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

Modelling Transport Phenomena during Spreading and Solidification

of Droplets in Plasma Projection

Dominique GOBINCNRS – France

NGU Seminar Nova Gorica (November 5, 2009)

Page 2: Modelling Transport Phenomena during Spreading and Solidification of Droplets in Plasma Projection Dominique GOBIN CNRS – France NGU Seminar Nova Gorica.

2

Contents

1. Motivation

2. Equations

3. Isothermal spreading

4. Spreading with solidification

5.Perspective

Page 3: Modelling Transport Phenomena during Spreading and Solidification of Droplets in Plasma Projection Dominique GOBIN CNRS – France NGU Seminar Nova Gorica.

3

Building up a coating

The functional properties of the coating depend on the cohesion

and adhesion of the splats

Gaz

Cathode

Anode

Cooling

Plasma

Substrate

Powder

Molten Particles

Coating

Page 4: Modelling Transport Phenomena during Spreading and Solidification of Droplets in Plasma Projection Dominique GOBIN CNRS – France NGU Seminar Nova Gorica.

4

Page 5: Modelling Transport Phenomena during Spreading and Solidification of Droplets in Plasma Projection Dominique GOBIN CNRS – France NGU Seminar Nova Gorica.

5

Characteristic times – Spatial scales

Splat Formation (spreading + solidification)

~ 10 µs 0.5 à 5 µm

Time interval between 2 impacts at the same place

10 à 100 µs

Layer Formation A few ms A few 10 µm

Time interval between two passes of the torch

A few s

Time scales Spatial scales

Page 6: Modelling Transport Phenomena during Spreading and Solidification of Droplets in Plasma Projection Dominique GOBIN CNRS – France NGU Seminar Nova Gorica.

6

Modelling issues

Define and control the process parameters

Gaz

Cathode

Anode

Refroidissement

Plasma

Substrat

Poudre

Particules fondues

DépôtModelling the

plasma

In-flight melting

(vaporization) of particles

Spreading and

solidification of droplets on

a cold substrate

Building-up the coating

Page 7: Modelling Transport Phenomena during Spreading and Solidification of Droplets in Plasma Projection Dominique GOBIN CNRS – France NGU Seminar Nova Gorica.

7

Ts

Tsplat and dsplat

time evolution

Substrate

Droplet spreading and solidification

T0 > Tm

V0 100 m/s

20 < d0 < 50

µm

Impacting Particle

Page 8: Modelling Transport Phenomena during Spreading and Solidification of Droplets in Plasma Projection Dominique GOBIN CNRS – France NGU Seminar Nova Gorica.

8

2. Equations

Page 9: Modelling Transport Phenomena during Spreading and Solidification of Droplets in Plasma Projection Dominique GOBIN CNRS – France NGU Seminar Nova Gorica.

9

Momentum Conservation

Mass Conservation

Modelling spreading

Pure fluid dynamics problem.Pure fluid dynamics problem.

The substrate is a boundary condition The substrate is a boundary condition

Page 10: Modelling Transport Phenomena during Spreading and Solidification of Droplets in Plasma Projection Dominique GOBIN CNRS – France NGU Seminar Nova Gorica.

10

Non-dimensionalizing variables (choosing Non-dimensionalizing variables (choosing reference values dreference values d0, V, V0, etc…) yields the , etc…) yields the dimensionless parameters of the problemdimensionless parameters of the problem

Momentum Conservation

Mass Conservation

Modelling spreading

Page 11: Modelling Transport Phenomena during Spreading and Solidification of Droplets in Plasma Projection Dominique GOBIN CNRS – France NGU Seminar Nova Gorica.

11

Coupling the equations of fluid dynamics Coupling the equations of fluid dynamics with with

the heat transfer equations the heat transfer equations

Energy Conservation

- in the splat

- in the substrate

Momentum Conservation

Mass Conservation

Modelling spreading with solidification

Page 12: Modelling Transport Phenomena during Spreading and Solidification of Droplets in Plasma Projection Dominique GOBIN CNRS – France NGU Seminar Nova Gorica.

12

During solidification two phases (solide and During solidification two phases (solide and fluid) are present. fluid) are present.

A phase function is defined : A phase function is defined :

Momentum Conservation

Mass Conservation

Modelling spreading with solidification

1 if liquid

0 if solid=

Page 13: Modelling Transport Phenomena during Spreading and Solidification of Droplets in Plasma Projection Dominique GOBIN CNRS – France NGU Seminar Nova Gorica.

13

Heat transfer and enthalpy formulation Heat transfer and enthalpy formulation

Energy Conservation

Modelling spreading with solidification

Page 14: Modelling Transport Phenomena during Spreading and Solidification of Droplets in Plasma Projection Dominique GOBIN CNRS – France NGU Seminar Nova Gorica.

14

Energy Conservation

Momentum Conservation

Mass Conservation

Liquid Fraction =1 liquid

0 solid

Conservation equations

Page 15: Modelling Transport Phenomena during Spreading and Solidification of Droplets in Plasma Projection Dominique GOBIN CNRS – France NGU Seminar Nova Gorica.

15

Parameters of the particles at impact

Nature SizeVelocity Temperature and state of melting

Parameters of the substrate NatureRugosityInitial temperatureSurface chemistry (wettability)

Physical parameters of the problemhe problem

Page 16: Modelling Transport Phenomena during Spreading and Solidification of Droplets in Plasma Projection Dominique GOBIN CNRS – France NGU Seminar Nova Gorica.

16

0 0 d V

Re

0 2

0 dρVWe

1. Operation parameters ::

Spreading and solidification of a splat

Splat

Substrate

- Contact thermal resistance

- Dynamic contact angle 2. Adjustable parameters :

Page 17: Modelling Transport Phenomena during Spreading and Solidification of Droplets in Plasma Projection Dominique GOBIN CNRS – France NGU Seminar Nova Gorica.

17

Numerical tool

Simulent-Drop : a software developed at the University of Toronto

(J. Mostaghimi et al.)

Newtonian fluid Constant properties (surface tension, contact resistance, conductivities, viscosity, …) Equilibrium solidification

Main hypotheses

Page 18: Modelling Transport Phenomena during Spreading and Solidification of Droplets in Plasma Projection Dominique GOBIN CNRS – France NGU Seminar Nova Gorica.

18 Computational domain

Full domain

• 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

Numerical tool : main features

Page 19: Modelling Transport Phenomena during Spreading and Solidification of Droplets in Plasma Projection Dominique GOBIN CNRS – France NGU Seminar Nova Gorica.

19- 19 -

Micrometric droplets(Conditions of plasma projection)

~1 mm> 10 µm d

Vimpact ~ 1 m/s> 100 m/s

msmsµs Characteristic times

Re ~ identiquesWe ~10 à 100 fois plus grand

Scales

Millimetric droplets (Free fall conditions)

Similitude ?

Page 20: Modelling Transport Phenomena during Spreading and Solidification of Droplets in Plasma Projection Dominique GOBIN CNRS – France NGU Seminar Nova Gorica.

20

3. Isothermal spreading

Page 21: Modelling Transport Phenomena during Spreading and Solidification of Droplets in Plasma Projection Dominique GOBIN CNRS – France NGU Seminar Nova Gorica.

21

Water droplet spreading

d0 = 2,75 mm , V0 = 1.18 m/s on soft wax (105°,95°)

Rioboo et al. (2001)

Water droplet spreading

d0 = 2,75 mm , V0 = 1.18 m/s on soft wax (105°,95°)

Rioboo et al. (2001)- 21 – 1

²

Isothermal impact of a water droplet

Simulation F. Loghmari

Page 22: Modelling Transport Phenomena during Spreading and Solidification of Droplets in Plasma Projection Dominique GOBIN CNRS – France NGU Seminar Nova Gorica.

220 2 4 6 8 10 12 14 16

0,0

0,5

1,0

1,5

2,0

2,5

3,0

de

gré

d'é

tale

me

nt (

D/D

0)

résultats de la simulation résultats expérimentaux

t* (tV0/D0)

Spr

eadi

ng f

acto

r d

(t)/

do

Reduced time : t* = t V o/ d o

SimulationExperiments

Page 23: Modelling Transport Phenomena during Spreading and Solidification of Droplets in Plasma Projection Dominique GOBIN CNRS – France NGU Seminar Nova Gorica.

23- 23 -

Wettability effect

Forward angle effect (θr = 95°)Forward angle effect (θr = 95°) Backward angle effect (θa = 105°)Backward angle effect (θa = 105°)

θa

Substrat

Forward dynamic contact angle Backward dynamic contact angle

θr

Substrat

Page 24: Modelling Transport Phenomena during Spreading and Solidification of Droplets in Plasma Projection Dominique GOBIN CNRS – France NGU Seminar Nova Gorica.

24

4. Spreading with solidification

Page 25: Modelling Transport Phenomena during Spreading and Solidification of Droplets in Plasma Projection Dominique GOBIN CNRS – France NGU Seminar Nova Gorica.

25

mm-size droplet simulation

Copper droplet on steel substrate d = 3 mm – V = 4 m/s – Ts = 25°C

Simulation Nabil Ferguen

Page 26: Modelling Transport Phenomena during Spreading and Solidification of Droplets in Plasma Projection Dominique GOBIN CNRS – France NGU Seminar Nova Gorica.

26- 26 - - 26 -

Impact velocity influence

With solidificationWith solidification

Vp=8 m/s

Vp=4 m/s

Vp=2 m/s

No solidificationNo solidification

Vp=8 m/s

Vp=4 m/s

Vp=2 m/s

Time evolution of the spreading factor

Page 27: Modelling Transport Phenomena during Spreading and Solidification of Droplets in Plasma Projection Dominique GOBIN CNRS – France NGU Seminar Nova Gorica.

27- 27 - - 27 -

Impact velocity influence

Vp = 8 m/s

Vp = 2 m/s

Vp=8 m/s

Vp=4 m/s

Vp=2 m/s

Time evolution of the spreading factor

Page 28: Modelling Transport Phenomena during Spreading and Solidification of Droplets in Plasma Projection Dominique GOBIN CNRS – France NGU Seminar Nova Gorica.

28- 28 -

21 TT

RTC

CTR Model

Non perfect contact between the drop and a rugous substrate =>

resistance to the heat flux : temperature discontinuity at the interface

- 28 -

Contact thermal resistance

Page 29: Modelling Transport Phenomena during Spreading and Solidification of Droplets in Plasma Projection Dominique GOBIN CNRS – France NGU Seminar Nova Gorica.

29- 29 - - 29 -

10-5 m²K.W-1

5.10-6 m²K.W-1

2.10-6 m²K.W-1

10-6 m²K.W-1

Influence of the contact thermal resistance

Page 30: Modelling Transport Phenomena during Spreading and Solidification of Droplets in Plasma Projection Dominique GOBIN CNRS – France NGU Seminar Nova Gorica.

30

High contact resistance

Copper droplet on steel substrate d = 3 mm – V = 4 m/s – Ts = 400°C

Simulation Nabil Ferguen

RTC = 10-5 m²K.W-1

Page 31: Modelling Transport Phenomena during Spreading and Solidification of Droplets in Plasma Projection Dominique GOBIN CNRS – France NGU Seminar Nova Gorica.

31 Copper droplet on steel substrate d = 3 mm – V = 4 m/s – Ts = 400°C

Simulation Nabil Ferguen

RTC = 10-6 m²K.W-1

Low contact resistance

Page 32: Modelling Transport Phenomena during Spreading and Solidification of Droplets in Plasma Projection Dominique GOBIN CNRS – France NGU Seminar Nova Gorica.

32

Influence of the initial substrate temperature

Ti Cr Cu

To = 300 K

To = 673 K

From Fukumoto et al. (1995)

Page 33: Modelling Transport Phenomena during Spreading and Solidification of Droplets in Plasma Projection Dominique GOBIN CNRS – France NGU Seminar Nova Gorica.

33

Splat formation

« Splat » Pre-heated substrate Tsub> Tt

Better adhesion ( 30 MPa)

« Splash » Cold substrate Tsub< Tt

Poor adhesion of the coating

( 4 MPa)

Morphological transition temperature Tt

Alumina on steel 304L

Page 34: Modelling Transport Phenomena during Spreading and Solidification of Droplets in Plasma Projection Dominique GOBIN CNRS – France NGU Seminar Nova Gorica.

34

Re = 23900 , We = 191

Influence of the substrate temperature

Ts = 1084 °C

Ffa

cteu

r d

’éta

lem

ent

No solidification

Pre-heating of the substrate : higher final splat diameter

Vp = 4 m/s ; dp = 2 mm ; T0 = 1100 °C, Tf = 1080 °C

Ts = 400°C 

Ts = 25°C

Ts = 800°C

Page 35: Modelling Transport Phenomena during Spreading and Solidification of Droplets in Plasma Projection Dominique GOBIN CNRS – France NGU Seminar Nova Gorica.

35

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

Page 36: Modelling Transport Phenomena during Spreading and Solidification of Droplets in Plasma Projection Dominique GOBIN CNRS – France NGU Seminar Nova Gorica.

36

5. Further developments

Page 37: Modelling Transport Phenomena during Spreading and Solidification of Droplets in Plasma Projection Dominique GOBIN CNRS – France NGU Seminar Nova Gorica.

37

• 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 from 106 to 5.108 K/s :undercooling about 0,1 to 0,2 Tm.

Include rapid solidification

Non equilibrium Solidification

Page 38: Modelling Transport Phenomena during Spreading and Solidification of Droplets in Plasma Projection Dominique GOBIN CNRS – France NGU Seminar Nova Gorica.

38

Experiments on mm-size droplets

Alumina droplet on steel substrate d = 5 mm – V = 10 m/s – Ts = 400°C

Film

S. G

ou

tier

– M

. V

ard

elle

Page 39: Modelling Transport Phenomena during Spreading and Solidification of Droplets in Plasma Projection Dominique GOBIN CNRS – France NGU Seminar Nova Gorica.

39

Special Thanks to :

• Nabil Ferguen : SPCTS Laboratory

• Simon Goutier : SPCTS Laboratory

• Fahmi Loghmari : FAST Laboratory

Thank you for your attention

Page 40: Modelling Transport Phenomena during Spreading and Solidification of Droplets in Plasma Projection Dominique GOBIN CNRS – France NGU Seminar Nova Gorica.

40

Page 41: Modelling Transport Phenomena during Spreading and Solidification of Droplets in Plasma Projection Dominique GOBIN CNRS – France NGU Seminar Nova Gorica.

41

Water droplet spreading

d0 = 2,75mm , V0 = 1.18m/s on soft wax (105°,95°)

Rioboo et al. (2001)

Water droplet spreading

d0 = 2,75mm , V0 = 1.18m/s on soft wax (105°,95°)

Rioboo et al. (2001)- 41 – 1

²

Isothermal impact of a water droplet

Simulation F. Loghmari


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