One-dimensional numerical analysis of the transient response of thermal protection systems

Abstract : Differential equations governing the transient response of thermal protection systems to a hyperthermal environment are presented. These equations are expanded into finite-difference equations which are suitable for numerical solution. The equations provide for three layers of different materials, the first two of which may have moving boundaries. Concentrated heat sinks, such as metallic structures, may be located at the back surfaces of the second or third layers or of both layers. The analysis was developed primarily for charring ablators but is also applicable to impregnated ceramic, subliming, and heat-sink thermal protection systems. The principal difficulty encountered in numerical analysis of charring ablators is the extensive computer time required to obtain solutions. Provision is made in the numerical equations to introduce options which reduce computer time. The errors resulting from these options under various conditions are discussed. Good agreement is obtained between numerical results and exact solutions.