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Velocity of weakly turbulent flames of finite thickness
Umeå University, Faculty of Science and Technology, Department of Physics.
Umeå University, Faculty of Science and Technology, Department of Physics.
2005 (English)In: Combustion theory and modelling, ISSN 1364-7830, E-ISSN 1741-3559, Vol. 9, no 2, 323-351 p.Article in journal (Refereed) Published
Abstract [en]

The velocity increase of a weakly turbulent flame of finite thickness is investigated using analytical theory developed in previous papers. The obtained velocity increase depends on the flow parameters: on the turbulent intensity, on the turbulent spectrum and on the characteristic length scale. It also depends on the thermal and chemical properties of the burning matter: thermal expansion, the Markstein number and the temperature dependence of transport coefficients. It is shown that the influence of the finite flame thickness is especially strong close to the resonance point, when the wavelength of the turbulent harmonic is equal to the cut off wavelength of the Darrieus-Landau instability. The velocity increase is almost independent of the Prandtl number. On the contrary, the Markstein number is one of the most important parameters controlling the velocity increase. The relative role of the external turbulence and the Darrieus-Landau instability for the velocity increase is studied for different parameters of the flow and the burning matter. The velocity increase for turbulent flames in methane and propane fuel mixtures is calculated for different values of the equivalence ratio. The present theoretical results are compared with previous experiments on turbulent flames. In order to perform the comparison, the theoretical results of the present paper are extrapolated to the case of a strongly corrugated flame front using the ideas of self-similar flame dynamics. The obtained theoretical results are in a reasonable agreement with the experimental data, taking into account the uncertainties of both the theory and the experiments. It is shown that in many experiments on turbulent flames the Darrieus-Landau instability is more important for the flame velocity than the external turbulence.

Place, publisher, year, edition, pages
Bristol: Institute of Physics Publ. , 2005. Vol. 9, no 2, 323-351 p.
Keyword [en]
Combustion, Energy & Fuels, Heat Transfer, Mathematical Modelling, Thermodynamics & Kinetic Theory
URN: urn:nbn:se:umu:diva-2175DOI: 10.1080/13647830500098399OAI: diva2:140046
Available from: 2007-03-22 Created: 2007-03-22 Last updated: 2011-03-07Bibliographically approved
In thesis
1. Turbulent burning, flame acceleration, explosion triggering
Open this publication in new window or tab >>Turbulent burning, flame acceleration, explosion triggering
2007 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

The present thesis considers several important problems of combustion theory, which are closely related to each other: turbulent burning, flame interaction with walls in different geometries, flame acceleration and detonation triggering.

The theory of turbulent burning is developed within the renormalization approach. The theory takes into account realistic thermal expansion of burning matter. Unlike previous renormalization models of turbulent burning, the theory includes flame interaction with vortices aligned both perpendicular and parallel to average direction of flame propagation. The perpendicular vortices distort a flame front due to kinematical drift; the parallel vortices modify the flame shape because of the centrifugal force. A corrugated flame front consumes more fuel mixture per unit of time and propagates much faster. The Darrieus-Landau instability is also included in the theory. The instability becomes especially important when the characteristic length scale of the flow is large.

Flame interaction with non-slip walls is another large-scale effect, which influences the flame shape and the turbulent burning rate. This interaction is investigated in the thesis in different geometries of tubes with open / closed ends. When the tube ends are open, then flame interaction with non-slip walls leads to an oscillating regime of burning. Flame oscillations are investigated for different flame parameters and tube widths. The average increase in the burning rate in the oscillations is found.

Then, propagating from a closed tube end, a flame accelerates according to the Shelkin mechanism. In the theses, an analytical theory of laminar flame acceleration is developed. The theory predicts the acceleration rate, the flame shape and the velocity profile in the flow pushed by the flame. The theory is validated by extensive numerical simulations. An alternative mechanism of flame acceleration is also considered, which is possible at the initial stages of burning in tubes. The mechanism is investigated using the analytical theory and direct numerical simulations. The analytical and numerical results are in very good agreement with previous experiments on “tulip” flames.

The analytical theory of explosion triggering by an accelerating flame is developed. The theory describes heating of the fuel mixture by a compression wave pushed by an accelerating flame. As a result, the fuel mixture may explode ahead of the flame front. The explosion time is calculated. The theory shows good agreement with previous numerical simulations on deflagration-to-detonation transition in laminar flows.

Flame interaction with sound waves is studied in the geometry of a flame propagating to a closed tube end. It is demonstrated numerically that intrinsic flame oscillations coming into resonance with acoustic waves may lead to violent folding of the flame front with a drastic increase in the burning rate. The flame folding is related to the Rayleigh-Taylor instability developing at the flame front in the oscillating acceleration field of the acoustic wave.

Place, publisher, year, edition, pages
Umeå: Fysik, 2007. 56 p.
Turbulent combustion, flame acceleration, detonation / explosion triggering, direct numerical simulations
National Category
Physical Sciences
urn:nbn:se:umu:diva-1050 (URN)978-91-7264-262-1 (ISBN)
Public defence
2007-06-01, N430, Naturvetarhuset, 90187 Umea, Sweden, 13:00 (English)
Available from: 2007-03-22 Created: 2007-03-22 Last updated: 2009-08-18Bibliographically approved

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