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Research Papers: Combustion and Reactive Flows

Limiting Length, Steady Spread, and Nongrowing Flames in Concurrent Flow Over Solids

[+] Author and Article Information
Ya-Ting Tseng

Department of Mechanical and Aerospace Engineering, Case Western Reserve University, 10900 Euclid Avenue, 418 Glennan Building, Cleveland, OH 44106yating@case.edu

James S. T’ien

Department of Mechanical and Aerospace Engineering, Case Western Reserve University, 10900 Euclid Avenue, 418 Glennan Building, Cleveland, OH 44106jst2@case.edu

J. Heat Transfer 132(9), 091201 (Jun 28, 2010) (9 pages) doi:10.1115/1.4001645 History: Received October 07, 2009; Revised April 19, 2010; Published June 28, 2010; Online June 28, 2010

A detailed two-dimensional transient model has been formulated and numerically solved for concurrent flames over thick and thin solids in low-speed forced flows. The processes of flame growth leading to steady states are numerically simulated. For a thick solid, the steady state is a nongrowing stationary flame with a limiting length. For a thin solid, the steady state is a spreading flame with a constant spread rate and a constant flame length. The reason for a nongrowing limiting flame for the thick solid is the balance between the flame heat feedback and the surface radiative heat loss at the pyrolysis front, as first suggested by Honda and Ronney. The reason for achieving a steady spread for thin solids is the balance between the solid burnout rate and the flame tip advancing rate. Detailed transient flame and thermal profiles are presented to illustrate the different flame growth features between the thick- and thin-solid fuel samples.

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Copyright © 2010 by American Society of Mechanical Engineers
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Figures

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Figure 1

Configuration in the computational model: schematic (a) of the ignition method and (b) of a spreading flame

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Figure 2

Locus of pyrolysis front and base over the infinitely thick solid with flow condition: XO2,∞=21%, V∞=5 cm/s

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Figure 3

Flame growth process over the thick solid. Upper half-plane: gas-phase temperature contour. The outermost contour has a value of 1350 K, and the difference between two adjacent contours is 150 K. Lower half-plane: vapor fuel reaction rate contour of ω̇F=10−4 g/cm3/s.

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Figure 4

Solid heat transfer process over the thick solid. Upper half-plane: heat fluxes over the solid surface; lower half-plane: solid-phase temperature contour. Difference between two adjacent contours is 0.2. Temperature is nondimensionalized by 300 K. The shaded portion of the solid is inert.

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Figure 5

Time history of heat fluxes at xp and Vp for the thick solid

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Figure 6

Pyrolysis front, pyrolysis base locus, and pyrolysis length versus time for the thin solid with ρsτ=28.4 mg/cm2. The flow entrance length=6.3 cm. Flow condition: XO2,∞=21%, V∞=5 cm/s.

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Figure 7

Velocities of pyrolysis front and base and q̇net,in″ at xp versus time for the thin solid with a constant flow entrance length

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Figure 8

Transient solid heat transfer process for the thin solid with a constant flow entrance length. Upper plane: Heat fluxes over the solid surface. Temperature contour of value 1350 K is also shown on the upper plane. Lower plane: solid-phase temperature contour. The vertical axis is from the surface to the center of the sample. Temperature is nondimensionalized by 300 K. The shaded portion of the solid is inert or leftover inert residue.

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Figure 9

Pyrolysis front, pyrolysis base locus and pyrolysis length versus time for the thin solid with ρsτ=28.4 mg/cm2. Inset: Velocities of pyrolysis front and pyrolysis base versus time. The flow entrance length is variable (from 6.3 cm to 27.6 cm). Flow condition: XO2,∞=21%, V∞=5 cm/s.

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