M. Belusko* and F. Bruno

Institute for Sustainable Systems and Technologies, University of South Australia, Australia
Corresponding Author, martin. belusko@unisa. edu. au

Abstract

Representations of thermal storage systems with phase change materials are predominantly developed through numerical modelling. However, as design tools, these models are of limited application. A number of representations are investigated which attempt to characterise thermal storage systems using the effectiveness-NTU technique. From these studies together with observed results from numerical modelling, a generic representation is presented for phase change materials in flat containers. This representation leads to the development of a generic characterisation of the effectiveness of a thermal storage system with respect to a single parameter. This characterisation can readily be used as a design tool for sizing and optimising a thermal storage unit with flat containers of phase change materials.

Keywords: thermal storage, phase change materials, effectiveness

1. Introduction

Numerous mathematical models of phase change material (PCM) in the flat plate arrangement in thermal storage units (TSU) have been developed over the years. These models are numerical models of encapsulated PCM subjected to convection [1]. These models have been used to determine the performance of the TSU for design and simulation purposes. However little attention has been placed on using these models to develop generic representations which can be readily used for the characterisation and ultimately the design and optimisation of a TSU with PCM.

TSU with plates of PCM for solar heating has been examined [2]. Finite difference models were developed which determined the number of transfer units (NTU) between the heat transfer fluid and PCM. The models tested a number of assumptions but always assumed that phase change occurred in one dimension, along the flow path. It was found that assuming an infinite NTU adequately described the TSU within a solar heating application. This NTU was a function of the convection heat transfer coefficient and heat transfer area of the wall. The NTU was assumed constant throughout the phase change process and only referred to the fluid side. However, during the phase change process, within a PCM container the heat transfer occurs between the fluid and the PCM at the liquid/solid front which changes with time. By assuming that the phase change process occurs in the direction of flow, it can be argued that the heat transfer area is reducing, decreasing the NTU.

An entropy optimisation representation for PCM tubes which also determined the NTU between the fluid and PCM at the liquid/solid front has also been developed [3]. This model accounted for the additional thermal resistance within the PCM during the phase change process, resulting in a
decreasing NTU during the phase change process. However this representation assumes the phase change process occurs uniformly with the solid/liquid front perpendicular to the direction of flow, opposite to that in [2]. Consequently, this method also assumes the heat transfer area is constant during the phase change process. Both approaches are potentially overestimating the NTU, however have demonstrated that the NTU is a useful parameter to evaluate the heat transfer in the process. A two dimensional model for PCM in tubes within a tank is described in [4]. The NTU was solved numerically and changed with time. Therefore the model effectively considered the heat flow between the solid/liquid front and the fluid. Consequently, the development of a simplified representation of the PCM is therefore dependant on being able to determine the NTU between the heat transfer fluid and the PCM at the phase change profile.

The representation developed in [3] enables the optimisation of the design of a TSU with PCM considering the exergy losses in the charging and discharging processes. It was shown that along with energy lost due to frictional losses, due to the 2nd Law of thermodynamics some of the energy stored is not released as it cannot meet the temperature requirements of the heat sink. However this technique does not readily lend itself to be used in an engineering design method where the objective is to meet a performance specification. The representation shown in [4] presents are more useful option, in which the TSU is characterised in terms of a heat exchange effectiveness and the NTU and effectiveness are a function of a dimensional time parameter. This approach will be expanded into a generalised representation of the TSU with PCM in plates, applying the s-NTU method, which does not involve numerical modelling.