Features of the interaction of the combustion front of diluted methane–oxygen mixtures with hollow cylindrical and conical obstacles at low pressures

It was shown that the front of the flame of a well-mixed diluted methane–oxygen mixture at 298 K and 100–300 Torr propagating to the ends of hollow cylindrical and conical obstacles does not form a vortex shedding behind them; however, that instability occurs under the same conditions in the flow of hot products after the obstacles. To find out the reason that vortex shedding is not observed behind the obstacle at flame propagation, but vortex shedding appears in the course of propagation of a reflected stream of hot products, we consider the curved flame front. Let us show that the thermal conductivity should reduce the curvature of the flame and lead to its stabilization. Indeed, the convex areas of the chemical reaction zone in a combustible mixture in relation to the cold ones shall give up more heat than in a flat flame: the heat from these is not only transmitted forward in the direction of flame propagation, but also in the lateral directions. The resulting cooling of the reaction zone will cause the backlog of the areas of the flame that burst forward. The opposite situation will be for concave areas where the temperature rises for the same reasons, reactions rates increase, and they spread forward faster as the flame spreads. Thus, the surface of the curved front of the flame aligns. In other words, the thermal conductivity has a stabilizing effect on the curved flame. This effect is missing in non-reactive gas. The calculations showed that the main observed feature of the flame front propagation against an obstacle in the form of a cylinder is taken into account: vortex shedding is not observed behind the obstacle at flame propagation; the simple consideration was given above. Thus, the qualitative model of compressible non-reactive/reactive Navier–Stokes equations in low Mach number approximation allows obtaining both the mode of the emergence of von Karman instability in chemically inert gas and the absence of the mode for flame propagation.