OXIMAP is a numerical (FEA-based) solution tool capable of calculating the carbon fiber and fiber coating oxidation patterns within any arbitrarily shaped carbon silicon carbide composite structure as a function of time, temperature, and the environmental oxygen partial pressure. The mathematical formulation is derived from the mechanics of the flow of ideal gases through a chemically reacting, porous solid. The result of the formulation is a set of two coupled, non-linear differential equations written in terms of the oxidant and oxide partial pressures. The differential equations are solved simultaneously to obtain the partial vapor pressures of the oxidant and oxides as a function of the spatial location and time. The local rate of carbon oxidation is determined at each time step using the map of the local oxidant partial vapor pressure along with the Arrhenius rate equation. The non-linear differential equations are cast into matrix equations by applying the Bubnov- Galerkin weighted residual finite-element method, allowing for the solution of the differential equations numerically.
The mathematical formulation and the numerical solution allow for two types of diffusion: a pressure gradient-driven diffusion (Darcy) and a mass concentration gradient-driven diffusion (Fick). The Darcian flow is governed by the material permeability, and the Fickian flow is governed by the areal porosity and gas diffusivity. OXIMAP allows for orthotropic transport properties, so that the permeability and areal porosity in the two perpendicular directions can have different values. The input into OXIMAP includes: the temperature history, the finite-element nodal coordinates and element connectivity, the material permeability and areal porosity in the principal material directions, the gas viscosity, the volumetric porosity, the initial carbon fiber volume fraction and the initial carbon fiber coating volume fraction, the carbon fiber and carbon fiber coating area fractions, the stoichiometric constants and the Arrhenius constants for the oxidation reaction, and the oxygen and oxide vapor-pressure boundary conditions.
This program was written by Roy M. Sullivan of Glenn Research Center.
Inquiries concerning rights for the commercial use of this invention should be addressed to NASA Glenn Research Center, Innovative Partnerships Office, Attn: Steve Fedor, Mail Stop 4–8, 21000 Brookpark Road, Cleveland, Ohio 44135. Refer to LEW-18212-1.