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Physics of Fluids / Volume 24 / Issue 2 / ARTICLES / Interfacial Flows

Phys. Fluids 24, 022108 (2012); http://dx.doi.org/10.1063/1.3684712 (34 pages)

Analytical study in the mechanism of flame movement in horizontal tubes

Kirill A. Kazakov

Department of Theoretical Physics, Physics Faculty, Moscow State University, 119991 Moscow, Russian Federation

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(Received 5 September 2011; accepted 3 January 2012; published online 16 February 2012)

The problem of premixed flame propagation in wide horizontal tubes is revisited. Employing the on-shell description of flames with arbitrary gas expansion, a nonlinear second-order differential equation for the front position of steady flame is derived. Solutions to this equation, obtained numerically, reveal two distinct physical regimes of laminar flame propagation controlled by the strong baroclinic effect. They differ by the front shape and flame speed, the ratio of the total consumption rates in the two regimes being 1.4 to 1.8, depending on the value of the gas expansion coefficient. Comparison with the existing experimental data on methane-air flames is made, and explanation of the main trends in the observed flame behavior is given. It is shown, in particular, that the faster (slower) regime of combustion is realized in mixtures close to (far from) the stoichiometric composition, with pronounced changeover in between.

© 2012 American Institute of Physics

Article Outline

  1. INTRODUCTION
  2. ON-SHELL DESCRIPTION OF HORIZONTALLY PROPAGATING FLAMES
    1. Master equation
    2. Large-slope expansion
      1. Evolution equation and dispersion relation. Boundary conditions
      2. Master equation in the leading order: Reduction to ordinary differential equation
      3. Numerical solutions: Two types of flames
  3. FLAME PROPAGATION IN WIDE CHANNELS
    1. Averaging procedure
    2. Decoupling of dynamical equations
    3. Renormalization of the local propagation law
  4. ANALYSIS OF EXPERIMENTAL DATA
    1. Relevance of 2D picture to flame propagation in tubes
    2. Assessment of heat losses
    3. Identification of physical solutions
    4. The range of applicability of the theory: Accuracy assessment
    5. Comparison with experimental data on methane-air flames
  5. DISCUSSION AND CONCLUSIONS

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KEYWORDS, PACS, and IPC

Keywords

aerodynamics, chemically reactive flow, combustion, flames, gas mixtures, laminar flow, nonlinear differential equations, organic compounds, pipe flow

PACS

  • 47.70.Pq

    Flames; combustion

  • 47.70.Fw

    Chemically reactive flows

  • 47.60.Dx

    Flows in ducts and channels

  • 47.40.-x

    Compressible flows; shock waves

  • 47.15.Rq

    Laminar flows in cavities, channels, ducts, and conduits

  • 47.11.-j

    Computational methods in fluid dynamics

International Patent Classification (IPC)

  • F23

    Combustion apparatus; Combustion processes

ARTICLE DATA

Digital Object Identifier
http://dx.doi.org/10.1063/1.3684712

PUBLICATION DATA

ISSN

1070-6631 (print)  
1089-7666 (online)

Publisher

$abstract.society.value is a Member of CrossRef American Institute of Physics

For access to fully linked references, you need to log in.
    V. V. Bychkov, “Bubble motion in a horizontal tube and the velocity estimate for curved flames,” Phys. Rev. E 55, 6898 (1997).

    K. A. Kazakov, “Exact equation for curved stationary flames with arbitrary gas expansion,” Phys. Rev. Lett. 94, 094501 (2005).

    K. A. Kazakov, “On-shell description of stationary flames,” Phys. Fluids 17, 032107 (2005)PHFLE6000017000003032107000001.

    H. El-Rabii, G. Joulin, and K. A. Kazakov, “Nonperturbative approach to the nonlinear dynamics of two-dimensional premixed flames,” Phys. Rev. Lett. 100, 174501 (2008).

    H. El-Rabii, G. Joulin, and K. A. Kazakov, “Stability analysis of confined V-shaped flames in high-velocity streams,” Phys. Rev. E 81, 066312 (2010).


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