Numerical simulation of flames as gas-dynamic discontinuities

The dynamics of thin premixed flames is computationally studied within the context of a hydrodynamic theory. A level-set method is used to track down the flame, which is treated as a free-boundary interface. The flow field is described by the incompressible Navier–Stokes equations, with different densities for the burnt and unburnt gases, supplemented by singular source terms that properly account for thermal expansion effects. The numerical scheme has been tested on several benchmark problems and was shown to be stable and accurate. In particular, the propagation of a planar flame front and the dynamics of hydrodynamically unstable flames were successfully simulated. This includes recovering the planar front in narrow domains, the Darrieus–Landau linear growth rate for long waves of small amplitude, and the nonlinear development of cusp-like structures predicted by the Michelson–Sivashinsky equation for a small density change. The stationary flame of a Bunsen burner with uniform and parabolic outlet flows were also simulated, showing in particular a careful mapping of the flow field. Finally, the evolution of a hydrodynamically unstable flame was studied for finite amplitude disturbances and realistic values of thermal expansion. These results, which constitute one of the main objectives of this study, elucidate the effect of thermal expansion on flame dynamics.

Keywords:

• Hydrodynamic theory
• Level set
• Gas-dynamic discontinuity
• Darrieus–Landau instability
• Thermal expansion

Acknowledgments

Special thanks are due to Dr. A. Almgren for her help and for numerous consultations that we had with her which facilitated adapting the IAMR code as part of our numerical scheme. This work has been partially supported by the National Science Foundation under grants DMS-0405129 and CTS-0552140.