With the three dimensional computational model extended based on that by Bejan in two dimensional condition, natural convection heat transfer from the single-layer horizontal spheres under the aligned arrangement is numerically investigated at Gr=103 for array changing from 3×3 to 15×15. The study found that with the increase of the number of array N, the plume makes the absolute value of negative pressure above the single-layer spheres bigger, which leads to the acceleration of air sucked up through the gaps among the spheres, thereby enhancing heat transfer; the local Nu number in the upstream of the spheres is more affected by the arrangement number since it has a greater influence on the temperature boundary layer in this region. Furthermore, the correlation of the average Nusselt number Nu of the central sphere with the arrangement number N is obtained, which could be predicted by the idea of limit in mathematics that the central sphere of the single-layer spheres has a Nu number of 4.162 8 that is not affected by the increase of the number of surrounding spheres,which reduces by 30.2% than that of single sphere at same Gr number. It provides some value of reference not only for the optimal design of the granular flow target of the accelerator driven subcritical system in China, but also for other industrial applications including multi-spherical systems.
WANG Dichang
,
LIU Zeyuan
,
LIU Jie
,
LU Wenqiang
. Numerical study of natural convection heat transfer from single-layer horizontal spheres under aligned arrangement[J]. Journal of University of Chinese Academy of Sciences, 2023
, 40(3)
: 303
-312
.
DOI: 10.7523/j.ucas.2021.0034
[1] Bergman T L, Lavine A S. Fundamentals of heat and mass transfer[M]. 8th ed. Hoboken:John Wiley & Sons, 2017:540-576.
[2] Openyshev P V, Sheremet M A. Influence of a porous insert on the fluid flow inside the gasifier shaft[J]. Key Engineering Materials, 2016, 685:235-239.DOI:10.4028/www.scientific.net/kem.685.235.
[3] Pichler M, Haddadi B, Jordan C, et al. Effect of particle contact point treatment on the CFD simulation of the heat transfer in packed beds[J]. Chemical Engineering Research and Design, 2021, 165:242-253.DOI:10.1016/j.cherd.2020.11.005.
[4] Yang L, Zhan W L. New concept for ADS spallation target:gravity-driven dense granular flow target[J]. Science China Technological Sciences, 2015, 58(10):1705-1711.DOI:10.1007/s11431-015-5894-0.
[5] Yamoah S, Akaho E H K, Ayensu N G A, et al. Analysis of fluid flow and heat transfer model for the pebble bed high temperature gas cooled reactor[J]. Research Journal of Applied Sciences, Engineering and Technology, 2012, 4(12):1659-1666.
[6] Yuge T. Experiments on heat transfer from spheres including combined natural and forced convection[J]. Journal of Heat Transfer, 1960, 82(3):214-220.DOI:10.1115/1.3679912.
[7] Amato W S, Chi T. Free convection heat transfer from isothermal spheres in water[J]. International Journal of Heat and Mass Transfer, 1972, 15(2):327-339.DOI:10.1016/0017-9310(72)90078-6.
[8] Kranse A A, Schenk J. Thermal free convection from a solid sphere[J]. Applied Scientific Research, Section A, 1966, 15(1):397-403.DOI:10.1007/BF00411573.
[9] Tsubouchi T, Sato S, Masuda H. Effect of Prandtl number on the natural convection heat transfer of small particles[J]. Transactions of the Japan Society of Mechanical Engineers, 1964, 30(219):1386-1393.DOI:10.1299/kikai1938.30.1386.
[10] Churchill S W. Comprehensive, theoretically based, correlating equations for free convection from isothermal spheres[J]. Chemical Engineering Communications, 1983, 24(4-6):339-352.DOI:10.1080/00986448308940090.
[11] Jia H, Gogos G. Laminar natural convection heat transfer from isothermal spheres[J]. International Journal of Heat and Mass Transfer, 1996, 39(8):1603-1615.DOI:10.1016/0017-9310(95)00259-6.
[12] Jia H, Gogos G. Transient laminar natural convection heat transfer from isothermal spheres[J]. Numerical Heat Transfer, Part A:Applications, 1996, 29(1):83-101.DOI:10.1080/10407789608913780.
[13] Yang S, Raghavan V, Gogos G. Numerical study of transient laminar natural convection over an isothermal sphere[J]. International Journal of Heat and Fluid Flow, 2007, 28(4):821-837.DOI:10.1016/j.ijheatfluidflow.2006.08.004.
[14] Liu Z Y, Chu Y, Liu J, et al. Numerical investigation of the laminar natural convection heat transfer from the equilateral triangular cluster of three horizontal spheres[J]. International Journal of Heat and Mass Transfer, 2019, 136:924-937.DOI:10.1016/j.ijheatmasstranster.2019.02.084.
[15] Chamberlain M J, Hollands K G T, Raithby G D. Experiments and theory on natural convection heat transfer from bodies of complex shape[J]. Journal of Heat Transfer, 1985, 107(3):624-629.DOI:10.1115/1.3247469.
[16] Raithby G D, Hollands K G T. A general method of obtaining approximate solutions to laminar and turbulent free convection problems[J]. Advances in Heat Transfer, 1975, 11:265-315.DOI:10.1016/s0065-2717(08)70076-5.
[17] Jafarpur K, Yovanovich M M. Laminar free convective heat transfer from isothermal spheres:a new analytical method[J]. International Journal of Heat and Mass Transfer, 1992, 35(9):2195-2201.DOI:10.1016/0017-9310(92)90063-x.
[18] Musong S G, Feng Z G, Michaelides E E, et al. Application of a three-dimensional immersed boundary method for free convection from single spheres and aggregates[J]. Journal of Fluids Engineering, 2016, 138(4):041304.DOI:10.1115/1.4031688.
[19] Zhang J, Liu J, Lu W Q. Study on laminar natural convection heat transfer from a hemisphere with uniform heat flux surface[J]. Journal of Thermal Science, 2019, 28(2):232-245.DOI:10.1007/s11630-018-1051-y.
[20] Bejan A, Fowler A J, Stanescu G. The optimal spacing between horizontal cylinders in a fixed volume cooled by natural convection[J]. International Journal of Heat and Mass Transfer, 1995, 38(11):2047-2055.DOI:10.1016/0017-9310(94)00312-J.
[21] Liu J, Zhao C J, Liu H, et al. Numerical study of laminar natural convection heat transfer from a hemisphere with adiabatic plane and isothermal hemispherical surface[J]. International Journal of Thermal Sciences, 2018, 131:132-143.DOI:10.1016/j.ijthermalsci.2018.05.013.
[22] Liu J, Liu H, Zhen Q, et al. Laminar natural convection heat transfer from a pair of attached horizontal cylinders set in a vertical array[J]. Applied Thermal Engineering, 2017, 115:1004-1019.DOI:10.1016/j.applthermaleng.2017.01.029.
[23] Liu J, Liu H, Zhen Q, et al. Numerical investigation of the laminar natural convection heat transfer from two horizontally attached horizontal cylinders[J]. International Journal of Heat and Mass Transfer, 2017, 104:517-532.DOI:10.1016/j.ijheatmasstransfer.2016.08.075.
[24] 石宏岩, 刘捷, 卢文强. 水平紧密接触品字形三圆管自然对流换热的数值模拟[J]. 中国科学院大学学报, 2018, 35(5):595-601.DOI:10.7523/j.issn.2095-6134.2018.05.004.
[25] Prhashanna A, Chhabra R. Free convection in power-law fluids from a heated sphere[J]. Chemical Engineering Science, 2010, 65(23):6190-6205.DOI:10.1016/j.ces.2010.09.003.
