# Prediction of the Open-Water Performance of Ducted Propellers with a Panel Method

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Numerical Methods

#### 2.1. Problem Definition

#### 2.2. Panel Code PROPAN

#### 2.3. RANS Code ReFRESCO

## 3. Results

#### 3.1. Grids and Numerical Set-Up

#### 3.2. Influence of the Wake Model

#### 3.3. Comparison Between PROPAN and ReFRESCO

#### 3.4. Prediction of the Open-Water Performance

## 4. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## Abbreviations

IST | Instituto Superior Técnico |

MARIN | Maritime Research Institute Netherlands |

QUICK | Quadratic upwind interpolation for convective kinematics |

RANS | Reynolds-averaged Navier-Stokes |

RWM | Rigid wake model |

SIMPLE | Semi-implicit method for pressure linked equations |

SST | Shear stress transport |

WAM | Wake alignment model |

## References

- Sánchez-Caja, A.; Rautaheimo, P.; Siikonen, T. Simulation of Incompressible Viscous Flow Around a Ducted Propeller Using a RANS Equation Solver. In Proceedings of the Twenty-Third Symposium on Naval Hydrodynamics, Val de Reuil, France, 17–22 September 2000; The National Academies Press: Washington, DC, USA, 2001; pp. 527–539. [Google Scholar]
- Sánchez-Caja, A.; Pylkkänen, J.V.; Sipilä, T.P. Simulation of the Incompressible Viscous Flow Around Ducted Propellers With Rudders Using a RANSE solver. In Proceedings of the 27th Symposium on Naval Hydrodynamics, Seoul, Korea, 5–10 October 2008; Curran Associates, Inc.: Red Hook, NY, USA, 2010; pp. 968–982. [Google Scholar]
- Abdel-Maksoud, M.; Heinke, H.-J. Scale Effects on Ducted Propellers. In Proceedings of the Twenty-Fourth Symposium on Naval Hydrodynamics, Fukuoka, Japan, 8–13 July 2002; The National Academies Press: Washington, DC, USA, 2003; pp. 744–759. [Google Scholar]
- Bhattacharyya, A.; Krasilnikov, V.; Steen, S. Scale effects on open water characteristics of a controllable pitch propeller working within different duct designs. Ocean Eng.
**2016**, 112, 226–242. [Google Scholar] [CrossRef] - Kim, J.; Paterson, E.G.; Stern, F. RANS simulation of ducted marine propulsor flow including subvisual cavitation and acoustic modeling. ASME J. Fluids Eng.
**2006**, 128, 799–810. [Google Scholar] [CrossRef] - Kerwin, J.E.; Kinnas, S.A.; Lee, J.-T.; Shih, W.-Z. A Surface Panel Method for the Hydrodynamic Analysis of Ducted Propellers. In Transactions of Society of Naval Architects and Marine Engineers; Society of Naval Architects and Marine Engineers: New York, NY, USA, 1987; p. 4. [Google Scholar]
- Hughes, M.J.; Kinnas, S.A.; Kerwin, J.E. Experimental validation of a ducted propeller analysis method. ASME J. Fluids Eng.
**1992**, 114, 214–219. [Google Scholar] [CrossRef] - Hughes, M.J. Implementation of a Special Procedure for Modeling the Tip Clearance Flow in a Panel Method for Ducted Propulsors. In Proceedings of the Propellers & Shafting ’97 Symposium, Virginia Beach, VA, USA, 23–24 September 1997; Society Naval Architects and Marine Engineers: Alexandria, VA, USA, 1997. Paper Number 17. [Google Scholar]
- Lee, H.; Kinnas, S.A. Prediction of Cavitating Performance of Ducted Propellers. In Proceedings of the Sixth International Symposium on Cavitation, Wageningen, The Netherlands, 11–15 September 2006. [Google Scholar]
- Oweis, G.F.; Fry, D.; Jessup, S.D.; Ceccio, S.L. Development of a tip-leakage flow—Part 1: The flow over a range of Reynolds numbers. ASME J. Fluid Eng.
**2006**, 128, 751–764. [Google Scholar] [CrossRef] - Baltazar, J.; Falcão de Campos, J.A.C.; Bosschers, J. Open-water thrust and torque predictions of a ducted propeller system with a panel method. Int. J. Rotating Mach.
**2012**, 2012, 474785. Available online: https://www.hindawi.com/journals/ijrm/2012/474785/ (accessed on 16 January 2018). [CrossRef] - Baltazar, J.; Rijpkema, D.; Falcão de Campos, J.A.C. A Comparison of Panel Method and RANS Calculations for a Ducted Propeller System in Open-Water. In Proceedings of the Third International Symposium on Marine Propulsors, Launceston, Australia, 5–8 May 2013; Binns, J., Brown, R., Bose, N., Eds.; Australian Maritime College, University of Tasmania: Newnham, TAS, Australia, 2013; pp. 338–346. [Google Scholar]
- Baltazar, J.; Falcão de Campos, J.A.C.; Bosschers, J. Potential Flow Modelling of Ducted Propellers with a Panel Method. In Proceedings of the Fourth International Symposium on Marine Propulsors, Austin, TX, USA, 31 May–4 June 2015; Kinnas, S.A., Ed.; The University of Texas at Austin: Austin, TX, USA, 2015; pp. 184–192. [Google Scholar]
- Vaz, G.; Bosschers, J. Modelling Three Dimensional Sheet Cavitation on Marine Propellers Using a Boundary Element Method. In Proceedings of the Sixth International Symposium on Cavitation, Wageningen, The Netherlands, 11–15 September 2006. [Google Scholar]
- Bosschers, J.; Willemsen, C.; Peddle, A.; Rijpkema, D. Analysis of Ducted Propellers by Combining Potential Flow and RANS Methods. In Proceedings of the Fourth International Symposium on Marine Propulsors, Austin, TX, USA, 31 May–4 June 2015; Kinnas, S.A., Ed.; The University of Texas at Austin: Austin, TX, USA, 2015; pp. 639–648. [Google Scholar]
- Gu, H.; Kinnas, S.A. Modeling of Contra-Rotating and Ducted Propellers via Coupling of a Vortex-Lattice with a Finite Volume Method. In Proceedings of the Propellers & Shafting 2003 Symposium, Virginia Beach, VA, USA, 17–18 September 2003; Society Naval Architects and Marine Engineers: Alexandria, VA, USA, 2003. [Google Scholar]
- Kinnas, S.A.; Fan, H.; Tian, Y. A Panel Method with a Full Wake Alignment Model for the Prediction of the Performance of Ducted Propellers. J. Ship Res.
**2015**, 59, 246–257. [Google Scholar] [CrossRef] - Kim, S.; Du, W.; Kinnas, S.A. Panel Method for Ducted Propellers with Sharp and Round Trailing Edge Duct With Fully Aligned Wake on Blade and Duct. In Proceedings of the Fifth International Symposium on Marine Propulsors, Espoo, Finland, 12–15 June 2017; Sánchez-Caja, A., Ed.; VTT Technical Research Center of Finland Ltd.: Espoo, Finland, 2017; pp. 627–636. [Google Scholar]
- Baltazar, J. On the Modelling of the Potential Flow About Wings and Marine Propellers Using a Boundary Element Method. Ph.D. Thesis, Instituto Superior Técnico, Lisbon, Portugal, 30 September 2008. [Google Scholar]
- Morino, L.; Kuo, C.-C. Subsonic potential aerodynamics for complex configurations: A general theory. AIAA J.
**1974**, 12, 191–197. [Google Scholar] - Vaz, G.; Jaouen, F.; Hoekstra, M. Free-Surface Viscous Flow Computations. Validation of URANS Code FreSCo. In Proceedings of the ASME 28th International Conference on Ocean, Offshore and Arctic Engineering, OMAE2009-79398, Honolulu, HI, USA, 31 May–5 June 2009; pp. 425–437. [Google Scholar]
- Menter, F.; Kuntz, M.; Langtry, R. Ten Years of Industrial Experience With the SST Turbulence Model. In Proceedings of the Fourth International Symposium on Turbulence, Heat and Mass Transfer, Antalya, Turkey, 12–17 October 2003; Hanjalić, K., Nagano, Y., Tummers, M.J., Eds.; Begell House: Danbury, CT, USA, 2003; pp. 625–632. [Google Scholar]
- Kuiper, G. The Wageningen Propeller Series; Maritime Research Institute Netherlands: Wageningen, The Netherlands, 1992; ISBN 9090072470. [Google Scholar]

**Figure 3.**Pressure Kutta condition for the duct trailing edge with a thick round geometry and L denoting the duct length.

**Figure 4.**Overview of the surface grids used for the inviscid calculations with PROPAN (

**a**) and RANS calculations with ReFRESCO (

**b**).

**Figure 5.**Panel arrangement for propeller blades, duct, hub and blade wake at $J=0.2$. Rigid wake model (

**a**); Wake alignment model (

**b**). Only one wake surface is shown.

**Figure 6.**Wake alignment model with reduced gap pitch of $P/D=0.9$. Detail of the gap strip and blade wake sheet (

**a**); Overview of one blade wake geometry for $J=0.2$ (

**b**).

**Figure 7.**Vortex pitch ${\beta}_{v}$ distribution at $x/R=0.2$ (

**a**) and $x/R=0.4$ (

**b**) for $J=0.2$. Influence of the wake model. The filled symbols refer to the tip vortex.

**Figure 8.**Wake geometry at $x/R=0.2$ (

**a**) and $x/R=0.4$ (

**b**) for $J=0.1$. The contours represent the ReFRESCO total vorticity field $|\overrightarrow{\omega}|/\mathrm{\Omega}$. The symbols represent the PROPAN wake geometry: rigid wake model (squares), wake alignment model (diamonds) and wake alignment model with reduced gap pitch (circles). The filled symbols refer to the tip vortex.

**Figure 9.**Blade chordwise pressure distribution at $r/R=0.95$ (

**a**); Duct chordwise pressure distribution at $\theta =0$ degrees (

**b**). $J=0.1$.

**Figure 10.**Wake geometry at $x/R=0.2$ (

**a**) and $x/R=0.4$ (

**b**) for $J=0.2$. The contours represent the ReFRESCO total vorticity field $|\overrightarrow{\omega}|/\mathrm{\Omega}$. The symbols represent the PROPAN wake geometry: rigid wake model (squares), wake alignment model (diamonds) and wake alignment model with reduced gap pitch (circles). The filled symbols refer to the tip vortex.

**Figure 11.**Blade chordwise pressure distribution at $r/R=0.95$ (

**a**); Duct chordwise pressure distribution at $\theta =0$ degrees (

**b**). $J=0.2$.

**Figure 12.**Wake geometry at $x/R=0.2$ (

**a**) and $x/R=0.4$ (

**b**) for $J=0.5$. The contours represent the ReFRESCO total vorticity field $|\overrightarrow{\omega}|/\mathrm{\Omega}$. The symbols represent the PROPAN wake geometry: rigid wake model (squares), wake alignment model (diamonds) and wake alignment model with reduced gap pitch (circles). The filled symbols refer to the tip vortex.

**Figure 13.**Blade chordwise pressure distribution at $r/R=0.95$ (

**a**); Duct chordwise pressure distribution at $\theta =0$ degrees (

**b**). $J=0.5$.

**Figure 14.**Wake geometry at $z=0$ for $J=0.2$. The contours represent the ReFRESCO total vorticity field $|\overrightarrow{\omega}|/\mathrm{\Omega}$. The symbols represent the PROPAN wake geometry: rigid wake model (squares), wake alignment model (diamonds) and wake alignment model with reduced gap pitch (circles). The filled symbols refer to the tip vortex.

**Figure 15.**Comparison between numerical and experimental data from open-water tests. Propeller and duct thrust (

**a**); Propeller torque and open-water efficiency (

**b**).

**Table 1.**Variation of open-water characteristics with different grid sizes compared to the finest grid. Panel method computations at $J=0.5$.

Grid Size (Blade + Duct + Hub) ^{1} | $\mathbf{\Delta}{\mathit{K}}_{{\mathit{T}}_{\mathit{P}}}$ | $\mathbf{\Delta}{\mathit{K}}_{{\mathit{T}}_{\mathit{D}}}$ | $\mathbf{\Delta}{\mathit{K}}_{\mathit{Q}}$ |
---|---|---|---|

20 × 11 + 100 × 40 + 39 × 32 | −4.76% | −7.42% | −5.97% |

30 × 16 + 130 × 80 + 51 × 48 | −0.60% | −3.34% | −1.42% |

40 × 21 + 160 × 120 + 63 × 64 | −0.79% | −1.30% | −1.23% |

50 × 26 + 190 × 160 + 75 × 80 | −0.49% | −0.37% | −0.74% |

60 × 31 + 220 × 200 + 87 × 96 | −0.15% | −0.19% | −0.25% |

70 × 36 + 250 × 240 + 98 × 112 | – | – | – |

^{1}The grid size refers to the chordwise and spanwise radial directions for each propeller blade, and to the streamwise and circumferential directions for the duct and hub.

**Table 2.**Variation of open-water characteristics with different grid sizes compared to the finest grid with M denoting million. RANS computations at $J=0.5$.

Grid Size | $\mathbf{\Delta}{\mathit{K}}_{{\mathit{T}}_{\mathit{P}}}$ | $\mathbf{\Delta}{\mathit{K}}_{{\mathit{T}}_{\mathit{D}}}$ | $\mathbf{\Delta}{\mathit{K}}_{\mathit{Q}}$ |
---|---|---|---|

1.1 M | 3.25% | 2.39% | 3.55% |

2.6 M | 2.78% | 2.78% | 2.75% |

7.7 M | 0.67% | 1.99% | 0.69% |

12.9 M | 0.21% | 0.99% | 0.28% |

26.8 M | – | – | – |

**Table 3.**Inviscid thrust and torque coefficients for $J=0.1$, $0.2$ and $0.5$ and comparison with experimental data [23]. Influence of the wake model.

Model | ${\mathit{K}}_{{\mathit{T}}_{\mathit{P}}}$ | ${\mathit{K}}_{{\mathit{T}}_{\mathit{D}}}$ | $10{\mathit{K}}_{\mathit{Q}}$ |
---|---|---|---|

$\mathit{J}=\mathbf{0.1}$ | |||

RWM | 0.412 | 0.206 | 0.5882 |

WAM | 0.313 | 0.231 | 0.4664 |

WAM with Reduced Gap Pitch | 0.284 | 0.226 | 0.4228 |

Experiments | 0.254 | 0.214 | 0.4387 |

$\mathit{J}=\mathbf{0.2}$ | |||

RWM | 0.383 | 0.160 | 0.5538 |

WAM | 0.297 | 0.176 | 0.4456 |

WAM with Reduced Gap Pitch | 0.273 | 0.171 | 0.4083 |

Experiments | 0.248 | 0.166 | 0.4279 |

$\mathit{J}=\mathbf{0.5}$ | |||

RWM | 0.266 | 0.054 | 0.4041 |

WAM | 0.208 | 0.057 | 0.3246 |

WAM with Reduced Gap Pitch | 0.193 | 0.055 | 0.3010 |

Experiments | 0.196 | 0.053 | 0.3506 |

© 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/).

## Share and Cite

**MDPI and ACS Style**

Baltazar, J.M.; Rijpkema, D.; Falcão de Campos, J.; Bosschers, J. Prediction of the Open-Water Performance of Ducted Propellers with a Panel Method. *J. Mar. Sci. Eng.* **2018**, *6*, 27.
https://doi.org/10.3390/jmse6010027

**AMA Style**

Baltazar JM, Rijpkema D, Falcão de Campos J, Bosschers J. Prediction of the Open-Water Performance of Ducted Propellers with a Panel Method. *Journal of Marine Science and Engineering*. 2018; 6(1):27.
https://doi.org/10.3390/jmse6010027

**Chicago/Turabian Style**

Baltazar, João Manuel, Douwe Rijpkema, José Falcão de Campos, and Johan Bosschers. 2018. "Prediction of the Open-Water Performance of Ducted Propellers with a Panel Method" *Journal of Marine Science and Engineering* 6, no. 1: 27.
https://doi.org/10.3390/jmse6010027