Thermoacoustic instabilities in gas turbine combustion systems, caused by a feedback loop between acoustic fluctuations and the flame, can be a major factor in determining the durability of the combustor. Of interest here are helical modes caused by a Kelvin-Helmholtz instability emanating from a region of high shear close to the outlet of the fuel injector. A liquid fuelled lean burn fuel injector, containing three air flow passages is studied in the present work using non-reacting compressible unsteady RANS CFD simulations. An acoustic wave is injected at the downstream boundary with excitation frequencies of 300Hz and 450Hz to compare to an unforced case. Analysis of the flow response is carried out using linear stability analysis, Proper Orthogonal Decomposition (POD) and Dynamic Mode Decomposition (DMD). The linear stability analysis required interpolation of the solution from the unstructured CFD grid onto a uniform cylindrical polar mesh. The analysis found an absolute instability in the shear region between two passages. This m = −2 mode is unstable over frequencies from 400Hz to 1000Hz with wavelengths of 1.08 to 1.41 of the injector outer diameter. For the unforced case the POD identifies the first two modes with azimuthal wave number m = 1 and these are seen to spiral from the splitter plate inwards to disturb the pilot and outwards to the main. The dominant frequency is around 450Hz which is consistent with measurements and close to the linear stability analysis value. For the 300Hz forced case POD identifies the first four modes as being helical but has difficulty determining the dominant azimuthal wave number. There is shown to be a significant interaction between the acoustic and helical modes and double the total resolved kinetic energy as compared to the unforced case. The 450Hz forced case shows the asymmetric m = 1 mode to be damped and the m = 2 helical mode is relatively unchanged. The resolved kinetic energy was only marginally higher than the unforced case and significantly lower than the 300Hz forced case. The DMD analysis showed how, as the forcing increased the flow through the injector, the flow is simultaneously pushed radially inwards and accelerated azimuthally. It also identified the region downstream of the splitter plate with significant fluctuations and is likely to be the wavemaker region responsible for the generation of helical instabilities. This work improves understanding of how helical modes of different azimuthal wave numbers react to acoustic forcing. The ability to manipulate the strength of these modes through alteration of the fuel injector geometry gives designers an additional tool to control thermo-acoustic instabilities.

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