Research Papers

The Combined Effects of Heat Loss and Reversibility on the Propagation of Planar Premixed Counterflow Flames

[+] Author and Article Information
Faisal Al-Malki

Department of Mathematics and Statistics,
Taif University,
Taif 21944, Saudi Arabia
e-mail: falmalki@tu.edu.sa

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF THERMAL SCIENCE AND ENGINEERING APPLICATIONS. Manuscript received March 23, 2018; final manuscript received May 29, 2018; published online August 20, 2018. Assoc. Editor: Matthew Oehlschlaeger.

J. Thermal Sci. Eng. Appl 10(6), 061011 (Aug 20, 2018) (6 pages) Paper No: TSEA-18-1151; doi: 10.1115/1.4040657 History: Received March 23, 2018; Revised May 29, 2018

We study in this paper the combined effect of heat loss and reversibility on the propagation of planar flames formed within the counterflow configuration. The problem has been formulated first using the thermodiffusive model with constant density and then solved numerically using finite elements. The impact of four main parameters, namely the reversibility r, the heat loss κ, the strain rate ε, and the activation energy β, on the propagation of planar flames has been discussed in details. The study has shown that planar flames under reversible conditions behave qualitatively similar to those observed for irreversible reactions, which agree with the asymptotic findings. In the presence of heat loss, the problem exhibits multiplicity of solutions whose number and stability were found to vary according to the strain rate ε. In addition, the study has predicted the existence of a certain value of the reversibility parameter r beyond which the impact of reversibility becomes negligible. Finally, we have examined the stability of the solutions and determined the domain of stability of solutions and their multiplicity for this problem.

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Fig. 1

A schematic illustration of planar flame propagating in a counterflow

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Fig. 2

Comparison between the asymptotic and numerical results for ε = 0.175

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Fig. 3

Reactivity μ versus heat-loss κ for selected values of ε when r = 0

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Fig. 4

Reactivity μ versus heat-loss r for selected values of ε when κ = 0.2

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Fig. 5

Flame position as r varies for selected values of ε when κ = 0.2

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Fig. 6

Reactivity μ versus heat-loss κ for selected values of ε when r = 100

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Fig. 7

Profiles of temperature θ, fuel mass fraction yF, product mass fraction yP, and the reaction rate ω/ωmax when ε = 0.4, κ = 0.1 and r = 100

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Fig. 8

Reactivity μ versus the strain rate ε for selected values of r when k = 0

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Fig. 9

Reactivity μ versus the strain rate ε for selected values of r when k = 0.2

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Fig. 10

Reactivity μ as a function of the activation energy β when κ = 0.1

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Fig. 11

Time evolutions of the reactivity for the upper branch solution and the lower branch solution when ε = 0.4, κ = 0.2, and r = 100

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Fig. 12

The region of solutions in the κε diagram when r = 100



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