Abstract
The problem of heat transfer intensification using spatially nonuniform boundary conditions is of great interest. In this paper, the influence of a nonuniform, nonperiodic distribution of heating on the flow structure and convective heat flux for developed turbulent regimes (Ra = 1.1 × 109) is studied. The numerical simulation of convective turbulence in a cubic cavity is performed for a nonuniform heating distribution at the lower boundary using open-source software the OpenFoam 4.1. Calculations were carried out for three types of the temperature distribution: localized heating at the center of the lower boundary; nine heaters of the same size, equidistant from each other; and fractal heating. The heating area is the same in all of these distributions. It is shown that in all cases of a nonuniform heating distribution in the cavity a large-scale circulation is formed. The dynamics and structure of large-scale circulation depend on the temperature distribution at the lower boundary of the cavity. Spontaneous reorientations of the large-scale circulation plane by angles of ±45° or ±90° are revealed. A comparison of the intensity of the heat flux through the layer (cavity) at a fixed temperature difference at horizontal boundaries is made. It is shown that the heat transfer intensity weakly depends on the temperature distribution on the lower boundary. The maximum difference in the Nusselt numbers for three types of the nonuniform temperature distribution did not exceed 5%. Comparison of numerical simulation results for the uniform and nonuniform heating distributions at Ra = 1.1 × 109 shows that a decrease in the heating area by 70% leads to a decrease in the Nusselt number by 10%. It is shown that the heat flux also decreases with decreasing heating area, at fixed temperatures in the heating and cooling regions, not proportionally to the change in the area. For practical applications, an important role is played by the stability of the heat flux, which is characterized by the absence of pulsations. It is shown that the use of fractal heating can significantly reduce the level of heat flux pulsations without losses in the efficiency of heat transfer.
Similar content being viewed by others
REFERENCES
Gershuni, G.Z., Zhukhovitskiy, E.M., and Nepomnyashchiy, A.A., Ustoichivost’ konvektivnykh techenii (Stability of Convective Flows), Moscow: Nauka, 1989.
Zimin, V.D. and Frick, P.G., Turbulentnaya konvektsiya (Turbulent Convection), Moscow: Nauka, 1988.
Siggia, E.D., High Rayleigh number convection, Ann. Rev. Fluid Mech., 1994, vol. 26, pp. 137–168. https://doi.org/10.1146/annurev.fl.26.010194.001033
Ahlers, G., Grossmann, S., and Lohse, D., Heat transfer and large-scale dynamics in turbulent Rayleigh-Benard convection, Rev. Mod. Phys., 2009, vol. 81, pp. 503–537. https://doi.org/10.1103/RevModPhys.81.503
Chilla, F. and Schumacher, J., New perspectives in turbulent Rayleigh–Benard convection, Eur. Phys. J. E, 2012, vol. 35, p. 58. https://doi.org/10.1140/epje/i2012-12058-1
Oztop, H.F., Estelle, P., Yan, W.-M., Al-Salem, K., Orfi, J., and Mahian, O., A brief review of natural convection in enclosures under localized heating with and without nanofluids, Int. Commun. Heat Mass Trans., 2015, vol. 60, pp. 37–44. https://doi.org/10.1016/j.icheatmasstransfer.2014.11.001
Sukhanovskii, A., Evgrafova, A., and Popova, E., Horizontal rolls over localized heat source in a cylindrical layer, Phys. Nonlin. Phenom., 2016, vol. 316, pp. 23–33. https://doi.org/10.1016/j.physd.2015.11.007
Miroshnichenko, I. and Sheremet, M., Turbulent natural convection heat transfer in rectangular enclosures using experimental and numerical approaches: A review, Renew. Sustain. Energy Rev., 2018, vol. 82, pp. 40–59. https://doi.org/10.1016/j.rser.2017.09.005
Castaing, B., Gunaratne, G., Heslot, F., Kadanof, L., Libchaber, A., Thomae, S., Wu, X.-Z., Zaleski, S., and Zanetti, G., Scaling of hard thermal turbulence in Rayleigh–Benard convection, J. Fluid Mech., 1989, vol. 204, pp. 1–30. https://doi.org/10.1017/S0022112089001643
Ripesi, P., Biferale, L., Sbragaglia, M., and Wirth, A., Natural convection with mixed insulating and conducting boundary conditions: low- and high-Rayleigh-number regimes, J. Fluid Mech., 2014, vol. 742, pp. 636–663. https://doi.org/10.1017/jfm.2013.671
Bakhuis, D., Ostilla-Monico, R., van der Poel, E.P., Verzicco, R., and Lohse, D., Mixed insulating and conducting thermal boundary conditions in Rayleigh–Benard convection, J. Fluid Mech., 2018, vol. 835, pp. 491–511. https://doi.org/10.1017/jfm.2017.737
Titov, V. and Stepanov, R., Heat transfer in the infinite layer with a fractal distribution of a heater, IOP Conf. Ser.: Mater. Sci. Eng., 2017, vol. 208, p. 012039. https://doi.org/10.1088/1757-899X/208/1/012039
Toppaladoddi, S., Succi, S., and Wettlaufer, J.S., Roughness as a route to the ultimate regime of the thermal convection, Phys. Rev. Lett., 2017, vol. 118, p. 074503. https://doi.org/10.1103/PhysRevLett.118.074503
Bolshukhin, M.A., Vasiliev, A.Yu., Budnikov, A.V., Patrushev, D.N., Romanov, R.I., Sveshnikov, D.N., Sukhanovsky, A.N., and Frick, P.G., Experimental benchmarking of CFD codes used in simulations of heat exchangers for nuclear-power applications, Vychisl. Mekh. Splosh. Sred, 2012, vol. 5, no. 4, pp. 469–480. https://doi.org/10.7242/1999-6691/2012.5.4.55
Vasiliev, A., Sukhanovskii, A., Frick, P., Budnikov, A., Fomichev, V., Bolshukhin, V., and Romanov, R., High Rayleigh number convection in a cubic cell with adiabatic sidewalls, Int. J. Heat Mass Trans., 2016, vol. 102, pp. 201–212. https://doi.org/10.1016/j.ijheatmasstransfer.2016.06.015
Smagorinsky, J., General circulation experiments with the primitive equations. I. The basic experiment, Mon. Weather Rev., 1963, vol. 39, no. 3, pp. 99–164. https://doi.org/10.1175/1520-0493(1963)091%3c0099:GCEWTP%3e2.3.CO;2
Sierpinski Carpet. https://en.wikipedia.org/wiki/. Accessed January 9, 2019.
Vasiliev, A., Frick, P., Kumar, A., Stepanov, R., Sukhanovsky, A., and Verma, M., Mechanism of reorientations of turbulent large-scale convective flow in a cubic cell, arxiv:1805.06718, 2019.
Bai, K., Ji, D., and Brown, E., Ability of a low-dimensional model to predict geometry-dependent dynamics of large-scale coherent structures in turbulence, Phys. Rev. E, 2016, vol. 93, p. 023117. https://doi.org/10.1103/PhysRevE.93.023117
Foroozani, N., Niemala, J.J., Armenio, V., and Sreenivasan, K.R., Reorientations of the large-scale flow in turbulent convection in a cube, Phys. Rev. E, 2017, vol. 95, p. 033107. https://doi.org/10.1103/PhysRevE.95.033107
Johnston, H. and Doering, C.R., Comparison of turbulent thermal convection between conditions of constant temperature and constant flux, Phys. Rev. Lett., 2009, vol. 102, p. 064501. https://doi.org/10.1103/PhysRevLett.102.064501
Bailon-Cuba, J., Emran, M.S., and Schumacher, J., Aspect ratio dependence of heat transfer and large-scale flow in turbulent convection, J. Fluid Mech., 2010, vol. 655, pp. 152–173. https://doi.org/10.1017/S0022112010000820
ACKNOWLEDGMENTS
The computations were carried out on the Triton computational cluster in the Institute of Continuous Media Mechanics, Ural Branch, Russian Academy of Sciences (Perm).
Funding
This work was supported by the Russian Foundation for Basic Research, project no. 16-41-590406-r_ural_a.
Author information
Authors and Affiliations
Corresponding authors
Additional information
Translated by A. Nikol’skii
Rights and permissions
About this article
Cite this article
Vasiliev, A.Y., Sukhanovskii, A.N. & Stepanov, R.A. Convective Turbulence in a Cubic Cavity under Nonuniform Heating of a Lower Boundary. J Appl Mech Tech Phy 61, 1049–1058 (2020). https://doi.org/10.1134/S0021894420070172
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0021894420070172