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Computational Modeling of Water Droplets Under Cooling and Freezing Conditions


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DOI: https://doi.org/10.15866/irease.v15i2.21571

Abstract


The crystallization of water droplets is a ubiquitous phenomenon, which plays afundamental role in many natural and artificial processes. This phenomenon gainedparticular interest in the aeronautical industry due to ice accretion on lifting surfaces andengine intakes. A performance study is made of several models for predicting cooling and freezing phenomena, ranging from one- and two-way coupling to full-fledged four-stage freezing methodologies. First, a performance study is made of the one- and two-way coupling methodologies in the portrayal of the interaction of the particles and the surrounding gas on free-falling water droplets with diameters ranging from 3 to 6 mm and relative humidity ratios of 0.29, 0.36. 0.52 and 1.00. Then a generalized four-stage freezing model is implemented, where the temperature evolution of a suspended water droplet is tracked, adding to the cooling in the free-falling conditions, the recalescence and solidification stages. The results indicate that, for high relative humidity ratio, the interaction particles-medium is preponderant and needs to be accounted for, which does not take place for low relative humidity ratios, where one-way coupling seems to be suitable approximation. Lastly, the full stage freezing model was able to capture the experimental trend of recalescence and solidification stages.
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Keywords


Droplet Cooling; Four-Stage Freezing Model; One-Way Coupling; Supercooling; Two-Way Coupling

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References


Y. Cao, Z. Wu, Y. Su, Z. Xu, Aircraft Flight Characteristics in Icing Conditions, Prog. Aerosp. Sci. 74 (2015) 62-80.
https://doi.org/10.1016/j.paerosci.2014.12.001

Y. Cao, W. Tan, Z. Wu, Aircraft Icing: An Ongoing Threat to Aviation Safety, Aerosp. Sci. Technol. 75 (2018) 353-385.
https://doi.org/10.1016/j.ast.2017.12.028

S. J. Stebbins, E. Loth, A. P. Broeren, M. Potapczuk, Review of Computational Methods for Aerodynamic Analysis of Iced Lifting Surfaces, Prog. Aerosp. Sci. 111 (2019) 100583.
https://doi.org/10.1016/j.paerosci.2019.100583

Z. A. Janjua, B. Turnbull, S. Hibberd, K.-S. Choi, Mixed Ice Accretion on Aircraft Wings, Phys. Fluids 30 (2018) 027101.
https://doi.org/10.1063/1.5007301

L. Li, Y. Liu, L. Tian, H. Hu, H. Hu, X. Liu, I. Hogate, A. Kohli, An Experimental Study on a Hot-air-based Anti-/De-icing System for Aeroengine Inlet Guide Vanes, Appl. Therm. Eng. 167 (2020) 114778.
https://doi.org/10.1016/j.applthermaleng.2019.114778

O. Gurevich, S. Smetanin, M. Trifonov, Analysis of the Impact of Control Methods on Turbofan Performance in Ice Crystal Conditions, in AIAA Propulsion and Energy 2020 Forum, AIAA, 2020.
https://doi.org/10.2514/6.2020-3682

Q. Sun, Y. Zhao, K.-S. Choi, X. Mao, Molecular Dynamics Simulation of Thermal De-icing on a Flat Surface, Appl. Therm. Eng. 189 (2021) 116701.
https://doi.org/10.1016/j.applthermaleng.2021.116701

A. Marboeuf, L. Bennani, M. Budinger, V. Pommier-Budinger, Electromechanical Resonant Ice Protection Systems: Numerical Investigation Through a Phase-field Mixed Adhesive/brittle Fracture Model, Eng. Fract. Mech. 230 (2020) 106926.
https://doi.org/10.1016/j.engfracmech.2020.106926

X. Huang, N. Tepylo, V. Pommier-Budinger, M. Budinger, E. Bonaccurso, P. Villedieu, L. Bennani, A Survey of Icephobic Coatings and their Potential use in a Hybrid Coating/active Ice Protection System for Aerospace Applications, Prog. Aerosp. Sci. 105 (2019) 74-97.
https://doi.org/10.1016/j.paerosci.2019.01.002

A. Ahmed, E.Wright, F. Abdel-Aziz, Y. Yan, Numerical Investigation of Heat Transfer and Flow Characteristics of a Double-wall Cooling Structure: Reverse Circular Jet Impingement, Appl. Therm. Eng. 189 (2021) 116720.
https://doi.org/10.1016/j.applthermaleng.2021.116720

D. Huanyu, C. Shinan, S. Mengjie, Effect of the Nozzle Arrangement of Atomization Equipment in Icing Cloud Simulation System on the Velocity Field of Water Droplets and Liquid Water Content Distribution, Appl. Therm. Eng. 172 (2020) 115196.
https://doi.org/10.1016/j.applthermaleng.2020.115196

de Castro, T., Andrade, C., Zaparoli, E., Mach Number Effect on The Heat Transfer Mechanism of Aircraft Anti-Icing Systems, (2014) International Review of Mechanical Engineering (IREME), 8 (3), pp. 547-554.

R. Ben-Abdallah, D. Leducq, H. Hoang, L. Fournaison, O. Pateau, B. Ballot-Miguet, A. Delahaye, Experimental Investigation of the Use of PCM in an Open Display Cabinet for Energy Management Purposes, Energy Convers. Manag. 198 (2019) 111909.
https://doi.org/10.1016/j.enconman.2019.111909

E. E. Khalil, M. Sobhi, CFD Simulation of Thermal and Energy Performance for a Display Cabinet Refrigerator Containing a Phase Change Material (PCM), in AIAA Propulsion and Energy 2020 Forum, 2020.
https://doi.org/10.2514/6.2020-3946

D. Mađerić, Z. Čarija, B. Pavković, B. Delač, Experimental and Numerical Study on Water Ice Forming on Pipe Columns in a Limited Volume Storage, Appl. Therm. Eng. (2021) 117080.
https://doi.org/10.1016/j.applthermaleng.2021.117080

C. Son, T. Kim, Development of an Icing Simulation Code for Rotating Wind Turbines, J. Wind. Eng. Ind. Aerodyn. 203 (2020) 104239.
https://doi.org/10.1016/j.jweia.2020.104239

O. Fakorede, Z. Feger, H. Ibrahim, A. Ilinca, J. Perron, C. Masson, Ice Protection Systems for Wind Turbines in Cold Climate: Characteristics, Comparisons and Analysis, Renew. Sust. Energ. Rev. 65 (2016) 662-675.
https://doi.org/10.1016/j.rser.2016.06.080

O. Parent, A. Ilinca, Anti-icing and De-icing Techniques for Wind Turbines: Critical Review, Cold Reg. Sci. Technol. 65 (2011) 88-96.
https://doi.org/10.1016/j.coldregions.2010.01.005

O. Habibzadeh-Bigdarvish, X. Yu, T. Li, G. Lei, A. Banerjee, A. J. Puppala, A Novel Full-scale External Geothermal Heating System for Dridge Deck De-icing, Appl. Therm. Eng. 185 (2021) 116365.
https://doi.org/10.1016/j.applthermaleng.2020.116365

K. Liu, S. Huang, C. Jin, H. Xie, F. Wang, Prediction Models of the Thermal Field on Ice-snow Melting Pavement with Electric Heating Pipes, Appl. Therm. Eng. 120 (2017) 269-276.
https://doi.org/10.1016/j.applthermaleng.2017.04.008

K. F. Jones, E. L. Andreas, Sea Spray Concentrations and the Icing of Fixed Offshore Structures, Q. J. R. Meteorol. Soc. 138 (2012) 131-144.
https://doi.org/10.1002/qj.897

Kim, A., Guryanov, G., Vavilov, A., Bugayev, A., Doudkina, Y., Development of Mounted Impact-Rotor Working Equipment for Destruction of Snow-Ice Formations, (2021) International Review of Mechanical Engineering (IREME), 15 (5), pp. 258-267.
https://doi.org/10.15866/ireme.v15i5.20805

J. P. Zarling, Heat and Mass Transfer From Freely Falling Drops at Low Temperatures, Technical Report 18, Cold Regions Research and Engineering Laboratory, Hanover, New Hampshire, USA, 1980.

S. Fukusako, M. Yamada, Recent Advances in Research on Water-freezing and Ice-melting Problems, Exp. Therm. Fluid Sci. 6 (1993) 90-105.
https://doi.org/10.1016/0894-1777(93)90044-J

J. P. Hindmarsh, A. B. Russell, X. D. Chen, Experimental and Numerical Analysis of the Temperature Transition of a Suspended Freezing Water Droplet, Int. J. Heat Mass Transf. 46 (2003) 1199-1213.
https://doi.org/10.1016/S0017-9310(02)00399-X

J. P. Hindmarsh, A. B. Russell, X. D. Chen, Experimental and Numerical Analysis of the Temperature Transition of a Freezing Food Solution Droplet, Chem. Eng. Sci. 59 (2004) 2503-2515.
https://doi.org/10.1016/j.ces.2004.03.007

M. Strub, O. Jabbour, F. Strub, J. P. Bédécarrats, Experimental Study and Modelling of the Crystallization of a Water droplet, Int. J. Refrig. 546 26 (2003) 59-68.
https://doi.org/10.1016/S0140-7007(02)00021-X

S. Tabakova, F. Feuillebois, S. Radev, Freezing of a Suspended Supercooled Droplet with a Heat Transfer Mixed Condition on its Outer Surface, AIP Conference Proceedings 1186 (2009) 240-247.
https://doi.org/10.1063/1.3265335

F. X. Tanner, Droplet Freezing and Solidification, first ed. (Springer U.S., Boston, MA, 2011).
https://doi.org/10.1007/978-1-4419-7264-4_16

Y. Hagiwara, S. Ishikawa, R. Kimura, K. Toyohara, Ice Growth and Interface Oscillation of Water Droplets Impinged on a Cooling Surface, J. Cryst. Growth in The 18th International Conference on Crystal Growth and Epitaxy (ICCGE-18) 468 (2017) 46-53.
https://doi.org/10.1016/j.jcrysgro.2016.12.095

Z. Meng, P. Zhang, Dynamic Propagation of Ice-water Phase Front in a Supercooled Water Droplet, Int. J. Heat Mass Transf. 152 (2020) 119468.
https://doi.org/10.1016/j.ijheatmasstransfer.2020.119468

S. Akhtar, M. Xu, A. P. Sasmito, Development and Validation of a Semi-analytical Framework for Droplet Freezing with Heterogeneous Nucleation and Non-linear Interface Kinetics, Int. J. Heat Mass Transf. (2020) 120734.
https://doi.org/10.1016/j.ijheatmasstransfer.2020.120734

T. G. Myers, M. G. Hennessy, M. Calvo-Schwarzwälder, The Stefan Problem with Variable Thermophysical Properties and Phase Change Temperature, Int. J. Heat Mass Transf. 149 (2020) 118975.
https://doi.org/10.1016/j.ijheatmasstransfer.2019.118975

Santim, C., Milanez, L., Numerical Study of Ice Melting Inside a Rectangular Cavity and a Horizontal Cylinder Including Convective Effects, (2013) International Review of Mechanical Engineering (IREME), 7 (5), pp. 874-881.

J. E. Castillo, Y. Huang, Z. Pan, J. A. Weibel, Asymmetric Solidification During Droplet Freezing in the Presence of a Neighboring Droplet, Int. J. Heat Mass Transf. 171 (2021) 121134.
https://doi.org/10.1016/j.ijheatmasstransfer.2021.121134

M. Xu, S. Akhtar, A. F. Zueter, M. A. Alzoubi, L. Sushama, A. P. Sasmito, Asymptotic Analysis of a Two-phase Stefan Problem in Annulus: Application to Outward Solidification in Phase Change Materials, Appl. Math. Comput. 408 (2021) 126343.
https://doi.org/10.1016/j.amc.2021.126343

S. Elghobashi, On Predicting Particle-laden Turbulent Flows, Appl. Sci. Res. 52 (1994) 309-329.
https://doi.org/10.1007/BF00936835

Z.Wu, Y. Cao, Numerical Simulation of Airfoil Aerodynamic Performance under the Coupling Effects of Heavy Rain and Ice Accretion, Adv. Mech. Eng. 8 (2016) 1-9.
https://doi.org/10.1177/1687814016667162

R. S. R. Sidin, R. H. A. IJzermans, M.W. Reeks, A Lagrangian Approach to Droplet Condensation in Atmospheric Clouds, Phys. Fluids. 21 (2009) 588 106603.
https://doi.org/10.1063/1.3244646

W. Luo, D. Jiang, T. Wu, C. Guo, C. Wang, R. Deng, S. Dai, Numerical Simulation of an Ice-strengthened Bulk Carrier in Brash Ice Channel, Ocean Eng. 196 (2020) 106830.
https://doi.org/10.1016/j.oceaneng.2019.106830

J. Ge, Z. Wang, K. Wan, Y. He, Z. Zhou, Z. Huang, Slagging Behavior Modeling in Coal Gasifiers using Two-way Coupled Slag Model with CFD, Fuel 281 (2020) 118736.
https://doi.org/10.1016/j.fuel.2020.118736

J. Barata, Modelling of Biofuel Droplets Dispersion and Evaporation, Renew. Energ. 33 (2008) 769-779.
https://doi.org/10.1016/j.renene.2007.04.019

C. Rodrigues, J. Barata, A. Silva, Modeling of Evaporating Sprays Impinging onto Solid Surfaces, J. Thermophys. Heat Trans. 31 (2017) 109-599.
https://doi.org/10.2514/1.T4733

M. Akyurt, G. Zaki, B. Habeebullah, Freezing Phenomena in Ice-water Systems, Energy Convers. Manag. 43 (2002) 1773-1789.
https://doi.org/10.1016/S0196-8904(01)00129-7

O. Mishima, H. E. Stanley, The Relationship between Liquid, Supercooled and Glassy Water, Nature 396 (1998) 329-335.
https://doi.org/10.1038/24540

T. Koop, B. Luo, A. Tsias, T. Peter, Water Activity as the Determinant for Homogeneous Ice Nucleation in Aqueous Solutions, Nature 406 (2000) 607 611-614.
https://doi.org/10.1038/35020537

V. Alexiades, A. D. Solomon, Mathematical Modeling of Melting and Freezing Processes second ed. (Hemisphere Publishing Corporation, 1993).
https://doi.org/10.1115/1.2930032

S. C. Gupta, The Classical Stefan Problem - Basic Concepts, Modelling and Analysis with Quasi-Analytical Solutions and Methods, second ed (Elsevier, 2017).
https://doi.org/10.1016/B978-0-444-63581-5.00012-9

X. Zhang, X. Wu, J. Min, X. Liu, Modelling of Sessile Water Droplet Shape Evolution during Freezing with Consideration of Supercooling Effect, Appl. Therm. Eng. 125 (2017) 644-651.
https://doi.org/10.1016/j.applthermaleng.2017.07.017

W. E. Ranz, W. R. Marshall, Evaporation from Drops: Part 1, Chem. Eng. Prog. 48 (1952) 141-146.

W. E. Ranz, W. R. Marshall, Evaporation from drops: Part 2, Chem. Eng. Prog. 48 (1952) 173-180.

S.-C. Yao, V. E. Schrock, Heat and mass transfer from freely falling drops, J. Heat Transf. 98 (1976) 120-126.
https://doi.org/10.1115/1.3450453

B. P. Leonard, A stable and accurate convective modelling procedure based on quadratic upstream interpolation, Comput. Methods Appl. Mech. Eng. 19 (1979) 59-98.
https://doi.org/10.1016/0045-7825(79)90034-3

S. V. Patankar, D. B. Spalding, A calculation procedure for heat, mass and momentum transfer in three-dimensional parabolic flows, Int. J. Heat Mass Transf. 15 (1972) 1787-1806.
https://doi.org/10.1016/0017-9310(72)90054-3

L. H. Thomas, Elliptic problems in linear differential equations over a network, Watson Sci. Comput. Lab Report, Columbia University, New 633 York, 1949.


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