Abstract
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.
Highlights
Noise emitted by the power generating devices is deemed an important environmental pollution, and there is an increasing emphasis on making these systems quieter [1]
Expectedly, by setting u 1⁄4 0, the transfer function G in Eq (54) tends to unity. This means that in the limit of zero frequency there is no dispersion of the entropy waves, which is consistent with the physics of the problem
The horizontal axis in this figure represents the nozzle outlet to inlet stagnation temperature ratio (q). This figure contains the results of Marble and Candel [14], which are independent of the variations in the stagnation temperature and assume an adiabatic flow
Summary
Noise emitted by the power generating devices is deemed an important environmental pollution, and there is an increasing emphasis on making these systems quieter [1]. In a combined analytical and numerical investigation, Duran et al [24,25] considered the subsonic case in Bake et al experiment [22] They showed that the compact model of Marble and Candel [14] can only predict the noise generation at low Mach numbers in their case studies [24,25]. A systematic evaluation of these effects upon the acoustic and entropic responses of nozzles has not been reported To address this issue, the current study adds the dissipation and dispersion of the entropy waves to a predictive model of indirect combustion noise. The current study adds the dissipation and dispersion of the entropy waves to a predictive model of indirect combustion noise This is achieved by considering the hydrodynamic and thermal effects of the flow field on entropy waves and further allowing for the entropy wave stretch in the nozzle. Prediction of the phase shift by considering the concept of ‘effective length’ in a non-compact nozzle with a finite length is another advantage of the current analytical approach
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