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

Abstract

a b s t r a c t Accurate prediction of limit cycle oscillations resulting from combustion instability has been a long-standing challenge. The present work uses a coupled approach to predict the limit cycle characteristics of a combustor, developed at Cambridge University, for which experimental data are available (Balachandran, Ph.D. thesis, 2005). The combustor flame is bluff-body stabilised, turbulent and partially-premixed. The coupled approach combines Large Eddy Simulation (LES) in order to characterise the weakly non-linear response of the flame to acoustic perturbations (the Flame Describing Function (FDF)), with a low order thermoacoustic network model for capturing the acoustic wave behaviour. The LES utilises the open source Computational Fluid Dynamics (CFD) toolbox, OpenFOAM, with a low Mach number approximation for the flow-field and combustion modelled using the PaSR (Partially Stirred Reactor) model with a global one-step chemical reaction mechanism for ethylene/air. LES has not previously been applied to this partially-premixed flame, to our knowledge. Code validation against experimental data for unreacting and partially-premixed reacting flows without and with inlet velocity perturbations confirmed that both the qualitative flame dynamics and the quantitative response of the heat release rate were captured with very reasonable accuracy. The LES was then used to obtain the full FDF at conditions corresponding to combustion instability, using harmonic velocity forcing across six frequencies and four forcing amplitudes. The low order thermoacoustic network modelling tool used was the open source OSCILOS (http://www.oscilos.com). Validation of its use for limit cycle prediction was performed for a well-documented experimental configuration, for which both experimental FDF data and limit cycle data were available. The FDF data from the LES for the present test case was then imported into the OSCILOS geometry network and limit cycle oscillations of frequency 342 Hz and normalised velocity amplitude of 0.26 were predicted. These were in good agreement with the experimental values of 348 Hz and 0.21 respectively. This work thus confirms that a coupled numerical prediction of limit cycle behaviour is possible using an entirely open source numerical framework.

Dispersion of Entropy Perturbations Transporting through an Industrial Gas Turbine Combustor

“…Based on the PaSR model, the filtered chemical reaction rate of the i -th species, , can be scaled by κ and modelled as [23, 40]: where denotes the mean concentration of species i exiting the mesh cell, and is the initial mean concentration of species i inside the same cell. Δ t is the computational time step, and denotes the density-weighted (Favre) filtering, defined as for an arbitrary variable ψ .…”

“…Previous large eddy simulations (LES) [21–23] and experiments [24] of combustor reacting flow-fields have shown that the main large-scale flow features, such as flow separation and recirculation zones, are the same whether the flame is fully-premixed [22], partially-premixed [23], or non-premixed [21, 24]. The mean and fluctuating velocity fields are both qualitatively and quantitatively very similar in all cases.…”

Flame Double Input Describing Function analysis

“…This shows that a large number of calculations is required to accurately estimate the FDIDF. This makes it currently non-affordable f or, say, compressible LES studies, in which many CPU hours are already required to calculate the FDF only [57] .…”

Acoustic Models for Cooled Helmholtz Resonators

“…In order to study the thermoacoustic modes, we use a low order thermoacoustic network modelling tool -in this case the open source OSCILOS [15,25] which has been validated against experiments [26]. As shown in Fig.…”