Inferring Flame Transfer Functions of Turbulent Conical Flames From Pressure Measurements

We use approximate Bayesian inference, accelerated by adjoint methods, to construct a quantitatively accurate model of the thermoacoustic behavior of a weakly turbulent conical flame in a duct. We first perform a series of automated experiments to generate a dataset. The data consist of time-series pressure measurements from which we extract (i) the eigenvalue, whose real part is the growth rate and imaginary part is the angular frequency, and (ii) the pressure eigenmode measured at several axial locations. We assimilate the data into a thermoacoustic network model to infer the unknown model parameters. We begin this process by rigorously characterizing the acoustics of the cold rig. We then introduce a series of different flames and infer their flame transfer functions (FTF) with quantified uncertainty bounds. The flame transfer function is obtained with the flames in situ, so it accounts for any confinement or heat loss effects. The inference process uses only pressure measurements, so the technique is suitable for complex combustors where optical access is not available, provided the eigenvalue or eigenmode of oscillations can be measured. We validate the method by comparing the inferred fluctuating heat release rate (HRR) against direct measurements. We find that the inferred quantities compare well with the direct measurements, but the uncertainty bounds can be large if the experimental error is large.