A Study of Natural Convection in Densified Cryogenic Propellants: The Effect of Heat Transfer on Circulation Patterns

A two-dimensional (radial and axial) single domain (liquid) mathematical model is adopted to investigate the development of the circulation patterns inside the liquid propellant due to heat transfer from the walls of the container and the heat and mass transfer to the vapor in the ullage. The physics based mathematical model consists of conservation of mass, momentum, and energy equations for the liquid subjected to appropriate boundary conditions at the liquid-vapor interface and variable heat flux boundary condition at the walls of the container. The density of the liquid is assumed to be temperature dependent only in the buoyancy term of the momentum equation (Boussinesq approximation). The resulting nonlinear governing equations are then solved by an implicit finite difference technique (where the pressure distribution is determined by solving the Poisson’s equation) to predict the transient temperature and velocity fields inside the propellant. The computational domain is stretched in both directions to improve the results near the walls of the container. The model is tested for a benchmark case to verify the accuracy of the numerical scheme. Finally, the model is used to conduct numerical experiments to study the effect of different heat transfer boundary conditions on the circulation patterns and the resulting thermal stratification in the densified propellant.