Abstract
Hydrogen is an element that can be stored via phase change through compression or liquification by varying temperature and pressure, or through physical or chemical bonding. This study provides a closed-form transient temperature model of a spherical liquid hydrogen storage tank heated over time with validation provided by a numerical model. The analytical temperature model couples the lumped capacitance approach with the transient heat equation, and the analytical thermal diffusivity model for the hollow glass bubble (HGB) insulation uses a combination of the effective medium theory (EMT), Parallel, and Series models. In the numerical model, the Newton-Raphson method is used to solve the transient energy and Navier-stokes equations to assess the effectiveness of the insulation. For the thermal conductivity model, as the wall thickness of the individual HGBs increases from 0.5μm to 50μm, the effective thermal conductivity of the insulation increases from 0.01W · m−1K−1 to 0.41W · m−1K−1. For a constant surface temperature from 280K to 320K, the numerical model illustrates that the time to critical point τ decreases from τ ≈ 60days to τ ≈ 41days. When the analytical model is iterated to the same τ at each surface temperature, the critical temperature TC is located radially at approximately 7.88m, rather than 7.85m, illustrating the limitations of the analytical model. An insulation design space relates the different thermal conductivity k and volumetric heat capacity ρCp values for the insulation at the critical pressure to find the corresponding τ. A power series relationship is found from the insulation design space for the critical time τ as a function of k and ρCp.
