A 3D finite-difference model for the effective thermal conductivity of thermal barrier coatings produced by plasma spraying

Abstract

Effective properties of thermal barrier coatings produced by plasma spraying can be quantified via different measurement techniques. Numerical modeling applied on 2D cross-sectional images of the coating represents an alternative method often applied in the literature. In the present study, a three-dimensional finite-difference-based model was developed for analyzing the heat transfer mechanisms through a porous structure and also for investigating the differences between 2D and 3D results. An artificial pore network was first specially generated from the microstructural information measured for a real coating cross-sectional image captured by scanning electron microscopy. The computed effective thermal conductivity based on 2D calculations performed on cross-sectional images of the 3D artificial structure was found to be nearly the same compared with the thermal conductivity evaluated from cross-sectional images of the real coating. In a second time, the 3D computed value of the effective thermal conductivity was found to be in better agreement with the measured value, in comparison with that computed on the basis of 2D cross-sectional images. In addition, the effective thermal conductivity was also evaluated with two different packages based on the finite element method (namely OOF2 and ANSYS): the computed thermal conductivity derived with these tools was found to be somewhat larger than the one obtained with the present FD model. Finally, the thermal conductivity computed for different artificial pore networks were compared with those obtained from 2D computations performed on their cross-sections, revealing the differences between 2D and 3D image-based modeling: a correlation was then derived between the results computed with 3D and 2D models.