Heat transfer through cryogenic propellant tank insulation during ground-hold conditions

A theoretical formulation is presented for predicting transient (leading to steady state) heat transfer characteristics through the thermal insulation of cryogenic rocket propellant tanks. Only the cylindrical sides of the pr opellant tanks are studied while the rocket is on the launch pad in a holdi ng condition. Effects of direct solar radiation, Earth-reflected/emitted ra diation, and mind velocity are considered for estimation of heat lends to t he propellants. A finite difference technique using a simple explicit metho d is adopted to establish time-dependent temperature distributions across s everal layers of the integrated insulation package. Stability, accuracy, an d computational requirements of the technique are reviewed with simple impl icit and Crank-Nicolson solution schemes. Computed results are compared wit h Galerkin finite element solutions using lineal and quadratic polynomial i nterpolants. Formulations for these finite element methods are also derived . The model can be used for characterizing insulation material, thickness o ptimization, estimation of boil-off rate, and verification of lower limit t emperature at the outer surface. Some results based on relevant input data are presented.