Adjoint-based sensitivity analysis of low-order thermoacoustic networks using a wave-based approach. (English) Zbl 1376.76061
Summary: Strict pollutant emission regulations are pushing gas turbine manufacturers to develop devices that operate in lean conditions, with the downside that combustion instabilities are more likely to occur. Methods to predict and control unstable modes inside combustion chambers have been developed in the last decades but, in some cases, they are computationally expensive. Sensitivity analysis aided by adjoint methods provides valuable sensitivity information at a low computational cost. This paper introduces adjoint methods and their application in wave-based low order network models, which are used as industrial tools, to predict and control thermoacoustic oscillations. Two thermoacoustic models of interest are analyzed. First, in the zero Mach number limit, a nonlinear eigenvalue problem is derived, and continuous and discrete adjoint methods are used to obtain the sensitivities of the system to small modifications. Sensitivities to base-state modification and feedback devices are presented. Second, a more general case with non-zero Mach number, a moving flame front and choked outlet, is presented. The influence of the entropy waves on the computed sensitivities is shown.
MSC:
| 76Q05 | Hydro- and aero-acoustics |
| 65F15 | Numerical computation of eigenvalues and eigenvectors of matrices |
| 76E30 | Nonlinear effects in hydrodynamic stability |
Keywords:
thermoacoustic stability; adjoint methods; sensitivity analysis; network models; nonlinear eigenvalue problemsReferences:
| [1] | Culick, F. E.C., Unsteady motions in combustion chambers for propulsion systems (2006), North Atlantic Treaty Organization (NATO), vol. 323, RTO AGARDograph/AG-AVT-039 · Zbl 0804.76074 |
| [2] | Dowling, A. P., The calculation of thermoacoustic oscillations, J. Sound Vib., 180, 4, 557-581 (1995) |
| [3] | Stow, S. R.; Dowling, A. P., Thermoacoustic oscillations in an annular combustor, ASME Turbo Expo, Article 2001-GT-0037 (2001) |
| [4] | Dowling, A. P.; Morgans, A. S., Feedback control of combustion oscillations, Annu. Rev. Fluid Mech., 37, 1, 151-182 (2005) · Zbl 1117.76072 |
| [5] | Dowling, A. P.; Stow, S. R., Acoustic analysis of gas turbine combustors, J. Propuls. Power, 19, 5, 751-764 (2003) |
| [6] | Hill, D. C., A theoretical approach for analyzing the restabilization of wakes, (Presented at AIAA Aersoapce Science Meeting Exhib. 30th, Reno, NV. Presented at AIAA Aersoapce Science Meeting Exhib. 30th, Reno, NV, AIAA Pap., vol. 0067 (1992)) |
| [7] | Luchini, P.; Bottaro, A., Adjoint equations in stability analysis, Annu. Rev. Fluid Mech., 46, 1, 493-517 (2014) · Zbl 1297.76068 |
| [8] | Juniper, M. P., Triggering in the horizontal Rijke tube: non-normality, transient growth and bypass transition, J. Fluid Mech., 667, 272-308 (2011) · Zbl 1225.76145 |
| [9] | Magri, L.; Juniper, M. P., Sensitivity analysis of a time-delayed thermo-acoustic system via an adjoint-based approach, J. Fluid Mech., 719, 183-202 (2013) · Zbl 1284.76338 |
| [10] | Rigas, G.; Jamieson, N. P.; Li, L. K.B.; Juniper, M. P., Experimental sensitivity analysis and control of thermoacoustic systems, J. Fluid Mech., 787, Article R1 pp. (2016), pp. 1-11 |
| [11] | Juniper, M. P.; Magri, L.; Bauerheim, M., Sensitivity analysis of thermo-acoustic eigenproblems with adjoint methods, (Center for Turbulence Research, Proceedings of the Summer Program (2014)) |
| [12] | Magri, L., Adjoint methods in thermo-acoustic and combustion instability (2015), Ph.D. thesis |
| [13] | Magri, L.; Bauerheim, M.; Juniper, M. P., Stability analysis of thermo-acoustic nonlinear eigenproblems in annular combustors. Part I. Sensitivity, J. Comput. Phys., 325, 395-410 (2016) · Zbl 1375.74028 |
| [14] | Campos, L. M.B.d. C., Generalized Calculus with Applications to Matter and Forces (2014), CRC Press Taylor & Francis Group: CRC Press Taylor & Francis Group Boca Raton · Zbl 1297.00007 |
| [15] | Nicoud, F.; Benoit, L.; Sensiau, C.; Poinsot, T., Acoustic modes in combustors with complex impedances and multidimensional active flames, AIAA J., 45, 2, 426-441 (2007) |
| [16] | Wieczorek, K.; Sensiau, C.; Polifke, W.; Nicoud, F., Assessing non-normal effects in thermoacoustic systems with mean flow, Phys. Fluids, 23, 107103 (2011) |
| [17] | Giannetti, F.; Luchini, P., Structural sensitivity of the first instability of the cylinder wake, J. Fluid Mech., 581, 167 (2007) · Zbl 1115.76028 |
| [18] | Magri, L.; Bauerheim, M.; Nicoud, F.; Juniper, M. P., Stability analysis of thermo-acoustic nonlinear eigenproblems in annular combustors. Part II. Uncertainty quantification, J. Comput. Phys., 325, 411-421 (2016) · Zbl 1375.74029 |
| [19] | Mensah, G. A.; Moeck, J. P., Assessment of thermoacoustic instabilities based on high-order adjoint perturbation theory, (Proceedings of the International Symposium: Thermoacoustic Instabilities in Gas Turbines and Rocket Engines: Industry Meets Academia (GTRE - 032) (2016)), 1-9 |
| [20] | Silva, C. F.; Runte, T.; Polifke, W.; Magri, L., Uncertainty quantification of growth rates of thermoacoustic instability by an adjoint Helmholtz solver, J. Eng. Gas Turbines Power, 139, 1, 1-11 (2016) |
| [21] | Crocco, L., Research on combustion instability in liquid propellant rockets, Symp. (Int.) Combust., 12, 1, 85-99 (1969) |
| [22] | Magri, L.; Juniper, M. P., Adjoint-based linear analysis in reduced-order thermo-acoustic models, Int. J. Spray Combust. Dyn., 6, 3, 225-246 (2014) |
| [23] | Gunzburger, M., Introduction into mathematical aspects of flow control and optimization, (Inverse Design and Optimisation Methods, Lecture Series 1997-05 (1997), von Karman Institute for Fluid Dynamics) |
| [24] | Aguilar, J., Sensitivity analysis in low order thermoacoustic networks (December 2015), Tech. Rep. |
| [25] | Mangesius, H.; Polifke, W., A discrete-time, state-space approach for the investigation of non-normal effects in thermoacoustic systems, Int. J. Spray Combust. Dyn., 3, 4, 331-350 (2011) |
| [26] | Strobio Chen, L.; Bomberg, S.; Polifke, W., Propagation and generation of acoustic and entropy waves across a moving flame front, Combust. Flame, 166, 170-180 (2016) |
| [27] | Bloxsidge, G. J.; Dowling, A. P.; Langhorne, P. J., Reheat buzz: an acoustically coupled combustion instability. Part 2. Theory, J. Fluid Mech., 193, 445-473 (1988) |
| [28] | Goh, C. S.; Morgans, A. S., The influence of entropy waves on the thermoacoustic stability of a model combustor, Combust. Sci. Technol., 185, 2, 249-268 (2013) |
| [29] | Dowling, A. P.; Mahmoudi, Y., Combustion noise, Proc. Combust. Inst., 35, 1, 65-100 (2015) |
| [30] | Morgans, A. S.; Duran, I., Entropy noise: a review of theory, progress and challenges, Int. J. Spray Combust. Dyn., 8, 4, 285-298 (2016) |
| [31] | Marble, F.; Candel, S., Acoustic disturbance from gas non-uniformities convected through a nozzle, J. Sound Vib., 55, 2, 225-243 (1977) · Zbl 0371.76049 |
| [32] | (Lieuwen, T. C.; Yang, V., Combustion Instabilities in Gas Turbine Engines: Operational Experience, Fundamental Mechanisms, and Modeling (2005), AIAA) |
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