Integración de ecuaciones diferenciales rígidas de valor de contorno en problemas de combustión con cinética de reacción detallada

Abstract

Detailed models of the flat, laminar, opposed jet diffusion flame involve the solution of the momentu, energy and species conservation equations coupled with stiff chemical kinetics. The problem has self similar solutions and can be solved through numerical integration of a set of second order, stiff, boundary valued, ordinary differential equations, each with a regular first order turning point arising from convection. Use of standard finite difference discretization (in the spatial domain) and expansion of the reaction rate source terms in a Taylor series abaut the backward iteration (in the temporal domain), lead to a matrix equation in which the coefficient matrix is a very large block tridiagonal matrix. It is also a band matrix and solution is obtained through LU descomposition. Instabiiities originating from the unevenly spaced grid and from diffusion of numerical errors towards the boundaries forced the use of a large number of equally spaced grid points which contrained the program to solution of relatively small kinetic problems (due to core storage limitations). This dilemma was resolved by developing a modified central difference discretization which assumes that the solution at a mesh point is given by the sum of exponentials. Using the new technique it was possible to obtain the solution of the opposed jet problem with 150 reactions and 70 species on the available CYBER 175 computer.

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