Calculation of the Thermal Conductivity and Gas Permeability in a Uniaxial Bundle of Fibers

Abstract

A model of the local microstructure of a bundle of fibers is simulated and used as the basis for calculations of transport properties. This, in turn, can be used in a macroscopic model of the chemical vapor infiltration process. An expanding/overlapping circle representation of the microstructure simulates the deposition of matrix in a uniaxial bundle of fibers. An iterative heat conduction algorithm is used to calculate the transverse thermal conductivity based on the thermal conductivities of the solid and gas phases. The permeability of gas through the microstructure is calculated for flow both parallel and transverse to overlapping cylinders using a Stokes equation and assuming a Darcy's law behavior. Both the simulations of the microstructure and associated calculations of the transport properties compare favorably with experimental data. Darcy's law for the behavior of gas in a bundle of fibers is shown to be valid for gas pressures of 5-13 kPa.

A stokes permeability solver for three-dimensional porous media

“…Once the finite difference solution converges sufficiently, the permeability, k, of the porous medium is calculated by volume averaging the local fluid velocity (in the direction of the flow) and applying the Darcy equation: k AP n L ( 6 ) where u is the average fluid velocity in the direction of the flow (x-direction) for the porous media and L is the length of the sample porous medium across which there is an applied pressure difference of AP [2]. For a given porous medium, three separate runs of the computer codes may be conducted to determine the (different) permeabilities for flow in the x, y, and z directions, by simply transposing the indices in the (three) nested loops used to read in the starting microstructure.…”

“…printf("13) Read in microstructure from one byte per pixel file \n"); printf("14) Read in microstructure from one integer (pixel) per line file \n"); 85 lvzj (j )=j iand(j ishft( i vzspot,-9 ),mask) C No neighbors in y and two neighbors (-1,+ 1) in z direction do 600 k=xtc(5)+l,xtc (6) kk=lvxk(k) One neighbor (-1) in y and one (+1) in z direction do 1400 k=xtc(13)+l,xtc (14) kk=lvxk(k) 502 values(ii,jj,kk,2)=values(ii,jj,kk,2 C No neighbors in x and two neighbors (-1,+1) in z direction do 602 k=ytc(5)+l,ytc (6) kk=lvyk(k)…”

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

“…[18][19][20][21][22][23] In a real preform, there are two classes of pores: micropores within fiber bundles, measuring several micrometers, and macropores between the bundles, measuring up to hundreds of micrometers. Compared with the micropores, the structural and gas transport properties of which are well described by the structures of unidirectional fibers, [20][21][22][24][25][26] the macropores show a quite different structural characteristic and their structural and gas transport properties vary among different fiber architectures. In this study, the macropore structure evolution of a 0°/90°plain woven composite is taken as research subject, because the macropore structure of this fabric style is determined clearly, but its structural and gas transport properties have still not been thoroughly studied yet.…”

Robust Numerical Simulation of Porosity Evolution in Chemical Vapor Infiltration

“…The computational difficulty lies in the fact that the pore microstructure may change topology and inaccessible pores may form during the process. Most existing models avoid modeling pore microstructure by modeling the macroscopic quantities, such as porosity, gas permeability, and surface area per unit volume [3,22,23], which are quantities dependent on the pore microstructure. Some models assume that inaccessible pores do not take place, which is only valid for the initial stage of the process [21].…”