Hostname: page-component-586b7cd67f-2brh9 Total loading time: 0 Render date: 2024-11-26T09:56:57.478Z Has data issue: false hasContentIssue false
  • English
  • Français

Evaporation-driven turbulent convection in water pools

Published online by Cambridge University Press:  08 October 2020

William A. Hay Open the ORCID record for William A. Hay [Opens in a new window]  and
Miltiadis V. Papalexandris Open the ORCID record for Miltiadis V. Papalexandris [Opens in a new window]
William A. Hay*
Affiliation:
Université catholique de Louvain, Institute of Mechanics, Materials and Civil Engineering, B1348 Louvain-la-Neuve, Belgium
Miltiadis V. Papalexandris
Affiliation:
Université catholique de Louvain, Institute of Mechanics, Materials and Civil Engineering, B1348 Louvain-la-Neuve, Belgium
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

In this paper we study turbulent thermal convection driven by free-surface evaporation at the top and a uniformly heated wall at the bottom. More specifically, we report on direct numerical simulations over 1.25 decades of Rayleigh number, Ra. At the top of the cubic domain, a shear-free boundary condition acts as an approximation of a free surface, and different evaporation rates form the basis of a temperature gradient assigned as a non-zero Neumann boundary condition. The corresponding lower wall temperature is fixed and we assess the thermal mixing on the water side of the air–water interface. The set-up is considered a simplified model of the turbulent natural convection in the upper volumes of spent-fuel pools of nuclear power plants. Surface temperatures are investigated over a range of 40 K, resulting in a sixteenfold increase in evaporation rates. Our work allows, for the first time, analysis of the features and mean flow statistics of this particular thermal convection configuration. Results show that a shear-free surface increases heat transfer within the domain; however, the exponent in the diagnosed power-law relation between the Nusselt and Rayleigh numbers, $Nu = 0.178Ra^{0.301}$, is similar to that of classical turbulent Rayleigh–Bénard convection. Further, the free slip accelerates the fluid after impingement on the upper boundary, significantly affecting the structure of the large-scale circulation in the container. Analysis of the flow statistics then shows how the shear-free surface introduces inhomogeneities in thermal boundary layer heights. Overall, the investigated turbulent convection configuration shows unique traits, borrowing from both turbulent Rayleigh–Bénard convection and evaporative cooling.

JFM classification

Convection: Convection in cavities Turbulent Flows: Turbulent convection
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 904 , 10 December 2020 , A14
Check for updates
Copyright
© The Author(s), 2020. Published by 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

REFERENCES

Ahlers, G., Brown, E., Araujo, F. F., Funfschilling, D., Grossmann, S. & Lohse, D. 2006 Non-Oberbeck-Boussinesq effects in strongly turbulent Rayleigh–Bénard convection. J. Fluid Mech. 569, 409–445.CrossRefGoogle Scholar
Ahlers, G., Grossman, S. & Lohse, D. 2009 Heat transfer and large scale dynamics in turbulent Rayleigh–Bénard convection. Rev. Mod. Phys. 81 (2), 503–537.CrossRefGoogle Scholar
Batchelor, G. K. 1959 Small-scale variation of convected quantities like temperature in turbulent fluid. Part 1. General discussion and the case of small conductivity. J. Fluid Mech. 5 (1), 113–133.CrossRefGoogle Scholar
Boelter, L. M. K., Gordon, H. S. & Griffin, J. R. 1946 Free evaporation into air of water from a free horizontal quiet surface. Ind. Engng Chem. 38 (6), 596–600.CrossRefGoogle Scholar
Bower, S. M. & Saylor, J. R. 2009 A study of the Sherwood–Rayleigh relation for water undergoing natural convection-driven evaporation. Intl J. Heat Mass Transfer 52, 3055–3063.CrossRefGoogle Scholar
Brown, E. & Ahlers, G. 2006 Rotations and cessations of the large-scale circulation in turbulent Rayleigh–Bénard convection. J. Fluid Mech. 568, 351–386.CrossRefGoogle Scholar
Bukhari, S. J. K. & Siddiqui, M. H. K. 2006 Turbulent structure beneath air-water interface during natural convection. Phys. Fluids 18 (3), 035106.CrossRefGoogle Scholar
Castaing, B., Gunaratne, G., Heslot, F., Kadanoff, L., Libchaber, A., Thomae, S., Wu, X.-Z., Zaleski, S. & Zanetti, G. 1989 Scaling of hard thermal turbulence in Rayleigh–Bénard convection. J. Fluid Mech. 204, 1–30.CrossRefGoogle Scholar
Chavanne, X., Chillà, F., Castaing, B., Hébral, B., Chabaud, B. & Chaussy, J. 1997 Observation of the ultimate regime in Rayleigh–Bénard convection. Phys. Rev. Lett. 79, 3648–3651.CrossRefGoogle Scholar
Cioni, S., Ciliberto, S. & Sommeria, J. 1997 Strongly turbulent Rayleigh–Bénard convection in mercury: comparison with results at moderate Prandtl number. J. Fluid Mech. 335, 111–140.CrossRefGoogle Scholar
Daya, Z. A. & Ecke, R. E. 2001 Does turbulent convection feel the shape of the container? Phys. Rev. Lett. 87 (218), 184501.CrossRefGoogle Scholar
Deardroff, J. W. & Willis, G. E. 1967 Investigation of turbulent thermal convection between horizontal plates. J. Fluid Mech. 28, 675–704.CrossRefGoogle Scholar
Flack, K. A., Saylor, J. R. & Smith, G. B. 2001 Near surface turbulence for evaporative convection. Phys. Fluids 13 (11), 3338–3345.CrossRefGoogle Scholar
Foroozani, N., Niemala, J. J., Armenio, V. & Sreenivasan, K. R. 2014 Influence of container shape on scaling of turbulent fluctuations in convection. Phys. Rev. E 90, 063003.CrossRefGoogle ScholarPubMed
Foroozani, N., Niemela, J. J., Armenio, V. & Sreenivasan, K. R. 2017 Reorientations of the large-scale flow in turbulent convection in a cube. Phys. Rev. E 95, 033107.CrossRefGoogle Scholar
Georgiou, M. & Papalexandris, M. V. 2018 Direct numerical simulation of turbulent heat transfer in a T-junction. J. Fluid Mech. 845, 581–614.CrossRefGoogle Scholar
Grötzbach, G. 1983 Spatial resolution requirements for direct numerical simulation of the Rayleigh–Bénard convection. J. Comput. Phys. 49, 241–264.CrossRefGoogle Scholar
Hay, W. A. & Papalexandris, M. V. 2019 Numerical simulations of turbulent thermal convection with a free-slip upper boundary. Proc. R. Soc. A 475, 20190601.CrossRefGoogle Scholar
Howard, L. N. 1966 Convection at high Rayleigh number. In Applied Mechanics (ed. Görtler, H.), pp. 1109–1115. Springer.CrossRefGoogle Scholar
Issa, R. I. 1985 Solution of the implicitly discretized fluid flow equations by operator-splitting. J. Comput. Phys. 62, 40–65.CrossRefGoogle Scholar
Kaczorowski, M. & Wagner, C. 2008 Analysis of the thermal plumes in turbulent Rayleigh–Bénard convection based on well-resolved numerical simulations. J. Fluid Mech. 618, 89–112.CrossRefGoogle Scholar
Kaczorowski, M. & Xia, K. 2013 Turbulent flow in the bulk of Rayleigh–Bénard convection: small-scale properties in a cubic cell. J. Fluid Mech. 722, 596–617.CrossRefGoogle Scholar
Katsaros, K. B., Liu, W. T., Businger, J. A. & Tillman, J. E. 1976 Heat transport and thermal structure in the interfacial boundary layer measured in an open tank of water in turbulent free convection. J. Fluid Mech. 83, 311–335.CrossRefGoogle Scholar
Kerr, R. M. 1996 Rayleigh number scaling in numerical convection. J. Fluid Mech. 310, 139–179.CrossRefGoogle Scholar
Krishnamurti, R. & Howard, L. N. 1981 Large-scale flow generation in turbulent convection. Proc. Natl Acad. Sci. USA 78 (4), 1981–1985.CrossRefGoogle ScholarPubMed
Lemmon, E. W., Huber, M. L. & McLinden, M. O. 2010 NIST Standard Reference Database 23: Reference Fluid Thermodynamic and Transport Properties – REFPROP, 9th edn. National Institute of Standards and Technology, Standard Reference Data Program.Google Scholar
Lessani, B. & Papalexandris, M. V. 2006 Time accurate calculation of variable density flows with strong temperature gradients and combustion. J. Comput. Phys. 212, 218–246.CrossRefGoogle Scholar
Lessani, B. & Papalexandris, M. V. 2008 Numerical study of turbulent channel flow with strong temperature gradients. Intl J. Numer. Meth. Heat Fluid Flow 18, 545–556.CrossRefGoogle Scholar
Lienhard IV, J. H. & Lienhard V, J. H. 2019 A Heat Transfer Textbook, 5th edn. Dover.Google Scholar
Lloyd, J. R. & Moran, W. R. 1974 Natural convection adjacent to horizontal surface of various planforms. Trans. ASME: J. Heat Transfer 96 (4), 443–447.CrossRefGoogle Scholar
Lohse, D. & Xia, K. 2010 Small-scale properties of turbulent Rayleigh–Bénard convection. Annu. Rev. Fluid Mech. 42, 335–364.CrossRefGoogle Scholar
Majda, A. & Sethian, J. 1985 The derivation and numerical solution of the equations for zero-Mach number combustion. Combust. Sci. Technol. 42, 185–205.CrossRefGoogle Scholar
Marrero, T. R. & Mason, E. A. 1972 Gaseous diffusion coefficients. J. Phys. Chem. Ref. Data 1 (1), 3–118.CrossRefGoogle Scholar
Martin, J. & Migot, B. 2019 Experimental study of the surface evaporation rate of a heated water pool at high temperature using infrared thermography. In 18th International Topical Meeting on Nuclear Reactor Thermal Hydraulics, pp. 2302–2313. American Nuclear Society.Google Scholar
Mason, E. A. & Saxena, S. C. 1958 Approximate formula for the thermal conductivity of gas mixtures. Phys. Fluids 1 (5), 361–369.CrossRefGoogle Scholar
Niemala, J. J., Skrbek, L., Sreenivasan, K. R. & Donnelly, R. J. 2000 Turbulent convection at very high Rayleigh numbers. Nature 404, 837–840.CrossRefGoogle Scholar
Oliviera, P. J. & Issa, R. I. 2001 An improved PISO algorithm for the computation of buoyancy driven flows. Numer. Heat Transfer, Part B 40, 473–493.Google Scholar
Papalexandris, M. V. 2019 On the applicability of Stokes’ hypothesis to low-Mach-number flows. Contin. Mech. Thermodyn. 32, 1245–1249.CrossRefGoogle Scholar
Poling, B. E., Prausnitz, J. M. & O'Connell, J. P. 2001 The Properties of Gases and Liquids. McGraw-Hill.Google Scholar
Rhie, C. M. & Chow, W. L. 1983 Numerical study of the turbulent flow past an airfoil with trailing edge separation. AIAA J. 21 (11), 1525–1532.CrossRefGoogle Scholar
Scheel, J. D. & Schumacher, J. 2014 Local boundary layer scales in turbulent Rayleigh–Bénard convection. J. Fluid Mech. 758, 344–373.CrossRefGoogle Scholar
Shishkina, O., Stevens, R., Grossman, S. & Lohse, D. 2010 Boundary layer structure in turbulent thermal convection and its consequences for the required numerical resolution. New J. Phys. 12 (7), 075022.CrossRefGoogle Scholar
Siggia, E. D. 1994 High Rayleigh number convection. Annu. Rev. Fluid Mech. 26, 137–168.CrossRefGoogle Scholar
Spangenberg, W. G. & Rowland, W. R. 1961 Convective circulation in water induced by evaporative cooling. Phys. Fluids 4 (6), 743–750.CrossRefGoogle Scholar
Stevens, R., Verzicco, R. & Lohse, D. 2010 Radial boundary layer structure and Nusselt number in Rayleigh–Bénard convection. J. Fluid Mech. 643, 495–507.CrossRefGoogle Scholar
Straus, J. M. 1973 On the upper bounding approach to thermal convection at moderate Rayleigh numbers. Geophys. Fluid Dyn. 5 (1), 261–281.CrossRefGoogle Scholar
Sun, C., Cheung, Y.-H. & Xia, K.-Q. 2008 Experimental studies of the viscous boundary layer properties in turbulent Rayleigh–Bénard convection. J. Fluid Mech. 605, 79–113.CrossRefGoogle Scholar
Tennekes, H. & Lumley, J. L. 1972 A First Course in Turbulence. MIT.CrossRefGoogle Scholar
Tilgner, A., Belmonte, A. & Libchaber, A. 1993 Temperature and velocity profiles of turbulent convection in water. Phys. Rev. E 47, R2253–R2256.CrossRefGoogle ScholarPubMed
Verzicco, R. & Camussi, R. 2003 Numerical experiments on strongly turbulent thermal convection in a slender cylindrical cell. J. Fluid Mech. 477, 19–49.CrossRefGoogle Scholar
Volino, R. J. & Smith, G. B. 1999 Use of simulataneous IR temperature measurements and DPIV to investigate thermal plumes in a thick layer cooled from above. Exp. Fluids 27, 70–78.CrossRefGoogle Scholar
Weller, H. G., Tabor, G., Jasak, H. & Fureby, C. 1998 A tensorial approach to computational continuum mechanics using object-oriented techniques. Comput. Phys. 12 (6), 620–631.CrossRefGoogle Scholar
Wilke, C. R. 1950 A viscosity equation for gas mixtures. J. Chem. Phys. 18 (4), 517–519.CrossRefGoogle Scholar
Xin, Y.-B. & Xia, K.-Q. 1997 Boundary layer length scales in convective turbulence. Phys. Rev. E 56, 3010–3015.CrossRefGoogle Scholar
Zikanov, O., Slinn, D. N. & Dhanak, M. R. 2002 Turbulent convection driven by surface cooling in shallow water. J. Fluid Mech. 464, 81–111.CrossRefGoogle Scholar