visualization of shear layer dynamics in a transversely

American Institute of Aeronautics and Astronautics

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Visualization of Shear Layer Dynamics in a Transversely Excited, Annular Premixing Nozzle

Jacqueline O’Connor1, Tim Lieuwen2 Georgia Institute of Technology, Atlanta, Georgia, 30318

Michael Kolb3 Technische Universität München, Garching, Germany

In this study, we investigate the response of a swirling annular jet flow and flame to

transverse acoustic excitation. Characterizing this response is a necessary step towards understanding velocity-coupled transverse combustion instabilities in lean, premixed flames. These effects are investigated using smoke visualization, particle image velocimetry (PIV), and high-speed flame imaging. This study particularly focuses on the effects of excitation on unsteady vortex development in the shear layers, as well as the effects of high-amplitude acoustics on the time-averaged flow field. First, the time-averaged characteristics of the flow are discussed under both nominal and forced conditions. The shape of the flow changes significantly at high forcing amplitudes as a result of changes in the vortex breakdown structure. Next, the shear layer dynamics with and without acoustic forcing are considered. The shear layers are visualized using smoke visualization and PIV, and the result of vortex rollup on the flame is imaged using high-speed imaging of the flame. We hypothesize that the convectively unstable shear layers and absolutely unstable vortex breakdown bubble play different dynamical roles in controlling the flame response to excitation. The unsteady vortex breakdown bubble is primarily important through its impact on the time-averaged flow field upon which perturbations evolve. It really only changes character at high acoustic forcing amplitudes, resulting in significant variations to the time-averaged flame and flowfield. The shear layer rollup, responding at the frequency of acoustic forcing, creates large-scale wrinkles on the flame and is the main driver of flame response.

I. Introduction his paper describes an investigation of the effect of transverse acoustic excitation on a swirling annular jet flow and flame. The physics discussed here relate closely to combustion dynamics, a problem that has plagued

numerous rocket and air-breathing engine development programs. The coupling of resonant acoustics in the combustion chamber and heat release fluctuations from the flame [2] causes structural damage and decreases operational flexibility and performance. In particular, instabilities have caused major challenges in the development of lean, premixed combustors used in low NOx gas turbines [3].

The key problem we focus on here is the manner in which the flame responds to oscillations in flow velocity. This is referred to as the “velocity coupled” response mechanism [4-9]. The flame is also excited by fuel/air ratio oscillations [10, 11], also known to be important but not analyzed in this study. Flow oscillations lead to flame wrinkling that, in turn, causes oscillations in flame surface area and rate of heat release. While acoustic oscillations can directly excite the flame, they also excite hydrodynamic instabilities associated with shear layers, wakes, or the vortex breakdown region [12-14]. There are a number of potential sources of flow disturbances that can lead to heat release oscillations. Two of these sources are directly acoustic in origin - transverse acoustic motions associated with the natural mode shapes of the combustion system, and longitudinal oscillations due to reflection from the flame [15, 16] and the oscillating pressure drop across the nozzle.

Many studies suggest that vortical flow oscillations significantly control the flame’s heat release response [17, 18]. In other words, acoustic oscillations excite flow instabilities that, in turn, excite the flame. As such, the receptivity of these flow instabilities to both transverse and longitudinal acoustic oscillations must be considered. In 1 Graduate Research Assistant, Aerospace Engineering, 270 Ferst Drive, Atlanta, GA, 30332-0150, AIAA Student Member 2 Professor, Aerospace Engineering, 270 Ferst Drive, Atlanta, GA, 30332-0150, AIAA Associate Fellow 3 Graduate Research Assistant, Lehrstuhl für Thermodynamik, D-85747 Garching, Germany

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49th AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition4 - 7 January 2011, Orlando, Florida

AIAA 2011-237

Copyright © 2011 by Jacqueline O'Connor, Michael Kolb, Tim Lieuwen. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission.


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the discussion below, we break this problem into two components, (1) pertinent fluid mechanic instabilities present in the swirling annular jet, and (2) flame response to this flow excitation.

A. Pertinent fluid mechanic instabilities The velocity disturbances that excite the flame consist of both acoustic waves, traveling at the speed of sound,

and vortical disturbances that travel with the flow. In this study, acoustic fluctuations propagate in a direction perpendicular to the mean flow field, and cause a non-axisymmetric acoustic disturbance field near the flame. Vortical disturbances occur naturally in the swirling flow field, but are also excited and modified by the acoustic field.

We start with a discussion of the key flow features in the absence of acoustic excitation. Figure 1 shows the major fluid mechanic features of a swirling annular jet. This is a very common configuration used in modern low NOx gas turbine combustion systems [3, 19].

a) b)

Figure 1. Basic swirling flow from the a) side view and b) top view.

Several features are apparent from the sketch in Figure 1. The key time-averaged features are an annular jet that exits the nozzle and passes between the recirculating fluid in the inner and outer recirculation zones. The inner recirculation zone is associated with interactions between the centerbody wake and vortex breakdown bubble. This time-averaged flow field essentially forms the “base” flow state upon which disturbances are initiated, and grow or decay. An extensive literature is available on the fluid mechanics of vortex stability and breakdown, including the reviews in Refs. [20, 21]. The breakdown zone size and location strongly depend on Reynolds number, swirl number, chamber geometry, and axial pressure gradient. Heat release has significant influences upon this “base” state as described by Rusak et al. [22]. This results in a change in the critical swirl number as well as the shape and dynamics of the vortex breakdown region, which also leads to a change in the spreading angle of the annular jet exiting the nozzle.

The annular jets and recirculating fluid regions are separated by two streamwise and spanwise shear layers. The shear layer, or Kelvin-Helmholtz, instability is convectively unstable and leads to rollup of the separating vortex sheet into tightly concentrated regions of vorticity [23]. The most amplified frequency of the two-dimensional shear layer occurs at a Strouhal number of St=fθ/Uo=0.032 [24]. The two spanwise shear layers interact further downstream at a point associated with the end of the annular jet potential core.

Coherent acoustic excitation introduces additional physics to the problem. There is a limited literature on the effects of transverse, and therefore non-axisymmetric, forcing of jets [25, 26]. One important effect of transverse forcing is to introduce longitudinal oscillations at the nozzle due to the oscillatory nozzle pressure drop. The direct influences on the swirling jet dynamics are less clear. Reynolds and coworkers [27] and Suzuki et al. [28] investigated the effect of non-axisymmetric forcing of non-swirling jets and showed that this could lead to bifurcation of the jet trajectory, a phenomenon known as “bifurcating” or “blooming” jets.

As mentioned above, an important feature of transverse forcing is that the disturbance is non-axisymmetric and affects different parts of the flow and flame with different intensities. Acoustic flow perturbations excite those


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portions of the flame perpendicular (i.e., at 0 and 180 degrees) to it, while they graze over the portions of the flamelocated at 90 and 270 degrees. This leads to displacement of the shear layer and flame at 0 and 180 degrees, but likely minimal excitation at 90 and 270 degrees. Furthermore, the presence of swirl introduces an additional degree of freedom by rotating the flame sheet disturbances. For example, the portion of the flame excited in the normal direction at 0 degrees is translated both axially and azimuthally, and at some time later at 90 degrees is excited only in a grazing fashion. In both cases, the excited flame disturbances continue rotating as they convect axially downstream, leading to a periodically varying disturbance field character. The swirl number, which controls the rate of azimuthal rotation relative to axial translation, is an important parameter for this downstream evolution.

In particular, the distinction between absolute and convective instability is important. The convectively unstable shear layers, being amplifiers, generally tend to respond at the excitation frequency, regardless of the excitation amplitude. Their downstream evolution is complex, however, and such processes as vortex pairing are crucially influenced by the relative values of the forcing frequency and most amplified frequencies [23, 29, 30]. In many instances, the flame lies in the shear layer, so that the instability characteristics of the shear layers dominate the flame response. Although the base state of the flow changes with heat release, the essential features of the unstable shear layers do not. This implies that key dynamical features of the flow that excite the flame remain qualitatively similar between non-reacting and reacting situations. This point should not be pressed to far, as heat release certainly has important influences on the shear layer development. For example, the dilatation effect of heat release acts as a vorticity sink in the shear layer where the flame is stabilized.

In contrast, absolute instabilities, such as the wake and vortex breakdown bubble, are self excited, limit-cycling “oscillators”. For example, experiments on absolutely unstable, two-dimensional bluff body wakes show that the excitation amplitude must exceed a certain value in order to “lock-in” or “entrain” the vortex shedding frequency to that of the imposed excitation [31, 32]. Such excited flow structures exhibit hysteresis in frequency-amplitude space that do not occur in excited shear layers.

We postulate that the distinction between the absolutely unstable (AI) vortex breakdown bubble and convectively unstable (CI) shear layers is key to understanding the response of the system at varying levels of acoustic excitation. The absolutely unstable breakdown bubble exhibits intrinsic dynamics that are relatively independent of low amplitudes of excitation [33, 34]. Therefore, the basic dynamics of this flow remains unchanged in the presence of low-amplitude acoustic forcing. Only in the presence of large amplitude dynamics that alter the vortex breakdown bubble [35] and cause frequency locking of bubble dynamics are the interactions between the excitation and vortex breakdown bubble dynamically significant.

B. Flame response to instabilities Numerous studies have investigated the effect of

longitudinal acoustic forcing on swirling jets, a configuration where the acoustic waves travel in the direction of the mean flow [36, 37]. The interactions of these flow instabilities with a longitudinally excited flame is clearly evident in a series of OH PLIF images, see Figure 2 from Ref. [1]. For example, the small scale inner and outer shear layer rollup is clearly evident in several of these images, most prominently in the right flame branch in 1a. Similarly the rollup of the flame by an outer shear layer or wake structure can be seen in 1b and 2b, and by the inner shear layer or inner recirculation zone in 1a and 2a. Finally, the interaction of the flame with the leading edge of the vortex breakdown bubble can be inferred from the flame standoff in 2c,1b, and 2b. Comparison of successive shots of these flames in this latter case (not shown) clearly shows this leading flame edge oscillating axially, presumably reflecting oscillations in vortex breakdown stagnation point [1].

There are two key aspects of how transverse excitation influences flames response to disturbances within the flame sheet regime: First, is the local displacement and wrinkling of the flame position, clearly evident in the images above, and second, the associated local and global fluctuation in heat release. Within the flame sheet approximation, the response of the flame to flow excitation is

Figure 2. OH PLIF images showing (a) vortex rollup in inner recirculation zone at 130 Hz, Re=21,000, u’/u0 =

0.9, (b) vortex rollup in outer recirculation zone at 210 Hz, Re=44,000, u’/u0 = 0.2 and (c) shear layer rollup in the flame

at 130 Hz, Re=21,000, (1) u’/u0 = 0.2 and at 270 Hz, Re=44,000, (2) u’/u0 = 0.05, from Thumuluru and

Lieuwen [1].


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largely controlled by flame kinematics, i.e., the propagation of the flame normal to itself into an oscillatory flow field. This is mathematically described by the so-called G-equation [38]:

( ) | | 0L

Gu n S G

tG ( ) | | 0L ) |) |(t

( ) |) | (1)

In this equation, the flame position is described by the parametric equation ( , ) 0G x t 0) 0 whose local normal vector is given by nn . Also, ( , )u u x t( , )u( ,,u ( )u( and SL denote the flow field just upstream of the flame and laminar burning velocity, respectively. In the unsteady case, the flame is being continually wrinkled by the unsteady flow field, uu .

Exciting progress has been made in the last decade in using measured velocity field characteristics as inputs to this equation to predict the spatio-temporal dynamics of two-dimensional or axisymmetric laminar flames. For example, Candel [39] showed that they were able to predict the global heat release using measured characteristics of the disturbance field. Similarly, Shanbhogue et al. [40] and Emerson et al. [41] showed that they could quantitatively predict the spatial distribution of the flame response amplitude using measured velocity field inputs obtained from PIV. The latter study was performed at flow velocities up to 50 m/s, showing the important progress being made at realistic flow conditions. The analogous problem for swirl-stabilized flames has received relatively little comparable treatment [15, 42, 43]. Additional physics are present in this case because transverse disturbances necessarily create a non-axisymmetric disturbance field.

In contrast, it can be expected that longitudinal disturbances excite an essentially axisymmetric acoustic and vortical disturbance field, leading to axisymmetric flame wrinkling. The non-axisymmetric excitation of the flame introduces an additional degree of freedom into the flame dynamics, as it leads to helical propagation of flame wrinkles. Some very preliminary theoretical work on this problem has been reported in Ref. [44], using highly idealized assumptions on the disturbance field.

As such, a key enabling task for this problem is predicting the functional relationship between ( , )G x t) , or the

unsteady heat release per unit axial distance dQ dx , and the incident transverse disturbance field, incuinc :

inc

dQ dx Fu Finc

F (2)

where F is a describing function relating these two quantities. This describing function is the key input required for insertion into an unsteady acoustics model for predicting system stability [45]. However, as alluded to above, the incident disturbance field, incuinc , may not actually be the key driver of the unsteady heat release, but rather the driver

of the unsteady vortical field that excites heat release oscillations, u and axial acoustic oscillations, aua . Therefore, a more physically useful expansion of the above expression is:

, ,a

x a t ainc inc inc

u udQ dx F F F Fu u uu uuu u

t aF F FatFF F

uuF F FaF

uF F Fau

Finc

FFF x aF F FFFFFFFinc incui

,a,t a,uiuinc incuinc,x,uu x a,

i

(3)

where FF is the transfer function between incident velocity fluctuations and vortical velocity fluctuations, ,x aF is

the transfer function between the incident velocity disturbance and the axial acoustic velocity fluctuation, and ,t aF is the “direct” flame transfer function as a result of the incident transverse acoustics. This expression shows that a physical description of F requires understanding of the more fundamental input-output relations FF , ,x aF , and

,t aF . In particular, understanding FF requires understanding the mechanisms through which a transverse sound wave excites the separating shear layer and leads to coherent vortical perturbations. The objective of this paper is to understand these mechanisms, which is a necessary first step towards developing these quantitative transfer functions.


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II. Experimental Facility and Data Analysis The details of the experimental configuration can be found in O’Connor et al., [43]. In the current experiments,

a single nozzle is used with a bulk velocity of Uo=10 m/s and a swirl numbers of 0.5 and 0.85. The flow is an annular swirling jet with an inner radius of r1=1.09 cm and an outer radius of r2=3.18 cm. This corresponds to a Reynolds number of Re=2Uor2/ν=21,500. The length of the centerbody is h=5.08 cm. The facility and nozzle are shown in Figure 3.

a) b)

h

r1r2

Flow from settling

chamber

Dump plane

Figure 3. Tunable transverse forcing combustion facility with a) the full facility and b) the nozzle detail.

This configuration emulates the shape of an azimuthal mode in an “unwrapped” annular combustor. The transverse acoustic field is produced by two sets of drivers on either side of the combustor. Each driver sits at the end of an adjustable tube that allows for acoustic tuning. The drivers on either side of the combustor can be controlled independently so that different wave patterns, both standing and traveling waves, 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 in the flame region. When the drivers are forced out-of-phase, a pressure node and velocity anti-node are set up at the center. The resulting disturbance field from these two forcing configurations can be significantly different.

Previously, particle image velocimetry (PIV) was used to measure the velocity field and the flame edge. PIV images were taken at a frame rate of 10 kHz and 500 velocity fields were calculated at each test condition. The resolution of the PIV images is 0.14 mm/pixel and an interrogation window size of 32x32 pixels with a 50% overlap was used in the velocity calculations. In the current configuration, the large-scale vortices, a result of collective interaction in the cases with acoustic forcing, can be resolved with several velocity vectors across the diameter of the structure.

The small-scale vortices that rollup as a result of the Kelvin-Helmholtz instability in the cases without acoustic forcing cannot be resolved by the PIV. For that reason, smoke visualization was also used for visualization of these smaller structures. A diagram of the smoke injection scheme is shown in Figure 4. This system allows for smoke injection in a roughly axisymmetric manner for both/either the inner and outer shear layers. By varying the smoke injection points, separate or combined visualization of the inner shear layer, outer shear layer, and recirculation zone is possible. Such visualization approaches have been used in several studies in order to track coherent structures in shear layers as well as the vortex breakdown region in swirling flows [25, 27]. The system is viewed either directly with a camera to image the three dimensional smoke evolution, or with cuts by illumination with a laser. This technique has been helpful in visualizing the shear layer dynamics close to the nozzle exit. Farther downstream and inside the vortex breakdown region, though, the olive oil smoke is too diffuse to track.


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Outer shear layer smoke injection

Inner shear layer smoke injection

Center recirculation zone smoke injection

Outer shear layer smoke injection

Inner shear layer smoke injection

Center recirculation zone smoke injection

Figure 4. Smoke injection points for both inner and outer shear layer seeding in annular nozzle.

III. Results and Discussion The experimental results are broken in to three sections: description of basic flow field characteristics,

discussion of the changes in the time-average flow field due to high-amplitude acoustic forcing, and characterization of the forced and unforced shear layer dynamics. All results are shown in dimensionless form. The velocities are normalized by the bulk approach flow velocity, oU m Amm A (where and A denote approach flow density and annulus area), the spatial coordinates by the nozzle outer diameter, D, and the vorticity by the bulk velocity divided by the annular gap width, Uo/(r2-r1).

A. Time-average flow field characteristics

The time averaged axial velocity and vorticity fields are shown in Figure 5 for both the non-reacting and reacting cases. In the axial velocity field, the annular jet is shown originating from the left that passes around the centrally located wake/vortex breakdown region. The shear layers shown in the time-average vorticity plot arise from the mixing of the annular jet and the inner/outer recirculation zones. The inner shear layer is significantly stronger than the outer, presumably because the velocity gradient between the jet and the vortex breakdown region is greater than that between the jet and the quiescent fluid outside the jet.

a) b)

Figure 5. Time averaged a) axial velocity and b) vorticity fields at Uo=10 m/s, swirl number of 0.85, non-reacting flow (top) and reacting flow (bottom), equivalence ratio of 0.9 with natural gas fuel.

The time-averaged flow fields of the non-reacting and reacting cases are different in several ways. First, the vortex breakdown bubble changes in size and shape, growing wider at the dump plane in the reacting case. Second, the jet spreading angle is higher in the reacting case, presumably because of the wider vortex breakdown bubble. Third, the average shear layer locations, as shown by the vorticity plots, also spread as a result of the two aforementioned effects. Note that this flow contains two distinct shear layers, one emanating from the inner edge and one from the outer edge of the annulus. The flame configuration is nominally that of a “V-shape” stabilized in the inner shear layer.


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B. Effect of acoustic forcing on time-averaged flow field As discussed above, high amplitudes of acoustic forcing can result in changes in the “base state” of the flow. In

this section, we consider the effect of high-amplitude forcing on the time-average flow topology. The most noticeable effect is an outward bending of the shear layers as the amplitude of acoustic forcing increases. This can be seen in Figure 6, where 500 smoke visualization images have been overlaid to show the time-average shear layer shape. The amplitude of acoustic forcing is reported by the strength of the transverse velocity fluctuation, v’, normalized by the bulk flow velocity, Uo.

a) b)

Figure 6. Bending of the shear layers for a) low (v’/Uo=0.08) and b) high (v’/Uo=0.35) acoustic amplitude, out-of-phase forcing at 400 Hz and a bulk velocity of 10 m/s and swirl number of 0.85.

Figure 6 shows how high-amplitude acoustic forcing significantly effects the time-average shape of the flow. This process can also be seen in Figure 7, which shows the time-average flame shape as a function of acoustic amplitude.

a

fed

cb

Figure 7. Line-of-sight overlays of 500 images of the flame at several forcing amplitudes a) 200 mV, b) 400

mV, c) 600 mV, d) 800 mV, e) 1000 mV and f) 1100 mV on the function generator (transverse acoustic fluctuation amplitudes are not available for this condition). Acoustic forcing is in-phase at 1800 Hz, flow

velocity of 10 m/s, swirl number of 0.5, and equivalence ratio of 0.9.

The divergence of the annular jet seems to stem from a change in topology of the vortex breakdown bubble. As the amplitude of forcing increases, the vortex breakdown region gets wider, pushing the shear layers out and increasing the jet spreading angle. This process does not seem to be monotonic, but occurs in a seeming discontinuous manner. This can be seen from Figure 7, where the step change between the last two images, image “e” and “f”, is much larger than that between any other congruent images. This phenomenon can also be seen in the velocity data as well, as shown in Figure 8 which plots the time-average velocity field of two non-reacting tests at two different acoustic forcing amplitudes.


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a) b) Figure 8. Bifurcation behavior in vortex breakdown structure in a non-reacting flow for a forcing amplitude

of a) v’/Uo=0.36 and b) v’/Uo=0.40 out-of-phase forcing at 800 Hz and a bulk velocity of 10 m/s and swirl number of 0.85. Lines of zero axial velocity are outlined in green to indicate the edges of vortex breakdown.

The change in flow behavior between the two amplitudes is highly repeatable at this frequency and forcing condition, and the flow stays in a similar configuration to Figure 8b as the amplitude of forcing is increased above 1200 mV. In the high forcing amplitude state, the vortex breakdown bubble becomes significantly larger and asymmetric. The left half of the jet is pushed far towards the dump plane, becoming a sort of wall-jet. The right half of the jet is diverted so severely that it is not viewable in the PIV window, which starts 6.5 mm above the dump plane. This phenomenon can also been observed in the smoke visualization studies. When conditions of this type were met, the smoke from the injection holes was almost immediately diffused and the shear layers were barely visible. This effect seems to be less dramatic, though, in the reacting flow, as seen by the comparison between the shear layer direction in Figure 7 and Figure 8.

This change in vortex breakdown bubble is not as uniformly significant at all forcing frequencies over the forcing amplitudes considered in this study, however. Other instances of significant changes in the vortex breakdown structure appear throughout the data at high amplitudes, but are not as repeatable as for the 800 Hz out-of-phase case shown above. Examples have been seen at both 400 Hz and 1200 Hz for both in- and out-of-phase forcing. At this point in time a systematic explanation for this bifurcation phenomenon is not available.

Previous studies of swirling jets [1, 34, 35] have shown that only at very high levels of acoustic forcing does the vortex breakdown bubble respond to the acoustics. Khalil et al. [35] showed that the location of vortex breakdown changes as a function of both amplitude and frequency. In the frequency range close to the natural instability frequency of the vortex breakdown region, the location of the vortex breakdown region distance from the dump plane can be changed as much as 50% of the unforced case. Thumuluru and Lieuwen [1] and Wang and Yang [34] both report dynamical response of the vortex breakdown bubble. While Thumuluru and Lieuwen show an increase in both vertical and lateral movement of the upper stagnation point with increases in longitudinal forcing amplitude, Wang and Yang report a dynamic change in the bubble size as fluid periodically fills and empties from the bubble. As discussed above, this non-linear behavior is a result of the fact that vortex breakdown is a manifestation of an absolute instability, whose response to external forcing is, therefore, amplitude dependent.

This time-average change in flame shape can have an important affect on flame response. As shown in Equation 1, the flame response is governed by two effects, the disturbance velocity normal to the flame front and the kinematic restoration that stems from the flame propagation at speed SL. The magnitude of the term u GGu G is a function of the angle of the flame to the incoming flow, which is directly related to the shear layer angle. More generally, the behavior of the flow is dependent on its time-average state.

C. Shear layer dynamics

The shear layer dynamics are strongly influenced by acoustic excitation. Figure 9 shows the unforced shear layers, both spanwise and streamwise, and the natural vortex rollup that occurs as a result of the Kelvin-Helmholtz instability in a series of images 0.2 ms apart. Images a-f in Figure 9a show the rollup event of one vortex at the dump plane as another two convect downstream. In Figure 9b, images a-e show the rollup of a vortex in the streamwise shear layer in a series of images that were taken from the top of the combustor with the laser sheet placed at a distance of 6.5 mm downstream of the dump plane.


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a)

a

b c d e f

1 mm

b)

a

b edc

1 mm

Figure 9. Instances of shear layer rollup in an unforced annular swirling jet in both the a) axial and b)

azimuthal shear layers, with mean flow velocity of 10 m/s, swirl number of 0.85.


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Figure 9a shows the spanwise shear layer rollup on the right-hand side of the nozzle. Small structures, approximately 1 mm across, roll up at the edge of the nozzle and convect downstream with the jet. Based on a mean flow speed of 10 m/s and the spacing of the vortices, the passage frequency is approximately 2500 Hz. Image b shows the beginning of the formation of a vortex in the outer shear layer. By image d the vortex has rolled up and begins to convect downstream. As it travels downstream, in images e-f, it also grows larger. It is clearly possible to see these fine-scale vortex rollup events in the outer shear layer. It is much more difficult to see these structures in the inner shear layer as a result of the highly turbulent vortex breakdown region adjacent to the inner shear layer. Just as a vortex is formed, it is quickly deformed and diffused by the inner recirculation zone.

Figure 9b shows the streamwise shear layer rollup measured 6.5 mm downstream of the dump plane. These structures are significantly larger than the spanwise structures and can be seen to roll up as the flow rotates counter-clockwise. In the inner streamwise shear layer, the coherent structures are larger and more diffuse as a result of their interaction with the inner recirculation zone. The images shown in Figure 9b show the rollup of a vortex, indicated by a yellow arrow. It can be seen rolling up and convecting counter-clockwise through the series of images.

An important question is the mechanism through which the shear layer, which has its own most amplified frequency, responds to the excitation. As the shear layer is convectively unstable, it responds to the acoustic forcing, even at low amplitudes. Ho and Huang [23] have shown that forcing where fo<<fr leads to a phenomenon known as “collective interaction.” As illustrated by the sketch taken from Ho and Nossier [29] in Figure 10, the vortices interact so that in one region they are drawn together, further amplifying the induced flow field that causes their rotation around each other and coalescence. In the other region, they are pulled apart from each other. Also shown is a flow visualization from the present experiment of apparently the same phenomenon. Unlike the unforced case where the structures resulting from natural vortex shedding were too small and weak to survive in the midst of the vortex breakdown bubble, these large collective interaction structures can be seen in the inner and outer shear layers.

Figure 10. Collective interaction in shear layers from Ho and Nossier [29] (left) and from the current study

(center and right) in the inner shear layer of the annular jet with acoustic forcing, out-of-phase forcing at 400 Hz at an amplitude of v’/Uo=0.35 and a bulk velocity of 10 m/s and swirl number of 0.85.

During a collective interaction event, several Kelvin-Helmholtz vortices rapidly merge and roll up into a larger structure whose passage frequency equals that of the excitation. In other words, an integer number of shear layer vortices with passage frequencies of approximately 2400 Hz merge into a larger vortex at a forcing frequency of 400 Hz. An example of such an event is shown in detail in Figure 11 and with less magnification in Figure 12. In Figure 11, what appears to be five smaller vortices, formed as a result of the Kelvin-Helmholtz instability, can be seen rolling into a larger structure, as described by Ho and Nossier [29] and shown in Figure 10. The time step between each image is 0.1 ms. Figure 12 shows the event with less magnification and with larger time steps, 0.3 ms, and shows another collective interaction event, followed by the shedding of the large structure and its convection downstream, as also shown by Ho and Nossier [29] in Figure 10. This process is repeated once per acoustic cycle.


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a

b c d e

Figure 11. Collective interaction event in the inner shear layer with a bulk velocity of 10 m/s, swirl number of

0.85, and out-of-phase acoustic forcing at 400 Hz at an amplitude of v’/Uo=0.35.

a dcb

e f g h

Figure 12. Collective interaction even showing the structure formation and separation at the same conditions

as Figure 11. Each image is 0.3 ms apart.


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Figure 13 shows this same event in the high-speed PIV data, circled in yellow. The PIV resolution is far too course to visualize the small shear layer vortices, but the larger merged vortical structure is evident, as shown in Figure 13. This field shows the velocity vectors superimposed on the out-of-plane vorticity, shown in the color bar on the right. The quantities plotted are the sum of the velocity and vorticity fluctuation at the forcing frequency and the mean at one instant of the acoustic cycle. The part of the cycle chosen corresponds to approximately the same moment in time as is shown in Figure 12g.

Figure 13. Collective interaction as seen in a velocity field from PIV for a non-reacting case at a bulk velocity

of 10 m/s, swirl number of 0.85, and out-of-phase acoustic forcing at 400 Hz at an acoustic amplitude of v’/Uo=0.35. Structure from collective interaction is shown in the yellow circle.

The large-scale structure rotating in a clockwise direction at r/D=0.5 and x/D=0.2 is clearly evident in the figure. At r/D=-0.5 and x/D=0.4, an oppositely rotating structure is present in the inner shear layer and had been formed half a cycle before the one previously described. This structure is not as visible in the smoke image due to the rapid diffusion of the smoke.

The vortex rollup on either side of the nozzle happens out-of-phase as a result of the asymmetric acoustic forcing. In the out-of-phase forcing case, the pressure fluctuations on either side of the nozzle are out-of-phase, as a result of the pressure node along the centerline. The pressure fluctuations cause alternating mass flow fluctuations on either side of the nozzle, causing alternating vortex shedding from the nozzle edge, which seems to indicate the existence of a helical structure on the inner shear layer. This process was described in detail in Ref. [43]. The asymmetry in the collective interaction vortex rollup is reflected in the resulting flame shape. Figure 14 shows an image of the flame during the same part of the cycle as described above.

a b dc

e f g h

Figure 14. Images of a the flame at a bulk velocity of 10 m/s, swirl number of 0.55, equivalence ratio of 0.9 and out-of-phase acoustic forcing at 400 Hz at an acoustic amplitude of v’/Uo=0.35. The sequence shows a

vortex rollup in the inner shear layer.


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In Figure 14, a flame wrinkle associated with a large scale vortex is shown on the flame edge with a yellow arrow. The asymmetry of the vortex rollup is also evident from this image as the vortices along either side of the flame are staggered. Figure 15 shows a comparison between the flame shape during out-of-phase and in-phase acoustic forcing conditions showing the staggered and symmetric flame wrinkle behavior, respectively.

a) b) Figure 15. Instantaneous flame images for a) out-of-phase and b) in-phase acoustic forcing at 400 Hz at a bulk

velocity of 10 m/s, swirl number of 0.55, equivalence ratio of 0.9.

Figure 15 shows the importance of the shear layer dynamics as it relates to flame response. In these two images, the acoustic forcing has changed, resulting in an asymmetric disturbance field in the case of out-of-phase forcing and a symmetric disturbance field in the case of in-phase forcing. This difference in symmetry and local flame response is a result of the convectively unstable shear layer to the acoustic forcing. As discussed previously, this is further evidence of how important a foundational appreciation of the velocity disturbance is to a greater understanding of the resultant flame response.

IV. Conclusions In this work, the effect of transverse acoustic excitation on both the time-average and instantaneous behavior of a

swirling flow and swirl-stabilized flame is considered. Several key concluding points are: 1. The time-average behavior of the flow field is a function of the disturbance amplitude. As the amplitude

changes, the structure of the vortex breakdown bubble, the result of an absolute instability of high swirl number flows, changes shape and size. Initial results indicate that this change in flow topology may be an abrupt bifurcation, but its dependence on forcing amplitude and frequency is still an area of study.

2. Even in a flow as complicated as a swirling annular jet, the unforced shear layer dynamics can still be seen. Small-scale vortex rollup in the spanwise and streamwise shear layers was visualized using high-speed smoke visualization. The natural frequency of the spanwise instability was calculated to be approximately 2500 Hz.

3. The convectively unstable shear layer is highly susceptive to acoustic forcing. Collective interaction, the gathering of smaller shear layer vortices into large vortices, is present when the forcing frequency is lower than the natural Kelvin-Helmholtz frequency. This phenomenon was also visualized with high-speed smoke visualization and the large-scale vortices can be measured using high-speed PIV as well.

4. Both the time-average and dynamical results of acoustic forcing have a significant effect on flame response. The centerbody stabilized flame in this study showed significant time-average shape changes at high acoustic forcing amplitudes, which is consistent with the non-reacting results. The change in time-average flame location has been shown, though a theoretical formulation discussed above, to have an effect on the amplitude of the dynamical effects of velocity perturbations and resultant heat release. Additionally, high-speed flame imaging shows the large-scale wrinkles that form as a result of the collective interaction mechanism in the inner shear layer. As the flame area periodically increases as a result of these passing vortices, the heat release fluctuates.

This coupling process is the key to understanding the combustion instabilities issue found in several gas turbine engines today. While previous generation combustor design has mitigated the effect of combustion instabilities by using several passive control techniques, the underlying theory of the instability is still not well understood,


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particularly in the case of transverse instabilities. High-amplitude instability studies like the one presented here help not only to illuminate the underlying physics present during these destructive combustion dynamics events, but can also help gas turbine manufacturers design around these coupling issues in the future.

Future work will continue to investigate the development of the vorticity field in the presence of transverse acoustic excitation. Additionally, we will continue to investigate the response of the flow and the flame at high amplitudes of acoustic forcing. Highly non-linear behavior in both the fluid mechanic and flame response has been measured here in previous studies [1] and this work will be continued with the use of simultaneous high-speed PIV and OH PLIF.

Acknowledgments This work has been partially supported by the US Department of Energy under contracts DEFG26-07NT43069

and DE-NT0005054, contract monitors Mark Freeman and Richard Wenglarz, respectively. Additional thanks to Aditya Kaimal and Matthew Chambers for their help with the project.

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