Reacting, circular mixing layers in transition to turbulence

The evolution of a reacting, circular mixing layer - a model of round-jet f low - in its transition to turbulence was studied by direct numerical simul ation. An economical Fourier pseudospectral method was combined with the th ird-order Adams-Bashforth scheme to integrate Navier-Stokes and scalar tran sport equations. The Reynolds number based on initial mixing-layer diameter and velocity difference was 1600. The initially thin mixing layer encloses a cylindrical core of fuel that mixes and reacts with the surrounding oxid izer. Both fast and finite-rate reactions were examined. The stages in tran sition are characterized by roll-up of the mixing layer into a sequence of vortex rings, pairing of adjacent rings, azimuthal instability, and breakdo wn to a disordered (turbulent) state. Reaction surfaces in the fast reactio n limit become extended, folded and pinched off at various times correspond ing to the dynamics of the vortices observed in the simulations. When the e quivalence 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, the flame is located well outside the rings and is r elatively unaffected. Following breakdown to turbulence, there is a steep i ncrease in flame surface area resulting in a noticeable change in fuel cons umption rate. At smaller reaction rates (small Damkohler numbers), the reac tion zones are diffuse and fill the vortical (mixed) regions. Product accum ulates in and its presence raises the temperature of vortex cores, but reac tion rates remain low due to low reactant concentrations. Reaction rates ar e highest in the braids between vortex rings where scalar dissipation rates and compressive strain rates show the highest values.