An alternative approach to describe flame acceleration in micro-tubes due to wall friction.
DOI:
https://doi.org/10.55632/pwvas.v91i1.576Abstract
Among various existing analytical models proposed to describe flame acceleration (FA) and deflagration-to-detonation transition (DDT), none accounts for all distinctive stages of the FA and DDT processes. To overcome 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 equation for an axial flow in a cylindrical tube, we set the pressure gradient to be proportional to the radial component of a velocity function and then absorbed the driving force into the temporal component of the resulting velocity differential equation. This leads to a model with two unknown parameters (coming from the temporal and radial component of the velocity function). Since the chemistry of the combustion is not considered in the model, these two parameters were computed by nonlinear fitting of the model to the experimental measurement showing good agreement between the model and the experiments.References
References
Chiang, E.Y.M.: Introduction to Bessel & Related Special Functions, pp. 9–30 (2008)
Akkerman, V., Bychkov, V., Petchenko, A., Eriksson, L.E.: Accelerating flames in cylindrical tubes with nonslip at the walls. Combustion and Flame 145(1-2), 206–219 (2006). doi:10.1016/j.combustflame.2005.10.011
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 Physics 72(4), 1–10 (2005).
doi:10.1103/PhysRevE.72.046307
Demirgok, B., Sezer, H., Akkerman, V.: Flame acceleration due to wall friction: Accuracy and intrinsic limitations
of the formulations. Modern Physics Letters B 29(32), 1–16 (2015). doi:10.1142/S021798491550205X
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 Physics 72(4), 1–10 (2005).
doi:10.1103/PhysRevE.72.046307
Bychkov, V., Akkerman, V.: Explosion triggering by an accelerating flame. Physical Review E - Statistical,
Nonlinear, and Soft Matter Physics 73(6), 1–11 (2006). doi:10.1103/PhysRevE.73.066305
Wu, M.H., Burke, M.P., Son, S.F., Yetter, R.A.: Flame acceleration and the transition to detonation of
stoichiometric ethylene/oxygen in microscale tubes. Proceedings of the Combustion Institute 31 II, 2429–2436
(2007). doi:10.1016/j.proci.2006.08.098
Downloads
Published
How to Cite
Issue
Section
License
Proceedings of the West Virginia Academy of Science applies the Creative Commons Attribution-NonCommercial (CC BY-NC) license to works we publish. By virtue of their appearance in this open access journal, articles are free to use, with proper attribution, in educational and other non-commercial settings.
