Advances in the modelling of dispersion and diffusion of entropy waves in gas-turbine combustors

Entropy waves are an important source of indirect combustion noise and potentially contribute to the generation of thermoacoustic instabilities in gas-turbine combustors. Entropy fluctuations generated by unsteady combustion are known to disperse and diffuse as they travel towards the combustor exit. However, in low-order acoustic network codes, typically used for the analysis of gas-turbine combustors, such effects are often neglected and the transport of entropy perturbations is modelled in a simple way, with the entropy waves either advected without attenuation or completely diffused. Recent studies in simple flows have shown that both the dispersion due to a non-uniform mean velocity profile and the turbulent mixing can give important contributions to the attenuation of entropy waves. In gas-turbine combustors the effect of turbulent mixing can be even more pronounced due to the presence of swirling flows and recirculation regions, which may have a strong influence on the decay of the entropy perturbations. In this work, recent advances in the modelling of diffusion and dispersion of entropy waves are discussed with a focus on applications to gas-turbine combustors. A Large-Eddy Simulation of entropy advection in a swirling flow is presented to highlight the importance of both shear dispersion and turbulent mixing in the attenuation of entropy waves and the necessity of including both phenomena in low-order network models for a reliable evaluation of the transport of entropy perturbations in real combustors. Recently developed models for the dispersion of entropy waves, to be used in the context of low-order network codes, are also analysed and a revised model is proposed to include the effects of turbulent mixing, which is usually neglected in most of the available models