On the Numerical Scheme to Solve a Realistic Chemical Vapor Infiltration Reactor Model

Integration Scheme ◽

Algebraic Equations ◽

Splitting Algorithm ◽

Reactor Model ◽

We describe the general mathematical model as well as the numerical integration procedure arising in modeling a realistic chemical vapor infiltration process. The numerical solution of the model ultimately leads to the solution of a large system of stiff differential algebraic equations. An operator splitting algorithm is employed to overcome the stiffness associated with chemical reactions, whereas a projection method is employed to overcome the difficulty arising from having to solve a large coupled system for the velocity and pressure fields. The resulting mathematical model and the numerical integration scheme are used to explore temperature, velocity, and concentration fields inside a chemical vapor infiltration reactor used in the manufacturing of aircraft brakes.

Mathematical Model for Chemical Vapor Infiltration in a Microwave-Heated Preform

Journal of the American Ceramic Society ◽

10.1111/j.1151-2916.1993.tb08313.x ◽

1993 ◽

Vol 76 (8) ◽

pp. 1924-1929 ◽

Cited By ~ 16

Author(s):

Deepak ◽

James W. Evans

Keyword(s):

Mathematical Model ◽

Chemical Vapor ◽

The interaction of chemical kinetics and diffusion in the dynamics of chemical vapor infiltration

Journal of Materials Research ◽

10.1557/jmr.1989.1515 ◽

1989 ◽

Vol 4 (6) ◽

pp. 1515-1524 ◽

Cited By ~ 42

Author(s):

Stanley Middleman

Keyword(s):

Gas Phase ◽

Film Growth ◽

Classical Model ◽

Chemical Vapor ◽

Reactor Model ◽

Cylindrical Pore ◽

Complex Chemistry ◽

And Diffusion ◽

The classical model of Chemical Vapor Infiltration (CVI) treats diffusion and surface reaction in a representative cylindrical pore. Two significant modifications to that approach are presented herein. One accounts for more complex chemistry by allowing for both gas-phase and surface reactions which lead to film growth. The other couples the pore model to a reactor model for the region external to the porous preform. The results demonstrate that it is possible to select chemical schemes that yield densification from the interior to the exterior of the preform, thus avoiding premature trapping of interior voids.

A Mathematical Model for Chemical Vapor Infiltration with Volume Heating

Journal of The Electrochemical Society ◽

10.1149/1.2069194 ◽

1992 ◽

Vol 139 (1) ◽

pp. 328-336 ◽

Cited By ~ 13

Author(s):

José I. Morell ◽

Demetre J. Economou ◽

Neal R. Amundson

Keyword(s):

Mathematical Model ◽

Chemical Vapor ◽

A mathematical model for chemical vapor infiltration with microwave heating and external cooling

Journal of Materials Research ◽

10.1557/jmr.1991.0810 ◽

1991 ◽

Vol 6 (4) ◽

pp. 810-818 ◽

Cited By ~ 25

Author(s):

Deepak Gupta ◽

James W. Evans

Keyword(s):

Mathematical Model ◽

Microwave Heating ◽

Microwave Power ◽

Heterogeneous Reaction ◽

Chemical Vapor ◽

Temperature Profiles ◽

External Cooling ◽

Structure Equations ◽

A mathematical model has been used to compute temperature profiles in ceramic preforms that are heated by microwaves. The temperature profiles were then input to a second part of the model describing chemical vapor infiltration of the preform, that is the diffusion of gaseous reactants, heterogeneous reaction, and evolution of the pore structure. Equations were solved numerically for parameters corresponding to the infiltration of SiC preforms by pyrolysis of trichloromethylsilane. While based on some simplifications, the model leads to the conclusion that infiltration proceeds more rapidly, and to a greater extent, with microwave heating/external cooling than in isothermal infiltration. The model suggests that infiltration might be optimized by manipulation of microwave power and external cooling. The computed extent of infiltration is seen to be very sensitive to the initial pore size.