Experimental investigation and tomography analysis of Darcy-Forchheimer flows in thermal protection systems

Abstract

n thermal protection systems (TPS), Darcy’s law or Darcy-Forchheimer’s law is employed to model the pyrolysis gas flow within the anisotropic porous ablator depending on the flow regime considered. A key challenge with using these laws is first, the knowledge of the validity domain of each flow regime in terms of a critical Reynolds number (������ ). Secondly, the lack of data on macroscopic properties, namely, the permeability and Forchheimer tensors is particularly challenging for the relevance of the models. The objective of this work is to contribute to overcoming these challenges by performing experimental and X-ray tomographic image-based characterization of Calcarb, a commercial carbon preform used for manufacturing TPS. For this purpose, fluid flow within Calcarb was studied experimentally in the Through-Thickness (TT) and the In-Plane (IP) directions for Reynolds numbers of 0.05 to 10.46 -representative of the TPS application. Tomography image-based micro-scale simulations, involving the direct resolution of the Navier–Stokes equations under both flow regimes, were also performed. Experimental results exhibit the anisotropic nature of Calcarb, namely through ������ values, corresponding to the Darcy flow regime limit, slightly different in the two directions (������ of 0.31 and 0.43) with measured permeability values of 1.248 × 10−10 m2 and 1.615 × 10−10 m2 for TT and IP directions respectively. In the Forchheimer regime, experimental Forchheimer coefficients �� were 2.0010 × 105 m−1 (TT) and 1.4948 × 105 m−1 (IP). During the simulation process, a numerical strategy was defined to obtain the permeability tensor yielding values within 8% of the experimental ones. The comparison of experimental results vs simulation results in the Forchheimer regime was performed through the analysis of the pressure gradients as functions of ���� in the ��, ��, and �� directions. The numerical estimations were compared successfully with experimental measurements, with a discrepancy of 5.2%, for ���� values up to 2.4