Optimal ignition placement in diffusion flames by nonlinear adjoint looping

Abstract

We derive and implement a gradient-based optimization framework to identify the best place to ignite a mixture of fuel and oxidizer. We have used the time-averaged in- crease in thermal energy as the cost function that indicates the success of ignition. We use direct numerical simulation (DNS) of the low Mach number Navier–Stokes equations with single-step finite-rate reaction chemistry to model spark ignition of an axisymmetric methane jet in air.We model the spark as a two-dimensional Gaussian function. We solve the adjoint of these equations to obtain the sensitivity of the cost function with respect to the position of the spark. We find that the optimal locations track the stoichiometric mixture fraction surface in the flow. At low Reynolds numbers, the optimization prefers locations downstream that allow upstream flame propagation.