A robust and efficient method to facilitate phase change energy storage system simulation


The demand for efficient thermal energy storage (TES) has soared with the increasing development of renewable energy sources. The popular configuration consisting of shell-and-tube phase change material (PCM) based on heater exchanger (HEX) has been extensively studied for potential application in TEM owing to its simple and compact features. Although there are numerous design performance indicators and metrics for optimal PCM TES design, most do not provide crucial detailed information regarding how the operational requirements are achieved, such as required outlet temperature and charge duration. The absence of system-level design protocols jeopardizes efforts to design cost-optimal PCM-based TES systems.

Effectiveness, described as the ratio of the actual heat discharged to the maximum possible dischargeable theoretical heat, has been identified as a useful design metric. It indicates the efficiency of using stored energy and is affected by the mass flow rate as well as the temperature of the inlet heat transfer fluid (HTF). However, effectiveness is considered an unreliable performance metric in most cases because it usually becomes an operational constraint determined by operational requirements. Exergy is another performance indicator that has been studied. It is described as the maximum achievable work quantity by a system approaching equilibrium with its surroundings. Previous findings established that both operating conditions and geometric variables associated with these performance indicators profoundly affect the latent heat thermal energy storage (LHTES) systems performance.

Optimizing LHTES systems is imperative for engineering design purposes. However, discretization of partial differential equations of the nonlinear melting/solidification process of PCMs results in large-scale and complex dynamic systems whose behavior is determined by a set of parameters. Existing optimal design approaches for addressing these problems are limited to repeated parameter evaluations leading to a significant computational burden. Thus, developing a reduced model (RM) of PCM-based LHTES systems could enable efficient global optimal design under operational constraints.

On this account, Professor Xingchao Wang from Colorado School of Mines together with a team of Lehigh University researchers: Dr. Chunjian Pan, Dr. Natasha Vermaak, Professor Carlos Romero and Professor Sudhakar Neti proposed an explicit analytical solution for propagating solidification front in both cylindrical and rectangular coordinates. Further, the analytical solution was used to develop an accelerated RM module for potential application in the optimal design of shell-and-tube-based LHTES HEX. To achieve efficient global optimal design, a Levelized Cost of Energy (LCOE) was utilized as a design performance metric, while the RM model was applied to address the system constraints through nonlinear programming. Their work is currently published in the International Journal of Heat and Mass Transfer.

The proposed RM model enabled the feasible design of a global optimal system-level LHTES system, including tube geometries, PCM properties and flow conditions. Optimal simulation results showed that higher effectiveness resulted in higher LCOE, suggesting that effectiveness is not a suitable performance metric. Whereas the channel length and velocity of the HTF exhibited a strong correlation with one another, both larger conductivity and latent PCM energy resulted in reduced LCOE. Although the longer heating duration required a larger amount of PCM energy, it was not associated with increased heat transfer rates.

In summary, the research team developed a computational reduced analytical solution for PCM solidification in cylindrical and rectangular domains and its subsequent application in cost-effective and optimal design of shell-and-tube based thermal energy storage systems was reported. By preventing the inappropriate design of heat transfer rate, using LCOE based performance metric provided a conducive ground for evaluating various thermal storage technologies and associated applications. In a statement to Advances in Engineering, Professor Xingchao Wang explained that LCOE is an effective and appropriate cost estimation technology for the optimal design of PCM-based LHTES systems for various applications in the energy sector.

Advances in Engineering

A robust and efficient method to facilitate phase change energy storage system simulation - Advances in Engineering

About the author

Dr. Xingchao Wang is a Research faculty of the Mechanical Engineering Department at Colorado School of Mines. Dr. Wang received his Ph.D. in Mechanical Engineering from Lehigh University and B.E. in Thermal Engineering from Tsinghua University. His expertise lies in heat transfer, thermodynamics, conventional and renewable energy systems modeling and optimization. Dr. Wang is also jointly appointed to the National Renewable Energy Laboratory (NREL). He is currently engaging in energy conversion research and technology development using renewable energy sources.


About the author

Chunjian Pan obtained his PhD in Mechanical Engineering from Lehigh University in 2019. After graduation, he worked at Purdue University as a Postdoc. He is an expert in thermal science modeling. One of his research topics is to develop fast reduced models that can be used for optimal system sizing and control applications by combing data-driven information and physics knowledge. The thermal systems he worked on including phase change material based latent heat thermal energy storage systems, geothermal reservoir heating mining, vapor compression cycles and metal hydride reactors.


Pan, C., Vermaak, N., Wang, X., Romero, C., & Neti, S. (2021). A fast reduced model for a shell-and-tube based latent heat thermal energy storage heat exchanger and its application for cost optimal design by nonlinear programmingInternational Journal of Heat and Mass Transfer, 176, 121479.

Go To International Journal of Heat and Mass Transfer

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