Exploration of Variable Conductance Effects During Input and Extraction of Heat From Phase Change Thermal Storage

Abstract

Previous efforts to model the effectiveness of heat input and extraction from a thermal storage unit have generally been based on the definition of a constant conductance of heat from the working fluid to the phase change storage material. In order to capture the effects of changing thermal resistance between the working fluid and melt front location, this paper presents a method using a resistor network analogy to account for thermal conductance as a function of melt fraction. This expression for thermal conductance is then implemented in an existing numerical framework. Results are validated by comparing calculations for a single unit cell using a quasi-steady Stefan problem approach, a finite difference scheme, and more general form solutions from literature. The variable approach is then compared with an average value for overall thermal conductivity, U, to characterize the performance of a thermal energy storage unit consisting of a series of these unit cells. Overall effectiveness in the thermal energy storage device is found to be within 0.6% agreement when comparing these methods, though local percent deviation can be as high as 113%. Depending on the needed accuracy and use case for such a numerical framework, suggestions are provided on whether an average value for U is sufficient for characterizing such a thermal energy storage device. Discussion is also provided on the flexibility of the computation schemes described by testing the sensitivity of the results via changes in dimension-less input parameters.

Development and Validation of a Latent Thermal Energy Storage Model Using Modelica

“…Similar to steady-state effectiveness-NTU predictions, we found that the effectiveness of high performance devices is not sensitive to variations in conductance [24]. Those findings justified the use of a space-and time-averaged conductance, which we determined from a simple thermal resistance network as a function of the phase change material melt fraction [25]. In tandem, the TES device was examined in the context of a larger subsystem, consisting of external heat exchangers used to transfer energy to and from the storage.…”

“…For the geometry given in Table 1, natural convection is not present. As noted in the introduction, previous work has been used to derive U [24,25]. The more elegant of these results will be used, namely that the overall heat transfer coefficient, U, can be found from the device geometry (A t , A w , h s ), thermophysical properties (k s ), convective coefficient, h, and the melt fraction, x e , which is a function of position in the device as well as time:…”

Comparison of Model Predictions and Performance Test Data for a Prototype Thermal Energy Storage Module

“…For the geometry given in Table 1, natural convection is not present. As noted in the introduction, previous work has been used to derive U [7,8]. The more elegant of these results will be used, namely that the overall heat transfer coefficient, U, can be found from the device geometry (A t , A w , h s ), thermophysical properties (k s ), convective coefficient, h, and the melt fraction, x e , which is a function of position in the device as well as time:…”

“…The methodology and results that are presented in this paper are built upon a larger body of work from this group over the last several years [6][7][8][9][10]. The first of these contains the derivation of a non-dimensional framework developed in order to analyze thermal energy storage technology [6].…”

“…That work was used to justify the use of an average conductance in future modeling; the effectiveness of high performance devices is not sensitive to variations in conductance [7]. Additional work has been done since then to determine a simpler relation for average conductance as a function of the melt fraction [8]. In tandem, the TES device was examined in the context of a larger subsystem, consisting of external heat exchangers used to input and reject heat to and from the storage.…”