The nonisothermal phase-change behavior of droplet deposition on a substrate has been studied. The governing equation for the flow field is solved using a finite-volume scheme with a two-step projection method on a fixed computational grid. The volume-of-fluid (VOF) method is used to track the free surface, and the continuum surface force (CSF) method is used to model the surface tension. An enthalpy formulation with a porosity model is adopted for solving the energy equation. A comparison with published experimental findings has been done to validate the numerical model. The effects of convection terms in the energy equation are examined, and droplet spreading and solidification along with substrate remelting have been analyzed. A parametric study relating the effects of substrate preheating and impact velocity on remelting, cooling rate, spreading, and solidification has also been carried out. It has been observed that the flow field within the droplet has a significant effect on the overall deposition process.

References

References
1.
Gupta
,
S. C.
,
2003
,
The Classical Stefan Problem
,
Elsevier
, Amsterdam, The Netherlands.
2.
Cannon
,
J. R.
,
1984
,
The One Dimensional Heat Equation
(Encyclopedia of Mathematics and Its Applications, Vol.
23
),
Cambridge University Press
, Cambridge, UK.
3.
Madejski
,
J.
,
1975
, “
Solidification of Droplets on a Cold Surface
,”
Int. J. Heat Mass Transfer
,
19
(
9
), pp.
1009
1013
.
4.
Rangel
,
R. H.
, and
Bian
,
X.
,
1997
, “
Metal-Droplet Deposition Model Including Liquid Deformation and Substrate Remelting
,”
Int. J. Heat Mass Transfer
,
40
(
11
), pp.
2549
2564
.
5.
Collings
,
E. W.
,
Markworth
,
A. J.
,
McCoy
,
J. K.
, and
Saunders
,
J. H.
,
1990
, “
Splat-Quench Solidification of Freely Falling Liquid-Metal Drops by Impact on a Planar Substrate
,”
J. Mater. Sci.
,
25
(
8
), pp.
3677
3682
.
6.
Trapaga
,
G.
,
Mathys
,
E. F.
,
Valencia
,
J. J.
, and
Szekely
,
J
.
,
1992
, “
Fluid Flow, Heat Transfer and Solidification of Molten Metal Droplets Impinging on Substrates: Comparison of Numerical and Experimental Results
,”
Metall. Trans. B
,
23
(
6
), pp.
701
718
.
7.
Liu
,
H.
,
Lavernia
,
E. J.
, and
Rangel
,
R. H.
,
1993
, “
Numerical Simulation of Substrate Impact and Freezing of Droplets in Plasma Spray Processes
,”
J. Phys. D: Appl. Phys.
,
26
(
11
), pp.
1900
1908
.
8.
Bennet
,
T.
, and
Poulikakos
,
D.
,
1993
, “
Splat-Quench Solidification: Estimating the Maximum Spreading of a Droplet Impacting a Solid Surface
,”
J. Mater. Sci.
,
28
(
4
), pp.
963
970
.
9.
Wang
,
S. P.
,
Wang
,
G. X.
, and
Matthys
,
E. F.
,
1998
, “
Melting and Resolidification of a Substrate in Contact With a Molten Metal: Operational Maps
,”
Int. J. Heat Mass Transfer
,
41
(
10
), pp.
1177
1188
.
10.
Liu
,
W.
,
Wang
,
G. X.
, and
Matthys
,
E. F.
,
1995
, “
Thermal Analysis and Measurements for a Molten Metal Drop Impacting on a Substrate: Cooling, Solidification and Heat Transfer Coefficient
,”
Int. J. Heat Mass Transfer
,
38
(
8
), pp.
1387
1395
.
11.
Schiaffino
,
S.
, and
Sonin
,
A. A.
,
1997
, “
Molten Droplet Deposition and Solidification at Low Weber Numbers
,”
Phys. Fluids
,
9
(
11
), pp.
3172
3187
.
12.
Fukumoto
,
M.
,
Nishioka
,
E.
, and
Matsubara
,
T.
,
1999
, “
Flattening and Solidification Behavior of a Molten Droplet on a Flat Substrate Surface Held at Various Temperatures
,”
Surf. Coat. Technol.
,
120–121
, pp.
131
137
.
13.
Wan
,
Y. P.
,
Zhang
,
H.
,
Jiang
,
X. Y.
,
Sampath
,
S.
, and
Prasad
,
V.
,
2001
, “
Role of Solidification, Substrate Temperature and Reynolds Number on Droplet Spreading in Thermal Spray Deposition: Measurements and Modeling
,”
ASME J. Heat Transfer
,
123
(
2
), pp.
382
389
.
14.
Nagashio
,
K.
,
Murata
,
H.
, and
Kuribayashi
,
K.
,
2004
, “
Spreading and Solidification Behavior of Molten Si Droplets Impinging on Substrates
,”
Acta Mater.
,
52
(
18
), pp.
5295
5301
.
15.
Ghafouri-Azar
,
R.
,
Shakeri
,
S.
,
Chandra
,
S.
, and
Mostaghimi
,
J.
,
2003
, “
Interactions Between Molten Metal Droplets Impinging on a Solid Surface
,”
Int. J. Heat Mass Transfer
,
46
(
8
), pp.
1395
1407
.
16.
Attinger
,
D.
, and
Poulikakos
,
D.
,
2001
, “
Melting and Resolidification of a Substrate Caused by Molten Microdroplet Impact
,”
ASME J. Heat Transfer
,
123
(
6
), pp.
1110
1122
.
17.
Hong
,
F. J.
, and
Qiu
,
H. H.
,
2005
, “
Modelling of Substrate Remelting, Flow, and Resolidification in Microcasting
,”
Numer. Heat Transfer, Part A
,
48
(
10
), pp.
987
1008
.
18.
Schmaltz
,
K. S.
,
1997
, “
The Impinging Behavior of a Molten Metal Droplet: Integration of Analytical, Numerical and Experimental Techniques
,” Ph.D. thesis, Department of Mechanical Engineering, Carnegie Mellon University, Pittsburgh, PA.
19.
Schmaltz
,
K. S.
,
Zarzalejo
,
L. J.
, and
Amon
,
C. H.
,
1999
, “
Molten Droplet Solidification and Substrate Remelting in Microcasting—Part II: Parametric Study and Effect of Dissimilar Materials
,”
Heat Mass Transfer
,
35
(
1
), pp.
17
23
.
20.
Zarzalejo
,
L. J.
,
Schmaltz
,
K. S.
, and
Amon
,
C. H.
,
1999
, “
Molten Droplet Solidification and Substrate Remelting in Microcasting—Part I: Numerical Modeling and Experimental Verification
,”
Heat Mass Transfer
,
34
(
6
), pp.
477
485
.
21.
Jafari
,
A.
,
Seyedein
,
S. H.
, and
Haghpanahi
,
M.
,
2008
, “
Modeling of Heat Transfer and Solidification of Droplet/Substrate in Microcasting SDM Process
,”
IUST Int. J. Eng. Sci.
,
19
(
5–1
), pp.
187
198
.
22.
Tong
,
A. Y.
, and
Holt
,
B. R.
,
1997
, “
Numerical Study on the Solidification of Liquid Metal Droplets Impacting Onto a Substrate
,”
Numer. Heat Transfer, Part A
,
31
(8), pp.
797
817
.
23.
Shukla
,
R.
, and
Kumar
,
A.
,
2015
, “
Substrate Melting and Resolidification During Impact of High-Melting Point Droplet Material
,”
J. Therm. Spray Technol.
,
24
(
8
), pp.
1368
1376
.
24.
Kothe
,
D. B.
,
Mjolness
,
R. C.
, and
Torrey
,
R. C.
,
1991
, “
RIPPLE: A Computer Program for Incompressible Flows With Free Surfaces
,” Technical Report No. LA-12007-MS.
25.
Carman
,
P. C.
,
1937
, “
Fluid Flow Through Granular Beds
,”
Trans. Inst. Chem. Eng.
,
15
, pp.
155
166
.
26.
Alavi
,
S.
, and
Passandideh-Fard
,
M.
,
2011
, “
Numerical Simulation of Droplet Impact and Solidification Including Thermal Shrinkage in a Thermal Spray Process
,”
Front. Heat Mass Transfer
,
2
, pp.
1
9
.
27.
Kershaw
,
D. S.
,
1978
, “
The Incomplete Cholesky-Conjugate Gradient Method for the Iterative Solution of Systems of Linear Equations
,”
J. Comput. Phys.
,
26
(
1
), pp.
43
65
.
28.
Hirt
,
C. W.
, and
Nichols
,
B. D.
,
1981
, “
Volume of Fluid (VOF) Method for the Dynamics of Free Boundaries
,”
J. Comput. Phys.
,
39
(
1
), pp.
201
225
.
29.
Youngs
,
D. L.
,
1982
, “
Time-Dependent Multi-Material Flow With Large Fluid Distortion
,”
Numerical Methods for Fluid Dynamics
, Academic Press, New York, pp.
273
285
.
30.
Rudman
,
M.
,
1997
, “
Volume-Tracking Methods for Interfacial Flow Calculations
,”
Int. J. Numer. Methods Fluids
,
24
(
7
), pp.
671
691
.
31.
Brackbill
,
J. U.
,
Kothe
,
D. B.
, and
Zemach
,
C.
,
1991
, “
A Continuum Method for Modeling Surface Tension
,”
J. Comput. Phys.
,
100
(
2
), pp.
335
354
.
32.
Voller
,
V. R.
, and
Prakash
,
C.
,
1987
, “
A Fixed Grid Numerical Modeling Methodology for Convection-Diffusion Mushy Region Phase-Change Problems
,”
Int. J. Heat Mass Transfer
,
30
(
8
), pp.
1709
1719
.
33.
Brent
,
A. D.
,
Voller
,
V. R.
, and
Reid
,
K. J.
,
1988
, “
Enthalpy-Porosity Technique for Modeling Convection-Diffusion Phase Change: Application to Melting of a Pure Metal
,”
Numer. Heat Transfer
,
13
(
3
), pp.
297
318
.
34.
Patankar
,
S. V.
,
1980
,
Numerical Heat Transfer and Fluid Flow
,
Hemisphere
, New York.
35.
Volkova
,
O.
,
Heller
,
H.
, and
Janke
,
D.
,
2003
, “
Microstructure and Cleanliness of Rapidly Solidified Steels
,”
ISIJ Int.
,
43
(
11
), pp.
1724
1732
.
You do not currently have access to this content.