Bayesian inference of physics-based models of acoustically-forced laminar premixed conical flames

Abstract

We perform twenty experiments on an acoustically-forced laminar premixed Bunsen flame and assimilate high-speed footage of the natural emission into a physics-based model containing seven parameters. The experimental rig is a ducted Bunsen flame supplied by a mixture of methane and ethylene. A high-speed camera captures the natural emission of the flame, from which we extract the position of the flame front. We use Bayesian inference to combine this experimental data with our prior knowledge of this flame’s behaviour. This prior knowledge is expressed through (i) a model of the kinematics of a flame front moving through a model of the perturbed velocity field, and (ii) a priori estimates of the parameters of the above model with quantified uncertainties. We find the most probable a posteriori model parameters using Bayesian parameter inference, and quantify their uncertainties using Laplace’s method combined with first-order adjoint methods. This is substantially cheaper than other common Bayesian inference frameworks, such as Markov Chain Monte Carlo. This process results in a quantitatively-accurate physics-based reduced-order model of the acoustically forced Bunsen flame for injection velocities ranging from $1.75\text{m/s}$ to $2.99\text{m/s}$ and equivalence ratio values ranging from 1.26 to 1.47, using seven parameters. We use this model to evaluate the heat release rate between experimental snapshots, to extrapolate to different experimental conditions, and to calculate the flame transfer function and its uncertainty for all the flames. Since the proposed model relies on only seven parameters, it can be trained with little data and successfully extrapolates beyond the training dataset. Matlab code is provided so that the reader can apply it to assimilate further flame images into the model.

Novelty and Significance Statement Thermoacoustic systems tend to be extremely sensitive to small parameter changes, which makes them difficult to model a priori from existing models in the literature. This means, however, that thermoacoustic models tend to be easy to train using data-driven methods because, with well-chosen experiments, their parameters can be easily observed from experimental data. This paper presents a novel use of Bayesian inference to combine experimental measurements, numerical simulations, and prior knowledge about flame behaviour. We outline our methodology and demonstrate its effectiveness using a laminar premixed Bunsen flame. Our approach yields a quantitatively-accurate physics-based model that predicts the expected value and uncertainty bounds of the flame transfer function between velocity and heat release rate perturbations. The proposed model contains only seven physical parameters, which is fewer parameters than non-physics-based models, and can therefore be trained on relatively little data. We also illustrate how the trained model effectively extrapolates beyond the training dataset. Our numerical code and experimental data are open access.