Modelling chemical vapour infiltration of pyrolytic carbon as moving boundary problem

Abstract

Chemical vapour infiltration (CVI) of pyrolytic carbon is described as a moving boundary problem to determine the evolution of the pyrolytic carbon layer in space and time. Derived from real geometries, a one-dimensional single pore model is developed yielding a nonlinear coupled system of partial differential equations for the concentrations of the gas phase species and the height of the carbon layer within cylindrical pores. The evolution of the moving boundary of the gas phase domain is governed by a non-differentiable minimisation condition. Additionally, a CVI reactor model to describe the infiltration of several cylindrical pores within a porous substrate is presented on the basis of the single pore model. Both models are new in that they combine the following features: (i) derivation of the equations rigorously taking into account the temporal change of the gas phase, (ii) the explicit construction of the position of the gas--solid interface, (iii) the influence of the local curvature of the carbon layer on its growth velocity, and (iv) modelling of chemical kinetics using a reduced reaction scheme with intermediate gas phase species and several surface reactions. The models are solved numerically using a staggered strongly decoupled scheme with implicit Euler time integration. The results allow the identification of process conditions and geometries for which a complete infiltration of the pores or the whole substrate is achieved. For low pressures, the predictions of the CVI reactor model are in agreement with the available experimental data.

Network model for the evolution of the pore structure of silicon-carbide membranes during their fabrication

“…Each time the solution of the governing equations in the network is obtained, the change in the size of all the pores is computed through Eq. (17), and the pores' sizes are updated. Then, the solution of the governing equations in the new network configuration (with shrunk pores) is obtained, the pores' sizes are updated, and so on.…”

“…One approach is based on the classical equations of transport [11][12][13]16,17]. For example, Langhoff and Schnak [17] modeled the CVI of pyrolytic carbon as a moving boundary problem, in order to determine the evolution of the structure of the pyrolytic carbon layer, using a onedimensional continuum model.…”

“…One approach is based on the classical equations of transport [11][12][13]16,17]. For example, Langhoff and Schnak [17] modeled the CVI of pyrolytic carbon as a moving boundary problem, in order to determine the evolution of the structure of the pyrolytic carbon layer, using a onedimensional continuum model. Such an approach can neither take into account the effect of the morphology of the pore space, i.e., its pore size distribution (PSD) and pore interconnectivity, on the transport of the gases, nor can it be predictive quantitatively, unless several adjustable parameters are introduced into the model.…”

Modeling of Pore Structure Evolution Between Bundles of Plain Woven Fabrics During Chemical Vapor Infiltration Process: The Influence of Preform Geometry

“…To our knowledge, there are mainly three ways to estimate the effective diffusivity in the CVI modeling. The first one 5,[33][34][35][36] is simplifying the porous media as straight cylindrical pores, so the inhibition of pore wall to the gas diffusion is not considered. The second one 24,37,38 is approximating the media as the capillary Bethe lattices.…”

Simulation of Chemical Vapor Infiltration and Deposition Based on 3D Images: A Local Scale Approach

“…The research focus has moved to the study of more complicated networks, multi‐component mass transport, and the effects of evolving pore structure on densification 14, 15. Over the past decade, optimizing CVI has been accomplished through global simulation taking reaction kinetics into account and highlighting the importance of flow rate 16–19…”