Santosh Hemchandra

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]

Instability Mechanism in a Swirl Flow Combustor: Precession of Vortex Core and Influence of Density Gradient

Combustion instability is a serious problem limiting the operating envelope of present day gas turbine systems using a lean premixed combustion strategy. Gas turbine combustors employ swirl as a means for achieving fuel-air mixing as well as flame stabilization. However swirl flows are complex flows comprised of multiple shear layers as well as recirculation zones which makes them particularly susceptible to hydrodynamic instability. We perform a local stability analysis on a family of base flow model profiles characteristic of swirling flow that has undergone vortex breakdown as would be the case in a gas turbine combustor A temporal analysis at azimuthal wavenumbers m = 0 and m = 1 reveals the presence of two unstable modes. A companion spatio-temporal analysis shows that the region in base flow parameter space for constant density density flow, over which m = 1 mode with the lower oscillation frequency is absolutely unstable, is much larger that that for the corresponding m = 0 mode. This suggests that the dominant self-excited unstable behavior in a constant density flow is an asymmetric, m=1 mode. The presence of a density gradient within the inner shear layer of the flow profile causes the absolutely unstable region for the m = 1 to shrink which suggests a possible explanation for the suppression of the precessing vortex core in the presence of a flame.

ABSOLUTE/CONVECTIVE INSTABILITY TRANSITION IN A BACKWARD FACING STEP COMBUSTOR: FUNDAMENTAL MECHANISM AND INFLUENCE OF DENSITY GRADIENT

Hydrodynamic instabilities of the flow field in lean premixed gas turbine combustors can generate velocity perturbations that wrinkle and distort the flame sheet over length scales that are smaller than the flame length. The resultant heat release oscillations can then potentially result in combustion instability. Thus, it is essential to understand the hydrodynamic instability characteristics of the combustor flow field in order to understand its overall influence on combustion instability characteristics. To this end, this paper elucidates the role of fluctuating vorticity production from a linear hydrodynamic stability analysis as the key mechanism promoting absolute/convective instability transitions in shear layers occurring in the flow behind a backward facing step. These results are obtained within the framework of an inviscid, incompressible, local temporal and spatio-temporal stability analysis. Vorticity fluctuations in this limit result from interaction between two competing mechanisms-(1) production from interaction between velocity perturbations and the base flow vorticity gradient and (2) baroclinic torque in the presence of base flow density gradients. This interaction has a significant effect on hydrodynamic instability characteristics when the base flow density and velocity gradients are colocated. Regions in the space of parameters characterizing the base flow velocity profile, i.e., shear layer thickness and ratio of forward to reverse flow velocity, corresponding to convective and absolute instability are identified. The implications of the present results on understanding prior experimental studies of combustion instability in backward facing step combustors and hydrodynamic instability in other flows such as heated jets and bluff body stabilized flames is discussed.

Direct Numerical Simulation Study of Premixed Flame Response to Fuel-Air Ratio Oscillations

The coupling between heat release oscillations produced by equivalence ratio fluctuations with combustor acoustic modes in lean premixed combustion systems, is a serious problem that limits the operation envelope of these devices. Such oscillations are produced by an oscillating pressure drop across air inlets and/or fuel injectors due to the presence of acoustic oscillations. This results in fluctuations in mass flow rates of air and/or fuel entering the combustor, thereby, changing the local equivalence ratio of the mixture at these injector/inlet locations. These perturbations in equivalence ratio are advected by the flow into the flame, causing its heat release to oscillate. Detailed reduced order models for the heat release response of premixed flames to equivalence ratio oscillations, based on this phenomenological picture, have been developed in the past. A key problem in validating these models is the ambiguity of interpretation of chemiluminescence signals when, the length scale of equivalence ratio fluctuations is smaller than the characteristic flame length. As such, the present work performs a DNS of a premixed methane-air flame, subject to unsteady forcing in upstream methane mass fraction. Predictions from prior reduced order modelling approaches are compared with present DNS results. The agreement between modelling and DNS predictions in the characteristics of flame response is good at low excitation frequencies and amplitudes. This agreement, however, degrades as forcing amplitude and frequency increase due to the influence of hydrodynamic coupling between the flow-fields on either side of the flame as well as damping of equivalence ratio perturbations by diffusion, on the dynamics of the flame.Copyright

Influence of Hydrodynamic Instability on the Heat Release Transfer Function of Premixed Flames

Gas expansion across the premixed flame surface causes deformations induced on the flame surface to grow in time due to hydrodynamical coupling between the unsteady flow and flame surface motions. This phenomenon is the well known hydro-dynamical instability (also know as the Darrieus-Landau (D-L) instability) of premixed flames. It is well established from several experimental studies that premixed flames subject to acoustic forcing distort and wrinkle under the influence of the unsteady velocity field generated by the forcing, thereby, changing its surface area and causing the net heat-release rate of the flame to oscillate. The D-L instability mechanism influences this heat-release oscillation through its influence on the underlying flame surface wrinkling. An understanding of this mechanism is necessary to develop reliable reduced-order modelling tools to predict the onset of combustion instabilities in Lean Premixed (LPM) systems. This paper presents a computational study of the influence of the D-L instability on the heat release transfer function of premixed flames subjected to harmonic velocity forcing. The effect of varying Markstein length and gas temperature ratio is presented. It is shown that when the induced flame surface perturbations are unstable w.r.t the D-L instability, the net heat release response is dominated by the oscillation in total burning area. In the stable case, the net response is due to the resultant of contributions from the net burning area oscillation as well as the area-averaged mass burning rate oscillation induced by unsteady spatial variations in laminar flame speed, sL . The boundary between these two response regimes is determined by the Markstein number for which flame surface perturbations are neutrally stable.© 2010 ASME

Impact of Flow Non-Axisymmetry on Swirling Flow Dynamics and Receptivity to Acoustics

In this study, we experimentally investigate both the intrinsic instability characteristics and forced response to transverse acoustic excitation of a non-reacting, swirling flow for application to combustion instability in annular gas turbine engines. The non-axisymmetry of the velocity field is quantified using an azimuthal mode decomposition of the time-averaged velocity field that shows that (1) the flow field is largely axisymmetric, (2) axisymmetry decreases with downstream distance, and (3) forcing does not significantly alter the time averaged shape of the flow field. The flow field is analyzed in a companion linear stability analysis that shows that the most unstable modes in the flow field are m=-1 and m=-2, which agrees with the experimental observations and shows that the intrinsic dynamics of this flow field are non-axisymmetric with respect to the jet axis. The linear stability analysis captures the spatial variation of mode strength for certain modes, particularly mode m=-1, but there are some deviations from the experimental results. Most notably, these deviations occur for mode m=0 at radii away from the jet axis. Experimental results of the forced response of the flow indicate that the intrinsic instability characteristics of the flow field have an impact on the forced-response dynamics. Response of the flow field to a velocity anti-node in a standing transverse acoustic field shows non-axisymmetric vortex rollup and the dominance of the m=-1 and m=-1 azimuthal modes in the fluctuating flow field. In the presence of a pressure anti-node, the m=0 mode of the fluctuating flow field is very strong at the jet exit, indicating an axisymmetric response, and ring vortex shedding is apparent in the flow measurements from high-speed Ply. However, further downstream, the strength of the axisymmetric mode decreases and the m=-1 and m=1 modes dominate, resulting in a tilting of the vortex ring as it convects downstream. Implications for flame response to transverse acoustic fields are discussed.

IMPACT OF PVC DYNAMICS ON SHEAR LAYER RESPONSE IN A SWIRLING JET

Combustion instability, or the coupling between flame heat release rate oscillations and combustor acoustics, is a significant issue in the operation of gas turbine combustors. This coupling is often driven by oscillations in the flow field. Shear layer roll up, in particular, has been shown to drive longitudinal combustion instability in a number of systems, including both laboratory and industrial combustors. One method for suppressing combustion instability would be to suppress the receptivity of the shear layer to acoustic oscillations, severing the coupling mechanism between the acoustics and the flame. Previous work suggested that the existence of a precessing vortex core (PVC) may suppress the receptivity of the shear layer, and the goal of this study is to first, confirm that this suppression is occurring, and second, understand the mechanism by which the PVC suppresses the shear layer receptivity. In this paper, we couple experiment with linear stability analysis to determine whether a PVC can suppress shear layer receptivity to longitudinal acoustic modes in a non-reacting swirling flow at a range of swirl numbers. The shear layer response to the longitudinal acoustic forcing manifests as an m=0 mode since the acoustic field is axisymmetric. The PVC has been shown both in experiment and linear stability analysis to have m=1 and m=-1 modal content. By comparing the relative magnitude of the m=0 and m=-1,1 modes, we quantify the impact that the PVC has on the shear layer response. The mechanism for shear layer response is determined using companion forced response analysis, where the shear layer disturbance growth rates mirror the experimental. results. Differences in shear layer thickness and azimuthal velocity profiles drive the suppression of the shear layer receptivity to acoustic forcing.

Combustion Instabilities in Lean Premixed Systems

Combustion instabilities are one of the most costly and technically challenging issues in lean, premixed combustion systems. While combustion instabilities, or thermacoustic oscillations more generally, have been noted in a variety of applications for several centuries, they are particularly problematic in lean, premixed combustion systems. Combustion instability is characterized by undesirably high acoustic and heat release rate oscillations inside a combustor chamber. In this chapter, we discuss the fundamentals of thermoacoustic feedback cycles, as well as the different coupling mechanisms by which combustor system acoustics create a feedback loop with flame heat release rate oscillations. Finally, an overview of combustion control strategies, particularly those employed in lean combustion systems, is discussed with references to future design and research directions.

Absolute/Convective Instability Transition in a Backward Facing Step Combustor: Fundamental Mechanism and Influence of Density Gradient

Hydrodynamic instabilities of the flow field in lean premixed gas turbine combustors can generate velocity perturbations that wrinkle and distort the flame sheet over length scales that are smaller than the flame length. The resultant heat release oscillations can then potentially result in combustion instability. Thus, it is essential to understand the hydrodynamic instability characteristics of the combustor flow field in order to understand its overall influence on combustion instability characteristics. To this end, this paper elucidates the role of fluctuating vorticity production from a linear hydrodynamic stability analysis as the key mechanism promoting absolute/convective instability transitions in shear layers occurring in the flow behind a backward facing step. These results are obtained within the framework of an inviscid, incompressible, local temporal and spatio-temporal stability analysis. Vorticity fluctuations in this limit result from interaction between two competing mechanisms — (1) production from interaction between velocity perturbations and the base flow vorticity gradient and (2) baroclinic torque in the presence of base flow density gradients. This interaction has a significant effect on hydrodynamic instability characteristics when the base flow density and velocity gradients are co-located. Regions in the space of parameters characterizing the base flow velocity profile, i.e. shear layer thickness and ratio of forward to reverse flow velocity, corresponding to convective and absolute instability are identified. The implications of the present results on prior observations of flow instability in other flows such as heated jets and bluff-body stabilized flames is discussed.Copyright

Reduced Order Modelling of Combustion Instability in a Backward Facing Step Combustor

This paper develops a fully coupled time domain Reduced Order Modelling (ROM) approach to model unsteady combustion dynamics in a backward facing step combustor The acoustic field equations are projected onto the canonical acoustic eigenmodes of the systems to obtain a coupled system of modal evolution equations. The heat release response of the flame is modelled using the G-equation approach. Vortical velocity fluctuations that arise due to shear layer rollup downstream of the step are modelled using a simplified 1D-advection equation whose phase speed is determined from a linear, local, temporal stability analysis of the shear layer just downstream of the step. The hydrodynamic stability analysis reveals a abrupt change in the value of disturbance phase speed from unity for Re Re-crit, where Remit for the present geometry was found to be approximate to 10425. The results for self-excited flame response show highly wrinkled flame shapes that are qualitatively similar to those seen in prior experiments of acoustically forced flames. The effect of constructive and destructive interference between the two contributions to flame surface wrinkling results in high amplitude wrinkles for the case when K-c -> 1.