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Research Papers: Fuel Combustion

Invariant Forms of Conservation Equations for Reactive Fields and Hydro-Thermo-Diffusive Theory of Laminar Flames

[+] Author and Article Information
Siavash H. Sohrab

Mem. ASME
Department of Mechanical Engineering,
Northwestern University,
2145 Sheridan Road,
Evanston, IL 60208-3111
e-mail: s-sohrab@northwestern.edu

1Corresponding author.

Contributed by the Advanced Energy Systems Division of ASME for publication in the JOURNAL OF ENERGY RESOURCES TECHNOLOGY. Manuscript received May 28, 2014; final manuscript received May 29, 2014; published online August 27, 2014. Editor: Hameed Metghalchi.

J. Energy Resour. Technol 137(1), 012203 (Aug 27, 2014) (10 pages) Paper No: JERT-14-1168; doi: 10.1115/1.4028070 History: Received May 28, 2014; Revised May 29, 2014

A scale-invariant model of statistical mechanics is described leading to invariant Enskog equation of change that is applied to derive invariant forms of conservation equations for mass, thermal energy, linear momentum, and angular momentum in chemically reactive fields. Modified hydro-thermo-diffusive theories of laminar premixed flames for (1) rigid-body and (2) Brownian-motion flame propagation models are presented and are shown to be mathematically equivalent. The predicted temperature profile, thermal thickness, and propagation speed of laminar methane–air premixed flame are found to be in good agreement with existing experimental observations.

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Topics: Flames
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Figures

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Fig. 1

Scale-invariant model of statistical mechanics. Equilibrium-β-Dynamics on the left-hand-side and nonequilibrium Laminar-β-Dynamics on the right-hand-side for scales β = g, p, h, f, e, c, m, a, s, k, and t as defined in Sec. 2. Characteristic lengths of (system, element, “atom”) are (Lβ , λβ, ℓβ) and λβ is the mean-free-path [45].

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Fig. 2

Schematic of steady propagating laminar premixed flame in infinite domain according to (a) modified theory and (b) classical theory [85]

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Fig. 3

Laminar premixed flame (a) propagating in laboratory; (b) stationary due to imposed convection; and (c) stationary with normalized velocity

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Fig. 4

Flame thermal structure according to (a) modified theory of laminar flame and (b) classical theory of laminar flame

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Fig. 5

(a) Finite value or reaction rate during τ-τi and (b) periodic onset of light during τ-τi

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Fig. 6

Measured temperature profiles for methane–air premixed flames in stagnation point flow with ϕ = 0.8, w'zo= (a) 30 (b) 50 (c) 70 (d) 90 cm/s [102]

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