# Design and Construction of a Modular Pump-Jet Thruster for Autonomous Surface Vehicle Operations in Extremely Shallow Water

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## Abstract

**:**

## 1. Introduction

## 2. PJM Application

#### The Pump-Jet

## 3. PJM Design

#### 3.1. Pump Design

#### 3.1.1. Geometric Data

#### 3.1.2. Propulsion Data

#### 3.1.3. Pump Head

#### 3.1.4. Impeller Design

- Meridian velocities at inlet and outlet
- Impeller outside diameters
- Impeller vane inlet and outlet angles
- Velocity triangles to be drawn for several streamlines (minimum of three streamlines)

- Selection of the inlet and outlet diameter of the pump impeller and the various geometric data
- Meridian flow analysis resulting in the surface of revolution
- Calculation of blade angles from hub to tip based on free vortex theory
- Geometrical transformation of each surface of revolution into a plane with flow angles
- Reverse transformation of cascade geometry and flow data to the back-to-back intersections on the surfaces of revolution

- The vane discharge angle ${\beta}_{2}$ was the most important design element since all theoretical characteristics were determined by the vane angle alone. All design constants depended on ${\beta}_{2}$. This value was fundamental for determining pump design since normal head and capacity increase when ${\beta}_{2}$ increases. This angle should be between 15° and 35° in order not to affect efficiency appreciably.
- ${K}_{u}={u}_{2}/\sqrt{2\phantom{\rule{0.166667em}{0ex}}g\phantom{\rule{0.166667em}{0ex}}{H}_{p}}$ is a speed constant used for calculating impeller diameters when RPM and pump head ${H}_{p}$ are defined as in our case. Smaller pumps require a higher value of ${K}_{u}$ to compensate losses.
- ${D}_{m}^{2}=({D}_{2o}^{2}+{D}_{2i}^{2})/2$ is the mean effective diameter, which, for mixed flow pumps, divides the flow throughout the impeller into two equal parts.
- The capacity constant ${K}_{m2}={c}_{m2}/\sqrt{2\phantom{\rule{0.166667em}{0ex}}g\phantom{\rule{0.166667em}{0ex}}H}$ value is important since it is obtained from experimental data. Differences from these data may lead to leakages and losses.
- Entrance velocity ${c}_{m1}=Q/A1$ is supposed to be the velocity just ahead of the vanes. This depends on ${K}_{m1}={c}_{m1}/\sqrt{2\phantom{\rule{0.166667em}{0ex}}g\phantom{\rule{0.166667em}{0ex}}H}$. Usually, depending on the impeller approach, ${c}_{m1}$ is equal to the velocity through the impeller eye or slightly lower.
- The minimum number of vanes ${z}_{blades}$ required is six for low ${\beta}_{2}$ and large pumps. Smaller impellers and impellers with smaller head require fewer vanes, but for our experiment, we chose three different numbers of vanes: 8, 9, and 10, to lower the slip factor. The number of vanes depends on ${\beta}_{2}$. The lower ${\beta}_{2}$, the lower the number of vanes.

#### 3.1.5. Pump Geometric Parameters

#### 3.1.6. Velocity Triangles

#### 3.1.7. Pump 3D Drawing

#### 3.1.8. Casing Design and Drawing

#### 3.2. Motors’ Layout and Choice

#### 3.3. Hardware Control System and Power Supply

## 4. PJM Construction and 3D Printing

## 5. Experimental Tests and Calibration

#### 5.1. Test Results

#### 5.2. Bollard Pull Tests

#### 5.3. Bollard Pull Tests at Different Steering Angles

## 6. Conclusions and Future Developments

## Author Contributions

## Acknowledgments

## Conflicts of Interest

## Nomenclature

L | Vehicle length (m) |

B | Vehicle breadth (m) |

d | Vehicle draft (m) |

T | Vehicle immersion (m) |

h | Water depth (m) |

$Cb$ | Block coefficient: $\frac{\nabla}{L\ast B\ast d}$ |

g | Gravity acceleration: 9.81 [m/s${}^{2}$] |

${\rho}_{w}$ | Water density: 1025 [kg/m${}^{3}$] |

${\rho}_{air}$ | Air density: 1.226 [kg/m${}^{3}$] |

${D}_{p}$ | Diameter of the PJM (m) |

${D}_{o}$ | Outlet diameter of the impeller (m) |

${h}_{o}$ | Height of the impeller outlet (m) |

${D}_{i}$ | Inlet diameter of the impeller (m) |

${A}_{i}$ | Impeller inlet area (m${}^{2}$) |

${A}_{o}$ | Impeller outlet area (m${}^{2}$) |

${A}_{d}$ | Nozzle discharge area (m${}^{2}$) |

${r}_{i}$ | Impeller radius (m) |

n | Main motor speed (RPM) |

T | pump-jet thrust (N) |

${T}_{\alpha}$ | pump-jet thrust at $\alpha $ angle (N) |

U | ASV speed (m/s) |

${V}_{o}$ | pump-jet jet outlet speed (m/s) |

${V}_{i}$ | pump-jet jet inlet speed (m/s) |

${\alpha}_{out}$ | Outlet angle with respect to the bottom (deg) |

${m}_{f}$ | Mass flow rate of the jet (kg/s) |

${Q}_{o}$ | Volumetric flow rate of the jet (kg/s) |

${h}_{loss}$ | Losses of pump head (m) |

${h}_{man}$ | Losses due to manufacturing imprecision (m) |

${h}_{n}$ | Losses due to nozzle (m) |

${h}_{i}$ | Losses due to intake (m) |

${p}_{i}$ | Inlet pressure (Pa) |

${p}_{o}$ | Outlet pressure (Pa) |

${H}_{p}$ | Pump head (m) |

${N}_{s}$ | Specific pump speed |

${z}_{blades}$ | Number of vanes |

${\beta}_{2}$ | Vane discharge angle (deg) |

${D}_{m}$ | $\sqrt{{D}_{2o}^{2}+{D}_{2i}^{2}}/2$ is the mean effective diameter (m) |

${c}_{m1}$ | Entrance velocity (m/s) |

${D}_{1t}$ | Tip diameter of impeller (m) |

${R}_{1t}$ | Tip radius of impeller (m) |

${D}_{1m}$ | Mean diameter of the blade (m) |

${R}_{1m}$ | Mean radius of the blade (m) |

${D}_{1r}$ | Root diameter (m) |

${D}_{1r}$ | Root radius (m) |

${D}_{2t}$ | Tip diameter at outlet (m) |

${R}_{2t}$ | Tip radius at outlet (m) |

${D}_{2m}$ | Mean diameter at outlet (m) |

${R}_{2m}$ | Mean radius at outlet (m) |

${D}_{2r}$ | Root diameter at outlet (m) |

${D}_{2r}$ | Root radius at outlet(m) |

${l}_{i}$ | Blade height at inlet (m) |

${l}_{o}$ | Blade height at outlet (m) |

${A}_{1m}$ | Inlet area (m${}^{2}$) |

${c}_{m1}$ | Inlet area (m${}^{2}$) |

${w}_{u1m}$ | Tangential resulting velocity at inlet (m/s) |

${c}_{u1}$ | Axial component ad inlet (m/s) |

${u}_{1m}$ | Radial velocity at inlet (m/s) |

${w}_{1m}$ | Resulting velocity at inlet (m/s) |

${A}_{2m}$ | Outlet area (m${}^{2}$) |

${c}_{m2}$ | Meridian velocity at outlet (m/s) |

${u}_{2m}$ | Radial velocity (m/s) |

${c}_{u2m}$ | Tangential component of velocity at outlet (m/s) |

${w}_{u2m}$ | Tangential resulting velocity at outlet (m/s) |

${c}_{2m}$ | Axial component ad outlet (m/s) |

${w}_{2m}$ | Resulting velocity at outlet (m/s) |

${\beta}_{1m}$ | Vane entrance angle (deg) |

${\beta}_{2m}$ | Vane outlet angle (deg) |

${P}_{Pump}$ | Pump power (W) |

$\alpha $ | pump-jet steering actuation angle (deg) |

${\alpha}_{0}$ | pump-jet steering actuation initial angle (deg) |

${\alpha}_{0}^{\prime}$ | pump-jet actual steering actuation initial angle (deg) |

${k}_{u}$ | Speed constant |

${\psi}_{p}$ | $1/2\phantom{\rule{0.166667em}{0ex}}K{u}^{2}$ head coefficient speed constant |

$\sigma $ | Slip factor |

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**Figure 12.**Inlet, outlet, and intermediate section meridian triangles for the design of the impeller.

Thrust T | 12.25 | (N) |

Pump Nominal Speed n | 1185 | (RPM) |

Pump Head ${H}_{p}$ | 1.70 | (m) |

Number of Impeller Blades ${z}_{blades}$ | 9 | |

Metric Specific Speed ${N}_{s}$ | 47 | |

US Units Specific Speed ${N}_{{s}_{gpm}}$ | 2430 | |

Speed Constant ${K}_{u}$ | 0.88 | |

Head Coefficient ${\psi}_{p}$ | 0.39 | |

Diameters Ratio $Di/Dm$ | 0.65 | |

Capacity Constant 1 ${K}_{m1}\phantom{\rule{0.166667em}{0ex}}10$ | 3.02 | |

Capacity Constant 2 ${K}_{m2}\phantom{\rule{0.166667em}{0ex}}10$ | 1.22 | |

Vane Entrance Angle ${\beta}_{1m}$ | 39.5 | (deg) |

Vane Outlet Angle ${\beta}_{2m}$ | 21.3 | (deg) |

Parameters | Pump Motor | Azimuth Motor | |
---|---|---|---|

Type | Maxon Ec-4Pole | Faulhaber 2232-BX4 | |

Nominal power | 123 | 13 | (W) |

Nominal voltage | 36 | 24 | (V) |

Nominal speed | 16,700 | 4840 | (RPM) |

Nominal torque (max. cont) | 63.1 | 14.6 | (mNm) |

Nominal current (max. cont) | 3.43 | 0.54 | (mNm) |

Stall torque | 1130 | 61.7 | (mNm) |

Max. efficiency | 89 | 74 | [%] |

Reduction Ratio | 14 | 59 | : 1 |

Max. continuous torque | 2.4 | 9 | (Nm) |

Max. efficiency | 89 | 74 | % |

Total weight | 239 | 140 | (g) |

Nominal reduced speed | 1193 | 82 | (RPM) |

Nominal reduced torque | 883 | 861 | (mNm) |

${\mathit{D}}_{\mathit{p}}$ | ${\mathit{D}}_{\mathit{o}}$ | Configuration | Nozzle Configuration |
---|---|---|---|

110 | 65 | ${z}_{blades=8}$ Small Nozzle Opening | Symmetrical Outlet |

110 | 77 | ${z}_{blades=8}$ Large Nozzle Opening | Symmetrical Outlet |

120 | 77 | ${z}_{blades=8}$ Small Nozzle Opening | Symmetrical Outlet |

120 | 77 | ${z}_{blades=8}$ Large Nozzle Opening | Symmetrical Outlet |

120 | 77 | ${z}_{blades=8}$ Varying Lateral Outlet Opening | Asymmetrical Outlet |

120 | 77 | ${z}_{blades=8}$ Varying Central Outlet Opening | Asymmetrical Outlet |

120 | 77 | ${z}_{blades=8}$ Varying Lateral Outlet Opening | Asymmetrical Outlet |

120 | 77 | ${z}_{blades=8}$ Varying Central Outlet Opening | Asymmetrical Outlet |

120 | 77 | ${z}_{blades=8}$ Varying Central Outlet Opening | Asymmetrical Outlet |

120 | 77 | ${z}_{blades=8}$ with Flow Straightener | Asymmetrical Outlet |

120 | 77 | Varying ${z}_{blades}:8\phantom{\rule{0.166667em}{0ex}},9\phantom{\rule{0.166667em}{0ex}},10$ | Asymmetrical Outlet |

120 | 80 | ${z}_{blades=9}$ | Asymmetrical Outlet |

120 | 80 | ${z}_{blades=9}$ at Various Angles | Asymmetrical Outlet |

Nominal Thrust | (N) | 12.3 |

Nominal Power Consumption | (W) | 95 |

Maximum Thrust | (N) | 14.5 |

Maximum Power Consumption | (W) | 125 |

Steerable Angle | (deg) | 360 Continuous Rotation |

Absolute Position Precision | (deg) | ≤0.01 |

Nominal Draft | (mm) | 100 |

Minimum Draft | (mm) | 35 |

Operating speed | (m/s) | 1.5 |

Diameter | (mm) | 120 |

Height | (mm) | 300 |

Weight | (kg) | 1.9 |

Operating Voltage | (V) | 36–24 |

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Odetti, A.; Altosole, M.; Bruzzone, G.; Caccia, M.; Viviani, M. Design and Construction of a Modular Pump-Jet Thruster for Autonomous Surface Vehicle Operations in Extremely Shallow Water. *J. Mar. Sci. Eng.* **2019**, *7*, 222.
https://doi.org/10.3390/jmse7070222

**AMA Style**

Odetti A, Altosole M, Bruzzone G, Caccia M, Viviani M. Design and Construction of a Modular Pump-Jet Thruster for Autonomous Surface Vehicle Operations in Extremely Shallow Water. *Journal of Marine Science and Engineering*. 2019; 7(7):222.
https://doi.org/10.3390/jmse7070222

**Chicago/Turabian Style**

Odetti, Angelo, Marco Altosole, Gabriele Bruzzone, Massimo Caccia, and Michele Viviani. 2019. "Design and Construction of a Modular Pump-Jet Thruster for Autonomous Surface Vehicle Operations in Extremely Shallow Water" *Journal of Marine Science and Engineering* 7, no. 7: 222.
https://doi.org/10.3390/jmse7070222