Large Activation Energy Analysis of Nonadiabatic Strained Premixed Laminar Flames with Nonunity Lewis Numbers

ABSTRACT

We present an asymptotic analysis of a strained premixed flame in the mixing layer between two counterflowing streams: one with fresh reactants at a temperature $T_{\mathrm{u}}$ and other with the burned gases at temperature $T_{\mathrm{b}}$, which may be different from the adiabatic combustion temperature $T_{\mathrm{e}}=q{Y}_{\mathrm{F}\mathrm{u}}/c_{\mathrm{p}}+T_{\mathrm{u}}$ of the fresh gases. A one-step irreversible Arrhenius reaction model, of high activation energy, is used for the asymptotic analysis, together with the thermal-diffusive approximation of constant density and transport properties – easily generalized to variable density and transport properties with the use of a heat-conduction-weighted coordinate. The analysis for near unity Lewis numbers of the fuel by Libby, Liñán and Williams (1983) is extended here to arbitrary nonunity Lewis numbers, of relevance to a wide variety of applications, ranging from hydrogen-fueled combustors to heavy fuel systems. In analogy with Liñán’s analysis of counterflow diffusion flames, three asymptotic distinguished regimes are identified for premixed flames for large activation energies and the appropriate Damköhler numbers – the ratio of the characteristic diffusion and reaction times. These regimes are the premixed flame regime, the partial burning regime and the nearly frozen ignition regime. The analytical expressions obtained for these regimes, of the dimensionless reaction rate as a function of the Damköhler number, are seen to describe with good accuracy the results obtained from the numerical integration of the full problem.

KEYWORDS:

• Activation energy asymptotics
• counterflow premixed flames
• nonadiabatic
• nonunity Lewis number
• extinction and ignition
• flamelet regimes

Acknowledgments

The senior author (AL) initiated his research work on combustion (under Gregorio Millán) in September 1958, when Theodore von Kármán organized in Madrid the First Congress of the International Council of the Aeronautical Sciences (ICAS). Von Kármán (1959) gave the Inaugural Lecture on “Some significant developments in Aerodynamics since 1946.” In this Congress, Antonio Ferri, of the Polytechnic Institute of Brooklyn (PIB), gave a lecture on hypersonic flow (Ferri 1958). Thus, AL first learned about Paul Libby (Ferri’s collaborator at PIB) and his work, because von Kármán considered a duty to express his thanks and appreciation for our friend Paul Libby for the assistance in collecting all the papers of the previous 12 years dealing with supersonic wing theory, slender aircraft, interference effects, higher-order approximations, hypersonic flows and boundary layer theory.

AL’s research work at the Spanish National Institute of Aeronautical Technique (INTA), related to Supersonic Combustion, was presented (with Ignacio Da Riva) in the third ICAS Congress, at Stockholm in 1962, with the title “Chemical nonequilibrium effects in hypersonic aerodynamics” (Liñán and Da Riva 1964). The Inaugural Lecture was given by the president of the Royal Society of Sweden (Professor Lundberg) with the tittle “Speed and safety in civil aviation” (Lundberg 1964); which changed the future course of commercial aviation, limited to subsonic aircraft flying in the stratosphere at transonic speeds.

After this congress, in September 1962, AL initiated, with a NASA-ESRO Fellowship, his 1-year research work at Caltech, which led to the degree of Aeronautical Engineer. In June 1963 on his way back to Madrid, he stopped at PIB, where (in absence of Antonio Ferri) he met Paul Libby for the first time. Thus, he initiated with him a most fruitful and heartful friendship continued after 1964 at UCSD. His summer stays in La Jolla, initiated at the beginning of the 1990ʹs, with one or two of his PhD students to collaborate with Forman Williams, were very much enriched by the visits of Paul Clavin, and also by those of Profs. Ken Bray of Cambridge and Michel Champion of Poitiers, who were propitiated by Paul Libby to work with him on Turbulent Combustion.

The leading author (MV) would like to thank Profs. Forman Williams, Paul Libby, Juan Carlos Lasheras and Kalyanasundaram Seshadri for their hospitality and many interesting and stimulating discussions during his summer stays at UCSD during the years 2000, 2001, 2002 and 2004.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Correction Statement

This article has been republished with minor changes. These changes do not impact the academic content of the article.