### Abstract

In this work we re-examine the counterflow diffusion flame problem focusing in particular on the flame–flow interactions due to thermal expansion and its influence on various flame properties such as flame location, flame temperature, reactant leakage and extinction conditions. The analysis follows two different procedures: an asymptotic approximation for large activation energy chemical reactions, and a direct numerical approach. The asymptotic treatment follows the general theory of Cheatham and Matalon, which consists of a free-boundary problem with jump conditions across the surface representing the reaction sheet, and is well suited for variable-density flows and for mixtures with non-unity and distinct Lewis numbers for the fuel and oxidiser. Due to density variations, the species and energy transport equations are coupled to the Navier–Stokes equations and the problem does not possess an analytical solution. We thus propose and implement a methodology for solving the free-boundary problem numerically. Results based on the asymptotic approximation are then verified against those obtained from the ‘exact’ numerical integration of the governing equations, comparing predictions of the various flame properties.

Original language | English (US) |
---|---|

Pages (from-to) | 1-28 |

Number of pages | 28 |

Journal | Combustion Theory and Modelling |

DOIs | |

State | Accepted/In press - Apr 1 2018 |

### Fingerprint

### Keywords

- counterflow diffusion flames
- extinction
- flow displacement
- large activation energy asymptotics
- thermal expansion

### ASJC Scopus subject areas

- Chemistry(all)
- Chemical Engineering(all)
- Modeling and Simulation
- Fuel Technology
- Energy Engineering and Power Technology
- Physics and Astronomy(all)

### Cite this

*Combustion Theory and Modelling*, 1-28. https://doi.org/10.1080/13647830.2018.1441444

**Counterflow diffusion flames : effects of thermal expansion and non-unity Lewis numbers.** / Koundinyan, Sushilkumar P.; Matalon, Moshe; Stewart, Donald Scott.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - Counterflow diffusion flames

T2 - effects of thermal expansion and non-unity Lewis numbers

AU - Koundinyan, Sushilkumar P.

AU - Matalon, Moshe

AU - Stewart, Donald Scott

PY - 2018/4/1

Y1 - 2018/4/1

N2 - In this work we re-examine the counterflow diffusion flame problem focusing in particular on the flame–flow interactions due to thermal expansion and its influence on various flame properties such as flame location, flame temperature, reactant leakage and extinction conditions. The analysis follows two different procedures: an asymptotic approximation for large activation energy chemical reactions, and a direct numerical approach. The asymptotic treatment follows the general theory of Cheatham and Matalon, which consists of a free-boundary problem with jump conditions across the surface representing the reaction sheet, and is well suited for variable-density flows and for mixtures with non-unity and distinct Lewis numbers for the fuel and oxidiser. Due to density variations, the species and energy transport equations are coupled to the Navier–Stokes equations and the problem does not possess an analytical solution. We thus propose and implement a methodology for solving the free-boundary problem numerically. Results based on the asymptotic approximation are then verified against those obtained from the ‘exact’ numerical integration of the governing equations, comparing predictions of the various flame properties.

AB - In this work we re-examine the counterflow diffusion flame problem focusing in particular on the flame–flow interactions due to thermal expansion and its influence on various flame properties such as flame location, flame temperature, reactant leakage and extinction conditions. The analysis follows two different procedures: an asymptotic approximation for large activation energy chemical reactions, and a direct numerical approach. The asymptotic treatment follows the general theory of Cheatham and Matalon, which consists of a free-boundary problem with jump conditions across the surface representing the reaction sheet, and is well suited for variable-density flows and for mixtures with non-unity and distinct Lewis numbers for the fuel and oxidiser. Due to density variations, the species and energy transport equations are coupled to the Navier–Stokes equations and the problem does not possess an analytical solution. We thus propose and implement a methodology for solving the free-boundary problem numerically. Results based on the asymptotic approximation are then verified against those obtained from the ‘exact’ numerical integration of the governing equations, comparing predictions of the various flame properties.

KW - counterflow diffusion flames

KW - extinction

KW - flow displacement

KW - large activation energy asymptotics

KW - thermal expansion

UR - http://www.scopus.com/inward/record.url?scp=85045116793&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85045116793&partnerID=8YFLogxK

U2 - 10.1080/13647830.2018.1441444

DO - 10.1080/13647830.2018.1441444

M3 - Article

AN - SCOPUS:85045116793

SP - 1

EP - 28

JO - Combustion Theory and Modelling

JF - Combustion Theory and Modelling

SN - 1364-7830

ER -