Abstract
Multiple coupled chemical reactions occurring within strained diffusion layers are key to a wide range of reactive flow problems. An integral approach is presented here to allow calculations of global properties of such reactive layers for complex multistep chemical kinetics and time-varying strain rates. The infinite-degree-of-freedom partial differential equations (PDEs) governing the dynamics of the species concentration profiles for reactants, intermediates, and products as well as the temperature are projected onto a set of ordinary differential equations having just a few degrees of freedom for the evolution of integral moments of these profiles. The presence of multistep reaction kinetics leads to a set of highly coupled nonlinear moment equations. Numerical solutions are presented for four-step methane-air kinetics coupled with thermal nitric oxide kinetics and are compared with direct solutions of the original PDEs. Some properties and numerical illustrations of key features of the internal layer structure and global flame properties, including the extinction phenomenon characteristic of large Zel'dovich number reaction kinetics, are discussed. The method presented brings comparatively detailed parametric studies of such problems within reach of rather modest computational requirements.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 1039-1059 |
| Number of pages | 21 |
| Journal | SIAM Journal on Applied Mathematics |
| Volume | 56 |
| Issue number | 4 |
| State | Published - Aug 1996 |
| Externally published | Yes |
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Keywords
- Combustion
- Global properties
- Integral methods
- Reacting flows
ASJC Scopus subject areas
- Mathematics(all)
- Applied Mathematics
Cite this
Integral method solution of time-dependent strained diffusion-reaction layers with multistep kinetics. / Dahm, Werner; Tryggvason, Grétar; Zhuang, Mei.
In: SIAM Journal on Applied Mathematics, Vol. 56, No. 4, 08.1996, p. 1039-1059.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Integral method solution of time-dependent strained diffusion-reaction layers with multistep kinetics
AU - Dahm, Werner
AU - Tryggvason, Grétar
AU - Zhuang, Mei
PY - 1996/8
Y1 - 1996/8
N2 - Multiple coupled chemical reactions occurring within strained diffusion layers are key to a wide range of reactive flow problems. An integral approach is presented here to allow calculations of global properties of such reactive layers for complex multistep chemical kinetics and time-varying strain rates. The infinite-degree-of-freedom partial differential equations (PDEs) governing the dynamics of the species concentration profiles for reactants, intermediates, and products as well as the temperature are projected onto a set of ordinary differential equations having just a few degrees of freedom for the evolution of integral moments of these profiles. The presence of multistep reaction kinetics leads to a set of highly coupled nonlinear moment equations. Numerical solutions are presented for four-step methane-air kinetics coupled with thermal nitric oxide kinetics and are compared with direct solutions of the original PDEs. Some properties and numerical illustrations of key features of the internal layer structure and global flame properties, including the extinction phenomenon characteristic of large Zel'dovich number reaction kinetics, are discussed. The method presented brings comparatively detailed parametric studies of such problems within reach of rather modest computational requirements.
AB - Multiple coupled chemical reactions occurring within strained diffusion layers are key to a wide range of reactive flow problems. An integral approach is presented here to allow calculations of global properties of such reactive layers for complex multistep chemical kinetics and time-varying strain rates. The infinite-degree-of-freedom partial differential equations (PDEs) governing the dynamics of the species concentration profiles for reactants, intermediates, and products as well as the temperature are projected onto a set of ordinary differential equations having just a few degrees of freedom for the evolution of integral moments of these profiles. The presence of multistep reaction kinetics leads to a set of highly coupled nonlinear moment equations. Numerical solutions are presented for four-step methane-air kinetics coupled with thermal nitric oxide kinetics and are compared with direct solutions of the original PDEs. Some properties and numerical illustrations of key features of the internal layer structure and global flame properties, including the extinction phenomenon characteristic of large Zel'dovich number reaction kinetics, are discussed. The method presented brings comparatively detailed parametric studies of such problems within reach of rather modest computational requirements.
KW - Combustion
KW - Global properties
KW - Integral methods
KW - Reacting flows
UR - http://www.scopus.com/inward/record.url?scp=0030214967&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0030214967&partnerID=8YFLogxK
M3 - Article
VL - 56
SP - 1039
EP - 1059
JO - SIAM Journal on Applied Mathematics
JF - SIAM Journal on Applied Mathematics
SN - 0036-1399
IS - 4
ER -