# 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

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**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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## Share and Cite

**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