Study On The Unconstrained Melting Characteristics Of Phase Change Materials In Hot Water Tanks And Heat Transfer Enhancement

Phase change materials(PCMs)have attracted considerable attention for solar water heating systems due to their latent heat capacities and almost constant temperature in the heat storage/release process.Being coupled to the hot water tank,PCMs can significantly enhance its thermal performance,and accordingly improve the solar fractions of the solar water heating systems.However,the relatively low thermal conductivities of PCMs,which lead to low charging/discharging rates during these processes,have become a great hinderance for the practical applications.To address these issues,a systematic study on the unconstrained melting characteristics,the methods of heat transfer enhancement and the design methods of the PCM encapsulated in latent heat storage unit was conducted in this paper.The main content and conclusions are as follows:(1)The solid PCM settling velocity oscillated during the model solution for the unconstrained melting model developed by directly coupling the force balance equation of the solid PCM,leading to the instability of the model.To address this issue,an analytical solution algorithm for the solid PCM settling velocity was deduced based on Nusselt liquid boundary layer theory.Accordingly,a novel hybrid model,which integrated analytical solid PCM settling velocities,was developed for modeling the unconstrained melting of PCMs in hot water tanks.Based on this model,the heat transfer characteristics of the phase change material in hot water tanks during unconstrained melting were analyzed.The results showed that the developed model effectively avoided the oscillation of solid PCM settling velocity,and its numerical results agreed well with the experimental results.At the beginning of the unconstrained melting process,thermal conductivity dominated the heat transfer of PCMs.As time progressed,the solid PCMs settled,and the natural convection and contact melting started to dominate the heat transfer.The settle of solid PCMs not only enhanced the heat transfer of PCM in the bottom region,but also improved the natural convective of liquid PCM at the side region.(2)The mushy zone constant is difficult to be determined quickly in practical applications for the unconstrained melting model developed by lowering the value of the mushy zone constant.Moreover,the unphysical deformation might occur for the solid PCM,leading to the unphysical results in the solution of this model.To address this issue,A numerical model with variable mushy zone constants was developed based on the enthalpy-porosity method.Base on this model,the influences of the parameters of the latent heat storage unit on the unconstrained melting performance of PCMs in hot water tanks was analyzed.The result showed that the solution time of the unconstrained melting model with variable mushy zone constants was much shorter than that of the hybrid model coupled with the analytical settling velocity of solid PCMs.The aspect ratio of the cylindrical container exerted little influence on the heat transfer coefficient at side wall surfaces,while it significantly affected the heat transfer coefficient at bottom wall surfaces.Larger total surface areas do not necessarily result in shorter total melting time.Further analysis indicated that flatter containers likely to be preferable to slenderer containers in practical designs.(3)Based on the above analysis,the cylindrical latent heat storage unit,which was widely used in hot water tanks,was modified to a novel geometry with a wavy side wall,with the goal of enhancing the PCM’s heat transfer by effectively utilizing both close-contact melting and natural convection.Based on the unconstrained melting model with variable mushy zone constants,its thermal performance was evaluated,and the effects of the wavelengths(L_w)and wave amplitude(a_w)were analyzed.The results showed that the charging and discharging rate of the proposed wave latent heat storage unit was 2.42 and 1.47times that of the conventional cylindrical latent heat storage unit,respectively.A pure decrease in L_w would not necessarily result in the decrease in the charging time,and the shortest time would be obtained when L_w reached a threshold value for a specified a_w.With the increase in a_w,the average heat transfer coefficient and the total heating wall surface area increased and the charging time decreased.In the discharging process,L_w and a_w exerted a negligible effect on the heat transfer coefficient,and the total surface area played an essential role in the variation of the discharging time.(4)Due to the nonlinear relationship between the unconstrained melting performance of PCMs and the design parameters of latent heat storage units under logarithmic conditions,the undetermined coefficient method is difficult to correlate such relationships.To address this issue,a stepwise regression-elimination method was developed,and the empirical correlation between the unconstrained melting performance of the PCM encapsulated in hot water tanks and the design parameters of the cylindrical and the wave latent heat storage units was established,respectively.The results showed that the developed stepwise regression-elimination method can well correlate the unconstrained melting performance and the design parameters of latent heat storage units,and the established empirical correlations had a good accuracy.Specifically,the relative error between the result predicted by the empirical correlation of the cylindrical latent heat storage units and the numerical results predicted by the unconstrained melting model was less than 4.83%,and such relative error for the wave latent heat storage units was less than 4.15%.The developed unconstrained melting models in this study would facilitate the analysis of the heat transfer characteristic and its influence during the unconstrained melting process of PCMs.The developed wave latent heat storage unit significantly enhances the heat transfer of PCM encapsulated in hot water tanks,and thus the thermal performance of the hot water tank would be improved as the wave latent heat storage unit is used.Moreover,the developed stepwise regression-elimination method would facilitate the design of latent heat storage units in practical applications.