Mechanisms for Flame Response in a Transversely Forced Flame

Transcription

1 7th US National Technical Meeting of the Combustion Institute Hosted by the Georgia Institute of Technology, Atlanta, GA March 20-23, 2011 Mechanisms for lame Response in a Transversely orced lame J. O Connor, C. Vanatta, J. Mannino, T. Lieuwen School of Aerospace Engineering, Georgia Institute of Technology, Atlanta, GA 30308, USA This paper analyzes the factors controlling the flame response to transverse acoustic forcing. Significant prior work has focused on longitudinal instabilities, where the flame transfer function is often defined as the heat release fluctuation divided by the axial velocity fluctuation in the burner nozzle. This single input transfer function definition does not generalize well for transverse instabilities, where the flame disturbance mechanism is not solely due to axial velocity fluctuations. In this work, we discuss the relative importance of axial and transverse acoustic velocity disturbances over a range of frequencies. Results show that the disturbance field is highly dependent on system acoustics. A velocity transfer function, describing the coupling between transverse acoustics in the combustor and longitudinal acoustics at the nozzle, is formulated and results are shown for both the non-reacting and reacting cases. 1. Introduction Combustion dynamics, a coupling between resonant combustor acoustics and flame heat release fluctuations, has been a problem with propulsion and power generation technologies since the middle of the twentieth century [1]. Initially explained by Rayleigh [2], this coupling can lead to high-cycle fatigue, reduced operability, and increased emissions. or gas turbines, these instabilities have become more pronounced as engines have been optimized for low emissions output [3]. The main emissions abatement strategy, lean combustion, has lead to a rise in the severity of these instabilities and the more frequent appearance of transverse instabilities in these engines. Transverse instabilities are a common instability mode in rockets [4-6], augmenters [7-9], and annular combustors [10, 11], but have only recently become a significant issue for canannular gas turbine combustors [12]. Traditionally, longitudinal instabilities have been the dominant mode in can-annular engines and significant work has been done to understand this instability [13-15]. More recently, work has been initiated to shed light on the flame response characteristics and coupling mechanisms for transversely forced flames [16-20]. Quantification of global flame response is often in the form of a flame transfer function. In the case of velocity coupled flame response, the definition of the flame transfer function is given as the normalized flame heat release fluctuation divided by a normalized reference velocity fluctuation [21], as is shown in Equation 1. Q ( fo, A) Q u ( f, A) u ref o (1)

2 lame transfer functions have been measured and calculated for longitudinally excited flames in several studies [22-27]. Here, the reference velocity has usually been defined as the axial velocity fluctuation at the edge of the nozzle exit, measured using a two microphone technique or hot-wire anemometry. An important goal in determining these transfer functions is that they isolate the flame response, and can be used as a submodel in a larger system dynamics model. However, because the actual velocity field along the flame front, u (x), may vary substantially in amplitude and phase from u ref, should not be interpreted as describing the flame response alone it also depends upon certain features of the combustor system as well. The flame is excited directly by acoustic velocity disturbances, as well as acoustically excited vortical disturbances. The flame responds quite differently to velocity disturbances arising from acoustic and vortical disturbances because of their substantially different phase speeds and length scales. As such, the same value of u ref may lead to very different characteristics of the vortical velocity field downstream [28]. To illustrate, the heat release expression for the longitudinally forced case is broken into two constituent disturbance parts in Equation 2 Q u u u ( ) (2) L L, a L, v L, a L L, where u L,a is the longitudinal acoustic velocity disturbance (and the assumed reference velocity in this expression), L is the flame transfer function describing the response of the flame to the longitudinal acoustic disturbance, L,ω is the velocity transfer function between the acoustic velocity disturbance and the vortical velocity disturbance formed at the dump plane, and ω is the flame transfer function between the vortical velocity disturbance and the resultant flame response. Significantly, it shows that by using a single reference velocity, u L,a in this case, the flame transfer function is not only a function of the actual flame response, L and ω, but also the shear layer response, L,ω. Thus, the exact same flame could exhibit different transfer functions,, if the shear layer response is different. This issue becomes more problematic in transversely forced flames, where more sources of flow disturbances exist [16]. The incident transverse acoustic perturbation may directly disturb the flame, similar to the work by Ghosh et al. [29] for rocket injectors. The transverse acoustic pressure field also leads to longitudinal acoustic fluctuations at the flame nozzle region, as shown by Staffelbach et al. [18] in simulation, and in experimental results from O Connor et al. [16]. The longitudinal acoustic disturbance, a result of the fluctuating pressure from the transverse mode, leads to excitation of a longitudinal acoustic field in and around the nozzle area. Additionally, vortical velocity disturbances are excited through both longitudinal and transverse acoustic excitation. The study of Rogers and Marble [7] shows an example of this coupling in a high blockage-ratio combustor, where a self-excited transverse instability lead to vortex shedding from the edges of the triangular bluff-body. These disturbance mechanisms and their pathways are shown in igure 1.

3 Transverse Acoustic Excitation TL Longitudinal Acoustics T L L low Instabilities lame Response T igure 1. Velocity disturbance mechanisms present in a transversely forced flame. Similar to the decomposition of the longitudinally forced disturbance field in Equation 2, the processes in igure 1 can be broken into their constituent parts, as shown in Equation 3: Q u u ( ) u (3) T T, a L TL T, a T L TL T, a The transverse acoustic disturbance, u T,a, is the assumed reference velocity in this case. In addition to the terms described above, T is the flame transfer function describing the flame response to the transverse acoustic disturbance, u T,a, and T,ω is the velocity transfer function describing the formation of a vortical velocity disturbance by an acoustic velocity disturbance at the edge of the dump plane. The focus of this work is the coupling between transverse acoustic fluctuations and longitudinal acoustic fluctuations in and around the nozzle, characterized by the transfer function TL, defined in Equation 4. TL u ( f, A) L, a u ( f, A) T, a o o (4) This transfer function describes the resulting axial velocity fluctuation divided by the incident transverse velocity fluctuation. If the gain of this transfer function is significantly greater than one, the flame response may be largely a result of the longitudinally driven pathways in this case, the more appropriate reference velocity for the transversely excited flame is the longitudinal acoustic disturbance. Conversely, if the amplitude of the transfer function was significantly less than unity, the dominant acoustic velocity fluctuation would be in the transverse direction and would drive both the vorticity generation, through T,ω, and the flame response. As the frequency of transverse acoustic excitation is modulated, the response of the nozzle changes due to acoustic response of the nozzle section. Studies by Schuller et al. [30] and Noiray et al. [31] have both used external transverse acoustic disturbances to characterize the resonant frequencies of unconfined burners. This same concept can be applied to the case of transverse instabilities. The axial velocity fluctuations will be greatest at the resonant frequencies of the nozzle cavity (not of the combustor), and this coupling will be highly

4 dependent upon system geometry. The transverse to longitudinal transfer function will therefore be highly frequency dependent and its magnitude will give an indication of the dominant acoustic disturbance direction experienced by the flame at the nozzle. The importance of this coupling implies that the flame transfer function in the case of transverse forcing will be neither decoupled from the hydrodynamic fluctuations nor the system acoustics, as the longitudinal transfer function was. It is important to note, then, that the results shown in these experiments cannot necessarily be extrapolated to other systems because of the geometric dependence built into the definition of this transfer function. 2. Experimental Setup In this section we overview the experimental facility and diagnostic systems used in this study. or more experimental facility details, see O Connor et al. [16]. The combustor mimics an annular combustor configuration and was designed to exhibit a strong transverse acoustic mode. A swirler nozzle is situated at the center of the chamber. The nozzle section outer and inner diameters are mm and mm, respectively, and the swirl number is 0.5. The fuel is natural gas and the equivalence ratio is Six acoustic drivers, three on each side, provide the acoustic excitation for the system. The acoustic drivers on either side of the combustor can be controlled independently. By changing the phase between the signals driving each side of the combustor, different wave patterns can be created inside the combustor. When the drivers are forced in-phase, a pressure anti-node and velocity node are created at the center of the experiment. When the drivers are forced out-of-phase, a pressure node and velocity anti-node are created at the center. Particle image velocimetry (PIV) is used to measure the velocity field in this experiment. A LaVision lowmaster Planar Time Resolved system allows for two-dimensional velocity measurements at 10 khz. The reference velocities in the transfer functions were calculated using the PIV data calculated with 16x16 pixel interrogation windows with 50% overlap and a resolution of 0.18 mm per pixel. Spatially averaged instantaneous velocities were calculated in both the axial and transverse direction at the nozzle. The reference axial velocity was calculated by integrating the axial velocity at each point along the radial direction at a downstream distance of x/d=0.05. The spatially averaged transverse velocity is calculated along the centerline of the flow, and integrated along a length of one nozzle outer diameter. These formulae are shown in Equation 5. ula, ( t) u ( x 0, r, t) rdr S S 1 u ( t) v ( x, r 0, t) dx D, Ta, D 0 (5) All results are non-dimensionalized. The velocities are normalized by the bulk approach flow velocity, m A (where ρ and A denote approach flow density and annulus area), the spatial coordinates by the nozzle diameter, D, and the vorticity by the bulk velocity divided by the annular gap width, U o /(r 2 -r 1 ). 3. Velocity fluctuations near the nozzle exit The time-average flow field is shown in igure 2, which shows both the time-averaged axial velocity and vorticity. The flow is from left to right. Key features of the flow are an annular reactant jet with a central vortex breakdown region and shear layers on the inner and outer edges of the annular jet. The flame is stabilized in the inner shear layer.

5 igure 2. Time-average a) axial velocity and b) vorticity for reacting flow at a bulk velocity of U o =10 m/s and a forcing frequency of f o =400 Hz in-phase. The first case under consideration is an in-phase forcing test at 400 Hz. In this case, a pressure anti-node is created over the centerline of the nozzle. The ratio of the acoustic wavelength to nozzle diameter is 26.7, which indicates that each radial station of the nozzle experiences roughly the same acoustic excitation from the fluctuating pressure field. igure 3 shows the spectral content of the axial velocity fluctuations at two downstream locations near the nozzle. igure 3. Spectra of axial velocity fluctuations at a) x/d=0.05 and b) x/d=0.27 for reacting flow at a bulk velocity of U o =10 m/s, equivalence ratio of 0.95, and a forcing frequency of f o =400 Hz in-phase. It is evident from the plots in igure 3 that there are significant axial velocity fluctuations (8-12% of the mean) at the forcing frequency in the nozzle region. At x/d=0.05, the fluctuations are close to the centerline of the annular jet, showing the longitudinal acoustic motion that results from the fluctuating transverse acoustic field over the nozzle. urther downstream at x/d=0.27, the axial velocity fluctuations at the forcing frequency are mainly in the shear layers as a result of the coherent structures convecting downstream in these regions. Additionally, there is significant low frequency axial motion in the vortex breakdown region. Similar spectral content, with a lower magnitude, is also seen in the vortex breakdown region in the cases without acoustic forcing.

6 4. Transverse to longitudinal velocity transfer function Data like those shown above and those from other frequencies tested show that significant axial fluctuations are excited by the transverse acoustic excitation at certain frequencies. To describe this coupling, this section quantifies the transverse to longitudinal velocity transfer function, as described in Equation 2. igure 4 shows the calculated velocity transfer function for the non-reacting flow case at a bulk velocity of U o =10 m/s and the reacting flow case at the same velocity and an equivalence ratio of In the transfer function gain and phase plots, the reacting in-phase data are offset by -20 Hz and the non-reacting out-of-phase data are offset by +20 Hz for clarity of the error bars. c) d) igure 4. Transverse to longitudinal velocity transfer function a) gain ( TL ), b) gain on a log scale (without error bars), c) phase (< TL ), and d) coherence (γ 2 ) for reacting flow with in-phase and out-of-phase, and non-reacting out-of-phase acoustic forcing at f o =400 Hz, a bulk flow velocity of U o =10 m/s, and equivalence ratio These transfer functions were obtained from data where the transverse velocity oscillation magnitude was nominally 10% of the mean axial velocity. ive ensemble averages were used to calculate these transfer function gains and to estimate the uncertainties [32]. The amplitude results from these transfer functions have two interesting features. irst, the gain has high values, on the order of 6, at Hz but drops to very small values by 800 Hz. Second, the amplitude peaks again at higher frequencies, particularly 1800 Hz. Although the transfer function amplitude at both these frequencies is large, signifying non-negligible transverse to axial velocity coupling, the flow response in these two cases is fundamentally

7 different. This can also be seen by looking at the spectrum as a function of radial location, as shown in igure 5. igure 5. Axial velocity spectra at x/d=0.05 for a) 400 Hz in-phase and b) 1800 Hz in-phase acoustic forcing a bulk flow velocity of U o =10 m/s and equivalence ratio In the 400 Hz case, the axial velocity fluctuations are concentrated in the annular jet, while in the 1800 Hz case, the motion takes place across the entire diameter of the jet, including the vortex breakdown region. urther downstream, this region stretches even farther in the radial direction as the jet spreads. Additionally, the coherence of the axial and transverse velocity fluctuations is nearly unity at 1800 Hz, as well as several other higher frequencies, while the coherence is very low near 400 Hz. This trend is true even downstream of the dump plane, as is shown in igure 6. Here, the magnitude of the axial velocity fluctuations at the forcing frequency is shown for the entire flow field. Like the spectra in igure 5, these plots show that the spatial distribution of axial velocity fluctuations is significantly different between the low frequencies and high frequencies, despite the similar magnitude in TL of the two. igure 6. Magnitude of the axial velocity fluctuations at the forcing frequency throughout the flow field for a) 400 Hz in-phase and b) 1800 Hz in-phase acoustic forcing a bulk flow velocity of U o =10 m/s and equivalence ratio This difference in response may be a manifestation of the nozzle acoustics. A rough calculation of the natural frequency of the nozzle (a half-wave) is 1800 Hz, in the range of the high coherence, high amplitude response frequencies seen in igure 4. This means that the external pressure fluctuation from the transverse field in the 1800 Hz forcing case is driving the

8 fluctuations in the nozzle near the resonant frequency, resulting in a large-scale axial response in and around the nozzle. Through a series of tests at frequencies between 1700 Hz and 1900 Hz in 10 Hz increments, it was shown that both the flame and flow response were maximized in the Hz region, indicating that the maximum axial flow oscillations occur in this frequency range. uture tests using a two-microphone technique in the nozzle will be able to further quantify this effect. The flow response in the axial direction at the nozzle resonant frequency affects the entire flow structure, even the vortex breakdown region, while the flow during off-resonant frequency excitation responds only in the annular jet core. This can lead to significant changes in the flame structure, as shown in the recent work by the authors [33]. This change in flame shape can be seen in igure 7. igure 7. Time-average flame shape for a) no acoustic forcing and b) high-amplitude acoustic forcing at 1800 Hz in-phase, for reacting flow at a bulk velocity of U o =10 m/s, equivalence ratio of Conclusions The velocity disturbance field of a transversely forced swirl-stabilized flame has several different pathways by which the flame response can be generated. In this work we focus on the transverse to longitudinal velocity coupling mechanism, which describes the coupling between the pressure fluctuations from the transverse acoustic field and the resultant longitudinal motion in and around the nozzle. A velocity transfer function, TL, was measured for several different frequencies and the connection to transfer function gain and nozzle acoustic response was discussed. In future, the authors plan to measure the velocity transfer function using a twomicrophone method with pressure sensors in the nozzle cavity. Also, a more nuanced definition of the flame transfer function for a transversely forced flame will be developed and results reported. References 1. Ducruix, S., Schuller, T., Durox, D., and Candel, S., Combustion dynamics and instabilities: Elementary coupling and driving mechanisms. Journal of Propulsion and Power, (5): p Rayleigh, L., The Theory of Sound. 2 ed. Vol , London: Macmillian. 3. Lieuwen, T. and V. Yang, Combustion Instabilities in Gas Turbine Engines: Operational Experience, undamental Mechanisms, and Modeling. Progress in Astronautics and Aeronautics Series, ed..k. Lu. 2006: AIAA.

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