0
Research Papers: Natural and Mixed Convection

Real-Time Observations of Density Anomaly Driven Convection and Front Instability During Solidification of Water

[+] Author and Article Information
Virkeshwar Kumar

Department of Mechanical Engineering,
Indian Institute of Technology Bombay,
Mumbai 400076, India
e-mail: Virkeshwar12@gmail.com

Atul Srivastava

Department of Mechanical Engineering,
Indian Institute of Technology Bombay,
Mumbai 400076, India
e-mail: atulsr@iitb.ac.in

Shyamprasad Karagadde

Department of Mechanical Engineering,
Indian Institute of Technology Bombay,
Mumbai 400076, India
e-mail: s.karagadde@iitb.ac.in

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received April 7, 2017; final manuscript received September 9, 2017; published online January 10, 2018. Assoc. Editor: Antonio Barletta.

J. Heat Transfer 140(4), 042503 (Jan 10, 2018) (12 pages) Paper No: HT-17-1193; doi: 10.1115/1.4038420 History: Received April 07, 2017; Revised September 09, 2017

Natural convection during solidification of liquids is known to impact the freezing characteristics and also lead to defect formation. In this study, we report the findings of real-time interferometric observation of bottom-cooled solidification of pure water in a cubical cavity. The results show first quantitative evidence of full-field thermal history during solidification, clearly depicting the anomalous expansion of water below 4 °C. Furthermore, based on the strength of natural convection, characterized by the Rayleigh number, we identify and report four distinct regimes of solidification, namely—conduction dominated, early convection, front instability, and sustained convection. A critical Rayleigh number that initiates instability in the solidifying front has been proposed, which is significantly different from conventional calculations of Rayleigh number relating to the initiation of flow. The study shows full-field quantitative evidence of a well-known phenomenon and provides a further understanding of flow driven nonhomogeneities in the solidifying interfaces.

FIGURES IN THIS ARTICLE
<>
Copyright © 2018 by ASME
Your Session has timed out. Please sign back in to continue.

References

Ehrhard, P. , Riley, D. S. , and Steen, P. H. , 2001, Interactive Dynamics of Convection and Solidification, Springer, Dordrecht, The Netherlands. [CrossRef]
Ghenai, C. , Mudunuri, A. , Lin, C. X. , and Ebadian, M. A. , 2003, “Double-Diffusive Convection During Solidification of a Metal Analog System (NH4Cl–H2O) in a Differentially Heated Cavity,” Exp. Therm. Fluid Sci., 28(1), pp. 23–35. [CrossRef]
Wang, S. Y. , Lin, C. X. , and Ebadian, M. A. , 1999, “Vortex Flow of Low Concentration NH4Cl–H2O Solution During the Solidification Process,” Int. J. Heat Mass Transfer, 42(22), pp. 4153–4163. [CrossRef]
Srivastava, A. , Muralidhar, K. , and Panigrahi, P. K. , 2004, “Comparison of Interferometry, Schlieren and Shadowgraph for Visualizing Convection Around a KDP Crystal,” J. Cryst. Growth, 267(1–2), pp. 348–361. [CrossRef]
Kehtarnavaz, H. , and Bayazitoglu, Y. , 2017, “Solidification of Binary Mixture in a Finite Planar Medium: Saline Water,” ASME J. Heat Transfer, 107(4), pp. 964–966. [CrossRef]
Hahn, D. W. , and Ozisik, M. N. , 2012, “Phase-Change Problems,” Heat Conduction, Wiley, Hoboken, NJ, pp. 452–495. [CrossRef] [PubMed] [PubMed]
Tanaka, H. , 1998, “Simple Physical Explanation of the Unusual Thermodynamic Behavior of Liquid Water,” Phys. Rev. Lett., 80, pp. 5750–5753. [CrossRef]
Lin, S. , Gao, D. Y. , and Yu, X. C. , 1990, “Thermal Stresses Induced by Water Solidification in a Cylindrical Tube,” ASME J. Heat Transfer, 112(4), pp. 1079–1082. [CrossRef]
Wettlaufer, J. S. , Worster, M. G. , and Huppert, H. E. , 1997, “Natural Convection During Solidification of an Alloy From Above With Application to the Evolution of Sea Ice,” J. Fluid Mech., 344, pp. 291–316. [CrossRef]
Beckermann, C. , Gu, J. P. , and Boettinger, W. J. , 2000, “Development of a Freckle Predictor Via Rayleigh Number Method for Single-Crystal Nickel-Base Superalloy Castings,” Metall. Mater. Trans. A, 31(10), pp. 2545–2557. [CrossRef]
Ramirez, J. C. , and Beckermann, C. , 2003, “Evaluation of a Rayleigh-Number-Based Freckle Criterion for Pb-Sn Alloys and Ni-Base Superalloys,” Metall. Mater. Trans. A, 34(7), pp. 1525–1536. [CrossRef]
Chakraborty, P. R. , and Dutta, P. , 2013, “Study of Freckles Formation During Directional Solidification Under the Influence of Single-Phase and Multiphase Convection,” ASME J. Therm. Sci. Eng. Appl., 5(2), p. 021004. [CrossRef]
Weaver, J. A. , and Viskanta, R. , 1986, “Freezing of Water Saturated Porous Media in Rectangular Cavity,” Int. Commun. Heat Mass Transfer, 13(3), pp. 245–252. [CrossRef]
Epstein, M. , and Cheung, F. B. , 1983, “Complex Freezing-Melting Interfaces in Fluid Flow,” Annu. Rev. Fluid Mech., 15(1978), pp. 293–319. [CrossRef]
Cheng, K. C. , Inaba, H. , and Gilpin, R. R. , 1988, “Effects of Natural Convection on Ice Formation Around an Isothermally Cooled Horizontal Cylinder,” ASME J. Heat Transfer, 110(4a), pp. 931–937. [CrossRef]
Bathelt, A. G. , and Viskanta, R. , 1981, “Heat Transfer and Interface Motion During Melting and Solidification Around a Finned Heat Source/Sink,” ASME J. Heat Transfer, 103(4), pp. 720–726. [CrossRef]
Ezan, M. A. , Erek, A. , and Dincer, I. , 2011, “A Study on the Importance of Natural Convection During Solidification in Rectangular Geometry,” ASME J. Heat Transfer, 133(10), p. 102301. [CrossRef]
Karagadde, S. , Yuan, L. , Shevchenko, N. , Eckert, S. , and Lee, P. D. , 2014, “3-D Microstructural Model of Freckle Formation Validated Using In Situ Experiments,” Acta Mater., 79, pp. 168–180. [CrossRef]
Boger, D. V. , and Westwater, J. W. , 1967, “Effect of Buoyancy on the Melting and Freezing Process,” ASME J. Heat Transfer, 89(1), pp. 81–89. [CrossRef]
Gilpin, R. R. , 1976, “The Influence of Natural Convection on Dendritic Ice Growth,” J. Cryst. Growth, 36(1), pp. 101–108. [CrossRef]
Merker, G. P. , Waas, P. , and Grigull, U. , 1979, “Onset of Convection in a Horizontal Water Layer With Maximum Density Effects,” Int. J. Heat Mass Transfer, 22(4), pp. 505–515. [CrossRef]
Tanaka, H. , and Miyata, H. , 1980, “Turbulent Natural Convection in a Horizontal Water Layer Heated From Below,” Int. J. Heat Mass Transfer, 23(9), pp. 1273–1281. [CrossRef]
Osorio, A. , Avila, R. , and Cervantes, J. , 2004, “On the Natural Convection of Water Near Its Density Inversion in an Inclined Square Cavity,” Int. J. Heat Mass Transfer, 47(19–20), pp. 4491–4495. [CrossRef]
Braga, S. L. , and Viskanta, R. , 1992, “Transient Natural Convection of Water Near Its Density Extremum in a Rectangular Cavity,” Int. J. Heat Mass Transfer, 35(4), pp. 861–875. [CrossRef]
Gau, C. , and Viskanta, R. , 1983, “Flow Visualization During Solid-Liquid Phase Change Heat Transfer—I: Freezing in a Rectangular Cavity,” Int. Commun. Heat Mass Transfer, 10(3), pp. 173–181. [CrossRef]
Ezan, M. A. , and Kalfa, M. , 2016, “Numerical Investigation of Transient Natural Convection Heat Transfer of Freezing Water in a Square Cavity,” Int. J. Heat Fluid Flow, 61(Pt. B), pp. 438–448. [CrossRef]
Ecker, A. , 1988, “Two-Wavelength Holographic Measurement of Temperature and Concentration During Alloy Solidification,” J. Thermophys., 2(3), pp. 193–196. [CrossRef]
McCay, M. H. , and McCay, T. D. , 1988, “Experimental Measurements of Solutal Layers in Unidirectional Solidification,” J. Thermophys., 2(3), pp. 197–202. [CrossRef]
Weiss, C. , Bergeon, N. , Mangelinck-Noël, N. , and Billia, B. , 2006, “Effects of the Interface Curvature and Dendrite Orientation in Directional Solidification of Bulk Transparent Alloys,” Mater. Sci. Forum, 508, pp. 337–342. [CrossRef]
Yabuki, T. , Hamaguchi, T. , and Nakabeppu, O. , 2012, “Interferometric Measurement of the Liquid-Phase Temperature Field Around an Isolated Boiling Bubble,” J. Therm. Sci. Technol., 7(3), pp. 463–474. [CrossRef]
Srivastava, A. , Muralidhar, K. , and Panigrahi, P. K. , 2012, “Optical Imaging and Three Dimensional Reconstruction of the Concentration Field Around a Crystal Growing From an Aqueous Solution: A Review,” Prog. Cryst. Growth Charact. Mater., 58(4), pp. 209–278. [CrossRef]
Varma, S. S. , and Srivastava, A. , 2016, “Real-Time Two-Color Interferometric Technique for Simultaneous Measurements of Temperature and Solutal Fields,” Int. J. Heat Mass Transfer, 98, pp. 662–674. [CrossRef]
Varma, S. S. , Rao, S. S. , and Srivastava, A. , 2017, “Simultaneous Measurement of Thermal and Solutal Diffusivities of Salt-Water Solutions From a Single-Shot Dual Wavelength Interferometric Image,” Exp. Therm. Fluid Sci., 81, pp. 123–135. [CrossRef]
Tsushima, N. , Narumi, A. , Nakane, I. , Kashiwagi, T. , and Akisawa, A. , 2005, “Visualization of Transient Solidification Process of Aqueous Solution by Dual Wavelength Holographic Interferometry,” ASME J. Heat Transfer, 127(8), p. 801. [CrossRef]
Spatz, T. L. , and Poulikakos, D. , 1992, “A Two-Wavelength Holographic Interferometry Study on the Solidification of a Binary Alloy Around a Horizontal Pipe,” ASME J. Heat Transfer, 114(4), p. 998. [CrossRef]
El-Wakil, M. M. , Myers, G. E. , and Schilling, R. J. , 1966, “An Interferometric Study of Mass Transfer From a Vertical Plate at Low Reynolds Numbers,” ASME J. Heat Transfer, 88(4), pp. 399–406. [CrossRef]
Tankin, R. S. , and Farhadieh, R. , 1971, “Effects of Thermal Convection Currents on Formation of Ice,” Int. J. Heat Mass Transfer, 14(7), pp. 953–961. [CrossRef]
Farhadieh, R. , and Tankin, R. S. , 1972, “Interferometric Study of Freezing of Sea Water,” J. Geophys. Res., 77(9), pp. 1647–1656. [CrossRef]
Vikas, D. , Basu, S. , and Dutta, P. , 2012, “In-Situ Measurements of Concentration and Temperature During Transient Solidification of Aqueous Solution of Ammonium Chloride Using Laser Interferometry,” Int. J. Heat Mass Transfer, 55(7–8), pp. 2022–2034. [CrossRef]
Goldstein, R. J. , 1996, Fluid Mechanics Measurements, Taylor and Francis, Philadelphia, PA.
Mishra, D. , Muralidhar, K. , and Munshi, P. , 1998, “Performance Evaluation of Fringe Thinning Algorithms for Interferometric Tomography,” Opt. Lasers Eng., 30(3–4), pp. 229–249. [CrossRef]
Abbate, G. , Bernini, U. , Ragozzino, E. , and Somma, F. , 1978, “The Temperature Dependence of the Refractive Index of Water,” J. Phys. D, 11(8), pp. 1167–1172. [CrossRef]
Mishra, D. , Muralidhar, K. , and Munshi, P. , 2013, “Measurements of Three Dimensional Temperature Field in Fluids Using Laser Interferometry,” Def. Sci. J., 49(3), pp. 243–255. [CrossRef]
Rao, S. S. , and Srivastava, A. , 2016, “Interferometric Study of Natural Convection in a Differentially-Heated Cavity With Al2O3-Water Based Dilute Nanofluids,” Int. J. Heat Mass Transfer, 92, pp. 1128–1142. [CrossRef]
Slack, G. A. , 1980, “Thermal Conductivity of Ice,” Phys. Rev. B, 22(6), pp. 3065–3071. [CrossRef]
Dantzig, J. A. , and Rappaz, M. , 2009, “Analytical Solutions for Solidification,” Solidification, EPFL Press, Lausanne, Switzerland, pp. 165–170. [CrossRef] [PubMed] [PubMed]
Seybert, C. D. , and Evans, J. W. , 2005, “PIV Measurements of Velocity of Water in the Presence of Ice and Comparison With Calculated Values,” Int. J. Heat Mass Transfer, 48(1), pp. 67–73. [CrossRef]
James, D. W. , 1968, “The Thermal Diffusivity of Ice and Water Between −40 and +60 °C,” J. Mater. Sci., 3(5), pp. 540–543. [CrossRef]

Figures

Grahic Jump Location
Fig. 1

Isometric (a), front (b), and side (c) views of the solidification cell showing the key components

Grahic Jump Location
Fig. 2

Isometric view of the Mach–Zehnder interferometer

Grahic Jump Location
Fig. 3

Conduction dominated interferometric images during solidification of water from bottom cooling at (a) t = 1.5 h, (b) t = 2.15 h, (c) t = 2.5 h, and (d)–(f) are the corresponding temperature fields (°C)

Grahic Jump Location
Fig. 4

Convection rolls formed in the interferometric images during solidification of water from bottom cooling at (a) t = 2.75 h, (b) t = 3.4 h, (c) t = 4.3 h, and (d)–(f) are the corresponding temperature fields (°C)

Grahic Jump Location
Fig. 5

Nonuniform interface formed in the interferometric images during solidification of water from bottom cooling at (a) t = 4.6 h, (b) t = 4.95 h, (c) t = 5.8 h, and (d)–(f) are the corresponding temperature fields (°C)

Grahic Jump Location
Fig. 6

Nondimensional temperature (θ) with respect to nondimensional height (η) of the liquid during solidification of water

Grahic Jump Location
Fig. 7

Contours of the temperature gradients (° C/m) in the liquid during solidification of water from bottom at different time instances: (a) t = 1.5 h, (b) t = 2.5 h, (c) t = 2.75 h, (d) t = 3.4 h, (e) t = 4.6 h, and (f) t = 4.95 h

Grahic Jump Location
Fig. 8

Temperature gradient (°C/m) in the liquid with respect to nondimensional height (η) of the liquid during solidification of water

Grahic Jump Location
Fig. 9

The evolution of solid fraction with time

Grahic Jump Location
Fig. 10

Time evolution of the Rayleigh number during solidification of water: The four regimes of solidification are marked and a representative interferometric image for each of the four regimes is shown in the inset

Grahic Jump Location
Fig. 11

Repeated experiments of nonuniform interface (marked in circles) and the corresponding Rayleigh numbers

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