# Performance Assessment of a Planing Hull Using the Smoothed Particle Hydrodynamics Method

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## Abstract

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## 1. Introduction

- Fu et al., (2014) [13] showed the results from a collaborative research effort involving two different CFD codes: CFDShip-Iowa and Numerical Flow Analysis – NFA. The results were presented and discussed examining the hydrodynamic forces, moments, hull pressures, accelerations, motions, and the multi-phase free-surface flow field generated by a prismatic planing craft at high speed in calm water and waves. The comparison between numerical and experimental data for still water conditions indicated that at high Froude Number (${F}_{r}$), the dynamic trim was generally under-predicted and the resistance over-predicted.
- Kandasamy et al., (2011) [14] exposed a Verification and Validation (V&V) analysis in full scale with the Unsteady Reynolds-Averaged Navier–Stokes (URANS) code CFDShip-Iowa for two high-speed semi-planing foil-assisted catamarans. Comparing the experimental data against the full-scale simulation results, the resistance comparison error was in the range of 9.6% to 15.5% and the dynamic trim angle comparison error was in the range of −44.1% to 0.8%.
- Yousefy et al., (2013) [15] conducted a comprehensive study on the existing numerical techniques for planing craft and they used several different commercially available CFD software programs (ANSYS-FLUENT, ANSYS-CFX, CFD Ship-Iowa, ShipFlow, Tdyn, CD-Adapco Star-CCM+) to determine the flow field around a planing hull.
- De Luca et al., (2016) [18] showed the results of a comprehensive V&V campaign of simulations of resistance test in still water condition using the hulls of the warped planing hulls of the Naples Systematic Series. The analysis depicts, for a wide range of speed and different hull shapes, the simulation uncertainty and the comparison errors. All the simulations in this study were carried out using the CFD software Star-CCM+.

## 2. DualSPHysics Code

#### 2.1. SPH Method

#### 2.2. Fluid-Solid Interaction

#### 2.3. Dynamic Boundary Conditions

#### 2.4. Open Boundary Conditions

#### 2.5. Coupling with Project Chrono

## 3. Benchmark Experimental Data

#### 3.1. Experimental Data

#### 3.2. Testing Facility

## 4. Numerical Setup

## 5. Results

#### 5.1. Hydrostatic Test

#### 5.2. Total Resistance, Dynamic Trim Angle, and Sinkage

#### 5.3. Whisker Spray

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

BEM | Boundary Element Method |

CCP | Cone Complementary Problem |

CFD | Computational Fluid Dynamics |

CFL | Courant-Friedrich-Lewy Number |

DBC | Dynamic Boundary Condition |

DII | Department of Industrial Engineering |

DVI | Differential Variational Inequality |

Fr | Froude Number |

FVM | Finite Volume Method |

GPU | Graphics Processing Unit |

HSMV | High-Speed Marine Vehicle |

ITTC | International Towing Tank Conference |

LCB | Longitudinal position of the Center of Buoyancy |

NFA | Numerical Flow Analysis |

NS | Navier–Stokes |

NSS | Naples Systematic Series |

Re | Reynolds Number |

(U)RANS | (Unsteady) Reynolds-Averaged Navier–Stokes |

SPH | Smoothed Particle Hydrodynamics |

V&V | Verification & Validation |

VOF | Volume of Fluid |

WCSPH | Weakly Compressible Smoothed Particle Hydrodynamics |

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**Figure 4.**Static sinkage (

**a**), static trim angle (

**b**), and net vertical force (

**c**) in hydrostatic condition (still water with zero-speed flow test).

**Figure 5.**Total Resistance (

**a**), dynamic trim angle (

**b**), and dynamic sinkage (

**c**) comparison between experimental and SPH simulations.

**Figure 6.**C1 hull at $Fr=1.443$, (

**A**) Whisker spray, (

**B**) Main spray, (

**C**) Spray edge (red line), (

**D**) Spray root, (

**E**) Reflection of the spray edge.

**Figure 7.**C1 hull simulated at $Fr=1.443$, (

**A**) Whisker spray, (

**B**) Main spray, (

**C**) Spray edge (red line), (

**D**) Spray root.

Authors | Year | Type of Study | Type of High-Speed Craft | Test Conditions | V&V * |
---|---|---|---|---|---|

Thornhill et al. [5] | 2003 | Experimental | Prismatic planing hull | Still water | no |

Begovic and Bertorello [6] | 2012 | Experimental | Prismatic and warped planing hull | Still water | no |

Matveev [7] | 2014 | Analytical | Warped planing hull | Still water | no |

Sukas et al. [8] | 2015 | Experimental and Numerical | Prismatic and Warped planing hull | Still water | yes |

Jiang et al. [9] | 2016 | Experimental and Numerical | Planing trimaran hull | Still water | yes |

De Marco et al. [10] | 2017 | Experimental and Numerical | Stepped hull | Still water | yes |

Niazmand Bilandi et al. [11] | 2018 | Analytical and Experimental | Stepped hull | Still water | no |

Tavakoli et al. [12] | 2020 | Experimental, Numerical, and Analytical | Warped planing hull | Still water, Regular waves | yes |

Hull Dimensions | Unit | C1 Hull | |
---|---|---|---|

${L}_{OA}$ | Length overall | [m] | 2.611 |

${L}_{WL}$ | Length waterline | [m] | 2.400 |

${B}_{WL}$ | Beam waterline | [m] | 0.743 |

${T}_{m}$ | Hull draft max | [m] | 0.167 |

$\Delta $ | Displacement | [kg] | 106.07 |

${S}_{WS}$ | Wetted Surface | [m^{2}] | 1.70 |

${\tau}_{S}$ | Static trim | [deg] | 0.0 |

$L/B$ | Length to beam ratio | 3.45 | |

$L/{\nabla}^{1/3}$ | Length to volume ratio | 5.11 |

**Table 3.**Percentage comparison error between experimental and SPH and simulations with $dp=0.006$ m for the three variables (total resistance, dynamic trim angle, and sinkage).

$\mathit{Fr}$ | Total Resistance | Dynamic Trim Angle | Dynamic Sinkage |
---|---|---|---|

0.618 | 3.52% | −17.92% | 319.73% |

0.824 | −1.89% | −6.89% | 53.41% |

1.031 | −5.34% | −6.55% | 0.53% |

1.237 | −0.55% | −6.15% | −16.95% |

1.443 | −3.29% | −2.04% | 16.20% |

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**MDPI and ACS Style**

Tagliafierro, B.; Mancini, S.; Ropero-Giralda, P.; Domínguez, J.M.; Crespo, A.J.C.; Viccione, G. Performance Assessment of a Planing Hull Using the Smoothed Particle Hydrodynamics Method. *J. Mar. Sci. Eng.* **2021**, *9*, 244.
https://doi.org/10.3390/jmse9030244

**AMA Style**

Tagliafierro B, Mancini S, Ropero-Giralda P, Domínguez JM, Crespo AJC, Viccione G. Performance Assessment of a Planing Hull Using the Smoothed Particle Hydrodynamics Method. *Journal of Marine Science and Engineering*. 2021; 9(3):244.
https://doi.org/10.3390/jmse9030244

**Chicago/Turabian Style**

Tagliafierro, Bonaventura, Simone Mancini, Pablo Ropero-Giralda, José M. Domínguez, Alejandro J. C. Crespo, and Giacomo Viccione. 2021. "Performance Assessment of a Planing Hull Using the Smoothed Particle Hydrodynamics Method" *Journal of Marine Science and Engineering* 9, no. 3: 244.
https://doi.org/10.3390/jmse9030244