冰浆作为一种固-液两相流体，由于其储能密度高、流动性及传热性能好而被广泛应用于蓄冷和冷量输送系统.结合Euler-Euler模型和群体平衡模型，考虑固-液相间作用以及固相颗粒的聚并、破碎和融化作用，在颗粒直径变化的基础上对冰浆在水平圆管内的流动与传热特性进行数值研究.研究结果表明：冰浆固相颗粒直径的变化与固相体积分数的变化呈正相关，较大的流速有利于颗粒直径的增大.在入口流速为10m/s与固相体积分数为10%的流动工况下，固相颗粒的直径最大值可从初始状态的125μm增长到139μm.相同流动条件下，当壁面热流密度为50kW/m2时，固相颗粒的直径可从初始状态的270μm直至完全融化，热流密度的增大会加快颗粒直径的减小，颗粒直径分布表现出与等温流动工况不同的特性.
As a solid-liquid two-phase fluid, ice slurry is widely used in cold storage and transport systems due to its high energy storage density, good fluidity and heat transfer performance. Most of the studies on the flow and heat transfer characteristics of ice slurry are based on uniform particle diameter. In the present study, the flow and heat transfer characteristics of ice slurry are numerically investigated in horizontal circular pipes based on the variation of particle diameter through the Euler-Euler two-phase flow model with population balance model (PBM), which considers the interaction between the solid and liquid phases as well as the aggregation, breakage and melting of particles. The results show that the ice particle diameter increases with the increase of solid volume fraction and flow rate. The particle diameter changes from 125μm to 139μm at solid volume fraction of 10% and inlet velocity of 10m/s under the isothermal flow condition. Whereas the particle diameter gradually decreases from the initial diameter to completely melting at wall heat flux of 50kW/m2. Increasing the heat flux leads to a faster decrease of particle diameter and the particle diameter distribution is different from that under the isothermal flow condition.
［1］刘圣春, 宋明, 代宝民, 等. 管道内冰浆流动压降特性模拟和实验研究 ［J］. 制冷学报, 2018, 39(2): 61-67.
LIU Shengchun, SONG Ming, DAI Baomin, et al. Numerical simulation and experimental study on flow pressure drop of ice slurry in piping systems ［J］. Journal of Refrigeration, 2018, 39(2): 61-67.
［2］刘瑞见, 梁坤峰, 贾雪迎, 等. 小型动态制冰机工作过程的结晶特性 ［J］. 化工学报, 2018, 69(2): 450-458.
LIU Ruijian, LIANG Kunfeng, JIA Xueying, et al. Crystallization characteristics of dynamic formation process of ice slurry in small-scale ice making machine ［J］. Journal of Chemical Industry and Engineering (China), 2018, 69(2): 450-458.
［3］刘曦, 林淑娴, 李岁, 等. 二氧化硅纳米颗粒对冰浆中冰晶粒径分布及存储演化特性的影响 ［J］. 化工学报, 2017, 68(3): 870-878.
LIU Xi, LIN Shuxian, LI Sui, et al. Effect of nanosilica on size distribution and evolution of ice crystal particles during storage of ice slurry ［J］. Journal of Chemical Industry and Engineering (China), 2017, 68(3): 870-878.
［4］李成浩, 孙志高, 张爱军, 等. 乳液浆体蓄冷性能实验研究 ［J］. 制冷学报, 2016, 37(6): 66-70+78.
LI Chenghao, SUN Zhigao, ZHANG Aijun, et al. Experimental study on cold storage performance of emulsion slurry ［J］. Journal of Refrigeration, 2016, 37(6): 66-70.
［5］WANG J H, WANG S G, ZHANG T F, et al. Numerical and analytical investigation of ice slurry isothermal flow through horizontal bends ［J］. International Journal of Refrigeration, 2018, 92(8): 37-54.
［6］KUMANO H, HIRATA T, HAGIWARA Y, et al. Effects of storage on flow and heat transfer characteristics of ice slurry ［J］. International Journal of Refrigeration, 2012, 35(1): 122-129.
［7］XU D, LIU Z Q, CAI L L, et al. A CFD-PBM approach for modeling ice slurry flow in horizontal pipes ［J］. Chemical Engineering Science, 2018, 176: 546-559.
［8］JIN T, LI Y J, WU S Q, et al. Numerical modeling for the flow and heat transfer of slush nitrogen in a horizontal pipe based on population balance equations ［J］. Applied Thermal Engineering, 2017, 123: 301-309.
［9］ZHANG P, SHI X J. Thermo-fluidic characteristics of ice slurry in horizontal circular pipes ［J］. International Journal of Heat and Mass Transfer, 2015, 89: 950-963.
［10］NAYAK B B, CHATTERJEE D. Convective heat transfer in slurry flow in a horizontal Y-shaped branch pipe ［J］. Powder Technology, 2017, 318: 46-61.
［11］LI D Y, BUFFO A, PODGORSKA W, et al. Investigation of droplet breakup in liquid-liquid dispersions by CFD-PBM simulations: The influence of the surfactant type ［J］. Chinese Journal of Chemical Engineering, 2017, 25(10): 1369-1380.
［12］李东岳. 搅拌反应器内液-液分散特性的CFD-PBM数值模拟 ［D］. 北京: 北京化工大学, 2016.
LI Dongyue. CFD-PBM investigation of the liquid-liquid dispersions in stirred tanks［D］. Beijing: Beijing University of Chemical Technology, 2016.
［13］MARCHISIO D L, VIGIL R D, FOX R O. Implementation of the quadrature method of moments in CFD codes for aggregation-breakage problems ［J］. Chemical Engineering Science, 2003, 58(15): 3337-3351.
［14］PENG S J, WILLIAMS R A. Direct measurement of floc breakage in flowing suspensions［J］. Journal of Colloid and Interface Science, 1994, 166(2): 321-332.
［15］CHE Y, TIAN Z, LIU Z, et al. A CFD-PBM model considering ethylene polymerization for the flow behaviors and particle size distribution of polyethylene in a pilot-plant fluidized bed reactor ［J］. Powder Technology, 2015, 286: 107-123.
［16］MELINDER A, IGNATOWICZ M. Properties of seawater with ice slurry use in focus ［J］. International Journal of Refrigeration, 2015, 52: 51-58.
