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On the Theory of Turbulent Flame Velocity
Umeå University, Faculty of Science and Technology, Physics.
Umeå University, Faculty of Science and Technology, Physics.
Umeå University, Faculty of Science and Technology, Physics.
2007 (English)In: Combustion Science and Technology, ISSN 0010-2202, Vol. 179, no 1&2, 137-151 p.Article in journal (Refereed) Published
Abstract [en]

The renormalization ideas of self-similar dynamics of a strongly turbulent flame front are applied to the case of a flame with realistically large thermal expansion of the burning matter. In that case a flame front is corrugated both by external turbulence and the intrinsic flame instability. The analytical formulas for the velocity of flame propagation are obtained. It is demonstrated that the flame instability is of principal importance when the integral turbulent length scale is much larger than the cutoff wavelength of the instability. The developed theory is used to analyze recent experiments on turbulent flames propagating in tubes.

Place, publisher, year, edition, pages
2007. Vol. 179, no 1&2, 137-151 p.
Keyword [en]
Darrieus-Landau flame instability, premixed turbulent flame, renormalization
Identifiers
URN: urn:nbn:se:umu:diva-2176DOI: 10.1080/00102200600808466OAI: oai:DiVA.org:umu-2176DiVA: diva2:140047
Available from: 2007-03-22 Created: 2007-03-22Bibliographically 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.
Keyword
Turbulent combustion, flame acceleration, detonation / explosion triggering, direct numerical simulations
National Category
Physical Sciences
Identifiers
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)
Opponent
Supervisors
Available from: 2007-03-22 Created: 2007-03-22 Last updated: 2009-08-18Bibliographically approved
2. Numerical study of flame dynamics
Open this publication in new window or tab >>Numerical study of flame dynamics
2007 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Modern industrial society is based on combustion with ever increasing standards on the efficiency of burning. One of the main combustion characteristics is the burning rate, which is influenced by intrinsic flame instabilities, external turbulence and flame interaction with walls of combustor and sound waves.

In the present work we started with the problem how to include combustion along the vortex axis into the general theory of turbulent burning. We demonstrated that the most representative geometry for such problem is a hypothetic “tube” with rotating gaseous mixture. We obtained that burning in a vortex is similar to the bubble motion in an effective acceleration field created by the centrifugal force. If the intensity of the vortex is rather high then the flame speed is determined mostly by the velocity of the bubble. The results obtained complement the renormalization theory of turbulent burning. Using the results on flame propagation along a vortex we calculated the turbulent flame velocity, compared it to the experiments and found rather good agreement.

All experiments on turbulent combustion in tubes inevitably involve flame interaction with walls. In the present thesis flame propagation in the geometry of a tube with nonslip walls has been widely studied numerically and analytically. We obtained that in the case of an open tube flame interaction with nonslip walls leads to the oscillating regime of burning. The oscillations are accompanied by variations of the curved flame shape and the velocity of flame propagation. If flame propagates from the closed tube end, then the flame front accelerates with no limit until the detonation is triggered. The above results make a good advance in solving one of the most difficult problems of combustion theory, the problem of deflagration to detonation transition. We developed the analytical theory of accelerating flames and found good agreement with results of direct numerical simulations. Also we performed analytical and numerical studies of another mechanism of flame acceleration caused by initial conditions. The flame ignited at the axis of a tube acquires a “finger” shape and accelerates. Still, such acceleration takes place for a rather short time until the flame reaches the tube wall. In the case of flame propagating from the open tube end to the closed one the flame front oscillates and therefore generates acoustic waves. The acoustic waves reflected from the closed end distort the flame surface. When the frequency of acoustic mode between the flame front and the tube end comes in resonance with intrinsic flame oscillations the burning rate increases considerably and the flame front becomes violently corrugated.

Place, publisher, year, edition, pages
Umeå: Fysik, 2007. 73 p.
Keyword
combustion, Direct Numerical Simulation (DNS), turbulence, flame-vortex interaction, flame acceleration, flame-acoustic interaction
National Category
Physical Sciences
Identifiers
urn:nbn:se:umu:diva-1313 (URN)978-91-7264-351-2 (ISBN)
Public defence
2007-09-21, KB3A9, KBC-huset, SE-901 87, Umeå University, Sweden, Umeå, 13:00 (English)
Opponent
Supervisors
Available from: 2007-08-28 Created: 2007-08-28 Last updated: 2009-08-19Bibliographically approved

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