# Characteristics of Slamming Pressure and Force for Trimaran Hull

^{1}

^{2}

^{3}

^{4}

^{5}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Numerical Models and Two-Dimensionality Verification

#### 2.1. Numerical Model

^{3}). The ship model is set 0.377 m above the water at the beginning of simulation. For the whole simulation area, the types of the boundary conditions for the four sides and bottom are set to be non-slip wall, while the top is set as the pressure outlet. The trimaran geometry used in the simulation is the same as the one in the authors’ previous experimental work [2]. The layout of pressure monitors (i.e., p1~p5) and the dimensions of experimental devices are shown in Figure 1.

#### 2.2. Two-Dimensionality Verification

## 3. Results and Discussion

#### 3.1. Simulation Parameters

^{2}).

#### 3.2. Pressure Analysis

#### 3.3. Force Analysis

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

- Dias, F.; Ghidaglia, J.M. Slamming: Recent Progress in the Evaluation of Impact Pressures. Annu. Rev. Fluid Mech.
**2018**, 50, 243–273. [Google Scholar] [CrossRef] - Sun, Z.; Jang, Y.C.; Zong, Z.; Xing, J.T.; Djidjeli, K. Slamming load on trimaran cross section with rigid and flexible arches. Mar. Struct.
**2019**, 66, 227–241. [Google Scholar] [CrossRef] - Wagner, H. Phenomena Associated With Impacts And Sliding on Liquid Surfaces. Z. Angew. Math. Mech.
**1932**, 12, 193–215. [Google Scholar] [CrossRef] - Lavroff, J.; Davis, M.R.; Holloway, D.S.; Thomas, G.A.; McVicar, J.J. Wave impact loads on wave-piercing catamarans. Ocean Eng.
**2017**, 131, 263–271. [Google Scholar] [CrossRef] - Jacobi, G.; Thomas, G.; Davis, M. An insight into the slamming behaviour of large high-speed catamarans through full-scale measurements. J. Mar. Sci. Technol.
**2014**, 19, 15–32. [Google Scholar] [CrossRef] - Yu, H.; Li, Z.J.; Hu, J.J. Slamming Load Forecasts and Analyses of a Trimaran Model Test. J. Ship Mech.
**2014**, 18, 623–634. [Google Scholar] - Davis, M.R.; French, B.J.; Thomas, G.A. Wave slam on wave piercing catamarans in random head seas. Ocean Eng.
**2017**, 135, 84–97. [Google Scholar] [CrossRef] - Panciroli, R.; Abrate, S.; Minak, G.; Zucchelli, A. Hydroelasticity in water-entry problems: Comparison between experimental and SPH results. Compos. Struct.
**2012**, 94, 532–539. [Google Scholar] [CrossRef] - Iranmanesh, A.; Passandideh-Fard, M. A three-dimensional numerical approach on water entry of a horizontal circular cylinder using the volume of fluid technique. Ocean Eng.
**2017**, 130, 557–566. [Google Scholar] [CrossRef] - Nair, V.V.; Bhattacharyya, S.K. Water entry and exit of axisymmetric bodies by CFD approach. J. Ocean Eng. Sci.
**2018**, 3, 156–174. [Google Scholar] [CrossRef] - McVicar, J.; Lavroff, J.; Davis, M.R.; Thomas, G. Fluid–structure interaction simulation of slam-induced bending in large high-speed wave-piercing catamarans. J. Fluids Struct.
**2018**, 82, 35–58. [Google Scholar] [CrossRef] - Chen, Z.Y.; Gui, H.B.; Dong, P.S.; Yu, C.L. Numerical and experimental analysis of hydroelastic responses of a high-speed trimaran in oblique irregular waves. Int. J. Nav. Archit. Ocean Eng.
**2019**, 11, 409–421. [Google Scholar] [CrossRef] - Bilandi, R.N.; Jamei, S.; Roshan, F.; Azizi, M. Numerical simulation of vertical water impact of asymmetric wedges by using a finite volume method combined with a volume-of-fluid technique. Ocean Eng.
**2018**, 160, 119–131. [Google Scholar] [CrossRef] - Krastev, V.K.; Facci, A.L.; Ubertini, S. Asymmetric water impact of a two dimensional wedge: A systematic numerical study with transition to ventilating flow conditions. Ocean Eng.
**2018**, 147, 386–398. [Google Scholar] [CrossRef] - Hu, Z.; Zhao, X.Z.; Li, M.Y.; Fang, Z.H.; Sun, Z.L. A numerical study of water entry of asymmetric wedges using a CIP-based model. Ocean Eng.
**2018**, 148, 1–16. [Google Scholar] [CrossRef] - Sun, Z.; Deng, Y.Z.; Zou, L.; Jiang, Y.C. Investigation of trimaran slamming under different conditions. Appl. Ocean Res.
**2020**, 104, 102316. [Google Scholar] [CrossRef] - Davis, M.R.; Whelan, J.R. Computation of wet deck bow slam loads for catamaran arched cross sections. Ocean Eng.
**2007**, 34, 2265–2276. [Google Scholar] [CrossRef] - Korobkin, A.; Khabakhpasheva, T.; Malenica, S.; Kim, Y. A comparison study of water impact and water exit models. Int. J. Nav. Archit. Ocean Eng.
**2014**, 6, 1182–1196. [Google Scholar] [CrossRef] - Korobkin, A. Analytical models of water impact. Eur. J. Appl. Math.
**2004**, 15, 821–838. [Google Scholar] [CrossRef] - Seng, S. Slamming And Whipping Analysis Of Ships. DTU Mech. Eng.
**2012**, 196, 903–1685. [Google Scholar]

**Figure 1.**Dimensions of trimaran model and schematic diagram of experimental setup ((

**a**) Sketch of trimaran model; (

**b**) Hull dimensions and pressure sensors layout; (

**c**) Schematic diagram of experimental layout).

**Figure 2.**Mesh distribution and the boundary condition setting used in simulation ((

**a**) Meshes of middle section; (

**b**) Overset mesh area and enlarged trimmed mesh around the side hull corner; (

**c**) Body surface and free surface mesh).

**Figure 3.**Comparison of pressure and acceleration time-histories simulations with different lengths in the X direction against experimental results ((

**a**–

**e**) the pressure time histories at p1~p5; (

**f**) the acceleration time-history).

**Figure 4.**The pressure time histories at different monitoring pointes along the X direction and the corresponding peak pressures ((

**a**,

**c**): pressure time histories of monitoring points under main hull p1 and wet-deck p4, respectively, along the X direction in Figure 1b; (

**b**,

**d**): the peak pressures at p1 and p4 vs. X-coordinates, respectively).

**Figure 5.**Pressure varying with penetration depth with different constant entry velocities, and the relation between pressure peak values and square of corresponding entry velocities ((

**a**,

**c**,

**e**,

**g**,

**i**): pressure vs. penetration depth at five monitoring points with different entry velocities; (

**b**,

**d**,

**f**,

**h**,

**j**): peak pressures values vs. square of the entry velocity at five monitoring points).

**Figure 6.**Pressure varying with penetration depth with different constant entry accelerations and pressure peak (after extracting the velocity dependent part) changing with accelerations ((

**a**–

**e**): pressure against penetration depth at five monitoring points for different entry accelerations; (

**f**) velocity against penetration depth; (

**g**–

**j**): peak pressures of monitoring points p2~p5 varying with corresponding accelerations).

**Figure 7.**The pressure contours at the same penetration depth under different entry velocities; the red line is the free surface level (each row of pictures correspond to V, 2 V, 3 V, 4 V, and 5 V, respectively; columns (

**a**–

**c**) correspond to the penetration of 0.089 m, 0.155 m, and 0.178 m, respectively).

**Figure 8.**The pressure contours at the same penetration depth under different entry acceleration, Table 2. g, −g, 0, g, and 2 g in order; columns (

**a**–

**c**) correspond to the penetration of 0.089 m, 0.155 m, and 0.178 m, respectively).

**Figure 9.**The vertical force varying the penetration depth for different constant entry velocity and ${F}_{v}$ estimated from these CFD results ((

**a**) Vertical forces against penetration depth under five velocities; (

**b**) The separated drag coefficient ${F}_{v}$ ).

**Figure 10.**The vertical force varying the penetration depth for different constant entry acceleration and ${F}_{a}$ estimated from these CFD results ((

**a**) Vertical forces against penetration depth under five acceleration; (

**b**) The separated drag coefficient ${F}_{a}$.)

Case | 1 | 2 | 3 | 4 | 5 |

Velocity (m/s) | V | 2 V | 3 V | 4 V | 5 V |

Case | 5 | 6 | 7 | 8 | 9 |

Acceleration (m/s) | 2 g | g | 0 | −g | −2 g |

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**MDPI and ACS Style**

Sun, Z.; Sui, X.; Deng, Y.; Zou, L.; Korobkin, A.; Xu, L.; Jiang, Y.
Characteristics of Slamming Pressure and Force for Trimaran Hull. *J. Mar. Sci. Eng.* **2021**, *9*, 564.
https://doi.org/10.3390/jmse9060564

**AMA Style**

Sun Z, Sui X, Deng Y, Zou L, Korobkin A, Xu L, Jiang Y.
Characteristics of Slamming Pressure and Force for Trimaran Hull. *Journal of Marine Science and Engineering*. 2021; 9(6):564.
https://doi.org/10.3390/jmse9060564

**Chicago/Turabian Style**

Sun, Zhe, Xupeng Sui, Yanzeng Deng, Li Zou, A. Korobkin, Lixin Xu, and Yichen Jiang.
2021. "Characteristics of Slamming Pressure and Force for Trimaran Hull" *Journal of Marine Science and Engineering* 9, no. 6: 564.
https://doi.org/10.3390/jmse9060564