Session: K6-03: HEAT TRANSFER IN ENERGY SYSTEMS - ENERGY STORAGE I

Paper Number: 130699

130699 - Analytical and Numerical Modeling of Thermal Transport in Liquid Hydrogen Tanks 

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. Previous works investigating liquid hydrogen storage tanks have primarily focused on the thermo-fluidic behavior of liquid hydrogen over time scales of seconds to hours as it undergoes boil-off due to external heating utilizing numerical modeling. Zero boil-off has been shown to be possible but requires an active external input to the tank system to remove the excess thermal energy of the liquid hydrogen. There is a dearth of research in analytically and numerically modeling the thermo-fluidic behavior before boil-off occurs to assess passive insulation performance and to enhance this performance through tank design modifications. This study expands upon the current literature by providing a closed-form transient temperature model with a Dirichlet boundary condition to provide validation to the numerical model with transient boundary conditions to mimic the day and night cycle. The numerical model builds upon the analytical model by including the polar direction, solving for both the Dirichlet and Neumann boundary conditions, and considering convective heat transfer effects. The analytical model is a modified form of the heat equation by coupling the lumped capacitance method with the transient heat equation, and in turn, the evolution of the temperature at any radial location within the tank can be found over time. An analytical model for the thermal diffusivity of the insulation first uses the effective medium theory (EMT) and Parallel model to relate the geometry of the individual SiO2 glass bubble (GB) unit cells with the overall GB insulation layer. This EMT-Parallel model is incorporated into a Series model that couples the GB insulation layer with the inner and outer stainless-steel shells that provide structural integrity to the tank. The transient temperature model is a function of the radius and time only, assuming symmetry in the polar and azimuthal directions, and the thermal diffusivity model is a function of temperature. In the numerical model, the Newton-Raphson method is used to solve the transient energy and Navier-stokes equations for a spherical liquid hydrogen storage tank in order to assess the effectiveness of the GB insulation by determining the time in days t_c until the liquid hydrogen reaches its critical temperature of 33K. The inner surface boundary of the tank is set at a constant pressure of 13.3 atm and an initial temperature of 22.5K. The pressure in this case is the critical pressure point for liquid hydrogen, in order to investigate the maximum time until the critical temperature is reached under ideal conditions.  For the transient Dirichlet boundary condition, the hydrogen remains in its liquid state for t_c=7.60 days for the numerical model before reaching its critical temperature. For the transient Neumann boundary condition, the hydrogen remains in its liquid state for t_c=9.00 days for the numerical model before reaching its critical temperature. When integrating a baffle design into the tank to limit convective heat transfer, the days until the critical point increases, and for the transient Dirichlet and Neumann boundary conditions, it takes t_c=7.70 days and t_c=9.13 days, respectively, until the critical temperature is reached. An insulation design space expands the results of this work by relating different thermal conductivity and volumetric heat capacity values for the insulation at the critical pressure to find the corresponding t_c. This study provides a blueprint to assess the performance of insulation materials with thermal properties that diverge from GBs in order to tailor the tank design as needed to optimize performance. 
 

Presenting Author: Charles Owens University of California, Irvine

Presenting Author Biography: Charles Owens received his B.A. in Physics from Pomona College, his M.S. in Mechanical Engineering from the University of Southern California, and is currently a 4th-year PhD candidate in Mechanical Engineering at the University of California, Irvine. His research focuses on thermal properties of mechanical metamaterials, including shape memory polymers, liquid crystal elastomers, and hydrogels, and how thermal transport in these architected materials are dependent on temperature and compression. His other research focuses include investigating thermal transport in liquid hydrogen storage tanks and designing and testing thermal switches for space-based applications.

Authors:

Charles Owens University of California, Irvine
Hoyeon Park University of California, Irvine
Robert Joseph Flores University of California, Irvine
Luke Wentlent Plug Power Inc.
Jack Brouwer University of California, Irvine
Jaeho Lee University of California, Irvine