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

Grétar Tryggvason, Werner Dahm

Research output: Contribution to journalArticle

15 Citations (Scopus)

Abstract

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.

Original languageEnglish (US)
Pages (from-to)207-220
Number of pages14
JournalCombustion and Flame
Volume83
Issue number3-4
DOIs
StatePublished - 1991
Externally publishedYes

Fingerprint

Chemical reactions
chemical reactions
extinction
profiles
moments
Ordinary differential equations
Partial differential equations
Reaction rates
Strain rate
temperature profiles
Temperature
burning rate
products
partial differential equations
strain rate
strip
reaction kinetics
differential equations
degrees of freedom
gradients

ASJC Scopus subject areas

  • Energy Engineering and Power Technology
  • Fuel Technology
  • Mechanical Engineering

Cite this

An integral method for mixing, chemical reactions, and extinction in unsteady strained diffusion layers. / Tryggvason, Grétar; Dahm, Werner.

In: Combustion and Flame, Vol. 83, No. 3-4, 1991, p. 207-220.

Research output: Contribution to journalArticle

@article{78bf2bd69f8b41019bd764623692d7ba,
title = "An integral method for mixing, chemical reactions, and extinction in unsteady strained diffusion layers",
abstract = "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.",
author = "Gr{\'e}tar Tryggvason and Werner Dahm",
year = "1991",
doi = "10.1016/0010-2180(91)90069-N",
language = "English (US)",
volume = "83",
pages = "207--220",
journal = "Combustion and Flame",
issn = "0010-2180",
publisher = "Elsevier Inc.",
number = "3-4",

}

TY - JOUR

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

AU - Tryggvason, Grétar

AU - Dahm, Werner

PY - 1991

Y1 - 1991

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.

UR - http://www.scopus.com/inward/record.url?scp=0025759872&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0025759872&partnerID=8YFLogxK

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 -