Impact of curvature on the kinematic response of small flames
 Daehyun Wee,
 Sungbae Park,
 Ahmed F. Ghoniem
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The objective of the study is to investigate the impact of curvature on the kinematic response of an axisymmetric curved laminar premixed flame, utilizing a phenomenological relationship between the curvature and the laminar burning velocity. The reference and the perturbed flame shapes are obtained by numerically or analytically integrating the flame kinematics equations. The steady reference flame shape deviates gradually from that obtained without the curvature effect as the effect of curvature intensifies. By having its tip rounded off, the overall flame height under curvature becomes lower. Perturbed flame shapes with curvature show more attenuated undulation than those without curvature effect. Linear perturbation analysis is performed to determine the frequencydomain response of the instantaneous heat release rate to upstream flow perturbations. In the low frequency range, results are qualitatively similar to those obtained using those obtained using the model without curvature, but substantial differences in the phase shift are observed as the frequency of perturbation increases. Flames under weak curvature effects show behaviors similar to a firstorder filter, whose cutoff frequency increases as the effect of curvature becomes stronger. Careful comparison reveals that the flame is mainly influenced by the modification of the burning velocity due to the curvature of the mean reference flame at the low frequency range while the influence of the timevarying perturbed burning velocity increases as the frequency of perturbation increases. A rule for scaling the response is proposed to match the results with and without the curvature effect, based on asymptotic analysis of the flame kinematics. Rescaling is effective for the lowfrequency range, and a good correspondence between the results with and without the curvature effect is achieved.
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 Title
 Impact of curvature on the kinematic response of small flames
 Journal

Journal of Engineering Mathematics
Volume 74, Issue 1 , pp 3752
 Cover Date
 20120601
 DOI
 10.1007/s1066501194815
 Print ISSN
 00220833
 Online ISSN
 15732703
 Publisher
 Springer Netherlands
 Additional Links
 Topics
 Keywords

 Conical flames
 Curvature
 Flame kinematics
 Transfer function
 Thermoacoustic instability
 Industry Sectors
 Authors

 Daehyun Wee ^{(1)}
 Sungbae Park ^{(2)}
 Ahmed F. Ghoniem ^{(3)}
 Author Affiliations

 1. Department of Environmental Science and Engineering, Ewha Womans University, 111 Daehyundong, Seodaemungu, Seoul, 120750, Republic of Korea
 2. Bosch Thermotechnology, Zweedsestraat 1, 7418 BG, Deventer, The Netherlands
 3. Department of Mechanical Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA, 02139, USA