Premixed flame–wall interaction in a narrow channel: impact of wall thermal conductivity and heat losses

Abstract

The flow physics controlling the stabilisation of a methane/air laminar premixed flame in a narrow channel (internal width $\ell _{i}=5~\text{mm}$) is revisited from numerical simulations. Combustion is described with complex chemistry and transport properties, along with a coupled simulation of heat transfer at and within the wall. To conduct a thorough analysis of the flame–wall interaction, the steady flame is obtained after applying a procedure to find the inlet mass flow rate that exactly matches the flame mass burning rate. The response of the premixed flame shape to various operating conditions is then analysed in terms of flame propagation velocity and flow topology in the vicinity of the reactive front. We focus on the interrelations between the flame speed, the configuration taken by the flame surface, the flow deviation induced by the heat released and the fluxes at the wall. Compared to an adiabatic flame, the flame speed increases with edge-flame quenching at an isothermal cold wall in the absence of a boundary layer, decreases with a boundary layer, to increase again with heat-transfer coupling within the wall. A regime diagram is proposed to delineate between flame shapes in order to build a classification versus heat-transfer properties. Under a small level of convective heat transfer with the ambient air surrounding the channel, the larger the thermal conductivity in the solid, the faster the reaction zone propagates in the vicinity of the wall, leaving the centreline reaction zone behind. The premixed flame front is then concave towards the fresh gases on the axis of symmetry (so-called tulip flame) with a flame speed higher than in the adiabatic case. Increasing the heat loss at the wall through convection with ambient air, the flame shape becomes convex (mushroom flame) and the flame speed decreases below its adiabatic level. Scaling laws are provided for the flame speed under these various regimes. Mesh resolution was calibrated, with and without heat loss, from simulations of one-dimensional detailed chemistry flames, leading to mesh resolution of $12.5~\unicode[STIX]{x03BC}\text{m}$ for detailed chemistry and $25.0~\unicode[STIX]{x03BC}\text{m}$ with a skeleton mechanism. The quality of the resolution was also assessed from multi-physics budgets derived from first principles, involving upstream-flame heat retrocession by the wall leading to flow acceleration, budgets bringing physical insights into flame/wall interaction. Additional overall mesh convergence tests of the multi-physics solution would have been desirable, but were not conducted due to the high computing cost of these fully compressible simulations, hence also solving for the acoustic field with low convective velocities.