A Dual Zone Thermodynamic Model for Refueling Hydrogen Vehicles

With the simple structure and quick refuelling process, the compressed hydrogen storage system is currently widely used. However, thermal effects during charging-discharging cycle may induce temperature change in storage tank, which has significant impact on the performance of hydrogen storage and the safety of hydrogen storage tank. To address this issue, we once propose a single zone lumped parameter model to obtain the analytical solution of hydrogen temperature and use the analytical solution to estimate the hydrogen temperature, but the effect of the tank wall is ignored. For better description of the heat transfer characteristics of the tank wall, a dual zone (hydrogen gas and tank wall) lumped parameter model will be considered for widely representation of the reference (experimental or simulated) data. Now, we extend the single zone model to the dual zone model which uses two different temperatures for gas zone and wall zone. The dual zone model contains two coupled differential equations. To solve them and obtain the solution, we use the method of decoupling the coupled differential equations and coupling the solutions of the decoupled differential equations. The steps of the method include: (1) Decoupling of coupled differential equations; (2) Solving decoupled differential equations; (3) Coupling of solutions of differential equations; (4) Solving coupled algebraic equations. Herein, three cases are taken into consideration: constant inflow/outflow temperature, variable inflow/outflow temperature and constant inflow temperature and variable outflow temperature. The corresponding approximate analytical solutions of hydrogen temperature and wall temperature can be obtained. The hydrogen pressure can be calculated from the hydrogen temperature and the hydrogen mass using the equation of state for ideal gas. Besides, the two coupled differential equations can also be solved numerically and the simulated solution can also be obtained. This study will help to set up a formula based approach of refuelling protocol for gaseous hydrogen vehicles.