Incorporating porous skeletons into PCMs is an effective strategy for enhancing their thermal properties. However, this approach increases the complexity of the heat transfer process and poses a challenge to accurate modeling. This study investigates the water freezing process in porous skeletons with various shapes and heat transfer directions through experiments and numerical simulations. The model employs the hybrid finite element method with mesh adaptation to optimize numerical solutions. The experimental and simulation results are in good agreement, which validates the accuracy of this model. The study aims to reveal the evolution mechanisms of the phase interface, temperature field, and freezing rate of water in various porous skeletons, enhancing the theoretical foundation and offering insights for practical applications. Results show that the square steel skeleton exhibits the highest freezing rate among the tested skeleton shapes, while the rhombus resin skeleton demonstrates the slowest. Furthermore, the square skeleton shows the smallest interface deflection before and after the pores, while the rhombus skeleton presents the largest. Additionally, vertical heat transfer from bottom to top increases the freezing rate by 38.97% compared to horizontal heat transfer from left to right.