Karthik Kashinath

Nonlinear Phenomena in Thermoacoustic Systems With Premixed Flames

Nonlinear analysis of thermoacoustic instability is essential for the prediction of the frequencies, amplitudes, and stability of limit cycles. Limit cycles in thermoacoustic systems are reached when the energy input from driving processes and energy losses from damping processes balance each other over a cycle of the oscillation. In this paper, an integral relation for the rate of change of energy of a thermoacoustic system is derived. This relation is analogous to the well-known Rayleigh criterion in thermoacoustics, however, it can be used to calculate the amplitudes of limit cycles and their stability. The relation is applied to a thermoacoustic system of a ducted slot-stabilized 2-D premixed flame. The flame is modeled using a nonlinear kinematic model based on the G-equation, while the acoustics of planar waves in the tube are governed by linearized momentum and energy equations. Using open-loop forced simulations, the flame describing function (FDF) is calculated. The gain and phase information from the FDF is used with the integral relation to construct a cyclic integral rate of change of energy (CIRCE) diagram that indicates the amplitude and stability of limit cycles. This diagram is also used to identify the types of bifurcation the system exhibits and to find the minimum amplitude of excitation needed to reach a stable limit cycle from another linearly stable state for single-mode thermoacoustic systems. Furthermore, this diagram shows precisely how the choice of velocity model and the amplitude-dependence of the gain and the phase of the FDF influence the nonlinear dynamics of the system. Time domain simulations of the coupled thermoacoustic system are performed with a Galerkin discretization for acoustic pressure and velocity. Limit cycle calculations using a single mode, along with twenty modes, are compared against predictions from the CIRCE diagram. For the single mode system, the time domain calculations agree well with the frequency domain predictions. The heat release rate is highly nonlinear but, because there is only a single acoustic mode, this does not affect the limit cycle amplitude. For the twenty-mode system, however, the higher harmonics of the heat release rate and acoustic velocity interact, resulting in a larger limit cycle amplitude. Multimode simulations show that, in some situations, the contribution from higher harmonics to the nonlinear dynamics can be significant and must be considered for an accurate and comprehensive analysis of thermoacoustic systems. [DOI: 10.1115/1.4023305]

Matrix-free continuation of limit cycles and their bifurcations for a ducted premixed flame

© Cambridge University Press 2014. Many experimental studies have demonstrated that ducted premixed flames exhibit stable limit cycles in some regions of parameter space. Recent experiments have also shown that these (period-1) limit cycles subsequently bifurcate to period-2n, quasiperiodic, multiperiodic or chaotic behaviour. These secondary bifurcations cannot be found computationally using most existing frequency domain methods, because these methods assume that the velocity and pressure signals are harmonic. In an earlier study we have shown that matrix-free continuation methods can efficiently calculate the limit cycles of large thermoacoustic systems. This paper demonstrates that these continuation methods can also efficiently calculate the bifurcations from the limit cycles. Furthermore, once these bifurcations are found, it is then possible to isolate the coupled flame-acoustic motion that causes the qualitative change in behaviour. This information is vital for techniques that use selective damping to move bifurcations to more favourable locations in the parameter space. The matrix-free methods are demonstrated on a model of a ducted axisymmetric premixed flame, using a kinematic G-equation solver. The methods find limit cycles and period-2 limit cycles, and fold, period-doubling and Neimark-Sacker bifurcations as a function of the location of the flame in the duct, and the aspect ratio of the steady flame.

Effects of Nonuniform Reactant Stoichiometry on Combustion Instability

This paper analyzes the forced response of swirl-stabilized lean-premixed flames to acoustic forcing in a laboratory-scale stratified burner. The double-swirler, double-channel annular burner was specially designed to generate acoustic velocity oscillations and radial fuel stratification at the inlet of the combustion chamber. Temporal oscillations of equivalence ratio along the axial direction are dissipated over a long distance, and therefore the effects of time-varying fuel/air ratio on the flame response are not considered. Simultaneous measurements of inlet velocity and heat release rate oscillations were made using a hot wire anemometer and photomultiplier tubes with narrowband OH*/CH* interference filters. Time-averaged CH* chemiluminescence intensities were measured using an intensified CCD camera. Results show that flame stabilization mechanisms vary depending on stratification ratio for a constant global equivalence ratio. For a uniformly premixed condition, an enveloped M-shaped flame is observed. For stratified conditions, however, a dihedral V-flame and a detached flame are developed for outer stream and inner stream fuel enrichment cases, respectively. Flame transfer function (FTF) measurement results indicate that a V-shaped flame tends to damp incident flow oscillations, while a detached flame acts as a strong amplifier relative to the uniformly premixed condition. The phase difference of FTF increases in the presence of stratification. More importantly, the dynamic characteristics obtained from the forced stratified flame measurements are well correlated with unsteady flame behavior under limit-cycle pressure oscillations. The results presented in this paper provide insight into the impact of nonuniform reactant stoichiometry on combustion instabilities, which has not been well explored to date.Copyright

EFFECT OF COOLING LINER ON ACOUSTIC ENERGY ABSORPTION AND FLAME RESPONSE

Gas turbine combustors with lean combustion injectors are prone to thermo-acoustic/combustion instabilities. Several passive techniques have been developed to control combustion instabilities, such as using Helmholtz resonators or viscous dampers using perforated liners that have potential for broadband acoustic damping. In this paper the role of single-walled cooling liners is considered in the damping of acoustic waves and on the flame transfer function in a sample bluff-body burner. Three liner geometries are considered: no bias flow (solid liner), normal effusion holes, and grazing effusion holes at 25° inclination. Cold flow experiments with speaker forcing are carried out to characterise the absorption properties of the liner and compared with an acoustic network model. The results show that whereas the bulk of the acoustic losses is due to the vortex recirculation zones, the liners contribute significantly to the absorption over a wide area of the frequency range. The flame transfer function gain is measured as a function of bias flow for a given operating condition of the burner. The experiments show that for the geometry considered, the global flame transfer function is little affected by cooling except in the case of the normal flow holes. Further analysis shows that whereas the total flame transfer function is not affected, the flame heat release becomes more spatially distributed along the axial length, and a 1D flame response shows distinct modes corresponding to the modal heat release locations.Copyright

Investigation of the effect of combustor cooling geometry on acoustic energy absorption

To control combustion instabilities occurring in LPP gas turbine combustors, several active and passive systems have been developed in recent years. The combustion chamber cooling geometry has the potential to influence instability feedback loops by absorbing acoustical energy inside the combustor. The design of the cooling liner and the geometry of the cooling plenum and the cooling air flow rate have a significant influence on the absorption characteristics of the system. This paper presents the results of a cold flow study which was carried out in the course of a comprehensive study on the influence of the cooling geometry on combustor thermoacoustics. Absorption characteristics of three different cooling liner geometries and non-perforated plates were determined over a frequency range from 50 Hz to 600 Hz for different cooling flow rates and different cooling plenum volumes. The experimental results compared well with results from a low order thermoacoustic network model. The acoustic energy absorption spectrum of a cooling liner with 90°-hole configuration was found to be strongly dependent on cooling flow rate and cooling plenum volume, whereas the absorption spectrum of cooling liners with 25°-holes were found to be strongly dependent on the cooling plenum volume, but less dependent on the cooling air flow rate. All cooling liner setups with perforations were capable of increased acoustic absorption over a broad band of frequencies compared to the case of non-perforated combustor walls.