Direct numerical simulation of turbulent, chemically reacting flows A THESIS SUBMITTED TO THE FACULTY OF THE GRADUATE SCHOOL OF THE UNIVERSITY OF MINNESOTA BY Jeffrey Joseph Doom IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY

This dissertation: (i) develops a novel numerical method for DNS/LES of compressible, turbulent reacting flows, (ii) performs several validation simulations, (iii) studies auto–ignition of a hydrogen vortex ring in air and (iv) studies a hydrogen/air turbulent diffusion flame. The numerical method is spatially non-dissipative, implicit and applicable over a range of Mach numbers. The compressible Navier–Stokes equations are rescaled so that the zero Mach number equations are discretely recovered in the limit of zero Mach number. The dependent variables are co–located in space, and thermodynamic variables are staggered from velocity in time. The algorithm discretely conserves kinetic energy in the incompressible, inviscid, non–reacting limit. The chemical source terms are implicit in time to allow for stiff chemical mechanisms. The algorithm is readily applicable to complex chemical mechanisms. Good results are obtained for validation simulations. The algorithm is used to study auto–ignition in laminar vortex rings. A nine species, nineteen reaction mechanism for H2/air combustion proposed by Mueller et al. [37] is used. Diluted H2 at ambient temperature (300 K) is injected into hot air. The simulations study the effect of fuel/air ratio, oxidizer temperature, Lewis number and stroke ratio (ratio of piston stroke length to diameter). Results show that auto–ignition occurs in fuel lean, high