**5. Shroud hydrodynamic effects analysis[25]**

For the PETREL, the propeller plays a significant role in the vehicle's hydrodynamic performance, so analysis of the hydrodynamic effect of a propeller with a shroud on a winged HUG was performed with Fluent Inc.'s (Lebanon,New Hampshire) CFD software FLUENT6.2.

#### **5.1 Models description**

To analyze the effects of the shroud, two simulations were performed, where one model is with the shroud and the other without. Two models are shown in Figure 23.

Fig. 23. The models studied in the paper

54 Autonomous Underwater Vehicles

*P=0.2c P=0.25c P=0.3c P=0.35c P=0.4c P=0.45c P=0.5c P=0.55c*

0 4 8 12 16 20 24 28 angle of attack α(°)

The pressure distribution of the rudder is illustrated in Figure 20, where we can find that there is higher pressure on the front flow face and was local higher pressure area on the back flow face of the tail, that means there exist roundabout flow at the tail of the rudder. Figure 21 shows the relationship between lift, drag and angle of attack. The relationship between *L/D* and angle of attack is also illustrated in the figure 21, the *L/D* value reduces ten times for the same scale with other two curves. It can be known that the maximal lift to drag ratio was about 8° and the angle of stall about 34°, so the angles of stall of three dimensional rudders are greater than two-dimension section. The hinge moment of rudders with different axis of rudder position is shown in Figure 22, where we can seen that the hinge moment varied with the angle of attack. The hinge moments are little while 0.4 *P c* = for the

Aiming at the key problems of the rudder design for autonomous underwater vehicle,the hydrodynamic characteristic of the NACA00xx series section at different angles of attack were simulated when velocity was 2m/s by using the two-dimensional computational fluid dynamics (CFD). For the rudder we design, the stall angle is about 34° for the three dimensional rudders and about 20° for the two-dimensional foil section, so the angle of stall of three dimensional rudders are greater than two-dimension foil section. The area of the rudder of PETREL was calculated using the DNV rules;The hinge moments are little

For the PETREL, the propeller plays a significant role in the vehicle's hydrodynamic performance, so analysis of the hydrodynamic effect of a propeller with a shroud on a winged HUG was performed with Fluent Inc.'s (Lebanon,New Hampshire) CFD software FLUENT6.2.

To analyze the effects of the shroud, two simulations were performed, where one model is

with the shroud and the other without. Two models are shown in Figure 23.

when 0.4 *P c* = for the rudder we design no matter how the angle of attack changed.


Fig. 22. Hinge moment with different angles of attack

rudder we design no matter how the angle of attack changed.

**5. Shroud hydrodynamic effects analysis[25]** 

**4.5 Results and discussion** 

**5.1 Models description** 

Hinge Moment Coefficient

*C*

M

#### **5.2 Effect of shroud on the glide drag**

The drag on the vehicle can be expresses as equation (16).

$$D = \frac{1}{2}\rho V^2 \mathbf{C}\_D A \tag{16}$$

Where, *D* is the force of drag in Newton, ρ is the density of water in kg/m³,*V* is the velocity of the vehicle in m/s, *A* is the reference area in m², *CD* is the drag coefficient (dimensionless). The reference area *A* of the PETREL is 0.096m2.

Figure 24 shows the overall drag of the two models in the glide mode. The propeller in this mode doesn't rotate. The overall drags of two models are calculated by CFD firstly and then are fitted by the semi-empirical formulae (16). The drag coefficients of two models are respectively 0.32 and 0.26. The average relative error of overall drag between CFD and semiempirical formulae is 4.7%. The overall drag increase 21%-26% with the propeller shroud compared with the model two according to the CFD computation results, so the shroud greatly increased the drag of the hybrid in glide mode. The drag components of the mode1 at the speed of 0.5m/s without angle of attack are shown in Fig. 25. The drag on the body, rudders and wings is mainly viscous forces, while the drags on the propeller, shroud and GPS antenna pole are primarily the pressure forces,. As shown in Figure 26, the propeller and its shroud make up over 30% of total resistance and the percentage will increase with the increment of the velocity. The reason for the high percentage is because of the great pressure drags on the shroud in the glide mode. The local velocity streamline diagram near the shroud of model one shown in the Figure 27. In the Figure, we can see that in *v* and *P*in are the velocity and pressure inside the shroud of water, out *v* and *P*out are the velocity and pressure outside the shroud of water. Because the propeller doesn't rotate in the glide mode, the velocity of water inside the shroud is slower than that outside the shroud, so there exits out in *v v* > . According to the Bernoulli equation there was *P P* in out > , so a pressure force *f* is produced by the pressure difference. The percentage of the shroud drag to total resistance is 26%-35% at the different speed due to the pressure force in the glide mode.

Hydrodynamic Characteristics of the Main Parts of a Hybrid-Driven Underwater Glider PETREL 57

out out *v P*,

in in *v P*,

1*f*

in in *v P*,

1*f*

out out *v P*,

Fig. 27. The local velocity streamline diagram of model1 ( 0.5 / *v ms* = )

*<sup>D</sup> <sup>e</sup>*

The specific energy consumption can be defined using classical aerodynamics [7] as

ratio occurred at the angle of attack 6°-8°for both the models at different speed.

*DU Bw w D C <sup>E</sup>*

Underwater gliders will have a higher glide efficiency when *Ee* is lower. So the lift to drag ratio *L*/*D* is a measure of glide efficiency, where bigger values represent higher glide

The Lift-to-drag ratio versus angle of attack is plotted in Fig. 28, the relations of model one is indicated by the solid lines. The Lift-to-drag ratio of model one is lower than the model two at different angles of attack, that means the vehicle with the shroud will have a lower glide efficient than that without. The Lift-to-drag ratio of model one is less than model two by 20% to 5% for the varied angles of attack within the range from 2°to 20°. The maximum lift-to-drag

*L*

*Bu Bu u L C* = = = = = (17)

*f*

1*f*

1*f*

**5.3 Effect of shroud on the glide efficiency** 

5.6×10-1 5.0×10-1 4.5×10-1 3.9×10-1 3.7×10-1 3.4×10-1 2.2×10-1 1.7×10-1 1.1×10-1 5.6×10-2 0.0×10-2

*Velocity*

*V*(m/s)

Fig. 28. Lift-to-drag ratio versus angle of attack

efficiency [7].

Fig. 24. The overall drags of the two models at difference velocities

Fig. 25. The drag components of the mode 1 at the speed 0.5m/s

Fig. 26. The drag distribution of vehicle at the different velocities

Fig. 27. The local velocity streamline diagram of model1 ( 0.5 / *v ms* = )

#### **5.3 Effect of shroud on the glide efficiency**

56 Autonomous Underwater Vehicles

model1: CFD model1: empirical formula model2: CFD model2: empirical formula

Fig. 24. The overall drags of the two models at difference velocities

Fig. 25. The drag components of the mode 1 at the speed 0.5m/s

Fig. 26. The drag distribution of vehicle at the different velocities

0 0.5 1 1.5 2 2.5 velocity m/s

0 0.5 1 1.5 2 2.5 velocity (m/s)

body gps propeller shourd rudders wings

presure drag

mode1;body model1:GPS model1:propeller model1:shroud model1:rudder model1:wings model2:body model2:gps model2:propeller model2:rudder model2:wings

viscous drag

force (N)

0

percentage of drag to total

resistance %

1

2

0.5

force (N)

1.5

The specific energy consumption can be defined using classical aerodynamics [7] as

$$E\_e = \frac{DUI}{Bu} = \frac{Bw}{Bu} = \frac{w}{u} = \frac{D}{L} = \frac{C\_D}{C\_L} \tag{17}$$

Underwater gliders will have a higher glide efficiency when *Ee* is lower. So the lift to drag ratio *L*/*D* is a measure of glide efficiency, where bigger values represent higher glide efficiency [7].

The Lift-to-drag ratio versus angle of attack is plotted in Fig. 28, the relations of model one is indicated by the solid lines. The Lift-to-drag ratio of model one is lower than the model two at different angles of attack, that means the vehicle with the shroud will have a lower glide efficient than that without. The Lift-to-drag ratio of model one is less than model two by 20% to 5% for the varied angles of attack within the range from 2°to 20°. The maximum lift-to-drag ratio occurred at the angle of attack 6°-8°for both the models at different speed.

Fig. 28. Lift-to-drag ratio versus angle of attack

Hydrodynamic Characteristics of the Main Parts of a Hybrid-Driven Underwater Glider PETREL 59

shroud on the static stability of model one is that, when the angle of attack is lower than the critical angle the shroud will makes the stability decreasing but makes the stability increasing when the angle of attack is higher than the critical angle. as shown in the Figure 31, the action of the shroud makes the stability slightly increased when the attack angle is

> 0 2 4 6 8 10 12 14 16 18 20 22 angle of attack α(°)

It was found that overall drag increased by 21 to 26 percent for the model with the propeller shroud compared with the one without a shroud, but with the same structure and size, the

The shroud made the lift-to-drag of the vehicle in glide mode decrease by as much as 20 percent when the angle of attack was 2º. As the angle of attack increased, the shroud's effect was minimized, and the decrease in lift-to-drag ratio ranged down to five percent at an angle of attack of 20º, meaning glide efficiency decreased due to the propeller shroud. Finally, the shroud decreases the stability of the HUG when the angle of attack is lower than the critical angle, but increases it when the angle of attack is higher than the critical angle. The critical angle is between 8º and 10º for velocities lower than one meter per second, and

These findings indicate that for an underwater glider, the shroud will increase drag and decrease the glide efficiency, but it is good for stability when the angle of attack is larger than 8º. Therefore, the shroud is not a successful design element for the HUG in glide mode,

 Using CFD to analyze the shroud's hydrodynamic effects shows that the vehicle should only be equipped with this feature for activities requiring operation in propeller mode.

The direct route flow field with the velocity of the hybrid underwater glider PETREL at 0.5m/s、1m/s、1.5m/s and 2m/s was simulated by using CFD ways. The simulation

between 10ºand 12ºfor velocities in the range of one to two meters per second.

but in propeller mode the shroud can increase the thrust of the vehicle.

higher than 12° .

**5.5 Conclusions** 

**6. Flow field analysis** 

results are shown in Figure 32.

**6.1 Velocity field** 


shroud's resistance is mainly pressure force.

0.5m/s 1.0m/s 1.5m/s 2.0m/s

Fig. 31. The moment of the shroud versus angle of attack of model one

moment of the shroud

## **5.4 Effect of shroud on the glide stability**

The underwater gliders usually are designed for static stability [17], the dimensionless hydrodynamic moment arm ' *l* α often used to represent the static stability of the underwater vehicles motion. The equations of the ' *l* αare shown in equations(7)and (8).

Existing oceanographic gliders are designed to be static stable in steady glides for the easy control and high energy economy. The hybrid-driven underwater glider PETREL was designed as static stability for the high energy economy in the glide mode.

Fig. 29. The static stability coefficient ' *l* αversus angle of attack of model one

Fig. 30. The static stability coefficient ' *l* αversus angle of attack of model two

Figure 29 show the static stability coefficient ' *l* α versus angle of attack of model one and model two. It is static stability for both of the two models in terms of our design intention. The stability decreases when the angle of attack gets bigger than 8°, but the stability slightly increases for model one when the angle of attack is more than 12°. The glide speed has little effect on the stability as shown in the Figure 29 and Figure 30. Figure 31 shows the moment of the shroud versus angle of attack of model one. The values of the moment were positive when the angle of attack is lower than 8° for the 0.5 *v* = m/s and 1 *v* = m/s, and the angle of attack is less than 10° for the 1.5 *v* = m/s and 2.0 *v* = m/s. The values of the moment were negative when the angle of attack gets higher than those critical angles. So the effect of shroud on the static stability of model one is that, when the angle of attack is lower than the critical angle the shroud will makes the stability decreasing but makes the stability increasing when the angle of attack is higher than the critical angle. as shown in the Figure 31, the action of the shroud makes the stability slightly increased when the attack angle is higher than 12° .

Fig. 31. The moment of the shroud versus angle of attack of model one

## **5.5 Conclusions**

58 Autonomous Underwater Vehicles

The underwater gliders usually are designed for static stability [17], the dimensionless

Existing oceanographic gliders are designed to be static stable in steady glides for the easy control and high energy economy. The hybrid-driven underwater glider PETREL was

> 0 2 4 6 8 10 12 14 16 18 20 22 angle of attack α(°)

0 2 4 6 8 10 12 14 16 18 20 22 angle of attack α(°)

> *l* α

model two. It is static stability for both of the two models in terms of our design intention. The stability decreases when the angle of attack gets bigger than 8°, but the stability slightly increases for model one when the angle of attack is more than 12°. The glide speed has little effect on the stability as shown in the Figure 29 and Figure 30. Figure 31 shows the moment of the shroud versus angle of attack of model one. The values of the moment were positive when the angle of attack is lower than 8° for the 0.5 *v* = m/s and 1 *v* = m/s, and the angle of attack is less than 10° for the 1.5 *v* = m/s and 2.0 *v* = m/s. The values of the moment were negative when the angle of attack gets higher than those critical angles. So the effect of

versus angle of attack of model two

versus angle of attack of model one

*l* α

designed as static stability for the high energy economy in the glide mode.

*l* α

> *l* α

often used to represent the static stability of the underwater

0.5m/s 1.0m/s 1.5m/s 2.0m/s

> 0.5m/s 1.0m/s 1.5m/s 2.0m/s

versus angle of attack of model one and

are shown in equations(7)and (8).

**5.4 Effect of shroud on the glide stability** 


vehicles motion. The equations of the '

*l*a'

Fig. 29. The static stability coefficient '

la'

Fig. 30. The static stability coefficient '

Figure 29 show the static stability coefficient '


hydrodynamic moment arm '

It was found that overall drag increased by 21 to 26 percent for the model with the propeller shroud compared with the one without a shroud, but with the same structure and size, the shroud's resistance is mainly pressure force.

The shroud made the lift-to-drag of the vehicle in glide mode decrease by as much as 20 percent when the angle of attack was 2º. As the angle of attack increased, the shroud's effect was minimized, and the decrease in lift-to-drag ratio ranged down to five percent at an angle of attack of 20º, meaning glide efficiency decreased due to the propeller shroud.

Finally, the shroud decreases the stability of the HUG when the angle of attack is lower than the critical angle, but increases it when the angle of attack is higher than the critical angle. The critical angle is between 8º and 10º for velocities lower than one meter per second, and between 10ºand 12ºfor velocities in the range of one to two meters per second.

These findings indicate that for an underwater glider, the shroud will increase drag and decrease the glide efficiency, but it is good for stability when the angle of attack is larger than 8º. Therefore, the shroud is not a successful design element for the HUG in glide mode, but in propeller mode the shroud can increase the thrust of the vehicle.

 Using CFD to analyze the shroud's hydrodynamic effects shows that the vehicle should only be equipped with this feature for activities requiring operation in propeller mode.
