The effect of entropy noise on combustion instability in the presence of advective shear dispersion

When a flame burns unsteadily, two types of flow perturbation are generated. The first are acoustic waves, which propagate away from the flame at the speed of sound (relative to the flow), and are known as "direct combustion noise". The second are temperature fluctuations, also known as hot/cold spots or entropy waves, which advect away from the flame with the local flow velocity. They are initially silent, but upon being accelerated generate new acoustic waves, known as "indirect combustion noise" or "entropy noise". This can affect both combustion instability, via the upstream propagating component, and exhaust noise, via the downstream propagating component. The entropy noise generated depends crucially on the advection process between the flame, where the entropy wave is generated, and the combustor exit, where it is accelerated. New models for entropy wave advection have recently been developed, based on simplified turbulent channel flow simulations. These show that entropy waves do not dissipate, suffering only shear dispersion due to spatial variations in the time-averaged flow velocity; turbulent fluctuations have negligible effect. The effect of entropy noise on combustion instability in the context of this new advection model has not previously been considered, and is the topic of the present paper. The effect on combustor modes for mean turbulent velocity profiles exhibiting difference degrees of shear dispersion has been investigated. It is found that for a large range of practical combustors, spanning a representative range of combustor lengths, entropy noise in the presence of advective shear dispersion has the potential to strongly affect thermoacoustic modes.