With the global rise of the low-altitude economy, countries around the world have been rolling out a series of policies aimed at promoting the application and commercialization of electric vertical take-off and landing (eVTOL) aircraft. However, all-electric eVTOLs face challenges such as low battery energy density, high power demands during operation, and difficulties in rapid recharging, which limit their range and potential use cases. As a result, there is an urgent need to investigate battery charging and swapping solutions for eVTOLs. This paper designs a battery charging and swapping system model for eVTOLs based on a closed-loop supply chain. Leveraging time-space network techniques, an efficient and flexible battery logistics transportation system is established between swapping stations and the charging station within the model. The study then optimizes battery swapping, transportation, and charging operations with the objective of maximizing operational revenue, enabling the coordinated operation of eVTOLs, swap stations, and charging stations. Finally, the model is solved using Gurobi, demonstrating its feasibility. Simulation results also indicate that the proposed model not only alleviates range anxiety for eVTOLs, thereby supporting their commercialization, but also facilitates active participation in power grid dispatch planning by optimizing battery charging strategies.