Reacting, Circular Mixing Layers in Transition to Turbulence

Abstract

The evolution of a reacting, circular mixing layer – a modelof round-jet flow – in its transition to turbulence was studied bydirect numerical simulation. An economical Fourier pseudospectral methodwas combined with the third-order Adams–Bashforth scheme to integrateNavier–Stokes and scalar transport equations. The Reynolds number basedon initial mixing-layer diameter and velocity difference was 1600. Theinitially thin mixing layer encloses a cylindrical core of fuel thatmixes and reacts with the surrounding oxidizer. Both fast andfinite-rate reactions were examined. The stages in transition arecharacterized by roll-up of the mixing layer into a sequence of vortexrings, pairing of adjacent rings, azimuthal instability, and breakdownto a disordered (turbulent) state. Reaction surfaces in the fastreaction limit become extended, folded and pinched off at various timescorresponding to the dynamics of the vortices observed in thesimulations. When the equivalence ratio is O(1) or smaller,the progress of reaction is determined by the dynamics of vortex rings.For larger ratios there is a qualitative difference: Initially, theflame is located well outside the rings and is relatively unaffected.Following breakdown to turbulence, there is a steep increase in flamesurface area resulting in a noticeable change in fuel consumption rate.At smaller reaction rates (small Damkohler numbers), the reaction zonesare diffuse and fill the vortical (mixed) regions. Product accumulatesin and its presence raises the temperature of vortex cores, but reactionrates remain low due to low reactant concentrations. Reaction rates arehighest in the braids between vortex rings where scalar dissipationrates and compressive strain rates show the highest values.