# Prediction of Propeller-Induced Hull Pressure Fluctuations via a Potential-Based Method: Study of the Effects of Different Wake Alignment Methods and of the Rudder

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## Abstract

**:**

## 1. Introduction

## 2. Methodology

#### 2.1. Boundary Element Method

#### 2.2. Wake Alignment Model

#### 2.3. Boundary Element/Reynolds-Averaged Navier-Stokes Interactive Scheme

#### 2.4. Boundary Element—Solver for the Oscillating Hull Pressure

## 3. Numerical and Experimental Models

#### 3.1. Experimental Model

#### 3.2. Hydrodynamic Model

#### 3.3. Pressure Boundary Element Model

#### 3.4. Unsteady Reynolds-Averaged Navier-Stokes Model

## 4. Results and Comparison with Experiment

## 5. Conclusions and Future Work

## Author Contributions

## Acknowledgments

## Conflicts of Interest

## References

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1 | RANS is the abbreviation of the Reynolds-averaged Navier–Stokes method. |

2 | BEM is the abbreviation of the boundary element method; RANS is the abbreviation of the Reynolds-averaged Navier-Stokes method. |

3 | The simulation is performed in the Texas Advanced Computing Center (TACC) at The University of Texas at Austin (Austin, TX 78703, USA). URL: http://www.tacc.utexas.edu. |

4 | KT is the abbreviation of thrust coefficient and is defined by Equation (10). KQ is the abbreviation of torque coefficient and is defined by Equation (11). |

**Figure 1.**(

**a**) Propeller under the axisymmetric inflow; (

**b**) Contributors of the perturbation velocity on the wake surface, taken from Kim [12].

**Figure 2.**Key wake with the local velocity vectors (red arrows in the middle figure) plotted on each nodal point of the wake, taken from Kim [12].

**Figure 3.**Numerical algorithm of the BEM/RANS2 interactive scheme.

**Figure 4.**(

**a**) Photo of the model test facility and (

**b**) pressure transducer arrangement and numbering.

**Figure 7.**Pressure-BEM model (

**a**) with and (

**b**) without the upper part of the rudder (the propeller is not a part of this model).

**Figure 8.**Comparison between the propeller force predicted by the BEM/RANS scheme and that from the experimental data4.

**Figure 9.**The predicted effective wake field at the advance ratios of (

**a**) Js = 0.7; (

**b**) Js = 0.9; and (

**c**) Js = 1.1. Only the effective wake distribution on the mid-chord disk is shown. The actual effective wake field may vary in the axial direction.

**Figure 10.**Comparison of steady wake geometry and unsteady blade wake geometries at different blade angles. The blade-angle ranges between 0 and 2$\mathsf{\pi}$ and is defined by the angle the blade has passed starting from the “upright position”. The “upright position” means the mid-camber point of the root section is located on the vertical axis above the hub (+y axis). (

**a**) steady wake; (

**b**) unsteady wake 0 degrees; (

**c**) unsteady wake 180 degrees. Please note the wake is shown relative to the propeller fixed system. So the hull is physicallly located above the propeller in (

**b**), but “below” the propeller in (

**c**). Thus, in both cases, (

**b**) and (

**c**), the propeller wake appears to be aligned in a direction parallel to the hull surface.

**Figure 11.**Comparison among the experimental pressure data, Unsteady Reynolds-averaged Navier-Stokes (URANS) method pressure history, and the pressure history predicted by pressure-BEM solver with either a steady or an unsteady wake.

**Figure 12.**Comparison of hull pressures predicted by the pressure-BEM solver with different treatment of the effective wake field: (a) Effective wake field is evaluated at the center of every blade BEM panel (blue solid line); (b) The effective wake field is extrapolated to the upstream curved surface close to the blade leading edge (red dash line).

**Figure 13.**Study of the level of simplification on the rudder geometry in the pressure-BEM model. The blade-angle ranges between 0 and 2$\mathsf{\pi}$ and is defined by the angle the blade has passed starting from the “upright position”. The “upright position” means the mid-camber point of the root section is located on the vertical axis above the hub (+y axis).

© 2018 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/).

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**MDPI and ACS Style**

Su, Y.; Kim, S.; Kinnas, S.A. Prediction of Propeller-Induced Hull Pressure Fluctuations via a Potential-Based Method: Study of the Effects of Different Wake Alignment Methods and of the Rudder. *J. Mar. Sci. Eng.* **2018**, *6*, 52.
https://doi.org/10.3390/jmse6020052

**AMA Style**

Su Y, Kim S, Kinnas SA. Prediction of Propeller-Induced Hull Pressure Fluctuations via a Potential-Based Method: Study of the Effects of Different Wake Alignment Methods and of the Rudder. *Journal of Marine Science and Engineering*. 2018; 6(2):52.
https://doi.org/10.3390/jmse6020052

**Chicago/Turabian Style**

Su, Yiran, Seungnam Kim, and Spyros A. Kinnas. 2018. "Prediction of Propeller-Induced Hull Pressure Fluctuations via a Potential-Based Method: Study of the Effects of Different Wake Alignment Methods and of the Rudder" *Journal of Marine Science and Engineering* 6, no. 2: 52.
https://doi.org/10.3390/jmse6020052