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Modelling Transport Phenomena during Spreading and Solidification

Modelling Transport Phenomena during Spreading and Solidification of Droplets in Plasma Projection. Dominique GOBIN CNRS – France. NGU Seminar Nova Gorica (November 5, 2009). Contents. Motivation Equations Isothermal spreading

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Modelling Transport Phenomena during Spreading and Solidification

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  1. Modelling Transport Phenomena during Spreading and Solidification of Droplets in Plasma Projection Dominique GOBIN CNRS – France NGU Seminar Nova Gorica (November 5, 2009)

  2. Contents • Motivation • Equations • Isothermal spreading • Spreading with solidification • Perspective

  3. Building up a coating Powder Cooling Molten Particles Substrate Cathode Plasma Coating Gaz Anode The functional properties of the coating depend on the cohesion and adhesion of the splats

  4. Characteristic times – Spatial scales

  5. Modelling issues Poudre Refroidissement Particules fondues Substrat Cathode Plasma Dépôt Gaz Anode Modelling the plasma Spreading and solidification of droplets on a cold substrate In-flight melting (vaporization) of particles Building-up the coating Define and control the process parameters

  6. Droplet spreading and solidification Impacting Particle T0 > Tm V0  100 m/s 20 < d0 < 50µm Tsplat and dsplat time evolution Ts Substrate

  7. 2. Equations

  8. Modelling spreading Pure fluid dynamics problem. The substrate is a boundary condition Mass Conservation Momentum Conservation

  9. Modelling spreading Non-dimensionalizing variables (choosing reference values d0, V0, etc…) yields the dimensionless parameters of the problem Mass Conservation Momentum Conservation

  10. Modelling spreading with solidification Coupling the equations of fluid dynamics with the heat transfer equations Mass Conservation Momentum Conservation Energy Conservation - in the splat - in the substrate

  11. Modelling spreading with solidification During solidification two phases (solide and fluid) are present. A phase function is defined : 1if liquid 0 if solid = Mass Conservation Momentum Conservation

  12. Modelling spreading with solidification Heat transfer and enthalpy formulation Energy Conservation

  13. Conservation equations Mass Conservation Momentum Conservation Energy Conservation 1 liquid 0 solid Liquid Fraction =

  14. Physical parameters of the problem Parameters of the particles at impact Nature Size Velocity Temperature and state of melting Parameters of the substrate Nature Rugosity Initial temperature Surface chemistry (wettability)

  15. Spreading and solidification of a splat 1. Operation parameters : • Dynamic contact angle 2. Adjustable parameters : Splat Substrate • Contact thermal resistance

  16. Numerical tool Simulent-Drop : a software developed at the University of Toronto (J. Mostaghimi et al.) Main hypotheses • Newtonian fluid • Constant properties (surface tension, contact resistance, conductivities, viscosity, …) • Equilibrium solidification

  17. Numerical tool : main features • Finite difference method • Fixed regular grid (Eulerian formulation) • Boundary condition using dynamic contact angles • Interface reconstruction : VoF method • 3-D Geometry (computational domain : a quarter of the domain) Typical grid Symmetry Full domain Computational domain

  18. Scales Micrometric droplets (Conditions of plasma projection) Millimetric droplets (Free fall conditions) Similitude ? Re ~ identiques We ~10 à 100 fois plus grand d ~1 mm > 10 µm Vimpact > 100 m/s ~ 1 m/s Characteristic times µs ms - 19 -

  19. 3. Isothermal spreading

  20. Isothermal impact of a water droplet Simulation F. Loghmari Water droplet spreading d0 = 2,75 mm , V0 = 1.18 m/s on soft wax q = (105°,95°) Rioboo et al. (2001) - 21 – 1 ²

  21. Simulation Experiments Spreading factor d(t)/do Reduced time : t* = t Vo/ do

  22. θr Substrat Backward dynamic contact angle Wettability effect θa Substrat Forward dynamic contact angle Backward angle effect (θa = 105°) Forward angle effect (θr = 95°) - 23 -

  23. 4. Spreading with solidification

  24. mm-size droplet simulation Simulation Nabil Ferguen Copper droplet on steel substrate d = 3 mm – V = 4 m/s – Ts = 25°C

  25. Vp=8 m/s Vp=4 m/s No solidification Vp=2 m/s With solidification Impact velocity influence Vp=8 m/s Vp=4 m/s Vp=2 m/s Time evolution of the spreading factor - 26 - - 26 -

  26. Impact velocity influence Vp = 8 m/s Vp=8 m/s Vp=4 m/s Vp=2 m/s Vp = 4 m/s Time evolution of the spreading factor Vp = 2 m/s - 27 - - 27 -

  27. Contact thermal resistance Non perfect contact between the drop and a rugous substrate => resistance to the heat flux : temperature discontinuity at the interface CTR Model - 28 - - 28 -

  28. Influence of the contact thermal resistance 10-5 m²K.W-1 5.10-6 m²K.W-1 2.10-6 m²K.W-1 10-6 m²K.W-1 - 29 - - 29 -

  29. High contact resistance RTC = 10-5 m²K.W-1 Simulation Nabil Ferguen Copper droplet on steel substrate d = 3 mm – V = 4 m/s – Ts = 400°C

  30. Low contact resistance RTC = 10-6 m²K.W-1 Simulation Nabil Ferguen Copper droplet on steel substrate d = 3 mm – V = 4 m/s – Ts = 400°C

  31. Influence of the initial substrate temperature Ti Cr Cu To = 300 K To = 673 K From Fukumoto et al. (1995)

  32. Splat formation Morphological transition temperature Tt Alumina on steel 304L « Splash » Cold substrate Tsub< Tt Poor adhesionof the coating ( 4 MPa) « Splat » Pre-heated substrate Tsub> Tt Better adhesion ( 30 MPa)

  33. No solidification Ffacteur d’étalement Influence of the substrate temperature Vp = 4 m/s ; dp = 2 mm ; T0 = 1100 °C, Tf = 1080 °C Re = 23900 , We = 191 Ts = 1084 °C Ts = 800°C Ts = 400°C  Ts = 25°C Pre-heating of the substrate : higher final splat diameter

  34. Transition Temperature ? • Desorption of adsorbates and condensates • Modification of wettability of the substrate • Modification the thermal resistance • Possible evolution of the surface state of the substrate

  35. 5. Further developments

  36. Non equilibrium Solidification • Basic hypothesis : solidification at equilibrium • Most models do not take into account undercooling, nucleation and growth : problem of multi-scale (micro + macro) simulation • But in plasma projection, the cooling velocity measured in the experiments reaches from106to 5.108 K/s : • undercooling about 0,1 to 0,2 Tm. •  Include rapid solidification

  37. Experiments on mm-size droplets Film S. Goutier – M. Vardelle Alumina droplet on steel substrate d = 5 mm – V = 10 m/s – Ts = 400°C

  38. Thank you for your attention • Special Thanks to : • Nabil Ferguen : SPCTS Laboratory • Simon Goutier : SPCTS Laboratory • Fahmi Loghmari : FAST Laboratory

  39. Isothermal impact of a water droplet Simulation F. Loghmari Water droplet spreading d0 = 2,75mm , V0 = 1.18m/s on soft wax q = (105°,95°) Rioboo et al. (2001) - 41 – 1 ²

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