Study On Flow And Heat Transfer Characteristics Of Ice Slurry In Horizontal Tube Based On Population Balance Model

Ice slurry,as a solid-liquid two-phase fluid,is widely used in air conditioning system,district cooling,food conservation and other fields due to its excellent fluidity and large heat capacity.The solid phase in ice slurry is ice crystal particles with a diameter of 0.1～1.0mm and uniformly distributed in the carrying fluid.The particle size has great influence on the flow and heat transfer characteristics of the ice slurry.In recent years,there have been numerous experimental and numerical researches on the thermo-fluidic performance of ice slurry under various working conditions.But the influence of particle diameter usually was investigated based on the average value,and the effect of particle size distribution was seldom studied.Therefore,Euler-Euler model(EEM)coupled with population balance model(PBM)was used in this paper as CFD-PBM model to numerically investigate the heterogeneous flow of ice slurry in a horizontal circular tube under conditions of isothermal flow,wall heating and wall cooling.And the results were compared with those of Euler-Euler two-phase flow model,in which the variation of diameter was not considered.In the numerical model,only coalescence,fragmentation,melting and growth phenomena were considered for the size variation of solid particles in ice slurry.It was indicated that the results of CFD-PBM model was more in line with the actual physical process,which were more accuracy that those of EEM under isothermal and non-isothermal conditions.In CFD-PBM model,the particle size had a positive correlation with the solid volume fraction of ice slurry.Increasing the velocity of ice slurry was beneficial to the growth of solid particle diameter.The change of particle diameter had little effect on the pressure drop of ice slurry in the tubeline.Under the flow conditions,the horizontal tube was 1300mm in length and23mm in diameter.The solid volume fraction and inlet velocity of ice slurry was 10%and 1.0m/s,where the initial diameter of solid particle was0.125mm.The results showed that the diameter of ice slurry solid particle increased from 0.1250mm in the initial state to 0.1276mm at the outlet.The solid particle diameter of ice slurry achieved 0.139mm at the top of the outlet.Under the heating conditions,the horizontal tube was 2000mm in length and 16mm in diameter.The solid volume fraction and inlet velocity were same to those of isothermal condition,but the initial diameter of solid particle was 0.27mm and the heat flux on tube wall was50k W/m~2.The results showed that the diameter of solid particle reduced to0.255mm along the flow direction from the initial diameter due to the melting of particle.The solid volume fraction decreased from 10%to1.21%at the outlet.Under the same conditions of the heating conditions,the initial diameter of solid particles was changed to 0.1mm and the heat flow on tube wall was changed to-30k W/m~2to simulate the cooling condition.The results showed that the solid volume fraction of ice slurry increased from 10%to 28.43%at the outlet.The diameter of solid particles grew from 0.100 mm to 0.130mm.The increase of wall heat flux in heating condition would accelerate the decrease of particle diameter,while the increase of cold flow in cooling condition would accelerate the increase of particle diameter.the particle size distribution in non-isothermal flow showed different characteristics from isothermal flow.In this paper,only heat and mass transfer calculations were considered in cooling conditions.However,supercooling phenomenon usually occurs during the actual cooling process of ice slurry phase,which would affect the variation of solid volume fraction and particle size.The change of solid phase volume fraction should consider the nucleation rate caused by crystallization and the change of particle diameter caused by particle nucleation in the PBM.Therefore,the supercooling experiment of distilled water droplets were carried out on the super-hydrophobic copper surface with a water contact angle of 156°±1.3°.The experimental results showed that the time duration of freezing process after supercooling release was related to the droplet diameter.The larger diameter of the distilled water droplet,the longer it takes for the droplet of freezing time delay and complete crystallization process.