0
Research Papers: Melting and Solidification

Simultaneous Spreading and Solidification of an Impacting Molten Droplet With Substrate Remelting

[+] Author and Article Information
Vimal Ramanuj

Department of Mechanical and
Aerospace Engineering,
University of Texas at Arlington,
Arlington, TX 76019
e-mail: vimal.ramanuj@mavs.uta.edu

Albert Y. Tong

Department of Mechanical and
Aerospace Engineering,
University of Texas at Arlington,
Arlington, TX 76019
e-mail: tong@uta.edu

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received October 23, 2015; final manuscript received September 21, 2016; published online November 16, 2016. Assoc. Editor: Gennady Ziskind.

J. Heat Transfer 139(3), 032301 (Nov 16, 2016) (11 pages) Paper No: HT-15-1670; doi: 10.1115/1.4034813 History: Received October 23, 2015; Revised September 21, 2016

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.

Copyright © 2017 by ASME
Your Session has timed out. Please sign back in to continue.

References

Gupta, S. C. , 2003, The Classical Stefan Problem, Elsevier, Amsterdam, The Netherlands.
Cannon, J. R. , 1984, The One Dimensional Heat Equation (Encyclopedia of Mathematics and Its Applications, Vol. 23), Cambridge University Press, Cambridge, UK.
Madejski, J. , 1975, “ Solidification of Droplets on a Cold Surface,” Int. J. Heat Mass Transfer, 19(9), pp. 1009–1013. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
Schiaffino, S. , and Sonin, A. A. , 1997, “ Molten Droplet Deposition and Solidification at Low Weber Numbers,” Phys. Fluids, 9(11), pp. 3172–3187. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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.
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. [CrossRef]
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. [CrossRef]
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.
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. [CrossRef]
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. [CrossRef]
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.
Carman, P. C. , 1937, “ Fluid Flow Through Granular Beds,” Trans. Inst. Chem. Eng., 15, pp. 155–166.
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.
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. [CrossRef]
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. [CrossRef]
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.
Rudman, M. , 1997, “ Volume-Tracking Methods for Interfacial Flow Calculations,” Int. J. Numer. Methods Fluids, 24(7), pp. 671–691. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
Patankar, S. V. , 1980, Numerical Heat Transfer and Fluid Flow, Hemisphere, New York.
Volkova, O. , Heller, H. , and Janke, D. , 2003, “ Microstructure and Cleanliness of Rapidly Solidified Steels,” ISIJ Int., 43(11), pp. 1724–1732. [CrossRef]

Figures

Grahic Jump Location
Fig. 1

Staggered grid arrangement

Grahic Jump Location
Fig. 10

Solidification front and isotherms at the instant of maximum remelt [20]

Grahic Jump Location
Fig. 8

Isotherms (left) and streamlines (right) at various time instants

Grahic Jump Location
Fig. 9

Axial temperature gradients at the droplet–substrate interface at various time instants

Grahic Jump Location
Fig. 2

Flow chart for enthalpy formulation

Grahic Jump Location
Fig. 3

Computational domain

Grahic Jump Location
Fig. 4

Remelting depth versus time

Grahic Jump Location
Fig. 5

Net heat flux and solidus location versus time

Grahic Jump Location
Fig. 6

Comparison of temperature variations

Grahic Jump Location
Fig. 7

Cooling rates and SDAS along the droplet–substrate interface

Grahic Jump Location
Fig. 11

Effect of substrate preheating on remelting depth

Grahic Jump Location
Fig. 12

Effect of substrate preheating on cooling rates

Grahic Jump Location
Fig. 17

Effect of impact velocity on spreading and solidification times

Grahic Jump Location
Fig. 18

Effect of impact velocity on spread factor

Grahic Jump Location
Fig. 14

Effect of substrate preheating on spread factor

Grahic Jump Location
Fig. 15

Effect of impact velocity on remelting depth

Grahic Jump Location
Fig. 16

Effect of impact velocity on cooling rates

Grahic Jump Location
Fig. 13

Effect of substrate preheating on spreading and solidification times

Grahic Jump Location
Fig. 19

Grid distribution

Grahic Jump Location
Fig. 20

Convergence in remelting depth and temperature at free surface

Grahic Jump Location
Fig. 21

Convergence in free surface and solidification front

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In