A New Approach to Quantify Flame Acceleration due to Wall Friction in a Micro-Slit.

Lateef Adewale Kareem


Various analytical models have been developed to describe velocity profile for flame acceleration (FA) and deflagration-to-detonation transition (DDT), but none accounts for observed acceleration to constant velocity seen in case of micro gaps (in which the flow stays laminar even at speed of sound). To fill such a gap, here we propose an alternative model, which is based on the first physical principles and agrees with the experimental finding that FA is subsequently replaced by steady flame propagation. Starting with the Navier-stokes for a radial flow between two flat plates, we set the pressure gradient to be proportional to the vertical component of a velocity function, split the resulting differential equation in velocity into the vertical and temporal component,  and then absorbed the driving force into the temporal component equation. The unknown parameters were computed by using nonlinear optimization to fit the model to the experimental measurement showing good agreement between the model and the experiments.


Premixed flames1; Flame acceleration; Deflagration-to-detonation transition; Direct numerical simulations

Full Text:



Akkerman, V., Bychkov, V., Petchenko, A., Eriksson, L.E.: Accelerating flames in cylindrical tubes with nonslipat the walls. Combustion and Flame145(1-2), 206–219 (2006). doi:10.1016/j.combustflame.2005.10.011

Demirgok, B., Sezer, H., Akkerman, V.: Flame acceleration due to wall friction: Accuracy and intrinsic limitationsof the formulations. Modern Physics Letters B29(32), 1–16 (2015). doi:10.1142/S021798491550205X3.

Bychkov, V., Petchenko, A., Akkerman, V., Eriksson, L.E.: Theory and modeling of accelerating flames in tubes.Physical Review E - Statistical, Nonlinear, and Soft Matter Physics72(4), 1–10 (2005).doi:10.1103/PhysRevE.72.0463074.

Chiang, E.Y.M.: Introduction to Bessel and Related Special Functions, pp. 9–30 (2008)

Copyright (c) 2020 Proceedings of the West Virginia Academy of Science

Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.