TY - JOUR

T1 - An integral method for mixing, chemical reactions, and extinction in unsteady strained diffusion layers

AU - Tryggvason, Grétar

AU - Dahm, Werner J.A.

N1 - Funding Information:
We would like to acknowledge useful discussions with Professor Robert Krasny in the Applied Mathematics group at Michigan, as well as the help of Mr.. Chester Chang in checking some of the calculations and in preparation of the figures. The work reported here was supported, in part, by the Gas Research Institute (GRI) under Contract Nos. 5087-260-1443 and 5088-260-1692, and by the Air Force Office of Scientific Research (AFOSR) under Grant No. AFOSR-89-0541.

PY - 1991/2

Y1 - 1991/2

N2 - An integral method is presented for determining the evolution of molecular mixing, finite rate chemical reactions, and local extinction in diffusion layers under the effect of an unsteady strain rate. The partial differential equations governing the reactant, product, and temperature profiles are used to derive ordinary differential equations governing the evolution of moments for the product and temperature profiles and for the reactant gradient profiles. The actual profiles enter these equations only through integral moments resulting from the reaction rate terms (referred to as "reaction integrals"). As a consequence, it is possible to accurately track the evolution of the profile moments, and thereby determine global properties of the layer such as burning rates and extinction conditions, using remarkably simple representations for the actual profiles to evaluate the reaction integrals. Here these profile shapes are specified as self-similar families of curves parameterized by just a few degrees of freedom, which then evolve from the moment equations. Results for combustion in isolated strained diffusion layers, as well as for consumption of a burning fuel strip, are generally within a few percent of the results from finite difference solutions of the full equations.

AB - An integral method is presented for determining the evolution of molecular mixing, finite rate chemical reactions, and local extinction in diffusion layers under the effect of an unsteady strain rate. The partial differential equations governing the reactant, product, and temperature profiles are used to derive ordinary differential equations governing the evolution of moments for the product and temperature profiles and for the reactant gradient profiles. The actual profiles enter these equations only through integral moments resulting from the reaction rate terms (referred to as "reaction integrals"). As a consequence, it is possible to accurately track the evolution of the profile moments, and thereby determine global properties of the layer such as burning rates and extinction conditions, using remarkably simple representations for the actual profiles to evaluate the reaction integrals. Here these profile shapes are specified as self-similar families of curves parameterized by just a few degrees of freedom, which then evolve from the moment equations. Results for combustion in isolated strained diffusion layers, as well as for consumption of a burning fuel strip, are generally within a few percent of the results from finite difference solutions of the full equations.

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U2 - 10.1016/0010-2180(91)90069-N

DO - 10.1016/0010-2180(91)90069-N

M3 - Article

AN - SCOPUS:0025759872

VL - 83

SP - 207

EP - 220

JO - Combustion and Flame

JF - Combustion and Flame

SN - 0010-2180

IS - 3-4

ER -