Impact of stern design on hydrodynamic drag of AUV's...
Transcript of Impact of stern design on hydrodynamic drag of AUV's...
Indian Journal of Geo Marine Sciences
Vol. 47 (01), January 2018, pp. 89-95
Impact of stern design on hydrodynamic drag of AUV's hull
Aymen Mohamed*1, Hedi Kchaou
2, Med Salah Abid
3 & Zied Driss
4
Laboratory of Electro-Mechanic Systems (LASEM), National School of Engineers of Sfax (ENIS), University of Sfax, B.P.
1173, Road Soukra km 3.5, 3038 Sfax, TUNISIA
*[E-mail: [email protected]]
Received 09 November 2015 ; revised 30 October 2016
Identification of hydrodynamic parameters of the bare hull model is a paramount step in AUV design. CFD investigation using
ANSYS Fluent basing on K-ω SST turbulence model and a different mesh density is established for the velocity ranging from
0.4 m/s to 1.4 m/s. The numerical calculation of the drag coefficient with y+= 2 are revealed in good agreement with
experimental data from towing tank tests of Jagadeesh et al1 despite the low Reynolds regime. Thus, the comparison between
different afterbody models shows the significant effect of the stern design on the hydrodynamic drag of the vehicle and the onset
of flow separation around the stern part.
[Key words: AUV, CFD, hydrodynamic, Turbulence, stern, flow separation.]
Introduction
Recently, with the advancing
development of computing performance and
numerical codes in prediction of fluid flow and
pressure fields, computer based simulations using
Computational Fluid Dynamics (CFD) are
susceptible to replicate conditions which are
delicates through the experimentation. Many
authors were benefited from this procedure to
collect much information about their experimental
models. Jagadeesh et al1 used the low Reynolds
turbulence models to estimate drag, lift and
moment coefficients for various velocities and
angles of attack. The numerical results show a
good agreement with measurements from towing
tank. Juong et al2 used CFD to optimize the
design of an AUV hull. They obtained a
reasonable value of the nozzle angle; drag force
and pressure and velocity fields. Malik et al3 used
CFD to calculate the hydrodynamic features for a
submersible AUV model in transient flow regime.
They were concluded that the CFD method is well
capable and economical way to evaluate the
hydrodynamic derivatives of submersible
platforms such as submarines, torpedoes and
autonomous underwater vehicles. Sakthivel et al4
used the standard model and non linear models
to study the flow around MAYA AUV over
higher angle of attack. They confirm that this last
behaves well with flow separation and
reattachment in 3D complex turbulent flows;
Dantas et al5 used CFD to study the influence of
control surfaces in maneuverability of an AUV.
They were concluded that the occurrence of the
control surface stall depends on a linear
relationship between the control surface
deflection and the angle of attack.
The accuracy of CFD predictions is
highly dependent on the quality and density of
meshing, settings of the TCM, thus required a
validation through Experimental Fluid Dynamics
(EFD) to ensure the reliability of the CFD model.
By combining both computational and
experimental work, a validated simulation model
could be obtained for the evaluation of the
hydrodynamic characteristics of an AUV and
would be a cheaper, faster and viable approach
compared to purely experimental work.
In the current investigation, the total drag
coefficient of Afterbody 1 is predicted using
numerical study for different operating speeds
ranging from 0.4 m/s (Re = 105000) to 1.4 m/s
(Re = 367000) at the depth of submergence
d=4D.Also, the design of the stern is modified to
INDIAN J. MAR. SCI., VOL. 47, NO. 01, JANUARY 2018
characterize the addiction of this modification to
the stability of steering.
The simulation of the hydrodynamic
characteristics is basically performed with
Reynolds-averaged Navier Stokes (RANS)
equations. As the k-ω SST is substantially more
accurate than k-ɛ in the near wall layers, we
established a detailed study about the demeanor
of flow in exchange for inflation layers
dimensions. To validate the drag coefficient, the
calculated drag coefficients are compared with
experimental results of Jagadeesh et al1.
Materials and Methods
The struts fixed to the hull displayed in
figure 1 for pushing the system has a significant
effect in changes of flow stream behind the
model. We are emphasized the crucial necessity
for the Suitable designs to get an appropriate
experimental results. The main physical
parameters defining the flow field are the
Reynolds number Re = ρU∇1/3/μ and the depth
distance d= 4D; where ρ is density of water (1000
kg/m3), U is the inlet velocity, and ∇ is volume of
the body (0.018 m3), and 𝜇 is the viscosity of
water (0.001 kg/m s).
Fig.1−Experimental setup in the towing tank
The myring6 design of experimental
model was described in figure 2 above.
Fig.2−Dimensions of experimental model )Afterbody1(
The modification in CAD model is
primarily on the rear part of the models. Two
specified different designs are studied in this
paper as shown in figure 3.
Fig.3−Modifications of Afterbody design
In this study, an incompressible, steady
and isotherm, Reynolds averaged Navier-Stokes
(RANS) model is applied to solve the (hull of
AUV) problem on a translating reference frame.
The basic idea behind this reference frame is the
assumption that it is the flow field which
translates, and not the hull, thus means that an
unsteady flow field translates into a steady flow
with respect to the hull. This approach simplifies
the problem in terms of boundary conditions, post
processing results, and computational cost.
For a problem of flow simulation, the
main control equations6 are:
Equation of continuity
∇U = 0 (1)
Equations of motion (N-S Equation)
ρdU
dt= ρg − ∇p + μ∇2U (2)
Where U is the velocity vector, 𝜌 is the mass
density of water, p is the pressure, g is the
acceleration of gravity, and 𝜇 is the fluid dynamic
viscosity coefficient.
Turbulence closure model
The k-ω SST turbulence model is a two-
equation eddy-viscosity model )3 and 4
(improved by Menter7 to combine the robust and
accurate formulation of the k-ω model in the near-
wall region with the free-stream independence of
the k-ɛ model in the far field: ∂
∂t ρk +
∂
∂xi
ρkui
=∂
∂xj Γk
∂k
∂xj + G k − Yk
+ Sk 3 ∂
∂t ρω +
∂
∂xi
ρωui
=∂
∂xj Γω
∂ω
∂xj + Gω − Yω + Dω
+ Sω 4
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MOHAMED et al.: IMPACT OF STERN DESIGN ON HYDRODYNAMIC DRAG OF AUV'S HULL
Where, G k represents the generation of turbulence
kinetic energy due to mean velocity gradients, Gω
represents the generation of ω, Γk and Γω
represent the effective diffusivity of k and ω,
respectively, Yk and Yω represent the dissipation
of k and ω due to turbulence, Dω represents the
cross-diffusion term, Skand Sω are user-defined
source terms.
K-ω SST model can be used as a Low-Re
turbulence model without any extra damping
functions as k-ω formulation within boundary
layer makes the model usable all the way down to
the wall through the viscous sub-layer.
In Ansys Fluent, the study is carried out
with velocity inlet for various velocities from 0.4
m/s to 1.4 m/s and outflow condition for outlet8.
The AUV surface with no slip wall and the other
surfaces in computational domain with free slip
wall as shown in Figure 4.
Fig.4−Computational domain and boundary conditions
Mesh generation
The grid is generated with both structured
and unstructured meshes with considering only
the half of the bodies due to the flow symmetry.
As proven by Menter7, k-ω SST is a fully
turbulent model which effectively utilized for a
high Reynolds number flow. Therefore, meshing
near the wall of model should be studied more
accurately than far field due to the significant
damping pulsation which reduces the Reynolds
number. So, to benefit of a good detection of flow
separation and shearing boundary layers features
in our TCM, we required a maximum thickness
for the volume adjacent to the surface. Thus, y+ is
non dimensional wall distance which depends on
the choice of TCM and characterizes the local
Reynolds number. The first node near the wall
should be located in the viscous sub-layer8 with
y+ closed as possible to 1, can be estimated with
the following relation:
𝑦+ =ρ𝑦 𝑢∗
μ 5
Where μ is the local dynamic viscosity of the
fluid, ρ is the density of the fluid, y+ is non
dimensional mesh volume distance from the body
wall surface, u∗ = τw
μ is the friction velocity, and
τw is the shear stress on the body surface. For all
solution residues, we adapted a convergence
criterion in order of 10-4
.
Figure 5 shows the grid of the hull model
within the area based on the tetrahedral elements
constructed the viscous sub-surface to the surface
and tetrahedral one in outer sub layer.
Fig.5−Grid surrounding Afterbody1
The accuracy of computational results is
largely affected by meshing density. So, through
the grid independence test, we try to get a proper
number of the grid which is consistent with
experimental facilities and CPU memory. Thus,
the thickness of the first layer within boundary
layers has an important effect in the calculated
results. For a specified y+, the first layer thickness
∆y 10
can be obtained using:
∆y = L∆y+ 80 Re −13/14 (6)
The boundary layer thickness δL 11
can be
estimated as:
δL/L = 0.382/Re −13/14 7
The grid index ratio is calculated as the
ratio between the grid indexes for each case to the
most refined case, normally the first. The increase
was defined as equal to 2 , as recommended by
Eca et al12
. The property of the investigated grid
densities for the velocity of 0.4 m/s was described
in table 1.
Table 1− Mesh properties of the hull (v=0.4 m/s)
y +
First cell
thickness ( h i )
Total number of
elements
Case 1 0.5 0.136 3118792
Case2 0.7 0.204 2980127
Case 3 1 0.272 2839733
Case 4 √2 0.383 2762985
Case 5 2 0.544 2691288
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INDIAN J. MAR. SCI., VOL. 47, NO. 01, JANUARY 2018
Results and Discussion
Meshing investigation is basically
performed in terms of the thickness of the first
inflation layer as k-ω SST is a full turbulent
model which is characterized by a special
independency to boundary layers features. As
displayed in figure 6, y+= 2 is exhibited as the
most adequate value of non dimensional wall
distance. Thus, the results of drag coefficient in
this case is revealed in good agreement with the
experimental results of Jagadeesh1 in despite of a
marginal errors over the different level of
velocity.
Fig.6−Relation between Cd and y+
Figure 7 illustrates the variation of drag
coefficient in terms of the increase in Reynolds
number for a fully submerged AUV model (H=
4d), as well the comparison between the present
numerical results with chosen designs and the
referred experimental data of Jagadeesh et al1.
The decrease of the drag coefficient of different
after body designs were revealed very clear as Re
increased. Thus, Afterbody2 presented the most
adequate model with minimum drag coefficient
notably observed after Re = 250000 when the
flow is more disturbed. Thus, the level of
turbulence of flow is a critical aspect for
developing evaluation of AUV conception.
Fig.7−Relation between Cd and Re
For the different after body designs,
pressure starts high (stagnation point) and drops
rapidly as the flow accelerates past the bow.
Then, it increases slightly to reach the level of
pressure of the free-stream (zero pressure
coefficients) as the cross-sectional area remains
constant. The onset of separation produces a small
reduction in pressure; then the low velocity of the
flow current behind the stern part causes the
significant increase in pressure coefficient as
shown in figure 8.
3.4
3.6
3.8
4
4.2
4.4
4.6
4.8
5
5.2
0.4 0.6 0.8 1 1.2 1.4
Cd
)1
0¯²
(
V ) m/s (
y+ = 0.5 y+ = 0.7 y+ = 1
y+ = 1.41 y+ = 2 EXP
3.5
3.7
3.9
4.1
4.3
4.5
4.7
4.9
5.1
104462 140986 177510 214035 250559 287083 323607 360132
Cd
)1
0¯²
(
Re
Afterbody 3 (CFD) Afterbody 2( CFD)Afterbody 1( CFD) Afterbody 1 (EXP)
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MOHAMED et al.: IMPACT OF STERN DESIGN ON HYDRODYNAMIC DRAG OF AUV'S HULL
Afterbody2 has the most significant
pressure coefficient at the tip of stern portion with
another stagnation point which presents
confluence of flow streams. Also, we
distinguished a little curvature in pressure
coefficient profile of Afterbody3 displayed with
green color in figure 8 for a distance between 1.36
m and 1.38 m from the bow tip. It is caused by a
specific design which is characterized by a
regarding uniform cross section within this small
portion of the stern. For this, pressure maintains a
relative stability in this region before continuing
its dropping in harmony with decreasing of cross
section.
Fig.8−Pressure coefficient vs position
The behavior of flow streams behind the
stern part characterized with varied velocities
generated a turbulent mixing of flow currents in
this region as shown in figure 9 with levels
between different designs. Also, the reducing of
the velocity in this location increases the
differential pressure thus producing the
phenomenon of cavitations.
Afterbody1 seems to be the noisiest
design with high level of eddy viscosity in
addition to longer boundary layers separation.
Thus, Afterbody3 is characterized with an early
separation of the boundary layers with the
observation of high velocity currents near the
hull's wall. However, Afterbody2 still is stable
with the minimum rate of disturbance.
Figure 10 shows the features of velocity
vectors behind the stern as the main portion to
study in this paper. Boundary layers separation at
the trailing edge introduced low velocity flow,
caused by the surface with no-slip condition,
thereby forming the wake zone. Afterbody1 has
the largest thickness of wake with a full level of
disturbance which generated a sharp shearing of
inflation layers appears near the hull's wall due to
the developed cavitations. Whereas, Afterbody2
is shown more adaptable to the current of flow
with a short wake and a weak rate of eddies
unlike to Afterbody3 which shows an acceptable
rate of wake in respect to the others conception.
The design which promotes laminar flow
is the best as the level of skin friction is mainly
depends to the behavior of the flow. As the cross
section is increased gradually from the nose to
generate an adequate pressure gradient over the
forward part of the hull, the flow was laminar.
Otherwise, Afterbody3 highlighted the flexibility
of its back form with boundary layers separation
through a low skin friction decreased smoothly
compared to the other designs as shown in figure
11. As the high shearing stress within boundary
layers is resulted from the level of disturbance of
flow currents, Afterbody3 represents the best
efficient concept against flow disturbance.
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INDIAN J. MAR. SCI., VOL. 47, NO. 01, JANUARY 2018
Fig.9−Velocity fields for v = 0.4 m/s
Fig.10−Velocity vectors around the sterns
Fig.11−Skin friction
Cavitations behind the AUV have
generated vortices which tend to increase the self-
noise of propulsion system. Afterbody2 represents
the suitable design with the least level of vortex
as shown in figure 12.Thus, the reduction of cross
sectional area along the length of the hull, causing
the flow to decelerate gradually and providing an
acceptable rate of flow currents disturbance.
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MOHAMED et al.: IMPACT OF STERN DESIGN ON HYDRODYNAMIC DRAG OF AUV'S HULL
Fig.12−Vortices created behind Afterbody designs
In spite of the large amount of vortex behind
Afterbody3, we can clearly distinguish the area of
relative stability in pressure with absence of
disturbance in this location which confirmed the
observation in the figure of the pressure
coefficient curves.
Conclusions
In this paper, we are interested on the
prediction of the drag coefficient and the flow
behavior of the bare hull AUV considering
various stern designs, which proves the necessity
to revise the configuration of the struts in
experimental facility. Using k-ω SST TCM, the
numerical results confirmed by experimental data
from towing tank shows that Afterbody2 is the
best model with the minimum rate of drag
coefficient, vortices and thickness of wake.
However, Afterbody3 is characterized by the
region of a fairly stability which can be a suitable
location to install the control surfaces in order to
have a good maneuverability.
Acknowledgments
Authors are grateful to the National School of
Engineers of Sfax (ENIS( and in particular the
Laboratory of Electro-Mechanic Systems
(LASEM),Tunisia, for providing the CPU time
required for the current numerical analysis.
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