Computation of effective thermal conductivity of carbon fiber felts through numerical simulation and development of reduced order models

One of the major drivers of heat transfer within a spacecraft heatshield is the effective thermal conductivity of the thermal protection material. For carbon-based thermal protection materials, this quantity is strongly connected to the thermal conductivity of the carbon fiber felt (preform) used to create the final composite. Use of effective thermal conductivity data from experiments in volume averaged numerical models is complex because: i) they are carried out in different media than its actual application, ii) changes on geometry or material properties require repetition of the experiments. Simulation of effective thermal conductivity using high fidelity simulations can overcome those problems. In this work, we propose a synthetic model based of the carbon fiber felt of CALCARB (R) using Porous Microstructure Analysis (PuMA) software. This model is first validated with available experimental data and applied to new experiments and to study the effect of pyrolysis gas mixture on the effective property. Simplified correlations are then developed, which predict with remarkable accuracy the effective thermal conductivity of the CALCARB (R) material. The developed model can be used to explore and predict effective conductivity at different conditions. In addition, the simplified algebraic correlations can be easily implemented in volume averaged material response codes to account in a more appropriate way for the effect of the percolating pyrolysis/atmospheric gas.