Near limit premixed flamelets in Hele-Shaw cells

Abstract

In this paper, we report a preliminary attempt to stabilize near limit premixed flamelets in Hele-Shaw cells. As a quasi-two-dimensional analog of flame balls, the flamelet is sustained by diffusive transport alone, with fuel supplied from the open ends of the Hele-Shaw cell, and heat dissipated to the ambient environment through conduction; radiative heat losses from both phases are neglected. Following Spalding's "one-dimensional idealization" approximation, we construct a 2-D model to account for the heat and mass transfer processes in both the gas and the solid phases, with the gap height as a parameter controlling the heat exchange rate between the two phases. For each of the three kinds of wall materials considered, two steady solution branches are obtained as a function of the gap height, one corresponding to large flames and the other to small flames. The large flame branch is critically dependent on the boundary and is therefore of little physical value. Linear stability analysis shows that the small flame branch is unstable to random perturbations. 2-D time dependent numerical simulations indicate that a slightly perturbed steady state on the small flame branch either evolves into a single flamelet drifting to the boundary as a whole, or splits into two drifting to the boundary along opposite directions. A partially open square Hele-Shaw combustor has been proposed and is shown to be able to support stabilized flamelets for a certain range of the degree of opening.