Intrinsic low-dimensional manifold method extended with diffusion

Abstract

It is necessary to use chemical reduction techniques for the modeling of complex burner systems. The intrinsic low-dimensional manifold (ILDM) method has proved to be a useful method to simplify detailed reaction mechanisms. However, diffusion is neglected in the construction of the manifold, which results in less accurate manifolds in regions where both chemistry and diffusion are significant, which is generally the case in a large part of the reaction zone. This paper presents a new reduction method, which uses the basic principles of intrinsic low-dimensional manifolds. A manifold is constructed in the composition phase space instead of the composition space, so that the gradients of species concentrations and enthalpy can be used to include diffusion within the manifold. The composition phase space is spanned by the species mass fractions, the enthalpy, and their corresponding diffusive fluxes. The second-order conservation equations are transformed into first-order equations by introducing flux terms. The resulting set of first-order equations are used to construct the manifold. The procedure used to define the manifold is equivalent to the ILDM method. The new method, called phase space ILDM (PS-ILDM), is applied to a simple but illustrative example, and finally a manifold for a CO/H2 mechanism is presented. The results show that the new method gives more accurate manifolds than the ILDM method for parts of the flame where both reaction and diffusion are important. In addition, fluctuations of enthalpy and element fractions due to preferential diffusion are included in the manifold. This may result in a database with a lower dimension and therefore a more effective reduction.