**2. Computational details**

#### **2.1 Mathematical model**

A criterion for determining of the flow regime of the water when the vehicles moving in it is proposed by Reynolds number [14-15]:

$$\mathbf{R}\_{\circ} = \rho v \mathbf{L} / \mu \tag{1}$$

Here ρ is the density of water, *v* is the velocity of vehicle, *L* is the characteristic length, μis the dynamic coefficient of viscosity. The transition point occurred when the Reynolds

number is near <sup>6</sup> 10 for the external flow field, which is called critical Reynolds numbers. It was laminar boundary layer when the <sup>5</sup> Re 5 10 < × , it was seem as turbulent flow while <sup>6</sup> Re 2 10 > × . The Reynolds number of the hybrid underwater glider PETREL at two different steering modes is shown in table 1.


Table 1. The Reynolds number at different steering modes

40 Autonomous Underwater Vehicles

ROV

Maneuverability

Low

High

By combining the advantages of the glider and the propeller-driven AUVs, A hybrid-driven underwater glider PETREL with both buoyancy-driven and propeller-driven systems is developed. Operated in buoyancy-driven mode, the PETREL carries out its mission to collect data in a wide area like a legacy glider. When more exact measurements of a smaller area or level flight are needed, the PETREL will be operated by using the propeller-driven system [5, 7]. This flexible driven glider contributes to have a long range while operated in the buoyancy driven mode like a glider, as well as improve the robust performance to deal with

AUG

AUV

Proper hydrodynamic design is important for the improvement of the performance of an underwater vehicle. A bad shape can cause excessive drag, noise, and instability even at low speed. At the initial stage of design, there are two ways to obtain the hydrodynamic data of the underwater vehicle, one is to make model experiment and the other is to use the computational fluid dynamics (CFD). With the development of the computer technology, some accurate simulation analysis of hydrodynamic coefficients have been implemented by using the computational fluid dynamic (CFD) software, instead of by experiments at a much higher cost over the past few years [12-13] . In consideration of the reduced time, lower cost, more flexible and easier optimumal design, the CFD method was used in this article. The fluent Inc.'s (Lebanon,New Hampshire) CFD software FLUENT 6.2 was adopted by this

This chapter focuses on the hydrodynamic effects of the main parts of a hybrid-driven underwater glider especially in the glide mode. By analyzing the results of the three main hydrodynamic parts, the wings, the rudders and the propeller, the characteristics of drag, glide efficiency and stability will be discussed, and suggestions for altering the HUG's

A criterion for determining of the flow regime of the water when the vehicles moving in it is

is the density of water, *v* is the velocity of vehicle, *L* is the characteristic length,

is the dynamic coefficient of viscosity. The transition point occurred when the Reynolds

(1)

Re = ρ*vL* μ

Fig. 2. Performances of three Underwater Vehicles

No limitation(1km)

Time (range)

Several hours(100km)

Several months(1000km)

article.

High

Low

Endurance

Here ρ

μ

**2. Computational details 2.1 Mathematical model** 

proposed by Reynolds number [14-15]:

some wicked circumstances by the propeller driven system [7].

design to improve its hydrodynamic performance are proposed.

The turbulence model will be adopted because the Reynolds numbers of the PETREL in two steering modes are all above the critical Reynolds numbers. Computations of drag, lift and moment and flow field are performed for both the model over a range of angles of attack by using the commercially available CFD solver FLUENT6.2. The Reynolds averaged Navier– Stokes equation based on SIMPLAC algorithm and the finite volume method were used by our study. In our study RNG k-ε model was adopted and the second-order modified scheme was applied to discrete the control equations to algebra equations. Assuming that the fluids were continuous and incompressible Newtonian fluids. For the incompressible fluid, the *RNG k* − εtransport equations are [12, 16]:

$$
\rho \frac{\partial}{\partial t}(k) + \rho \frac{\partial}{\partial \mathbf{x}\_i}(k\boldsymbol{\mu}\_i) = \frac{\partial}{\partial \mathbf{x}\_j} \left( \alpha\_i \mu\_{\text{eff}} \frac{\partial k}{\partial \mathbf{x}\_j} \right) + \mathbf{G}\_k - \rho \mathbf{c} + \mathbf{S}\_k \tag{2}
$$

$$
\rho \frac{\partial}{\partial t}(\varepsilon) + \rho \frac{\partial}{\partial \mathbf{x}\_i}(\varepsilon u\_i) = \frac{\partial}{\partial \mathbf{x}\_j} \left( \alpha\_\varepsilon \mu\_{\varepsilon \overline{\mathbf{f}}} \frac{\partial \varepsilon}{\partial \mathbf{x}\_j} \right) + \mathbf{C}\_{1\varepsilon} \frac{\varepsilon}{k} \mathbf{G}\_k - \mathbf{C}\_{2\varepsilon} \rho \frac{\sigma^2}{k} - \mathbf{R}\_\varepsilon + \mathbf{S}\_\varepsilon \tag{3}
$$

Here *Sk* and *S*ε are source items, μ*eff* is effective viscosity, *Gk* is turbulence kinetic energy induced by mean velocity gradient.

$$\mathbf{G}\_k = -\rho \overline{\hat{u}\_i \hat{u}\_j} \frac{\partial \mathbf{u}\_j}{\partial \mathbf{x}\_i} \tag{4}$$

σ *<sup>k</sup>* andσ ε is respectively the reversible effect Prandtl number for *k* and ε . <sup>1</sup> *C* 1.42 ε = , <sup>2</sup> *C* 1.68 ε=

In the *RNG* model,a turbulence viscosity differential equation was generated in the nondimensional treatment.

$$\mathrm{ch}\left(\frac{\rho^{\circ}k}{\sqrt{\varepsilon\mu}}\right) = 1.72 \frac{\hat{\nu}}{\sqrt{\hat{\nu}^{\circ} - 1 + C\_{\nu}}} \mathrm{d}\,\hat{\nu} \tag{5}$$

here, ˆ μ*eff* ν μ = ,*C* 100 ν ≈ . Taking the integral of the(5),the exact description of active turbulence transport variation with the effective Reynolds number can be acquired, which makes the mode having a better ability to deal with low Reynola number and flow near the wall. For the large Reynola number, the equation(5)can be changed into (3-6).

Hydrodynamic Characteristics of the Main Parts of a Hybrid-Driven Underwater Glider PETREL 43

1. inlet boundary condition: setting the velocity inlet in front of the head section with a

2. outlet boundary condition: setting the free outflet behind the foot section with a

To verify the precision of the calculation, we computed the drag coefficients of Slocum underwater glider [17] at different angle of attack as shown in table 2. The table 3 shows the verification of numerical simulation results of drag of AUV shell of Tianjin University. The

> *C*<sup>D</sup> (experiment)


2.3 6.3×105 0.25 0.268 7.20%

2.7 5.8×105 0.27 0.274 1.46%

number Drag Experiment(N) Drag

0.81 2.5×106 7.4 6.903 6.72%

1.4 4.4×106 20.3 19.92 1.87%

2.0 6.2×106 37.5 37.34 0.427%

An orthogonal experimental with four factors and three levels was conducted by keeping the main body size of the vehicle as constant. The four factors are wing chord, aspect ratio, backswept and distance between the center of wing root and the center of body. The

velocity is *v ms* = 0.5 / . The airfoil of the wings was NACA0010. The orthogonal

simulation experiments were done at the situation of angle of attack is 6

Table 3. Verification of numerical simulation results of drag of AUV shell

**3.1 Orthogonal experimental design and results analysis** 

*C*<sup>D</sup> (CFD)

CFD(N)

Error percentage

Error percentage

α

= ° and the

3. wall boundary condition: setting the vehicle surface as static non-slip wall.

Boundary conditions:

**2.3 Results verification** 

Angle of attack α(degree)

Velocity /(m/s)

distance of one and a half times of the length .

distance of double length of the vehicle.

4. pool wall boundary condition: non-slip wall.

error percentage of our calculation is less than 9.35%.

Table 2. Verification of numerical simulation results of *C*<sup>D</sup>

Reynolds

**3. Wing hydrodynamic design [18]**

**3.1.1 Orthogonal experimental design** 

experimental table was shown as table 4.

Reynolds number *Re*

$$
\mu\_\iota = \rho \mathbf{C}\_\mu \frac{k^2}{\mathcal{E}} \tag{6}
$$

Here , 0.0845 *C*μ = The RNG *k* − ε model was adopted due to the initial smaller Reynola number of boundary layer, and the more exact results can be gained by substituting the differential model into the RNG *k* − εmodel.
