Interaction of equivalence ratio fluctuations and flow fluctuations in acoustically forced swirl flames

The generation and turbulent transport of temporal equivalence ratio fluctuations in a swirl combustor are experimentally investigated and compared to a one-dimensional transport model. These fluctuations are generated by acoustic perturbations at the fuel injector and play a crucial role in the feedback loop leading to thermoacoustic instabilities. The focus of this investigation lies on the interplay between fuel fluctuations and coherent vortical structures that are both affected by the acoustic forcing. To this end, optical diagnostics are applied inside the mixing duct and in the combustion chamber, housing a turbulent swirl flame. The flame was acoustically perturbed to obtain phase-averaged spatially resolved flow and equivalence ratio fluctuations, which allow the determination of flux-based local and global mixing transfer functions. Measurements show that the mode-conversion model that predicts the generation of equivalence ratio fluctuations at the injector holds for linear acoustic forcing amplitudes, but it fails for non-linear amplitudes. The global (radially integrated) transport of fuel fluctuations from the injector to the flame is reasonably well approximated by a one-dimensional transport model with an effective diffusivity that accounts for turbulent diffusion and dispersion. This approach however, fails to recover critical details of the mixing transfer function, which is caused by non-local interaction of flow and fuel fluctuations. This effect becomes even more pronounced for non-linear forcing amplitudes where strong coherent fluctuations induce a non-trivial frequency dependence of the mixing process. The mechanisms resolved in this study suggest that non-local interference of fuel fluctuations and coherent flow fluctuations is significant for the transport of global equivalence ratio fluctuations at linear acoustic amplitudes and crucial for non-linear amplitudes. To improve future predictions and facilitate a satisfactory modelling, a non-local, two-dimensional approach is necessary.

Flow Response of an Industrial Gas Turbine Combustor To Acoustic Forcing Extracted From Unforced Data

Gas turbine combustors are commonly operated with lean premix flames, allowing for high efficiencies and low emissions. These operating conditions are susceptible to thermoacoustic pulsations, originating from acoustic-flame coupling. To reveal this coupling, experiments or simulations of acoustically forced combustion systems are necessary, which are very challenging for real-scale applications. In this work we investigate the possibility to determine the flame response to acoustic forcing from snapshots of the unforced flow. This approach is based on three central hypothesis: first, the flame response is driven by flow fluctuations, second, these flow fluctuations are dominated by coherent structures driven by hydrodynamic instabilities, and third, these instabilities are driven by stochastic forcing of the background turbulence. As a consequence the dynamics in the natural flow should be low-rank and very similar to those of the acoustically forced system. In this work, the methodology is applied to experimental data of an industry-scale swirl combustor. A resolvent analysis is conducted based on the linearized Navier-Stokes equations to assure analytically the low-rank behavior of the flow dynamics. Then, these dynamics are extracted from flow snapshots using spectral proper orthogonal decomposition (SPOD). The extended SPOD is applied to determine the heat release rate fluctuations that are correlated with the flow dynamics. The low-rank flow and flame dynamics determined from the analytic and data-driven approach are then compared to the flow response determined from a classic phase average of the acoustically forced flow, which allow the research hypothesis to be evaluated. It is concluded that for the present combustor, the flow and flame dynamics are low-rank for a wider frequency range and the response to harmonic forcing can be determined quite accurately from unforced snapshots. The methodology further allows to isolate the frequency range where the flame response is predominantly driven by hydrodynamic instabilites.

A Numerical Study on the Effects of Acoustic Forcing on Fuel Spray Dynamics in Gas Turbines

In the case of aircraft engines, the fuel is injected as a liquid spray which may play a role in thermoacoustic instabilities through creating changes to the mixture fraction inside the combustion chamber. This study uses two-phase incompressible non-reacting large eddy simulation with Lagrangian particle tracking to show how spray droplets of different sizes can be affected by large scale hydrodynamic structures and acoustic forcing. The forcing is applied at the inlets of a truncated computational domain that only includes the geometry downstream of the fuel injector using the newly developed PODFS (proper orthogonal decomposition Fourier series) method. The PODFS is a model that can reproduce the effects of acoustic forcing by extracting planes of data from an auxiliary acoustically forced compressible unsteady Reynolds averaged Navier-Stokes simulation. A proper orthogonal decomposition analysis shows that fuel droplets of a typical size seen in jet engines are more sensitive to acoustic and hydrodynamic structures than droplets with an order of magnitude larger or smaller diameter, consistent with their Stokes number. Phase and azimuthally averaged results show that fluctuations of the spray mixture fraction represented by large droplets affect the total spray mixture fraction much more than fluctuations of the small droplets. An additional intermittent spray dispersion mechanism was identified that is due to intermittent vorticity being generated between the two outer injector flow passages. An injector design modification has been suggested that will reduce the prevalence of this mechanism.