A chemical-diffusive model for simulating detonative combustion with constrained detonation cell sizes

Abstract

This paper presents a way that improves the use of the chemical-diffusive model (CDM) in a fluid dynamics code to simulate the multidimensional structure of propagating gaseous detonation waves. In the CDM, a set of critical parameters is calibrated and used in a reaction rate that converts fuel to product. The parameters are currently chosen to reproduce properties of a one-dimensional standard laminar flame and the Zel’dovich-Neumann-Döring (ZND) detonation when a reaction is incorporated in the compressible Navier-Stokes equations. The ability of the CDM to compute cellular structure of stoichiometric hydrogen-air detonations is compared to results obtained using a detailed chemistry model and experimental measurements. Both the CDM and the detailed chemical model produce very similar detonation cells in terms of shape and size, but these cells are smaller than experimental values by a factor of two to three. In a new approach, the CDM is calibrated using experimental detonation cell data. A relation between the effective activation energy and the ratio of the detonation cell size to the ZND half-reaction distance is used to incorporate known properties of detonation and detonation cells in the CDM optimization procedure. Numerical simulations using the new CDM parameters reproduce detonation cells of the same size and shape as experimental measurement.