Prediction of the Thermoacoustic Combustion Instabilities in Practical Annular Combustors

Abstract

A three-dimensional finite element code is used for the eigenvalue analysis of the ther moacoustic combustion instabilities modeled through the Helmholtz equation. A full an nular combustion chamber, equipped with several burners, is examined. Spatial distributions for the heat release intensity and for the time delay are used for the linear flame model. Burners, connecting the plenum and the chamber, are modeled by means of the transfer matrix method. The influence of the parameters characterizing the burners and the flame on the stability levels of each mode of the system is investigated. The obtained results show the influence of the 3D distribution of the flame on the modes. Addi tionally, the results show what types of modes are most likely to yield humming in an an nular combustion chamber. The proposed methodology is intended to be a practical tool for the interpretation of the thermoacoustic phenomenon (in terms of modes, frequencies, and stability maps) both in the design stage and in the check stage of gas turbine combus tion chambers. I n t r o d u c t io nModem gas turbines for power generation are generally equipped with lean premixed (LP) combustion burners able to produce very low NOx emissions in order to satisfy the strict regu lations for pollutant emissions. Unfortunately, LP combustion sys tems are often affected by combustion instabilities that emerge as a problem to be avoided since they may generate structural vibra tions that may lead to failure of the system in the worst case. The thermoacoustic interaction between acoustic pressure oscillations and flame heat release fluctuations is regarded as the main origin of combustion instabilities in gas turbines, according to the Ray leigh criterion [1], Over the years, several authors have proposed different approaches to model this phenomenon [2][3][4], Low order models can be applied when simplified geometries, such as simple one dimensional or annular ducts, are examined. Initial studies were carried out by Merk [5], Afterwards, other studies were carried out on afterburners by Bloxsidge et al. [6] and on the Rijke tube by Heckl [7]. Bohn and Deuker [8] were the first to suggest the use of the low-order models as an acoustic network. In this case, the combustor system is modeled as a series of subsystems, using mathematical transfer function matrices to connect these lumped acoustic elements, one to each other. This methodology had a very large spread in the analysis of the influence of flow parame ters on the thermoacoustic oscillations, giving rise to several in-house codes [9][10][11][12].More recently, large eddy simulation (LES) [13][14][15][16][17] has been also proposed in order to investigate the phenomenon of combus tion instability aiming at coupling pressure oscillations with turbu lent combustion phenomena. Selle et al. [13], Benoit [14], and Huang et al. [16] demonstrated the potentiality of LES simulations to solve the thermoacoustic problem. Giauque et al. [15] showed the potentiality of LES simulations in obtaining detailed r...

Weakly nonlinear analysis of thermoacoustic instabilities in annular combustors

“…This leads to finding the solutions of a nonlinear dispersion relation f (ω, A 1 , A 2 , ϕ) = 0 and evaluating their stability. Some introductory work has been carried out by Campa, Cinquepalmi & Camporeale (2013), Campa & Camporeale (2014) using a Helmholtz solver, where the stability with respect to only the amplitude of the mode was considered.…”

Stability analysis forn-periodic arrays of fluid systems

“…Again, taking advantage of the block-circulant structure of A and A H we can decouple the sub-units by using the transformation P from (5). Applying this transformation, we arrive at systems of three equations -the direct and adjoint evolution equation, as well as the optimality condition -for each of our sub-units.…”

“…The ubiquity of fluid systems characterized by an n-periodic arrangement of identical units or by multi-periodic geometric features has spawned a great deal of analyses and simulations: flow in wavy or grooved channels [9,15,16,40] or past arrays of roughness elements and vortex generators [6], acoustics in periodic wave-guides [1], energy extraction from an buoy array [12] and, of course, flow in turbomachines [8,13,14,20,23,24,30] and combustors [5,28,29,31,38,39,45] are but a few examples that fall under this category. Not surprisingly, specific analysis and simulation techniques that efficiently address this periodicity have been developed, in particular for turbomachinery applications, typically describing blade-to-blade dynamics, aeroelastic properties, and rotor-stator interactions.…”

Pollutant Formation during the Occurrence of Flame Instabilities under Very-Lean Combustion Conditions in a Liquid-Fuel Burner

“…A reduced operating temperature allows minimizing the emissions of nitrogen oxides [1], but can result in instability in the combustion chamber, compromising the combustor structure and performance [2][3][4]. In fact under ultra-lean and lean conditions gas turbine burners exhibit flame instability, flashback or lean blowout (LBO), until the flame extinction [5,6].…”