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

A coupled numerical approach is investigated for predicting combustion instability limit cycle characteristics when the combustor contains a long flame. The test case is the ORACLES combustor, with a turbulent premixed flame a metre long: it exhibits limit cycle oscillations at ∼ 50 Hz and normalised velocity amplitude ahead of the flame of ∼ 0.29. The approach obtains the flame response to acoustic excitation using Large Eddy Simulations (LES), and couples this with a low-order wave-based network representation for the acoustic waves within the combustor. The flame cannot be treated as acoustically compact; the spatial distribution of both its response and the subsequent effect on the acoustics must be accounted for. The long flame is uniformly segmented axially, each segment being much shorter than the flow wavelengths at play. A series of “local” flame describing functions, one for the heat release rate response within each segment to velocity forcing at a fixed reference location, are extracted from the LES. These use the Computational Fluid Dynamics toolbox, OpenFOAM, with an incompressible approximation for the flow-field and combustion modelled using the Partially Stirred Reactor model with a global onestep reaction mechanism. For coupling with the low-order acoustic network modelling, compact acoustic jump conditions are derived and applied across each flame segment, while between flame segments, wave propagation occurs. Limit cycle predictions from the proposed coupled method agree well with those predicted using the continuous 1-D linearised Euler equations, validating the flame segmentation implementation. Limit cycle predictions (frequency 51.6 Hz and amplitude 0.38) also agree well with experimental measurements, validating the low-order coupled method as a prediction tool for combustors with long flames. A sensitivity analysis shows that the predicted limit cycle amplitude decreases rapidly when acoustic losses at boundaries are accounted for, and increases if combustor heat losses downstream of the flame are accounted for. This motivates more accurate determination of combustor boundary and temperature behaviour for thermoacoustic predictions

The flow over a flat plate at a Reynolds number of 750 is numerically investigated via fine large-eddy simulation (LES), first at normal ( $90\textdegree $ ) and then at oblique ( $45\textdegree $ ) incidence flow direction with a uniform steady inlet. The results are in complete agreement with the direct numerical simulation (DNS) and experimental data, thereby serving as a validation for the present simulations. For the normal ( $90\textdegree $ ) uniform inflow case, coherent vortices are alternately shed from both leading edges of the plate, whereas for the oblique ( $45\textdegree $ ) uniform inflow case the vortices shed from the two sides of the plate interact strongly resulting in a quasi-periodic force response. The normal flat plate is then analysed with an incident gust signal with varying amplitude and time period. For these incident coherent gust cases, a reference test case with variable coherent inlet is first studied and the results are compared to a steady inlet simulation, with a detailed analysis of the flow behaviour and the wake response under the incident gust. Finally, the flat plate response to 16 different gust profiles is studied. A transient drag reconstruction for these incident coherent gust cases is then presented based on a frequency-dependent transfer function and phase spectrum analysis.