Consequences of non-normality and nonlinearity in flow / premixed flame / acoustic interactions for combustion instability
Final Report Abstract
Thermoacoustic systems such as jet engines or gas turbines for power generation are prone to self-excited, high-amplitude oscillations, leading to material fatigue or structural damage. This is particularly true when performing at a “green”, i.e. low-emission, operating point. For a linearly stable non-normal system, oscillation amplitudes may grow temporarily before eventually decaying. If this so-called transient growth leads to amplitudes sufficiently high to trigger nonlinear effects, the system may evolve towards an oscillating state at high amplitudes. The concepts of non-normality and nonlinearity were first established in the field of hydrodynamics, where they offered an explanation for bypass-transition to turbulence. At the start of the present project, only highly idealized model problems had been studied under the aspect of transient growth and nonlinear triggering in the field of thermoacoustics. The goal was thus to provide tools for the analysis of non-normal effects in systems of more applied interest such as premixed flames. Non-normal transient growth is investigated in thermoacoustic systems with simple 1D geometries, where mean flow effects are trivial and where the acoustic field is dominated by planar waves. The low-order models describing the premixed flame (i.e. G-Equation) and the acoustic field (i.e. including mean temperature gradients and flow) are rich representations of the respective dynamics. One of the key findings with respect to non-normal dynamics is that non-normal transient growth around a stable fix point – although existent and theoretically sound – is not a threat for triggering in such thermoacoustic systems. For these simple systems, the magnitude of non-normal transient growth is small and does not suffice to trigger nonlinearities. Also, it occurs only over short periods of time. The above observations hold independent of the energy norm used to quantify non-normal transient growth. It is shown that the energy metric merely prescribes the perspective from which non-normal transient growth needs to be interpreted. An additional, yet unexpected finding was the existence of an intrinsic thermoacoustic feedback loop. The intrinsic feedback loop may cause instability in an anechoic environment, where all sound waves generated by the flame are radiated away, which is contradictory to established thinking that thermoacoustic instability requires feedback with the global acoustic field. The most important outcome of the present study is that adopting a systems framework to describe thermoacoustics is a promising approach. The systems approach is a robust and rigorous platform, where insights from different fields of research can be consistently combined using a “common language”. It offers a large set of tools that are well established and readily available. Its main benefit, however, is that it offers a holistic view which provides the basis for a more general and fresh understanding of thermoacoustic dynamics. The models developed and analyzed in this project, as well as phenomena such as internal thermoacoustic feedback, were found by adopting a systemic perspective. These insights have spawned fresh impulses to thermoacoustic research. The discovery of internal thermoacoustic feedback is yet a matter of fruitful discussion.
Publications
- A contribution to the discussion on thermoacoustic energy from a systemic perspective. n3l – Int’l Summer School and Workshop on Non-Normal and Nonlinear Effects in Aero- and Thermoacoustics, Munich, Germany, June 18 – 21, 2013.
Ralf S. Blumenthal, Arun K. Tangirala, R.I. Sujith, Wolfgang Polifke
- Novel perspectives on the dynamics of premixed flames. Combustion and Flame, 160(7):1215–1224, 2013
R. S. Blumenthal, P Subramanian, R. I. Sujith, and W. Polifke
(See online at https://doi.org/10.1016/j.combustflame.2013.02.005) - On the jump conditions for flow perturbations across a moving heat source. In 21st International Congress on Sound and Vibration (ICSV21), Beijing, China, 2014
L. Strobio Chen, S. Bomberg, and W. Polifke
- Distributed Time Lag Response Functions for the Modeling of Combustion Dynamics. Combustion Theory and Modelling
Volume 19, 2015 - Issue 2, pp 223-237
P. Subramanian, R. S. Blumenthal, W. Polifke, and R. Sujith
(See online at https://doi.org/10.1080/13647830.2014.1001438) - Intrinsic thermoacoustic instability of premixed flames. Combustion and Flame, 162(1):75–85, 2015
T. Emmert, S. Bomberg, and W. Polifke
(See online at https://doi.org/10.1016/j.combustflame.2014.06.008) - Thermal Versus Acoustic Response of Velocity Sensitive Premixed Flames. Proceedings of the Combustion Institute, Vol. 35. 2015, Issue 3, pp. 3185-3192.
S. Bomberg, T. Emmert, and W. Polifke
(See online at https://doi.org/10.1016/j.proci.2014.07.032) - Propagation and Generation of Acoustic and Entropy Waves Across a Moving Flame Front. Combustion and Flame, Vol. 166. 2016, pp. 170-180.
L. Strobio Chen, S. Bomberg, W. Polifke
(See online at https://doi.org/10.1016/j.combustflame.2016.01.015) - A systems perspective on non-normality in low-order thermoacoustic models: full norms, semi-norms and transient growth.
International Journal of Spray and Combustion Dynamics,
Vol. 9. 2017,Issue 1, pp. 19–43.
R. S. Blumenthal, A. K. Tangirala, R. I. Sujith, W. Polifke
(See online at https://doi.org/10.1177/1756827716652474) - Acoustic and Intrinsic Thermoacoustic Modes of a Premixed Combustor. Proceedings of the Combustion Institute, Vol. 36. 2017, Issue 3, pp. 3835-3842.
T. Emmert, S. Bomberg, S. Jaensch, W. Polifke
(See online at https://doi.org/10.1016/j.proci.2016.08.002) - An Analytical Model for the Impulse Response of Laminar Premixed Flames to Equivalence Ratio Perturbations. Proceedings of the Combustion Institute, Vol. 36. 2017, Issue 3, pp. 3725-3732.
A. Albayrak, R. S. Blumenthal, A. Ulhaq, W. Polifke
(See online at https://doi.org/10.1016/j.proci.2016.06.002) - Hybrid CFD/Low-Order Modeling of Nonlinear Thermoacoustic Oscillations. Proceedings of the Combustion Institute, Vol. 36. 2017, Issue 3, pp. 3827-3834.
S. Jaensch et al.,
(See online at https://doi.org/10.1016/j.proci.2016.08.006)
