Numerical simulation of three-dimensional instabilities of spherical flame structures

Abstract

The paper is concerned with the non-stationary numerical simulation of freely propagating spherically symmetric flame structures at low Lewis number in a lean hydrogen-air mixture. The three-dimensional thermodiffusive equations with a single-step chemical reaction with Arrhenius-like temperature dependence of the reaction rate and a Stefan-Boltzmann-type radiation are integrated by means of a highly accurate Fourier-pseudo-spectral method with a semi-implicit time scheme in a parallelized version. This computational effort is necessary to fulfill the requirements resulting from the wide range of scales which are present in this reaction-diffusion problem. The algorithm is applied to compute the evolution of thermodiffusive flames, where we particularly investigate the influence of the initial flame radius and the radiative heat loss onto the development of freely evolving spherical flames. In the computations we obtain different scenarios of expanding flame structures as found in recent experimental studies under microgravity conditions, for example, the extinction because of excessive heat loss, the splitting due to cellular instability, and the observation of quasi-steady three-dimensional flame balls. Furthermore, we show the necessity of simulations in all physical dimensions to incorporate three-dimensional instabilities which in rotationally symmetric calculations cannot be included. Finally, we show the time evolution of flame structures which are initially disturbed by an artificial function to simulate natural perturbation of flame balls.