Analysis and Identification of Local and Global Nonlinearities in Thermo-Acoustic Systems
Final Report Abstract
Thermo-acoustic instabilities are a cause for concern in applications as diverse as rocket engines, gas turbines or domestic heating systems. In the framework of the Project nonlinear dynamic models of thermo-acoustic interactions and a corresponding frequencydomain system model have been developed for the prediction and analysis of limit cycles of thermo-acoustic instabilities. A neural network identification scheme has been used for dynamic model construction from the observation of input-output time series data (acoustic forcing as the input, heat release ofthe source obtained from transient CFD or G-equation computations as the output). This approach can also be used for configurations of appUed interest, e.g. turbulent swirUng flames. One disadvantage ofthe approach is that it requires much trial and error and one encounters problems typical for nonUnear optimization - dependence on initial guess, failure to find a global optimum, excessive number of regressors, etc. All alternative to nonlinear system identification is a physics-based, low-order modeling approach based on proper orthogonal modes (POD). A multivariate method, which collects snapshot data for a range of parameters, has been used to describe successfully the heat source dynamics over a range of amplitudes and frequencies. It has been observed that accuracy and StabiUty depend in a sensitive manner on the number of retained POD modes. Also it has become obvious that the appUcation to turbulent flames, say, would be a very challenging problem. Nonlinear dynamic heat source models obtained from nonlinear identification or POD can be directly coupled with a time domain simulation of a full thermo-acoustic system, e.g. a so-called Galerkin method. As an alternative, a nonlinear frequency domain system model with coupled modes has been developed in this project. The method is based on an extension of neural network based identification to the frequency domain, using higher order transfer functions (a natural extension of Unear frequency responses to higher dimensions). This approch is computationally significantly more efficient and allows in-depth analysis of the non-linear transfer of oscillation energy between participating modes. Furthermore, it has been observed that in cases where coupling to higher order modes is strong, the sinusoidal describing function (one mode approximation) predicts incorrect limit cycle amplitudes. The approach has some drawbacks since it is an extension ofthe polynomial type representation of the nonlinearity in time domain to the frequency domain. When the delay time of the heat source is large, the polynomial degree of the approximation is high and a large of number of parameters may appear. Again, the approach can be extended to complex geometries and a possible coupling with the gas dynamics nonlinearity is also possible. Finally, an approach has been developed to study the non-normal behavior of thermoacoustic systems. The method is attractive inasmuch as it allows to consider large delay times, as they are typically found in heat sources of technical interest.
Publications
- "Linear identification ofthe unsteady heat transfer of a cylinder in pulsating crossflow", 2nd International Conference on Jets, Wakes and Separated Flows, Berlin, Germany, 2008
Föller. S., Selimefendigil, P., Polifke, W.
- "Non-linear identification of the unsteady heat transfer ofa cylinder in pulsating crossflow", 2nd International Conference on Jets, Wakes and Separated Flows, Berlin, Germany, 2008
Selimefendigil, E., Föller, S., Polifke, W.
- "Identification of heat transfer dynamics for nonmodal stability analysis of thermoacoustic systems", 7th International Conference of Numerical and Applied Mathematics (ICNAAM 09), 18-24 September, Crete, Greece, 2009
Selimefendigil, E, Sujith, R.L, Polifke, W.
- "Low order model of heat source in pulsating flow based on proper orthogonal decomposition", in SFB-TR 40 Jahresbericht, Editors: Adams, N. A., Radespiel, R., Sattelmayer, T., Schröder, W. and Weigand, B., 2009
Selimefendigil, F, Polifke, W.
- "Identification and Analysis of Nonlinear Heat Sources in Thermo- Acoustic Systems", TU München, 2010
Selimefendigil, F.
