The error of neglecting natural convection in high temperature vertical shell-and-tube latent heat thermal energy storage systems

There is little understanding of the relative importance of natural convection when designing latent heat thermal energy storage (LHTES) systems based on geometric parameters and/or phase change material (PCM) properties. For high temperature shell-and-tube LHTES systems, this study aims: (i) to determine the error of ignoring natural convection, and (ii) to quantify this error for different geometric parameters and PCM properties. In particular, the study defines the circumstances under which natural convection is important and the error of choosing a 'conduction-only modelling approach'. To do so, the performance of LHTES systems with nine geometric aspect ratios and three commercial PCMs (of different melting points) were analyzed by means of a validated CFD model. The results showed that the error is a function of the process under analysis (melting or solidification) and the ratio of stored/delivered energy divided by the maximum capacity of PCM (i.e. its effectiveness). Geometry also plays a critical role in the relative importance of natural convection. The study demonstrates that a specific system geometry (i.e. a dimensionless number defined based on the inner and outer radius as well as the length of shell-and-tube geometry: S = R-2 - r(0)(2)/2r(0)L) can be used to determine the relevance of natural convection. It was found that regardless of PCM type, the error is of neglecting natural congestion is small if S < 0.005. For S > 0.005, the error depends on the following non-dimensional groups: r(0)/L, Ra, Ste, and Bi. As might be expected, the Rayleigh number was found to be the most influential group. Notably, a critical Rayleigh number value (8 x 10(5)) was found, below which the error of neglecting natural convection is < 1%. Finally, two correlations were developed in order to quantify the error achieved - one for melting and another for solidification.