Derivation of the Thermal Conductivity in a Latent Thermal Energy Storage Unit for Use in Simplified System Models

TL;DR

This paper derives a simplified thermal conductivity model for a latent thermal energy storage unit with a finned tube structure, enabling efficient system simulations for Carnot Batteries.

Contribution

It introduces a method to determine effective thermal conductivity of a finned tube LTES unit for use in simplified transient models.

Findings

Effective thermal conductivity can be approximated using a numerical model.

The simplified model aligns well with complex reference simulations.

Results facilitate integration of LTES units into system-level models.

Abstract

Latent Thermal Energy Storages (LTES) can store thermal energy in a narrow temperature range. Therefore, they are favorable for integration into Rankine-based Carnot Batteries. For the design of such systems, simulations based on accurate models are desirable. However, physical phenomena such as natural convection in LTES units cannot be modeled directly in transient system models. Simplified models are required. Therefore, the objective of this work is to derive simplified LTES unit models for use in system models. In transient simulations the state of charge of the LTES influences its temperature profile. The temperature profile depends on the geometry of the LTES unit. Therefore, the geometry must be considered to model the transient behavior of an LTES unit. The LTES unit under investigation has a shell and tube heat exchanger structure. The phase change material (PCM) is located between the hexagonal fins and in the space between the finned tubes. Aluminum fins are used. They have a high thermal conductivity and thus compensate for the low thermal conductivity of the sodium nitrate used as PCM. The interaction between fins and PCM is complex. Therefore, a numerical approach can be used to gain insight into the behavior of the LTES unit. To transfer the results of a complex model to a simplified model where fins and PCM are not considered individually, the effective thermal conductivity of a single finned tube can be used to approximate the performance of the LTES unit. In this study, a model of a section with a single finned tube is developed using the COMSOL software. The effective thermal conductivity of the system is determined by varying the effective thermal conductivity in a simplified model and comparing the results with reference cases based on a complex modeling approach. The results can serve as model input for simplified system models of Carnot Batteries, among others.