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Heating of the fuel mixture due to viscous stress ahead of accelerating flames in deflagration-to-detonation transition
KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering.
Department of Physics, Umeå University.
Department of Physics, Umeå University.
Department of Thermo- and Fluid Dynamics, Chalmers University of Technology.
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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.

Place, publisher, year, edition, pages
2008. Vol. 372, no 27-28, 4850-4857 p.
Keyword [en]
CURVED STATIONARY FLAMES, WIDE TUBES, NONSLIP, WALLS, PROPAGATION, SIMULATION, MECHANISM
National Category
Physical Sciences
Identifiers
URN: urn:nbn:se:kth:diva-9147DOI: 10.1016/j.physleta.2008.04.066ISI: 000257416200020Scopus ID: 2-s2.0-44749086431OAI: oai:DiVA.org:kth-9147DiVA: diva2:25284
Note

QC 20100915

Available from: 2008-09-24 Created: 2008-09-24 Last updated: 2017-06-15Bibliographically 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

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