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: aymenenis@gmail.com]

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

90

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)

92

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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