Benjamin Duret - CORIA - Direct numerical simulation of phase change in LH2 tanks subject to sloshing.

Sloshing of liquid hydrogen (LH2) during transportation or in micro-gravity conditions can lead to important issues in aerospace applications and, more recently, in its development as an energy vector in the transport industry. Since the work of Abramson [1], who proposed several analytical models to predict sloshing in tanks with different geometries, there have been many studies on sloshing, but few that considered sloshing of vaporizing/boiling cryogenic fluids (for instance [2]). Besides the forces exerted by the liquid on the tank’s walls, sloshing induces changes in the thermodynamic behavior of the liquid, leading to significant pressure changes when phase change occurs. This phenomenon, called boil-off, may lead to a release of gaseous hydrogen during transportation to avoid the self-pressurization of the tank. The subsequent mass loss is considered one of the most severe drawbacks of this energy [3].
The LH2’s boil-off can be triggered and enhanced by many processes, such as an increased surface area due to the sloshing, the heat flux entering through the walls, etc. These reasons prompted us to investigate this phenomenon using our in-house DNS code ARCHER. Recently, the mass-conservative interface capturing (Coupled Level Set/Volume Of Fluid) method have been adapted to account for the liquid mass variation due to phase change. In addition, the compressible Navier-Stokes equations are solved using a pressure-based method with appropriate jumps conditions at the interface, which allows us to capture the Stefan flow at the liquid/gas interface, acoustic effects, and the thermal dilatation of both phases. Furthermore, the method can handle several gas structures captured inside the liquid, each with independent temperature, density, and pressure. A detailed description of the system of equations solved, the implemented numerical methods, and their application will be presented in the seminar.
Then, results obtained with this formalism for a compressible vaporizing two-phase flow HIT and a sloshing configuration with LH2 will be shown and discussed during this talk, illustrating the method’s potential.

References
[1] Abramson, H. N. (1966). The dynamic behavior of liquids in moving containers, with applications to space vehicle technology (No. NASA-SP-106).
[2] Van Foreest, A. (2010). Modeling of cryogenic sloshing, including heat and mass transfer. In 46th AIAA/ASME/SAE/ASEE joint propulsion conference & exhibit (p. 6891).
[3] Ustolin, F., Paltrinieri, N., & Berto, F. (2020). Loss of integrity of hydrogen technologies: A critical review. international journal of hydrogen energy, 45(43), 23809-23840.