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Numerical study of flame dynamics
Umeå University, Faculty of Science and Technology, Physics.
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 [en]
combustion, Direct Numerical Simulation (DNS), turbulence, flame-vortex interaction, flame acceleration, flame-acoustic interaction
National Category
Physical Sciences
Identifiers
URN: urn:nbn:se:umu:diva-1313ISBN: 978-91-7264-351-2 (print)OAI: oai:DiVA.org:umu-1313DiVA: diva2:140628
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
List of papers
1. Flame propagation along the vortex axis
Open this publication in new window or tab >>Flame propagation along the vortex axis
2006 (English)In: Combustion theory and modelling, ISSN 1364-7830, E-ISSN 1741-3559, Vol. 10, no 4, 581-601 p.Article in journal (Refereed) Published
Abstract [en]

The problem of how to include fast burning along the vortex axis into the general description of turbulent flames is discussed. It is shown that, from such a point of view, the most representative geometry of the flow is burning in a hypothetic 'tube' with rotating gaseous mixture. Direct numerical simulations of flame propagation in the hypothetic tube are performed on the basis of the complete system of hydrodynamic equations, including thermal conduction, diffusion, viscosity and chemical kinetics written in the rotational reference frame. The geometry of an axisymmetric flame front is studied, which allows reducing the dimension of the problem by one, thus saving computational time. The numerical results are analysed using the ideas of bubble rising in the acceleration field created by the centrifugal force. It is shown that the velocity of flame propagation is determined mostly by the velocity of bubble rising when the frequency of the tube rotation is sufficiently large. When the rotational frequency is moderate, then the velocity of flame propagation is determined by the planar flame velocity, by the hydrodynamic flame instability and by the gas rotation. Calculations given in the present paper are in agreement with the previous theoretical and experimental results.

Keyword
Premixed flame, Turbulent vortex, Hydrodynamic instability, Bubble rising
Identifiers
urn:nbn:se:umu:diva-2477 (URN)10.1080/13647830600552006 (DOI)
Available from: 2007-08-28 Created: 2007-08-28 Last updated: 2017-12-14Bibliographically 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, E-ISSN 1563-521X, 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: 2007-03-22 Last updated: 2017-12-14Bibliographically 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, E-ISSN 1556-2921, 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: 2007-03-22 Last updated: 2017-12-14Bibliographically 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: Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, ISSN 1063-651X, E-ISSN 1095-3787, 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: 2007-03-22 Last updated: 2017-12-14Bibliographically 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, E-ISSN 1556-2921, 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: 2007-03-22 Last updated: 2017-12-14Bibliographically 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, E-ISSN 1556-2921, 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: 2017-12-14Bibliographically approved
7. 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, E-ISSN 1079-7114, 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: 2017-12-14Bibliographically approved
8. Flame–sound interaction in tubes with nonslip walls
Open this publication in new window or tab >>Flame–sound interaction in tubes with nonslip walls
2007 (English)In: Combustion and Flame, ISSN 0010-2180, E-ISSN 1556-2921, Vol. 149, no 4, 418-434 p.Article in journal (Refereed) Published
Abstract [en]

Flame interaction with sound is studied for a premixed flame propagating to the closed end of a tube with nonslip walls. The flow geometry is similar to that in the classical Searby experiments on flame–acoustic interaction [Combust. Sci. Technol. 81 (1992) 221]. The problem is solved by direct numerical simulations of the combustion equations. The flame–sound interaction strongly influences oscillations of the flame front. Particularly, sound noticeably increases the oscillation amplitude in comparison with that in an open tube with nonreflecting boundary conditions at the ends studied previously. Oscillations become especially strong in the second part of the tube, where flame pulsations are in resonance with the acoustic wave. Parameters of the flame oscillations are investigated for different values of the tube width and length. It is demonstrated that the oscillations are stronger in wider tubes, though the investigated tube width is limited by the computational facilities. In sufficiently wide tubes, violent folding of a flame front is observed because of the flame–acoustic resonance. By increasing the Lewis number, one also increases the oscillation amplitude.

Keyword
Premixed burning, Flame–sound interactions, Direct numerical simulations
Identifiers
urn:nbn:se:umu:diva-2484 (URN)10.1016/j.combustflame.2007.02.003 (DOI)
Available from: 2007-08-28 Created: 2007-08-28 Last updated: 2017-12-14Bibliographically approved

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  • ieee
  • modern-language-association-8th-edition
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