New Advances in the Understanding of the Stabilization Mechanism of High-Speed Deflagrations in Channels
Among diverse modes of flame propagation in smooth channels, supersonic high-speed deflagrations, which have a high propensity to transition to detonation after a transient acceleration, have been rarely studied. Recently, a work entitled “On the stabilization mechanism of high-speed deflagrations in narrow channels with heat loss” has been published in the “Proceedings of the Combustion Institute” by the group of D. Valiev, Center for Combustion Energy, Tsinghua University.
The so-called “choked flames”, propagating at speeds close to the sound speed in the burned products, are relatively commonly observed in obstructed passages. However, recent experiments on combustion of hydrogen-air mixtures at cryogenic temperatures (Kuznetsov et al., Int. J. Hydrogen Energy, 2022 & Shen et al., Proc. Combust. Inst., 2023) showed that it may be possible to obtain nearly stationary supersonic flame propagation in smooth channels. Recognizing that cryogenic combustion is characterized by large thermal expansion, reaching values over 20, these results prompted an investigation into the potential role of gas expansion in attaining supersonic deflagrations.

Figure 1 : Temporal evolution of the scaled flame tip velocity for different thermal expansion coefficients (Pe=20). Dash-dotted lines are the value of theoretical CJ deflagration velocity FCJ.
Motivated by the above considerations, the authors conduct a systematic, parametric computational study of flame propagation in narrow channels with the goal of investigating the combined effects of heat loss, thermal expansion, and wall friction, on high-speed deflagration limits. As shown in Fig.1, the high-speed deflagrations are characterized by the periodic oscillations of the flame tip velocity. Even so, the average velocities are fairly close to their respective theoretical Chapman-Jouguet deflagration velocity values, corresponding to the dash-dotted lines in Fig.1.
In Fig.2, the four flame propagation regimes are mapped. Two boundary lines approximately outline the limits of the high-speed deflagration mode. The existence of the Hcr boundary indicates that the wall heat loss is a key factor in attaining the high-speed deflagration through DDT suppression. The critical heat loss parameter Hcr increases with the thermal expansion coefficient Θ, indicating that the high-speed deflagrations are likely the result of attaining a form of dynamic balance between the thermal expansion and wall heat loss.

Figure 2 : The distribution of extinction, low-speed deflagration, DDT, and high-speed deflagration for different thermal expansion coefficients Θ and heat loss parameters H.
In Fig. 3, the numerical schlieren images are shown for the time instants within a single oscillation cycle. The existence of two pressure/shock waves in front of the flame is seen. The leading shock wave tends to get weaker with distance between the curved reaction front and the leading shock decreases gradually during the flame acceleration stage.
The wave interaction process is illustrated in Fig. 4. The inset contains the zoomed image for the three oscillation cycles. It is seen that the leading shock indeed undergoes the repetitive process of acceleration and deceleration. During the acceleration stage, there is an increase in the volume of

Figure 3: Numerical schlieren images for the times instants in the one oscillation cycle.
burnt gas generated per unit time. This additional burnt gas volume subsequently gets cooled down by wall heat loss, and a backward flow is created. This slows down the flame and weakens the leading shock. Re-acceleration is triggered by the combined effects of non-slip at the wall and gas expansion.
Provided by: Damir Valiev Research Group
Approved by: Yu Cheng Liu, Xiaoqing You

Figure 4: Wave diagram based on the temporal scan of the axial schlieren profile
Summary: In this study, the limits of supersonic deflagration in smooth channels in terms of gas expansion were studied for the first time. A novel mechanism for attaining the supersonic deflagrations in channels is proposed, based on the idea of the dynamic balance between thermal expansion and wall heat loss. Significant new insights into the structure of the deflagration front and shock waves are provided. A unique process of the periodic reinforcing and deceleration of the leading shock is identified.
The first author of the paper is Canruo Chen, a Ph.D. student from the Center for Combustion Energy at Tsinghua University. Associate Professor Damir Valiev is the corresponding author. The work was sponsored by the National Natural Science Foundation of China (NSFC) through Grant No. 52176118, and by the startup funding from Tsinghua University.
The article link: https://doi.org/10.1016/j.proci.2024.105318.