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- Liberman, M. A., et al.
(author)
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Numerical studies of curved stationary flames in wide tubes
- 2003
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In: Combustion theory and modelling. - : Informa UK Limited. - 1364-7830 .- 1741-3559. ; 7:4, s. 653-676
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Journal article (peer-reviewed)abstract
- The nonlinear problem of the propagation of curved stationary flames in tubes of different widths is studied by means of direct numerical simulation of the complete system of hydrodynamic equations including thermal conduction, viscosity, fuel diffusion and chemical kinetics. While only a planar flame can propagate in a narrow tube of width smaller than half of the cut-off wavelength determined by the linear theory of the hydrodynamic instability of a flame front, in wider tubes stationary curved flames propagate with velocities considerably larger than the corresponding velocity of a planar flame. It is shown that only simple 'single-hump' slanted stationary flames are possible in wide tubes, and 'multi-hump' flames are possible in wide tubes only as a nonstationary mode of flame propagation. The stability limits of curved stationary flames in wider tubes and the secondary Landau-Darrieus instability are investigated. The dependence of the velocity of the stationary flame on the tube width is studied. The analytical theory describes the flame reasonably well when the tube width does not exceed some critical value. The dynamics of the flame in wider tubes is shown to be governed by a large-scale stability mechanism resulting in a highly slanted flame front. In wide tubes, the skirt of the slanted flame remains smooth with the length of the skirt and the flame velocity increasing progressively with the increase of the tube width above the second critical value. Results of the analytical theory and numerical simulations are discussed and compared with the experimental data for laminar flames in wide tubes.
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- Liberman, M. A., et al.
(author)
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Self-acceleration and fractal structure of outward freely propagating flames
- 2004
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In: Physics of fluids. - : AIP Publishing. - 1070-6631 .- 1089-7666. ; 16:7, s. 2476-2482
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Journal article (peer-reviewed)abstract
- Flame acceleration associated with development of the Landau-Darrieus hydrodynamic instability is studied by means of direct numerical simulation of the Navier-Stokes equations including chemical kinetics in the form of the Arrhenius law. The fractal excess for radially expanding flames in cylindrical geometry is evaluated. Two-dimensional (2-D) simulation of radially expanding flames in cylindrical geometry displays a radial growth with 1.25 power law temporal behavior after some transient time. It is shown that the fractal excess for 2-D geometry obtained in the numerical simulation is in good agreement with theoretical predictions. The difference in fractal dimension between 2-D cylidrical and three-dimensional spherical radially expanding flames is outlined. Extrapolation of the obtained results for the case of spherical expanding flames gives a radial growth power law that is consistent with temporal behavior obtained in the survey of experimental data.
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