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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