# 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

^{*}

## 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

- Van Wijngaarden, E. Recent developments in predicting propeller-induced hull pressure pulses. In Proceedings of the 1st International Ship Noise and Vibration Conference, London, UK, 20–21 June 2005. [Google Scholar]
- Tani, G.; Viviani, M.; Hallander, J.; Johansson, T.; Rizzuto, E. Propeller underwater radiated noise: A comparison between model scale measurements in two different facilities and full scale measurement. Appl. Ocean Res.
**2016**, 56, 48–66. [Google Scholar] [CrossRef] - Salvatore, F.; Testa, C.; Greco, L. Coupled hydrodynamics-hydroacoustics BEM modeling of marine propellers operating in a wakefield. In Proceedings of the First International Symposium on Marine Propulsors (SMP ’09), Trondheim, Norway, 22–24 June 2009; pp. 537–547. [Google Scholar]
- Kellett, P.; Turan, O.; Incecik, A. A study of numerical ship underwater noise prediction. Ocean Eng.
**2013**, 66, 113–120. [Google Scholar] [CrossRef] - Seol, H.; Jung, B.; Suh, J.-C.; Lee, S. Prediction of non-cavitating underwater propeller noise. J. Sound Vib.
**2002**, 257, 131–156. [Google Scholar] [CrossRef] - Li, D.-Q.; Hallander, J.; Johansson, T.; Karlsson, R. Cavitation dynamics and underwater radiated noise signature of a ship with cavitating propeller. In Proceedings of the VI International Conference on Computational Methods in Marine Engineering (MARINE 2015), Rome, Italy, 15–17 June 2015. [Google Scholar]
- Lee, K.; Lee, J.; Kim, D.; Kim, K.; Seong, W. Propeller sheet cavitation noise source modeling and inversion. J. Sound Vib.
**2014**, 333, 1356–1368. [Google Scholar] [CrossRef] - Seol, H.; Suh, J.-C.; Lee, S. Development of hybrid method for the prediction of underwater propeller noise. J. Sound Vib.
**2005**, 288, 345–360. [Google Scholar] [CrossRef] - Tian, Y.; Jeon, C.H.; Kinnas, S.A. Effective Wake Calculation/Application to Ducted Propellers. J. Ship Res.
**2014**, 58, 1–13. [Google Scholar] [CrossRef] - Su, Y.; Kinnas, S.A. A Generalized Potential/RANS Interactive Method for the Prediction of Propulsor Performance. J. Ship Res.
**2017**, 61, 214–229. [Google Scholar] [CrossRef] - Tian, Y.; Kinnas, S.A. A Wake Model for the Prediction of Propeller Performance at Low Advance Ratios. Int. J. Rotating Mach.
**2012**, 2012, 372364. [Google Scholar] [CrossRef] - Kim, S. An Improved Full Wake Alignment Scheme for the Prediction of Open/Ducted Propeller Performance in Steady and Unsteady Flow. Master’s Thesis, Ocean Engineering Group, CAEE, The University of Texas at Austin, Austin, TX, USA, August 2017. [Google Scholar]
- Lee, H. Modeling of Unsteady Wake Alignment and Developed Tip Vortex Cavitation. Ph.D. Thesis, Ocean Engineering Group, CAEE, The University of Texas at Austin, Austin, TX, USA, August 2002. [Google Scholar]
- He, L.; Kinnas, S.A. Numerical simulation of unsteady propeller/rudder interaction. Int. J. Nav. Archit. Ocean Eng.
**2017**, 9, 677–692. [Google Scholar] [CrossRef] - Hwang, Y.; Sun, H.; Kinnas, S.A. Prediction of Hull Pressure Fluctuations Induced by Single and Twin Propellers. In Proceedings of the Society of Naval Architects and Marine Engineers Propellers/Shafting 2006 Symposium, Williamsburg, VA, USA, 12–13 September 2006. [Google Scholar]
- Lee, H.; Kinnas, S.A. Application of BEM in the Prediction of Unsteady Blade Sheet and Developed Tip Vortex Cavitation on Marine Propellers. J. Ship Res.
**2004**, 48, 15–30. [Google Scholar] - Drela, M. XFOIL: An analysis and design system for low Reynolds number airfoils. In Low Reynolds Number Aerodynamics; Springer: Berlin/Heidelberg, Germany, 1989; Volume 54. [Google Scholar]
- Kinnas, S.A.; Yu, X.; Tian, Y. Prediction of Propeller Performance under High Loading Conditions with Viscous/Inviscid Interaction and a New Wake Alignment Model. In Proceedings of the 29th Symposium on Naval Hydrodynamics, Gothenburg, Sweden, 26–31 August 2012. [Google Scholar]

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).

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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