Asymptotic analysis is conducted for outwardly propagating spherical flames with large activation energy. The spherical flame structure consists of the preheat zone, reaction zone, and equilibrium zone. Analytical solutions are separately obtained in these three zones and then asymp- totically matched. In the asymptotic analysis, we derive a correlation describing the spherical flame temperature and propagation speed changing with the flame radius. This cor- relation is compared with previous results derived in the limit of infinite value of activation energy. Based on this correla- tion, the properties of spherical flame propagation are inves- tigated and the effects of Lewis number on spherical flame propagation speed and extinction stretch rate are assessed. Moreover, the accuracy and performance of different mod- els used in the spherical flame method are examined. It is found that in order to get accurate laminar flame speed and Markstein length, non-linear models should be used.
In this paper, the extended finite element method (XFEM) is adopted to analyze the interaction between a single macroscopic inclusion and a single macroscopic crack as well as that between multiple macroscopic or microscopic defects under thermal/mechanical load. The effects of different shapes of multiple inclusions on the material thermomechanical response are investigated, and the level set method is coupled with XFEM to analyze the interaction of multiple defects. Further, the discretized extended finite element approximations in relation to thermoelastic problems of multiple defects under displacement or temperature field are given. Also, the interfaces of cracks or materials are represented by level set functions, which allow the mesh assignment not to conform to crack or material interfaces. Moreover, stress intensity factors of cracks are obtained by the interaction integral method or the M-integral method, and the stress/strain/stiffness fields are simulated in the case of multiple cracks or multiple inclusions. Finally, some numerical examples are provided to demonstrate the accuracy of our proposed method.
