Modelling Transport Phenomena during Spreading and Solidification of Droplets in Plasma Projection...

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Modelling Transport Phenomena during Spreading and Solidification

of Droplets in Plasma Projection

Dominique GOBINCNRS – France

NGU Seminar Nova Gorica (November 5, 2009)

2

Contents

1. Motivation

2. Equations

3. Isothermal spreading

4. Spreading with solidification

5.Perspective

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

4

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

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

7

Ts

Tsplat and dsplat

time evolution

Substrate

Droplet spreading and solidification

T0 > Tm

V0 100 m/s

20 < d0 < 50

µm

Impacting Particle

8

2. Equations

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

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

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

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=

13

Heat transfer and enthalpy formulation Heat transfer and enthalpy formulation

Energy Conservation

Modelling spreading with solidification

14

Energy Conservation

Momentum Conservation

Mass Conservation

Liquid Fraction =1 liquid

0 solid

Conservation equations

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

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 :

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

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

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 ?

20

3. Isothermal spreading

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

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

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

24

4. Spreading with solidification

25

mm-size droplet simulation

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

Simulation Nabil Ferguen

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

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

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

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

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

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

32

Influence of the initial substrate temperature

Ti Cr Cu

To = 300 K

To = 673 K

From Fukumoto et al. (1995)

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

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

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

36

5. Further developments

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

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

39

Special Thanks to :

• Nabil Ferguen : SPCTS Laboratory

• Simon Goutier : SPCTS Laboratory

• Fahmi Loghmari : FAST Laboratory

Thank you for your attention

40

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