Charles H. Panzarella

On the validity of purely thermodynamic descriptions of two-phase cryogenic fluid storage

This paper presents a comprehensive analysis of the transport processes that control the self-pressurization of a cryogenic storage tank in normal gravity. A lumped thermodynamic model of the vapour region is coupled with the Navier-Stokes and energy equations governing heat, mass and momentum transport in the liquid. These equations are discretized using a Galerkin finite-element method with implicit time integration. Three case studies are considered based on three different heating configurations imposed on the tank wall: liquid heating, vapour heating and uniform heating. For each case, the pressure and temperature rise in the vapour and the flow and temperature distributions in the liquid are determined. Results are compared to a lumped thermodynamic model of the entire tank. It is shown that the final rate of pressure rise is about the same in each case and close to that predicted by thermodynamics even though the actual pressures are different because of varying degrees of thermal stratification. Finally, a subcooled liquid jet is used to mix the liquid and limit the pressure rise. Even so, there is still some thermal stratification in the liquid, and as a result the final vapour pressure depends on the particular heat distribution.

Nonlinear dynamics in horizontal film boiling

This paper uses thin-film asymptotics to show how a thin vapour layer can support a liquid which is heated from below and cooled from above, a process known as horizontal film boiling. This approach leads to a single, strongly-nonlinear evolution equation which incorporates buoyancy, capillary and evaporative effects. The stability of the vapour layer is analysed using a variety of methods for both saturated and subcooled film boiling. In subcooled film boiling, there is a stationary solution, a constant-thickness vapour film, which is determined by a simple heat-conduction balance. This is Rayleigh–Taylor unstable because the heavier liquid is above the vapour, but the instability is completely suppressed for sufficient subcooling. A bifurcation analysis determines a supercritical branch of stable, spatially-periodic solutions when the basic state is no longer stable. Numerical branch tracing extends this into the strongly-nonlinear regime, revealing a hysteresis loop and a secondary bifurcation to a branch of travelling waves which are stable under certain conditions. There are no stationary solutions in saturated film boiling, but the initial development of vapour bubbles is determined by directly solving the time-dependent evolution equation. This yields important information about the transient heat transfer during bubble development.

Self-Pressurization of Large Spherical Cryogenic Tanks in Space

The pressurization of large cryogenic storage tanks under microgravity conditions is investigated by coupling a lumped thermodynamic model of the vapor region with a complete solution of the flow and temperature fields in the liquid. Numerical results indicate that in microgravity both buoyancy and natural convection are still important and play a significant role in phase distribution and tank pressurization. A spherical vapor region initially placed at the center of the tank deforms and moves to one side of the tank before any significant pressure rise. Long-term results obtained with the vapor region near the tank wall show that, even in microgravity, natural convection leads to thermal stratification in the liquid and significantly alters the initial pressure rise. The final rate of pressure rise agrees with a lumped thermodynamic model of the entire system, but the final pressure levels depart from thermodynamic predictions because of initial transients. The history of the maximum liquid superheat and subcooling is also determined for each configuration.

Comparison of Several Zero-Boil-Off Pressure Control Strategies for Cryogenic Fluid Storage in Microgravity

Four different tank pressure control strategies based on various combinations of active cooling and/or forced mixing are investigated numerically. The first, and most effective, strategy uses a subcooled liquid jet to simultaneously mix and cool the bulk liquid. The second strategy is based on separate mixing and cooling via a forced uncooled liquid jet and an independent cold finger. The third strategy uses a cold finger alone with no forced mixing. Finally, the fourth strategy examines the effect of mixing alone without any active cooling. Detailed numerical solutions are obtained for each case by solving the Navier―Stokes and energy equations in the liquid region coupled to a lumped heat and mass treatment of the vapor region. It is shown that the most rapid and effective means of countering self-pressurization is achieved with a subcooled liquid jet. In the case of separate mixing and cooling, the pressure can still be reduced, but over a much longer period of time. Finally, cooling without any forced mixing is able to limit the pressure rise, but not very effectively, although for long-duration storage in which rapid pressure control is not required, this may still constitute a viable approach. While presenting the results of the various simulation case studies, an in-depth comparative analysis of transport phenomena associated with each case is also performed from which salient engineering recommendations are derived for optimization of the zero-boil-off design.

SIMULATIONS OF ZERO BOIL-OFF IN A CRYOGENIC STORAGE TANK

The pressurization of a cryogenic storage tank is investigated by using a numerical model that takes into account the transport of heat and mass into the vapor region. A finite-element model is used to obtain the complete solution for heat nad mass transport in the liquid region, and this is coupled to a lumped parameter model of the vapor region. The pressure rise is determined for a number of different heat distributions imposed on the tank wall. It is shown that the final rate of pressure rise agress with a thermodynamic model of the entire tank (liquid and vapor regions) for all of the cases considered here. The zero boil-off concept is then tested by incorporating a liquid jet which enters the tank at a prescribed flowrate and temperature. It is shown that this jet is capable of controlling the pressure rise, but the final pressures are different depending on the tank wall heat distribution even when the total heat input is the same.

Ventless pressure control of two-phase propellant tanks in microgravity

Abstract: This work studies pressurization and pressure control of a large liquid hydrogen storage tank. A finite element model is developed that couples a lumped thermodynamic formulation for the vapor region with a complete solution of the Navier‐Stokes and energy equations for the flow and temperature fields in the liquid. Numerical results show that buoyancy effects are strong, even in microgravity, and can reposition a vapor bubble that is initially at the center of the tank to a region near the tank wall in a relatively short time. Long‐term tank pressurization with the vapor bubble at the tank wall shows that after an initial transient lasting about a week, the final rate of pressure increase agrees with a purely thermodynamic analysis of the entire tank. However, the final pressure levels are quite different from thermodynamic predictions. Numerical results also show that there is significant thermal stratification in the liquid due to the effects of natural convection. A subcooled jet is used to provide simultaneous cooling and mixing in order to bring the tank pressure back down to its initial value. Three different jet speeds are examined. Although the lowest jet speed is ineffective at controlling the pressure because of insufficient penetration into the liquid region, the highest jet speed is shown to be quite effective at disrupting thermal stratification and reducing the tank pressure in reasonable time.