Metallic foams are novel materials that can be used as thermal insulation in many applications. The low volume fraction of solid, the small cell size and the low conductivity of enclosed gases limit the heat flow in foams. Varying the density, geometry and or material composition from point to point within the foam, one can produce functionally graded foams that may insulate more efficiently. The goal of this research is to investigate the use of functionally graded metal foam in thermal protection systems (TPS) for reusable launch vehicles.; First, the effective thermal conductivity of the foam is derived based on a simple cubic unit cell model. Then two problems under steady state of heat transfer have been considered. The first one is the optimization of functionally graded foam insulation for minimum heat transmitted to the structure and the second is minimizing the mass of the functionally graded foam insulation for a given aerodynamic heating. In both cases optimality conditions are derived in closed-form, and numerical methods are used to solve the resulting differential equations to determine the optimal grading of the foam. In order to simplify the analysis the insulation was approximated by finite layers of uniform foams when studying the transient heat transfer case. The maximum structure temperature was minimized by varying the solidity profile for a given total thickness and mass. The principles that govern the design of TPS for transient conditions were identified.; To take advantage of the load bearing ability of metallic foams, an integrated sandwich TPS/structure with metallic foam core is proposed. Such an integrated TPS will insulate the vehicle interior from aerodynamic heating as well as carry the primary vehicle loads. Thermal-structural analysis of integrated sandwich TPS panel subjected to transient heat conduction is developed to evaluate their performances. The integrated TPS design is compared with a conventional fibrous Safill TPS design. The weights of both designs are minimized subject to temperature constraints, stress constraints or both. Global buckling, shear crimping and face wrinkling are investigated for the integrated sandwich structure during the launch. It is found that for designs with variable insulation thickness, structure thickness and subjected to structure temperature constraint only, an integrated sandwich design tends to require as thick insulation as possible, while a Safill design requires thin structure. Shear crimping is most critical among all the three failure modes we studied in the integrated sandwich design.
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