Gasdynamics modeling of countergradient transport in open and impinging turbulent premixed flames

A model for countergradient transport recently developed by us for one-dimensional freely propagatingturbulent premixed flames is extended here to the case of flames impinging on a wall. According to this approach the progress variable flux ρ u ″ c ″ ¯ is split into a gasdynamics (pressure-driven, countergradient) component and a turbulent (diffusive, gradient) one. The first component, which does not depend directly on turbulence, is estimated using a gasdynamics model based on the key assumption of constant reactant total pressure which, together with mass and momentum conservation, permits determination of the conditional velocities in reactant and product streams. The second component is estimated instead with the standard positive turbulent diffusion coefficient given by the k — ∈ model (independently of overall transport being of gradient or countergradient nature). The approach makes it possible to resolve the problem of countergradient transport without using empirical constants and for one-dimensional freely propagating flames to express the solution in analytical form. The model shows reasonable agreement with the experimental results when applied to a Bunsen-type open flame in the direction orthogonal to the flame front and to three impinging flames (for which the turbulent component of transport can be neglected). Impinging flames are the most critical for validation of the model as the wall counteracts the reduction of pressure across the flame connected with heat release. We show, in fact, here that the effect of the local difference between conditional pressures in the reactants and products streams due to the moving flamelets is not very significant in the open flame but becomes decisive in the impinging one. We demonstrate also that, in agreement with experimental data, countergradient, transport in our model strongly depends on the location of the flame relative to the wall (the closer the flame to thewall, the weaker the phenomenon).