Finite element formulation to study thermal stresses in nanoencapsulated phase change materials for energy storage

Abstract

Nanoencapsulated phase change materials (nePCMs)-which are composed of a core with a phase change material and of a shell that envelopes the core-are currently under research for heat storage applications. Mechanically, one problem encountered in the synthesis of nePCMs is the failure of the shell due to thermal stresses during heating/cooling cycles. Thus, a compromise between shell and core volumes must be found to guarantee both mechanical reliability and heat storage capacity. At present, this compromise is commonly achieved by trial and error experiments or by using simple analytical solutions. On this ground, the current work presents a thermodynamically consistent and three-dimensional finite element (FE) formulation considering both solid and liquid phases to study thermal stresses in nePCMs. Despite the fact that there are several phase change FE formulations in the literature, the main novelty of the present work is its monolithic coupling-no staggered approaches are required-between thermal and mechanical fields. Then, the FE formulation is implemented in a computational code and it is validated against onedimensional analytical solutions. Finally, the FE model is used to perform a thermal stress analysis for different nePCM geometries and materials to predict their mechanical failure by using the Rankine's criterion.

Numerical formulation of physical phenomena in nanoparticles for their application to nanofluids

“…One of the main problems encountered when nePCMs undergo thermal cycles is that their shell may fail mechanically, as it has been reported in [17]. The thermal stresses arising in the shells of the nePCMs could be one of the reasons for this failure, as investigated in [85].…”

“…The evaluation of the nanoparticle model is performed by a three-dimensional FE code developed by the authors. In particular, a thermodynamically consistent FE formulation was developed in [85] by considering thermomechanical coupling and three phase change approaches: enthalpy, heat source and heat capacity. This formulation was implemented in the research code FEAP [35], which belongs to the University of California at Berkeley (USA).…”

“…With regard to the equivalent stress distribution and in agreement with [85], Rankine's criterion is used to predict the mechanical failure of the nePCM, which usually occurs at the shell. In order to measure the accuracy of the predicted σ R , a bilateral Confidence Interval (CI) around the mean µ is defined as:…”

“…For this purpose, a probabilistic tool is obtained by combining both MC and FE methods. The former considers up to 22 random variables and the input samples are generated by using the Latin Hypercube Sampling (LHS) technique [95], while the latter is a thermomechanical with phase-change FE code previously developed by the authors of the present work [85]. From the uncertainty analysis, distributions of maximum Rankine's equivalent stress -failure criterion for the shell-and of energy density are obtained.…”

“…There-fore, understanding the reasons behind the mechanical failure of the nePCM shell is necessary. In this vein, a thermomechanical finite element (FE) model with phase change was developed in a previous work [113] to predict the failure of the nePCM shells during thermal processes. Experimental measurements and characterisation of nePCMs are not exempt from uncertainties, which are intrinsically related to the nature of the measurement process.…”