Development of a Flame Transfer Function Framework for Transversely Forced Flames

Abstract

This paper describes a framework for the development of a flame transfer function for transversely forced flames. While extensive flame transfer function measurements have been made for longitudinally forced flames, the disturbance field characteristics governing the flame response of a transversely forced flame are different enough to warrant separate investigation. In this work, we draw upon previous investigations of the flame disturbance pathways in a transversely forced flame to describe the underlying mechanisms that govern the behavior of the flame transfer function. Previous transverse forcing studies have shown that acoustic coupling in the nozzle region can result in both transverse and longitudinal acoustic fluctuations at the flame, and that the acoustic coupling is a function of combustor geometry, and hence, frequency. The results presented here quantify this coupling across a large range of frequencies using a velocity transfer function, FTL. The shape of the velocity transfer function gain indicates that there is strong acoustic coupling between the main combustor section and the nozzle at certain frequencies. Next, measured flame transfer functions are compared with results from theory. These theoretical results are derived from two level-set models of flame response to velocity disturbance fields, where velocity inputs are derived from experimental results. Data at several test conditions are presented and larger implications of this research are described with respect to gas turbine combustor design.

Transverse combustion instabilities: Acoustic, fluid mechanic, and flame processes

“…The flame is dominantly sensitive to flow disturbances (referred to as "velocity coupling"), as well as any fuel/air ratio oscillations excited by these disturbances ("fuel/air ratio coupling"), while its direct sensitivity to pressure fluctuations ("pressure coupling") is weak relative to these other sources in low Mach number flows 8 [195]. The pathways for longitudinal oscillations are present in this figure because of the importance of transverse to longitudinal coupling [76].…”

“…While much research in the area of combustion instability in rockets is on-going, many lessons from this research can be applied to air-breathing architectures. For example, an analogue of injector coupling is similarly a dominant mechanism of transverse oscillations in annular combustors [75,76], and is the focus of Sec. 5.2.1.…”

“…7), and 2 Figure 8. Data from this experiment has provided information about the velocity disturbance field present in transversely-forced, swirl-stabilized flames [76,85,[87][88][89].…”

“…denotes some suitable reference perturbation velocity [76]. The analysis using the FTF has been used for both premixed [76,93,127,179] and non-premixed flames as well [171,180,181]. While these transfer functions can be quite complex, a commonly used simplification for the flame response is the so-called…”

Visualization of Shear Layer Dynamics in a Transversely Forced Flow and Flame

“…where F ω is the flame describing function between incident velocity fluctuations and vortical velocity fluctuations, F L;a is the describing function between the incident velocity disturbance and the induced axial acoustic velocity fluctuation, and F T;a is the direct flame describing function as a result of the incident transverse acoustics [43]. This expression shows that a physical description of F requires understanding of the more fundamental flame input/output relations F ω , F L;a , and F T;a .…”