Hostname: page-component-78c5997874-v9fdk Total loading time: 0 Render date: 2024-11-02T18:14:31.243Z Has data issue: false hasContentIssue false
  • English
  • Français

The influence of heating on liquid jet spreading and hydraulic jump

Published online by Cambridge University Press:  29 November 2019

Yunpeng Wang  and
Roger E. Khayat Open the ORCID record for Roger E. Khayat [Opens in a new window]
Yunpeng Wang
Affiliation:
Department of Mechanical and Materials Engineering, University of Western Ontario, London, ON, N6A 5B9, Canada
Roger E. Khayat*
Affiliation:
Department of Mechanical and Materials Engineering, University of Western Ontario, London, ON, N6A 5B9, Canada
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

The free-surface flow and thermal fields formed by an axisymmetric liquid jet impinging on a circular heated disk are examined theoretically. The disk is maintained either at a prescribed heat flux or temperature. The study explores the effect of inertia, wall heat flux and wall temperature on the momentum and thermal boundary layers as well as the film thickness and the location and height of the hydraulic jump. Only non-metallic liquids are considered, for which the kinematic viscosity is generally larger than the thermal diffusivity, causing the thermal boundary layer to remain thinner than the momentum boundary layer. The effect of surface tension resulting in the Marangoni stress at the free surface and the hoop stress at the jump is also explored. Our results corroborate well existing experimental, theoretical and numerical studies. Both the momentum and thermal boundary layers are found to decrease with increased inertia or thermal input at the disk. The thermal boundary layer is found to always reach the free surface for an imposed constant wall heat flux. The two transition locations where the boundary layers reach the free surface move downstream with inertia but move in opposite directions with increasing wall heat flux or wall temperature. Enhanced heating from the wall also tends to increase the jump radius and depress its height. More importantly, the hydraulic jump leads to a shock-type drop in the Nusselt number, confirming existing numerical findings. Finally, we show that the Nusselt number is independent of the wall temperature for a fluid of constant properties.

JFM classification

Wakes/Jets: Jets
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 883 , 25 January 2020 , A59
Copyright
© 2019 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Agrawal, D. C. & Menon, V. J. 1992 Surface tension and evaporation: an empirical relation for water. Phys. Rev. A 46, 2166–2169.CrossRefGoogle Scholar
Baonga, J. B., Gualous, H. L. & Imbert, M. 2006 Experimental study of hydrodynamic and heat transfer of free liquid jet impinging a flat circular heated disk. Appl. Therm. Engng 26, 1125–1138.CrossRefGoogle Scholar
Basu, S. & Cetegen, B. M. 2007 Effect of hydraulic jump on hydrodynamics and heat transfer in a thin liquid film flowing over a rotating disk analyzed by integral method. Trans. ASME J. Heat Transfer 129, 657–663.CrossRefGoogle Scholar
Bhagat, R. K., Jha, N. K., Linden, P. F. & Wilson, D. I. 2018 On the origin of the circular hydraulic jump in a thin liquid film. J. Fluid Mech. 851, R5.CrossRefGoogle Scholar
Bohr, T., Dimon, P. & Putzkaradze, V. 1993 Shallow-water approach to the circular hydraulic jump. J. Fluid Mech. 254, 635–648.CrossRefGoogle Scholar
Bohr, T., Ellegaard, C., Hansen, A. E. & Haaning, A. 1996 Hydraulic jumps, flow separation and wave breaking: an experimental study. Physica B 228, 1–10.CrossRefGoogle Scholar
Bohr, T., Putkaradze, V. & Watanabe, S. 1997 Averaging theory for the structure of hydraulic jumps and separation in laminar free-surface flows. Phys. Rev. Lett. 79, 1038–1041.CrossRefGoogle Scholar
Brdlik, P. M. & Savin, V. K. 1965 Heat transfer between an axisymmetric jet and a plate normal to the flow. J. Engng Phys. 8, 91–98.CrossRefGoogle Scholar
Bush, J. W. M. & Aristoff, J. M. 2003 The influence of surface tension on the circular hydraulic jump. J. Fluid Mech. 489, 229–238.CrossRefGoogle Scholar
Chaudhury, Z. H. 1964 Heat transfer in a radial liquid jet. J. Fluid Mech. 20, 501–511.CrossRefGoogle Scholar
Craik, A., Latham, R., Fawkes, M. & Gibbon, P. 1981 The circular hydraulic jump. J. Fluid Mech. 112, 347–362.CrossRefGoogle Scholar
De Gennes, P. G., Brochard-Wyart, F. & Quere, D. 2004 Capillarity and Wetting Phenomena. Springer.CrossRefGoogle Scholar
Dressaire, E., Courbin, L., Crest, J. & Stone, H. A. 2010 Inertia dominated thin-film flows over microdecorated surfaces. Phys. Fluids 22, 073602-07.CrossRefGoogle Scholar
Duchesne, A., Andersen, A. & Bohr, T. 2019 Surface tension and the origin of the circular hydraulic jump in a thin liquid film. Phys. Rev. Fluids 4, 084001.CrossRefGoogle Scholar
Duchesne, A., Lebon, L. & Limat, L. 2014 Constant Froude number in a circular hydraulic jump and its implication on the jump radius selection. Europhys. Lett. 107, 54002.CrossRefGoogle Scholar
Fulcher, G. S. 1992 Analysis of recent measurements of the viscosity of glasses. J. Am. Ceram. Soc. 75, 1043–1055.CrossRefGoogle Scholar
Granato, A. V. 2002 The specific heat of simple liquids. J. Non-Cryst. Solids 307–310, 376–386.CrossRefGoogle Scholar
Jagtap, K. C., Kale, N. B., Kale, V. V., Pawar, K. S. & Deshmukh, S. A. 2017 Heat transfer enhancement through liquid jet impingement. Intl Res. J. Engng Technol. 4, 1365–1369.Google Scholar
Kafoussias, N. G. & Williams, E. W. 1995 The effect of temperature-dependent viscosity on the free convective laminar boundary layer flow past a vertical isothermal flat plate. Acta Mech. 110, 123–137.CrossRefGoogle Scholar
Kasimov, A. R. 2008 A stationary circular hydraulic jump, the limits of its existence and its gas dynamic analogue. J. Fluid Mech. 601, 189–198.CrossRefGoogle Scholar
Khayat, R. E. 2016 Impinging planar jet flow and hydraulic jump on a horizontal surface with slip. J. Fluid Mech. 808, 258–289.CrossRefGoogle Scholar
Khayat, R. E. & Kim, K. 2006 Thin-film flow of a viscoelastic fluid on an axisymmetric substrate of arbitrary shape. J. Fluid Mech. 552, 37–71.CrossRefGoogle Scholar
Korson, L., Dorst-Hansen, W. & Millero, F. J. 1969 Viscosity of water at various temperatures. J. Phys. Chem. 73, 34–39.CrossRefGoogle Scholar
Kundu, P. K., Cohen, I. M. & Bowling, D. R. 2016 Fluid Mechanics, 6th edn. Elsevier.Google Scholar
Lienhard, J. 2006 Heat transfer by impingement of circular free-surface liquid jets. In Proceedings of the 18th National and 7th International ISHMT-ASME Heat and Mass Transfer Conference, Guwahati, India (ed. Mishra, S. C., Prasad, B. V. S. S. S. & Garimella, S. V.), pp. 211–226. Tata McGraw-Hill.Google Scholar
Ling, J. X. & Dybbs, A. 1992 The effect of variable viscosity on forced convection over a flat plate submersed in a porous medium. ASME J. Heat Transfer 114, 1063–1065.CrossRefGoogle Scholar
Liu, X., Gabour, L. A. & Lienhard, J. 1993 Stagnation-point heat transfer during impingement of laminar liquid jets: analysis including surface tension. Trans. ASME J. Heat Transfer 115, 99–105.CrossRefGoogle Scholar
Liu, X. & Lienhard, J. 1989 Liquid jet impingement heat transfer on a uniform flux surface. Trans. ASME J. Heat Transfer 106, 523–530.Google Scholar
Lubarda, V. & Talke, K. A. 2011 Analysis of the equilibrium droplet shape based on an ellipsoidal droplet model. Langmuir 27, 10705–10713.CrossRefGoogle ScholarPubMed
Mauro, J. C., Yue, Y., Ellison, A. J., Gupta, P. K. & Allan, D. C. 2009 Viscosity of glass-forming liquids. Proc. Natl Acad. Sci. USA 106 (47), 19780–19784.CrossRefGoogle ScholarPubMed
Maynes, D. & Crockett, J. 2014 Apparent temperature jump and thermal transport in channels with streamwise rib and cavity featured superhydrophobic walls at constant heat flux. Trans. ASME J. Heat Transfer 136, 011701.Google Scholar
Miller, R., Garrett, S. J., Griffiths, P. T. & Hussain, Z. 2018 Stability of the Blasius boundary layer over a heated plate in a temperature-dependent viscosity flow. Phys. Rev. Fluids 3, 113902.CrossRefGoogle Scholar
Mohajer, B. & Li, R. 2015 Circular hydraulic jump on finite surfaces with capillary limit. Phys. Fluids 27, 117102.CrossRefGoogle Scholar
Okhotin, A. S., Zhmakin, L. I. & Ivanyuk, A. P. 1992 Universal temperature dependence of the thermal conductivity and viscosity coefficients. Intl J. Heat Mass Transfer 35, 3059–3067.CrossRefGoogle Scholar
Peleg, M. 2017 Temperature–viscosity models reassessed. Crit. Rev. Food Sci. Nutr. 58, 1–10.Google ScholarPubMed
Prince, J. F., Maynes, D. & Crockett, J. 2012 Analysis of laminar jet impingement and hydraulic jump on a horizontal surface with slip. Phys. Fluids 24, 102103.CrossRefGoogle Scholar
Rahman, M. M., Faghri, A. & Hankey, W. L. 1992 Fluid flow and heat transfer in a radially spreading thin liquid film. Numer. Heat Transfer A21, 71–90.CrossRefGoogle Scholar
Rampp, M., Buttersack, C. & Ludeman, H. D. 2000 c,T-Dependence of the viscosity and the self-diffusion coefficients in some aqueous carbohydrate solutions. Carbohydr. Res. 328, 561–572.CrossRefGoogle ScholarPubMed
Rao, A. & Arakeri, J. H. 2001 Wave structure in the radial film flow with a circular hydraulic jump. Exp. Fluids 31, 542–549.CrossRefGoogle Scholar
Rojas, N., Argentina, M. & Tirapegui, E. 2010 Inertial lubrication theory. Phys. Rev. Lett. 104, 187801-4.CrossRefGoogle ScholarPubMed
Rojas, N., Argentina, M. & Tirapegui, E. 2013 A progressive correction to the circular hydraulic jump scaling. Phys. Fluids 25, 042105.CrossRefGoogle Scholar
Saad, N. R., Douglas, W. J. M. & Mujumdar, A. S. 1977 Prediction of heat transfer under an axisymmetric laminar impinging jet. Ind. Engng Chem. Fundam. 16, 148–154.CrossRefGoogle Scholar
Sahasrabudhe, S. N., Rodriguez-Martinez, V., O’Meara, M. & Farkas, B. E. 2017 Density, viscosity, and surface tension of five vegetable oils at elevated temperatures: measurement and modeling. Intl J. Food Prop. 20, 51965–51981.Google Scholar
Scherer, G. W. 1992 Editorial comments on a paper by Gordon S. Fulcher. J. Amer. Ceramic Soc. 75, 1060–1062.CrossRefGoogle Scholar
Schlichtling, H. & Gersten, K. 2000 Boundary-Layer Theory. Springer.CrossRefGoogle Scholar
Searle, M., Maynes, D. & Crockett, J. 2017 Thermal transport due to liquid jet impingement on super hydrophobic surfaces with isotropic slip. Intl J. Heat Mass Transfer 110, 680–691.CrossRefGoogle Scholar
Seeton, C. J. 2006 Viscosity–temperature correlation for liquids. Tribol. Lett. 22, 67–78.CrossRefGoogle Scholar
Segur, J. B. & Oberstar, H. E. 1951 Viscosity of glycerol and its aqueous solutions. Ind. Engng Chem. 43, 2117–2120.CrossRefGoogle Scholar
Singh, S. & Das, A. K. 2018 Computational simulation of radially asymmetric and hydraulic jumps and jump–jump interactions. Comput. Fluids 170, 1–12.CrossRefGoogle Scholar
Sung, J., Choi, H. G. & Yoo, J. Y. 1999 Finite element simulation of thin liquid film flow and heat transfer including a hydraulic jump. Intl J. Numer. Meth. Engng 46, 83–101.3.0.CO;2-D>CrossRefGoogle Scholar
Takamura, K., Fischer, H. & Morrow, N. R. 2012 Physical properties of aqueous glycerol solutions. J. Petrol. Sci. Engng 98–99, 50–60.CrossRefGoogle Scholar
Tani, I. 1949 Water jump in the boundary layer. J. Phys. Soc. Japan 4, 212–215.CrossRefGoogle Scholar
Wang, X. S., Dagan, Z. & Jiji, L. M. 1989 Heat transfer between a circular free impinging jet and a solid surface with nonuniform wall temperature or wall heat flux – 2. Solution for the boundary layer region. Intl J. Heat Mass Transfer 32, 1361–1371.CrossRefGoogle Scholar
Wang, Y. & Khayat, R. E. 2018 Impinging jet flow and hydraulic jump on a rotating disk. J. Fluid Mech. 839, 525–560.CrossRefGoogle Scholar
Wang, Y. & Khayat, R. E. 2019 The role of gravity in the prediction of the circular hydraulic jump radius for high-viscosity liquids. J. Fluid Mech. 862, 128–161.CrossRefGoogle Scholar
Watanabe, S., Putkaradze, V. & Bohr, T. 2003 Integral methods for shallow free-surface flows with separation. J. Fluid Mech. 480, 233–265.CrossRefGoogle Scholar
Watson, E. 1964 The spread of a liquid jet over a horizontal plane. J. Fluid Mech. 20, 481–499.CrossRefGoogle Scholar