Researchers from Skoltech have published a paper in the journal Physica D presenting an analysis of steady propagating combustion waves — from slow flames to supersonic detonation waves. The study relies on the authors’ mathematical model, which captures the key physical properties of complex combustion processes and yields accurate analytical and numerical solutions. Supported by a Russian Science Foundation grant, the findings are important for understanding the physical mechanisms behind the transition from deflagration to detonation, as well as for developing safer engines, fuel combustion systems, and protection against unwanted explosions in industrial settings.
The scientists identified several main types of combustion waves. The most powerful is strong detonation — a supersonic shock wave that sharply compresses and heats the mixture, triggering a chemical reaction. This type of wave is highly stable. In weak detonations and weak deflagration waves, there is no abrupt shock front. The chemical reaction only begins if the mixture has been preheated to a temperature where it can ignite. These regimes occur rarely, under specific conditions, and can easily break down or transition into another wave type. Finally, ordinary flames are slow, subsonic waves. Their speed depends on how quickly the heat released by the reaction manages to warm the fresh, cold fuel ahead.
To arrive at these results, the researchers used two complementary approaches. First, they applied analytical methods to derive approximate formulas describing wave structure in different zones. These formulas reveal general patterns. Then, they ran precise numerical simulations based on the full model equations to verify the formulas. This dual approach not only confirmed the theoretical findings but also provided a clear picture of how combustion waves — their temperature, pressure, and reaction progress — evolve under changing conditions. A key outcome was comparing the simplified model’s solutions with those from far more complex and complete gas dynamics equations (the Navier–Stokes equations for compressible reacting flows). The close agreement demonstrated that, despite its relative simplicity, the authors’ model correctly captures the fundamental physics of combustion waves, making it a powerful tool for further theoretical research.
“This study shows that even heavily simplified models can serve as a powerful tool for understanding complex dynamic processes. We not only confirmed that our model qualitatively matches the Navier–Stokes equations but also laid the groundwork for future studies — for example, analyzing wave stability or exploring transient combustion regimes,” shared Shamil Magomedov, the study lead author and a PhD student in the Engineering Systems program at Skoltech.
The study’s supervisor, Associate Professor Aslan Kasimov at the Skoltech AI Center, emphasized both the theoretical and practical significance of the work: “This model is significantly simpler than the full equations, yet complex enough to allow effective investigation of how combustion develops in all its forms. The complete classification of all steady combustion regimes was just the first step. Now we can study how stable these regimes are, how they interact with each other, and under what conditions the dangerous transition from ordinary slow flame to explosive detonation wave occurs. This is directly relevant to controlling combustion processes and preventing accidents in engines and industrial facilities.”
