TY - JOUR
T1 - Stability of a premixed flame in stagnation-point row against general disturbances
AU - Jackson, Thomas
AU - Matalon, Moshe
N1 - Funding Information:
This work was supported in part by the National Aeronautics and Space Administration while the authors were in residence at the Institute for Computer Applications in Science and Engineering, NASA Langley Research Center, Hampton, VA 23665. TW also acknowledges supported by the AFOSR under contract 91-0180 and MM acknowledges support by the NSF under grant DMS-9104029.
PY - 1993/4/1
Y1 - 1993/4/1
N2 - In a previous analysis, the stability of a premixed flame in a stagnation point flow was discussed for a restricted class ’of disturbances that are self-similar to the basic undisturbed flow. Thus, flame fronts with corrugations only in the cross stream direction have been considered. In this paper, we consider a more general class of three-dimensional flame front perturbations, which permits corrugations in the streamwise direction as well. It is shown that, because of the stretch experienced by the flame, the hydrodynamic instability is limited only to disturbances of short wavelength. If, in addition, diffusion effects have a stabilizing influence, as would be the case for mixtures with Lewis number greater than one, a stretched flame could be absolutely stable. Instabilities occur when the Lewis number is below some critical value less than one. Neutral stability boundaries are presented in terms of the Lewis number, the strain rate and the appropriate wavenumbers. Beyond the stability threshold, the two-dimensional, self-similar modes always grow first. However, if disturbances of long wavelength are excluded, it is possible for the three-dimensional modes to be the least stable ones. Accordingly, the pattern that will be observed on the flame front, at the onset of the instability, will consist of either ridges in the direction of stretch, or the more common three-dimensional cellular structure.
AB - In a previous analysis, the stability of a premixed flame in a stagnation point flow was discussed for a restricted class ’of disturbances that are self-similar to the basic undisturbed flow. Thus, flame fronts with corrugations only in the cross stream direction have been considered. In this paper, we consider a more general class of three-dimensional flame front perturbations, which permits corrugations in the streamwise direction as well. It is shown that, because of the stretch experienced by the flame, the hydrodynamic instability is limited only to disturbances of short wavelength. If, in addition, diffusion effects have a stabilizing influence, as would be the case for mixtures with Lewis number greater than one, a stretched flame could be absolutely stable. Instabilities occur when the Lewis number is below some critical value less than one. Neutral stability boundaries are presented in terms of the Lewis number, the strain rate and the appropriate wavenumbers. Beyond the stability threshold, the two-dimensional, self-similar modes always grow first. However, if disturbances of long wavelength are excluded, it is possible for the three-dimensional modes to be the least stable ones. Accordingly, the pattern that will be observed on the flame front, at the onset of the instability, will consist of either ridges in the direction of stretch, or the more common three-dimensional cellular structure.
UR - http://www.scopus.com/inward/record.url?scp=9744223267&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=9744223267&partnerID=8YFLogxK
U2 - 10.1080/00102209308907624
DO - 10.1080/00102209308907624
M3 - Article
AN - SCOPUS:9744223267
SN - 0010-2202
VL - 90
SP - 385
EP - 403
JO - Combustion science and technology
JF - Combustion science and technology
IS - 5-6
ER -