On the Response of a Lean-premixed Hydrogen Combustor to Acoustic and Dissipative-dispersive Entropy Waves

Combustion of hydrogen or hydrogen containing blends in gas turbines and industrial combustors can activate thermoacoustic combustion instabilities. Convective instabilities are an important and yet less investigated class of combustion instability that are caused by the so called “entropy waves”. As a major shortcoming, the partial decay of these convective-diffusive waves in the post-flame region of combustors is still largely unexplored. This paper, therefore, presents an investigation of the annihilating effects, due to hydrodynamics, heat transfer and flow stretch upon the nozzle response. The classical compact analysis is first extended to include the decay of entropy waves and heat transfer from the nozzle. Amplitudes and phase shifts of the responding acoustical waves are then calculated for subcritical and supercritical nozzles subject to acoustic and entropic forcing. A relation for the stretch of entropy wave in the nozzle is subsequently developed. It is shown that heat transfer and hydrodynamic decay can impart considerable effects on the entropic response of the nozzle. It is further shown that the flow stretching effects are strongly frequency dependent. The results indicate that dissipation and dispersion of entropy waves can significantly influence their conversion to sound and therefore should be included in the entropy wave models.