A simple analytical model to study and control azimuthal instabilities in annular combustion chambers

This study describes a simple analytical method to compute the azimuthal modes appearing in annular combustion chambers and help analyzing experimental, acoustic and large eddy simulation (LES) data obtained in these combustion chambers. It is based on a one-dimensional zero Mach number formulation where N burners are connected to a single annular chamber. A manipulation of the corresponding acoustic equations in this configuration leads to a simple dispersion relation which can be solved by hand when the interaction indices of the flame transfer function are small and numerically when they are not. This simple tool is applied to multiple cases: (1) a single burner connected to an annular chamber (N = 1), (2) two burners connected to the chamber (N = 2), and (3) four burners (N = 4). In this case, the tool also allows to study passive control methods where two different types of burners are mixed to control the azimuthal mode. Finally, a complete helicopter chamber (N = 15) is studied. For all cases, the analytical results are compared to the predictions of a full three-dimensional Helmholtz solver and a very good agreement is found. These results show that building very simple analytical tools to study azimuthal modes in annular chambers is an interesting path to control them.     

Flame dynamics and unsteady heat release rate of self-excited azimuthal modes in an annular combustor

This paper presents an experimental study into the structure and dynamics of the phase-averaged heat release rate during self-excited spinning and standing azimuthal modes in an annular combustion chamber. The flame response was characterised using two methods: high-speed OH^∗ chemiluminescence imaged above the annulus to investigate the structure of the phase-averaged fluctuations in heat release rate, and high-speed OH-PLIF measured across the centreline of two adjacent flames to investigate phase-averaged flame dynamics. Two-microphone measurements were obtained at three circumferential locations to determine the modes and the amplitude of the velocity fluctuations. It was found that the flame responds differently to spinning and standing wave modes. During standing wave modes, the amplitude of the unsteady heat release rate of each flame (sector) varied according to its location in the mode shape with maximum fluctuations occurring at the pressure anti-nodes and minimum fluctuations occurring at the pressure nodes. At the pressure anti-nodes, peak fluctuations result from the production of flame surface area by axisymmetric flame motions caused by the modulation of flow at the burner inlet by the pressure fluctuations. However, at the pressure nodes, an anti-symmetric, transverse flapping motion of the flame occurred producing negligible unsteady heat release rate over the oscillations cycle via the mechanism of cancellation. During spinning modes, the structure of the heat release rate was found to be asymmetric and characterised by the preferential suppression of shear layer disturbances depending on the spin direction.     

Model-based control of combustion instabilities in annular combustors

Lean premixed combustors produce lower NO_x emissions, but are particularly prone to damaging combustion instabilities. Active control can be used to stabilize combustion instabilities. So far model-based control strategies have tended to focus on longitudinal rather than annular combustors, even though many gas turbines have annular geometries. In this work, a computational thermoacoustic model is used to simulate unstable annular combustors, providing a platform on which to develop and test control strategies. The model contains multiple fuel valves for actuation, which respond to multiple pressure sensors according to a controller matrix. Two strategies for designing the controller matrix are developed. The first involves stabilizing each of the unstable circumferential modes independently; the second involves controlling the transfer function matrix between sets of actuators and sensors. The resulting controllers are implemented in simulations using the thermoacoustic model. They are seen to stabilize instabilities in a variety of combustors, including one with nonaxisymmetry due to burner differences and one with both circumferential and longitudinal unstable modes.     

Modal dynamics of self-excited azimuthal instabilities in an annular combustion chamber

In this paper we describe the time-varying amplitude and its relation to the global heat release rate of self-excited azimuthal instabilities in a simple annular combustor operating under atmospheric conditions. The combustor was modular in construction consisting of either 12, 15 or 18 equally spaced premixed bluff-body flames around a fixed circumference, enabling the effect of large-scale interactions between adjacent flames to be investigated. High-speed OH^∗ chemiluminescence imaged from above the annulus and pressure measurements obtained at multiple locations around the annulus revealed that the limit cycles of the modes are degenerate in so much as they undergo continuous transitions between standing and spinning modes in both clockwise (CW) and anti-clockwise (ACW) directions but with the same resonant frequency. Similar behaviour has been observed in LES simulations which suggests that degenerate modes may be a characteristic feature of self-excited azimuthal instabilities in annular combustion chambers. By modelling the instabilities as two acoustic waves of time-varying amplitude travelling in opposite directions we demonstrate that there is a statistical prevalence for either standing m = 1 or spinning m = ±1 modes depending on flame spacing, equivalence ratio, and swirl configuration. Phase-averaged OH^∗ chemiluminescence revealed a possible mechanism that drives the direction of the spinning modes under limit-cycle conditions for configurations with uniform swirl. By dividing the annulus into inner and outer annular regions it was found that the spin direction coincided with changes in the spatial distribution of the peak heat release rate relative to the direction of the bulk swirl induced along the annular walls. For standing wave modes it is shown that the globally integrated fluctuations in heat release rate vary in magnitude along the acoustic mode shape with negligible contributions at the pressure nodes and maximum contributions at the pressure anti-nodes.     

Acoustic decoupling of longitudinal modes in generic combustion systems

Conditions are examined under which acoustic modes of a chamber filled with hot combustion products can be considered to be decoupled from the plenum acoustics supplying the fresh reactants through a feeding manifold. It is shown that this is controlled by a coupling index Ξ = (ρ_bc_b)/(ρ_uc_u)S₁/S₂ ? (T_u/T_b)^1/2(S₁/S₂), where T_u and T_b are the fresh and burned gases temperatures and S₂/S₁ is the expansion ratio between the chamber and injection unit cross sections. It is demonstrated that the acoustic response of a coupled system can be analyzed by considering the plenum and the chamber acoustics separately for small values of the coupling parameter Ξ. Longitudinal self-sustained combustion oscillations may then lock on (i) the plenum resonant frequencies, thus becoming independent of downstream modifications of the combustion chamber acoustics, or on (ii) the combustion chamber modes, thus becoming essentially indifferent to the plenum acoustics. The case of a plenum featuring a Helmholtz resonance is investigated in further detail when the chamber exhaust impedance is varied. Exact relations under which the plenum and the chamber modes are decoupled are derived when the chamber is open to atmospheric conditions or when it is equipped with a sonic nozzle. Predictions are compared to measurements for a generic system equipped with a swirl injector, a compact chamber and terminated by an open atmospheric pressure exhaust. It is shown that in this case, self-sustained longitudinal combustion-instabilities develop preferentially near the plenum mode frequencies and are weakly sensitive to modifications in the chamber geometry.     

Semi-empirical correlations for gas turbine emissions, ignition, and flame stabilization

For operating conditions where the fuel evaporation rate is fast compared to the fuel vapor/air mixing rate, a characteristic time model has been formulated to predict gaseous emissions and efficiency in terms of combustor inlet conditions and geometry. The model, which involves kinetic and fluid mechanic times, has been used to design low NO_x burners, and study of several different conventional engine combustors suggests that the correlation may be universal. A related model, which includes a fuel droplet evaporation time, is being validated with data from laboratory combustors for spark ignition and lean flame stabilization. The preliminary application of this latter model to engine situations is described.     

Turbulence generation upstream of an annular premixed flame

A Taylor-Couette combustor was used to examine turbulence generation upstream of a downward propagating annular premixed flame. The flame is ignited at the top, open end of the combustor and is found to undergo first deceleration and then acceleration with enhanced surface wrinkling, while intensities of axial and circumferential velocity fluctuations upstream of the flame, initially negligible, are strongly amplified. The experimental observations are consistent with earlier computational predictions for downward flame propagation in tubes.     

Flow forcing techniques for numerical simulation of combustion instabilities

Investigation of combustion instabilities in gas turbine combustors require the knowledge of flame transfer functions. Those can be obtained by experimental measurement or by Large Eddy Simulations (LES). Because calculations are usually limited to a portion of the whole combustor, boundary conditions are of crucial importance. It is common practice to inject acoustic perturbations for the flame transfer function measurement in form of velocity perturbations (u′(t)). We present an alternative method based on a characteristic treatment of the Euler Equations. It consists of injecting sound waves traveling into the computational inlet while letting outgoing waves leave the domain without reflection. This method has several advantages concerning the study of flame transfer functions compared to injecting velocity perturbations. Both techniques are compared for cases where analytical solutions may be derived (a duct without flame and a planar laminar flame) and for one case where a CFD code is necessary (a laminar Bunsen-type flame).     

Mixing and stabilization study of a partially premixed swirling flame using laser induced fluorescence

A laboratory-scale swirling burner, presenting many similarities with gas turbines combustors, has been studied experimentally using planar laser induced fluorescence (PLIF) on OH radical and acetone vapor in order to characterize the flame stabilization process. These diagnostics show that the stabilization point rotates in the combustion chamber and that air and fuel mixing is not complete at the end of the mixing tube. Fuel mass fraction decays exponentially along the mixing tube axis and transverse profiles show a gaussian shape. However, radial pressure gradients tend to trap the fuel in the core of the vortex that propagates axially in the mixing tube. As the mixing tube vortex enters the combustion chamber, vortex breakdown occurs through a precessing vortex core (PVC). The axially propagating vortex shows a helicoidal trajectory in the combustion chamber which trace is observed with transverse acetone PLIF. As a consequence, the stabilizing point of the flame in the combustion chamber rotates with the PVC structure. This phenomenon has been observed in the present study with a high speed camera recording spontaneous emission of the flame. The stabilization point rotation frequency tends to increase with mass flow rates. It was also shown that the coupling between the PVC and the flame stabilization occurs via mixing, explaining one possible coupling mechanism between acoustic waves in the flow and the reaction rate. This path may also be envisaged for flashback, an issue that will be more completely treated in a near future.