Smoothed particle hydrodynamics (SPH) simulation of impinging jet flows containing abrasive rigid bodies

  • Xiangwei DongEmail author
  • Zengliang Li
  • Chen Jiang
  • Yanxin Liu


A fully Lagrangian model for simulating impinging jet flows containing abrasive particles is established based on smoothed particle hydrodynamics (SPH) method. In the model, both the fluid and the solid are described by SPH, where the jet flow is modeled as the viscous fluid and the metallic target is modeled as the elastic–plastic material. The main novelty of the model is that abrasive particles are explicitly included in the jet flow and modeled as arbitrarily shaped rigid bodies. The interactions among the fluid, solid and abrasives are modeled through suitable techniques that are commonly used in SPH. The simulation of material removal caused by the impact of continuous abrasive-jet flow is conducted as a challenging example to verify the applicability of the model. This new model is attractive for relevant applications, such as solid particle erosion and abrasive water-jet machining. The advantages of the model lie in its conceptual simplicity, straightforward implementation and the relative ease of incorporating new physics.


Fully Lagrangian model Smoothed particle hydrodynamics (SPH) Fluid–structure interaction Jet flow containing rigid bodies Metallic surface 



This research is partially sponsored by the project of China Postdoctoral Science Foundation (Grant No. 2017M622307), Shandong Natural Science Foundation (ZR201709210320). This research is also partially sponsored by Qingdao Government Project of Application and Basic Research (Grant No. BY20170213), and by the Fundamental Research Funds for the Central Universities (Grant No. 18CX02153A).

Compliance with ethical standards

Conflict of interest

On behalf of all authors, the corresponding author states that there is no conflict of interest.


  1. 1.
    Mieszala M, Torrubia PL, Axinte DA et al (2017) Erosion mechanisms during abrasive waterjet machining: model microstructures and single particle experiments. J Mater Process Technol 247:92–102CrossRefGoogle Scholar
  2. 2.
    Axinte DA, Srinivasu DS, Kong MC et al (2009) Abrasive waterjet cutting of polycrystalline diamond: a preliminary investigation. Int J Mach Tools Manuf 49(10):797–803CrossRefGoogle Scholar
  3. 3.
    Junkar M, Jurisevic B, Fajdiga M et al (2006) Finite element analysis of single-particle impact in abrasive water jet machining. Int J Impact Eng 32(7):1095–1112CrossRefGoogle Scholar
  4. 4.
    Kumar N, Shukla M (2012) Finite element analysis of multi-particle impact on erosion in abrasive water jet machining of titanium alloy. J Comput Appl Math 236(18):4600–4610CrossRefzbMATHGoogle Scholar
  5. 5.
    Li WY, Wang J, Zhu H et al (2013) On ultrahigh velocity micro-particle impact on steels—a single impact study. Wear 305(1):216–227CrossRefGoogle Scholar
  6. 6.
    Anwar S, Axinte DA, Becker AA (2011) Finite element modelling of a single-particle impact during abrasive waterjet milling. Proc Inst Mech Eng Part J J Eng Tribol 225(8):821–832CrossRefGoogle Scholar
  7. 7.
    Takaffoli M, Papini M (2009) Finite element analysis of single impacts of angular particles on ductile targets. Wear 267(1):144–151CrossRefGoogle Scholar
  8. 8.
    Lv Z, Huang C, Zhu H et al (2015) FEM analysis on the abrasive erosion process in ultrasonic-assisted abrasive waterjet machining. Int J Adv Manuf Technol 78(9–12):1641–1649CrossRefGoogle Scholar
  9. 9.
    Azimian M, Schmitt P, Bart HJ (2015) Numerical investigation of single and multi impacts of angular particles on ductile surfaces. Wear 342:252–261CrossRefGoogle Scholar
  10. 10.
    Takaffoli M, Papini M (2012) Numerical simulation of solid particle impacts on Al6061-T6 part I: three-dimensional representation of angular particles. Wear 292:100–110CrossRefGoogle Scholar
  11. 11.
    Ma L, Bao R, Guo Y (2008) Waterjet penetration simulation by hybrid code of SPH and FEA. Int J Impact Eng 35(9):1035–1042CrossRefGoogle Scholar
  12. 12.
    Hongxiang J, Changlong D, Songyong L, et al (2014) Numerical simulation of rock fragmentation under the impact load of water jet. Shock Vib vol 2014Google Scholar
  13. 13.
    Jiang H, Liu Z, Gao K (2017) Numerical simulation on rock fragmentation by discontinuous water-jet using coupled SPH/FEA method. Powder Technol 312:248–259CrossRefGoogle Scholar
  14. 14.
    Liu X, Liu S, Ji H (2015) Numerical research on rock breaking performance of water jet based on SPH. Powder Technol 286:181–192CrossRefGoogle Scholar
  15. 15.
    Hsu CY, Liang CC, Teng TL et al (2013) A numerical study on high-speed water jet impact. Ocean Eng 72:98–106CrossRefGoogle Scholar
  16. 16.
    Anwar S, Axinte DA, Becker AA (2013) Finite element modelling of abrasive waterjet milled footprints. J Mater Process Technol 213(2):180–193CrossRefGoogle Scholar
  17. 17.
    Torrubia PL, Axinte DA, Billingham J (2015) Stochastic modelling of abrasive waterjet footprints using finite element analysis. Int J Mach Tools Manuf 95:39–51CrossRefzbMATHGoogle Scholar
  18. 18.
    Wang YF, Yang ZG (2008) Finite element model of erosive wear on ductile and brittle materials. Wear 265(5):871–878CrossRefGoogle Scholar
  19. 19.
    ElTobgy MS, Ng E, Elbestawi MA (2005) Finite element modeling of erosive wear. Int J Mach Tools Manuf 45(11):1337–1346CrossRefGoogle Scholar
  20. 20.
    Hadavi V, Papini M (2015) Numerical modeling of particle embedment during solid particle erosion of ductile materials. Wear 342:310–321CrossRefGoogle Scholar
  21. 21.
    Liu ZG, Wan S, Nguyen VB et al (2014) A numerical study on the effect of particle shape on the erosion of ductile materials. Wear 313(1):135–142CrossRefGoogle Scholar
  22. 22.
    Bui HH, Sako K, Fukagawa R (2007) Numerical simulation of soil–water interaction using smoothed particle hydrodynamics (SPH) method. J Terramech 44(5):339–346CrossRefGoogle Scholar
  23. 23.
    Gong W, Wang J, Na G (2011) Numerical simulation for abrasive water jet machining based on ALE algorithm. Int J Adv Manuf Technol 53(1–4):247–253Google Scholar
  24. 24.
    Irazábal J, Salazar F, Oñate E (2017) Numerical modelling of granular materials with spherical discrete particles and the bounded rolling friction model. Application to railway ballast. Comput Geotech 85:220–229CrossRefGoogle Scholar
  25. 25.
    Idelsohn SR, Oñate E, Pin FD (2003) A Lagrangian meshless finite element method applied to fluid–structure interaction problems. Comput Struct 81(8):655–671CrossRefGoogle Scholar
  26. 26.
    Franci A, Oñate E, Carbonell JM (2016) Velocity-based formulations for standard and quasi-incompressible hypoelastic-plastic solids. Int J Numer Methods Eng 107(11):970–990MathSciNetCrossRefzbMATHGoogle Scholar
  27. 27.
    Takaffoli M, Papini M (2012) Material deformation and removal due to single particle impacts on ductile materials using smoothed particle hydrodynamics. Wear 274:50–59CrossRefGoogle Scholar
  28. 28.
    Liu GR, Liu MB (2003) Smoothed particle hydrodynamics: a meshfree particle method. World Scientific, SingaporeCrossRefzbMATHGoogle Scholar
  29. 29.
    Monaghan JJ, Lattanzio JC (1985) A refined particle method for astrophysical problems. Astron Astrophys 149(1):135–143zbMATHGoogle Scholar
  30. 30.
    Mou-Bin LIU, Li S (2016) On the modeling of viscous incompressible flows with smoothed particle hydro-dynamics. J Hydrodyn Ser B 28(5):731–745CrossRefGoogle Scholar
  31. 31.
    Monaghan JJ (1994) Simulating free surface flows with SPH. J Comput Phys 110(2):399–406MathSciNetCrossRefzbMATHGoogle Scholar
  32. 32.
    Wilkins ML (1999) Computer simulation of dynamic phenomena. In: Computer simulation of dynamic phenomena. SpringerGoogle Scholar
  33. 33.
    Johnson GR, Cook WH (1985) Fracture characteristics of three metals subjected to various strains, strain rates, temperatures and pressures. Eng Fract Mech 21(1):31–48CrossRefGoogle Scholar
  34. 34.
    Monaghan JJ, Gingold RA (1983) Shock simulation by the particle method SPH. J Comput Phys 52:374–389CrossRefzbMATHGoogle Scholar
  35. 35.
    Monaghan JJ (1992) Smoothed particle hydrodynamics. Annu Rev Astron Astrophys 30:543–574CrossRefGoogle Scholar
  36. 36.
    Randies PW, Libersky LD (1996) Smoothed particle hydrodynamics: some recent improvements and applications. Comput Methods Appl Mech Eng 139:375–408MathSciNetCrossRefzbMATHGoogle Scholar
  37. 37.
    Molteni D, Colagrossi A (2009) A simple procedure to improve the pressure evaluation in hydrodynamic context using the SPH. Comput Phys Commun 180(6):861–872MathSciNetCrossRefzbMATHGoogle Scholar
  38. 38.
    Campbell J, Vignjevic R, Libersky L (2000) A contact algorithm for smoothed particle hydrodynamics. Comput Methods Appl Mech Eng 184(1):49–65MathSciNetCrossRefzbMATHGoogle Scholar
  39. 39.
    Dong XW, Liu GR, Li Z et al (2016) A smoothed particle hydrodynamics (SPH) model for simulating surface erosion by impacts of foreign particles. Tribol Int 95:267–278CrossRefGoogle Scholar
  40. 40.
    Bui HH, Fukagawa R, Sako K et al (2008) Lagrangian meshfree particles method (SPH) for large deformation and failure flows of geomaterial using elastic–plastic soil constitutive model. Int J Numer Anal Meth Geomech 32(12):1537–1570CrossRefzbMATHGoogle Scholar
  41. 41.
    Macdonald RA, Macdonald WM (1981) Thermodynamic properties of fcc metals at high temperatures. Phys Rev B 24(4):385–386CrossRefGoogle Scholar
  42. 42.
    Dhar S, Krajac T, Ciampini D et al (2005) Erosion mechanisms due to impact of single angular particles. Wear 258(1):567–579CrossRefGoogle Scholar
  43. 43.
    Qu QL, Wu JL, Guo BD et al (2013) Numerical simulation of sphere impacting water by SPH with hydrodynamics. Adv Mater Res 625:104–108CrossRefGoogle Scholar
  44. 44.
    Banerjee B (2005) An evaluation of plastic flow stress models for the simulation of high-temperature and high-strain-rate deformation of metals. Physics 21:129–134MathSciNetGoogle Scholar
  45. 45.
    Leroch S, Varga M, Eder SJ et al (2016) Smooth particle hydrodynamics simulation of damage induced by a spherical indenter scratching a viscoplastic material. Int J Solids Struct 81:188–202CrossRefGoogle Scholar
  46. 46.
    Dai Z, Huang Y, Cheng H et al (2017) SPH model for fluid–structure interaction and its application to debris flow impact estimation. Landslides 14(3):917–928CrossRefGoogle Scholar
  47. 47.
    Dong X, Li Z, Feng L et al (2017) Modeling, simulation, and analysis of the impact (s) of single angular-type particles on ductile surfaces using smoothed particle hydrodynamics. Powder Technol 318:363–382CrossRefGoogle Scholar
  48. 48.
    Monaghan JJ (1994) Simulating free surface flows with SPH. J Comput Phys 110(2):399–406MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© OWZ 2019

Authors and Affiliations

  • Xiangwei Dong
    • 1
    Email author
  • Zengliang Li
    • 1
  • Chen Jiang
    • 2
    • 3
  • Yanxin Liu
    • 1
  1. 1.College of Mechanical and Electronic EngineeringChina University of Petroleum (East China)QingdaoChina
  2. 2.Key Laboratory of Traffic Safety on the Track (Central South University), Ministry of EducationCentral South UniversityChangshaChina
  3. 3.Joint International Research Laboratory of Key Technology for Rail Traffic SafetyCentral South UniversityChangshaChina

Personalised recommendations