# Performance Evaluation of a Novel Propulsion System for the Spherical Underwater Robot (SURIII)

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## Abstract

**:**

## 1. Introduction

## 2. Mechanical Design and Analysis

#### 2.1. Inspiration for Design

#### 2.2. Mechanical Design and Analysis of Propulsion System

#### 2.3. Structure Design of SURIII

#### 2.4. Motions of SURIII

## 3. Hydrodynamic Analysis

- SURIII is a spherical robot;
- The flow field is water;
- The temperature of flow field is 20 °C.

#### 3.1. Dynamic Model of SURIII

^{6×6}is the sum of system mass matrix and added mass matrix, $\dot{v}$ is the vector of generalized accelerations, C(v) $\in $ R

^{6}is the Coriolis and centripetal matrix. D(v) $\in $ R

^{6}is the damping matrix, G $\in $ R

^{6}is vector of restoring forces and moments, $\tau \in $ R

^{6}is the vector of generalized forces which input by control system and include the propulsive force and moment, $\tau $

_{wind}and $\tau $

_{wave}are vectors of forces generated by wind and wave. But effects of wind and wave usually occur in complicated marine environment, for our robot, these two factors can be neglectful. Hence, the dynamic equation can be simplified to Equation (2),

_{zz}is the resultant of inertia tensor. Also, M can be described as follows,

_{RB}+ M

_{A}

_{RB}is the mass of the robot, M

_{A}is the added mass. Moreover, C(v) is the sum of rigid body and hydrodynamic Coriolis matrix, so it can be expressed as,

_{1}and nonlinear damping term D

_{q}(v) and D(v) is give as,

_{1}+ D

_{q}(v)

#### 3.2. Related Parameters

_{RB}is received by weighing the robot in air. The SURIII is 6.9 kg, so the 3D model is:

_{A}is the mass of a fluid sphere, so its 3D model is:

_{1}= 1 × 10

^{−4}. The diag {u,v,w,r} is the velocity matrix of the SURIII, where u is the velocity of the surge motion, v is the velocity of the sway motion, w is the velocity of heave motion, r is the rotation velocity of the yaw motion. These two parameters are both very small, so D

_{1}v can be ignored. The Equation (7) may be expressed as:

_{q}(v)v equals to the resistance of the robot underwater,

_{d}is the drag of water, C

_{d}is the drag coefficient, $\rho $ is the density of the fluid, V is the relative speed between SURIII and fluid in different motions, A is the effective cross-sectional area of SURIII.

_{d}only associated with the Reynolds number [25] and its formula is:

_{e}is the Reynolds number, u is the velocity of the surge motion, D is the diameter of the robot,$\nu $ is the kinematic viscosity of the water and $\nu =1\times {10}^{-6}\text{}\mathrm{Pa}\xb7\mathrm{s}$ at the temperature of 20 °C. The experimental maximum velocity of surge motion is 0.15 m/s [11], the diameter of the robot is 0.4 m, so the R

_{e}equals to 6 × 10

^{4}and this value is more than 10

^{4}and less than 3 × 10

^{5}. The drag coefficient in surge motion can be selected from Table 2 [26,27]. If R

_{e}equals to 6 × 10

^{4}, C

_{d}is 0.4.

_{d}can be expressed as:

^{2}. The drag of water cannot be calculated in this case, thus the CFD simulation is conducted to get the estimation of it.

## 4. CFD Simulation

- Analysis of physical problems and pre-processor of the hydrodynamic model;
- Solver execution;
- Results of the post-processing.

#### 4.1. Pre-Processor of the CFD Simulation

- (1)
- The thruster has some complicated surfaces and their area are very small, so these surfaces are pre-processed as regular surfaces;
- (2)
- Some irregular solids have been changed to cylinder or cuboid shape;
- (3)
- Some parts such as screws and nuts have been omitted. And the simulation models are shown in Figure 12.

^{−4}in the solver control. Three hydrodynamic models (up, down and forward) are calculated for the CFD simulation.

#### 4.2. Results in the Post-Processing

^{2}. According to the Equation (14) and the drag coefficient can be calculated as 0.386. This drag coefficient has a 3.5% error compared to drag coefficient determined by Reynolds number for the sphere. It indicates that edges and gaps in the heave motion effect little.

^{2}. The drag coefficient can be calculated by Equation (14) and is equals to 0.394, it has a 1.5% error compared to the drag coefficient determined by Reynolds number which indicates the robot can be similarly considered as a sphere in surge motion.

## 5. Experiments and Results

- Step 1:
- Choose #2 and #4 vectored water-jet thrusters to work (Figure 11c);
- Step 2:
- Adjust the direction of propulsive forces as the Y direction;
- Step 3:
- Set the load cell to obtain 200 values and provide the power supply at 7.2 V;
- Step 4:
- Stop for 30 s and repeat the step 3 and 4 for 10 times.

- Step 1:
- Choose #2, #3 and #4 vectored water-jet thrusters to work (Figure 11a);
- Step 2:
- Adjust the direction of propulsive forces as Y direction;
- Step 3:
- Set the load cell to obtain 200 values and provide the power supply at 7.2 V;
- Step 4:
- Stop for 30 s and repeat the step 3 and 4 for 10 times.

- Step 1:
- Choose #1, #2, #3 and #4 vectored water-jet thrusters to work (Figure 11e);
- Step 2:
- Adjust the direction of propulsive forces as Z direction;
- Step 3:
- Set the load cell to obtain 200 values and provide the power supply at 7.2 V;
- Step 4:
- Stop for 30 s and repeat the step 3 and 4 for 10 times.

## 6. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 5.**The pre-process of the static analysis. (

**a**) Up motion; (

**b**) Forward motion; (

**c**) Down motion.

**Figure 6.**Deformation of the propulsion system. (

**a**) Deformation of the propulsion system for SURII; (

**b**) Deformation of the propulsion system for SURIII.

**Figure 15.**Down motion in heave. (

**a**) Pressure contour; (

**b**) Velocity vector; (

**c**) Velocity streamline.

**Figure 17.**Forward motion in surge. (

**a**) Pressure contour; (

**b**) Velocity vector; (

**c**) Velocity streamline.

**Figure 19.**The average propulsive force of different experimental cases. (

**a**) Case I; (

**b**) Case II; (

**c**) Case III.

DoF | Surge | Sway | Heave | Roll | Pitch | Yaw |
---|---|---|---|---|---|---|

Utilization ratio | 100% | 31% | 96% | 33% | 7% | 100% |

R_{e} | R_{e} < 10^{4} | 10^{4} < R_{e} < 3 × 10^{5} | 3 × 10^{5} < R_{e} < 10^{6} |
---|---|---|---|

C_{d} | 24/R_{e} + 6.48 × R_{e}^{−0.573} + 0.36 | 0.4 | 0.4 |

C_{d} | 30/R_{e} + 0.46 | 0.46 | 0.46 |

C_{d} | 24/R_{e} + (1 + 0.0654 R_{e}^{2/3})^{2/3} | 0.4 | 0.40 |

C_{d} | (0.325 + (0.124 + 24/R_{e}^{1/2})) | - | - |

C_{d} | (0.63 + 4.8 × R_{e}^{−0.5})^{2} | 0.4 | - |

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**MDPI and ACS Style**

Gu, S.; Guo, S. Performance Evaluation of a Novel Propulsion System for the Spherical Underwater Robot (SURIII). *Appl. Sci.* **2017**, *7*, 1196.
https://doi.org/10.3390/app7111196

**AMA Style**

Gu S, Guo S. Performance Evaluation of a Novel Propulsion System for the Spherical Underwater Robot (SURIII). *Applied Sciences*. 2017; 7(11):1196.
https://doi.org/10.3390/app7111196

**Chicago/Turabian Style**

Gu, Shuoxin, and Shuxiang Guo. 2017. "Performance Evaluation of a Novel Propulsion System for the Spherical Underwater Robot (SURIII)" *Applied Sciences* 7, no. 11: 1196.
https://doi.org/10.3390/app7111196