Modelling Transport Phenomena during Spreading and Solidification of Droplets in Plasma Projection...
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Transcript of Modelling Transport Phenomena during Spreading and Solidification of Droplets in Plasma Projection...
![Page 1: Modelling Transport Phenomena during Spreading and Solidification of Droplets in Plasma Projection Dominique GOBIN CNRS – France NGU Seminar Nova Gorica.](https://reader035.fdocuments.us/reader035/viewer/2022062515/56649f4c5503460f94c6cdd2/html5/thumbnails/1.jpg)
Modelling Transport Phenomena during Spreading and Solidification
of Droplets in Plasma Projection
Dominique GOBINCNRS – France
NGU Seminar Nova Gorica (November 5, 2009)
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Contents
1. Motivation
2. Equations
3. Isothermal spreading
4. Spreading with solidification
5.Perspective
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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
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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
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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
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Ts
Tsplat and dsplat
time evolution
Substrate
Droplet spreading and solidification
T0 > Tm
V0 100 m/s
20 < d0 < 50
µm
Impacting Particle
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2. Equations
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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
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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
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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
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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=
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Heat transfer and enthalpy formulation Heat transfer and enthalpy formulation
Energy Conservation
Modelling spreading with solidification
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Energy Conservation
Momentum Conservation
Mass Conservation
Liquid Fraction =1 liquid
0 solid
Conservation equations
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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
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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 :
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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
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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
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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 ?
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3. Isothermal spreading
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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
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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
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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
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4. Spreading with solidification
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mm-size droplet simulation
Copper droplet on steel substrate d = 3 mm – V = 4 m/s – Ts = 25°C
Simulation Nabil Ferguen
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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
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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
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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
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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
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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
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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
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Influence of the initial substrate temperature
Ti Cr Cu
To = 300 K
To = 673 K
From Fukumoto et al. (1995)
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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
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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
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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
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5. Further developments
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• 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
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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
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Special Thanks to :
• Nabil Ferguen : SPCTS Laboratory
• Simon Goutier : SPCTS Laboratory
• Fahmi Loghmari : FAST Laboratory
Thank you for your attention
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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