The Effect of Viscosity on Hydrodynamic Stability of a Plane Flame Front

Frankel, Michael L.; Sivashinsky, G. I.

doi:10.1080/00102208208923598

Cited by 120 publications

(52 citation statements)

References 3 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…[17][18] The behavior of the disturbed flame front, i.e. growing exponentially with time, is observed only when the amplitude is sufficiently small.…”

Section: Dispersion Relationsmentioning

confidence: 99%

Effects of the Unburned-Gas Temperature and Lewis Number on the Intrinsic Instability of High-Temperature Premixed Flames

Kadowaki

Yahata

Kobayashi

2011

JTST

View full text Add to dashboard Cite

The effects of the unburned-gas temperature and Lewis number on the intrinsic instability of high-temperature premixed flames under the constant-enthalpy conditions were investigated by two-dimensional unsteady calculations of reactive flows.A sinusoidal disturbance with sufficiently small amplitude was superimposed on a planar flame to obtain the relation between the growth rate and wave number, i.e. the dispersion relation. As the unburned-gas temperature became higher, the growth rate increased and the unstable range widened. This was due to the increase of the burning velocity of a planar flame. In addition, the obtained numerical results were consistent with the theoretical solutions in small wave-number region. As the Lewis number became smaller ( larger ), the growth rate increased ( decreased ) and the unstable range widened ( narrowed ), which was due to diffusive-thermal effects. The dispersion relation yielded the linearly most unstable wave number, i.e. the critical wave number. The critical wave number increased as the unburned-gas temperature became higher. Thus, the critical wavelength shrank, and then the cell size shrank. To clarify the characteristics of cellular flames induced by intrinsic instability, a finite disturbance with the critical wavelength was superimposed. The superimposed disturbance evolved, and a cellular-shaped front formed. In all Lewis numbers, the behavior of cellular flames became milder as the unburned-gas temperature became higher, even though the growth rate increased. The normalized burning velocities of cellular flames decreased monotonously.This was because that the thermal-expansion effects became weaker owing to the decrease of the difference in temperature between the burned and unburned gases, which was generated by the conditions of constant enthalpy, i.e. constant burned-gas temperature.

show abstract

“…[17][18] The behavior of the disturbed flame front, i.e. growing exponentially with time, is observed only when the amplitude is sufficiently small.…”

Section: Dispersion Relationsmentioning

confidence: 99%

Effects of the Unburned-Gas Temperature and Lewis Number on the Intrinsic Instability of High-Temperature Premixed Flames

Kadowaki

Yahata

Kobayashi

2011

JTST

View full text Add to dashboard Cite

show abstract

“…Since, apart from for the pressure, the steady, flame solution is independent of the Prandtl number, and P r is known to have only a very weak effect on flame stability [6,12], throughout this paper we set P r = 0.75. Here will consider the case n = 2 in order to retain analytical simplicity of the steady flame structure (the equation for Y 0 is then linear and decoupled from the T 0 and F 0 equations), and such that it has precisely the same structure as in the CDM considered previously [14], with which we seek to compare.…”

Section: The Modelmentioning

confidence: 99%

“…The constant density model (CDM) used by Sivashinsky [5] ignores any hydrodynamic effects, and is formally valid only in the limit of small heat of reaction. Several workers then independently obtained long-wavelength asymptotic solutions of the linear stability problem, in the context of the Reactive Navier-Stokes equations [6][7][8]. These 'slowly varying flame' analyses capture mainly hydrodynamic effects on the flame stability.…”

Section: Introductionmentioning

confidence: 99%

Effect of thermal expansion on the linear stability of planar premixed flames for a simple chain-branching model: The high activation energy asymptotic limit

Sharpe

2008

Combustion Theory and Modelling

View full text Add to dashboard Cite

Published paperThe linear stability of freely propagating, adiabatic, planar premixed flames is investigated in the context of a simple chain-branching chemistry model consisting of a chain-branching reaction step and a completion reaction step. The role of chain-branching is governed by a crossover temperature. Hydrodynamic effects, induced by thermal expansion, are taken into account and the results compared and contrasted with those from a previous purely thermal-diffusive constant density linear stability study. It is shown that when thermal expansion is properly accounted for, a region of stable flames predicted by the constant density model disappears, and instead the flame is unstable to a long-wavelength cellular instability. For a pulsating mode, however, thermal expansion is shown to have only a weak effect on the critical fuel Lewis number required for instability. These effects of thermal expansion on the two-step chain-branching flame are shown to be qualitatively similar to those on the standard one-step reaction model. Indeed, as found by constant density studies, in the limit that the chain-branching crossover temperature tends to the adiabatic flame temperature, the two-step model can be described to leading order by the one-step model with a suitably defined effective activation energy.

show abstract

“…The second contribution to the stretch is due to the rate of strain of the gas flow, n-Vv-n, where v is the velocity of the fresh gas. The analysis provides also an expression of the proportionality constant, the Markstein length C, which has been obtained under very general conditions in terms of the physicochemical properties of the reactive mixture [8][9][10][11][12][13][14]. It is worth noticing that this interpretation in terms of the stretch holds because Eq.…”

Section: Introductionmentioning

confidence: 99%

Local burning velocity in a Bunsen jet flame

García-Soriano

Castillo

Higuera³

et al. 2012

Comptes Rendus. Mécanique

View full text Add to dashboard Cite

A PIV-based system has been set-up for the simultaneous measurement of the local burning velocity of premixed flames and the flame stretch due to the flame front curvature and the incoming flow strain rate. For moderately short jet flames, these measurements allow an indirect determination of the Markstein length, according to Clavin and Joulin (C-J) theory. For tall flames, the flame curvature becomes relatively large in a region around the tip where the C-J theory breaks down. However, our experiments confirm the appearance of a new linear relation between burning velocity and curvature at the flame tip. This relation defines a new proportionality factor which is probably associated to the evolution from rounded tips to slender tips when the jet velocity is increased.

show abstract

The Effect of Viscosity on Hydrodynamic Stability of a Plane Flame Front

Cited by 120 publications

References 3 publications

Effects of the Unburned-Gas Temperature and Lewis Number on the Intrinsic Instability of High-Temperature Premixed Flames

Effects of the Unburned-Gas Temperature and Lewis Number on the Intrinsic Instability of High-Temperature Premixed Flames

Effect of thermal expansion on the linear stability of planar premixed flames for a simple chain-branching model: The high activation energy asymptotic limit

Local burning velocity in a Bunsen jet flame

Contact Info

Product

Resources

About