Modelling study on freezing process of water droplet on inclined cold plate surface with droplet dynamic behavior considered

Dang, Qun; Song, Mengjie; Zhang, Xuan; Pekař, Libor; Hosseini, Seyyed Hossein

dc.title	Modelling study on freezing process of water droplet on inclined cold plate surface with droplet dynamic behavior considered	en
dc.contributor.author	Dang, Qun
dc.contributor.author	Song, Mengjie
dc.contributor.author	Zhang, Xuan
dc.contributor.author	Pekař, Libor
dc.contributor.author	Hosseini, Seyyed Hossein
dc.relation.ispartof	International Journal of Heat and Mass Transfer
dc.identifier.issn	0017-9310 Scopus Sources, Sherpa/RoMEO, JCR
dc.date.issued	2022
utb.relation.volume	197
dc.type	article
dc.language.iso	en
dc.publisher	Elsevier Ltd
dc.identifier.doi	10.1016/j.ijheatmasstransfer.2022.123327
dc.relation.uri	https://www.sciencedirect.com/science/article/pii/S0017931022007979
dc.relation.uri	https://www.sciencedirect.com/science/article/pii/S0017931022007979/pdfft?isDTMRedir=true&download=true
dc.subject	sessile water droplet	en
dc.subject	inclined surface	en
dc.subject	dynamic behavior	en
dc.subject	freezing process	en
dc.subject	modeling study	en
dc.description.abstract	Droplet freezing on inclined surfaces exists widely in engineering fields. To accurately predict and control the freezing process of a sessile water droplet on inclined surface, a theoretical model based on the heat-enthalpy method is presented in this study, with two types of dynamic behavior considered, deformation and spreading. After the validation of model by droplet profiles and freezing duration from experiments, the freezing characteristics are analyzed, including contact area, frozen height and vertex offset, etc. As found, the effect of inclined angle on less than 10.34 µL water droplet is greater than that on larger than 10.34 µL droplet, due to the mutual relation between surface tension and gravity effect. When the inclined angle of surface changes from 0° to 40°, the contact area keeps at 11.61 mm2 for 10 µL water droplet, and increases by 5.64% from 23.04 to 24.34 mm2 for 25 µL water droplet. The initial heights of 10 and 25 µL water droplets decrease by 0.85% from 1.18 mm to 1.17 mm and by 1.91% from 1.51 mm to 1.49 mm, respectively. That means it is easier frozen for the same water droplet on bigger inclined angle surface. This study is beneficial for the optimization of anti-frosting and defrosting technologies. © 2022	en
utb.faculty	Faculty of Applied Informatics
dc.identifier.uri	http://hdl.handle.net/10563/1011105
utb.identifier.obdid	43884081
utb.identifier.scopus	2-s2.0-85135922243
utb.identifier.wok	000863058900004
utb.identifier.coden	IJHMA
utb.source	j-scopus
dc.date.accessioned	2022-08-31T06:47:09Z
dc.date.available	2022-08-31T06:47:09Z
dc.description.sponsorship	IADL20200104; National Natural Science Foundation of China, NSFC: 52076013; Beijing Municipal Science and Technology Commission, BMSTC: 3212024
dc.description.sponsorship	National Natural Science Foundation of China [52076013]; Beijing Municipal Science & Technology Commission [3212024]; Open Fund of Key Laboratory of Icing [IADL20200104]
utb.ou	Department of Automation and Control Engineering
utb.contributor.internalauthor	Pekař, Libor
utb.fulltext.affiliation	Qun Danga, Mengjie Songa,∗, Xuan Zhanga, Libor Pekař b,d, Seyyed Hossein Hosseini c a Department of Energy and Power Engineering, School of Mechanical Engineering, Beijing Institute of Technology, Beijing 100081, China b Department of Automation and Control Engineering, Faculty of Applied Informatics, Tomas Bata University in Zlín, Nad Stráněmi 4511, Zlín 76005, Czech Republic c Department of Chemical Engineering, Ilam University, Ilam 69315-516, Iran d Department of Technical Studies, College of Polytechnics Jihlava, Tolstého 16, 586 01 Jihlava, Czech Republic ∗ Corresponding author. E-mail address: mengjie.song@gmail.com (M. Song).
utb.fulltext.dates	Received 8 June 2022 Revised 20 July 2022 Accepted 3 August 2022 Available online 11 August 2022
utb.fulltext.references	[1] M.J. Song, S.W. Lei, S.H. Hosseini, X.Y. Luo, Z.H. Wang, An experimental study on the effect of horizontal cold plate surface temperature on frosting characteristics under natural convection, Appl. Therm. Eng. 211 (2022) 118416. [2] S.W. Lei, M.J. Song, C.B. Dang, Y.J. Xu, K.K. Shao, Experimental study on the effect of surface temperature on the frost characteristics of an inverted cold plate under natural convection, Appl. Therm. Eng. 211 (2022) 118470. [3] L. Zhang, M.J. Song, S.M. Deng, J. Shen, C.B. Dang, Frosting mechanism and behaviors on surfaces with simple geometries: a state-of-the-art literature review, Appl. Therm. Eng. 215 (2022) 118984. [4] H.Y. Deng, S.N. Chang, M.J. Song, The optimization of simulated icing environment by adjusting the arrangement of nozzles in an atomization equipment for the anti-icing and deicing of aircrafts, Int. J. Heat Mass Transf. 155 (2020) 119720. [5] W.L. Lian, Y.M. Xuan, Experimental investigation on a novel aero-engine nose cone anti-icing system, Appl. Therm. Eng. 121 (2017) 1011–1021. [6] S.W. Lei, M.J. Song, S.M. Deng, J. Shen, C.B. Dang, Experimental study on the effect of surface temperature on the frost characteristics of a vertical cold plate under natural convection, Exp. Therm. Fluid Sci. 215 (2022) 118984. [7] J. Koszut, K. Boyina, G. Popovic, J. Carpenter, S. Wang, N. Miljkovic, Superhydrophobic heat exchangers delay frost formation and reduce defrost energy input of aircraft environmental control systems, Int. J. Heat Mass Transf. 189 (2022) 122669. [8] S.W. Lei, M.J. Song, P. Libor, J. Shen, A numerical study on frosting and its early stage under forced convection conditions with surface and environmental factors considered, Sustain. Energy Technol. Assess. 45 (2021) 101202. [9] G. Chaudhary, R. Li, Freezing of water droplets on solid surfaces: an experimental and numerical study, Exp. Therm. Fluid Sci. 57 (2014) 86–93. [10] M.H. Kim, D.R. Kim, K.S. Lee, Stochastic approach to the anti-freezing behaviors of superhydrophobic surfaces, Int. J. Heat Mass Transf. 106 (2017) 841–846. [11] S. Sastry, Water: ins and outs of ice nucleation, Nature 438 (2005) 746–747. [12] O.R. Enríquez, Á.G. Marín, K.G. Winkels, J.H. Snoeijer, Freezing singularities in water drops, Phys. Fluids 24 (2012) 091102. [13] J.H. Snoeijer, P. Brunet, Pointy ice-drops: how water freezes into a singular shape, Am. J. Phys. 80 (2012) 764–771. [14] X. Zhang, X. Liu, X.M. Wu, J.C. Min, Experimental investigation and statistical analysis of icing nucleation characteristics of sessile water droplets, Exp. Therm. Fluid Sci. 99 (2018) 26–34. [15] A.G. Marin, O.R. Enriquez, P. Brunet, P. Colinet, J.H. Snoeijer, Universality of tip singularity formation in freezing water drops, Phys. Rev. Lett. 113 (5) (2014) 54301. [16] Y.L. Li, M.X. Li, C.B. Dang, X.T. Liu, Effects of dissolved gas on the nucleation and growth of ice crystals in freezing droplets, Int. J. Heat Mass Transf. 184 (2022) 122334. [17] Z.Y. Jin, Z.N. Wang, D.Y. Sui, Z.G. Yang, The impact and freezing processes of a water droplet on different inclined cold surfaces, Int. J. Heat Mass Transf. 97 (2016) 211–223. [18] C.E. Clavijo, J. Crockett, D. Maynes, Hydrodynamics of droplet impingement on hot surfaces of varying wettability, Int. J. Heat Mass Transf. 108 (2017) 1717–1726. [19] F.Q. Zhu, W.Z. Fang, T.H. New, Y.G. Zhao, C. Yang, Freezing morphologies of impact water droplets on an inclined subcooled surface, Int. J. Heat Mass Transf. 181 (2021) 121843. [20] Z.Y. Jin, H.H. Zhang, Z.G. Yang, The impact and freezing processes of a water droplet on a cold surface with different inclined angles, Int. J. Heat Mass Transf. 103 (2016) 886–893. [21] M.F. Ismail, P.R. Waghmare, Universality in freezing of an asymmetric drop, Appl. Phys. Lett. 109 (2016) 234105. [22] A. Starostin, V. Strelnikov, L.A. Dombrovsky, S. Shoval, O. Gendelman, E. Bormashenko, Effect of asymmetric cooling of sessile droplets on orientation of the freezing tip, J. Colloid Interface Sci. 620 (2022) 179–186. [23] X. Zhang, X.M. Wu, J.C. Min, X. Liu, Modelling of sessile water droplet shape evolution during freezing with consideration of supercooling effect, Appl. Therm. Eng. 125 (2017) 644–651. [24] X. Zhao, B. Dorng, W.Z. Li, B.L. Dou, An improved enthalpy-based lattice Boltzmann model for heat and mass transfer of the freezing process, Appl. Therm. Eng. 111 (2017) 1477–1486. [25] T.V. Vu, A.V. Truong, N.T.B. Hoang, D.K. Tran, Numerical investigations of solidification around a circular cylinder under forced convection, J. Mech. Sci. Technol. 30 (2016) 5019–5028. [26] M.L. Lu, M.J. Song, Z.J. Ma, X.T. Wang, L. Zhang, A modeling study of sessile water droplet on the cold plate surface during freezing under natural convection with gravity effect considered, Int. J. Multiph. Flow 143 (2021) 103749. [27] J.J. Sun, J.Y. Gong, G.J. Li, A lattice Boltzmann model for solidification of water droplet on cold flat plate, Int. J. Refrig. 59 (2015) 53–64. [28] T.V. Vu, C.T. Nguyen, Q.H. Luu, Numerical study of a liquid drop on an inclined surface with solidification, Int. J. Heat Mass Transf. 144 (2019) 118636. [29] M.L. Lu, M.J. Song, X.L. Pang, C.B. Dang, L. Zhang, Modeling study on sessile water droplet during freezing with the consideration of gravity, supercooling, and volume expansion effects, Int. J. Multiph. Flow 147 (2022) 103909. [30] T.V. Vu, G. Tryggvason, S. Homma, J.C. Wells, Numerical investigations of drop solidification on a cold plate in the presence of volume change, Int. J. Multiph. Flow 76 (2015) 73–85. [31] J.D. Coninck, J.C. Fernández-Toledano, F. Dunlop, T. Huillet, A. Sodji, Shape of pendent droplets under a tilted surface, Phys. D 415 (2021) 132765. [32] T. Young, An essay on the cohesion of fluids, Philos. Trans. R. Soc. 95 (1805) 65–87. [33] A.W. Adamson, A.P. Gast, Physical Chemistry of Surfaces, 6th ed., Wiley, New York, 1997. [34] A.I. ElSherbini, A.M. Jacobi, Liquid drops on vertical and inclined surfaces I. An experimental study of drop geometry, J. Colloid Interface Sci. 273 (2004) 556–565. [35] A. Rathinasamy, D. Ahmadian, P. Nair, Second-order balanced stochastic Runge-Kutta methods with multi-dimensional studies, J. Comput. Appl. Math. 377 (2020) 112890. [36] I.K. Argyros, J. Ceballosb, D. González, J.M. Gutiérrez, Extending the applicability of Newton’s method for a class of boundary value problems using the shooting method, Appl. Math. Comput. 384 (2020) 125378. [37] H. Lomas, Calculation of front and rear contact angles: I. drops on inclined planes, J. Colloid Interface Sci. 33 (4) (1970) 548–553. [38] Y.H. Jiang, W. Xu, M.A. Sarshar, C.H. Choi, Generalized models for front and rear contact angles of fakir droplets on pillared and pored surfaces, J. Colloid Interface Sci. 552 (15) (2019) 359–371. [39] Q. Dang, M.J. Song, C.B. Dang, T.Z. Zhan, L. Zhang, Experimental study on solidification characteristics of sessile urine droplets on a horizontal cold plate surface under natural convection, Langmuir 38 (25) (2022) 7846–7857. [40] X. Zhang, X. Liu, J.C. Min, X.M. Wu, Shape variation and unique tip formation of a sessile water droplet during freezing, Appl. Therm. Eng. 147 (2019) 927–934. [41] J.E. Castillo, Y. Huang, Z. Pan, J.A. Weibel, Quantifying the pathways of latent heat dissipation during droplet freezing on cooled substrates, Int. J. Heat Mass Transf. 164 (2021) 120608.
utb.fulltext.sponsorship	The corresponding author acknowledges the financial supports from the National Natural Science Foundation of China (No. 52076013 ), Beijing Municipal Science & Technology Commission (No. 3212024), and Open Fund of Key Laboratory of Icing and Anti/De-icing (Grant No. IADL20200104).
utb.wos.affiliation	[Dang, Qun; Song, Mengjie; Zhang, Xuan] Beijing Inst Technol, Sch Mech Engn, Dept Energy & Power Engn, Beijing 100081, Peoples R China; [Pekar, Libor] Tomas Bata Univ Zlin, Fac Appl Informat, Dept Automation & Control Engn, Nad Stranemi 4511, Zlin 76005, Czech Republic; [Hosseini, Seyyed Hossein] Ilam Univ, Dept Chem Engn, Ilam 69315516, Iran; [Pekar, Libor] Coll Polytech Jihlava, Dept Tech Studies, Tolsteho 16, Jihlava 58601, Czech Republic
utb.scopus.affiliation	Department of Energy and Power Engineering, School of Mechanical Engineering, Beijing Institute of Technology, Beijing, 100081, China; Department of Automation and Control Engineering, Faculty of Applied Informatics, Tomas Bata University in Zlín, Nad Stráněmi 4511, Zlín, 76005, Czech Republic; Department of Chemical Engineering, Ilam University, Ilam, 69315-516, Iran
utb.fulltext.projects	52076013
utb.fulltext.projects	3212024
utb.fulltext.projects	IADL20200104
utb.fulltext.faculty	Faculty of Applied Informatics
utb.fulltext.ou	Department of Automation and Control Engineering
utb.identifier.jel	-