Multiscale Modeling And Front Tracking For Chemical Vapor Inltration Process

In this thesis, we focus on the numerical simulation to the Chemical VaporInfiltration process (CVI process) during which the Silicon Carbide Composite Ce-ramic materials are reinforced by carbon fibers. Based on multi-scale modeling, anew model is proposed to probe into the residual pore distribution in the statisti-cal sense in materials with non-periodic structure and property of scale separation.Since 1990, by constructing a series of equations on only single scale and computinglocal porosity in order to describe the change of pore structure in preform, classicalCVI models have provided a way of tracking CVI process. Nevertheless, inherentdeficiencies in these models bring obvious deviations from theoretical and experi-mental ones. In 2008, Yun Bai, Xingyue Yue and Qingfeng Zeng proposed a revisedmulti-scale model, which divided the preform into two scales and then set up microand macro models respectively. In the meantime, this revised model successfullyworked out singularity problems existed in classical ones and has been proved to beconvergent.Note that the revised model chie?y consider materials with periodic/local pe-riodic structure, while in this thesis we turn to study case of non-periodic structureduring post-CVI process, which by our definition refers to the stage of SiC depo-sition on surface of fibers only. Like what was done in the revised model, bothmicro and macro models are introduced. In the micro level, reconstruction of microreaction-di?usion concentration equation in each sample was done, we then couplethe micro concentration equation with level set equation by virtue of a relationshipbetween micro concentration and velocity in normal direction on fiber fronts. LevelSet function is exploited not only to implicitly capture evolution of fronts but alsoestimate micro porosity and e?ective reaction area. While in the macro level, underthe framework of Heterogenous Multiscale Method (HMM), we obtain macro con-centration equation and solve for macro concentration. Moreover, overall porosityon entire computational domain is also computed. We then propose an algorithmto combine micro and macro models in order to depict the time-evolution processof whole numerical simulation. Meanwhile, numerical examples and related analysisare provided in later chapter of the thesis.