Numerical methodology for simulating premixed flame propagation within closed vessels

A Navier-Stokes/embedded-manifold numerical methodology to simulate the propagation of premixed flames in closed vessels will be discussed. The methodology is based on the hydrodynamic theory wherein the flame is confined to a surface that propagates at a speed that has been derived by considering the transport and chemical processes occurring inside the flame zone. Unlike freely propagating flames, which evolve under nearly isobaric conditions, the mean pressure in the vessel increases in time, the gas is compressed, its temperature rises, and the burning rate increases substantially. The numerical solver we developed can handle these temporal variations in laminar and turbulent flows, and using an immersed boundary method, it accurately assures the implementation of the boundary conditions for vessels of arbitrary geometry. Results of flame propagation in rectangular and spherical (circular) vessels will be presented and compared to analytical solutions. Future studies will address multi-dimensional flames, where fluctuations of the flame surface result from instabilities and/or turbulence.