATING PROPULSORS
The initial propulsor module was a scalable parallel
implementation of the method developed by Janus
(1989) where rotating and stationary blocks deform and
then re-connect within a pre-defined deformation zone.
The connectivity between the blocks in relative motion
is always one-to-one and information is exchanged
across the interface through point-to-point messages in
a complex but periodic pattern. While this technique is
suitable for handling a large class of problems, it runs
into some difficulties in cases where the interface needs
to be positioned in between physically proximate
geometry components. To overcome this limitation, the
sliding interface technique (Chen at al., 2001) was
implemented wherein the blocks slide across each other
at the interface without any deformation or one-to-one
connectivity. In this approach the blocks on the two
sides of the interface can have different numbers of
points in the circumferential direction but must match
up in the radial direction. Thus the mismatch between
cell faces is confined to the circumferential citrection
and the use a one dimensional interpolation scheme
based on arc length keeps errors to the minimum.
VALIDATION STUDIES
The flow solver has undergone a large number of
validation studies on a wide range of flow problems
ranging from accelerating cylinders to centrifugal
compressors. The steady flow validations include
inflected stern (Taylor et al., 1991), prolate spheroid
(Taylor et al., 1995), wingbody junction (Sheng et al.,
1994) and various SUBOFF configurations (Sheng et
al., 1995 & Jonnalagadda et al., 1997) along with the
P4119 (Sheng et al., 1996) and P5168 propeller flows.
In validating unsteady flow, comparisons with
experimental results have been made for vortex
preservation/convection, maneuvering prolate spheroid
(Taylor et al., 1995), flapping hydrofoil (Taylor et al.,
1993) and a low speed centrifugal compressor (Sheng at
al., 1997 & 1996~. The physical quantities compared
include pressure, velocity, forces, moments, shear stress
as well as the effect of grid resolution, time-step,
turbulence and other algorithmic parameters on these
variables.
_~= _
-God , ~ . ~ . ~
~ D:: --10~D ~0 18,0
- .~:~t ~~}
· ,._.
As.
c - ~ _
_
~^
us
-
~:
-
-
b(:-
-9
._~ ~
lo,,
ever
~ . .~
A__ 5
—1~ _ ~ i ..
o~
_ <~
e - ~0
_~- I ~ I --o
.~
~5
s o
... Pv
an.. 5
5 x:
Hi, a
-
Figure 2 Comparison of axial force coefficients
computed using two turbulence models
do:
~ o.~s _
4
::
: ;,
_ ~' _
hi:
~~ ~—E
:~ coypu" q_~
sly is
:~.+
:~
:~
..~.
a, .
.~..
.^ .,.
. at.
-God -age ~ te~ ~~t
.. ~ (:: 0~)
Figure 3 Comparison of lateral force coefficients
computed using two turbulence models
Validation of force and moment computations
performed on the SUB OFF geometry as well as the
thrust and torque computations on the P5 168 are
particularly significant in the context of maneuvering
simulations with rotating propulsors since they are
necessary precursors to any maneuvering simulations.
In figures 34, the axial and lateral force coefficients
and yawing moment coefficient computed using two
OCR for page 629
turbulence models for a SUBOFF bare hull with stern
appendages are compared with experimental data
(Huang et al, 1992) for 3 angles of drift. The results
show that the q-co model tends to substantially
overpredict resistance while the k-£ model is generally
within 5%. The lateral force coefficient and the yawing
moment coefficient show a drift in accuracy towards
the higher yaw angles. Figure 5 shows that the
computed thrust and torque coefficients (open water)
for the 5168 propeller agree well with experiment
(Chesnekas et al., 1998) for a range of advance ratios.
~~e ~ ~ ~ ~ ' 1 ~
.
.
hag
Thou am:
0~0118 _ ~ h'~oltr a' =,~: ~
Hi _ '^
.~
. ;
8~: _ .
·. ~
o
r,
.o
:~ ~
amp.
-~3
~.~
=~.^, at. ~
-
.~
_ OC~d
_ Bed t
~~ - t
85;~7 '
.~
- 004 1 ~ . 1 ~ , ,
'I ~ ~ _~.0 0.0 ' 10
.
—~~ ~ ~ | :d~ee)
Figure 4 Comparison of yawing moment coefficients
computed using two turbulence models.
?4
-
~ :~5
u
o
e"
~ 1 ~
=.
e:
a, ~ _
.
~ _~ ~
\ —lime like
ec Up—~ ~~
c_~tct t~ .
. ~
:
-
·_-,
\
0~ 1 L5:
Adhere Beet, 1 ~ ~
Figure 5 Comparison of computed thrust and torque
coefficients for Propeller 5168.
MANllEVERING SIMULATIONS
An early step towards a full maneuvering simulation
was the periodic flow solution shown in Figure 6 for a
SUBOFF configuration with rotating propeller and
control surfaces with gaps. The model is at a fixed
attitude of 5 degrees roll and 10 degrees pitch and yaw.
The 4.5 million point, Unblock grid was run at a
Reynolds number of 12 million at a time step requiring
350 cycles per revolution of the propeller and took 160
hours to complete on 50 processors of a Cray T3E-900.
Figure 6 Axial velocity contours for submarine drifting
at fixed incidence.
The same grid and blocking scheme was used for a
rudder-induced maneuver by coupling the computed
forces and moments with the GOOF code and using
displacements and attitude quaternions to move and
orient the grid at each time step. The rudder was
deflected by 10 degrees in the time taken by the model
to travel a quarter of its body length. The rudder was
then left in that position till the end of the simulation.
Since this was a notional submarine model, the mass
and moments of inertia used were ad hoc and the
simulation was a test of the elements that made up the
maneuvering code and their proper integration.
Contours of the X-component of the velocity at various
stages of the maneuver are shown in Figure 7.
OCR for page 630
Figure 7 Contours of axial component of velocity at
various lateral deflections for rudder induced maneuver
The large simulation times associated with the
previous runs were due to the small time step imposed
on the simulation process by physics of the rotating
propulsor. The use of a body force propulsor would
allow the use of much larger time steps with some loss
in the fidelity of the simulation. This was done in the
form of a sailplane induced maneuver simulated using a
modified version of the grid used in the previous
simulations with the propeller replaced by the body
force model. Due to the larger time step used, the total
simulation time was 53.2 hours on 50 processors of a
Cray T3E-900. The predicted trajectory and axial
velocity cuts at various points during the simulation are
shown in Figure 8
Figure 8 position and orientation along trajectory at
selected times with axial velocity contours.
ONR BODY1 RADIO CONTROLLED MODEL
The ONR Body 1 Radio Controlled Model
(RCMXFaller et al., 2001a) is a fully instrumented free-
running model submarine with rudders, sternplanes and
sail and is propelled by a centerline mounted 3-bladed
propeller. The model has a mass of 2260 kilograms and
is about 6 meters in length.
Maneuvering experiments (Faller et al., 2001b)
conducted at the Maneuvering and Seakeeping Basin at
the Naval Surface Warfare Center, Carderock Division
using the RCM include constant heading and depth
runs, horizontal and vertical overshoots as well as
controlled and fixed plane turns.
ROM MANEUVERING SIMllIAIIONS
RCM maneuvering simulations were done using both
the body force model and a rotating propulsor. The
body force simulation was done using a 57 block 6.06
million point grid. The rotating propulsor simulation
was done using a 73 block, 7.1 million point grid. An
initial straight and level solution was run with each grid
until a converged solution was obtained. These
solutions served as the initial conditions for the
maneuvering simulations.
Ideally the RCM should have pro angular rates,
accelerations and non-axial velocities at the start of the
experiment. In reality initial conditions include small
but non-zero values for the three angular rates, angular
accelerations as well as for the non-axial velocity and
acceleration components. The attitude also tends to be
slightly off the ideal with a roll angle of around 3
degrees. While the prescribed motion module can be
used to some extent to match certain aspects of the
initial conditions, a perfect match of the corresponding
angular rates and accelerations is highly impractical.
The simulations include two types of maneuvers
viz. vertical overshoots (VOVR) and horizontal
overshoots (HOVR). In a VOVR maneuver, the stern-
plane is deflected to a maximum value and left at the
value until the pitch angle of the submarine reaches a
certain value known as the Execution Pitch Angle
(EPA). At the EPA, the deflection is reversed until the
maximum deflection angle is reached in the opposite
direction. In the case of the HOVR, the rudder is
deflected until it reaches a maximum and is then
deflected in the reverse direction upon the model
reaching the Execution Yaw Angle (EYA). All the
cases discussed in this paper correspond to a model
speed of 3.048m/s (lOft/s).
OCR for page 631
Simulation speed was 0.037 seconds/hour with a time
step of 0.001 seconds on a Cray T3E-900.
In Figure 11, the computed Z-component of the
forces acting on the body show the right trends and
inflection points with some error in magnitude. Some
drift is seen towards the end of the simulation but this
might be partly due to the maximum sternplane
deflection not matching the experiment. The X-
component is mainly influenced by the propeller and is
not significant for this body-force based simulation.
Since the roll is not modeled, the Y-component is zero.
The velocities in Figure 12 show similar trends, but the
positions shown in Figure 13 are predicted extremely
well. The computed moment histories are compared
with experiment in Figure 14 and show all the major
trends in spite of the differences in control surface
deflection histories near the maximum. The angular
rates and orientations are compared in Figure 15 and in
Figure 16 respectively and are in reasonable agreement.
Both the experimental force and moment histories show
a sinusoidal pattern of unknown origin imposed on the
larger trends. It is speculated that this variation is
related to the propeller. There was a reduction in the
quality of the grid near the control surfaces because the
interpolation was done using only three grids to span 50
degrees of deflection. The spikes in the computed force
and moment histories were caused by this deterioration
in grid quality.
.,,
Figure 9 RCM with direction and orientation of axes.
RESULTS
The computed results from four simulation runs will
be presented using the nomenclature from the
experiment. Four runs were made with the body-force
propulsor while a fifth was run with an actual rotating
propeller using the sliding interface module. The body
force runs include 1 VOVR (Run 41) and 3 HOVR
(Runs 13, 18 & 27) simulations. Run 13 is very similar
to Run 18 and the results of this simulation are not
presented here. The final run is a repeat of Run 18 with
a rotating propulsor. All the quantities compared with
experiment are in the body-fixed coordinate system
except for the displacements and orientations. The
directions of the various axes and the color coding used
to refer to them are shown in Figure 9. All simulations
presented here were run with 3 multigrid levels and
using 3 multigrid cycles per timestep. The he two-
equation model was used at a Reynolds number of 18.6
million based on model length.
RUN41
RUN41 was a VOVR maneuver with a maximum
stern-plane deflection of 26.6 degrees and an EPA of 5
degrees. The rudder was under automatic control but
the deflections were of the order of 0.6 degrees. The
initial 2.4 seconds of the experiment with no stern-
plane deflection were not simulated in order to reduce
the computational cost. The rudder deflection was kept
at zero for the entire simulation and the initial roll angle
of the model was not simulated. The maximum grid
deflection in the experiment was 26.6 degrees but the
simulated maximum stern-plane angle had to be
restricted to 25 degrees since the grids were generated
assuming a maximum deflection of 25 degrees.
RUN 18
Run 18 was a HOVR maneuver with a maximum
rudder deflection of 20 degrees and an EYA of 30
degrees with the stern-plane being fixed at the neutral
angle of 0.54 degrees. This case was run with a time
step of 0.004 seconds with a simulation speed of
0.25s/hr on 57 processors of an IBM-SP3.
The prescribed motion module was used to give an
initial roll to the model before starting the maneuvering
simulation. The computed force histories in Figure 17
compare well with experiment except for the sinusoidal
pattern seen earlier. The velocities and positions also
match well in Figure 18 and Figure 19 respectively. The
computed moment histories in Figure 20 capture all the
major trends with small variations in magnitudes. In
Figure 21 the roll rate is reasonable given the lack of
the propeller while Q and R show trends in keeping
with the moment histories. The orientation in Figure 22
shows good agreement with a gradual deterioration
towards the end of the simulation.
RUN 27
Run 27 was a HOVR maneuver with a maximum
rudder deflection of 10 degrees and an EYA of 30
degrees with the stern-plane being fixed at around 0
OCR for page 632
degrees. Runtimes and time steps were similar to that of
Run 18.
This maneuver was executed at a slower rate and in a
direction opposite to that of Run 18. The quality of the
agreement with experiment is similar to that of Run 18
except for the roll rate Figure 27) and the roll (Figure
28) which compare extremely well. This could be due
to the slow rate or the direction of this maneuver or
both.
Figure 10 Axial velocity cut showing effects of
propeller and deflected rudder.
RUN 18 W1MI PROPELLER
This HOVR simulation includes the propeller
rotating at a fixed speed of 480 RPM and was simulated
using the sliding interface technique. A time step of
.001 seconds was used for this simulation yielding
simulation speeds ranging from 0.03 seconds/hr (Cray
T3E-900) to 0.034 seconds/hour (I13M-SP)
The Y-component of the force history was predicted
more accurately by the propelled simulation (Figure 29)
though the sinusoidal pattern was still absent. The
prediction of the moment about the Taxis (Figure 32)
was also better. As a result the predicted yaw rate
(Figure 33) and the predicted yaw Figure 34) match
extremely well with experiment. Even though the initial
3° roll of the RCM was not modeled for this case, the
roll rate shows better agreement with the experiment
than the body-force case.
DISCUSSION
One of key features of unsteady simulations of the
kind presented here is that small errors tend to
accumulate and get amplified and cause the simulation
to drift. This implies that force and moments may have
to be computed with a level of accuracy not usually
expected of steady computations. To achieve this,
particular attention has to be paid to transition,
turbulence modeling, grid refinement and algorithmic
issues. Several partial runs were made to study the
effects of turbulence model, timestep, sub-iteration
count, initial conditions on the trajectories and none of
these factors were found to make a substantial impact
on the trends presented here.
The RCM experiments were carefully conducted to in
minimize experimental uncertainty using
instrumentation with very high accuracy (Failer et al.,
2001b). Qualitatively, the repeatability of the
experiments were also extremely high. However, in the
absence of quantitative measures of imprecision, the
uncertainty bounds on the experiment could not be
computed. The effective moments of inertia of the
RCM were measured with an accuracy of 1% and an
estimate of the added mass term was then subtracted
from the measured value. Thus there is a possibility that
the moments of inertia have a high degree of
uncertainty in comparison to the rest of the
experimental data.
The angular rates and accelerations in maneuvering
simulations are strongly coupled with the linear
accelerations and velocities through complex
hydrodynamic interactions. This makes error tracing
and analysis extremely difficult since it is not easy to
distinguish between cause and effect.
CONCLUSIONS
Given the complexity and the myriad sources of
errors that can impact the kind of unsteady simulations
presented here, the agreement with experimental data
can be considered to be extremely good. However,
there is also a need to identify and reduce the errors
such that longer simulations can be run without being
overwhelmed by the gradual error accumulation.
Further work is needed in the areas of turbulence
modeling, grid refinement and vortex preservation
before such simulations can be run with a high degree
of confidence in the results. It is hoped that the
comparison with the component force and moment
histories will shed some light on any changes in
solution methodology aid "ridding strategies that will
have to be made to further improve accuracy.
ACKNOWIEDGE~ENTS
This work was supported by grant
N00014011045501050428 from the Office of Naval
Research. The grant monitor is Dr. L. Patrick Purtell.
This support is greatly appreciated. This work was also
supported in part by a grant of HPC time from the
Arctic Region Supercomputing Center and MSRC-
OCR for page 633
NAVO/Stennis under a DoD HPC Challenge Project.
This support is gratefully acknowledged.
R~a~
[1] Anderson, W.K., Thomas, JO., and van Leer, B.,
"Comparison of Finite Volume Flux Vector Splittings
for the Euler Equations," AIAA Journal, Vol. 24, No. 9,
Sept. 1986, pp. 1453-146().
[2l Boger, D.A., Davoudzadeh, F., Dreyer, J.J.,
McDonald, H., Schott, C.G., Zierke, W.C., Arabshahi,
A., Briley, W.R., Busby, J.A., Chen, J.P., Jiang, M.,
Jonnalagadda, R., McGinley, J., Pankajakshan, R.,
Sheng, C., Stokes, M.L., Taylor, L.K., and Whitfield,
D.L., "A Physics-Based Means of Computing the Flow
Around a Maneuvering Underwater Vehicle,"
Technical Report No. TR 97-002, Jan. 1997.
[3] Briley, W.R., and McDonald, H., An Overview and
Generalization of Implicit Navier-Stokes Algorithms
and Approximate Factorization," Computers and
Fluids, 2000.
[4] Chen, J.P. and Briley, W.R., " A Parallel Flow
Solver for Unsteady Multiple Blade Row
Turbomachinery Simulations," ASMEi2001-GT-0348,
Jun 2001.
[5] Chesnekas, C.J., and Jessup, S.D., "Cavitation and
3-D LDV Tip-Flowfield Measurements of Propeller
5168," CRDKNSWC/HD-1460 02. May 1998.
[6] Coakley, T.J., "Turbulence Modelling Methods for
the Compressible Navier-Stokes Equations," AIAA 16th
Fluid Dynamics and Plasma Dynamics Conference,
July 12-14, 1993, Danvers, Massachusetts.
[7] Faller, W.E. Merrill, C.F., "ONR Bodyl
Submarine Radio Controlled Model Experiments Part I:
Model Geometry," NSWCCD-50-TR-2001/015, April
2001.
[8] Faller, W.E., Hess, D.E., and Merrill, C.F., "ONR
Bodyl Submarine Radio Controlled Model
Experiments Part II: Baseline Maneuvering Data,"
NSWCCD-50-TR-2001/039, July 2001.
[9] Huang, T.T., Liu, H-L, Goves, N.C., Forlini, T.J.,
Blanton. J.N.. and Gowin~. S.. "Measurement of Flows
with Various
Appendages," 19th Symposium on Naval
Hydrodynamics, Seoul, Korea, August 1992.
7 — — — 7 — —
Over an Axisvmmetric Bodv
[10] Janus, J.M., "Advanced SD CFD Algorithm for
Turbomachinery," Ph.D. Dissertation, Mississippi State
University, May 1989.
[ll]Janus, J.M., and Whitfield, D.L., "A Simple Time-
Accurate Turbomachinery Algorithm with Numerical
Solutions of an Uneven Blade Count Configuration,"
AIAA Paper No. 89-0206, January 1989.
[12] Jiang, M., Pankajakshan, R., Remotigue, M.G.,
Taylor, L.K., "Dynamic Grid Generation for the
Simulation of Submarine Maneuvers," ~h International
Conference on Grid Generation in Computational Field
Simulation, Whistler, British Columbia, Canada,
September 2000.
[13] Jonnalagadda, R., Taylor, L.K., and Whitfield,
D.L., "Multiblock Multigrid Incompressible RANS
Computation of Forces and Moments on Appended
SUBOFF Configurations at Incidence," AIA'4 Paper
No. 97-0624, 1997.
f14lLiou, W,W, and Shih, T.H., "Transonic Turbulent
Flow Predictions with New Two-Equation Turbulence
Models," NASA CR 198444, Jan. 1994.
[15] McDonald, H. and Whitfield, D.L., "Self Propelled
Maneuvering Vehicles," Proceedings of the 21St
Symposium on Naval Hydrodynamics, National
Research Council, 1991, pp. 478489.
t161 Pankajakshan, R., Taylor, L.K., Jiang, M.,
Remotigue, M.G., Briley, W.R., and Whitfield, D.L.,
"Parallel Simulations for Control-Surface Induced
Submarine Maneuvers," AIA~4 Paper No. 2000-0962,
January 2000.
f17] Pankajakshan, R., Taylor, L.K., Sheng, C., Briley,
W.R., and Whitfield, D.L., "Scalable Parallel Implicit
Multigrid Solution of Unsteady Incompressible Flow,"
Frontiers of Computational Fluid Dvnamics 2002,
World Scientific Publishing Company Pte. Ltd. 2002,
pp. 181-195.
E18] Remotigue, M.G., Pankajakshan, R., Jiang, M.,
Taylor, L.K., Briley, W.R., and Whitfield, D.L.,
"Dynamic Grid Generation for Simulation of
Submarine Maneuvers: Part II," 8th International
Conference on Numerical Grid Generation in
Computational Field Simulations, Honolulu, Hawaii,
2002.
[l9]Remotigue, M.G., "A Pre-Processing System for
Structured Multi-Block Parallel Computations," 8th
International Conference on Numerical Grid Generation
OCR for page 634
in Computational Field Simulations, Honolulu, Hawaii,
2002. [30] Taylor, L.K. and Whitfield, D.L., "Investigation of
the Accuracy of an Unsteady Incompressible Euler
[201 Roe, P.L., "Approximate Riemann Solvers, Equation Algorithm" Proceedings of the International
Parameter Vector, and Difference Schemes," Journal of
Computational Physics, Vol. 43, 1981, pp. 357-372.
[21] Sheng, C., Chen, J.P., Taylor, L.K. Jiang, M., and
Whitfield, D.L., "Unsteady Multigrid Method for
Simulatiing 3-D Incompressible Navier-Stokes Flows
on Dynamic Relative Motion Grid," AIM Paper No.
97-0446, Jan. 1997.
[22] Sheng, C., Taylor, L.K., Chen, J.P., Jiang, M., and
Whitfield, D.L., Multigrid Computations of 3-D
Incompressible Internal and External Viscous Rotating
Flows," MSSU-EIRS-ERC-9~1, Feb. 1996.
[23] Sheng, C, Taylor, L K., and Whitfield, D.L., "An
Efficient Multigrid Accleration for Solving the 3-D
Incompressible Navier-Stokes Equations in Generalized
Curvilinear Coordinates," AIM Paper No. 94-2335,
1994.
[24]Sheng, C., Taylor, L.K., and Whitfield, D.L.,
"Multignd Algorithm for Three-Dimensional
Incompressible High-Reynolds Number Turbulent
Flows," AIAA Journal, Vol. 33, No. 11, Nov. 1995, pp.
2073-2079.
[25] Shih, T.H., and Lumley, J.L., "Kolmogorov
Behaviour of Near-Wall Turbulence and its Application
in Turbulence Modelling," Computational Fluid
DYnamics, Vol. 1, 1993, pp. 43-56.
[26] Stevens, B.L, and Lewis, F.L., Aircraft Control and
Simulation, John Wiley and Sons, Inc. New York,
1992, pp. 3940.
[27]Taylor, L.K., Arabshahi, A., and Whitfield, D.L.,
"Unsteady Three-Dimensional Incompressible Navier-
Stokes Computations for a 6:1 Prolate Spheroid
Undergoing Time-Dependant Maneuvers," AIM Paper
No. 95-0313, 1995.
t28] Taylor, L.K. Busby, J.A., Jiang, M., Arabshahi, A.,
Sreenivas, K., and Whitfield, D.L., "Time Accurate
Incompressible Navier-Stokes Simulation of the
Flapping Foil Experiment, Proceedings of the Ah
International Conference on Numerical Ship
Hydrodynamics, Iowa City, IA, Aug. 1993.
[29] Taylor, L.K. and Whitfield, D.L., "Unsteady
Three-Dimensional Incompressible Euler and Navier-
Stokes Solver for Stationary and Dynamic Grids,"
MM-Paper No. 91-1650, 1991.
Conference on Scientific Computing and Modeling,
Eastern Illinois University, Oct. 1995.
[31] Thomas, P.D., and Lombard, C.K., "Geometric
Conservation Law and its Application to Flow
Computations on Moving Grids," AIAA Journal, Vol.
17, No. 10, 1978, pp. 1030-1037.
[32]Whitfield, D.L, and Taylor, L.K., "Discretized
Newton-Relaxation Solution of High Resolution Flux-
Difference Split Schemes," AIM Paper No. 91-1539,
1991.
[33] Whitfield, D.L, and Taylor, L.K., "Numerical
Solution of the Two-Dimensional Time-Dependant
Incompressible Euler Equations," MSSU-EIRS-ERC-
93-14, April 1994.
[34] Yang, Z., Georgiadis, N., Zhu, J. and Shih, T.H.,
"Calculations of Inlet/Nozzle Flows Using a New ke
Model," AIM Paper 95-2761, 1995.
OCR for page 635
2 -—
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Figure 11 Comparison of forces for Run 41
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Figure 12 Comparison of velocities for Run 41
it. -
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Figure 13 Comparison of position for Run 41 Figure 16
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Figure 14 Comparison of moments for Run 41
~ 14
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Figure 15 Comparison of angular rates for Run 41
. _
7
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To~- ~S~Fnp~r~ _f ~;.~ ~ ~ i ~ ~.~.i
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Comparison of orientation for Run 41
OCR for page 636
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3" ~ '3~33 fords
': ~ i:3
:..'
~ i :.:.ii.ii.~_ ; _~:i 'I ~
—Inns A___
T.i~ ~ ~
Figure 17 Comparison of forces for Run 18
.4
Is
~ 2
3~
8: ~ _
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en
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-1
a - 'pupation
,~,~v ~ 3- S;~9S-::V3 ~ <<,^~ 3.o~~~56.
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'''"'
I'd'' ~ ~'23~ ~
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—e~ REV—-r
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Figure 18 Comparison of velocities for Run 18
lo.
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,:3i~ _ 32,
:' _ c0~ aft: i:
—~—,, Experlment ~~:
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Figure 19 Comparison of position for Run 18
~-
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in.
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.
- _ Compmadon
A,, Experiment
~;; ~P~IJd~
~ 'i'.j, 4~.,OiO~.b . .,:: ::':i: ::*. :< . S 2 : A . :. ~ t
_~
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Tim t.~1
Figure 20 Comparison of moments for Run 18
1
_ :C~mp~6w
· ~ ~ EXpof~lt~
i.:f.: :.: Rudder
;—7~ Fit ?~ I'
lo
i' ~ ~
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~ _
~ -18 _
_- _
a _
~ r~
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Tim A)
Figure 21 Comparison of angular rates for Run 18
IN _
:~
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S. i.i i ... i....; ~:
.= ..
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it::
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it
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Figure 22 Comparison of orientation for Run 18
OCR for page 637
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· ~ 3~ .. A . ., i, bomb,, t$J~
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:. T:
:3'': :'
::
:;
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'A ' S~ And ·..C..ii"'.V---.::: v.::
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Figure 23 Comparison of forces for Run 27
.
at.
_
._ ~
:'
., .
-1
_ .
_~omp~tion
.? ~ ill . 3.~...,W,F,V,,,,,~ ~ ~ Expenme~
.. . i
~ . .
, W
. . .~
—Ed
~ 1 1 ~
:. 5: :~e
Aid (a.)
Figure 24 Comparison of velocities for Run 27
:69
1
:~
_. ~
4
. ~
-__
._._
~ ,.
_ _, .
= pomp - .tlon .,
.,.
-~ -. E~rimen'
~ Rudder
._ ·:
c; ~
~ . .
Tall
....
-
P-~ -
= ~ L : :=_~ —~,
__ far ' :`
_ Roll
Figure 25 Comparison of position for Run27 Figure 28
. _~.
Yen ~ - ~_~.
~ ~ - - ~:~:~
.;.: :.,:.::jijj :::::j.~:.j:::j:~ al i: ~
. , ,, . —~ . i—3
22: ~ i,' ~
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-: ~ E~'iiment :~' f A
+ - '> .. ~ ~
:: R. Our ~ ~ ~
i ~ ~ - al
. . ~
. ' ~
~ AH
To ~~
Figure 26 Comparison of moment for Run 27
I:
is. .16
a
.
-
~ IU
. — ., .,., , .~
~ , I ~ 1
_ . .
—Worry - tent
a,. ~ Experiment 8~ -
.
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.
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i.
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Figure 27 Comparison of angular rates for Run 27
w
~ - a Compumion
- -
-,. }A - Met
; --My Rawer I,,
P4,~
Io ~ ~ ~ '
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18
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::
Comparison of orientation for Run 27
OCR for page 638
- ~
is
·4 -
~ ~ -
: ~
.1: -
.1~1l
Figure 29 Comparison of forces for Run 18 with
propeller
u '
At:
^,:~,s,~ >USED A 55J
~~ 2 ~ i' ~
:. 5,,
1 _~
_ S—UW,iOn 1p~lhF)
· in,
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° ~ f~d~ ~ ~
sit
, ~ .__
_ , :W
:
'it
i.
:~
~ ha
,:
.;:
~ i'~
Figure 30 Comparison of velocities for Run 18 with
propeller
~ _
_ ~
At.
>_a
= ~trro~u - ' ~
+—Gbn~on(Body Force} ~ -
·* Expert ~?
. q[~—
2:~
.— I: As ~~
~ ~ ^ ~ ~ ~
, C~7 .
..
<.
I, _
:
· n~ use
Figure 31 Comparison of positions for Runl8 with
propeller
.~ _ I 1: ~ 1 1 _ a I I |, F
~~s,:s~. ~,s ~ ;, sass X..S<~xS {v ~ set ~ : so ii'.. .~
n ~ ~ —Ma {Propell~lr~ ~~ ~¢
__ ~, ^~ ~~ldli-` (~forc*:ll ~: ~
. ~~- 'A ,, . ~ _ , ~ ~ -_
~ a ~~ ~ 81 s ~ ~ ~
U ;~;~^ it, '-I: ~ ~ ~~ ~
_ _~ ~.ai6, it. . ~ I; Id,. ~ .l *.
a ~ I Menu———f Amp force) ~~.~ ~ ~ ~~~ y~f
--e - ~ "p~i~ ' I <,< ~ few
_ s;^ Ret ~ _ ~
; ''1 ~ , 1 . ::' ~ -I 1 s'
Ja al b ~ i:
-I ~ ll~4s,
Figure 32 Comparison of moments for Run 18 with
propeller
ear
.
~:4
Or
:l
= ID
em
by .. ~~
:~ , ~ ~
~ sad
~ ~~',,,6~*F
::: ~ ::::
.. 2: ~ >
_ I ~~ ! ~~ ~ —~ ~ _
—Oa my
Exp~ii~niS
:s,:s;.:::~ F——
~ , ~ s,
~ use
Figure 33 Comparison of angular rates for Run 18
with propeller.
_w . ~
~ ~ A ~
I'' ~e :.
~1 ,8 is ~ I, ~ i L . . ~ _ —
.'" ~ ...
::: ~
: ~. -it
:041E ~:~' user
:' ~- :~
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-.H _~on~pe~ at,
- ~ S.r.~on {loopy For - t I,
~ '~per~ent
~ _ . ~~, ~~ w" ~
i'' ~
.:
$[ 11 i'l ~ ' I ~
~ ~ ~ b
~ it ABE..
Figure 34 Comparison of orientations for Run 18
with propeller
OCR for page 639
DISCUSSION
In-Young Koh
Naval Surface Warfare Center, Carderock
Division, USA
What is the benefit of using UNCLE as
compared to Fluent (commercial code) for the
Navy users?
AUTHORS' REPLY
I (D. Whitfield) am not that familiar with Fluent.
However, I did not know that it had the
capability to perform 6-DOF maneuvering
calculations based on a high resolution solver
with rotating propulsor and moving control
surfaces on grids with y-plus of one at Reynolds
numbers of 10**9.
Representative terms from entire chapter:
maneuvering simulations
