Communications in Mathematical Sciences

Volume 15 (2017)

Number 4

Homogenization for chemical vapor infiltration process

Pages: 1021 – 1040

DOI: http://dx.doi.org/10.4310/CMS.2017.v15.n4.a5

Authors

Changjuan Zhang (School of Mathematical Sciences, Soochow University, Suzhou, China)

Yun Bai (School of Computer and Communication Sciences, École Polytechnique Fédérale de Lausanne, Switzerland)

Shixin Xu (School of Mathematical Sciences, Soochow University, Suzhou, China)

Xingye Yue (School of Mathematical Sciences, Soochow University, Suzhou, China)

Abstract

Multi-scale modeling and numerical simulations of the isothermal chemical vapor infiltration (CVI) process for the fabrication of carbon fiber reinforced silicon carbide (C/SiC) composites were presented in [Bai, Yue and Zeng, Commun. Comput. Phys., 7(3):597–612, 2010]. The homogenization theory, which played a fundamental role in the multi-scale algorithm, will be rigorously established in this paper. The governing system, which is a multi-scale reaction-diffusion equation, is different in the two stages of CVI process, so we will consider the homogenization for the two stages respectively. One of the main features is that the reaction only occurs on the surface of fiber, so it behaves as a singular surface source. The other feature is that in the second stage of the process when the micro pores inside the fiber bundles are all closed, the diffusion only occurs in the macro pores between fiber bundles and we face up with a problem in a locally periodic perforated domain.

Keywords

CVI process, multi-scale model, homogenization, surface reaction, locally periodic perforation

2010 Mathematics Subject Classification

35B27, 35J25

Full Text (PDF format)

Published 16 May 2017