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Numerical studies of curved stationary flames in wide tubes
Department of Physics, Uppsala University.
Department of Physics, Uppsala University.
Department of Physics, Uppsala University.
Department of Physics, Uppsala University.
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2003 (English)In: Combustion theory and modelling, ISSN 1364-7830, E-ISSN 1741-3559, Vol. 7, no 4, 653-676 p.Article in journal (Refereed) Published
Abstract [en]

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.

Place, publisher, year, edition, pages
2003. Vol. 7, no 4, 653-676 p.
Keyword [en]
Computer simulation, Diffusion, Hydrodynamics, Nonlinear systems, Problem solving, Reaction kinetics, Thermal conductivity, Tubes (components), Viscosity, Curved stationary flames
National Category
Physical Sciences
Identifiers
URN: urn:nbn:se:kth:diva-9144DOI: 10.1088/1364-7830/7/4/004ISI: 000188292300004OAI: oai:DiVA.org:kth-9144DiVA: diva2:25274
Note
QC 20100915Available from: 2008-09-24 Created: 2008-09-24 Last updated: 2017-12-13Bibliographically approved
In thesis
1. Flame Dynamics and Deflagration-to-Detonation Transition
Open this publication in new window or tab >>Flame Dynamics and Deflagration-to-Detonation Transition
2008 (English)Doctoral thesis, comprehensive summary (Other scientific)
Abstract [en]

Various premixed flame phenomena are studied by means of direct numerical simulations of the complete system of hydrodynamic equations. Rigorous study of flame dynamics is essential for all premixed combustion problems where multidimensional effects cannot be disregarded.The present thesis consists of six parts. The first part deals with the fundamental problem of curved stationary flames propagation in free-slip tubes of different widths. It is shown that only simple "single-hump" slanted stationary flames are possible in tubes wider than some stability limit. The flame dynamics is shown to be governed by a large-scale stability mechanism resulting in a highly slanted flame front.The second part of the thesis is dedicated to studies of acceleration and fractal structure of outward freely propagating flames. It is shown that the development of Landau-Darrieus instability results in the formation of fractal-like flame front structure. Two-dimensional simulation of radially expanding flames displays a radial growth with 1.25 power law temporal behavior. It is shown that the fractal excess for 2D geometry obtained in thenumerical simulation is in good agreement with theoretical predictions.In third part the flame acceleration in tubes with non-slip at the walls is studied in the extremely wide range of flame front velocity. Flame accelerates from small initial velocity to supersonic speed in the laboratory reference frame. Flame acceleration undergoes three stages: 1) initial exponential acceleration in the quasi-isobaric regime, 2) almost linear increase of the flame speed to supersonic values, 3) saturation to a stationary high-speed deflagration velocity, which is correlated with the Chapman-Jouguet deflagration speed. The saturation velocity is in line with previous experimental results.In fourth part the role of viscous stress in heating of the fuel mixture in deflagration-to-detonation transition in tubes is studied both analytically and numerically. The developed analytical theory determines temperature distribution ahead of an accelerating flame. The heating effects of viscous stress and the compression wave become comparable at sufficiently high values of the Mach number. Viscous stress makes heating and explosion of the fuel mixture preferential at the walls.In fifth part we reveal the physical mechanism of ultra-fast flame acceleration in obstructed channels used in modern experiments on detonation triggering. It is demonstrated that delayed burning between the obstacles creates a powerful jet-flow, driving the acceleration. The flame front accelerates exponentially; theanalytical formula for the growth rate is obtained. The theory is validated by extensive direct numerical simulations and comparison to previous experiments.The last part of the thesis concerns the transition from deflagration to detonation. It is found that in sufficiently wide free-slip channels and for sufficiently fast flames Landau-Darrieus instability may invoke nucleation of hot spots within the wrinkled flame folds, triggering an abrupt transition from deflagrative to detonative combustion. Results on DDT in channels with non-slip at the walls are also presented.

Place, publisher, year, edition, pages
Stockholm: KTH, 2008. viii, 75 p.
Keyword
flame, premixed, instability, fractal, deflagration, detonation, DDT, simulation
National Category
Physical Sciences
Identifiers
urn:nbn:se:kth:diva-4875 (URN)978-91-7415-115-2 (ISBN)
Public defence
2008-10-03, Sal B2, Materialvetenskap, Brinellvägen 23, KTH, Stockholm, 13:00 (English)
Opponent
Supervisors
Note
QC 20100915Available from: 2008-09-30 Created: 2008-09-09 Last updated: 2010-09-16Bibliographically approved
2. The role of Landau-Darrieus instability in flame dynamics and deflagration-to-detonation transition
Open this publication in new window or tab >>The role of Landau-Darrieus instability in flame dynamics and deflagration-to-detonation transition
2007 (English)Licentiate thesis, comprehensive summary (Other scientific)
Abstract [en]

The role of intrinsic hydrodynamic instability of the premixed flame (known as Landau-Darrieus instability) in various flame phenomena is studied by means of direct numerical simulations of the complete system of hydrodynamic equations. Rigorous study of flame dynamics and effect of Landau-Darrieus instability is essential for all premixed combustion problems where multidimensional effects cannot be disregarded.

The present thesis consists of three parts. The first part deals with the fundamental problem of curved stationary flames propagation in tubes of different widths. It is shown that only simple "single-hump" slanted stationary flames are possible in wide tubes, and "multi-hump" flames in a laminar flow are possible in wide tubes only as a non-stationary mode of flame propagation. The stability limits of curved stationary flames in wider tubes are obtained, together with the dependence of the velocity of the stationary flame on the tube width. The flame dynamics in wider tubes is shown to be governed by a large-scale stability mechanism resulting in a highly slanted flame front.

The second part of the thesis is dedicated to studies of acceleration and fractal structure of outward freely propagating flames. It is shown that in direct numerical simulation the development of Landau-Darrieus instability results in the formation of fractal-like flame front structure. The fractal excess for radially expanding flames in cylindrical geometry is evaluated. Two-dimensional 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 2D geometry obtained in the numerical simulation is in good agreement with theoretical predictions. The difference in fractal dimension between 2D 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.

The last part of the thesis concerns the role of Landau-Darrieus instability in the transition from deflagration to detonation. It is found that in sufficiently wide channels Landau-Darrieus instability may invoke nucleation of hot spots within the folds of the developing wrinkled flame, triggering an abrupt transition from deflagrative to detonative combustion. It is found that the mechanism of the transition is the temperature increase due to the influx of heat from the folded reaction zone, followed by autoignition. The transition occurs when the pressure elevation at the accelerating reaction front becomes high enough to produce a shock capable of supporting detonation.

Place, publisher, year, edition, pages
Stockholm: KTH, 2007. vi, 58 p.
Keyword
flame, premixed, instability, front, Landau, Darrieus, fractal, freely, deflagration, detonation, transition, DDT, modeling, simulation
National Category
Other Materials Engineering
Identifiers
urn:nbn:se:kth:diva-4334 (URN)978-91-7178-612-8 (ISBN)
Presentation
2007-04-20, Konferensrum K 408, Materialvetenskap, KTH, Brinellvägen 23, Stockholm, 14:00
Opponent
Supervisors
Note
QC 20101119Available from: 2007-04-17 Created: 2007-04-17 Last updated: 2010-11-19Bibliographically approved

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