# Numerical Study of Fluid–Solid Interaction in Elastic Sluice Based on SPH Method

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Numerical Model

#### 2.1. Governing Equations

#### 2.2. SPH Methodology

#### 2.3. Particle Velocity Correction

#### 2.4. Flow–Solid Interface Treatment

#### 2.4.1. Dynamic Interface Conditions

#### 2.4.2. Motion Interface Conditions

## 3. Model Validation

#### 3.1. Comparison of Water Flow Patterns

#### 3.2. Comparison of Gate Opening and Free Liquid Level

_{1}and the numerical simulation data points as N

_{2}using the similarity equation:

_{1i}is the experimental data vertical coordinate values, and y

_{2i}is the value of the vertical coordinate of the simulation results.

#### 3.3. Fluid–Solid Pressure Comparison

## 4. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

- Liu, M.; Zhang, Z. Smoothed particle hydrodynamics (sph) for modeling fluid-structure interactions. Sci. China Phys. Mech. Astron.
**2019**, 62, 1–38. [Google Scholar] [CrossRef] - Wang, Y.; Gao, B.; Ren, W. Aerodynamic load and structure stress analysis on hood of high-speed railway tunnel. Chin. J. Theor. Appl. Mech.
**2017**, 49, 48–54. [Google Scholar] - Liu, J.; Bao, X.; Tan, H.; Wang, J.; Guo, D. Dynamical artificial boundary for fluid medium in wave motion problems. Chin. J. Theor. Appl. Mech.
**2017**, 49, 1418–1427. [Google Scholar] - Du, T.; Wang, Y.; Huang, C.; Liao, L. Study on coupling effects of underwater launched vehicle. Chin. J. Theor. Appl. Mech.
**2017**, 49, 782–792. [Google Scholar] - Chen, W.; Fu, Y.; Guo, S.; Jiang, C. Fluid-solid coupling and dynamic response of vortex-induced vibration of slender ocean cylinders. Adv. Mech.
**2017**, 47, 25–91. [Google Scholar] - He, T.; Zhang, K.; Wang, T. AC-CBS-based partitioned semi-implicit coupling algorithm for fluid-structure interaction using stabilized second-order pressure scheme. Commun. Comput. Phys.
**2017**, 21, 1449–1474. [Google Scholar] [CrossRef] - Zhou, D.; He, T.; Tu, J. A modified CBS finite element approach for fluid-structure interaction. Chin. J. Theor. Appl. Mech.
**2012**, 44, 494–504. [Google Scholar] - Chen, W.; Ji, C.; Xu, W. Numerical investigation on the asymmetric vibration and symmetry hysteresis of flow-induced vibration of two side-by-side cylinders. Chin. J. Theor. Appl. Mech.
**2015**, 47, 731–739. [Google Scholar] - Sun, X.; Zhang, J.; Huang, B. An application of the cbs scheme in the fluid-membrane interaction. Chin. J. Theor. Appl. Mech.
**2013**, 45, 787–791. [Google Scholar] - Liu, Z.; Nan, S.; Shi, Y. Hemodynamic parameters analysis for coronary artery stenosis of intermediate severity model. Chin. J. Theor. Appl. Mech.
**2017**, 49, 1058–1064. [Google Scholar] - Bazilevs, Y.; Calo, V.M.; Hughes, T.J.R.; Zhang, Y. Isogeometric fluid-structure interaction: Theory, algorithms, and computations. Comput. Mech.
**2008**, 43, 3–37. [Google Scholar] [CrossRef] - Antona, R.; Vacondio, R.; Avesani, D.; Righetti, M.; Renzi, M. Towards a High Order Convergent ALE-SPH Scheme with Efficient WENO Spatial Reconstruction. Water
**2021**, 13, 2432. [Google Scholar] [CrossRef] - Capasso, S.; Tagliafierro, B.; Viccione, G. Application of an SPH-DEM Coupled Model for Elastic Fluid–Structure Interaction. Environ. Sci. Proc.
**2022**, 21, 34. [Google Scholar] - Zhang, A.M.; Ming, F.R.; Wang, S.P. Coupled SPHS-BEM method for transient fluid-structure interaction and applications in underwater impacts. Appl. Ocean. Res.
**2013**, 43, 223–233. [Google Scholar] [CrossRef] - Wu, K.; Yang, D.M.; Wright, N. A coupled SPH-DEM model for fluid-structure interaction problems with free-surface flow and structural failure. Comput. Struct.
**2016**, 177, 141–161. [Google Scholar] [CrossRef] - Raymond, S.J.; Jones, B.; Williams, J.R. A strategy to couple the material point method(MPM) and smoothed particle hydrodynamics (SPH) computational techniques. Comput. Part. Mech.
**2018**, 5, 49–58. [Google Scholar] [CrossRef] - Liu, F.; Yu, Y.; Wang, Q.; Luo, Y. A coupled smoothed particle hydrodynamic and finite particle method: An efficient approach for fluid-solid interaction problems involving free-surface flow and solid failure. Eng. Anal. Bound. Elem.
**2020**, 118, 143–155. [Google Scholar] [CrossRef] - Yao, X.; Huang, D. PD-SPH modeling and analysis of fluid-structure interaction problem. Eng. Mech.
**2022**, 39, 17–25. [Google Scholar] - He, T. Numerical simulation of fluid-structure interaction strong coupling based on ALE finite element method. Chin. J. Mech.
**2018**, 50, 395–404. [Google Scholar] - Boscheri, W.; Dumbser, M. A direct Arbitrary-Lagrangian–Eulerian ADER-WENO finite volume scheme on unstructured tetrahedral meshes for conservative and non-conservative hyperbolic systems in 3D. J. Comput. Phys.
**2014**, 275, 484–523. [Google Scholar] [CrossRef] - Liu, G.R.; Liu, M.B. Smoothed Particle Hydrodynamics: A Meshfree Particle Method; World Scientific: Singapore, 2003. [Google Scholar]
- Zienkiewicz, O.C.; Taylor, R.L. The Finite Element Method; McGraw-Hill: New York, NY, USA, 2000. [Google Scholar]
- Zhang, H.; Hao, Z.; Feng, Z. Application of lattice Boltzmann method in simulating droplet impact on liquid level. J. Hydraul. Eng.
**2008**, 39, 1316–1320. [Google Scholar] - Wang, Z.; Li, D.; Hu, Y. An SPH stress correction algorithm and its application in free surface flow. Chin. J. Comput. Mech.
**2017**, 34, 101–105. [Google Scholar] - Lu, W.; Fei, X.; Yang, Y. Improvement of the tensile instability in SPH scheme for the FEI (Fluid-Elastomer Interaction) problem. Eng. Anal. Bound. Elem.
**2019**, 106, 116–125. [Google Scholar] - Liu, M.B.; Liu, G.R. Smoothed Particle Hydrodynamics (SPH): An Overview and Recent Developments. Arch. Comput. Methods Eng.
**2010**, 17, 25–76. [Google Scholar] [CrossRef] - Avesani, D.; Dumbser, M.; Chiogna, G.; Bellin, A. Analternative smooth particle hydrodynamics formulation to simulate chemotaxis in porous media. J. Math. Biol.
**2017**, 74, 1037–1058. [Google Scholar] [CrossRef] [PubMed] - Ng, K.C.; Low, W.C.; Chen, H.; Tafuni, A.; Nakayama, A. A three-dimensional fluid-structure interaction model based on SPH and lattice-spring method for simulating complex hydroelastic problems. Ocean Eng.
**2022**, 260, 112026. [Google Scholar] [CrossRef] - Khayyer, A.; Gotoh, H.; Falahaty, H.; Shimizu, Y. An enhanced ISPH–SPH coupled method for simulation of incompressible fluid–elastic structure interactions. Comput. Phys. Commun.
**2018**, 232, 139–164. [Google Scholar] [CrossRef] - Deng, L. Application of Variable-length Co-rotating Beam Element in Geometric Nonlinear Dynamic Analysis of Flexible Beam. Ph.D. Thesis, Dalian University of Technology, Dalian, China, 2021. [Google Scholar]
- Meng, Z.-F.; Zhang, A.-M.; Yan, J.-L.; Wang, P.-P.; Khayyer, A. A hydroelastic fluid–structure interaction solver based on the iemann-SPH method. Comput. Methods Appl. Mech. Eng.
**2022**, 429, 110028. [Google Scholar] - Rakhshaa, M.; Pazoukib, A.; Serbana, R.; Negrut, D. Using a half-implicit integration scheme for the SPH-based solution of fluid–solid interaction problems. Comput. Methods Appl. Mech. Eng.
**2019**, 345, 100–122. [Google Scholar] [CrossRef] - Yilmaz, A.; Kocaman, S.; Demirci, M. Numerical modeling of the dam-break wave impact on elastic sluice gate: A new benchmark case for hydroelasticity problems. Ocean Eng.
**2021**, 231, 108870. [Google Scholar] [CrossRef] - Monaghan, J.J. Smoothed particle hydrodynamics. Rep. Progr. Phys.
**2005**, 68, 1703–1759. [Google Scholar] [CrossRef] - Gray, J.P.; Monaghan, J.J.; Swift, R.P. SPH elastic dynamics. Comput. Methods Appl. Mech. Eng.
**2001**, 190, 6641–6662. [Google Scholar] [CrossRef] - Antoci, C.; Gallati, M.; Sibilla, S. Numerical simulation of fluid-structure interaction by SPH. Comput. Struct.
**2007**, 85, 879–890. [Google Scholar] [CrossRef] - Gallati, M.; Braschi, G. Simulazione Lagrangiana di flussi consuperficie libera in problemi di idraulica. L’acqua
**2000**, 5, 7–18. [Google Scholar] - Vignjevic, R.; De Vuyst, T.; Campbell, J. The use of an homogeneous repulsive force for contact treatment in SPH. In Proceedings of the Fifth World Congress of Computational Mechanics WCCM V, Vienna, Austria, 7–12 July 2002. [Google Scholar]

**Figure 2.**Comparison between simulation results and experimental free liquid level height curves for different $\lambda $ values at t = 0.36 s in a classical dam failure problem.

**Figure 4.**Dynamic boundary conditions and solid particle a (White color represents solid particles and Blue color represents water particles).

**Figure 6.**Comparison of gate opening and water body flow pattern at different moments and with experimental results from [36].

**Figure 7.**Comparison of gate transverse/longitudinal displacement results with experimental results from [34].

**Figure 8.**Comparison of free liquid level curves with experimental results from [34].

$\mathit{\lambda}$ | $\mathit{\lambda}$ = 0.97 | $\mathit{\lambda}$ = 0.93 | $\mathit{\lambda}$ = 0.88 |
---|---|---|---|

Similarity | 84.1% | 91.9% | 88.3% |

Serial Number | Calculation Condition | Parameter Value |
---|---|---|

1 | Particle spacing (m) | 0.001 |

2 | Number of particles in the water column | 17,997 |

3 | Number of elastomer particles | 1672 |

4 | Sidewall particle count | 2757 |

5 | Density of water (kg/m^{3}) | 1000 |

6 | Density of elastic gate (kg/m^{3}) | 1100 |

7 | Young’s modulus (N/m^{3}) | 4.27 × 10^{6} |

8 | Artificial stress factor (e,q) | 0.3 and 4 |

9 | Time step (s) | 5 × 10^{−6} |

10 | Physical time (s) | 0.4 |

Numerical Method | SPH Method X Displacement | FEM Method X Displacement | SPH Method Y Displacement | FEM Method X Displacement |
---|---|---|---|---|

Similarity | 93.6% | 85.9% | 91.1% | 80.4% |

Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content. |

© 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Zhang, J.; Wang, B.; Jiang, Q.; Hou, G.; Li, Z.; Liu, H.
Numerical Study of Fluid–Solid Interaction in Elastic Sluice Based on SPH Method. *Water* **2023**, *15*, 3738.
https://doi.org/10.3390/w15213738

**AMA Style**

Zhang J, Wang B, Jiang Q, Hou G, Li Z, Liu H.
Numerical Study of Fluid–Solid Interaction in Elastic Sluice Based on SPH Method. *Water*. 2023; 15(21):3738.
https://doi.org/10.3390/w15213738

**Chicago/Turabian Style**

Zhang, Jianwei, Bingpeng Wang, Qi Jiang, Ge Hou, Zhirui Li, and Hongze Liu.
2023. "Numerical Study of Fluid–Solid Interaction in Elastic Sluice Based on SPH Method" *Water* 15, no. 21: 3738.
https://doi.org/10.3390/w15213738