  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 m/s to 2.99 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.
