Numerical study of two-dimensional effects associated with laser-induced ignition in hydrogen-oxygen mixtures

Abstract

Numerical simulation of reacting flows (combustion processes, chemical vapour deposition, hypersonics etc.) is a demanding task due to the strong interaction of flow field, chemistry and molecular transport. Mathematical modelling is performed by solving the set of Navier-Stokes equations (i.e., conservation of mass, energy, momentum, and species mass) which involves an enormous numerical and computational effort due to the large number of equations, the strong coupling and the non-linearity of the partial differential equation system. A numerical method for the solution of the stiff partial differential equation systems is described allowing the globally implicit simulation of unsteady chemically reacting laminar flows in up to two space dimensions. Spatial discretization on structured grids that are adapted statically leads to large differential-algebraic equation systems which are solved numerically by implicit extrapolation or BDF (backward differentiation formula) methods. Due to the large dimension of the differential-algebraic equation system, the sparse structure of the Jacobian (which is needed for the implicit solvers) has to be used for the evaluation of the Jacobian as well as for the solution of the linear equation systems. Results are presented for the one- and two-dimensional simulation of laser-induced ignition of hydrogen-oxygen mixtures in a finite cylinder. It is shown that the reduction of the problem to one spatial dimension is not appropriate for a description of the physical phenomenon considered. Additionally, results of a successful numerical simulation of the ignition by a physically realistic tailled shape of the igniting laser beam are presented. This is a truly two-dimensional physical phenomenon, and cannot be described by a one-dimensional approach.