A CFD Model of Evaporation in Liquid Hydrogen without the Need for Tuning Coefficients

The Hertz-Knudsen-Schrage equation, derived from kinetic theory, describes evaporation and condensation but requires accommodation coefficients as inputs. Reported values of the coefficient are controversial and span 3 orders of magnitude for common fluids such as water. The data for cryogenic fluids is severely limited. Computational modeling of evaporation in liquid hydrogen is critical to evaluate the cryo-storage stability of fuel depots to enable long-term space missions. However, the coefficient is often reduced to a tuning parameter to achieve numerical stability. Recent results indicate that transition state theory could provide an analytical description of the accommodation coefficients based on the physical parameters of the liquid and the vapor. Here, a new computational method to model evaporation is developed using a combination of transition state theory and kinetic theory to alleviate the need for tuning coefficient values. A custom CFD model for steady evaporation from a liquid hydrogen meniscus is built using user-defined functions in Ansys Fluent. Numerical simulations are conducted using inputs from an experimental cryo-neutron imaging dataset. At each instantaneous time step, a sharp liquid-vapor interface is assumed, held static and a zone of cells on either side of the interface is identified as an “active region”. This region is instrumented with custom non-uniform mass and energy sources/sinks. The accommodation coefficient is computed in-situ by probing corresponding liquid and vapor cells on either side of the interface. The non-uniform evaporation flux is then integrated over the meniscus to obtain an instantaneous net evaporation rate and compared with the experimentally measured evaporation rate for validation.