Simulating Diffusion in Detonations

John Ziegler, California Institute of Technology

The goal of this research is the Direct Numerical Simulation of the Mach reflection phenomenon and diffusive multi-species mixing as it occurs in gaseous detonations. These physical processes occur at and near the multi-dimensional triple point structures and shear mixing layers of detonation fronts. This work tackles the problems of modeling and algorithms to obtain accurate simulations. Due to a lack of computational power, resolution, and efficient algorithms, previous research, at best, has mostly modeled detonations using the 3D reactive Euler equations with simplified chemistry.

To date, generally two different numerical methods have been used: a 2nd order finite volume MUSCL scheme, and a 6th order finite difference hybrid WENO/centered-difference scheme. A systematic verification study was completed, starting with the DMR (Double Mach Reflection) problem to compare under-resolved and resolved simulations. A convergence study for the non-reactive DMR was conducted, using comparisons of free shear layer theory and investigating the visual convergence of the results. To aid in this goal, a manufactured solution of the convecting, steady, radially symmetric Lamb-Oseen Vortex was constructed. Also, a verification study of diffusive reacting flow was completed. The reactive 3D (2D cylindrical) two species reactive Navier-Stokes equations for a resolved spark ignition problem and preliminary under-resolved diffusive detonation simulations have been conducted using the 2nd order method. These results will be extended to the reduced-species models of oxygen-hydrogen detonation and the more unstable hydrocarbon fuels.

The ultimate goal of this research is a stable, high order, robust formulation that can be used for an extension to 3D simulations. Currently infeasible with our present resources, but as a goal in the far future is a 3D simulation of the spark ignition and detonation problems.

Abstract Author(s): Jack Ziegler