Macroscopic Modeling of an Agglomerated and Sintered Particle in Air Plasma Spraying

  • K. Bobzin
  • M. Öte
  • M. A. Knoch
  • I. AlkhasliEmail author
Peer Reviewed


Existing modeling techniques can determine the heat transfer within idealized spherical particles with homogenous morphology. Agglomerated particles are not homogenous and consist of multiple smaller particles which are packed together. The reduced contact area between the individual smaller particles results in a drastic reduction in the effective thermal conductivity of the agglomerate. Conversely, it can enhance the heat transfer due to the increased particle surface area and gas penetration into the agglomerate. Moreover, the momentum transfer from the plasma to the agglomerate differs from that of a homogenous spherical particle, which can significantly affect the heating dynamics of the agglomerate. All of the mentioned phenomena have been taken into account in a novel particle modeling approach by resolving the 3-D geometry of the agglomerates and the flow around it. The presented model is coupled with the particle-laden free jet model. Differences in kinematics and heating dynamics of the agglomerates have been analyzed with regard to their packing densities. The presented model was compared to a simplified approach where the agglomerates were represented by spherical particles with their mass corresponding to the agglomerates with different packing distances. The comparison proved the necessity of 3-D resolution of the particle morphology.


agglomerated particles ceramic particles particle heating particle modeling plasma spraying 



This work was supported by the German Research Foundation (DFG) conducted in the context of the Collaborative Research Centre SFB1120 “Precision Melt Engineering” at RWTH Aachen University.


  1. 1.
    P. Fauchais et al., Knowledge Concerning Splat Formation. An Invited Review, J. Therm. Spray Technol., 2004, 13(3), p 337-360CrossRefGoogle Scholar
  2. 2.
    H. Voggenreiter et al., Influence of Particle Velocity and Molten Phase on the Chemical and Mechanical Properties of HVOF-Sprayed Structural Coatings of Alloy 316L, ASM International, Materials Park, 1995Google Scholar
  3. 3.
    P. Fauchais and M. Vardelle, Sensors in Spray Processes, J. Therm. Spray Technol., 2010, 19(4), p 668-694CrossRefGoogle Scholar
  4. 4.
    D.Y.C. Wei, B. Farouk, and D. Apelian, Melting Metal Powder Particles in an Inductively Coupled R.F. Plasma Torch, Metall. Trans., 1988, 19(2), p 213-226CrossRefGoogle Scholar
  5. 5.
    E. Bourdin, P. Fauchais, and M.I. Boulos, Transient Heat Conduction Under Plasma Conditions, Int. J. Heat Mass Transf., 1983, 26, p 567-582CrossRefGoogle Scholar
  6. 6.
    P. Fauchais, Understanding Plasma Spraying, J. Phys. D Appl. Phys., 2004, 37(9), p 86-108CrossRefGoogle Scholar
  7. 7.
    D. Khelfi, A.A. El-Hadj, and N. Aït-Messaoudène, Modeling of a 3D Plasma Thermal Spraying and the Effect of the Particle Injection Angle, in Conference Proceeding of Revue des Energies Renouvelables CISM’08 (2008), p 205-216Google Scholar
  8. 8.
    M. Pasandideh-Fard et al., Splat Shapes in a Thermal Spray Coating Process: Simulations and Experiments, J. Therm. Spray Technol., 2002, 11(2), p 206-217CrossRefGoogle Scholar
  9. 9.
    M. Vardelle et al., Influence of Particle Parameters at Impact on Splat Formation and Solidification in Plasma Spraying Processes, J. Therm. Spray Technol., 1995, 4(1), p 50-58CrossRefGoogle Scholar
  10. 10.
    R. Djebali, A Confrontation of Lattice Boltzmann, Finite Difference and Taguchi Experimental Design Results for Optimizing Plasma Spraying Operating Conditions Toward Deposit Requirements, Int. J. Energy Optim. Eng., 2017, 6(4), p 16-34Google Scholar
  11. 11.
    R. Djebali, Optimization Study of the Operating Conditions to Improve the Quality of Surfaces Coating Obtained by Plasma Spraying Process, J. Therm. Eng., 2017, 3(4), p 1411-1418CrossRefGoogle Scholar
  12. 12.
    R. Djebali et al., Scrutiny of Spray Jet and Impact Characteristics Under Dispersion Effects of Powder Injection Parameters in APS Process, Int. J. Therm. Sci., 2016, 100, p 229-239CrossRefGoogle Scholar
  13. 13.
    R. Djebali, B. Pateyron, and M. El Ganaoui, A Lattice Boltzmann Based Investigation of Powder In-Flight Characteristics During APS Process, Part II. Effects of Parameter Dispersions at Powder Injection, Surf. Coat. Technol., 2013, 220, p 157-163CrossRefGoogle Scholar
  14. 14.
    R. Djebali, B. Pateyron, and M. ElGanaoui, Scrutiny of Plasma Spraying Complexities with Case Study on the Optimized Conditions Toward Coating Process Control, Case Stud. Therm. Eng., 2015, 6, p 171-181CrossRefGoogle Scholar
  15. 15.
    H. Zhang, S. Hu, and G. Wang, Simulation of Powder Transport in Plasma Jet via Hybrid Lattice Boltzmann Method and Probabilistic Algorithm, Surf. Coat. Technol., 2006, 201(3-4), p 886-894CrossRefGoogle Scholar
  16. 16.
    Y.Z. Sun and Y.B. Dang, Numerical Simulation of Atmospheric Pressure Plasma Jet Using Lattice Boltzmann Method, AMM, 2010, 44-47, p 1838-1842CrossRefGoogle Scholar
  17. 17.
    Z. Driss, B. Necib, and H.-C. Zhang, Thermo-Mechanics Applications and Engineering Technology, Springer, Cham, 2018CrossRefGoogle Scholar
  18. 18.
    K. Bobzin et al., Macroscopic Particle Modeling in Air Plasma Spraying, Surf. Coat. Technol., 2019, 364, p 449-456CrossRefGoogle Scholar
  19. 19.
    Y. Borisov, A. Bushma, and I. Krivtsun, Modeling of Motion and Heating of Powder Particles in Laser, Plasma, and Hybrid Spraying, J. Therm. Spray Technol., 2006, 15(4), p 553-558CrossRefGoogle Scholar
  20. 20.
    I. Ahmed and T.L. Bergman, Three-Dimensional Simulation of Thermal Plasma Spraying of Partially Molten Ceramic Agglomerates, J. Therm. Spray Technol., 2000, 9(2), p 215-224CrossRefGoogle Scholar
  21. 21.
    X. Chen et al., Heat Transfer to a Particle under Plasma Conditions with Vapor Contamination from the Particle, Plasma Chem. Plasma Process., 1985, 5(2), p 119-141CrossRefGoogle Scholar
  22. 22.
    S. Dyshlovenko et al., Modelling of Plasma Particle Interactions and Coating Growth for Plasma Spraying of Hydroxyapatite, Surf. Coat. Technol., 2005, 200(12), p 3757-3769Google Scholar
  23. 23.
    K. Bobzin et al., Simulation of the Particle Melting Degree in Air Plasma Spraying, in Proceedings HTPP: 14th High-Tech Plasma Processes Conference, vol 89 (2017)Google Scholar
  24. 24.
    F. Ben Ettouil et al., Fast Modeling of Phase Changes in a Particle Injected Within a DC Plasma Jet, J. Therm. Spray Technol., 2007, 16(5-6), p 744-750CrossRefGoogle Scholar
  25. 25.
    J.W. McKelliget et al., An Integrated Mathematical Model of the Plasma Spraying Process, in Thermal Spray 1998: Meeting the Challenges of the Twenty First Century, vol 15 (1998), p 335-340Google Scholar
  26. 26.
    D.K. Das and R. Sivakumar, Modelling of the Temperature and the Velocity of Ceramic Powder Particles in a Plasma Flame—I. Alumina, Acta Metall. Mater., 1990, 38(11), p 2187-2192CrossRefGoogle Scholar
  27. 27.
    K. Saha, S. Chaudhuri, and B.M. Cetegen, Modeling of Ceramic Particle Heating and Melting in a Microwave Plasma, J. Heat Transf., 2010, 133(3), p 10Google Scholar
  28. 28.
    “Thermal Spray Materials Guide V2017.04,” 04.2017, Accessed 21 Jan 2019
  29. 29.
    M. Öte, Understanding Multi-Arc Plasma Spraying, Shaker Verlag, Aachen, 2016Google Scholar
  30. 30.
    K. Bobzin et al., Development of Simulative Approaches for Precisely Designing the Properties of Plasma Sprayed Coatings for Application in Injection Moulding, in 3rd ECCOMAS Young Investigators Conference Proceedings, vol 3, (2015), p 6-10Google Scholar
  31. 31.
    K. Bobzin et al., Modelling the Plasma Jet in Multi-arc Plasma Spraying, J. Therm. Spray Technol., 2016, 25(6), p 1111-1126CrossRefGoogle Scholar
  32. 32.
    K. Bobzin and M. Öte, Modeling Multi-arc Spraying Systems, J. Therm. Spray Technol., 2016, 25(5), p 920-932CrossRefGoogle Scholar
  33. 33.
    K. Bobzin and M. Öte, A Numerical Investigation: Air Plasma Spraying by Means of a Three-Cathode Spraying Torch, in Thermal Spray 2015: Proceedings from the International Thermal Spray Conference (2015), p 217-222Google Scholar
  34. 34.
    K. Bobzin et al., A Numerical Investigation: Influence of the Operating Gas On the Flow Characteristics of a Three-Cathode Air Plasma Spraying System, in Thermal Spray 2013: Proceedings of International Thermal Spray Conference (2013), p 400-405Google Scholar
  35. 35.
    J.E. Bardina, P.G. Huang, and T.J. Coakley, Turbulence Modeling Validation: Testing and Development, NASA Technical Memorandum 110446 (1997)Google Scholar
  36. 36.
    M. Vardelle et al., Plasma–Particle Momentum and Heat Transfer: Modelling and Measurements, AlChE J., 1983, 29(2), p 236-243CrossRefGoogle Scholar
  37. 37.
    S. Dyshlovenko et al., Numerical Simulation of Hydroxyapatite Powder Behaviour in Plasma Jet, Surf. Coat. Technol., 2004, 179(1), p 110-117CrossRefGoogle Scholar
  38. 38.
    D.-Y. Xu, X.-C. Wu, and X. Chen, Motion and Heating of Non-spherical Particles in a Plasma Jet, Surf. Coat. Technol., 2003, 171(1-3), p 149-156CrossRefGoogle Scholar
  39. 39.
    J. Mostaghimi et al., Modeling Thermal Spray Coating Processes. A Powerful Tool in Design and Optimization, Surf. Coat. Technol., 2003, 163-164, p 1-11CrossRefGoogle Scholar
  40. 40.
    M.P. Planche, R. Bolot, and C. Coddet, In-Flight Characteristics of Plasma Sprayed Alumina Particles. Measurements, Modeling, and Comparison, J. Therm. Spray Technol., 2003, 12(1), p 101-111CrossRefGoogle Scholar
  41. 41.
    T.K. Thiyagarajan et al., Simulation Studies to Optimize the Process of Plasma Spray Deposition of Yttrium Oxide, J. Phys. Conf. Ser., 2010, 208, p 12116CrossRefGoogle Scholar
  42. 42.
    K. Bobzin and M. Öte, Numerical Coupling of the Particulate Phase to the Plasma Phase in Modeling of Multi-Arc Plasma Spraying, in Proceedings HTPP: 14th High-Tech Plasma Processes Conference (2017)Google Scholar
  43. 43.
    K. Bobzin and M. Öte, Modelling the Plasma–Particle Interaction in Multi-arc Plasma Spraying, J. Therm. Spray Technol., 2016, 26(3), p 279-291CrossRefGoogle Scholar
  44. 44.
    K. Bobzin et al., A Numerical Parameter Study on Plasma Jet and Particle Behavior in Multi-Arc Plasma Spraying, J. Therm. Spray Technol. (JTST), 2017, 26, p 811-830CrossRefGoogle Scholar
  45. 45.
    K. Bobzin et al., Numerical Study on Plasma Jet and Particle Behavior in Multi-arc Plasma Spraying, J. Therm. Spray Technol., 2017, 26(5), p 811-830CrossRefGoogle Scholar
  46. 46.
    L.-Z. Zhang, Conjugate Heat and Mass Transfer in Heat Mass Exchanger Ducts, Elsevier Academic Press, Amsterdam, 2014Google Scholar
  47. 47.
    T.L. Perelman, On Conjugated Problems of Heat Transfer, Int. J. Heat Mass Transf., 1961, 3(4), p 293-303CrossRefGoogle Scholar
  48. 48.
    A. Burcat and B. Ruscic, Third Millennium Ideal Gas and Condensed Phase Thermochemical Database for Combustion with Updates from Active Thermochemical Tables, Argonne National Laboratory, Lemont, 2005CrossRefGoogle Scholar

Copyright information

© ASM International 2019

Authors and Affiliations

  1. 1.Surface Engineering Institute at RWTH Aachen UniversityAachenGermany

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