# Numerical Analysis of Azimuth Propulsor Performance in Seaways: Influence of Oblique Inflow and Free Surface

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Propulsor Model and Simulated Conditions

## 3. Numerical Method

## 4. Propulsor Operation in Oblique Flow Conditions

^{2}× D

^{4}) and (ρ × n

^{2}× D

^{5}), respectively. When post-processing the simulation results, the force and moment coefficients are time-averaged over the last 20 propeller revolutions.

#### 4.1. Integral Forces and Moments on the Propulsor

_{D}for the duct flow at J = 0.6, where the aforementioned flow transition effect becomes appreciable, results in the following figures: Re

_{D}= 1.8 × 10

^{5}for the outer duct surface, and Re

_{D}= 3.0 × 10

^{5}for the outer duct surface. Flow transition affects the extent of flow separation on the duct, and also the flow pattern over the duct trailing edge. It is mainly the trailing edge flow that influences the flow velocity through the duct and results in changes in propeller thrust and torque. In most cases, for conventional shaft ducted propellers, it has been observed that transition leads to a somewhat larger expansion rates of propeller slipstream, and hence lower velocity through the propeller compared to fully turbulent flow conditions [7]. It leads to an increase of propeller thrust and torque as observed in Figure 7 and Figure 8, where the results of calculation using the transition model show higher values of KTP and KQP at high advance coefficients. At lower advance coefficients (J < 0.6), in straight flow, propeller torque is very well predicted, while at higher advance coefficients (J > 0.6), KQP is under-predicted, as it can be seen from Figure 8. Since propeller torque is not influenced by the gap flow effect, one can conclude that in the range of loading conditions J ≤ 0.6, the influence of flow transition is minor, and the main reason for the differences in KTP should probably be attributed to uncertainties associated with the gap flow in both the physical and numerical models. In oblique flow, the flow around the gap is no longer axisymmetric, and consequently, the contributions of gap walls to pod resistance and propeller thrust change. In such cases, the gap flow is also strongly influenced by the configurations of hub and pod in the vicinity of the gap, as well as by the vortices shed from the pod housing. Therefore, in the case of oblique flow, even small differences in flow pattern between the simulations and tests may result in large differences in contributions to thrust from the gap walls.

#### 4.2. Single Blade Loads

## 5. Propulsor Operation in the Presence of Free Surface

#### 5.1. Implications of Numerical Simulation in Multiphase Flow

#### 5.2. Propulsor Ventilation at Free Sailing Conditions

_{0}, KQP

_{0}and KTD

_{0}, which refer to the corresponding values obtained from the solution without the influence of free surface at J = 0.6. Both the propeller thrust and torque remain almost unchanged until H/Dp = 1.3, and then they decrease gradually as the propulsor gets closer to the water surface. The reduction in loading becomes appreciable at H/Dp = 0.8, where both the KTP and KQP are reduced to about 3% of their values in unbounded flow. Under the above conditions, and until H/Dp = 0.7, the propulsor is still free of ventilation.

#### 5.3. Propulsor Ventilation at Trawling and Bollard Conditions

_{0}and KTD

_{0}, which refer to the corresponding values obtained from the solution in unbounded flow.

## 6. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 2.**Definitions of forces and moments and sign conventions: (

**a**) propulsor loads; (

**b**) blade loads.

**Figure 3.**Rotating propeller region and sliding mesh interfaces: (

**a**) propeller region; (

**b**) sliding interfaces.

**Figure 4.**Details of computation mesh: (

**a**) surface mesh on propeller and duct; (

**b**) volume mesh around propulsor and free surface.

**Figure 5.**Measured (red) and computed (blue) propeller thrust, KTP, and propeller torque, KQP, at different heading angles and loading conditions.

**Figure 6.**Measured (red) and computed (blue) duct thrust, KTD, and total unit thrust, KTTOT, at different heading angles and loading conditions.

**Figure 7.**Measured (red) and computed (blue—fully turbulent model, green—transition model) propeller thrust, KTP, at the two propeller pitch settings, P/D, and different loading conditions.

**Figure 8.**Measured (red) and computed (blue—fully turbulent model, green—transition model) propeller torque, KQP, at the two propeller pitch settings, P/D, and different loading conditions.

**Figure 9.**Measured (red) and computed (blue) duct side force, KSD, and total unit side force, KSTOT, at different heading angles and loading condition of J = 0.6.

**Figure 10.**Measured (red) and computed (blue) duct side force, KSD, and total unit side force, KSTOT, at different heading angles and loading conditions of J = 0.3 and J = 0.0.

**Figure 11.**Measured (red) and computed (blue) steering moment, KMY, excluding duct contribution, at different heading angles and loading conditions.

**Figure 12.**Computed steering moment on the duct, KMYD, at different heading angles and loading conditions.

**Figure 13.**Power spectral density of duct thrust, KTD, at J = 0.6, for the positive and negative heading angles of 35 degrees.

**Figure 14.**Examples of flow pattern around propulsor at large heading angles, J = 0.6: (

**a**) −35 degrees; (

**b**) −60 degrees. View from top.

**Figure 15.**Measured and computed time histories of blade loads at J = 0.6 for the heading angle +35°: (

**a**) blade thrust, KTb; (

**b**) blade bending moment, KMZb.

**Figure 16.**Measured and computed time histories of blade loads at J = 0.6 for the heading angle −35°: (

**a**) blade thrust, KTb; (

**b**) blade bending moment, KMZb.

**Figure 17.**Computed velocity fields on the control plane upstream of the propeller at J = 0.6 for positive and negative heading angles: (

**a**) +35 degrees; (

**b**) −35 degrees. View from downstream.

**Figure 18.**Contours of volume fraction at different solution time instances for propulsor submergence H/Dp = 1.0, at J = 0.6.

**Figure 19.**Variations in propeller thrust, KTP, and propeller torque, KQP, with propulsor submergence, H/Dp, at J = 0.6. (KTP

_{0}, KQP

_{0}refer to the corresponding values in unbounded flow).

**Figure 20.**Variations in duct thrust, KTD, with propulsor submergence, H/Dp, at J = 0.6. (KTD

_{0}refers to the corresponding value in unbounded flow).

**Figure 22.**Contours of volume fraction under fully ventilated conditions at the submergence values of H/Dp = 0.6 and 0.5, J = 0.6.

**Figure 23.**Computed time histories of single blade thrust, KTb, for different magnitudes of submergence, H/Dp, at J = 0.6.

**Figure 25.**Ventilation inception vortex at the conditions of heavy propulsor loading: (

**a**) H/Dp = 0.9, at J = 0.2 (trawling); (

**b**) H/Dp = 0.8, at J = 0.0 (bollard).

**Figure 26.**Variations in propeller thrust, KTP, with propulsor submergence, H/Dp, at J = 0.2 and J = 0.0. (KTP

_{0}refers to the corresponding value in unbounded flow).

**Figure 27.**Variations in propeller thrust, KTD, with propulsor submergence, H/Dp, at J = 0.2 and J = 0.0. (KTD

_{0}refers to the corresponding value in unbounded flow).

**Figure 28.**Contours of volume fraction under fully ventilated conditions at low speed operation conditions: (

**a**) J = 0.2, H/Dp = 0.8; (

**b**) J = 0.0, H/Dp = 0.7.

**Figure 29.**Computed time histories of single blade thrust, KTb, for different magnitudes of submergence, H/Dp, at J = 0.2.

Thruster Particular | Value |
---|---|

Vertical distance from propeller centre to upper end of strut (mm) | 342 |

Gondola length (mm) | 181 |

Strut chord length (mm) | 86 |

Propeller P-1374 direction of rotation | Right-handed |

Propeller diameter, Dp (mm) | 250 |

Hub diameter (mm) | 60 |

Design pitch ratio, P_{0.7}/Dp | 1.1 |

Blade skew (degrees) | 25 |

Expanded blade area ratio | 0.6 |

Number of blades | 4 |

Duct type | 19A |

Duct length (mm) | 125 |

Duct inner diameter (mm) | 252.78 |

Blade tip clearance, tc/Dp | 0.0056 |

Duct max. outer diameter (mm) | 303.96 |

Duct leading edge radius (mm) | 2.78 |

Duct trailing edge radius (mm) | 1.39 |

Advance Coefficient, J ^{1} | Heading Angle (°) |
---|---|

0.6 (free sailing) | ±60, ±35, ±15, 0 |

0.3 (trawling) | ±35, ±15, 0 |

0 (bollard) | 0 |

^{1}J = V/(n × Dp).

Advance Coefficient, J | Heading Angle (°) | Submergence, H/Dp ^{1} |
---|---|---|

0.6 (free sailing) | 0 | 2, 1.7, 1.5, 1.3, 1.0, 0.9, 0.8, 0.6, 0.5 |

0.2 (trawling) | 0 | 1.5, 1.0, 0.9, 0.8, 0.7 |

0 (bollard) | 0 | 1.0, 0.9, 0.8, 0.7 |

^{1}H is the vertical distance from propeller center to water surface level; Dp is the propeller diameter.

−35° | −15° | 0° | 15° | 35° | ||||||
---|---|---|---|---|---|---|---|---|---|---|

Quantity | CFD | EXP | CFD | EXP | CFD | EXP | CFD | EXP | CFD | EXP |

KTb | 0.055 | 0.049 | 0.058 | 0.056 | 0.062 | 0.059 | 0.061 | 0.063 | 0.071 | 0.071 |

σ (KTb) % | 36.4 | 38.9 | 16.8 | 17.5 | 5.8 | 6.3 | 11.6 | 13.1 | 22.1 | 22.0 |

10 KQb | 0.071 | 0.086 | 0.075 | 0.089 | 0.079 | 0.098 | 0.078 | 0.095 | 0.087 | 0.087 |

σ (KQb) % | 24.8 | 23.5 | 12.3 | 12.1 | 4.2 | 4.8 | 8.0 | 8.5 | 15.1 | 19.0 |

10 KMYb | 0.021 | 0.016 | 0.021 | 0.015 | 0.019 | 0.008 | 0.020 | 0.011 | 0.016 | 0.012 |

σ (KMYb) % | 126.3 | 194.4 | 51.2 | 95.7 | 20.6 | 64.9 | 53.6 | 100.1 | 157.6 | 247.0 |

10 KMZb | −0.130 | −0.117 | −0.136 | −0.152 | −0.143 | −0.171 | −0.140 | −0.170 | −0.158 | −0.180 |

σ (KMZb) % | 26.5 | 35.4 | 13.4 | 15.6 | 4.6 | 4.6 | 8.5 | 10.0 | 15.7 | 17.5 |

−35° | −15° | 0° | 15° | 35° | ||||||
---|---|---|---|---|---|---|---|---|---|---|

Quantity | CFD | EXP | CFD | EXP | CFD | EXP | CFD | EXP | CFD | EXP |

KTb | 0.071 | 0.070 | 0.074 | 0.075 | 0.076 | 0.071 | 0.077 | 0.078 | 0.081 | 0.079 |

σ (KTb) % | 11.9 | 12.0 | 7.1 | 8.0 | 4.0 | 4.7 | 5.3 | 5.6 | 8.1 | 10.8 |

10 KQb | 0.087 | 0.099 | 0.091 | 0.096 | 0.092 | 0.112 | 0.093 | 0.108 | 0.097 | 0.101 |

σ (KQb) % | 8.3 | 9.8 | 5.4 | 6.9 | 3.0 | 3.6 | 3.7 | 4.9 | 5.3 | 9.3 |

10 KMYb | 0.014 | 0.008 | 0.012 | 0.001 | 0.012 | −0.006 | 0.011 | −0.004 | 0.010 | 0.000 |

σ (KMYb) % | 80.8 | 165.2 | 52.1 | 689.6 | 29.2 | 48.4 | 52.4 | 106.2 | 105.9 | 3776.1 |

10 KMZb | −0.167 | −0.176 | −0.173 | −0.198 | −0.175 | −0.205 | −0.177 | −0.206 | −0.185 | −0.222 |

σ (KMZb) % | 8.6 | 9.5 | 5.8 | 6.4 | 3.4 | 3.5 | 4.1 | 5.3 | 5.8 | 8.4 |

Quantity | w/o FS | H/Dp = 2 | H/Dp = 1.5 | H/Dp = 1 | H/Dp = 0.8 | H/Dp = 0.7 | H/Dp = 0.6 | H/Dp = 0.5 |
---|---|---|---|---|---|---|---|---|

KTb | 0.062 | 0.062 | 0.062 | 0.061 | 0.060 | 0.059 | 0.058 | 0.056 |

σ (KTb) % | 5.8 | 5.5 | 5.7 | 5.4 | 4.5 | 3.6 | 15.0 | 35.4 |

10 KQb | 0.079 | 0.078 | 0.079 | 0.078 | 0.077 | 0.076 | 0.073 | 0.067 |

σ (KQb) % | 4.1 | 4.2 | 4.6 | 4.3 | 3.7 | 3.1 | 14.0 | 34.7 |

10 KMYb | 0.020 | 0.020 | 0.020 | 0.021 | 0.021 | 0.022 | 0.011 | 0.000 |

σ (KMYb) % | 19.8 | 20.2 | 19.9 | 19.6 | 17.5 | 14.5 | 85.5 | 3481.4 |

10 KMZb | −0.143 | −0.142 | −0.143 | −0.141 | −0.139 | −0.137 | −0.130 | −0.120 |

σ (KMZb) % | 4.5 | 4.0 | 4.5 | 4.0 | 3.0 | 2.4 | 17.0 | 40.1 |

Quantity | w/o FS | H/Dp = 1.5 | H/Dp = 1 | H/Dp = 0.9 | H/Dp = 0.8 | H/Dp = 0.7 |
---|---|---|---|---|---|---|

KTb | 0.079 | 0.077 | 0.078 | 0.078 | 0.077 | 0.069 |

σ (KTb) % | 3.6 | 3.3 | 3.6 | 3.7 | 11.3 | 26.7 |

10KQb | 0.096 | 0.093 | 0.095 | 0.094 | 0.090 | 0.077 |

σ (KQb) % | 2.8 | 2.7 | 3.0 | 3.1 | 11.2 | 28.3 |

10KMYb | 0.011 | 0.012 | 0.012 | 0.012 | -0.005 | 0.025 |

σ (KMYb) % | 25.7 | 24.9 | 26.8 | 30.2 | 203.2 | 52.2 |

10KMZb | −0.183 | −0.179 | −0.181 | −0.181 | −0.170 | −0.143 |

σ (KMZb) % | 3.3 | 2.6 | 3.0 | 3.0 | 13.9 | 33.9 |

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**MDPI and ACS Style**

Berchiche, N.; Krasilnikov, V.I.; Koushan, K.
Numerical Analysis of Azimuth Propulsor Performance in Seaways: Influence of Oblique Inflow and Free Surface. *J. Mar. Sci. Eng.* **2018**, *6*, 37.
https://doi.org/10.3390/jmse6020037

**AMA Style**

Berchiche N, Krasilnikov VI, Koushan K.
Numerical Analysis of Azimuth Propulsor Performance in Seaways: Influence of Oblique Inflow and Free Surface. *Journal of Marine Science and Engineering*. 2018; 6(2):37.
https://doi.org/10.3390/jmse6020037

**Chicago/Turabian Style**

Berchiche, Nabila, Vladimir I. Krasilnikov, and Kourosh Koushan.
2018. "Numerical Analysis of Azimuth Propulsor Performance in Seaways: Influence of Oblique Inflow and Free Surface" *Journal of Marine Science and Engineering* 6, no. 2: 37.
https://doi.org/10.3390/jmse6020037