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Autonomous Underwater Vehicles (AUVs) are robots able to perform tasks without human intervention (remote operators). Research and development of this class of vehicles has growing, due to the excellent characteristics of the AUVs to operate in different situations. Therefore, this study aims to analyze turbulent single fluid flow over different geometric configurations of an AUV hull, in order to obtain test geometry that generates lower drag force, which reduces the energy consumption of the vehicle, thereby increasing their autonomy during operation. In the numerical analysis was used ANSYS-CFX® 11.0 software, which is a powerful tool for solving problems involving fluid mechanics. Results of the velocity (vectors and streamlines), pressure distribution and drag coefficient are showed and analyzed. Optimum hull geometry was found. Lastly, a relationship between the geometric parameters analyzed and the drag coefficient was obtained.

An Autonomous Underwater Vehicle, or AUV, is defined as a robot which travels underwater without physical communication with the land and without the necessity of the human operator. The AUVs are included in the group of Unmanned Underwater Vehicles, better known as UUVs.

During the last years, several AUVs have been developed and researches in the area are becoming more frequent, due to the extremely favorable characteristics that these robots have, like the ability to operate autonomously in hostile environments, such as unexplored areas, enemy water territories (in wartime), contaminated or deepwater areas, etc. All these features make the use of AUVs very interesting for military, scientific and industrial sectors.

Most existing AUVs use batteries as an energy source for the propulsion system. High value of drag force generated during the displacement of the robot increases the energy consumption of the system and therefore the AUV autonomy will be lowered, which is undesirable for any engineer.

Viscous fluid passing around axisymmetric body such a cylinder, sphere and spheroid has been reported in many studies [

Many authors uses CFD in submersible vehicle projects and optimizations due to the large amount of information obtained with reduced cost and time compared with experimental tests. Barros et al. [

Therefore this paper aims to predict fluid flow around the hull of an AUV. Here is created a numerical model analyzing some geometric configurations for the hull of an AUV, to obtain geometry that generates low drag and is suitable for application to this class of vehicles.

The hull of AUV is torpedo type (cylindrical body with a large ratio between the length and the diameter), due to its good features, which explains the widespread use of this type of hull by all major manufacturers of AUVs.

To model the profiles of the bow and stern of the vehicle it was used the Myring Equations. These theoretical equations describe curves for bow and stern of the torpedo bodies which generate the smallest possible drag coefficient [

・ Bow,

・ Stern,

where all parameters of these equations, with the exception of the parameter n, are geometric, and are shown in

In this paper the geometric parameters considered are shown in

The influence of the parameters n and θ in the drag of the hull was the focus of this paper. Profiles with n equal to 1, 2, 3 and 4, and θ equal to 15˚, 20˚, 25˚ and 30˚ were examined. The choice of these ranges of the bow and stern was based in previous works found in the literature [

The dimensions of the fluid domain were obtained after various computational tests until to reach an optimal

Parameter | Value (mm) |
---|---|

a | 215 |

b | 1155 |

c | 430 |

D | 200 |

size of the field, allied to good results with good accuracy and low computational time.

^{®} 11.0 software. A mesh was made for each variation in curves of the bow and stern. These non-structured meshes were obtained after various refinements, and have approximately 550,000 tetrahedral elements.

Much care must be taken when constructing numerical meshes aimed at solving problems of flow around immersed bodies. Here, many factors were taken into account [

where Re is Reynolds number of the flow, calculated as follows:

where ρ is the fluid density,

To investigate the single-phase flow of sea water around the hull of AUV, it was considered three-dimensional, permanent, incompressible and isothermal turbulent flow.

The general equations used in this work are:

・ Mass conservation equation,

where

・ Momentum conservation equation,

where ^{2}) and μ_{eff} is the effective viscosity, calculated by:

where

It is necessary to add in the model new equations governing the phenomenon of turbulence that is present in the flow. The turbulence consists of fluctuations in the flow field in time and space (time-dependent velocity and pressure fields). It is a complex process and can have a significant effect on the flow characteristics. Turbulence occurs when the inertial forces acting on the fluid becomes significantly higher than the viscous forces and is characterized by a high Reynolds Number of the flow. Turbulence can also be caused by surface roughness, which induces secondary flow (i.e. vortices) [

The turbulence model adopted in this work is the Shear Stress Transport model (SST model), which is based on the turbulence k-ω model. This model was used because of its good treatment of external flow with high Reynolds numbers. It was considered flow fully turbulent around the AUV.

The SST model introduces two new variables in the problem, which are k, which is the turbulent kinetic energy, and ω, which is the turbulent frequency. These variables are calculated by:

・ Turbulent kinetic energy equation,

where P_{k} is the turbulence production, C_{k}_{1} = 2.000 and C_{k}_{2} = 0.009.

・ Turbulence frequency equation,

where C_{ω}_{1} = 2.000, C_{ω}_{2} = 0.556 and C_{ω}_{3} = 0.075. In the SST model the parameters μ_{t}, p' and P_{k} are given as follows:

where p_{d} is the dynamic pressure, calculated by the equation

Total pressure, p_{t}, is calculated by:

where p_{s} is the static pressure.

According to Warsi [

The friction drag is due to the boundary layer surface shear stress, while pressure drag is due to pressure difference in the flow direction resulting from formation of the wake in the downstream region.

The drag on a body is usually expressed in terms of a dimensionless drag coefficient. The total drag coefficient, C_{d}, is calculated by:

where C_{df} is the friction drag coefficient, C_{dp} is the pressure drag coefficient (form drag), F_{df} is the friction drag force, F_{dp} is the pressure drag force, U_{*} is the free stream fluid velocity and A_{f} is the frontal area of AUV. F_{df} and F_{dp} are calculated by:

where τ is the shear stress, A is the AUV superficial area and î is the unitary vector in parallel flow direction.

The fluid adopted in all simulations was sea water with 35 g/L of salinity, on the depth of 1000 m (temperature of 15˚C and static pressure 10.2 MPa). The properties of the fluid are showed in ^{6}.

To validate the methodology for constructing the numerical mesh, as well as the mathematical model used in this

Condition | Value | |
---|---|---|

Inlet | Prescribed velocity | 2.83 m/s (5.5 knot) |

Wall | Prescribed pressure^{c} | 10.2 MPa |

AUV surface^{a} | Prescribed velocity | 0 m/s |

Outlet^{b} | Prescribed pressure^{c} | 10.2 MPa |

Symmetry Plane | Symmetry | - |

a. No slip and smooth wall; b. Opening condition; c. Pressure on the depth of 1000 m.

Fluid | ρ [kg/m^{3}] | μ [mPa.s] |
---|---|---|

Sea water | 1027 | 1.25 |

Characteristic | Consideration |
---|---|

Flow regime | Permanent |

Convergence criterion | Variation in C_{d} less than 10^{−5} |

Advection scheme | High resolution |

Interpolation scheme for pressure | Trilinear |

Interpolation scheme for velocity | Trilinear |

study, we analyzed the axial flow on two well-known geometries: a cylinder and ellipsoid of revolution (

The simulations for validation are subject to the same considerations, boundary conditions and mathematical model described in the previous sections.

The drag coefficient, C_{d}, as well as corresponding friction drag coefficient, C_{df}, and pressure drag coefficient, C_{dp}, obtained numerically will be compared with those obtained experimentally.

The following is detailed for geometry was conducted to evaluate how the experimental coefficient of drag:

a) Cylinder: Length L = 1800 mm and diameter D = 200 mm. Reference [_{d}, C_{df} and C_{dp}, obtained experimentally for Re ≥ 10^{4}, as a function of ratio L/D. For L/D = 9, C_{d} ≈ 0.85, where approximately 90% is referent of C_{dp};

b) Ellipsoid: Length of major axis L' = 1800 mm and length of minor axis L² = 200 mm. Reference [_{d} (Equation (18)), C_{df} and C_{dp}, obtained experimentally for Re ≥ 10^{5}, as a function of ratio L'/L''. For the analyzed case, C_{d} ≈ 0.117, where approximately 100% is referent of C_{df}.

Figures 9-12 illustrate, respectively, the velocity field around the cylinder (streamlines), the velocity vector field around the cylinder, the velocity field around the ellipsoid (streamlines) and the velocity vector field around the ellipsoid by vectors, in the longitudinal symmetry plane for the analyzed cases. Because the shape of cylinder is very different of ellipsoid, in the flow pattern more intense turbulence zones are found, specially in the wake zone. In cylinder case is visible more intense recirculation zones in the flow behind the cylinder (wake region), in comparison with the ellipsoid, thus, increasing C_{dp} factor. For this reason C_{d} for cylinder is dramatically higher than the ellipsoid.

For analyze the drag of AUV hull by varying the shape of the bow (

_{ave}, and the difference of pressure between the point x = 0 and the point x = 1.8 m in longitudinal axis of AUV (

It was found that with increasing the parameter n we have an increase in the total drag, C_{d}, and particularly in

Results | C_{df}/C_{d} | C_{dp}/C_{d} | C_{d} |
---|---|---|---|

Experimental^{a} | 10% | 90% | 0.85 |

Numerical | 5% | 95% | 0.91 |

a. Reference [

Results | C_{df}/C_{d} | C_{dp}/C_{d} | C_{d} |
---|---|---|---|

Experimental^{a} | 100% | 0% | 0.117 |

Numerical | 91% | 9% | 0.103 |

a. Reference [

n | C_{df}/C_{d} [-] | C_{dp}/C_{d} [-] | τ_{ave} [Pa] | Δp [Pa] | C_{d} [-] |
---|---|---|---|---|---|

1 | 86.2% | 13.8% | 13.7356 | 3356 | 0.1227 |

2 | 86.0% | 14.0% | 13.5922 | 3486 | 0.1238 |

3 | 85.1% | 14.9% | 13.5411 | 3486 | 0.1254 |

4 | 83.6% | 16.4% | 13.4463 | 3449 | 0.1271 |

the portion corresponding to the drag pressure, C_{dp}. However, it is seen that these parameters does not vary much over the range computed. In all cases, the predominant fraction of the drag is due to friction, C_{df}, accounting for over 80% of total drag. It is verified that the increasing the parameter n the parameters τ_{ave} increase and Δp oscillate. Based on data obtained was defined the profile with n = 2 as ideal shape for the bow. The profile with n = 2 is the most efficient because it gives to the hull a lower drag (only 0.9% above the drag of the hull profile when n = 1) and a good internal volume of the bow (25.0% above of the hull profile when n = 1), which would facilitate the accommodation of all internal systems of the vehicle.

With the bow profile with parameter n = 2 fixed, were simulated cases changing the parameter θ which alters the stern shape (

It is found that the best performance profile is that when parameter θ = 20˚, giving to the hull the lowest drag coefficient, which is 2.5% less than the hull with the worst profile analyzed in this section, which is the profile with θ = 30˚. Is verified that the increasing the parameter θ the parameters τ_{ave} increase and Δp decrease.

The ideal geometry among the analyzed cases is shown in

Based on the simulations results it was obtained a correlation between the parameters n and θ with C_{d} (Equation (19)). This equation were obtained by the method of the least squares, with determination coefficient of 0.99694, and valid for the ranges 1 ≤ n [-] ≤ 4 and 15 ≤ θ [degree] ≤ 30.

The optimal design gives the hull a drag coefficient of 0.1230, which is very close to the drag coefficient of the ellipsoid (just 5.1% upper), with the advantages of easier construction and approximately 10.3% more in volume.

Θ | C_{df}/C_{d} [-] | C_{dp}/C_{d} [-] | τ_{ave} [Pa] | Δp [Pa] | C_{d} [-] |
---|---|---|---|---|---|

15° | 83.6% | 16.4% | 12.8694 | 3621 | 0.1235 |

20° | 84.2% | 15.8% | 13.3103 | 3544 | 0.1230 |

25° | 86.0% | 14.0% | 13.5922 | 3486 | 0.1238 |

30° | 83.6% | 16.4% | 13.2253 | 3454 | 0.1262 |

_{s}, in the total pressure, due the big depth (1000 m) in that the study was performed.

In this paper the hydrodynamic single-phase flow around the AUV hull is discussed. The study is related to sea water flow in the turbulent regime by using the ANSYS-CFX^{®} 11.0 commercial software. The simulations revealed the good mathematical treatment used, with good precision between numerical and experimental results. It reached an optimized design for AUV hull that has a drag coefficient of 0.1230, which is very close to the drag coefficient of the ellipsoid, with 10.3% more volume, and is about 7 times smaller than the cylinder, proving the efficiency of the use of bow and stern smoothed profiles.

The authors would like to express their thanks to Brazilian Research Agencies CNPq, CAPES and FINEP and ARMTEC Technology in Robotics for supporting this work, and are also grateful to the authors of the references

in this paper that helped in the improvement of quality