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Turbulent burning, flame acceleration, explosion triggering
Umeå University, Faculty of Science and Technology, Physics.
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 [en]
Turbulent combustion, flame acceleration, detonation / explosion triggering, direct numerical simulations
National Category
Physical Sciences
Identifiers
URN: urn:nbn:se:umu:diva-1050ISBN: 978-91-7264-262-1 (print)OAI: oai:DiVA.org:umu-1050DiVA: diva2:140054
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
List of papers
1. Velocity of weakly turbulent flames of finite thickness
Open this publication in new window or tab >>Velocity of weakly turbulent flames of finite thickness
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
Keyword
Combustion, Energy & Fuels, Heat Transfer, Mathematical Modelling, Thermodynamics & Kinetic Theory
Identifiers
urn:nbn:se:umu:diva-2175 (URN)10.1080/13647830500098399 (DOI)
Available from: 2007-03-22 Created: 2007-03-22 Last updated: 2011-03-07Bibliographically approved
2. On the Theory of Turbulent Flame Velocity
Open this publication in new window or tab >>On the Theory of Turbulent Flame Velocity
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.

Keyword
Darrieus-Landau flame instability, premixed turbulent flame, renormalization
Identifiers
urn:nbn:se:umu:diva-2176 (URN)10.1080/00102200600808466 (DOI)
Available from: 2007-03-22 Created: 2007-03-22Bibliographically approved
3. Flame oscillations in tubes with nonslip at the walls
Open this publication in new window or tab >>Flame oscillations in tubes with nonslip at the walls
2006 (English)In: Combustion and Flame, ISSN 0010-2180, Vol. 145, no 4, 675-687 p.Article in journal (Refereed) Published
Abstract [en]

A laminar premixed flame front propagating in a two-dimensional tube is considered with nonslip at the walls and with both ends open. The problem of flame propagation is solved using direct numerical simulations of the complete set of hydrodynamic equations including thermal conduction, diffusion, viscosity, and chemical kinetics. As a result, it is shown that flame interaction with the walls leads to the oscillating regime of burning. The oscillations involve variations of the curved flame shape and the velocity of flame propagation. The oscillation parameters depend on the characteristic tube width, which controls the Reynolds number of the flow. In narrow tubes the oscillations are rather weak, while in wider tubes they become stronger with well-pronounced nonlinear effects. The period of oscillations increases for wider tubes, while the average flame length scaled by the tube diameter decreases only slightly with increasing tube width. The average flame length calculated in the present work is in agreement with that obtained in the experiments. Numerical results reduce the gap between the theory of turbulent flames and the experiments on turbulent combustion in tubes.

Keyword
Premixed flames, Nonlinear oscillations, Direct numerical simulations
Identifiers
urn:nbn:se:umu:diva-2177 (URN)10.1016/j.combustflame.2006.01.013 (DOI)
Available from: 2007-03-22 Created: 2007-03-22Bibliographically approved
4. Theory and modeling of accelerating flames in tubes
Open this publication in new window or tab >>Theory and modeling of accelerating flames in tubes
2005 (English)In: Physical Review E. Statistical, Nonlinear, and Soft Matter Physics, ISSN 1063-651X, Vol. 72, no 4, 046307- p.Article in journal (Refereed) Published
Abstract [en]

The analytical theory of premixed laminar flames accelerating in tubes is developed, which is an important part of the fundamental problem of flame transition to detonation. According to the theory, flames with realistically large density drop at the front accelerate exponentially from a closed end of a tube with nonslip at the walls. The acceleration is unlimited in time; it may go on until flame triggers detonation. The analytical formulas for the acceleration rate, for the flame shape and the velocity profile in the flow pushed by the flame are obtained. The theory is validated by extensive numerical simulations. The numerical simulations are performed for the complete set of hydrodynamic combustion equations including thermal conduction, viscosity, diffusion, and chemical kinetics. The theoretical predictions are in a good agreement with the numerical results. It is also shown how the developed theory can be used to understand acceleration of turbulent flames.

Identifiers
urn:nbn:se:umu:diva-2178 (URN)10.1103/PhysRevE.72.046307 (DOI)
Available from: 2007-03-22 Created: 2007-03-22Bibliographically approved
5. Accelerating flames in cylindrical tubes with nonslip at the walls
Open this publication in new window or tab >>Accelerating flames in cylindrical tubes with nonslip at the walls
2006 (English)In: Combustion and Flame, ISSN 0010-2180, Vol. 145, no 1-2, 206-219 p.Article in journal (Refereed) Published
Abstract [en]

An analytical theory of flame acceleration in cylindrical tubes with one end closed is developed. It is shown that all realistic flames with a large density drop at the front accelerate exponentially because of the nonslip at the tube walls. Such acceleration mechanism is not limited in time and, eventually, it may lead to detonation triggering. It is found that the acceleration rate decreases with the Reynolds number of the flow. On the contrary, the acceleration rate grows with the thermal expansion of the burning matter. It is shown that the flame shape and the velocity profile remain self-similar during the flame acceleration. The theory is validated by extensive direct numerical simulations. The simulations are performed for the complete set of combustion and hydrodynamic equations including thermal conduction, diffusion, viscosity, and chemical kinetics. The simulation results are in very good agreement with the analytical theory.

Keyword
Premixed flames, Flame acceleration, Deflagration-to-detonation transition, Direct numerical simulations
Identifiers
urn:nbn:se:umu:diva-2179 (URN)10.1016/j.combustflame.2005.10.011 (DOI)
Available from: 2007-03-22 Created: 2007-03-22Bibliographically approved
6. Flame Acceleration in the Early Stages of Burning in Tubes
Open this publication in new window or tab >>Flame Acceleration in the Early Stages of Burning in Tubes
Show others...
2007 (English)In: Combustion and Flame, ISSN 0010-2180, Vol. 150, no 4, 263-276 p.Article in journal (Refereed) Published
Abstract [en]

Acceleration of premixed laminar flames in the early stages of burning in long tubes is considered. The acceleration mechanism was suggested earlier by Clanet and Searby [Combust. Flame 105 (1996) 225]. Acceleration happens due to the initial ignition geometry at the tube axis when a flame develops to a finger-shaped front, with surface area growing exponentially in time. Flame surface area grows quite fast but only for a short time. The analytical theory of flame acceleration is developed, which determines the growth rate, the total acceleration time, and the maximal increase of the flame surface area. Direct numerical simulations of the process are performed for the complete set of combustion equations. The simulations results and the theory are in good agreement with the previous experiments. The numerical simulations also demonstrate flame deceleration, which follows acceleration, and the so-called “tulip flames.”

Keyword
Premixed flames, Flame acceleration, Tulip flames, Direct numerical simulations
Identifiers
urn:nbn:se:umu:diva-8326 (URN)10.1016/j.combustflame.2007.01.004 (DOI)
Available from: 2008-01-17 Created: 2008-01-17 Last updated: 2009-12-09Bibliographically approved
7. Explosion triggering by an accelerating flame
Open this publication in new window or tab >>Explosion triggering by an accelerating flame
2006 (English)In: Physical Review E. Statistical, Nonlinear, and Soft Matter Physics, ISSN 1063-651X, Vol. 73, no 6, 066305- p.Article in journal (Refereed) Published
Abstract [en]

The analytical theory of explosion triggering by an accelerating flame is developed. The theory describes the structure of a one-dimensional isentropic compression wave pushed by the flame front. The condition of explosion in the gas mixture ahead of the flame front is derived; the instant of the explosion is determined provided that a mechanism of chemical kinetics is known. As an example, it is demonstrated how the problem is solved in the case of a single reaction of Arrhenius type, controlling combustion both inside the flame front and ahead of the flame. The model of an Arrhenius reaction with a cutoff temperature is also considered. The limitations of the theory due to the shock formation in the compression wave are found. Comparison of the theoretical results to the previous numerical simulations shows good agreement.

Keyword
gas mixtures, explosions, flames, combustion, reaction kinetics theory
Identifiers
urn:nbn:se:umu:diva-2181 (URN)10.1103/PhysRevE.73.066305 (DOI)
Available from: 2007-03-22 Created: 2007-03-22Bibliographically approved
8. Violent folding of a flame front in a flame-acoustic resonance
Open this publication in new window or tab >>Violent folding of a flame front in a flame-acoustic resonance
2006 (English)In: Physical Review Letters, ISSN 0031-9007, Vol. 97, no 16, 164501- p.Article in journal (Refereed) Published
Abstract [en]

The first direct numerical simulations of violent flame folding because of the flame-acoustic resonance are performed. Flame propagates in a tube from an open end to a closed one. Acoustic amplitude becomes extremely large when the acoustic mode between the flame and the closed tube end comes in resonance with intrinsic flame oscillations. The acoustic oscillations produce an effective acceleration field at the flame front leading to a strong Rayleigh-Taylor instability during every second half period of the oscillations. The Rayleigh-Taylor instability makes the flame front strongly corrugated with elongated jets of heavy fuel mixture penetrating the burnt gas and even with pockets of unburned matter separated from the flame front

Identifiers
urn:nbn:se:umu:diva-2182 (URN)10.1103/PhysRevLett.97.164501 (DOI)
Available from: 2007-03-22 Created: 2007-03-22 Last updated: 2009-08-19Bibliographically approved

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Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
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  • en-GB
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Output format
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