Different Modes of Combustion Wave on a Lattice Burner - Vasily B. Novozhilov; Boris V. Lidskii; Vladimir S. Posvyanskii (Mathematics, 2022)
The stabilization of a planar premixed flame front on a lattice (porous) burner is considered. The developed model captures all the important features of the phenomenon, while also admitting qualitative analytical investigation. It has been rigorously mathematically proven that there exist two different stabilization regimes: one with flame front located nearby the surface of the burner, and another with the flame front located inside the lattice. These two regimes result in qualitatively different gas temperature profiles along the flow that is monotonic and non-monotonic, respectively. The boundary between the two regimes is described in terms of dependence of the lattice solid material temperature on flow Peclet number. With similar temperature profiles, such dependencies may be both monotonic and non-monotonic. The transition between the two types of dependencies is controlled by the Arrhenius number. Conclusions of the study are supported by numerical analysis. They also compare favorably with the available experimental data. The novelty of the present approach is a fundamentally rigorous analytical analysis of the problem. The proposed analytical model, based on <semantics>δ</semantics>-function approximation of the chemical source term, agrees well (within 7% relative error) with the model based on the distributed description of the chemical reaction zone. The obtained results are important from both a theoretical and practical point of view. They demonstrate the existence of the two qualitatively different operating regimes for lattice burners, thus impacting design solutions for such devices. The results will be of great interest to the broader academic community, particularly in research areas where similar wave structures may emerge.