Linear stability analysis of a premixed flame with transverse shear
Abstract
One-dimensional planar premixed flames propagating in a uniform flow are susceptible to hydrodynamic instabilities known (generically) as Darrieus–Landau instabilities. Here, we extend that hydrodynamic linear stability analysis to include a lateral shear. This generalization is a situation of interest for laminar and turbulent flames when they travel into a region of shear (such as a jet or shear layer). It is shown that the problem can be formulated and solved analytically and a dispersion relation can be determined. The solution depends on a shear parameter in addition to the wavenumber, thermal expansion ratio, and Markstein lengths. The study of the dispersion relation shows that perturbations have two types of behaviour as wavenumber increases. First, for small shear, we recover the Darrieus–Landau results except for a region at small wavenumbers, large wavelengths, that is stable. Initially, increasing shear has a stabilizing effect. But, for sufficiently high shear, the flame becomes unstable again and its most unstable wavelength can be much smaller than the Markstein length of the zero-shear flame. Lastly, the stabilizing effect of low shear can make flames with negative Markstein numbers stable within a band of wavenumbers.
- Authors:
-
- Univ. of Illinois at Urbana-Champaign, Urbana, IL (United States)
- Publication Date:
- Research Org.:
- California Institute of Technology (CalTech), Pasadena, CA (United States)
- Sponsoring Org.:
- USDOE National Nuclear Security Administration (NNSA), Office of Defense Programs (DP)
- OSTI Identifier:
- 1343118
- Grant/Contract Number:
- NA0002382
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Journal of Fluid Mechanics
- Additional Journal Information:
- Journal Volume: 765; Journal ID: ISSN 0022-1120
- Publisher:
- Cambridge University Press
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; flames; instability; reacting flows
Citation Formats
Lu, Xiaoyi, and Pantano, Carlos. Linear stability analysis of a premixed flame with transverse shear. United States: N. p., 2015.
Web. doi:10.1017/jfm.2014.728.
Lu, Xiaoyi, & Pantano, Carlos. Linear stability analysis of a premixed flame with transverse shear. United States. https://doi.org/10.1017/jfm.2014.728
Lu, Xiaoyi, and Pantano, Carlos. Mon .
"Linear stability analysis of a premixed flame with transverse shear". United States. https://doi.org/10.1017/jfm.2014.728. https://www.osti.gov/servlets/purl/1343118.
@article{osti_1343118,
title = {Linear stability analysis of a premixed flame with transverse shear},
author = {Lu, Xiaoyi and Pantano, Carlos},
abstractNote = {One-dimensional planar premixed flames propagating in a uniform flow are susceptible to hydrodynamic instabilities known (generically) as Darrieus–Landau instabilities. Here, we extend that hydrodynamic linear stability analysis to include a lateral shear. This generalization is a situation of interest for laminar and turbulent flames when they travel into a region of shear (such as a jet or shear layer). It is shown that the problem can be formulated and solved analytically and a dispersion relation can be determined. The solution depends on a shear parameter in addition to the wavenumber, thermal expansion ratio, and Markstein lengths. The study of the dispersion relation shows that perturbations have two types of behaviour as wavenumber increases. First, for small shear, we recover the Darrieus–Landau results except for a region at small wavenumbers, large wavelengths, that is stable. Initially, increasing shear has a stabilizing effect. But, for sufficiently high shear, the flame becomes unstable again and its most unstable wavelength can be much smaller than the Markstein length of the zero-shear flame. Lastly, the stabilizing effect of low shear can make flames with negative Markstein numbers stable within a band of wavenumbers.},
doi = {10.1017/jfm.2014.728},
journal = {Journal of Fluid Mechanics},
number = ,
volume = 765,
place = {United States},
year = {Mon Jan 19 00:00:00 EST 2015},
month = {Mon Jan 19 00:00:00 EST 2015}
}
Web of Science
Works referenced in this record:
Effects of premixed flames on turbulence and turbulent scalar transport
journal, February 2010
- Lipatnikov, A. N.; Chomiak, J.
- Progress in Energy and Combustion Science, Vol. 36, Issue 1
Extinction of a nonadiabatic flame propagating through spatially periodic shear flow
journal, February 1995
- Brailovsky, I.; Sivashinsky, G.
- Physical Review E, Vol. 51, Issue 2
Instabilities, Pattern Formation, and Turbulence in Flames
journal, January 1983
- Sivashinsky, G. I.
- Annual Review of Fluid Mechanics, Vol. 15, Issue 1
On Flame Stretch
journal, April 1983
- Matalon, Moshe
- Combustion Science and Technology, Vol. 31, Issue 3-4
On flame extinction by a spatially periodic shear flow
journal, December 1998
- Kagan, L.; Sivashinsky, G.; Makhviladze, G.
- Combustion Theory and Modelling, Vol. 2, Issue 4
Premixed flame propagation in a high-intensity, large-scale vortical flow
journal, July 1996
- Aldredge, R. C.
- Combustion and Flame, Vol. 106, Issue 1-2
Weakly Turbulent, Wrinkled Flames in Premixed Gases
journal, April 1986
- Searby, G.; Clavin, P.
- Combustion Science and Technology, Vol. 46, Issue 3-6
Flame propagation and extinction in large-scale vortical flows
journal, January 2000
- Kagan, L.; Sivashinsky, G.
- Combustion and Flame, Vol. 120, Issue 1-2
Influence of hydrodynamics and diffusion upon the stability limits of laminar premixed flames
journal, November 1982
- Pelce, Pierre; Clavin, Paul
- Journal of Fluid Mechanics, Vol. 124, Issue -1
On a distorted flame front as a hydrodynamic discontinuity
journal, November 1976
- Sivashinsky, G. I.
- Acta Astronautica, Vol. 3, Issue 11-12
Influence of Momentum and Heat Losses on the Large-Scale Stability of Quasi-2D Premixed Flames
journal, June 1994
- Joulin, G.; Sivashinsky, G.
- Combustion Science and Technology, Vol. 98, Issue 1-3
A petascale direct numerical simulation study of the modelling of flame wrinkling for large-eddy simulations in intense turbulence
journal, August 2012
- Hawkes, Evatt R.; Chatakonda, Obulesu; Kolla, Hemanth
- Combustion and Flame, Vol. 159, Issue 8
Flames as gasdynamic discontinuities
journal, November 1982
- Matalon, M.; Matkowsky, B. J.
- Journal of Fluid Mechanics, Vol. 124, Issue -1
SHORT COMMUNICATION On Flame Propagation Through Periodic Flow Fields
journal, November 1991
- Ashurst, William T.; Sivashinsky, Gregory I.
- Combustion Science and Technology, Vol. 80, Issue 1-3
Flame Extinction by Periodic Flow Field
journal, April 1991
- Berestycki, Henri; Sivashinsky, Gregory I.
- SIAM Journal on Applied Mathematics, Vol. 51, Issue 2
Curved and stretched flames: the two Markstein numbers
journal, September 2011
- Clavin, Paul; Graña-Otero, José C.
- Journal of Fluid Mechanics, Vol. 686
Turbulent premixed combustion: Flamelet structure and its effect on turbulent burning velocities
journal, February 2008
- Driscoll, J.
- Progress in Energy and Combustion Science, Vol. 34, Issue 1
On Quenching of the Reaction Wave Moving Through Spatially Periodic Shear Flow
journal, December 1993
- Brailovsky, I.; Sivashinsky, G.
- Combustion Science and Technology, Vol. 95, Issue 1-6
Strain rate effects on the nonlinear development of hydrodynamically unstable flames
journal, January 2011
- Creta, F.; Matalon, M.
- Proceedings of the Combustion Institute, Vol. 33, Issue 1
Propagation of wrinkled turbulent flames in the context of hydrodynamic theory
journal, June 2011
- Creta, F.; Matalon, M.
- Journal of Fluid Mechanics, Vol. 680
Effects of molecular diffusion and of thermal expansion on the structure and dynamics of premixed flames in turbulent flows of large scale and low intensity
journal, March 1982
- Clavin, P.; Williams, F. A.
- Journal of Fluid Mechanics, Vol. 116
On the intrinsic dynamics of premixed flames
journal, July 1990
- Sivashinsky, G. I.
- Philosophical Transactions of the Royal Society of London. Series A: Physical and Engineering Sciences, Vol. 332, Issue 1624, p. 135-148
Nonlinear analysis of hydrodynamic instability in laminar flames—I. Derivation of basic equations
journal, November 1977
- Sivashinsky, G. I.
- Acta Astronautica, Vol. 4, Issue 11-12
Intrinsic Flame Instabilities in Premixed and Nonpremixed Combustion
journal, January 2007
- Matalon, Moshe
- Annual Review of Fluid Mechanics, Vol. 39, Issue 1