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Direct numerical simulations of Rayleigh-Bénard convection in water with non-Oberbeck-Boussinesq effects. (English) Zbl 1430.76302

Summary: Rayleigh-Bénard convection in water is studied by means of direct numerical simulations, taking into account the variation of properties. The simulations considered a three-dimensional (3-D) cavity with a square cross-section and its two-dimensional (2-D) equivalent, covering a Rayleigh number range of \(10^6\leqslant Ra\leqslant 10^9\) and using temperature differences up to 60 K. The main objectives of this study are (i) to investigate and report differences obtained by 2-D and 3-D simulations and (ii) to provide a first appreciation of the non-Oberbeck-Boussinesq (NOB) effects on the near-wall time-averaged and root-mean-squared (r.m.s.) temperature fields. The Nusselt number and the thermal boundary layer thickness exhibit the most pronounced differences when calculated in two dimensions and three dimensions, even though the \(Ra\) scaling exponents are similar. These differences are closely related to the modification of the large-scale circulation pattern and become less pronounced when the NOB values are normalised with the respective Oberbeck-Boussinesq (OB) values. It is also demonstrated that NOB effects modify the near-wall temperature statistics, promoting the breaking of the top-bottom symmetry which characterises the OB approximation. The most prominent NOB effect in the near-wall region is the modification of the maximum r.m.s. values of temperature, which are found to increase at the top and decrease at the bottom of the cavity.

MSC:

76F65 Direct numerical and large eddy simulation of turbulence
76F35 Convective turbulence
80A19 Diffusive and convective heat and mass transfer, heat flow
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[1] Ahlers, G.1980Effect of departures from the Oberbeck-Boussinesq approximation on the heat transport of horizontal convecting fluid layers. J. Fluid Mech.98 (1), 137-148.
[2] Ahlers, G., Brown, E., Araujo, F. F., Funfschilling, D., Grossmann, S. & Lohse, D.2006Non-Oberbeck-Boussinesq effects in strongly turbulent Rayleigh-Bénard convection. J. Fluid Mech.569, 409-445. · Zbl 1104.76004
[3] Ahlers, G., Calzavarini, E., Araujo, F. F., Funfschilling, D., Grossmann, S., Lohse, D. & Sugiyama, K.2008Non-Oberbeck-Boussinesq effects in turbulent thermal convection in ethane close to the critical point. Phys. Rev. E77 (4), 046302.
[4] Boussinesq, J.1903 Théorie Analytique de la Chaleur: Mise en Harmonie avec la Thermodynamique et avec la Théorie Mécanique de la Lumière, vol. 2. Gauthier-Villars. · JFM 32.0890.01
[5] Brown, E. & Ahlers, G.2007Temperature gradients, and search for non-Boussinesq effects, in the interior of turbulent Rayleigh-Bénard convection. Eur. Phys. Lett.80 (1), 14001.
[6] Castaing, B., Gunaratne, G., Heslot, F., Kadanoff, L., Libchaber, A., Thomae, S., Wu, X.-Z., Zaleski, S. & Zanetti, G.1989Scaling of hard thermal turbulence in Rayleigh-Bénard convection. J. Fluid Mech.204, 1-30.
[7] Demou, A. D., Frantzis, C. & Grigoriadis, D. G. E.2018A numerical methodology for efficient simulations of non-Oberbeck-Boussinesq flows. Intl J. Heat Mass Transfer125, 1156-1168.
[8] Demou, A. D., Frantzis, C. & Grigoriadis, D. G. E.2019A low-Mach methodology for efficient direct numerical simulations of variable property thermally driven flows. Intl J. Heat Mass Transfer132, 539-549.
[9] Du Puits, R., Resagk, C., Tilgner, A., Busse, F. H. & Thess, A.2007Structure of thermal boundary layers in turbulent Rayleigh-Bénard convection. J. Fluid Mech.572, 231-254. · Zbl 1165.76343
[10] Fröhlich, J., Laure, P. & Peyret, R.1992Large departures from Boussinesq approximation in the Rayleigh-Bénard problem. Phys. Fluids4 (7), 1355-1372. · Zbl 0758.76022
[11] Garon, A. M. & Goldstein, R. J.1973Velocity and heat transfer measurements in thermal convection. Phys. Fluids16 (11), 1818-1825.
[12] Gray, D. D. & Giorgini, A.1976The validity of the Boussinesq approximation for liquids and gases. Intl J. Heat Mass Transfer19 (5), 545-551. · Zbl 0328.76066
[13] Grossmann, S. & Lohse, D.2000Scaling in thermal convection: a unifying theory. J. Fluid Mech.407, 27-56. · Zbl 0972.76045
[14] Grossmann, S. & Lohse, D.2001Thermal convection for large Prandtl numbers. Phys. Rev. Lett.86 (15), 3316.
[15] Hiroaki, T. & Hiroshi, M.1980Turbulent natural convection in a horizontal water layer heated from below. Intl J. Heat Mass Transfer23 (9), 1273-1281.
[16] Horn, S. & Shishkina, O.2014Rotating non-Oberbeck-Boussinesq Rayleigh-Bénard convection in water. Phys. Fluids26 (5), 055111. · Zbl 1287.76208
[17] Horn, S., Shishkina, O. & Wagner, C.2013On non-Oberbeck-Boussinesq effects in three-dimensional Rayleigh-Bénard convection in glycerol. J. Fluid Mech.724, 175-202. · Zbl 1287.76208
[18] Kizildag, D., Rodríguez, I., Oliva, A. & Lehmkuhl, O.2014Limits of the Oberbeck-Boussinesq approximation in a tall differentially heated cavity filled with water. Intl J. Heat Mass Transfer68, 489-499.
[19] Liu, S., Xia, S.-N., Yan, R., Wan, Z.-H. & Sun, D.-J.2018Linear and weakly nonlinear analysis of Rayleigh-Bénard convection of perfect gas with non-Oberbeck-Boussinesq effects. J. Fluid Mech.845, 141-169. · Zbl 1406.76077
[20] Manga, M. & Weeraratne, D.1999Experimental study of non-Boussinesq Rayleigh-Bénard convection at high Rayleigh and Prandtl numbers. Phys. Fluids11 (10), 2969-2976. · Zbl 1149.76468
[21] Oberbeck, A.1879Über die Wärmeleitung der Flüssigkeiten bei Berücksichtigung der Strömungen infolge von Temperaturdifferenzen. Ann. Phys.243 (6), 271-292. · JFM 11.0787.01
[22] van der Poel, E. P., Stevens, R. J. A. M. & Lohse, D.2013Comparison between two- and three-dimensional Rayleigh-Bénard convection. J. Fluid Mech.736, 177-194. · Zbl 1294.76128
[23] Roy, A. & Steinberg, V.2002Reentrant hexagons in non-Boussinesq Rayleigh-Bénard convection: effect of compressibility. Phys. Rev. Lett.88 (24), 244503.
[24] Sebilleau, F., Issa, R., Lardeau, S. & Walker, S. P.2018Direct numerical simulation of an air-filled differentially heated square cavity with Rayleigh numbers up to 10^11. Intl J. Heat Mass Transfer123, 297-319.
[25] Shishkina, O., Stevens, R. J. A. M., Grossmann, S. & Lohse, D.2010Boundary layer structure in turbulent thermal convection and its consequences for the required numerical resolution. New J. Phys.12 (7), 075022.
[26] Sugiyama, K., Calzavarini, E., Grossmann, S. & Lohse, D.2007Non-Oberbeck-Boussinesq effects in two-dimensional Rayleigh-Bénard convection in glycerol. Eur. Phys. Lett.80 (3), 34002. · Zbl 1183.76765
[27] Sugiyama, K., Calzavarini, E., Grossmann, S. & Lohse, D.2009Flow organization in two-dimensional non-Oberbeck-Boussinesq Rayleigh-Bénard convection in water. J. Fluid Mech.637, 105-135. · Zbl 1183.76765
[28] Sugiyama, K., Ni, R., Stevens, R. J. A. M., Chan, T. S., Zhou, S.-Q., Xi, H.-D., Sun, C., Grossmann, S., Xia, K.-Q. & Lohse, D.2010Flow reversals in thermally driven turbulence. Phys. Rev. Lett.105 (3), 034503.
[29] Tilgner, A., Belmonte, A. & Libchaber, A.1993Temperature and velocity profiles of turbulent convection in water. Phys. Rev. E47 (4), R2253.
[30] Trias, F. X., Soria, M., Oliva, A. & Pérez-Segarra, C. D.2007Direct numerical simulations of two-and three-dimensional turbulent natural convection flows in a differentially heated cavity of aspect ratio 4. J. Fluid Mech.586, 259-293. · Zbl 1178.76208
[31] Valori, V., Elsinga, G., Rohde, M., Tummers, M., Westerweel, J. & van der Hagen, T.2017Experimental velocity study of non-Boussinesq Rayleigh-Bénard convection. Phys. Rev. E95 (5), 053113.
[32] Wang, J. & Xia, K.-Q.2003Spatial variations of the mean and statistical quantities in the thermal boundary layers of turbulent convection. Eur. Phys. J. B32 (1), 127-136.
[33] Wang, Q., Xu, B.-L., Xia, S.-N., Wan, Z.-H. & Sun, D.-J.2017Thermal convection in a tilted rectangular cell with aspect ratio 0.5. Chin. Phys. Lett.34 (10), 104401.
[34] Weiss, S., He, X., Ahlers, G., Bodenschatz, E. & Shishkina, O.2018Bulk temperature and heat transport in turbulent Rayleigh-Bénard convection of fluids with temperature-dependent properties. J. Fluid Mech.851, 374-390. · Zbl 1415.76316
[35] Wu, X.-Z. & Libchaber, A.1991Non-Boussinesq effects in free thermal convection. Phys. Rev. A43 (6), 2833.
[36] Xia, K.-Q., Lam, S. & Zhou, S.-Q.2002Heat-flux measurement in high-Prandtl-number turbulent Rayleigh-Bénard convection. Intl J. Heat Mass Transfer88 (6), 064501.
[37] Zhou, Q. & Xia, K.-Q.2013Thermal boundary layer structure in turbulent Rayleigh-Bénard convection in a rectangular cell. J. Fluid Mech.721, 199-224. · Zbl 1287.76132
[38] Zhu, X., Mathai, V., Stevens, R. J. A. M., Verzicco, R. & Lohse, D.2018Transition to the ultimate regime in two-dimensional Rayleigh-Bénard convection. Phys. Rev. Lett.120 (14), 144502.
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