Energy analysis of unsteady negative edge flames in a periodic flow

Non-premixed laminar or turbulent flames can undergo extinction when scalar dissipation rates exceed a critical value. When local extinction occurs, negative edge flames that act to expand the region of extinction are initially present. Steady negative edge flames have been previously studied in a combustor designed to support the negative propagation velocity of the flame edge, but unsteady negative edge flames have not received significant attention. The current study uses numerical simulations in a simple flowfield to produce unsteady negative edge flames which oscillate in response to imposed strain rate fluctuations in order to understand the dynamic response of extinction edge propagation. An energy balance through the edge shows that the unsteady behavior can be well described by a simple extension of the energy balance from steady flames. Furthermore, the edge velocity was calculated, and a physical interpretation of the extinction velocity was derived using the energy budget. The time scale of the imposed strain rate fluctuations was varied to show a limited response time for the extinction edge flame dynamics.