Modeling of isobaric–isothermal chemical vapor infiltration: effects of reactor control parameters on a densification

Reuge, Nicolas; Vignoles, Gérard L.

doi:10.1016/j.jmatprotec.2004.07.064

Cited by 34 publications

(23 citation statements)

References 26 publications

(31 reference statements)

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“…Low pressures are also common in CVI, since it is a convenient way to reduce the Thiele modulus ; accordingly, the Knudsen number is usually not negligible. A large amount of modelling efforts have been made (Starr and Smith, 1990;Ofori and Sotirchos, 1996a;Reuge and Vignoles, 2005;Vignoles, 2006), featuring or not Knudsen transport, but few has been said about thermal transpiration in these works.…”

Section: Latinmentioning

confidence: 99%

Rarefied Pure Gas Transport in Non-isothermal Porous Media: Validation and Tests of the Model

et al. 2008

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Abstract. Viscous flow, effusion, and thermal transpiration are the main gas transport modalities for a rarefied gas in a macro-porous medium. They have been well quantified only in the case of simple geometries. This paper presents a numerical method based on the homogenization of kinetic equations producing effective transport properties (permeability, Knudsen diffusivity, thermal transpiration ratio) in any porous medium sample, as described e. g.by a digitized 3D image. The homogenization procedure -neglecting the effect of gas density gradients on heat transfer through the solid -leads to closure problems in R 6 for the obtention of effective properties ; they are then simplified using a Galerkin method based on a 21-element basis set. The kinetic equations are then discretized in R 3 space with a finite-volume scheme. The method is validated against experimental data in the case of a closed test tube. It shows to be coherent with past approaches of thermal transpiration. Then, it is applied to several 3D images of increasing complexity. Another validation is brought by comparison with other distinct numerical approaches for the evaluation of the Darcian permeability tensor and of the Knudsen diffusion tensor. Results show that thermal transpiration has to be described by an effective transport tensor which is distinct from the other tensors.

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Section: Latinmentioning

confidence: 99%

Rarefied Pure Gas Transport in Non-isothermal Porous Media: Validation and Tests of the Model

et al. 2008

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“…CVI is a very slow and thus expensive technique; consequently, there is a huge need in process optimisation based on detailed mathematical modelling and precise and efficient numerical simulations. Many different variants of CVI exist: isothermal (Reuge and Vignoles, 2005;Sotirchos, 1991;Zhang and Hüttinger, 2001;Jin and Wang, 2000, 2003McAllister and Wolf, 1991;Chung et al, 1991), thermal gradient CVI (Tago et al, 2001) forced flow CVI (Probst et al, 1999;Roman et al, 1995;microwave heating, Morell et al, 1993;Midha and Economou, 1998), etc. In this work we concentrate on the isothermal isobaric CVI of pyrolytic carbon since experimental data are available for this process.…”

Section: Introductionmentioning

confidence: 99%

“…The processes in the gas phase are often assumed steady-state (Middleman, 1989;Reuge and Vignoles, 2005;Zhang and Hüttinger, 2001;McAllister and Wolf, 1991;Chung et al, 1991;Tago et al, 2001;Hou et al, 1999) which is critical since the temporal evolution of the geometry due to deposition influences the transport mechanisms within this phase. At a first glance, the values of the so-called condensation ratio (the ratio of the density and the mass of the solid product and the concentration of the gas-phase species) being superior to 10 4 might seem to support the assumption of a steady-gas phase by many authors.…”

Section: Introductionmentioning

confidence: 99%

“…The question of complete infiltration of the given porous substrate is thus of significant importance. In many studies, porosities are calculated (Reuge and Vignoles, 2005;McAllister and Wolf, 1991;Tago et al, 2001;Morell et al, 1993;Midha and Economou, 1998;Hou et al, 1999;Kulik et al, 2004), but the position of the interface is not tracked. Consequently, the question whether the given substrate is completely infiltrated or not remains open.…”

Section: Introductionmentioning

confidence: 99%

“…More complicated geometries have also been considered: a network of uniformly sized cylindrical capillaries (Sotirchos, 1991), a system of plies consisting of woven tows of bundles of filaments (Chung et al, 1991), and a random packing of fully overlapping capillaries (Reuge and Vignoles, 2005;Morell et al, 1993), and a random pore model (McAllister and Wolf, 1991). The evolution of such complex geometries is mostly governed in dependence of the porosity of the preform.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Modelling chemical vapour infiltration of pyrolytic carbon as moving boundary problem

Langhoff¹,

Schnack²

2008

Chemical Engineering Science

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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.

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Isothermal Chemical Vapor Infiltration Modeling by Random Walks in CMT 3D Images at Two Scales

Vignoles

Szelengowicz

Ros

et al. 2010

Mechanical Properties and Performance of Engineering Ceramics and Composites V

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International audienceThe production cycle of high-quality Ceramic-Matrix Composites (CMCs) often involves interphase or matrix deposition by Chemical Vapor Infiltration (CVI). This costly step has motivated many modeling approaches, in order to provide guidelines for process control and optimization. In this context, numerical tools for direct modeling of isothermal, isobaric CVI in complex 3D images of the composite architecture, acquired e.g. by X-ray Computerized Microtomography (CMT) have been developed. To address inter- and intra-bundle length scales inherent to a composite with a woven textile reinforcement, a numerical strategy has been set up, based on two numerical tools. They solve diffusion-reaction equations and handle simultaneously the progressive evolution of the porous structure. They involve distinct random walk methods and image handling routines. The small-scale program uses Pearson random walks simulating rarefied gas transport; the fluid/solid interface is explicitly represented as a set of triangles through a Simplified Marching Cube approach. Direct simulation of CVI in intra-bundle pores is possible with such a tool. Effective laws for the evolution of porosity, surface and transport properties as infiltration proceeds are inferred from these simulations by averaging and are considered as inputs for the next modelling step. The large-scale solver uses Brownian motion simulation; the porous medium is considered as a continuum with locally heterogeneous and anisotropic diffusivities, and the deposition reaction is handled through a survival probability computation. Simulation of the infiltration of a whole composite material part is possible with this program. Validation of these tools on test cases, as well as some examples on actual materials, are shown and discussed

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Modeling of isobaric–isothermal chemical vapor infiltration: effects of reactor control parameters on a densification

Cited by 34 publications

References 26 publications

Rarefied Pure Gas Transport in Non-isothermal Porous Media: Validation and Tests of the Model

Rarefied Pure Gas Transport in Non-isothermal Porous Media: Validation and Tests of the Model

Modelling chemical vapour infiltration of pyrolytic carbon as moving boundary problem

Isothermal Chemical Vapor Infiltration Modeling by Random Walks in CMT 3D Images at Two Scales

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