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

Abstract

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.

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

“…Thus, an AU flow acts as a self-excited oscillator with a well defined, characteristic frequency. CU and AU flows interact with the combustor acoustic field through the unsteady heat release that they generate [19].…”

“…The density variation introduces a fluctuating baroclinic torque which can constructively or destructively interact with other mechanisms and thereby, modify the instability characteristics of the flow. We also perform a local spatio-temporal analysis to identify the absolute/convective [19] nature of the unstable modes. We identify regions of absolute/convective instability in a parametric space spanned by local swirl number (S), defined as the ratio of the maximum azimuthal to maximum axial flow velocity and back flow ratio (β), defined as the ratio of the magnitude of the cen-terline axial velocity to the maximum axial velocity.…”

Role of Shear Layer Instability in Driving Pressure Oscillations in a Backward Facing Step Combustor

“…The presence of shear layers and recirculation zones allows for the possibility of the flow becoming self excited due to the occurrence of regions of local absolute instability in these flows. This has been shown by past local [6][7][8][9] and global [10] hydrodynamic stability analyses. Sufficiently large regions of local absolute instability can result in the flow becoming globally self-excited [11,12].…”

“…Next, flame induced density gradients can stabilize locally absolutely unstable regions (see eg. refs [6][7][8] for recent studies) resulting in unstable hydrodynamic modes becoming marginally unstable or even stable globally, while still being locally convectively unstable [11,12]. Hence, background broadband velocity oscillations in the combustor that include an acoustic eigenfrequency within their frequency range can couple with the flame generating acoustic velocity oscillations at the acoustic eigenfrequency through the heat release oscillations they generate.…”

Pattern formation during transition from combustion noise to thermoacoustic instability via intermittency

“…showed that the formation of large scale vortices and their interaction with the flame front causes a periodic heat release rate during the occurrence of intermittency. The evolution of large scale vortices (or large scale coherent structures) downstream of the backward-facing step appears to follow that of convectively unstable flows (Lieuwen 2012;Manoharan & Hemchandra 2015) where the disturbances are amplified as the flow propagates. A recent study by Kirthy et al (2016) on a backward-facing step combustor reported that spatial amplification of velocity disturbances in a globally stable but locally convectively unstable flow could result in thermoacoustic instability.…”