INFLUENCE OF TRANSVERSE ACOUSTIC MODAL STRUCTURE ON THE FORCED RESPONSE OF A SWIRLING NOZZLE FLOW

Transcription

1 Proceedings of ASME Turbo Expo 2012 GT2012 June 11-15, 2012, Copenhagen, Denmark GT INFLUENCE OF TRANSVERSE ACOUSTIC MODAL STRUCTURE ON THE FORCED RESPONSE OF A SWIRLING NOZZLE FLOW Jacqueline O Connor, Tim Lieuwen Georgia Institute of Technology Atlanta, Georgia, USA ABSTRACT This study describes continued investigations of the response of a swirling flow to transverse acoustic excitation. This work is motivated by transverse combustion instabilities in annular gas turbine engine architectures. This instability provides a spatially varying acoustic velocity disturbance field around the annulus, so that different nozzles encounter different acoustic disturbance fields. In this study, we simulate this effect by looking at a standing wave acoustic field where the nozzle is located at either a velocity anti-node, referred to as out-of-phase forcing, and a velocity node, referred to as in-phase forcing. The out-of-phase forcing condition provides an asymmetric forcing field about the center plane of the flow and excites an asymmetric response in the flow field; the in-phase forcing provides a symmetric forcing condition and results in symmetric flow response near the nozzzle. The symmetric versus asymmetric flow response was measured in two ways. First, in the r-x plane where axial and radial components of velocity are measured using high-speed particle image velocimetry (PIV), a helical and ring vortex rollup of the shear layers is evident in the asymmetric and symmetric forcing condition, respectively. Additionally, the swirling motion of the jet is measured in the r-θ plane at two downstream locations and a spatial decomposition is used to calculate the strength of azimuthal modes in radial velocity fluctuations. At the forcing frequency, the m=0 mode is strongly excited at the nozzle exit with symmetric forcing, while asymmetric forcing results in a strong peak in the m=1 mode, or the first helical mode. The results in this plane of view are congruent with those in the r-x plane. Further downstream, however, the mode strengths change as the vorticity is religned and natural asymmetries of the swirling jet set in. Finally, the low frequency self-excited motion of the vortex core was measured and characterized in the unforced flow. It is composed of an m=-1 and m=-2 mode, and the physical interpretation of these mode numbers is highlighted. High amplitude acoustic forcing decreases the amplitude of oscillation of this structure in both the in-phase and out-ofphase forcing, but to varying degrees. NOMENCLATURE A m Counter-rotating mode amplitude B m Co-rotating mode amplitude D, D out Outer diameter of nozzle D in Inner diameter of nozzle N Number of azimuthal modes R Radius of centerbody S Swirl number S L Laminar flame speed m Azimuthal mode number r Radial direction t Time u Velocity vector û Fourier transform of velocity u Axial velocity u Axial velocity fluctuation u o Bulk velocity u r,int Radial velocity integrated in radial direction v Transverse velocity v Transverse velocity fluctuation x Axial direction z In-plane direction Ω Vorticity β Flame aspect ratio θ Azimuthal direction ω Angular frequency 1 Copyright 2012 by ASME

2 INTRODUCTION Combustion instabilities have plagued the development and operation of high performance combustion technologies for almost a century. These instabilities, the result of a coupling between flame heat release fluctuations and resonant acoustics inside the combustion chamber [1], have proven to be destructive to engine hardware, burdensome on engine operating costs, and detrimental to engine performance and emissions. In particular, instabilities have caused major challenges in the development of lean, premixed combustors used in low NO x gas turbines [2]. A variety of mechanisms exist through which coupling between the resonant acoustics and flame heat release fluctuations can occur [3]. In premixed systems, two types of coupling mechanisms equivalence ratio coupling, where the fuel flow is pulsed as a result of the acoustic fluctuations [4], and velocity coupling, by which the flame area is modulated through the action of velocity fluctuations in the flow field [5-8] are the dominant sources of flame heat release fluctuations. In this study, we consider the action of velocity coupling for flames undergoing transverse flow oscillations. Much research has considered the response of flames to longitudinal acoustic forcing, a significant issue in can-annular combustion systems [9-12]. In this case, the acoustic fluctuations oscillate in the direction of the flow field, creating a symmetric forcing condition for the flame. This applies to flames in both laboratory test stands as well as actual engine configurations. In the case of transverse instabilities, which are prevalent in annular gas turbine combustion architectures [13-16], each nozzle experiences a different disturbance field than its neighbors. For example, a nozzle situated near a velocity node experiences large pressure oscillations (that in turn, excite axial nozzle velocity oscillations), with negligible transverse velocity oscillations. A nozzle situated near a pressure node experiences significant transverse flow oscillations. A nozzle in a traveling wave field experiences both pressure and velocity oscillations [17]. In this paper, we specifically focus on the acoustic velocity node and anti-node configurations, corresponding to symmetric and asymmetric acoustic velocity fields, respectively. To explore the response of the flow to these different acoustic symmetry conditions, we have used high-speed particle image velocimetry (PIV) to measure the velocity field under a variety of acoustic forcing conditions. The work presented here follows closely from our prior publications [17, 18], with the key new contributions stemming from expanded insight into the shear layer and vortex breakdown region structures. Figure 1 illustrates the basic geometry considered in this study, showing an annular, swirling jet that is excited by a transverse acoustic field. This notional picture shows the annular swirling jet with two spanwise shear layers, emanating from each edge of the annular nozzle, and the large central recirculation zone downstream of a centerbody. Although the results presented in the current study are for a non-reacting flow, the nominal flame position is shown for reference. Here, the flame is stabilized in the inner shear layer of the centerbody. Figure 1. Notional drawing of the time-average flow field of an annular swirling jet with vortex breakdown. The spanwise shear layers, vortex breakdown bubble, and flame are shown here. Dotted lines indicate contours of zero axial velocity and several streamlines are depicted. Figure 1 shows a typical swirling annular jet with vortex breakdown. Vortex breakdown stems from the instability of the swirling jet and arises from the conversion of radial and axial vorticity to azimuthal vorticity [19, 20]. Though several states of vortex breakdown are possible [21], the one of primary interest here is the bubble-type vortex breakdown state (VBB), which appears at higher swirl numbers. A large literature on the mechanisms of breakdown and swirling flow structure exists, e.g., see Liang and Maxworthy [22], Billant et al. [23], and others [24, 25]. As is also evident in Figure 1, this geometry introduces two spanwise shear layers originating from the inner and outer annulus edges, and two streamwise shear layers associated with the azimuthal flow. These shear layers are subject to the Kelvin-Helmholtz instability, which can be convectively or absolutely unstable, depending upon the reverse flow velocity and swirl number [26]. In addition, the centerbody introduces a wake flow. In the current study, the swirl number is high enough such that the vortex breakdown bubble and centerbody wake have merged to create a single central recirculation zone [27]. Harmonic forcing can have a significant effect on the dynamical behavior of this flow field. In this discussion, though, it is important to recognize the different types of instabilities present in the flow, particularly their absolute or convectively unstable nature. This specific flow field can be roughly broken into the convectively unstable shear layers and the globally unstable swirling vortex breakdown bubble (VBB). This demarcation should not be taken too far, though, as interactions do occur, particularly between the flow structures in the VBB and the inner shear layer. Nonetheless, the 2 Copyright 2012 by ASME

3 dramatically different manner in which these flow structures respond to forcing makes this distinction a useful one. First, we address the convectively unstable shear layers. The free shear layer is a convectively unstable flow, where the separating vortex sheet rolls up into concentrated regions of vorticity that pair with downstream distance [28, 29]. As a disturbance amplifier, shear layers respond strongly to acoustic forcing [26, 30]. In this case, the vortex passage frequency locks onto the forcing frequency, generally through a vortex pairing or collective interaction phenomenon [31]. Acoustic forcing has been shown to have similar effects on the shear layers in a variety of flow geometries, including circular, annular, and swirling jets [32-36]. Shear layer response in the current geometry has been considered in previous work by the authors [17, 37]. Consider next forcing effects on the VBB, a result of a global instability in the flow field. Here, the global instability of vortex breakdown appears to be key to understanding the response characteristics. Globally unstable systems execute self-excited, limit cycle motions, even in the absence of external forcing [38]. For example, swirl flows often exhibit intrinsic narrowband oscillations, manifested by structures such as the precessing vortex core (PVC) or other helical coherent structures [39]. Because of the globally unstable nature of the VBB, low amplitude forcing often has minimal impacts upon it. This behavior is to be contrasted with that exhibited by the convectively unstable shear layers and the entire VBB itself, whose space/time position is influenced by the outer flow oscillations. If the acoustic excitation amplitude is high, significant changes in the shape and natural oscillations of the vortex breakdown bubble can occur. This is due to a phenomenon known as lock-on or entrainment, where the system oscillations are "entrained" by the external forcing and oscillate at the forcing frequency rather than the unforced frequency [40]. Additionally, high amplitude acoustic forcing can change the time-average shape of the flow, causing the vortex breakdown bubble to grow in both size and strength [35, 41, 42]. In particular, several factors influence the response of the PVC to acoustic forcing, including both flow and geometric parameters. In some cases where the VBB exhibits intrinsic narrowband oscillations, external excitation at that natural frequency of oscillation can further amplify it [40]. For example, LES studies by Iudiciani and Duwig [42] show that low frequency forcing ( St 0.6 ) resulted in a decrease in the strength of the PVC fluctuation amplitude, while higher frequency fluctuations resulted in increases in PVC fluctuation amplitude. The presence of transverse forcing adds an additional degree of freedom to the forced problem because of the nonaxisymmetric nature of the forcing [36, 43, 44]. High Reynolds number, unforced swirling flows are not instantaneously symmetric [21]; e.g., swirl biases the strength of co- and counter-signed helical instabilities. Moreover, nonaxisymmetric forcing can preferentially excite certain nonaxisymmetric modes in a different manner than they would otherwise naturally manifest themselves. This effect of forcing symmetry on the flame response has been measured experimentally and discussed in previous work by the authors [17]. Here, the difference in the vortical response of the flow field between symmetric (in-phase) and asymmetric (out-ofphase) forcing has been shown to have a significant effect on the character of the flame response. This can be seen in flame luminescence imaging, examples of which are shown in Figure 2. a) b) Figure 2. Examples of flame response, via luminescence imaging, for a) in-phase (symmetric) and b) out-of-phase (asymmetric) forcing conditions for a flow velocity of 10 m/s, swirl number of 0.5, and equivalence ratio of 0.9. Images are 0.6 ms apart in each filmstrip. In these images, it is evident that the flame wrinkling changes with acoustic field symmetry. For asymmetric forcing, an asymmetric, helical pattern exists on the flame near the nozzle exit, while in the symmetric forcing case, a symmetric ring vortex creates axisymmetric wrinkles on the flame surface, at least near the flame base. The differences in flow response 3 Copyright 2012 by ASME

4 that create this flame response effect are the motivating factors for this work. The remainder of this paper is organized as follows. First, the experimental setup is briefly overviewed and several data analysis methods detailed. Next, the results section begins by presenting the time-average flow fields, as well as the dynamical behavior of the unforced flow field. These serve as a baseline for the forcing results, which show the effect of both symmetric and asymmetric forcing on the shear layers as well as the self-excited motion of the vortex breakdown bubble. Finally, we discuss the implications for these results on the understanding of transverse instabilities in gas turbine engines. EXPERIMENTAL SETUP AND ANALYSIS In this section we overview the experimental facility and diagnostic systems used in this study. Further details are provided in O Connor et al. [37]. The combustor mimics an annular combustor configuration and was designed to support a strong transverse acoustic mode. A swirler nozzle is situated at the center of the chamber with an outer diameter of mm, inner diameter of mm, and geometric swirl number of 0.85 [45]. This swirl number calculation used the vane angle of 45⁰, inner diameter of 22.1 mm and outer diameter of 31.8 mm are used. Six acoustic drivers, three on each side, provide the acoustic excitation for the system. The acoustic drivers on either side of the combustor are controlled independently. By changing the phase between the signals driving each side of the combustor, different wave patterns, both standing and traveling waves, can be created. When the drivers are forced in-phase, an approximate acoustic pressure anti-node and acoustic velocity node are created at the center of the experiment this will be referred to as the symmetric forcing condition. When the drivers are forced outof-phase, an approximate acoustic pressure node and acoustic velocity anti-node are created at the center this will be referred to as the asymmetric forcing condition. The symmetry of the acoustic forcing corresponds to the motion of the acoustic velocity field, as it is the acoustic velocity that is coupling with the vortical velocity to excite flow response. Particle image velocimetry is used to measure the velocity field in this experiment. A LaVision Flowmaster Planar Time Resolved system allows for two-dimensional velocity measurements at 10 khz. In this study, two sets of PIV data were taken. The first set of PIV data examined the flow in the axial flow direction. In this case, the sheet entered the experiment from a window at the exit plane of the combustor and reached a width of approximately 12 cm at the dump plane. This alignment will be referred to as the r-x alignment. A second set of PIV data were taken to look at the swirling component of the flow. Here, a laser sheet with a thickness of approximately 1 mm and a width of 10 cm entered the front window at a height of 0.7 cm above the dump plane. An Edmunds Optics 45-degree first surface mirror was placed above the exit port window and the camera was aligned and focused on the image on this mirror. Special care was taken to ensure that there was no distortion in the particle image in the mirror; mirror/camera alignment was checked often. This alignment will be referred to as the r-θ alignment. Several techniques were used to quantify the behavior of the response of the flow to transverse acoustic forcing. The use of high-speed PIV diagnostics allowed for spectral analysis of the data, which was used extensively in this study. First, spectra of several quantities were calculated using fast Fourier transforms. 500 images were taken at 10 khz, resulting in a spectral resolution of 20 Hz and a maximum resolvable frequency of 5 khz. The frequency domain velocity was also used to decompose the flow field into spatial azimuthal mode shapes in the r-θ flow field. This technique has been used by other authors [46, 47] to calculate the mode shapes in jets and axisymmetric wakes. In this analysis, the radial and azimuthal velocities are extracted from the instantaneous velocity fields at 8 radial locations and 21 points around each radius. The Fourier transformed velocity field is then decomposed as: N im uˆ r,, A r, e B r, e m 0 m m im Here, uˆ r,, is the complex Fourier transform of the velocity fluctuation. A r, and B r, are the m complex amplitudes of the modes of the counter-swirling (clockwise) and co-swirling (counter-clockwise) disturbances, respectively. Finally, m is the mode number describing the spatial fluctuation in the azimuthal directions that can have N 1 2 N 1 2, where N is integer values between and the number of points measured in the azimuthal direction. Several results from this analysis are presented in this paper. It should be noted that each mode strength, A m and B m, has not only a spatial modal dependency, but also a frequency dependency. This means that the spatial mode distributions over a variety of mode numbers, m, can be plotted at specific frequencies, or integrated over frequency ranges. The first analysis approach eliminates the frequency dependence by calculating mode strengths, u r,int, that have been integrated over all frequencies ( Hz). These values are then normalized by the spectral bandwidth in order to give an average spectral density (units of Hz -1 ). This is done to compare amplitudes to the narrowband analysis described in the second analysis. The second analysis looks at the mode strength at the forcing frequency only. This quantity captures the motion due to and in response to acoustic excitation; in particular, it captures the convectively unstable response of the shear layers. m (1) 4 Copyright 2012 by ASME

5 RESULTS Time Average Flow Features Figure 3 shows the non-reacting, velocity (left) and azimuthal vorticity normalized by the bulk velocity divided by D D u, (right). The axial the annular gap width, outer inner o velocity plot shows the jets on either side of the centerline with the reverse flow region in the center that is merged with the centerbody wake. The two shear layers on each side of the annular jets are evident in the vorticity plot. The time-averaged azimuthal velocity field is shown in Figure 4, obtained at the measurement plane x/d=0 and x/d = 1; the x/d=0 plane is at the bottom of the field of view in the x-r plane, 0.7 cm from the dump plane. These time-average views show a swirling jet with a relatively uniform profile in the radial direction across the annular width. However, combustor confinement clearly affects the shape of the jet at this location, as the flow is able to spread freely in the r-direction, while it is confined in the z-direction. b) Figure 4. Time-average swirling velocity field at a) x/d=0 downstream and b) x/d=1 showing velocity vectors and contours of velocity magnitude for the non-reacting annular swirling jet at u o =10 m/s, S=0.85. Unforced Flow Dynamics The unforced flow has several inherent dynamical features. First, concentrated vortical regions stemming from the rollup of the convectively unstable shear layers are present. In this case, the dominant shear layer mode is helical, typical of swirling flows [22]. This can be seen in Figure 5, which shows an instantaneous snapshot of the velocity and vorticity field in the unforced case. Figure 3. Time-average velocity streamlines and vectors (left) and normalized azimuthal vorticity (right) for the unforced, non-reacting annular swirling jet at u o =10 m/s, S=0.85. Figure 5. Instantaneous velocity and normalized azimuthal vorticity (in color contour) data showing helical vortex rollup of both inner and outer shear layer, for the unforced, non-reacting annular swirling jet at u o =10 m/s, S=0.85. a) 5 Copyright 2012 by ASME

6 a) d) b) e) c) f) Figure 6. Coherent jet core motion shown through the filtered velocity field in the r-θ plane at x/d=1 and a) t=0.5 ms, b) 4.1 ms, c) 10.1 ms, d) 13.1 ms, e) 17.1 ms, f) 20.1 ms, for a non-reacting, unforced flow at u o =10 m/s, S=0.85. Gray areas approximate the location of the inner and outer shear layers. 6 Copyright 2012 by ASME

7 Additionally, a self-excited structure in the vortex breakdown region is evident from the r-θ view. Here, data from the x/d=1 plane is shown as this downstream location shows the most intense motion in the central recirculation zone. In this location, the vortex breakdown bubble begins to widen, as can be seen in Figure 3, and is sufficiently far from the centerbody boundary condition. Returning to the central recirculation zone, the structure in this zone induces fluctuations at low frequencies, 200 Hz and below, as it precesses about the flow centerline. The frequency content of these motions is discussed later. To visualize this structure, filtered velocity data in the r-θ plane are shown in Figure 6 as a series of images at progressive instances in time. Here, the velocity data have been low-pass filtered at 200 Hz, where the dominant fluctuations in the flow occur as described above, using a second-order Butterworth filter. Additionally, the gray regions represent the approximate areas of the inner and outer shear layers at this downstream location. Two concurrent motions are evident from this series of velocity fields in Figure 6. The first is a fluctuation in the overall shape of the jet, while the second is due to two smallerscale coherent structures in the central recirculation zone. First, as is seen in the time-average image in Figure 4b, the jet at x/d=1 spreads preferentially towards the top-left and bottomright quadrants of the image. In the time series of the low frequency motion, a semi-periodic squeezing and contracting of the jet along the axis along which the jet is biased is observed. This bias can be clearly seen in Figure 6b and Figure 6d, as is indicated with dotted lines in time-instances t=0.5 ms and t=13.1 ms. Motion of the jet in the opposite direction is evident at the subsequent time, in Figure 6c and Figure 6f and shown using dotted lines in time-instances t=10.1 ms and t=20.1, with a transitional time shown in time-instances t=4.1 ms and t=17.1 ms. This motion is indicative of an m 2 mode in the jet; here the jet pulses in each direction twice as the smaller structures rotate once around the center of the jet. This motion seems to indicate the existence of a precessing vortex core, as described in Ref. [39]. The second motion is smaller scale, and involves two coherent structures that precess about the center of the flow field. These can be seen in several of the images in Figure 6, circled with a dashed line. While these coherent structures clearly precess around the center of the flow field for parts of the cycle, they also overlap. For example, the structures are separate in Figure 6a-c for time-instances t= ms, while they overlap at time-instances in Figure 6 at t= ms. This motion exists in addition to the precessing vortex core described above, and seems to indicate the existence of a second structure in the vortex core. Figure 7 shows calculations from the azimuthal modal decomposition of the radial velocity fluctuations; in this plot, the modal coefficients have been integrated over the entire frequency range ( Hz) and several radii (r/d = 0 1) in order to represent the complete energy contained in that mode. Here, it is evident that modes m 2 and m 1 dominate over the rest of the mode energies; this is congruent with the physical observations discussed with reference to Figure 6. The spatial distribution of these modes is shown in Figure 8, which plots the mode energy (integrated over the entire frequency spectrum) versus radius for several important modes. Figure 7. Distribution of mode amplitude integrated from Hz and over radii r/d=0-1 plotted as a function of mode number at x/d=1 for a non-reacting, unforced flow at u o =10 m/s, S=0.85. Figure 8. Distribution of mode amplitude integrated from Hz plotted as a function radius for several mode numbers at x/d=1 for a non-reacting, unforced flow at u o =10 m/s, S=0.85. Gray areas approximate the location of the inner and outer shear layers. In order to illustrate how this modal energy is distributed in frequency, Figure 9, plots the spectrum of fluctuations for several mode numbers. The plot shows that the majority of the fluctuation energy is in modes m 2 and m 1 at frequencies below 200 Hz. 7 Copyright 2012 by ASME

8 about the center plane of the experiment, the shear layers roll up into ring vortices on both the inner and outer edge of the annular jet, a symmetric response (the m 0 mode) at the dump plane to a symmetric forcing condition. In the out-ofphase forcing case, the asymmetric forcing condition, the shear layers roll up into helical structures, an obviously asymmetric response to the asymmetric acoustic forcing. The downstream evolution of these structures will be discussed later. Examples of this response are shown in Figure 10. Figure 9. Spectra of several mode numbers integrated over radius and frequency in the r plane at xd 1, for a non-reacting, unforced flow at u o =10 m/s, S=0.85. These results provide a baseline for the next analyses, which investigate the effect of in-phase (symmetric) versus outof-phase (asymmetric) forcing on the flow structures described here. In each of the cases presented here, the in-phase forcing amplitude was v u o 0.05 and the out-of-phase forcing amplitude was v u o 0.4. Response at the Forcing Frequency Before presenting data, two main points should be emphasized about the response of the flow at the forcing frequency. The first, a direct result of the nature of a standing acoustic field, is that the in-phase and out-of-phase forcing conditions result in very different acoustic velocity fluctuation amplitudes. As discussed above, in-phase, or symmetric, forcing results in an approximate velocity node along the centerline and hence very low amplitude acoustic velocity fluctuations in the region of the flow. Conversely, the out-ofphase, or asymmetric, forcing condition results in an approximate velocity anti-node and high amplitudes of acoustic velocity fluctuations. The second effect stems directly from the symmetry of the acoustic forcing. As discussed above, asymmetric forcing results in asymmetric flow response; this is a trend that has been observed in a variety of flows and forcing configurations. This has shown to be a key idea in our analysis of the response of the swirling jet shear layers. The structures that most readily respond to acoustic forcing are the convectively unstable shear layers. As disturbance amplifiers, these structures respond strongly to acoustic forcing and are highly influenced by the symmetry of the acoustic field. In shear layers, the response of these structures to symmetric verses asymmetric forcing fields is quite different. In the in-phase forcing case, a symmetric forcing configuration a) b) c) d) Figure 10. Comparison of instantaneous (a,c) and filtered (b,d) velocity at the forcing frequency for a,b) in-phase and c,d) out-of-phase forcing at 400 Hz, non-reacting flow at u o =10 m/s, S=0.85. White lines trace the vortex path. Here, in Figure 10, both the instantaneous as well as the filtered velocity field at the forcing frequency is shown. This filtered velocity field is calculated by reconstructing the velocity field at the forcing frequency only, as detailed in previous publications [37]. The filtered velocity is appropriate to show in this case because the shear layers are responding directly to the acoustics and further inspection and comparison of the instantaneous and filtered velocity and vorticity fields reveals great similarity. Changes in the modal structure of the swirling flow are also evident between in-phase and out-of-phase forcing. Figure 11 shows the modal decomposition (integrated over all frequencies and radii between r/d=0-1) for the unforced, out-of-phase forcing, and in-phase forcing cases at high amplitude forcing at a downstream location of x/d=0. This location was chosen to capture the vortex rollup motion in the shear layers, as depicted in Figure Copyright 2012 by ASME

9 a) Figure 11. Distribution of mode amplitude at the forcing frequency integrated over radii r/d=0-1 plotted as a function of mode number at x/d=0 for a non-reacting, flow forced with 400 Hz forcing at u o =10 m/s, S=0.85. Here, it is evident that different forcing configurations have different effects on the modal content of the flow. For example, out-of-phase forcing significantly amplifies modes m 1, m 2, and m 1, two counter-swirling and a co-swirling helical modes, respectively. The amplification of these two modes asymmetrically is indicative of the asymmetric response of the flow and the helical vortex in the shear layers. The strong m 1 mode represents the helical vortex rollup evident in the inner shear layer, as seen in Figure 10. The in-phase forcing strongly amplifies the symmetric m 0 mode; this finding is congruent with the ring vortex shedding observed in the r-x view. Additionally, the m 1 and m 1 modes are present at very similar amplitudes. In the inner shear layer region, between r/d= , the phase between the fluctuations at these two modes is zero within the uncertainty in phase estimation (15 degrees). The excitation of these two modes is also indicative of a symmetric response of the flow. Additional information can be garnered from the radial distribution of fluctuation amplitude of each of these modes. Figure 12 shows the distribution of energy for in-phase and outof-phase forcing, at the forcing frequency, for several mode numbers. b) Figure 12. Distribution of mode amplitude at the forcing frequency plotted as a function radius for several mode numbers for a non-reacting, flow forced at 400 Hz a) inphase and b) out-of-phase forcing at u o =10 m/s, S=0.85. Gray areas approximate the location of the inner and outer shear layers at x/d=0, where these data were taken. In the out-of-phase forcing case, the dominant mode, m 1, is prevalent in the inner shear layer, as would be expected given their convectively unstable nature. This response is congruent with the helical response seen in the r-x view in Figure 10. In the in-phase forcing case, the response seems to focus in the inner shear layer for modes m 1 and m 1, and in both the inner and outer shear layer for mode m 0. Further downstream, however, the distribution of energy amongst the modes changes, as is shown in Figure 13, which plots the distribution of modal amplitude at x/d=1. 9 Copyright 2012 by ASME

10 Figure 13. Distribution of mode amplitude at the forcing frequency integrated over radii r/d=0-1 plotted as a function of mode number at x/d=1 for a non-reacting, flow forced with 400 Hz forcing at u o =10 m/s, S=0.85. In this case, the effect of in-phase, symmetric forcing has been almost completely lost, manifesting as only a slight increase in the amplitude of modes m 0, m 1, and m 1 over the unforced flow. This may be due to two factors. First, the action of swirl causes the ring vortices to tilt [22], introducing an inherent asymmetry in the flow structure downstream. Additionally, the m 0 mode is stable in a swirling jet. Theoretical analysis by several authors [48] indicates that the symmetric mode is stable for these flow profiles because of the action of swirl. While unswirling jets often exhibit instabilities of the m 0 mode, the action of swirl adds an asymmetric bias to the flow and causes the most unstable modes to be asymmetric. Apparently, the fact that the m=0 mode is stable causes this disturbance to be rapidly suppressed. In the out-of-phase forcing case, however, the amplitude of mode m 1 has grown significantly, while the amplitude of mode m 1 has also grown. The phase between the fluctuations at these two modes is close to zero, but because the amplitudes are different, the resulting manifestation of these modes is a counter-swirling helix resulting from mode m 1, as was seen at the x/d=0 station as well. The strength of the helical shear layer instability is much higher at x/d=0, as can be seen in Figure 10, because the amplitude of mode m 1 is so much greater than that of any other mode number. At x/d=1, however, the strength of the shear layer vortex has decayed, and this is reflected in the similarity of the amplitudes of modes m 1 and m 1. Additionally, theoretical analysis predict that the co-swirling mode, m 1, is most unstable in swirling flow profiles of this type [48]. In this case, this the response at m 1 may be due to the natural instability of the jet, while the m 1 response of the jet stems from the acoustic forcing. Response of the Self-Excited Motions In this section, we examine the response of the flow at the low frequency only, integrated from Hz, in order to capture the influence that acoustic forcing has on the intrinsically occurring motions. As described with reference to Figure 6, the swirling jet has two main motions, a jet column deformation that is described by the m 2 mode, and a pair of coherent structures described by the m 1 mode. In this section, we use modal decomposition to see the effect of the symmetry of forcing. Again, we consider motions at a downstream distance of x/d=1, where the most vigorous recirculation zone motion is located. First, the spectral content of several of these modes is shown in Figure 14. Here, peaks at the 400 Hz forcing frequency are evident in both the out-of-phase and in-phase high amplitude forcing cases, although to a much lesser extent in the in-phase forcing condition. Modes m 2, m 1, and for the out-of-phase forcing case, m 1, have significant low frequency content. a) b) Figure 14. Spectra of several mode numbers integrated over radius and frequency in the r plane at x/d=1, for a non-reacting, flow forced at 400 Hz a) in-phase and b) outof-phase at u o =10 m/s, S=0.85. Figure 15 shows the response of the low frequency content to high amplitude acoustic forcing. Here, the in-phase and out- 10 Copyright 2012 by ASME

11 of-phase results are compared against the unforced results; each mode coefficient is integrated between Hz and radially between r/d=0-1. Figure 15. Distribution of mode amplitude at the low frequencies integrated over radii r/d=0-1 plotted as a function of mode number at x/d=1 for a non-reacting, flow forced with 400 Hz forcing at u o =10 m/s, S=0.85. Here again, it is evident that different forcing symmetries have different effects on the modal content of the velocity fluctuations. In both the in-phase and out-of-phase forcing cases, high amplitude forcing decreases the amplitude of the self-excited behavior at modes m 2 and m 1, but adds energy to the mode m 1. The magnitude to which these effects take hold is dissimilar, particular in the variation in strength of mode m 2. Changes in the radial distribution of this energy are evident in Figure 16, which shows the mode energy for several modes, integrated between Hz, as a function of radius. Like before, the in-phase forcing significantly changes the structure of radial dependence of the modes, particularly mode m 2. a) b) Figure 16. Distribution of mode amplitude at the low frequencies plotted as a function radius for several mode numbers for a non-reacting, flow forced at 400 Hz a) inphase and b) out-of-phase forcing at x/d=1 for u o =10 m/s, S=0.85. Gray areas approximate the location of the inner and outer shear layers. It is evident from data in both the r-x and r-θ planes, as well as at the forcing frequency and in the low frequency range, the symmetry of forcing has a significant effect on the response of the swirling annular flow to transverse acoustic forcing. CONCLUSIONS This study has described the effect of transverse acoustic forcing symmetry on a swirling annular jet. This study was motivated by transverse instabilities in annular gas turbine engines, where different nozzles will be subjected to different portions of the acoustic field. To mimic this effect, two acoustic forcing conditions were considered: the asymmetric, out-ofphase forcing case with a velocity anti-node along the centerline, and the symmetric, in-phase forcing case with a pressure anti-node along the centerline. A summary of the results is given in Table 1. Table 1. Summary of results describing coherent structures and their corresponding frequency ranges/mode numbers for different acoustic forcing conditions. Forcing Frequency Motion Mode number No forcing 0<f<5000 Jet m=-2 deformation No forcing 0<f<5000 Dual helix m =-1 In-phase f=f o Ring vortex m=0 x/d=0 In-phase f=f o Tilted m=1 x/d > 0 vortex Out-of-phase f=f o Helical vortex m =1, m=-1 The results show that the symmetry of acoustic forcing has an effect on both the flow at the forcing frequency, the shear 11 Copyright 2012 by ASME

12 layer response in particular, and the low frequency, self-excited motion in the vortex breakdown bubble. This study has important implications for both understanding and modeling of the behavior of full combustors undergoing transverse instabilities. Results from previous studies from the authors, as well as the results discussed here, indicate that the flame response would be different in these two cases. This is because the flame is responding to the velocity disturbances normal to its surface and the symmetry of forcing changes the topology of the flow field. In future work, a wider variety of forcing frequencies, amplitudes, and flow conditions will be investigated to broaden our understanding of this issue. Additionally, previous studies of vortex breakdown dynamics have shown that substantial changes in the behavior of these structures can arise with combustion. To that end, further testing will investigate the effects of heat release on central recirculation zone dynamics. ACKNOWLEDGMENTS The authors would like to recognize Travis Smith, Charlotte Neville, Michael Malanoski, and Michael Aguilar for their help in data acquisition for this work. This work has been partially supported by the US Department of Energy under contracts DEFG26-07NT43069 and DE-NT , contract monitors Mark Freeman and Richard Wenglarz, respectively. REFERENCES 1. Rayleigh, B.J.W.S., The Theory of Sound Lieuwen, T. and V. Yang, Combustion Instabilities in Gas Turbine Engines. Progress in Astronautics and Aeronautics, ed. F.K. Lu. Vol , Washington D.C.: AIAA. 3. Ducruix, S., T. Schuller, D. Durox, and S. Candel, Combustion dynamics and instabilities: elementary coupling and driving mechanisms. Journal of Propulsion and Power, (5): p Lee, J.G., K. Kim, and D.A. Santavicca, Measurement of equivalence ratio fluctuation and its effect on heat release during unstable combustion. Proceedings of the Combustion Institute, (1): p Poinsot, T.J., A.C. Trouve, D.P. Veynante, S.M. Candel, and E.J. Esposito, Vortex-driven acoustically coupled combustion instabilities. Journal of Fluid Mechanics, : p Ghoniem, A.F., A. Annaswamy, D. Wee, T. Yi, and S. Park, Shear flow-driven combustion instability: Evidence, simulation, and modeling. Proceedings of the Combustion Institute, (1): p Schadow, K.C. and E. Gutmark, Combustion instability related to vortex shedding in dump combustors and their passive control. Progress in Energy and Combustion Science, (2): p Wang, S., V. Yang, G. Hsiao, S.Y. Hsieh, and H.C. Mongia, Large-eddy simulations of gas-turbine swirl injector flow dynamics. Journal of Fluid Mechanics, : p Hirsch, C., D. Fanaca, P. Reddy, W. Polifke, and T. Sattelmayer. Influence of the swirler design on the flame transfer function of premixed flames ASME. 10. Palies, P., D. Durox, T. Schuller, and S. Candel, The combined dynamics of swirler and turbulent premixed swirling flames. Combustion and Flame, : p Bellows, B.D., M.K. Bobba, J.M. Seitzman, and T. Lieuwen, Nonlinear Flame Transfer Function Characteristics in a Swirl-Stabilized Combustor. Journal of Engineering for Gas Turbines and Power, (954). 12. Steinberg, A.M., I. Boxx, M. Stöhr, C.D. Carter, and W. Meier, Flow-flame interactions causing acoustically coupled heat release fluctuations in a thermo-acoustically unstable gas turbine model combustor. Combustion and Flame, (12): p Staffelbach, G., L.Y.M. Gicquel, G. Boudier, and T. Poinsot, Large Eddy Simulation of self excited azimuthal modes in annular combustors. Proceedings of the Combustion Institute, (2): p Hauser, M., M. Lorenz, and T. Sattelmayer. Influence of Transversal Acoustic Excitation of the Burner Approach Flow on the Flame Structure. in ASME Turbo Expo Glasgow, Scotland. 15. Kunze, K., C. Hirsch, and T. Sattelmayer. Transfer function measurements on a swirl stabilized premix burner in an annular combustion chamber ASME. 16. Acharya, V., Shreekrishna, D.H. Shin, and T. Lieuwen, Swirl effects on harmonically excited, premixed flame kinematics. Combustion and Flame, 2011(in press). 17. O'Connor, J. and T. Lieuwen, Further Characterization of the Disturbance Field in a Transversely Excited Swirl-Stabilized Flame. Journal of Engineering for Gas Turbines and Power, (1). 18. O'Connor, J., C. Vanatta, J. Mannino, and T. Lieuwen, Mechanisms for Flame Response in a Transversely Forced Flame, in 7th US National Technical Meeting of the Combustion Institute2011: Atlanta, GA. 19. Brown, G.L. and J.M. Lopez, Axisymmetric vortex breakdown Part 2. Physical mechanisms. Journal of Fluid Mechanics, (4): p Darmofal, D.L. The role of vorticity dynamics in vortex breakdown. in 24th fluid dynamic conference AIAA. 12 Copyright 2012 by ASME

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