Journal of Engineering Mathematics

, Volume 74, Issue 1, pp 37-52

First online:

Impact of curvature on the kinematic response of small flames

  • Daehyun WeeAffiliated withDepartment of Environmental Science and Engineering, Ewha Womans University Email author 
  • , Sungbae ParkAffiliated withBosch Thermotechnology
  • , Ahmed F. GhoniemAffiliated withDepartment of Mechanical Engineering, Massachusetts Institute of Technology

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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 frequency-domain 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 first-order 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 time-varying 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 low-frequency range, and a good correspondence between the results with and without the curvature effect is achieved.


Conical flames Curvature Flame kinematics Transfer function Thermoacoustic instability