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The role of Landau-Darrieus instability in flame dynamics and deflagration-to-detonation transition
KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering.
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 [en]
flame, premixed, instability, front, Landau, Darrieus, fractal, freely, deflagration, detonation, transition, DDT, modeling, simulation
National Category
Other Materials Engineering
Identifiers
URN: urn:nbn:se:kth:diva-4334ISBN: 978-91-7178-612-8 (print)OAI: oai:DiVA.org:kth-4334DiVA: diva2:11848
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
List of papers
1. Numerical studies of curved stationary flames in wide tubes
Open this publication in new window or tab >>Numerical studies of curved stationary flames in wide tubes
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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.

Keyword
Computer simulation, Diffusion, Hydrodynamics, Nonlinear systems, Problem solving, Reaction kinetics, Thermal conductivity, Tubes (components), Viscosity, Curved stationary flames
National Category
Physical Sciences
Identifiers
urn:nbn:se:kth:diva-9144 (URN)10.1088/1364-7830/7/4/004 (DOI)000188292300004 ()
Note
QC 20100915Available from: 2008-09-24 Created: 2008-09-24 Last updated: 2010-09-15Bibliographically approved
2. Self-acceleration and fractal structure of outward freely propagating flames
Open this publication in new window or tab >>Self-acceleration and fractal structure of outward freely propagating flames
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2004 (English)In: Physics of fluids, ISSN 1070-6631, E-ISSN 1089-7666, Vol. 16, no 7, 2476-2482 p.Article in journal (Refereed) Published
Abstract [en]

Flame acceleration associated with development of the Landau-Darrieus hydrodynamic instability is studied by means of direct numerical simulation of the Navier-Stokes equations including chemical kinetics in the form of the Arrhenius law. The fractal excess for radially expanding flames in cylindrical geometry is evaluated. Two-dimensional (2-D) 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 2-D geometry obtained in the numerical simulation is in good agreement with theoretical predictions. The difference in fractal dimension between 2-D 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.

Keyword
Computational geometry, Computer simulation, Extrapolation, Hydrodynamics, Navier Stokes equations, Reaction kinetics, Cylindrical geometry, Fractal dimensions, Power law
National Category
Physical Sciences
Identifiers
urn:nbn:se:kth:diva-9145 (URN)10.1063/1.1729852 (DOI)000221951400036 ()
Note
QC 20100915Available from: 2008-09-24 Created: 2008-09-24 Last updated: 2010-09-15Bibliographically approved
3. Numerical Simulation of Deflagration-to-Detonation Transition: the Role of Hydrodynamic Instability
Open this publication in new window or tab >>Numerical Simulation of Deflagration-to-Detonation Transition: the Role of Hydrodynamic Instability
2006 (English)In: International Journal of Transport Phenomena, ISSN 1028-6578, Vol. 8, no 3, 253-277 p.Article in journal (Refereed) Published
Abstract [en]

The role of the flame folding, induced by the classical Darrieus-Landau instability, on the transition from deflagration to detonation is studied by numerical simulations of premixed gas combustion spreading from the closed end of a semi-infinite, smooth-walled channel. It is found that in sufficiently wide channels the Darrieus-Landau instability may invoke nucleation of hot spots within the folds of the developing wrinkled flame, triggering an abrupt transition from deflagrative to detonative combustion. 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. This requires the fold to be sufficiently narrow and deep. The influence of adhesive and rough walls on the transition is discussed.

Keyword
flame, combusion, detonation, explosion, flame instabilities
National Category
Physical Sciences
Identifiers
urn:nbn:se:kth:diva-9146 (URN)
Note
QC 20100915Available from: 2008-09-24 Created: 2008-09-24 Last updated: 2010-09-15Bibliographically approved

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