Development of a Hybrid Method for Quantification of Acoustic Attenuation in a Gas Turbine Combustor with Dampers
Supervisor | Subject |
|---|---|
| Prof. Dr.-Ing. Thomas Sattelmayer | Gas Turbine, high-frequency thermoacoustics, Combustion Instabilities, resonators, CFD-CAA, FEM |
Editor | Cooperation/Funding |
| Gerrit Heilmann, M.Sc., Payam Mohammadzadeh Keleshtery, M.Sc. | This project is funded by the SIEMENS, whose support is gratefully acknowledged. |
Motivation and Objectives
A widely used countermeasure to prevent the occurrence of high-frequency combustion instabilities in gas turbines is the implementation of damping devices. Efficient dissipation of acoustic energy by such dampers and hence the disruption of the thermoacoustic feedback cycle requires appropriate dimensioning and an effective placement strategy. Therefore, the main objective of this project is to develop a hybrid method for the quantification of acoustic attenuation in the high-frequency regime associated with the combustion chamber of high efficient H-class gas turbines from Siemens. These types of combustion chambers feature high frequency dampers which are located in a region between the basket and the transition segment according to Fig.1.
Modeling Approach
The numerical method includes a combination of linear field method with network approaches together with analytical models. The linear field methodology consists of CFD/CAA method, where the modeling task is to calculate the acoustic field in the combustion chamber based on the Helmholtz equation (HE). In general, the hybrid approach, separating the computation of mean flow fields in time domain and dynamic perturbations in frequency domain help to identify the acoustic behavior of combustion chambers and associated damping elements at comparatively low cost. Complex elements such as pilot burner, the main stage fuel-air mixers, the upstream flow restrictors and the downstream guide vane section are considered by coupling the spatially resolved FEM domains via transfer matrices, which are obtained using a network approach. The impedance of the dampers is in turn calculated and incorporated using an analytical model.
Results
Recent theoretical work was focused on the development of an energetically correct method for the coupling of transfer matrices, which consider Mach number effects with the spatially resolved Helmholtz equation modeling neglecting convective effects. A model of a complex tubular combustor (H-class gas turbine) was developed employing the new coupling method.
The numerous eigenmodes of this tubular combustor including the dampers and peripheries in the high frequency range are currently determined. The complex distribution of the absolute dynamic pressure in axial as well as radial position is illustrated representatively for one acoustic mode in the high-frequency range in Fig. 2. The distribution of the acoustic pressure varies depending on the eigenfrequency. The fully resolved pilot burner and the fuel-air mixers are replaced by the relevant transfer matrices.
Using forced excitation, the entire frequency spectrum is scanned for modes exhibiting strong response, in order to identify the most relevant modes as it is depicted in Fig. 3. The frequencies are normalized using an arbitrary value. The height and the width of each peak correlate with the damping rate. To optimize the damper characteristics, the damping rate as well as the driving rate of each individual eigenmode of the system will be quantified. The instability driving potential can be determined using an in-house driving model [2]. The unstable modes known as critical modes are then distinguished with respect to the resulting growth rate. The modes featuring less damping and more driving are identified as critical modes.
To identify the critical modes precisely, a nonlinear time domain method should be implemented as well. Using Mode Order Reduction (MOR), the relevant eigenmodes are transformed back into the time domain from the eigenmodes calculated in the frequency domain to observe nonlinear saturation effects.
References
[1] T. C. Lieuwen, and V. Yang, ”Gas Turbine Emissions”, Cambridge University Press, Ed., 2013.
[2] T. Hummel, F. Berger, M. Hertweck, B. Schuermans, and T. Sattelmayer, ”High- Frequency Thermoacosutic Modulation Mechanisms in Swirl-Stabilized Gas Turbine Combustors Part two: Modeling and Analysis” Proceedings of ASME Turbo Expo, 2016.