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OCR for page 940
~ a ~-~r - -- - --- - -- - — —- - -a—- -—~ --__
Fukuoka, JAPAN, 8-13 July 2
Computation of Viscous Flow
around Fast Ship Superstructures
O. E! Moctar (HSVA, currently Germanischer Lloyd, Germany),
V. Bertram (HSVA, Germany)
There is more control over what to view and
what to block out.
CFD can capture more flow details.
In principle, CFD allows also full-scale simu-
lations.
The technique is non-intrusive.
Abstract
A commercial RANSE solver is applied to
compute the flow around ship superstructures. The
water surface is approximated by a flat surface. For
smoke tracing, multi-phase flow can be simulated
solving an additional transport equation for the
smoke concentration. Similarly, thermic distribu-
tions can be traced solving an energy equation. The
applications are a surface effect ship and a fast
ferry. The surface effect ship is quite simple in
geometry and the grid employs only hexahedral
elements. Results are shown for various angles of
attack. The cruise ship superstructure is more com-
plex and tetrahedral elements are used to simulate
also smoke propagation. A considerable difficulty
for practical applications is the time-consuming
creation of the CAD description of the ship super-
structure.
1. Introduction
Aerodynamic issues are increasingly of
interest for ships and offshore platforms. Potential
applications include:
Smoke and exhaust tracing
Operational conditions for take-off and landing
of helicopters
Wind resistance and drift forces
Ventilation of rooms
The traditional approach to study aerody-
namic flows around ships employs model tests in
wind tunnels, Fig.1. These tests are a proven tool
supporting design and relatively fast and cheap.
Forces are quite easy to measure, but insight into
local flow details can be difficult in some spaces.
Computational fluid dynamics (CFD) is
increasingly used in related fields to investigate
aerodynamic flows e.g. around buildings or cars.
CFD offers some advantages over wind tunnel
tests:
The complete flow field can be stored and
allowing evaluation at any time in the future.
~ ~ ~ ~ ~ _~w
intrusive smoke tracing technique
Despite these advantages, CFD has so far
rarely been employed for aerodynamic analyses of
ships. This is due to a combination of obstacles:
The complex geometry of superstructures
makes grid generation labor-intensive.
Reynolds numbers and domain topology re-
quire relatively high cell counts,
The flows are turbulent and require often un-
steady simulations due to large-scale vortex
generation.
Recent progress in available hardware and
grid generation techniques allows now a re-
evaluation of CFD for aerodynamic flows around
ship superstructures.
Hybrid grids with tetrahedral and prism
elements near the ship allow partially automatic
grid generation for complex domain boundaries.
The resulting higher cell count is acceptable for
aerodynamic flows because the Reynolds numbers
are lower (typically by a factor 15) than for hydro-
dynamic ship flows and thus there are fewer ele-
ments needed to resolve the boundary layer.
OCR for page 941
Our applications here show how to design
suitable grids and what type of results can be ob-
tained. They also point towards more required
validation work and remaining problems in ob-
taining suitable electronic descriptions of ship su-
perstructure geometries.
2. Literature review
Despite the increasing importance of aero-
dynamic flows for ships and offshore platforms,
there are only few published CFD applications in
the field.
F0rde et al. (1992) solve the Euler equa-
tions for a surface effect ship (SES). The air resis-
tance accounts for 25% of the total resistance for
this 50 knot ship. The CFD guided improvement of
the forebody of the superstructure reduced the wind
resistance by Who. F0rde and Gjerde (1999) em-
ploy a RANSE code to compute the aerodynamic
flow around a 40 knot catamaran.
Tai and Carico (1995), Tai (1996) simulate
the aerodynamic flow around a destroyer using a
RANSE code to determine the flow conditions on
deck for landing helicopters. Tai (1995) presents
similar applications for another ship.
The Danish Maritime Institute conducted
extensive aerodynamic CFD investigations for
maritime structures. Building on previous work by
Leer-Andersen and Hughes (1996) at DTU, Aage et
al. (1997), Hvid et al. (1997) describe RANSE
applications for a ferry and an offshore platform
with focus on wind forces and smoke tracing. Jen-
sen et al. (1997) describe the capabilities of CFD
for cruise vessels and others maritime structures,
but conclude that the grid generation effort is still
too large to see CFD as commercially viable alter-
native to wind tunnel testing: "The comparison of
CFD, wind-tunnel tests, and full-scale measure-
ments show an overall good agreement, even if
large discrepancies are indeed seen at some wind
directions. The differences between CFD and
model-test results are not generally larger than
between full-scale and model-scale results. Actu-
ally, the differences are not much larger than often
found when the same vessel is tested in different
wind tunnels. Therefore, it is concluded that de-
termination of wind loads on ships and offshore
structures by CFD is a realistic computational al-
ternative to the experimental methods. However,
due to the time involved in generating the compu-
tational mesh and in computing the solution, the
CFD method is not at the moment economically
competitive to routine wind-tunnel model testing."
SIREHNA in France has simulated aero-
dynamic flow for smoke tracing at a combatant
(www.ec-nantes.fr/sirehna). Details are not pub-
lished.
Stanford University has conducted aero-
dynamic studies for US Navy landing ships, cro-
magnon.stanford.edu/jship. This study compared
data for full-scale measurements, wind tunnel tests,
and CFD simulations. The CFD grids employed
650,000 cells for the commercial RANSE code
FLUENT.
Jin et al. (2001) employ FLUENT to
simulate smoke tracing for various alternatives of a
tanker superstructure design. The computations use
exclusively tetraeder grids with 500,000 cells
slightly simplifying the computational model for
the bow geometry and omitting details like on-deck
pipes and radar masts.
E1 Moctar et al. (2001 a,b) presented re-
sults of aerodynamic RANSE simulations for a
cruise vessel with a rather detailed geometric
model. The simulations included also smoke trac-
ing and thermodynamic analysis of the exhaust of
funnels.
3. RANSE Code
We employed the code Comet, ICCM
(2001~. The fundamental theory and main em-
ployed options are described below.
The aerodynamic flows around ship super-
structures are slow enough to be considered incom-
pressible. The fundamental field equations describe
conservation of mass (continuity equation) and
conservation of momentum (Reynolds-averaged
Navier-Stokes equations = RANSE). The time
averaging is an ensemble averaging, i.e. the aver-
age is considered to be taken over a time span large
compared to the turbulent fluctuations, but small
compared to the large vortex shedding. In the fol-
lowing, all equations are to be understood as time
averaged in this way.
The RANSE equations are given in inte-
gral form as the code is based on the f~nite-volume
method approach:
—J. pdV +J. p~v-vs) ds= 0 (1)
v s
OCR for page 942
—J. pvdV +) pv(v-vs)ds=
| (S-pI-pv'v') dS + | f dV (2)
s v
Bold symbols denote vectors and Tensors.
p is the fluid density, V the volume, S the surface
area of a control volume (CV), ds the outward
normal on the surface. v is the (time averaged)
velocity vector of the fluid, vs the velocity vector of
the CV surface, p the pressure, v' the turbulent
fluctuation of the velocity, f a resultant body force
per unit volume, t the time, I the unit tensor, and S
the viscous part of the stress tensor. For incom-
pressible (Newtonian) fluids the components of S
are proportional to the fluid's rate of deformation:
S = ,u (grad v + (grad v)T) (3)
,u is the dynamic viscosity. The Reynolds
stress tensor pvi'vj' is expressed as a function of
time-averaged quantities using a turbulence model
following the eddy-viscosity hypothesis of Boussi-
nesq:
-p Vi'Vj'= At (3vi/3xj+Ovj/3xi) - (2/3) p djj k
(4)
~ = Cad, p k2/e is eddy viscosity which is a
function of the local turbulence, Cam, an empirical
constant, dij the components of the unit tensor. We
solve corresponding transport equations for the
turbulent kinetic energy k=0.5 v' v' and its dissipa-
tion rate £ = (pit) (grad v': (grad V')T):
d
| pkdV +| pk(v-vs)ds=
dt V s
| qk-dS + | (P-p£) dV
s v
dt l P £ dV + ,( p £ (v-vs) ds = J. qua ds
+ 1 (ClPe/k- C2pe2/k-C4p £ div v) dV (6)
v
qk and q£ are the diffusion fluxes for k and £:
qk = (~l+~k/6k) grad k (7)
qua = (`U+Lk/Ce) grad £ (8)
P is the production of turbulent energy by shear:
P= -p v'v': grad v (9)
Cl, C2, C4, Ok, G~ IT, 6cj are empirical constants.
We employed the RNG-k-£ model of Speziale und
Thangam (1992), which differs from the standard
k-£ model in two aspects:
1. An additional source term in the transport
equation for £, which is associated with the ef-
fect of the rate of mean flow distortion on tur-
bulence dissipation rate. This extra term is be-
lieved to be important when the nondimen-
sional shear is large compared to unity.
2. Other empirical constants are chosen:
Cu
0.085
c6
0.012
The above described transport equations
are discretized in a finite-volume method (FVM).
The domain is discretized by control volumes. We
employed tetraeder, prism, and hexaeder elements
in our grids.
The variables are stored at the cell center
(colocated variable arrangement). The field equa-
tions are discretized employing assorted interpola-
tion and differencing schemes. The resulting alge-
braic system of equations is solved numerically.
Volume and surface integrals are determined using
a second-order midpoint rule. The convective flux
of the variable 0 through cell side j is approximated
as follows:
J. p ~ (v-vs) dS ~ oj J. p (v-vs) dS ~ ojp(v-vs~j S
sj s
=oj my
(10)
<5' The mass flux my through the cell face is
taken from the previous iteration following a sim-
ple Picard iteration approach. The remaining un-
known oj at the center of the cell face j is deter-
mined combining a central difference scheme
(CDS) with an upwind differencing scheme (UDS).
The CDS employed a correction to ensure second
order accuracy for arbitrary cell, Demirdzic and
Muzaferija (1995~. Second-order CDS can lead to
unphysical oscillations if the Peclet number ex-
ceeds 2 and large gradients are involved. UDS on
the other hand are unconditionally stable, but lead
to higher unphysical diffusion. To obtain a good
compromise between accuracy and stability, the
schemes were blended as follows:
tj = 0jUDS +\j (ojCDS ~ UDS'
OCR for page 943
The blending factor ~ was chosen be-
tween 0.9 and 0.95 near the hull and 0.8 further
away. This choice is motivated by the higher cell
density near the hull. Unphysical oscillations ap-
pear often at the begin of the simulation for grids
involving tetraedal and prism cells. These oscilla-
tions are smoothed by a higher UDS contribution in
the beginning which is reduced in the course of the
iteration. The stability and computational efficiency
is further increased in Comet following the de-
ferred correction approach of Kohsla and Rubin
(19741. Only the first-order approximation contrib-
utes to the coefficient matrix, while the correction
term is calculated explicitly using values from the
previous iteration and is added to the source term.
In the converged solution, explicit and implicit
contributions of the UDS cancel each other and
only CDS remains.
The diffusive fluxes through cell faces are ap-
proximated using a second-order midpoint rule.
The Euler implicit method was used to integrate in
time. This first-order fully-implicit approximation
is unconditionally stable.
Pressure and velocity are coupled by a
variant of the SIMPLE algorithm as derived in
Ferziger and Peric (19961.
The system of equations are under-relaxed
to dampen changes between iterations. All equa-
tions except the pressure correction equations were
under-relaxed using a relaxation factor 0.6. The
pressure correction equations were under-relaxed
using a relaxation factor 0.04 for steady flow
simulation, 0.1 to 0.5 for unsteady simulations
finding in each case a suitable compromise be-
tween stability and convergence speed.
v, k, and ~ are initialized at all cell centers.
For parameter studies (e.g. wind direction or
speed), the values of the previous parameter are
taken which typically saves 20% CPU time. At the
inlet, v, k, and ~ are specified. At the outlet all
gradients in flow direction are set to zero. At sym-
metry boundaries (rigid water surface) normal
velocities and normal derivatives of parallel veloc-
ity components and scalar quantities are set to zero.
On the hull, we enforce the no-slip condition via a
standard wall function (following capacity restric-
tions rather than physical insight) and set the ki-
netic energy to zero. The dissipation rate ~ is fixed
at the first point near the wall to a value corre-
sponding to the computed kinetic energy following
the assumption of local balance of turbulence.
Filigree elements like railings can be
treated as porous surfaces (baffle elements) avoid-
ing geometrical modelling with excessive cell
counts. The basic transport equations retain their
form then, with ds in the surface integral being
replaced by P dS, and if the source terms are up-
dated to account for interaction between fluid and
solid parts of the porous medium. The surface po-
rosity P relates the area available to flow Sf to the
total control surface vector s:
=Ps
(12)
P is a symmetric matrix. There are, how-
ever, many situations where it is neither necessary
nor practical to define the surface porosity in this
degree of generality. In those cases the actual ve-
locity v (which is discontinuous at discontinuity in
porosity) is combined with the surface porosity to
give a continuous averaged velocity
vsup = P v
called superficial velocity ( m = v Sf = vsup s). This
approach is adopted in Comet.
(13)
4. Applications
4.1. Surface effect ship
Surface effect ships (SES) reach often
speeds in excess of 40 knots. Aerodynamic resis-
tance plays a bigger role for these ships than for
conventional ships. We selected for our application
the French SES "AGNES 200", Guezou (1993),
Table I.
Table I: Main data "AGNES 200"
Dispi. 250 t Cushion length 41.4 m
L a 51 m Cushion width 8.0 m
O
L 45 m T (on cushion) 1.1 m
PIP
Boa 13 m Speed V 40 kn
As a first step, a CAD description of the
SES was generated in ICEM-CFD, which served as
basis for further grid generation. The f~nite-volume
grid used an inner cylindrical domain surrounded
by an outer block-shaped domain, Fig.2. The grid
extended from 1 ship length L=Lpp ahead of the
forward perpendicular to 1.5 L behind aft perpen-
dicular, 1.5 L in vertical direction, and 1.5 L to
each side from the plane of symmetry. The inner
cylindrical domain was designed such that a for
OCR for page 944
each rotation by 5° cell nodes would again coincide
with cell nodes in the outer domain, i.e. for each 5°
increase in relative wind angle we could again
work with matching interfaces in the code. The
relatively simple geometry of the SES superstruc-
ture allowed to use hexahedral elements for the
whole domain. Results shown here were obtained
with a grid using 2.9 million cells.
. _
. _
it_
Ad.
Fig.2: Grid detail for SES with inner cylindrical
domain
foredeck, there are corresponding low pressure
zones.
Fig.4 shows streamlines starting after the
cabin. There are large recirculation regions above
the helicopter deck and behind the stern. Between
the funnels there are strong vortices as visualized
by "cork screw" streamlines.
Figs.S and 6 show streamlines starting in the
foreship. The two layers differ by O.Sm in height of
the starting points. The starting height yields here
totally different streamline characteristics which is
an indication of the strong three-dimensionality of
the flow.
~~:~
. ~:
---
Fig.3: Pressure distribution for,u=180°
For wind coming from relative wind angle
,u=180° (e.g. pure wind resistance due to the mov-
ing ship), the computed pressure distribution looks
as expected, Fig.3. At the skirt front, the flow is
retarded to almost stagnation resulting in high pres-
sures. Smaller high-pressure regions appear on the
funnels in areas not in the wind shade of the cabin
and on the forward inclined front of the cabin. At
the edges and particularly on the cabin top and
. ~-
: ~~
-
Fig.4: Streamlines behind cabin for ,u=180°; side
view (top) and detail between funnels (bottom)
For the lower layer, Fig.S, the outer
streamlines are sucked into the recess between
foreship and cabin. Afterwards the follow largely
the side of the ship. The center lines hit the lower
edge of the cabin, and are then diverted to the sides
where the speed is reduced to such an extent that
the streamline tracing breaks down.
OCR for page 945
~~ ~ i: :~ ~~ ::~
U: ~ Hi: : ~ :~:: :~:: :: ::::
~ :~::: ~~ ~~ :
:::~: i:
: ~ ~~ ::~:: :: ~ :
: : ~ Id
~ d ~::o ;~:~~
~:~:::~::~:::~:: :~ ::: ::::: :: ::: ::~ : ::::: ~ -
Fig.5: Streamlines starting in foreship, lower layer
For the upper layer, Fig.6, the center
streamlines are diverted upwards over the cabin
forming recirculation areas behind the cabin. The
streamlines at the side are no longer sucked into the
recess between cabin and foreship, but follow on
the upper deck sideways around the cabin.
A moderate oblique flow direction of 170°
changes the flow noticeably. The high-pressure
region at the forward cabin incline is increased,
Fig.7. On the luff side, the low-pressure regions
disappear almost, on lee the low-pressure regions
are more pronounced. The flow is partially by-
passing the superstructure, but the cork-screw
streamlines indicating strong vortices behind the
superstructure are still dominant, Fig.8.
The flow changes observed for 170° be-
come more pronounced with increasing angle as
demonstrated for 150°, Figs.9 and 10. There is a
distinct blockage effect of the superstructure ex-
pressed in the pressures on the lee side. The flow is
now predominantly in transverse direction and less
complicated as there are hardly any superstructure
elements downstream of other superstructure ele-
ments. The flow resembles the flow around a foil.
Fig.6: Streamlines starting in foreship, upper layer
Fig.7: Pressure distribution for '170°
OCR for page 946
=~:~:~s 'I ~ - ~
A ~~ :~ ~~ ~~ Ail: ~~ ~~ ~~ it. I. .~. .: ~~.j A. ~ ~ !
Fig.8: Streamlines starting in foreship, ,u=170°
_
~ .,_ ~~ as_
[ ~~ ~~ ~ ~ L-
: ~ ~~ ~ ~~ ~~ ~ ~ ~ ~ ..~. : : :
Fig.10: Streamlines starting in foreship, ~150°
Fig.9: Pressure distribution for p=150°
Fig. 11: Streamlines further away in foreship,
,u=150°
On the downwind side, the flow is sucked partially
along the ship sides before it detaches approaching
its original flow direction again, as becomes appar-
ent when zooming out to a larger perspective,
Fig. 1 1.
Results for the SES including a helicopter
on deck are intended to be presented in Lindenau et
al. (2002~.
OCR for page 947
4.2. Two-phase flow for funnel
A reference application for a typical ge-
neric cruise vessel was produced from published
deck plans of actual modern cruise vessels. Several
grids of increasing fineness were created with the
largest having approximately 5 million cells,
Figs.12 and 13. The grid consists of 10 layers of
prism cells at the ship surface with the residual
space of the computational domain being automati-
cally meshed with tetrahedral elements. Ongoing
research focuses on determining proper grid reso-
lution, and we expect that 1-2 million cells may
suffice for most applications in practice. The aero-
dynamic CFD analysis showed extensive recircula-
tion regions at the upper deck of the cruise vessel.
One of these recirculation areas appears directly
behind the funnel structure, Fig.14.
Fig. 12: Grid for cruise vessel
, . ..
. . . . . . . . . . . . . . . . . .
Fig. 13: Grid detail for cruise vessel
For exhaust propagation we modeled the
flow as two-phase flow in Comet. We specified the
exhaust temperature and velocity and then traced
the development in an externally specified wind
distribution, Fig.15. We used a uniform wind speed
over height at the domain inlet. We tested this pro-
cedure first for a funnel on a flat plate, Fig.16. This
initial test gave plausible results. There were no
validation data. We then performed a similar study
for the cruise ship in wind direction coming from
150° (oblique head wind), Fig.17. The results look
again plausible. Current research performs similar
computations for a "Superfast" ferry, Mechsner
(2001), where there are also wind tunnel experi-
ments for comparison. These will be presented in
Schmode et al. (2001~.
Fig. 14: Streamlines behind funnel
Fig.15: Exhaust temperature at funnel
.. . . . . . . . . . At. ~ ~ ~ . . ~ ~ ....... , ~ , ~ .; .
Fig.16: Funnel on plate with smoke contours
OCR for page 948
Fig.17: Cruise ship in ,u=170° with smoke contours
5. Conclusion
The progress in hardware and grid genera-
tion capabilities allows now aerodynamic analyses
of ship superstructures that are in some aspects
superior and in some aspects inferior to wind tunnel
tests. Grid generation remains a key issue in such
computations. The level of detail achieved by CFD
is by now comparable to that of model tests.
Acknowledgement
The research presented here was partially
funded by the German ministry of education and
research BMBF. Olaf Lindenau and Scott Gatchell
supported us in the pre- and post-processing.
References
Aage, C.; Hvid, S.L.; Hughes, P.H.; Leer-
Andersen, M. "Wind loads on ships and offshore
structures estimated by CFD," 8th Int. Conf. Be-
haviour of Offshore Structures BOSS'97, Delft,
1997, pp.237-251
Demirdzic, I.; Muzaferija, S., "Numerical method
for coupled fluid flow, heat transfer and stress
. .
analysts using unstructured moving meshes with
cells of arbitrary topology", Computer Methods in
Applied Mechanics and End. Vol.125, 1995
E1 Moctar, O.; Gatchell, S.; Bertram, V. "RANSE
simulations for aerodynamic flows around ship
superstructures," 4th Num. Towing Tank SYmp.,
Hamburg, 2001
El Moctar, O.; Gatchell, S.; Bertram, V.,
"Aerodynamische Stromungssimulation fur Schif-
fe " Hansa 138/9 2001 pp.20-21
, , ,
Ferziger, J.; Peric, M., Computational methods for
fluid dynamics, 1996, Springer-Verlag
F0rde, M.; 0rbekk, E.; Kubberud, N. "Reduction of
aerodynamic drag of a high speed catamaran by
using advanced CFD calculations," IS' Int. Conf.
Appl. CFD, Basel, 1992
F0rde, M.; Gjerde, K. "High speed catamaran
aerodynamics," CFD'99, Ulsteinvik, 1999
Guezou, J.P. "AGNES 200: Up-to-date technical
information and potential use for commercial and
military applications," FAST'93, Yokohama, 1993,
pp.21-34
Hvid, S.L.; Leer-Andersen, M.; Hughes, P.H.
"Wind load prediction on offshore structures using
CFD," Conf. Application of Fluid Dynamics in the
Safe Design of Topsides and Superstructures, Inst.
Of Marine Eng., London, 1997
Jensen, A.G.; S0ndergaard, T.; Livesey, F. "Wind
comfort for cruise/passenger vessels," Cruise &
Ferry, 1997
Jin, E.; Yoon, J.; Kim, Y. "A CFD-based paramet-
ric study on the smoke behaviour of a typical mer-
chant ship," PRADS'01, Shanghai, 2001, pp.459-
465
Kohsla, P.K.; Rubin, S.G., "A diagonally dominant
second-order accurate implicit scheme," Computers
& Fluids Vol.2, 1974
Launder, B.E.; Spalding, D.B., "The numerical
computation of turbulent flows," Computer Me-
thods in Applied Mechanics and Eng. Vol.3, 1974
Leer-Andersen, M.; Hughes, P.H., "Computations
of wind loads on ships and offshore structures,"
Dept. Naval Arch. & Ofshore Eng., Danish Techni-
cal Univ., 1996
Lindenau, O.; Bertram, V.; El Moctar, O.M.;
Gatchell, S. "Aerodynamic simulations for an SES
employing virtual reality post-processing tech-
niques", 3r~ High-Performance Marine Vehicles
Conf. HIPER'02, Bergen, 2002
Mechsner, A., "Zwei RoPax-Fahren der Superlative
von HDW" Schiff&Hafen 3 2001 pp.31-33
, , ,
OCR for page 949
Patankar, S.V.; Spalding, D.B., "A calculation
procedure for heat, mass and momentum transfer in
three-dimensional parabolic flows," Int. J. Heat
Transfer Vol. 15, 1972
Schmode, D.; Bertram, V.; E1 Moctar, O.M.
"Aerodynamic flow computations for a Superfast
ferry", 3r~ High-Performance Marine Vehicles
Conf. HIPER'02, Bergen, 2002
Speziale, C.G.; Thangham, S., "Analysis of an
RNG based turbulence model for separated flows,"
Int. J. Eng. Science Vol.30, 1992
Tai, T.C. "Effect of ship motion on DD-963 ship
airwake simulated by multizone Navier-Stokes
solution" 21St SYmp. Naval HYdrodyn. Trond-
, ,
helm, 1996
Tai, T.C. "Simulation of LED ship airwake by
Navier-Stokes method," 6th Asian Congr. Fluid
Mechanics, Singapore, 1995
Tai, T.C.; Caric, D., "Simulation of DD-963 ship
airwake by Navier-Stokes method," J. of Aircraft
32/6, 1995, pp.1399-1401
Representative terms from entire chapter:
aerodynamic flows
