Effect of equivalence ratio on the modal dynamics of azimuthal combustion instabilities
Introduction
Recent studies on the nature of azimuthal modes in annular combustors have shown that due to their discrete rotational symmetry, instabilities in these systems can give rise to more complex behaviour [21], [13], [23], [5], [9], [19] compared with longitudinal modes in isolated single flame systems (for example [2]), which omit some dynamical features observed in annular systems. One of the important differences between these systems is that flames in annular combustion chambers are subjected to azimuthal (or transverse) pressure waves, and due to their symmetry, pressure fluctuations travel around the annulus in either clockwise (CW) or anti-clockwise (ACW) directions. Furthermore, evidence so far suggests that in the case of turbulent swirling flames pure spinning or standing modes are rare, and that oscillations are characterised by time-varying amplitude and phase of the acoustic waves ( and ) travelling in opposite directions around the annulus [11], [21], [22], [14]. Rapid changes in the magnitude of these component waves generates mixed azimuthal modes that can exhibit a time varying statistical preference for predominantly spinning and standing modes. This rapid mode switching behaviour is what is meant by the term modal dynamics [18], [11].
A number of theoretical studies have suggested that either the oscillation amplitude or the degree of asymmetry in the heat release or the flow may control the modal dynamics [17], [18], [11], [3], [4]. Moreover, given that these instabilities occur in practical flows which are characterised by their highly turbulent nature, it has also been proposed that turbulence plays an important role in mode switching between spinning and standing states [18], [11]. Pressure time-series have been used to observe mode switching in recent experimental and numerical studies [21], [22], which can be analysed in terms of the ratio of a spin ratio [5], or through the phase change of the combined pressure indicator C(t) (introduced later in Section 2.2). These studies have shown that mode switching proceeds slowly in comparison with the acoustic timescales. A connection has also made between the azimuthal symmetry of the magnitude of the heat release fluctuations and the mode of oscillation, and the mean azimuthal velocity profile [22]. However, because the mode switching phenomenon has only recently been reported it has yet to be properly investigated or explained.
This is important as low-order approaches typically apply a flame response model to couple the unsteady velocity and heat release at each flame, and therefore model the flame response [8], [20], [12]. However, given that the time varying structure of the flames and therefore their response is dependent on the modal dynamics and mode orientation [6], [7], [16], [15], [10], then a complete flame describing function (FDF) may be required to couple both the transverse and longitudinal velocity oscillations to the heat release rate, in order to take account of transverse velocity fluctuations, which can alter the heat release in non-symmetric flames [1].
This paper is a first step in this direction by characterising the prevalence, time-scales, and connection between different mode parameters which occur during mode switching events. An experimental approach is particularly useful for such an investigation, as relatively long run times ensure many thousands of oscillation cycles are captured, making these suitable for investigating events occurring over long time-scales. We present results describing how the modal dynamics vary with equivalence ratio and show how mode-switching is slow in comparison with the acoustic time-scales and occurs over time-scales which are of the same order as bulk convection times. Following this, the spin ratio and orientation of the nodal lines are related statistically, demonstrating that they are dynamically connected and providing new insight into the physical mechanisms responsible for mode switching.
Section snippets
Laboratory scale annular combustor
Figure 1 shows the experimental setup of the annular combustor which is described in detail in Refs. [23], [22]. 18 premixed C2H4–air flames were arranged around a circle of diameter of mm, supplied from a common plenum ( mm, mm). Inside the plenum is a honeycomb flow straightener, a layer of wire wool, a series of grids, and a hemispherical body of diameter mm for flow conditioning and acoustic damping. The annular combustion chamber consists of inner and outer steel
Equivalence ratio effects on the modal dynamics
We demonstrated previously that the mode of oscillation for the current configuration () over a range of equivalence ratios shows a bimodal distribution, in which either standing or ACW spinning modes were preferred [22]. As this distribution was obtained for a range of equivalence ratios, it can be considered as the general stability of the system across a range of operating conditions. However, given this bimodal behaviour, it is interesting to also consider the effect of equivalence
Conclusions
In the present study the modal dynamics and mode switching behaviour exhibited during high amplitude self-excited fluctuations in a lab scale annular combustor have been investigated and characterised. The modal dynamics are shown to be strongly affected by equivalence ratio, with low and high ratios producing predominantly spinning and standing waves respectively, and intermediate ratios resulting in slow mode switching between these states or bimodal switching behaviour. The modal dynamics of
Acknowledgments
The authors wish to acknowledge insightful comments and discussion on the manuscript with Mathew Juniper.
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