Flow regimes of a liquid film carried away by a gas flow in a flat horizontal channel under isothermal conditions

A. V. Minakov ; A. S. Lobasov ; A. V. Shebelev ; D. V. Zaicev ; O. A. Kabov

Sibirskij žurnal industrialʹnoj matematiki, Tome 25 (2022) no. 3, pp. 104-119.

Résumé

A three-dimensional mathematical model of the flow of a liquid film carried away by a gas flow in a flat horizontal minichannel under isothermal conditions has been developed. A numerical simulation of the film flow regimes in the evaporative cooling system has been carried out. Dependences of the development of the deformation on the control parameters of motion, such as the Reynolds numbers for liquid and gas, are studied. The hydrodynamic flow regimes found in the experiment were confirmed by the results of numerical simulation. Thus, five different modes were considered: channel flooding, smooth film, two-dimensional waves, three-dimensional waves and film rupture. An analysis of the simulation results showed that the model qualitatively correctly reproduces all the features of the film behaviour in the studied modes. A satisfactory agreement between the calculation and experiment results was obtained in terms of the surface shape and film thickness, as well as in terms of wavelengths and ridge passing frequencies. It is shown that the calculation well reproduces in a whole the beginning of the instability development in a liquid film.

Détail

Keywords: liquid films, flow regimes, evaporative cooling system, experiment, numerical simulation, VoF method.

Bibliographie

[1] K. A. Bar-Cohen, P. Wang, “Thermal management of on-chip hot spots”, J. Heat Transfer., 134 (2012), 051017

[2] K. A. Bar-Cohen, A. A. Wative, “Cooling Electric Equipment”, Mech. Engineers Handbook., Sect. 1. Chapt. 12, v. 4, 2015, 451–499

[3] D. B. Tuckerman, R. F.W. Pease, “High-performance heat sinking”, VLSI, IEEE Electron Device Lett., EDL-2:5 (1981), 126–129

[4] G. Swift, A. Migliori, J. Wheatley, “Construction of and measurements with an extremely compact crossflow heat exchanger”, Heat Transfer Engrg., 6:2 (1985), 39–46

[5] E. G. Colgan, B. Furman, M. Gaynes, W. S. Graham, N. C. LaBianca, J. H. Magerlein, R. R. Schmidt, “A practical implementation of silicon microchannel coolers for high power chips”, IEEE Trans. Components and Packaging Technologies, 30:2 (2007), 218–225

[6] J. A. Khan, A. K. M. M. M. Morshed, R. Fang, “Towards ultra-compact high heat flux microchannel heat sink”, Procedia Engrg., 90 (2014), 11–24

[7] S. G. Kandlikar, S. Colin, Y. Peles, S. Garimella, R. F. Pease, J. J. Brandner, D. B. Tuckerman, “Heat transfer in microchannels-2012 status and research needs”, J. Heat Transfer., 135:9 (2013), 091017

[8] P. Stephan, C. Brandt, “Advanced capillary structures for high performance heat pipes”, Proc. 1 Int. Conf. on Microchannels and Minichannels, Rochester–N. Y., 2003, 69–75

[9] C. Woodcock, C. Ng-oma, M. Sweet, Y. Wang, Y. Peles, “Ultra-high heat flux dissipation with Piranha Pin Fins”, Int. J. Heat and Mass Transfer, 128 (2019), 504–515

[10] M. H. Nasr, C. E. Green, P. A. Kottke, X. Zhang, T. E. Sarvey, Y. K. Joshi, M. S. Bakir, A. G. Fedorov, “Flow regimes and convective heat transfer of refrigerant flow boiling in ultra-small clearance microgaps”, Int. J. Heat and Mass Transfer, 108 (2017), 1702–1713

[11] O. A. Kabov, Yu. V. Lyulin, I. V. Marchuk, D. V. Zaitsev, “Locally heated shear-driven liquid films in microchannels and minichannels”, Int. J. Heat and Fluid Flow, 28 (2007), 103–112

[12] O. A. Kabov, D. V. Zaitsev, V. V. Cheverda, A. Bar-Cohen, “Evaporation and flow dynamics of thin, sheardriven liquid films in microgap channels”, Experimental Thermal and Fluid Sci, 35:825 (2011), 825–831

[13] O. Kabov, D. Zaitsev, E. Tkachenko, “Interfacial thermal fluid phenomena in shear-driven thin liquid films”, Proc. 16 Int. Heat Transfer Conf. (Beijing, China, 2018), 1061–1067 | DOI

[14] M. Potash, P. C. Jr. Wayner, “Evaporation from a two-dimensional extended meniscus”, Internat. J. Heat and Mass. Transfer, 15 (1972), 1851–1863

[15] P. C. Stephan, C. A. Busse, “Analysis of the heat transfer coefficient of grooved heat pipe evaporator walls”, Internat. J. Heat and Mass. Transfer, 35 (1992), 383–391

[16] V. S. Ajaev, O. A. Kabov, “Heat and mass transfer near contact lines on heated surfaces”, Internat. J. Heat and Mass. Transfer, 108 (2017), 918–932

[17] A. L. Karchevsky, V. V. Cheverda, I. V. Marchuk, T. G. Ponomarenko, V. S. Sulyaeva, O. A. Kabov, “Heat flux density evaluation in the region of contact line of drop on a sapphire surface using infrared thermography measurements”, Microgravity Sci. Technol., 33 (2021), 53 | DOI

[18] N. Schweizer, P. Stephan, “Experimental study of bubble behavior and local heat flux in pool boiling under variable gravity conditions”, Multiphase Sci. Technol, 21 (2009), 329–350

[19] A. L. Karchevsky, I. V. Marchuk, O. A. Kabov, “Calculation of the heat flux near the liquid-gas-solid contact line”, Appl. Math. Model., 40 (2016), 1029–1037

[20] O. A. Kabov, D. V. Zaitsev, D. P. Kirichenko, V. S. Ajaev, “Investigation of moist air flow near contact line using microdroplets as tracers”, Interfacial Phenomena and Heat Transfer, 4:2-3 (2016), 207–216 | DOI

[21] M. Gibbons, P. Di Marco, A. J. Robinson, “Local heat transfer to an evaporating superhydrophobic droplet”, Internat. J. Heat and Mass. Transfer, 121 (2018), 641–652

[22] J. Jo, J. Kim, S. J. Kim, “Experimental investigations of heat transfer mechanisms of a pulsating heat pipe”, Energy Convers. Manag, 181 (2019), 331–341

[23] K. Schweikert, A. Sielaff, P. Stephan, “Heat flux during dipcoating of a superheated substrate”, Interfacial Phenom. Heat Transfer, 7 (2019), 269–281

[24] J. P. Burelbach, S. G. Bankoff, S. H. Davis, “Nonlinear stability of evaporating/condensing liquid film”, J. Fluid Mech., 195 (1988), 463–494

[25] O. E. Shklyaev, E. Fried, “Stability of an evaporating thin liquid film”, J. Fluid Mech., 584 (2007), 157–183

[26] E. Sultan, A. Boudaoud, M. Ben Amar, “Diffusion-limited evaporation of thin polar liquid films”, J. Engrg. Math., 50 (2004), 209–222

[27] E. Sultan, A. Boudaoud, M. Ben Amar, “Evaporation of a thin film: diffusion of the vapour and Marangoni instabilities”, J. Fluid Mech., 543 (2005), 183–202

[28] V. B. Bekezhanova, O. A. Kabov, “Influence of internal energy variations of the interface on the stability of film flow”, Interfacial Phenomena and Heat Transfer, 4:2-3 (2016), 133–156 | DOI

[29] E. Ya. Gatapova, O. A. Kabov, “Shear-driven flows of locally heated liquid films”, Int. J. Heat and Mass Transfer, 51:19-20 (2008), 4797–4810

[30] R. Liu, O. A. Kabov, “Instabilities in a horizontal liquid layer in cocurrent gas flow with an evaporating interface”, Physical Review E. Statistical, Nonlinear, and Soft Matter Physics, 85:6 (2012), 066305 | DOI

[31] Yu. O. Kabova, V. V. Kuznetsov, O. A. Kabov, T. Gambaryan-Roisman, P. Stephan, “Evaporation of a thin viscous liquid film sheared by gas in a microchannel”, Int. J. Heat and Mass Transfer, 68 (2014), 527–541 | DOI

[32] C. Redon, F. Brochard-Wyart, F. Rondelez, “Dynamics of Dewetting”, Phys. Review Letters, 66:6 (1991), 715–719

[33] V. S. Ajaev, “Instability and Rupture of Thin Liquid Films on Solid Substrates”, Interfacial Phenomena and Heat Transfer, 1:1 (2013), 81–92

[34] P. G. de Gennes, F. Brochard-Wyart, D. Quere, Capillarity and Wetting Phenomena: Drops, Bubbles, Pearls, Waves, Springer-Verl, 2004

[35] O. A. Kabov, “Breakdown of a liquid film flowing over the surface with a local heat source”, Thermophys. Aeromech., 7:4 (2000), 513–520

[36] D. V. Zaitsev, O. A. Kabov, A. R. Evseev, “Measurement of locally heated liquid film thickness by a doublefiber optical probe”, Experiments in Fluids, 34 (2003), 748–754

[37] D. V. Zaitsev, A. A. Semenov, O. A. Kabov, “Effect of viscosity on thermocapillary breakdown of a falling liquid film”, Thermophys. Aeromech., 23:4 (2016), 625–628

[38] N. Mulji, S. Chandra, “Rupture and dewetting of water films on solid surfaces”, J. Colloid and Interface Sci., 352:1 (2010), 194–201

[39] S. Kim, J. Kim, H. Y. Kim, “Formation, growth, and saturation of dry holes in thick liquid films under vapor-mediated Marangoni effect”, Phys. Fluids, 31 (2019), 112105

[40] D. Yu. Kochkin, D. V. Zaitsev, O. A. Kabov, “Thermocapillary rupture and contact line dynamics in the heated liquid layers”, Interfacial Phenomena and Heat Transfer, 8:1 (2020), 1–9 | DOI

[41] C. W. Hirt, B. D. Nichols, “Volume of fluid (VOF) method for the dynamics of free boundaries”, J. Comput. Phys., 39 (1981), 201–225 | DOI

[42] J. U. Brackbill, D. B. Kothe, C. Zemach, “A continuum method for modeling surface tension”, J. Comput. Phys., 100 (1992), 335–354 | DOI

[43] R. L. Hoffman, “A study of the advancing interface I. Interface shape in liquid gas systems”, J. Colloid Interface Sci., 50:2 (1975), 228–241 | DOI

[44] R. G. Cox, “The dynamics of the spreading of liquids on a solid surface. Part 1. Viscous flow”, J. Fluid Mech. 1986, 168, 169194 | DOI

[45] Y. D. Shikhmurzaev, “Moving contact lines in liquid/liquid/solid systems”, J. Fluid Mech., 334:1 (1997), 211–249

[46] S. F. Kistler, “Hydrodynamics of wetting”, Wettability, 49 (1993), 311–431

[47] A. V. Minakov, “Numerical algorithm for moving boundary fluid dynamics problems and its testing”, Comput. Math. Math. Phys., 54:10 (2014), 1560–1570 | DOI

[48] A. V. Minakov, A. A. Shebeleva, A. A. Yagodnitsyna, A. V. Kovalev, A. V. Bilsky, “Flow regimes of viscous immiscible liquids in t-type microchannels”, Chem. Engrg. Technology, 42:5 (2019), 1037–1044

[49] E. A. Chinnov, O. A. Kabov, “Two-phase flow in pipes and capillary channels”, High Temperatures, 44:5 (2006), 773–791

[50] G. Yadigaroglu, G. Hetsroni, G. F. Hewitt, “Flow Regimes”, Introduction to Multiphase Flow, Ch. 4, Springer-Verl., 2018, 95–140

[51] E. A. Chinnov, F. V. Ron-shin, O. A. Kabov, “Two-phase flow patterns in short horizontal rectangular microchannels”, Int. J. Multiphase Flow, 80 (2016), 57–68

[52] F. V. Ronshin, Y. A. Dementyev, E. A. Chinnov, V. V. Cheverda, O. A. Kabov, “Experimental investigation of adiabatic gas-liquid flow regimes and pressure drop in slit microchannel”, Microgravity Science and Technology, 31:5 (2019), 693–707