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Flame Dynamics and Deflagration-to-Detonation Transition
KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Applied Material Physics.
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 [en]
flame, premixed, instability, fractal, deflagration, detonation, DDT, simulation
National Category
Physical Sciences
Identifiers
URN: urn:nbn:se:kth:diva-4875ISBN: 978-91-7415-115-2 (print)OAI: oai:DiVA.org:kth-4875DiVA: diva2:415
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
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: 2017-12-13Bibliographically 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: 2017-12-13Bibliographically 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
4. Heating of the fuel mixture due to viscous stress ahead of accelerating flames in deflagration-to-detonation transition
Open this publication in new window or tab >>Heating of the fuel mixture due to viscous stress ahead of accelerating flames in deflagration-to-detonation transition
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2008 (English)In: Physics Letters A, ISSN 0375-9601, E-ISSN 1873-2429, Vol. 372, no 27-28, 4850-4857 p.Article in journal (Refereed) Published
Abstract [en]

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 analytical theory is developed in the limit of low Mach number; it determines temperature distribution ahead of an accelerating flame with maximum achieved at the walls. The heating effects of viscous stress and the compression wave become comparable at sufficiently high values of the Mach number. In the case of relatively large Mach number, viscous heating is investigated by direct numerical simulations. The simulations were performed on the basis of compressible Navier–Stokes gas-dynamic equations taking into account chemical kinetics. In agreement with the theory, viscous stress makes heating and explosion of the fuel mixture preferential at the walls. The explosion develops in an essentially multi-dimensional way, with fast spontaneous reaction spreading along the walls and pushing inclined shocks. Eventually, the combination of explosive reaction and shocks evolves into detonation.

Keyword
CURVED STATIONARY FLAMES, WIDE TUBES, NONSLIP, WALLS, PROPAGATION, SIMULATION, MECHANISM
National Category
Physical Sciences
Identifiers
urn:nbn:se:kth:diva-9147 (URN)10.1016/j.physleta.2008.04.066 (DOI)000257416200020 ()2-s2.0-44749086431 (Scopus ID)
Note

QC 20100915

Available from: 2008-09-24 Created: 2008-09-24 Last updated: 2017-06-15Bibliographically approved
5. Physical Mechanism of Ultrafast Flame Acceleration
Open this publication in new window or tab >>Physical Mechanism of Ultrafast Flame Acceleration
2008 (English)In: Physical Review Letters, ISSN 0031-9007, E-ISSN 1079-7114, Vol. 101, no 16, 164501-1-164501-4 p.Article in journal (Refereed) Published
Abstract [en]

We explain the physical mechanism of ultrafast flame acceleration in obstructed channels used in modern experiments on detonation triggering. It is demonstrated that delayed burning between the obstacles creates a powerful jetflow, driving the acceleration. This mechanism is much stronger than the classical Shelkin scenario of flame acceleration due to nonslip at the channel walls. The mechanism under study is independent of the Reynolds number, with turbulence playing only a supplementary role. The flame front accelerates exponentially; the analytical formula for the growth rate is obtained. The theory is validated by extensive direct numerical simulations and comparison to previous experiments.

Keyword
Computer simulation, Direct numerical simulation, Reynolds number, Analytical formulas, Channel walls, Flame accelerations, Flame fronts, Physical mechanisms, Ultrafast
National Category
Physical Sciences
Identifiers
urn:nbn:se:kth:diva-9148 (URN)10.1103/PhysRevLett.101.164501 (DOI)000260141300023 ()2-s2.0-54849405187 (Scopus ID)
Note
QC 20100915. Uppdaterad från submitted till published (20100915).Available from: 2008-09-24 Created: 2008-09-24 Last updated: 2017-12-13Bibliographically approved
6. Different stages of flame acceleration from slow burning to Chapman-Jouguet deflagration
Open this publication in new window or tab >>Different stages of flame acceleration from slow burning to Chapman-Jouguet deflagration
2009 (English)In: Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, ISSN 1539-3755, Vol. 80, no 3, 036317- p.Article in journal (Refereed) Published
Abstract [en]

Numerical simulations of spontaneous flame acceleration are performed within the problem of flame transition to detonation in two-dimensional channels. The acceleration is studied in the extremely wide range of flame front velocity changing by 3 orders of magnitude during the process. Flame accelerates from realistically small initial velocity (with Mach number about 10(-3)) to supersonic speed in the reference frame of the tube walls. It is shown that flame acceleration undergoes three distinctive stages: (1) initial exponential acceleration in the quasi-isobaric regime, (2) almost linear increase in the flame speed to supersonic values, and (3) saturation to a stationary high-speed deflagration velocity. The saturation velocity of deflagration may be correlated with the Chapman-Jouguet deflagration speed. The acceleration develops according to the Shelkin mechanism. Results on the exponential flame acceleration agree well with previous theoretical and numerical studies. The saturation velocity is in line with previous experimental results. Transition of flame acceleration regime from the exponential to the linear one, and then to the constant velocity, happens because of gas compression both ahead and behind the flame front.

Keyword
chemically reactive flow, combustion, flames, Mach number, supersonic flow
National Category
Physical Sciences
Identifiers
urn:nbn:se:kth:diva-9149 (URN)10.1103/PhysRevE.80.036317 (DOI)000270383500059 ()2-s2.0-70349970663 (Scopus ID)
Note
QC 20100915. Uppdaterad från submitted till published (20100915). Tidigare titel: Different stages of flame acceleration in the process of detonation triggeringAvailable from: 2008-09-24 Created: 2008-09-24 Last updated: 2010-09-15Bibliographically approved

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