Simulation of the flame describing function of a turbulent premixed flame using an open-source LES solver

Abstract

Numerical simulations were used to characterise the non-linear response of a turbulent premixed flame to acoustic velocity fluctuations. The test flame simulated was the bluff body stabilised flame which has been the subject of a detailed experimental study (Balachandran et al., 2005, Combustion & Flame). Simulations were performed using Large Eddy Simulation (LES) via the open source Computational Fluid Dynamics (CFD) software, Code S aturne, with combustion modelled by combining a Flame Surface Density (FSD) method with a fractal approach for the wrinkling factor. The cold flow field and the unforced reacting flow were used for preliminary code validation. In order to characterise the non-linear response of the unsteady heat release rate to acoustic forcing, a harmonically varying velocity fluctuation, for which both the forcing frequency and normalised forcing amplitude were varied, was imposed. The flame response was characterised via a Flame Describing Function (FDF), also known as a nonlinear flame transfer function, for which the gain and phase shift depend on forcing amplitude as well as forcing frequency. The response at four frequencies was compared to experimental data in detail, confirming that the LES results captured both the qualitative flame dynamics and the quantitative response of the heat release rate with very reasonable accuracy. The full FDF was then obtained across more frequencies, again showing a good fit with the experimental data, other than for a slight under-prediction in gain, most probably due to neglecting the effect of wall heat loss and the effect of combustion modelling. The agreement was significantly better than has been obtained previously for this test case using numerical simulations. Finally, it was found that increasing combustor length had little affect on the flame response, which may prove useful for future long combustor stability and limit cycle analysis. This work thus confirms that LES, in this case via the open source Code S aturne, provides a useful tool for characterising the response of lean premixed turbulent flames.

Prediction of combustion instability limit cycle oscillations by combining flame describing function simulations with a thermoacoustic network model

“…The case has an "acoustically short" flame within the combustor which simplifies determination of the FDF and its coupling with low order network models. For the fully-premixed case, LES has been recently performed [34] and the obtained FDF agrees well with experimental data. However, unstable thermoacoustic behaviour and hence limit cycle oscillations are only observed in the partially-premixed case (possible flame flash back has limited conditions considered under fullypremixed conditions).…”

“…A and f are varied independently in the simulations in order to obtain the FDF. Forcing of this form has been used to simulate harmonic loudspeaker forcing of a flame in previous numerical studies [30,[34][35][36][37]. This approach means that, at the computational inlet, the "acoustic" perturbations are mapped to "hydrodynamic" fluctuations for the purpose of the flame response as this is well known to be dominated by hydrodynamics.…”

“…It is a pure turbulent flow past a bluff body, for which previous LES studies [34,61,90] have been performed. For comparisons, the previous LES studies are referred to as LES-1 and LES-2, corresponding to the results from refs.…”

“…Consequently, low-Mach number or "incompressible LES" [34][35][36][37] can be used to determine the FDF as the flame response is well known to be unaffected by compressibility effects [20,29,38]. The use of low-Mach number or incompressible LES to identify the FDF is explained and justified in detail in other recent references [34][35][36][37]. Based on these ideas, the present study uses a similar low-Mach number LES solver to study an acoustically forced partially-premixed flame in order to identify the full FDF.…”

Bifurcation and nonlinear analysis of a time-delayed thermoacoustic system

“…Morgans and her co-workers [13][14] used a network model combined with flame describing function to predict the nonlinear thermoacoustic behaviour in combustors. Juniper [15] employed adjoint looping of the nonlinear governing equations as well as an optimization routine to study the triggering mechanism, including the non-normality, transient growth and bypass transition.…”