# Experimental Validation of Fluid–Structure Interaction Computations of Flexible Composite Propellers in Open Water Conditions Using BEM-FEM and RANS-FEM Methods

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## Abstract

**:**

## 1. Introduction

## 2. General Description of Propellers and Flow Conditions

#### 2.1. Propellers

- Propeller bronze: this propeller is assumed completely rigid.
- Propeller epoxy: this propeller is the most flexible one.
- Propeller 45: [+45${}^{\xb0}$/−45${}^{\xb0}$] laminate lay-up.
- Propeller 90: [0${}^{\xb0}$/90${}^{\xb0}$] laminate lay-up.

#### 2.2. Material Properties

#### 2.3. Flow Conditions

## 3. Structure Model

## 4. Fluid Models

#### 4.1. BEM Model

#### 4.2. RANS Model

#### Thrust and Torque RANS Discretisation Uncertainties

## 5. Fluid–Structure Coupling

#### 5.1. BEM-FEM Coupling

#### 5.2. RANS-FEM Coupling

## 6. Comparison of Experimental, BEM and RANS Results for the Bronze Propeller

#### 6.1. Open Water Diagram Bronze Propeller

#### 6.1.1. Comparison of Experimental and BEM Results

#### 6.1.2. Comparison of Experimental and RANS Results

#### 6.2. Comparison of BEM and RANS Pressure Distributions

## 7. Flexible Propeller Cavitation Tunnel Experiments

#### 7.1. Test Set-Up

- Two synchronized and calibrated cameras with FireWire interface; resolution: $1388\times 1038$ pixels; maximum frame rate 16 fps at full resolution.
- Stroboscopic lights with flash duration in the micro second range. Flash duration is kept as short as possible to avoid motion blur at the blade tip.
- The shaft encoder mounted on the shaft, provides 360 pulses per revolution.
- A pulse selector is able to select one of these 360 pulses as a trigger, which is sent to the stroboscopes and the cameras. Therefore, a trigger can be supplied, with a resolution of one degree for every blade position. The cameras and the strobe are synchronized such that the strobe flash falls within the time frame that the camera shutter is open.

#### 7.2. Measurement Technique

## 8. Experimental, Modelling and Discretisation Uncertainties Flexible Propeller Cases

#### 8.1. Experimental Uncertainties

#### 8.2. Modelling Uncertainties

- using the design propeller geometry instead of the as-built geometry,
- using the design propeller stiffness instead of the actual propeller stiffness,
- neglecting of the cavitation tunnel walls.

#### 8.3. Discretisation Uncertainties

#### 8.4. Total Uncertainties

## 9. Comparison of Experimental, BEM-FEM and RANS-FEM Results

## 10. Conclusions, Recommendations and Further Work

## Author Contributions

## Acknowledgments

## Conflicts of Interest

## References

- Mulcahy, N.; Prusty, B.; Gardiner, C. Hydroelastic tailoring of flexible composite propellers. Ship Offshore Struct.
**2010**, 5, 359–370. [Google Scholar] [CrossRef] - He, X.; Hong, Y.; Wang, R. Hydroelastic optimisation of a composite marine propeller in a non-uniform wake. Ocean Eng.
**2012**, 39, 14–23. [Google Scholar] [CrossRef] - Taketani, T.; Kimura, K.; Ando, S.; Yamamoto, K. Study on performance of a ship propeller using a composite material. In Proceedings of the Third International Symposium on Marine Propulsors, Launceston, Australia, 5–8 May 2013. [Google Scholar]
- Solomon Raj, S.; Ravinder Reddy, P. Bend-twist coupling and its effect on cavitation inception of composite marine propeller. Int. J. Mech. Eng. Technol.
**2014**, 5, 306–314. [Google Scholar] - Kuo, J.; Vorus, W. Propeller blade dynamic stress. In Proceedings of the Tenth Ship Technology and Research (STAR) Symposium, Norfolk, VA, USA, 21–24 May 1985; pp. 39–69. [Google Scholar]
- Georgiev, D.; Ikehata, M. Hydro-elastic effects on propeller blades in steady flow. J. S. Nav. Archit. Jpn.
**1998**, 184, 1–14. [Google Scholar] - Young, Y. Time-dependent hydro-elastic analysis of cavitating propulsors. J. Fluids Struct.
**2007**, 23, 269–295. [Google Scholar] [CrossRef] - Blasques, J.; Berggreen, C.; Andersen, P. Hydro-elastic analysis and optimization of a composite marine propeller. Mar. Struct.
**2010**, 23, 22–38. [Google Scholar] [CrossRef] - Ghassemi, H.; Ghassabzadeh, M.; Saryazdi, M. Influence of the skew angle on the hydro-elastic behaviour of a composite marine propeller. J. Eng. Marit. Environ.
**2012**, 226, 346–359. [Google Scholar] - Sun, H.; Xiong, Y. Fluid-structure interaction analysis of flexible marine propellers. Appl. Mech. Mater.
**2012**, 226–228, 479–482. [Google Scholar] [CrossRef] - Lee, H.; Song, M.; Suh, J.; Chang, B. Hydro-elastic analysis of marine propellers based on a BEM-FEM coupled FSI algorithm. Int. J. Nav. Archit. Ocean Eng.
**2014**, 6, 562–577. [Google Scholar] [CrossRef] - Maljaars, P.; Dekker, J. Hydro-elastic analysis of flexible marine propellers. In Maritime Technology and Engineering; Guedes Soares, C., Santos, T., Eds.; CRC Press-Taylor & Francis Group: London, UK, 2014; pp. 705–715. [Google Scholar]
- Atkinson, P.; Glover, E. Propeller Hydro-Elastic Effects; Propellers ’88 Symposium; SNAME: Virginia Beach, VA, USA, 1988. [Google Scholar]
- Lin, H.; Lin, J. Nonlinear hydroelastic behavior of propellers using a finite element method and lifting surface theory. J. Mar. Sci. Technol.
**1996**, 1, 114–124. [Google Scholar] [CrossRef] - Salvatore, F.; Streckwall, H.; van Terwisga, T. Propeller cavitation modelling by CFD-Results from the VIRTUE 2008 Rome workshop. In Proceedings of the First International Symposium on Marine Propulsors, Trondheim, Norway, 22–24 June 2009. [Google Scholar]
- Vaz, G.; Hally, D.; Huuva, T.; Bulten, N.; Muller, P.; Becchi, P.; Herrer, J.; Whitworth, S.; Macé, R.; Korsström, A. Cavitating flow calculations for the E779A propeller in open water and behind conditions: Code comparison and solution validation. In Proceedings of the Fourth International Symposium on Marine Propulsors, Austin, TX, USA, 31 May–4 June 2015. [Google Scholar]
- Chae, E.; Akcabay, D.; Young, Y. Influence of flow-induced bend-twist coupling on the natural vibration responses of flexible hydrofoils. J. Fluids Struct.
**2017**, 69, 323–340. [Google Scholar] [CrossRef] - Chae, E.; Akcabay, D.; Lelong, A.; Astolfi, J.; Young, Y. Numerical and experimental investigation of natural flow-induced vibrations of flexible hydrofoils. Phys. Fluids
**2016**, 28, 075102. [Google Scholar] [CrossRef] - Chen, J.; Hallet, S.; Wisnom, M. Modelling complex geometry using solid finite element meshes with correct composite material orientations. Comput. Struct.
**2010**, 88, 602–609. [Google Scholar] [CrossRef] [Green Version] - Maljaars, P.; Kaminski, M.; den Besten, J. Finite element modelling and model updating of small scale composite propellers. Compos. Struct.
**2017**, 176, 154–163. [Google Scholar] [CrossRef] - Vaz, G. Modelling of Sheet Cavitation on Hydrofoils and Marine Propellers Using Boundary Element Methods. Ph.D. Thesis, Instituto Superior Técnico, Lisbon, Portugal, 2005. [Google Scholar]
- Vaz, G.; Bosschers, J. Modelling of 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]
- Maljaars, P.; Grasso, N.; Kaminski, M.; Lafeber, W. Validation of a steady BEM-FEM coupled simulation with experiments on flexible small scale propellers. In Proceedings of the Fifth International Symposium on Marine Propulsors, Espoo, Finland, 12–15 June 2017. [Google Scholar]
- ITTC 1978. Report of performance committee. In Proceedings of the 15th International Towing Tank Conference, The Hague, The Netherlands, 3–10 September 1978. [Google Scholar]
- ReFRESCO. ReFRESCO Community Site. Available online: http://www.refresco.org (accessed on 12 March 2018).
- Vaz, G.; Jaouen, F.; Hoekstra, M. Free-surface viscous flow computations. Validation of URANS code FRESCO. In Proceedings of the ASME 2009 28th International Conference on Ocean, Offshore and Arctic Engineering, Honolulu, HI, USA, 31 May–5 June 2009. [Google Scholar]
- Klaij, C.; Vuik, C. Simple-type preconditioners for cell-centered, colocated finite volume discretization of incompressible Reynolds-averaged Navier–Stokes equations. Int. J. Numer. Methods Fluids
**2013**, 71, 830–849. [Google Scholar] [CrossRef] - Menter, F.; Egorov, Y.; Rusch, D. Steady and unsteady flow modelling using the k-skl model. In Proceedings of the Turbulence Heat and Mass Transfer, Dubrovnik, Croatia, 25–29 September 2006. [Google Scholar]
- Rijpkema, D.; Baltazar, J.; Falcao de Campos, J. Viscous flow simulations of propellers in different Reynolds number regimes. In Proceedings of the Fourth International Symposium on Marine Propulsors, Austin, TX, USA, 31 May–4 June 2015. [Google Scholar]
- Eça, L.; Hoekstra, M. A procedure for the estimation of the numerical uncertainty of CFD calculations based on grid refinement studies. J. Comput. Phys.
**2014**, 262, 104–130. [Google Scholar] [CrossRef] - Jongsma, S.; van der Weide, E.; Windt, J. Implementation and verification of a partitioned strong coupled fluid–structure interaction approach in a finite volume method. In Proceedings of the International Conference in Hydrodynamics, Egmond aan Zee, The Netherlands, 18–23 September 2016. [Google Scholar]
- Turek, S.; Hron, J. Proposal for numerical benchmarking of fluid–structure interaction between an elastic object and laminar incompressible flow. In Fluid–Structure Interaction-Modelling, Simulation, Optimization; Number 53; Springer: Berlin/Heidelberg, Germany, 2006; pp. 371–385. [Google Scholar]
- Sutton, J.; Ortue, J.; Schreier, H. Image Correlation for Shape, Motion and Deformation Measurements: Basic Concepts, Theory and Applications; Springer: New York, NY, USA, 2009. [Google Scholar]
- Zondervan, G.; Grasso, N.; Lafeber, W. Hydrodynamic design and model testing techniques for composite ship propellers. In Proceedings of the Fifth International Symposium on Marine Propulsion, Espoo, Finland, 12–15 June 2017. [Google Scholar]
- Glauert, H. The Elements of Aerofoil and Airscrew Theory, 2nd ed.; Cambridge University Press: New York, NY, USA, 1947. [Google Scholar]

**Figure 2.**Numerical uncertainty of thrust and torque, U and order of accuracy p for various advance ratios.

**Figure 7.**Pressure coefficient, ${C}_{p}$, on the suction side for $J=0.37$, RANS (

**left**) BEM (

**right**). The insert figure shows the BEM pressure distribution after the tip pressure correction.

**Figure 8.**Pressure coefficient, ${C}_{p}$, on the pressure side for $J=0.37$, RANS (

**left**) BEM (

**right**). The insert figure shows the BEM pressure distribution after the tip pressure correction.

**Figure 9.**Pressure coefficient, ${C}_{p}$, on the suction side for $J=0.64$, RANS (

**left**) BEM (

**right**). The insert figure shows the BEM pressure distribution after the tip pressure correction.

**Figure 10.**Pressure coefficient, ${C}_{p}$, on the pressure side for $J=0.64$, RANS (

**left**) BEM (

**right**). The insert figure shows the BEM pressure distribution after the tip pressure correction.

**Figure 11.**Pressure coefficient, ${C}_{p}$, on the suction side for $J=0.85$, RANS (

**left**) BEM (

**right**). The insert figure shows the BEM pressure distribution after the tip pressure correction.

**Figure 12.**Pressure coefficient, ${C}_{p}$, on the pressure side for $J=0.85$, RANS (

**left**) BEM (

**right**). The insert figure shows the BEM pressure distribution after the tip pressure correction.

**Figure 16.**Uncertainty intervals for bend (

**left**) and twist (

**right**) deformations of mid-chord points of epoxy propeller blade 1 against the radial position on the blade, for the measured and calculated responses.

**Figure 17.**Uncertainty intervals for bend (

**left**) and twist (

**right**) deformations of mid-chord points of propeller 45 blade 1 against the radial position on the blade, for the measured and calculated responses.

**Figure 18.**Uncertainty intervals for bend (

**left**) and twist (

**right**) deformations of mid-chord points of propeller 90 blade 2 against the radial position on the blade, for the measured and calculated responses.

E (GPa) | $\mathit{\upsilon}$ (-) | G (GPa) |
---|---|---|

3.60 | 0.300 | 1.39 |

${\mathit{E}}_{\mathbf{11}}$ (GPa) | ${\mathit{E}}_{\mathbf{22}}$ (GPa) | ${\mathit{E}}_{\mathbf{33}}$ (GPa) | ${\mathit{\upsilon}}_{\mathbf{12}}$ (-) | ${\mathit{\upsilon}}_{\mathbf{13}}$ (-) | ${\mathit{\upsilon}}_{\mathbf{23}}$ (-) | ${\mathit{G}}_{\mathbf{12}}$ (GPa) | ${\mathit{G}}_{\mathbf{13}}$ (GPa) | ${\mathit{G}}_{\mathbf{23}}$ (GPa) |
---|---|---|---|---|---|---|---|---|

18.8 | 18.8 | 8.00 | 0.132 | 0.275 | 0.275 | 2.81 | 2.49 | 2.49 |

$\mathit{J}\mathbf{=}\frac{\mathbf{60}\mathit{v}}{\mathit{nD}}$ | v (m/s) | n (rpm) | ${\mathit{Re}}_{\mathbf{0.7}\mathit{r}}\mathbf{\times}{\mathbf{10}}^{\mathbf{6}}$ | |
---|---|---|---|---|

Prop. Epoxy, blade 1 | 0.37 | 1.88 | 900 | 1.28 |

Prop. Epoxy, blade 1 | 0.64 | 3.97 | 1098 | 1.60 |

Prop. Epoxy, blade 1 | 0.85 | 6.73 | 1392 | 2.10 |

Prop. 45, blade 1 | 0.38 | 1.92 | 900 | 1.28 |

Prop. 45, blade 1 | 0.64 | 3.99 | 1098 | 1.60 |

Prop. 45, blade 1 | 0.85 | 6.75 | 1398 | 2.10 |

Prop. 90, blade 2 | 0.38 | 1.98 | 900 | 1.28 |

Prop. 90, blade 2 | 0.66 | 4.09 | 1098 | 1.60 |

Prop. 90, blade 2 | 0.85 | 6.74 | 1398 | 2.10 |

${\mathit{N}}_{\mathit{c}}$ | ${\mathit{N}}_{\mathit{r}}$ | ${\mathit{N}}_{\mathit{n}}$ | Tip Displ. (mm) |
---|---|---|---|

116 | 120 | 4 | 16.76 |

58 | 60 | 4 | 16.76 |

58 | 60 | 8 | 16.76 |

29 | 30 | 4 | 16.74 |

Boundary Condition | |
---|---|

Inlet | Prescribed inflow velocity. |

Inner outlet | Neumann boundary condition on velocity and pressure. |

Outer outlet | Dirichlet boundary condition on pressure, Neumann on velocity. |

Propeller, hub and shaft surfaces | Velocity is zero, no wall functions applied (y+ should be <1). |

Outer surface flow domain | Normal and tangential velocity are zero and free, respectively. |

Grid | Amount of Cells | Relative Step Size |
---|---|---|

A | 917,000 | 2.18 |

B | 2,390,000 | 1.58 |

C | 3,790,000 | 1.36 |

D | 9,460,000 | 1.00 |

**Table 7.**${K}_{T}$ and $10{K}_{Q}$ for rigid propeller Reynolds-averaged-Navier–Stokes and boundary element method calculations.

${\mathit{K}}_{\mathit{T}}$ (BEM) | ${\mathit{K}}_{\mathit{T}}$ (RANS) | % | 10${\mathit{K}}_{\mathit{Q}}$ (BEM) | 10${\mathit{K}}_{\mathit{Q}}$ (RANS) | % | |
---|---|---|---|---|---|---|

$J=0.37$ | 0.255 | 0.222 | −13% | 0.344 | 0.331 | −4% |

$J=0.64$ | 0.177 | 0.149 | −16% | 0.278 | 0.247 | −11% |

$J=0.85$ | 0.114 | 0.089 | −22% | 0.208 | 0.172 | −17% |

RANS-FEM Result | Modelling Uncert. 1 | Modelling Uncert. 2 | Discretisation Uncert. | Total Uncert. | |
---|---|---|---|---|---|

$J=$ 0.37 | 4.34 | −0.157; 0.0 | −0.212; 0.211 | −0.386; 0.386 | −0.468; 0.440 |

$J=$ 0.64 | 4.11 | −0.184; 0.0 | −0.200; 0.201 | −0.025; 0.025 | −0.273; 0.202 |

$J=$ 0.85 | 4.20 | −0.233; 0.0 | −0.185; 0.183 | −0.290; 0.290 | −0.415; 0.343 |

RANS-FEM Result | Modelling Uncert. 1 | Modelling Uncert. 2 | Discretisation Uncert. | Total Uncert. | |
---|---|---|---|---|---|

$J=$ 0.37 | −2.29 | 0.0; 0.066 | −0.089; 0.090 | −0.508; 0.508 | −0.515; 0.520 |

$J=$ 0.64 | −1.95 | 0.0; 0.083 | −0.093; 0.091 | −0.092; 0.092 | −0.131; 0.154 |

$J=$ 0.85 | −2.58 | 0.0;0.128 | −0.101; 0.102 | −0.335; 0.335 | −0.350; 0.373 |

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**MDPI and ACS Style**

Maljaars, P.; Bronswijk, L.; Windt, J.; Grasso, N.; Kaminski, M.
Experimental Validation of Fluid–Structure Interaction Computations of Flexible Composite Propellers in Open Water Conditions Using BEM-FEM and RANS-FEM Methods. *J. Mar. Sci. Eng.* **2018**, *6*, 51.
https://doi.org/10.3390/jmse6020051

**AMA Style**

Maljaars P, Bronswijk L, Windt J, Grasso N, Kaminski M.
Experimental Validation of Fluid–Structure Interaction Computations of Flexible Composite Propellers in Open Water Conditions Using BEM-FEM and RANS-FEM Methods. *Journal of Marine Science and Engineering*. 2018; 6(2):51.
https://doi.org/10.3390/jmse6020051

**Chicago/Turabian Style**

Maljaars, Pieter, Laurette Bronswijk, Jaap Windt, Nicola Grasso, and Mirek Kaminski.
2018. "Experimental Validation of Fluid–Structure Interaction Computations of Flexible Composite Propellers in Open Water Conditions Using BEM-FEM and RANS-FEM Methods" *Journal of Marine Science and Engineering* 6, no. 2: 51.
https://doi.org/10.3390/jmse6020051