Analytical Modeling of the Injector Response to High Frequency Modes in a Tubular Multi-Jet-Combustor

Abstract

Gas turbine combustors with multi-jet burners have been shown to provide better fuel flexibility compared to large swirl burners and can meet current low emissions standards at increasing turbine inlet temperatures. In case thermoacoustic combustion instabilities occur, the resonant feedback loop of the thermoacoustic mode in the chamber leads to injector coupling, which has not yet been investigated in same depth as in rocket engines in the past. The higher order mode inside the combustor initiates longitudinal modes in the upstream injector tubes leading to flame surface and location modulations as potential drivers of instability. Furthermore, fuel injection in the mixing tubes generate equivalence ratio fluctuations, which have an additional influence on flame dynamics. As these effects deteriorate emissions, flashback safety and lead to increased wear or even severe damage of the combustor, proper calculation of the acoustic injector response is an important aspect of combustor stability modelling. The paper at hand aims for an analytical model to describe the injector response to higher order modes as an alternative to the existing approaches, which are largely based on numerical computations. For this purpose, lumped parameter models are used to calculate the wave scattering at the injector tube-chamber interface. It is shown that the Rankine-Hugoniot conditions at the area jump can be applied to high frequency acoustics in a similar manner as to low frequency acoustics. Numerical simulations in COMSOL are used to verify the model for the first and second transversal and the first radial mode.