A combined uncertainty and sensitivity analysis of melting in a cubical cavity, Part B: Combined analysis

Abstract

Latent heat thermal energy storage systems are an attractive way to store thermal energy nearly isothermally. Nowadays, numerical methods are increasingly employed for their design. However, the results obtained with these methods are accompanied by a high degree of uncertainty, which results in leeway in the validation of the models. This leeway leads to seemingly perfectly validated numerical models, although they often contain strong simplifications and the input parameters have large uncertainties. To shed more light on this contradiction, we perform a combined uncertainty and sensitivity analysis of a classical validation problem — a paraffin melting from one side in a cuboid. The input parameters of the combined uncertainty and sensitivity analysis are the thermophysical properties of the phase change material (PCM) and the boundary and initial conditions of the experiment. We show that the uncertainty of the liquid fraction after $\text{2}\text{h}$ is around $\pm \text{7}\text{\%}$ if the thermophysical properties are implemented correctly. This is significantly lower than what would be expected considering the large variation of thermophysical property values found in the literature. The thermal conductivity of the solid, the melting point, and the solid density are the input parameters with the greatest influence on the global liquid fraction. Therefore, these parameters should be measured with higher accuracy to further improve the accuracy of the simulation. In addition to the liquid fraction, the heat flux flowing through the hot and cold sides of the simulation domain and the maximum velocity in the fluid phase are also considered targets of the combined uncertainty and sensitivity analysis. Here we see that the heat flux of the cold side is the target variable with the greatest uncertainty. Interestingly, for one time instance, the same liquid fraction and an almost identical phase front can be achieved with very different input variables, highlighting the importance of using several target variables for the validation.