Three-Dimensional CFD Investigation of Fractal Fin-Assisted Solidification of Erythritol in a Shell-and-Tube Latent Heat Thermal Energy Storage Unit

Erythritol is a promising phase change material for medium-temperature thermal energy storage, but its low thermal conductivity leads to slow heat release from the material during solidification. A three-dimensional numerical study of erythritol solidification in a cylindrical shell-and-tube latent heat thermal energy storage unit with three different internal arrays – a finless annulus baseline, traditional pin fins, and a deterministic fractal-fin configuration – is presented. A one-fifth sector was modelled in ANSYS Fluent using the enthalpy-porosity method. Buoyancy forces were modelled using the Boussinesq approximation, and the mesh-independence, mushy-zone, and time-step sensitivity tests were performed for numerical validation, along with a natural-convection phase-change benchmark from the existing literature. The production mesh comprised 732,581 cells and 3,524,743 nodes, with a time step of 1 s. For the finned annulus, pin-fin, and fractal fin arrays, the quantities of added conductor were nearly the same, differing by only 0.11%, but the fractal array afforded 100.4% more fin-PCM interfacial area. The total solidification times were 41,000 s for the finless array, 38,500 s for the pin-finned array, and 36,500 s for the fractal array; the liquid fractions at 20,000 s were 0.348, 0.286, and 0.227, respectively, and the measured mean energy recovery rates at 20,000 s were 7.49 W, 7.51 W, and 8.03 W. The findings suggest that branching conductive structures by using a fractal network with an approximately constant volume of added conductor per generation shortens conduction paths during late-stage solidification of erythritol.