# Impact of Leading Edge Roughness in Cavitation Simulations around a Twisted Foil

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## Abstract

**:**

## 1. Introduction

## 2. Governing Equations

#### 2.1. Phase Change Modelling

#### 2.2. Vorticity Transport Equation

## 3. Computational Domain

## 4. Leading Edge Roughness

- select the surface area where the roughness should be applied, i.e., in the 4% chord length from the leading edge,
- create the face list of all of the faces on the selected surface area,
- modify the face list to adjust the desired roughness elements concentration,
- find and mark all of the cells which are in a certain distance from the modified face list; this distance represents the roughness elements height,
- create a cell list from the marked cells,
- remove the marked cells from the computational domain.

## 5. Solution Procedure and Discretization

## 6. Results

#### 6.1. Pressure Distribution

#### 6.2. Lift Coefficient

#### 6.3. Cavitation Pattern

#### 6.4. Cavitation-Vortex Interaction

## 7. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Location and numberings of the pressure probes used in the Delft twist11 foil tests [6].

**Figure 8.**Isometric view of the numerical results of Figure 7e.

**Figure 10.**Isometric view of the numerical results of Figure 9c.

**Figure 11.**Distribution of vorticity properties for the smooth and tripped cases at Y = 0.5. (

**a**) Magnitude of Q-criterion. (

**b**) Magnitude of velocity curl. (

**c**) Magnitude of stretching term. (

**d**) Magnitude of dilatation term. (

**e**) Magnitude of baroclinic term.

Terms | Description |
---|---|

${\omega}_{j}\frac{\partial {u}_{i}}{\partial {x}_{j}}$ | Vorticity stretching and turning due to the flow velocity gradients. |

${\omega}_{i}\frac{\partial {u}_{j}}{\partial {x}_{j}}$ | Vorticity dilatation due to the velocity divergence. |

$\frac{1}{{\left({\rho}_{m}\right)}^{2}}{\u03f5}_{ijk}\frac{\partial {\rho}_{m}}{\partial {x}_{j}}\frac{\partial p}{\partial {x}_{k}}$ | Vorticity baroclinic torque due to misalignment of the density and the pressure gradients. |

$\nu \frac{{\partial}^{2}{\omega}_{i}}{\partial {x}_{j}\partial {x}_{j}}$ | Vorticity diffusion due to the flow viscosity. |

Phase | Density (kg/m${}^{3}$) | Dynamic Viscosity (m${}^{2}$/s) |
---|---|---|

Liquid | 1000 | ${10}^{-6}$ |

Vapor | $2.3\times {10}^{-2}$ | $4.27\times {10}^{-4}$ |

**Table 3.**Comparison of the shedding frequency and the time averaged Lift coefficient for the smooth and tripped cases.

Mesh | ${\mathit{C}}_{\mathbf{lift}}$ | ${\mathit{C}}_{\mathbf{lift}}$ Comparative Error (%) | ${\mathit{f}}_{\mathbf{Hz}}$ | ${\mathit{f}}_{\mathbf{Hz}}$ Comparative Error (%) |
---|---|---|---|---|

Smooth | 0.453 | −11.5 | 34.1 | 4.9 |

Tripped | 0.417 | −18.2 | 33.0 | 1.5 |

Exp. [6] | 0.51 | - | 32.5 | - |

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**MDPI and ACS Style**

Asnaghi, A.; Bensow, R.E.
Impact of Leading Edge Roughness in Cavitation Simulations around a Twisted Foil. *Fluids* **2020**, *5*, 243.
https://doi.org/10.3390/fluids5040243

**AMA Style**

Asnaghi A, Bensow RE.
Impact of Leading Edge Roughness in Cavitation Simulations around a Twisted Foil. *Fluids*. 2020; 5(4):243.
https://doi.org/10.3390/fluids5040243

**Chicago/Turabian Style**

Asnaghi, Abolfazl, and Rickard E. Bensow.
2020. "Impact of Leading Edge Roughness in Cavitation Simulations around a Twisted Foil" *Fluids* 5, no. 4: 243.
https://doi.org/10.3390/fluids5040243