This paper presents a data-driven identification framework with the objective to retrieve a flame model from the nonlinear limit cycle. The motivation is to identify a flame model for configurations, which do not allow the determination of the flame dynamics: that is commonly for industrial applications where (i) optical access for non-intrusive measurements of velocity and heat release fluctuations are not feasible and (ii) unstable combustion is monitored via multiple pressure recordings.
To demonstrate the usefulness of the method, we chose three test cases: (i) a classical Rijke tube; (ii) an experiment of a laminar flame (EM2C case) (iii) and a high-pressure, turbulent premixed flame (DLR case). The procedure is as follows: First, acoustic network models for the three cases are generated for which the in-house software taX is employed. Next, the acoustic network models are embedded in an optimization framework with the objective to identify flame parameters that match the experimental limit cycle data: based on the instability frequency and pressure amplitudes, we formulate physical constraints and an objective function in order to identify the flame model parameters gain nopt and time delay τopt in the nonlinear regime. We demonstrate for the three cases that the identified flame parameters reproduce the unstable combustion processes and highlight the usefulness of the method for control purposes.