Giovanni Campa

Prediction of the Thermoacoustic Combustion Instabilities in Practical Annular Combustors

A three-dimensional finite element code is used for the eigenvalue analysis of the thermoacoustic combustion instabilities modeled through the Helmholtz equation. A full annular 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. Additionally, the results show what types of modes are most likely to yield humming in an annular 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 combustion chambers.

Thermoacoustic Analysis of Combustion Instability Through a Distributed Flame Response Function

Modern gas turbines equipped with lean premixed dry low emission combustion systems suffer the problem of thermoacoustic combustion instability. The acoustic characteristics of the combustion chamber and of the burners, as well as the response of the flame to the fluctuations of pressure and equivalence ratio, exert a fundamental influence on the conditions in which the instability may occur. A three dimensional finite element code has been developed in order to solve the Helmholtz equation with a source term that models the heat release fluctuations. The code is able to identify the frequencies at which thermoacoustic instabilities are expected and the growth rate of the pressure oscillations at the onset of instability. The code is able to treat complex geometries such as annular combustion chambers equipped with several burners. The adopted acoustic model is based upon the definition of the Flame Response Function (FRF) to acoustic pressure and velocity fluctuations in the burners.In this paper, data from CFD simulations are used to obtain a distribution of FRF of the κ-τ type as a function of the position within the chamber. The intensity coefficient, κ, is assumed to be proportional to the reaction rate of methane in a two-step mechanism. The time delay τ is estimated on the basis of the trajectories of the fuel particles from the injection point in the burner to the flame front.The paper shows the results obtained from the application of FRF with spatial distributions of both κ and τ. The present paper also shows the comparison between the application of the proposed model for the FRF and the traditional application of the FRF over a concentrated flame in a narrow area at the entrance to the combustion chamber. The distribution of the intensity coefficient and the time delay proves to have an influence, both on the eigenfrequency values and on the growth rates, in several of the examined modes.The proposed method is therefore able to establish a theoretical relation of the characteristics of the flame (depending on the burner geometry and operating conditions) to the onset of the thermoacoustic instability.Copyright

Influence of Nonlinear Flame Models on Sustained Thermoacoustic Oscillations in Gas Turbine Combustion Chambers

In the recent years a great interest has been devoted to the understanding of the nonlinear dynamics characterizing the thermoacoustic combustion instabilities. Although linear techniques are able to predict whether the non-oscillating steady state of a thermoacoustic system is “asymptotically” stable (without oscillations) or unstable (increasing oscillations), a thermoacoustic system can reach a permanent oscillating state (the so called “limit cycle”), even when it is linearly stable, if a sufficiently large impulse occurs. A nonlinear analysis is able to predict the existence of this oscillating state and the nature of the bifurcation process.The aim of this work is to investigate the behavior of gas turbine combustion chambers in presence of nonlinear flame models. The bifurcation diagrams, obtained by using a continuation technique in the frequency domain, give the amplitude of the oscillations as a function of a chosen flame parameter. The Helmholtz equation is used to model the combustion chamber and nonlinear terms are introduced in the flame model, starting from the classical k–τ formulation. A three-dimensional finite element method (FEM) is used for discretization of the computational domain and a solver of quadratic eigenvalue problems is combined with Newton technique in order to identify the points of the bifurcation diagram. First, a simple Rijke tube configuration, as can be found in the literature, is examined in order to obtain bifurcation diagrams. Then, the nonlinear analysis is extended to simplified annular configurations. The obtained results show how the nonlinear behavior is influenced by varying some control parameters, such as the time delay, yielding useful indications to designers and experimentalists.Copyright

A QUANTITATIVE COMPARISON BETWEEN A LOW ORDER MODEL AND A 3D FEM CODE FOR THE STUDY OF THERMOACOUSTIC COMBUSTION INSTABILITIES

The study of thermoacoustic combustion instabilities has an important role for safety operation in modern gas turbines equipped with lean premixed dry low emission combustion systems. Gas turbine manufacturers often adopt simulation tools based on low order models for predicting the phenomenon of humming. These simulation codes provide fast responses and good physical insight, but only one-dimensional or two-dimensional simplified schemes can be generally examined. The finite element method can overcome such limitations, because it allows to examine three-dimensional geometries and to search the complex eigenfrequencies of the system. Large Eddy Simulation (LES) techniques are proposed in order to investigate the instability phenomenon, matching pressure fluctuations with turbulent combustion phenomena to study thermoacoustic combustion oscillations, even if they require large numerical resources. The finite element approach solves numerically the Helmholtz equation problem converted in a complex eigenvalue problem in the frequency domain. Complex eigenvalues of the system allow us to identify the complex eigenfrequencies of the combustion system analyzed, so that we can have a valid indication of the frequencies at which thermoacoustic instabilities are expected and of the growth rate of the pressure oscillations at the onset of instability. Through the collaboration among Ansaldo Energia, University of Genoa and Polytechnic University of Bari, a quantitative comparison between a low order model, called LOMTI, and the three-dimensional finite element method has been examined, in order to exploit the advantages of both the methodologies.Copyright

Two-step approach for pressure oscillations prediction in gas turbine combustion chambers

Currently, gas turbine manufacturers frequently face the problem of strong acoustic combustion-driven oscillations inside combustion chambers. These combustion instabilities can cause extensive wear and sometimes even catastrophic damage of combustion hardware. This requires prevention of combustion instabilities, which, in turn, requires reliable and fast predictive tools. We have developed a two-step method to find a set of operating parameters under which gas turbines can be operated without going into self-excited pressure oscillations. As the first step, an unsteady Reynolds-averaged Navier–Stokes simulation with the flame speed closure model implemented in the OpenFOAM® environment is performed to obtain the flame transfer function of the combustion set-up. As the second step time-domain simulations employing low-order network model implemented in Simulink® are executed. In this work, we apply the proposed method to the Beschaufelter RingSpalt test rig developed at the Technische Universität München. The sensitivity of thermoacoustic stability to the length of a combustion chamber, flame position, gain and phase of flame transfer function and outlet reflection coefficient are studied.

Modelling of Thermoacoustic Combustion Instabilities Phenomena: Application to an Experimental Rig for Testing Full Scale Burners

This paper concerns the acoustic analysis of self–sustained thermoacoustic pressure oscillations that occur in a test rig equipped with full scale lean premixed burner. The experimental work is conducted by Ansaldo Energia and CCA (Centro Combustione Ambiente) at the Ansaldo Caldaie facility in Gioia del Colle (Italy), in cooperation with Politecnico di Bari. The test rig is characterized by a longitudinal development with two acoustic volumes, plenum and combustion chamber, coupled by the burner. The length of both chambers can be varied with continuity in order to obtain instability at different frequencies. A previously developed three dimensional finite element code has been applied to carry out the linear stability analysis of the system, modelling the thermoacoustic combustion instabilities through the Helmholtz equation under the hypothesis of low Mach approximation. The heat release fluctuations are modelled according to the κ-τ approach. The burner, characterized by two conduits for primary and secondary air, is simulated by means of both a FEM analysis and a Burner Transfer Matrix (BTM) method in order to examine the influence of details of its actual geometry. Different operating conditions, in which self–sustained pressure oscillations have been observed, are examined. Frequencies and growth rates of unstable modes are identified, with good agreement with experimental data in terms of frequencies and acoustics pressure wave profiles.Copyright

Influence of Nonlinear Effects on the Limit Cycle in a Combustion Chamber Equipped With Helmholtz Resonator

The influence of the introduction of a Helmholtz resonator as a passive damper in a gas turbine combustion chamber on the bifurcation mechanism that characterizes the transition to instability is investigated. Bifurcation diagrams are tracked in order to identify the conditions for which the machine works in a stable zone and which are the operative parameters that bring the machine to unstable conditions. This work shows that a properly designed passive damper system increases the stable zone, moving the unstable zone and the bistable zone (in the case of a subcritical bifurcation) to higher values of the operative parameters, while have a limited influence on the amplitude of limit cycle. In order to examine the effect of the damper, a gas turbine combustion chamber is first modeled as a simple cylindrical duct, where the flame is concentrated in a narrow area at around one quarter of the duct. Heat release fluctuations are coupled to the velocity fluctuations at the entrance of the combustion chamber by means of a nonlinear correlation. This correlation is a polynomial function in which each term is an odd-powered term. The corresponding bifurcation diagrams are tracked and the passive damper is designed in order to increase the stability zone, so reducing the risk to have an unstable condition. Then both plenum and combustion chamber are modeled with annular shape and the influence of Helmholtz resonators on the bifurcation is examined.Copyright