disturbance field characteristics of a transversely

1 Copyright © 2010 by ASME

Proceedings of ASME Turbo Expo 2010: Power for Land, Sea and Air GT2010

June 14-18, 2010, Glasgow, UK

GT2010-22133

Disturbance Field Characteristics of a Transversely Excited Annular Jet

Jacqueline O’Connor Georgia Institute of Technology

Atlanta, GA, USA

Shweta Natarajan Georgia Institute of Technology

Atlanta, GA, USA

Michael Malanoski Georgia Institute of Technology

Atlanta, GA, USA

Tim Lieuwen Georgia Institute of Technology

Atlanta, GA, USA

ABSTRACT This paper describes an investigation of transverse acoustic

instabilities in premixed, swirl-stabilized flames. Additional measurements, beyond the scope of the current work, are described in O’Connor et al. [1]. Transverse excitation of swirling flow involves complex interactions between acoustic waves and fluid mechanic instabilities. The flame’s response to transverse acoustic excitation is a superposition of both acoustic and vortical disturbances that fluctuate in both the longitudinal and transverse direction. In the nozzle near field region, the disturbance field is a complex superposition of convecting vortical disturbances, as well as longer wavelength transverse and longitudinal acoustic disturbances. Farther downstream, the disturbance field is dominated by the transverse acoustic field. The phasing between the disturbances on the inside and outside of the burner annulus, as well as the left and right sides of the burner annulus is a strong function of the transverse disturbance field characteristics. For cases where the burner centerline is an approximate pressure node and velocity anti-node, the mass flow out of the left and right sides of the burner actually oscillates out-of-phase with respect to each other. In contrast, for cases where the centerline is a pressure anti-node, the burner responds symmetrically about the burner and annulus centerlines. These results show that the burner response characteristics strongly depend upon their location in the acoustic mode shape.

INTRODUCTION

The objective of this study is to improve understanding of transverse combustion instabilities in premixed combustors. Combustion dynamics is 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] can cause structural

damage, decrease 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].

Transverse instabilities have been discussed frequently in the afterburner [4-7], solid rocket [8, 9], and liquid rocket literature [10-15]. For low NOx gas turbines, most of the work over the last two decades has focused on the longitudinal instability problem [16-18]. Significantly less work has been done on the analysis and characterization of transverse instabilities for gas turbine type applications, characterized by a swirling, premixed flame [19-24]. There are, however, two key application areas where transverse acoustic oscillations are of significant practical interest. The first occurs in annular combustion systems, such as the instabilities in the Solar Mars 100, Alstom GT24, GE LM6000, Siemens V84.3A, and others [20, 25-27]. Because of the larger length scales involved, these instabilities often occur at similar frequencies (e.g., 100’s of Hertz) as the longitudinal oscillations encountered in these systems. As these modes cannot be simulated without the full annulus, several of these companies report the results of longitudinal instability tests obtained on single nozzle rigs scaled to have similar longitudinal acoustic frequencies as the observed transverse instabilities [25, 28, 29]. The second application where transverse instabilities are of interest is the higher frequency transverse oscillations encountered in can combustion systems. These instabilities occur at relatively high frequencies, in the 1-5 kHz range, and scale with the combustor can diameter. While relatively little treatment of these high frequency oscillations can be found in the technical literature, there is significant discussion of them in the gas turbine operator/user community; e.g., see Combined Cycle Journal [30] or Sobieski and Sewell’s chapter in Combustion Instabilities in Gas Turbine Engines [26].


Transverse acoustic oscillations in combustors introduce a variety of new coupling processes and disturbance field phenomena relative to longitudinal modes. The focus of the next two sections is to elucidate these differences. In essence, the key problem of interest is the manner in which the flame responds to oscillations in flow velocity. This is referred to as the “velocity coupled” response mechanism [31-35], to be distinguished from the also important “fuel/air ratio coupling” [36, 37] mechanism, or the probably negligible “pressure coupling” mechanism [38]. Flow oscillations lead to flame wrinkling that, in turn, causes oscillations in flame surface area and rate of heat release. In the discussion below, we break this problem into two components (1) nature of the velocity field that is exciting the flame, and (2) flame response to this flow excitation.

Velocity Field Disturbing the Flame While acoustic oscillations can directly excite the flame,

they also excite organized flow instabilities associated with shear layers, wakes, or the vortex breakdown bubble [39-41]. Taken together, 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 frequencies/mode shapes of the combustion system, and longitudinal oscillations in the nozzle due to the oscillating pressure difference across the nozzle. An alternative way of thinking about the latter case is that transversely traveling acoustic wave diffract around the nozzle and enter the nozzle passages, leading to longitudinal mass flow oscillations at the burner exit. Recent simulations by Staffelbach [19] suggest that it is these longitudinal mass flow oscillations that most significantly control the flame response to the imposed transverse disturbance.

Recent studies suggest that it is vortical flow oscillations that most significantly control the flame’s heat release response [42-44]. 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. For example, consider the convectively unstable shear layers, which form tightly concentrated regions of vorticity through the action of vortex rollup and pairing [45]. The transverse acoustic oscillation will disturb them in both normal and parallel directions, see Figure 1. Normally incident transverse acoustic oscillations will push them from side to side in a flapping manner, while parallel incidence will graze over them.

Top ViewSide View

Transverseacousticexcitation

Grazing interaction

Normal interaction

Figure 1. Transverse excitation interacts both normal to

the flame and grazing the flame.

In contrast, longitudinal oscillations will lead to an axially oscillating core flow velocity that will excite an oscillation in shear layer strength [46, 47]. Other literature on the response of wakes and swirling flows to longitudinal and transverse excitation can be found in [40, 48, 49]. These potential sources of excitation are summarized in the figure below.

Transverse Acoustic Excitation

LongitudinalAcoustics

Flow Instabilities• Shear layer• Wake• Vortex breakdown


Flame Response

Transverse Acoustic Excitation

LongitudinalAcoustics



Flame Response Figure 2. Disturbance pathway in transversely excited

flame.

These four disturbance modes are difficult to separate in complicated geometries and all four play a roll in exciting the flame. Although the initial disturbance is transverse, the disturbance velocity field that is created in the region of the flame is highly two or three-dimensional. The only known literature to date that explores this topic shows very clearly the two-dimensionality of the disturbance field [19, 20]. This is significant in that the flame will experience a varying type of disturbance along its length. For example, a point in the middle of the flame may experience a strong transverse acoustic excitation source locally, as well as the disturbance from a vortex that was excited at the nozzle exit and has convected downstream. Complex interactions like these are difficult to separate, and it is one of the goals of this work to understand these characteristics of the disturbance field.


The significant impedance jump across the flame also introduces important differences between the disturbance field resulting from incident longitudinal and transverse disturbances. In the longitudinal excitation case, a nominally axisymmetric burner will see roughly the same amplitude/phase of acoustic excitation at all azimuthal points; e.g., the source of shear layer forcing will be uniform. In contrast, the flame will partially reflect/refract a transversely propagating traveling acoustic wave, resulting in different excitation fields on either side of the flame. In other words, one side of the flame is “shielded” by the impedance jump imposed by the other side. Several studies [50-52] have shown that an acoustic disturbance is considerably changed as it travels across a flame as a result of dilatation. This point has been dramatically illustrated in recent experiments of Ghosh and Yu for transversely excited H2/O2 cryogenic flames, as seen in Figure 3 Note the significantly different degree of flame wrinkling of the two flame branches.

Figure 3. OH* Chemiluminescence at various phases of a flame forced at 1150 Hz showing the “shielding” effect

[50].

Flame response to Flow Excitation In this section, we consider how transverse excitation influences how flames respond to disturbances. Within the flame sheet approximation, the response of the flame to flow excitation is 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 G-equation [53]:

( ) | | 0LG u n S Gt

∂+ ⋅ − ∇ =

∂ (1)

In this equation, the flame position is described by the

parametric equation ( , ) 0G x t = whose local normal vector is given by n . Also, ( , )u u x t= 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, u . The key thing to note from this equation is that the flame does not

distinguish between disturbance sources that are axial or transverse in nature – rather, its response is controlled by the scalar u n⋅ - i.e., the component of the flow velocity in a direction normal to the instantaneous flame front As such, the response of a two-dimensional flame to a given perturbation field is fundamentally the same, regardless of whether the disturbance field is transverse or axial in nature

However, additional physics are present for axisymmetric flames, because transverse disturbances will 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 azimuthal disturbance propagation along the flame sheet in a helical fashion. Some initial work on this problem has been reported by Acharya et al. [54].

Having discussed some basic features of the transverse forcing problem, we conclude this section with an overview of the rest of this paper. Characteristics of the two-dimensional velocity disturbance field in a transversely forced, swirl-stabilized flame are investigated using time-resolved particle image velocimetry (PIV) [55]. First, the experimental setup is explained and an overview of the diagnostic system is given. Next, the disturbance field is characterized using several metrics to capture the different types of disturbances found in the region of the flame. Finally, several conclusions are drawn as to the underlying physics of the disturbance field and the effect of the velocity disturbance field on the flame behavior.

NOMENCLATURE A Gain of Fourier transform

D Outer diameter of nozzle f Frequency G Flame position p Pressure po Time averaged pressure p Spatially averaged instantaneous pressure

r Radius from nozzle centerline SL Laminar flame speed t Time u Axial velocity ū Spatially averaged instantaneous axial velocity uo Time averaged axial velocity û Harmonically reconstructed axial velocity

u Total velocity vector v Transverse velocity v Spatially averaged instantaneous transverse velocity vo Time averaged transverse velocity


v Harmonically reconstructed transverse velocity x Axial coordinate

γ Ratio of specific heats

φ Phase of Fourier transform

ω Vorticity

ωo Time averaged vorticity

ω Harmonically reconstructed vorticity

EXPERIMENTAL FACILITY AND DATA ANALYSIS The experimental facility used in this study is a single

nozzle rig that was designed to support purely transverse acoustic modes in the combustion chamber. The inner chamber dimensions are 1.14 m x 0.36 m x 0.08 m, with the 1.14 m dimension is in the transverse direction. This configuration mimics the shape of an azimuthal mode in an annular combustor for the flame stabilized in at the nozzle in the center. 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. By changing the phase between the signals driving each side of the combustor, 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 created at the center. The resulting flame response from these two forcing configurations can be significantly different. The experiment is shown in Figure 4.

Figure 4. Tunable transverse forcing combustion facility.

Although up to three nozzles can be supported, the current configuration has a single nozzle. The nozzle consists of a swirler with 12 non-aerodynamic blades with a 45º pitch and 5.1 cm centerbody. The outer diameter of the swirler is 3.18 cm and the inner diameter is 2.21 cm. The nozzle configuration, including the theoretical mode shapes around the nozzle for different acoustic forcing conditions, is shown in Figure 5.

D

u’ – out of phasep’ – in phasep’ – out of phase

u’ – in phase

1

2

1.091.593.18

r cmr cmD cm

===

1r2r

Top view

++

+-

p’ – out of phaseu’ – in phase

u’ – out of phasep’ – in phase

D

u’ – out of phasep’ – in phasep’ – out of phase

u’ – in phase

1

2

1.091.593.18

r cmr cmD cm

===

1r2r

Top view

++

+-

p’ – out of phaseu’ – in phase

u’ – out of phasep’ – in phase

Figure 5. Nozzle configuration and acoustic velocity and

pressure perturbations for in phase and out of phase acoustic forcing, not shown to scale.

The effect of in and out-of-phase forcing on the spatially averaged transverse velocity (defined in Equation 3) is illustrated in Figure 6, showing how it changes from large to small values. The non-zero value of the transverse velocity observed for the in phase case is likely due to slight imbalances in excitation amplitudes of the left and right speakers.

0 2 4 6 8 10

-0.4

-0.2

0

0.2

0.4

0.6

t*fo

v`/u

o

In PhaseOut of Phase

Figure 6. Spatially averaged transverse velocity

fluctuations along the nozzle centerline for 400 Hz acoustic forcing at 10 m/s non-reacting flow.

Particle Image Velocimetry (PIV) is used to measure the

velocity field and the flame edge. The window at the front of the combustor is a 22.9 cm x 22.9 cm quartz window originating 0.635 cm downstream of the dump plane. The PIV system is a LaVision Flowmaster Planar Time Resolved system that allows for two-dimensional, high-speed velocity measurements. The laser is a Litron Lasers Ltd. LDY303He


Nd:YLF laser with a wavelength of 527nm and a 5 mJ/pulse pulse energy at a 10 kHz repetition rate. The laser is capable of repetition rates up to 10 kHz in each head. The Photron HighSpeed Star 6 camera has a 640x448 pixel resolution with 20x20 micron pixels on the sensor at a frame rate of 10 kHz. The PIV calculation was done using DaVis 7.2 software from LaVision. In the current study, PIV images were taken at a frame rate of 10 kHz with a time between laser shots of 30 microseconds at a bulk approach velocity of 10 m/s and 15 microseconds at a bulk approach velocity of 40 m/s. 500 velocity fields were calculated at each test condition.

Several methods were used to process the data. DaVis 7.2 was used to calculate velocity fields, vorticity fields, and divergence fields from the particle images. Since the high-speed PIV system produces time-resolved velocity fields, spectral analysis was used in much of this study. Three main data processing methods were used.

First, spectra were calculated for each point in space in the velocity fields, the vorticity fields, and the divergence fields. The amplitude and phase of the Fourier transform of the velocity, A (x) and φ(x), were calculated at each spatial point and used to harmonically reconstruct the time varying flow field at the forcing frequency using the relation:

( ( ))ˆˆ( , ) Re ( ) i t xu x t A x e ω ϕ− +⎡ ⎤= ⎣ ⎦ (2)

Second, spatially averaged instantaneous velocities were

calculated in both the axial and transverse direction at the nozzle in order to compare the magnitude of the fluctuations in different directions. The calculation of spatially averaged transverse velocity is calculated along the centerline of the flow, across a length of one nozzle diameter. These formulas are shown in Equation 3. These signals are filtered using a 2nd order Butterworth bandpass filter at ±200 Hz around the forcing frequency.

2

1

2 22 1

2 ( 0, , )( )

2 ( )

r

r

u x r t rdru t

r r

π

π

=

=−

∫,

0

1( ) ( , 0, )D

v t v x r t dxD

= =∫ (3)

Finally, the local unsteady pressure was estimated using a

linearized energy equation as seen in Equation 4.

1 ( , ) ( , ) 0o

p x t u x tp tγ

∂+∇ =

∂i (4)

The dilatation field is estimated from the two-dimensional velocity field. While not much dilatation is expected in the out-of-plane direction, this estimate does present a source of error in the pressure calculation. Because of the large length scale of the dilatation field (e.g., the acoustic wavelength is 0.85 meters at 400 Hz), this calculation is extremely sensitive to noise. As such, indicated pressures are averaged axially across the entire viewing window (2 diameters) using the formula:

2

0

1( , ) ( , , )2

Dp r t p x r t dx

D= ∫ (5)

All results are non-dimensionalized. The velocities are

normalized by the bulk approach flow velocity, mAρ

(where ρ

and A denote approach flow density and annulus area), the spatial coordinates by the nozzle diameter, D, time by the inverse of the forcing frequency, 1/fo, and the vorticity by the bulk velocity divided by the annular gap width, Uo/(r2-r1).

RESULTS AND DISCUSSION

This section is organized by first discussing the time averaged flow features, then the qualitative features of the unsteady flow, and finally the quantitative characteristics of the unsteady flow. The time averaged axial velocity and mean vorticity fields for a non-reacting flow are shown in Figure 7.

Figure 7. Time average axial velocity and mean vorticity in non-reacting flow. Bulk velocity is Uo=40 m/s, jet and

shear layer centers are marked in black.

The black lines indicate the jet and shear layer centers. These were calculated by finding the location of maximum velocity and vorticity, respectively, at each axial location. Later in the paper we will plot the evolution of different unsteady quantities along these trajectories.

The response of the swirling flow to transverse acoustic excitation results in a highly multi-dimensional disturbance field. Figure 2 shows four different pathways by which the flame can be disturbed. In general, the disturbances are of two types, acoustic and vortical. The acoustic disturbances propagate at the speed of sound and, in this case, set up a dominantly transverse standing wave with relatively weak transverse phase variations. In addition, vortical disturbances triggered by the acoustic motion at the nozzle exit convect downstream at the local flow velocity. These vortical

0 0.5 1 1.5

-1

-0.5

0

0.5

1

x/D

r/D

-0.5

0

0.5

0 0.5 1 1.5

-1

-0.5

0

0.5

1

x/D

r/D


disturbances induce fluctuations in both the axial and the transverse velocity. This results in transverse velocity fluctuations that are a superposition of both the acoustic and the vortical motion.

These two types of disturbances, acoustic and convecting disturbances, can be visualized best when considering the coherent disturbances, or the magnitude of the disturbance at the forcing frequency. Spectral analysis shows that both the acoustic and the convecting motions respond very clearly at the forcing frequency with broadband noise background at other frequencies. In the following visualizations (Figures 8-11), only the harmonically reconstructed motion at the forcing frequency is shown. Figure 8 illustrates an overlay of the instantaneous velocity vectors (consisting of both acoustic and vortical disturbances) and isocontours of the vorticity fluctuations. While similar trends were seen for all the flow velocities measured in this study (10 m/s, 20 m/s, 40 m/s), the highest velocity case is shown here as the inner and outer shear layers are most clearly distinguished from each other.

0 0.5 1 1.5

-1

-0.5

0

0.5

1

x/D

r/D

60deg

0 0.5 1 1.5

-1

-0.5

0

0.5

1

x/D

r/D

120deg

0 0.5 1 1.5

-1

-0.5

0

0.5

1

x/D

r/D

180deg

0 0.5 1 1.5

-1

-0.5

0

0.5

1

x/D

r/D

240deg

0 0.5 1 1.5

-1

-0.5

0

0.5

1

x/D

r/D

0deg


Figure 8. Harmonically reconstructed velocity and

vorticity field for fo=400 Hz out-of-phase acoustic forcing, non-reacting flow at Uo=40 m/s bulk velocity. The solid vorticity isocontours is at Uo/(r2-r1)=-0.1 and the dotted

vorticity isocontours is at 0.1.

Several physical processes are evident over the six phases pictured here. First, transverse fluctuation of the flow is dominant from approximately one diameter downstream to the end of the frame. Second, transverse flapping of the jet region is evident. Finally, the unsteady formation and downstream convection of vorticity is present. The unsteady vorticity is generated in the two annular shear layers and rolls up into larger structures in the separating wakes associated with the inner and outer recirculation zones. While two counter-rotating structures are clearly evident at the annular slot exit, see Figure 8 at 0 degrees, they subsequently merge farther downstream to form a single structure that is located in the jet core, see Figure 8 at 120 degrees. Note that this merging process occurs between staggered vorticity whose vorticity direction is the same.

To illustrate these points further, each of these fluctuating components, the vorticity, the axial velocity, and the transverse velocity, are plotted separately. Figure 9, Figure 10, and Figure 11 show the harmonically reconstructed vorticity, axial velocity, and transverse velocity disturbances across several phases of the acoustic cycle.

In the first vorticity image, a positive vorticity fluctuation is evident at the nozzle exit. The fluctuation location can be seen by the black arrows in the 0 degrees figure. Prior disturbances that were created at the nozzle base and convected downstream are still noticeable at a downstream location of 1 diameter.

In the third image, 120 degrees, these disturbances have convected downstream a distance of approximately 0.5 diameters. The inner and outer vorticity disturbances merge in the jet core and then continue to travel downstream with the jet.

0 0.5 1 1.5

-1

-0.5

0

0.5

1

x/D

r/D300deg


Figure 9. Harmonically reconstructed vorticity fluctuations for fo=400 Hz out-of-phase acoustic forcing, non-reacting

flow at Uo=40 m/s bulk velocity.

The arrows in Figure 10 point to the coherent axial velocity fluctuations in the shear layers. Note that the axial

disturbance in one shear layer is out of phase with that of the adjoining shear layer. These disturbances, induced by the coalesced vorticity disturbances in the jet core seen above, also convect downstream.


Figure 10. Harmonically reconstructed axial velocity

fluctuations for fo=400 Hz out-of-phase acoustic forcing, non-reacting flow at Uo=40 m/s bulk velocity.

Finally, the coherent transverse velocity disturbances are shown. The vorticity induced disturbance in the transverse

direction manifests itself in the jets, as seen by the black arrows. These also travel downstream with the vortex. This fluctuation is superposed on the bulk fluctuation due to the transverse acoustic excitation.


Figure 11. Harmonically reconstructed transverse

velocity fluctuations for fo=400 Hz out-of-phase acoustic forcing, non-reacting flow at Uo=40 m/s bulk velocity.

The two types of disturbances are clearly seen in these surface plots. Vortical disturbances originate at the nozzle exit,

and induce a dominantly axial motion in the shear layer and a dominantly transverse motion in the jet core. Also evident from these plots is that the motions in adjacent shear layers oscillate out-of-phase with each other. As the axial velocity disturbance in the inner left shear layer rises at 0 degrees, it falls in the inner right shear layer. Furthermore, the motions on the left side of the annulus are out-of-phase with those on the right side. As will be explained in the context of Figure 5, this is apparently due to the 180 degree phase change of the pressure (note that the centerline is a pressure node for the out of phase acoustic forcing), a feature that will be discussed later.

The vortex also induces a transverse motion along the jet core, which is superposed with the periodic transverse acoustic motion that can be seen as the rise, fall, and downstream convection of the transverse surface throughout the series of plots. These effects can be seen quantitatively in Figure 12, Figure 13, and Figure 14, where the magnitude of the harmonically reconstructed vorticity, axial velocity, and transverse velocity fluctuations from the surfaces above are plotted along the jet and shear layer centerlines.

Figure 12 shows the fluctuation of coherent vorticity along the jet centers. The top subplot shows the left jet, and the bottom subplot shows the right jet. Although vorticity originates in the shear layers, it subsequently rolls up into larger structures in the separating wake zones that, in turn, merge farther downstream. This merged structure appears to be located in the jet core.

The top subplot of Figure 13 shows the motion of the coherent axial velocity at several different phases of the cycle in the outer left shear layer, indicated by the leftmost arrow in Figure 10. For example, at 0 degrees in Figure 13 (solid blue line), the maximum disturbance amplitude is at a downstream distance of 0.2. After 115 degrees of the cycle (solid red line) this disturbance has convected and is now at a downstream distance of 0.6.

The bottom portion of this figure compares the shape and amplitude of the disturbance at 0 degrees in all four shear layers. It is evident, again from Figure 13, that the outer left shear layer and the outer right shear layer have similar disturbance amplitudes, but are out-of-phase, as was shown in Figure 10.


Figure 12. Harmonically reconstructed vorticity

fluctuations along the left jet across several phases (top), and right jet across several phases (bottom) for fo=400 Hz out-of-phase acoustic forcing, non-reacting flow at Uo=40

m/s bulk velocity.


fluctuations along the outer left shear layer across several phases (top), and across all four shear layers at 0

degrees (bottom) for fo=400 Hz out-of-phase acoustic forcing, non-reacting flow at Uo=40 m/s bulk velocity.

Figure 14 shows the coherent transverse velocity. The top

subplot shows the left jet, and the bottom subplot shows the right jet. Again, disturbances can be seen convecting downstream, as in Figure 11 above. For example, the 0 degree line (solid blue) has a minimum value at a downstream value of 0.4, and this disturbance can be seen again at 115 degrees (solid red) at a location of 0.8.

Figure 14. Harmonically reconstructed transverse

velocity fluctuations along the left jet (top), and right jet (bottom) across several phases for fo=400 Hz out-of-

phase acoustic forcing, non-reacting flow at Uo=40 m/s bulk velocity.

Several important physical mechanisms can be deduced

from these series of plots. First, there is a bulk transverse motion, which is associated with the acoustic field. Second, the downstream convection of the vortical motion is evident. Third, the movement in the adjacent shear layers is out-of-phase in the out of phase forcing case. For example, the inner left shear layer and the inner right shear layer disturbances are out-of-phase for the axial velocity fluctuations, particularly in the region of 0 to 10 mm downstream. The opposite, in-phase, behavior is also present for the in phase forcing cases, as seen in Figure 15 and Figure 16. In this case, the coherent vorticity disturbances convecting in the jet cores have different signs, inducing opposite phase relations between the axial velocities in the adjacent shear layers, as well as the transverse velocities in the jet cores, which are not shown here.


fluctuations along the left jet across several phases (top), and right jet across several phases (bottom) for fo=400 Hz


in-phase acoustic forcing, non-reacting flow at Uo=10 m/s bulk velocity.



degrees (bottom) for fo=400 Hz in-phase acoustic forcing, non-reacting flow at Uo=10 m/s bulk velocity.

These results do not change significantly with a flame present. To illustrate this point, the phase resolved motion of the vorticity disturbances is shown in Figure 17. The key difference appears to be a much longer lasting vortical disturbance, particularly in the left jet.



degrees (bottom) for fo=400 Hz out-of-phase acoustic forcing, reacting flow at Uo=10 m/s bulk velocity.

The comparison of axial velocity between the four shear layers for the in phase forcing shows that this forcing configuration causes in-phase fluctuations between adjacent shear layers. This difference in shear layer response is apparently due to the different acoustic conditions at the

centerline of the annulus. The out-of-phase acoustic forcing creates a velocity anti-node at the centerline of the combustor and a pressure node, causing the pressure on either side of the centerline to oscillate out-of-phase, see Figure 5. Conversely, in-phase forcing creates a pressure anti-node and a velocity node, as also shown in Figure 5. The oscillating pressure field over the nozzle exit creates fluctuations in mass flow through the nozzle, which is manifested in fluctuations in the strength of the shear layer. The mass flow fluctuations on either side of the nozzle are approximately out-of-phase when the acoustic forcing is out-of-phase. Conversely, the mass flow on either side of the nozzle is in-phase when the acoustic forcing is in-phase. These mass flux conditions correlate with the phase of the pressure on either side of the nozzle. Mass flow fluctuations lead to vorticity fluctuations at the corner of the nozzles, as seen at the very first upstream locations. The vorticity, initially out-of-phase and located at the nozzle edges, convects downstream and merges in the jet. This merged structure induces the out-of-phase axial velocity fluctuations in the shear layer and the convecting transverse velocity fluctuations in the jet cores. The process described here is summarized in Figure 18 for the out-of-phase forcing case.

v’

p’

'mˆ 'ω

ˆ 'uˆ 'v

v’

p’

'mˆ 'ω

ˆ 'uˆ 'v

Figure 18. Instantaneous snapshot of fluctuations in out of phase acoustic forcing case, with an acoustic velocity

maximum, acoustic pressure node, asymmetric mass flow fluctuations, asymmetric vorticity fluctuations,

asymmetric axial velocity fluctuations, and unidirectional transverse velocity fluctuations.

These trends are further illustrated in Figure 19 and Figure 20, where the average axial velocity in the left half of the annulus, right half of the annulus, and overall average is compared with the pressure fluctuations on either side of the nozzle.


0 2 4 6 8 10-1

0

1

u`/u

o

t*fo

LeftRightTotal

0 2 4 6 8 10-0.04-0.02

00.020.04

t*fo

p`/p

o

LeftRight

Figure 19. Spatially averaged axial velocity and pressure fluctuations at the nozzle exit for fo=400 Hz out-of-phase

acoustic forcing at Uo=10 m/s non-reacting flow.

0 2 4 6 8 10-1

0

1

u`/u

o

t*fo

LeftRightTotal

0 2 4 6 8 10-0.04-0.02

00.020.04

t*fo

p`/p

o

LeftRight

Figure 20. Spatially averaged axial velocity and pressure

fluctuations at the nozzle exit for fo=400 Hz in-phase acoustic forcing at Uo=10 m/s non-reacting flow.

The phase between the axial velocities and pressures shown in Figure 19 and Figure 20 was calculated from their Fourier transform at f = fo. The estimated uncertainty in these values is 15 degrees. The phase between the pressure on either side of the nozzle for out-of-phase acoustic forcing is 120 degrees, and for in-phase forcing is -65 degrees. The phase between the spatially averaged axial velocity on either side of the nozzle for out-of-phase forcing is 220 degrees, and for in-phase forcing is -5 degrees. These phases show that the acoustic forcing has a significant impact on the characteristics of the disturbance field. If the left and right sides of the burner annulus were acoustically isolated from each other, we would expect these phases to be 0 and 180 degrees. However, because the left and right sides of the annulus are in acoustic communication with each other, which presumably would tend to equalize the pressure, these values differ from the “ideal” values of 0 and 180 degrees. The phase of the pressure field in

the downstream half of the viewing window, away from the nozzle, is -175 degrees in the out-of-phase acoustic forcing case, and -1 degrees in the in-phase acoustic forcing case.

The magnitudes of the average axial velocities between in-phase and out-of-phase forcing are very similar, despite being out-of-phase. The acoustic forcing amplitudes in both cases is relatively constant and as such, the fluctuation amplitudes are similar. This is not the case, however, in the average transverse velocity. The out-of-phase forcing situation creates a high-amplitude sinusoidal velocity signal, while the average transverse velocity in the in-phase forcing case is much weaker, as shown in Figure 6.

The flame is susceptible to this multi-dimensional disturbance field because of the stabilization of the flame in shear layers. The base of the flame experiences the longitudinal velocity fluctuations that are dominant in the shear layer as well as the vortex rollup and convection also present in the jet. Downstream, though, the flame is subject to the high amplitude transverse motion that dominates in the far field.

CONCLUDING REMARKS In this work, we have analyzed the multi-dimensional

disturbance field caused by transverse acoustic excitation of a premixed, swirl-stabilized flame. Both non-reacting and reacting experiments were used to gain insight into the complicated disturbance field. The following conclusions can be drawn from this work.

1. Transversely excited flames are excited by a superposition of acoustic and vortical disturbances, including direct transverse acoustic excitation, longitudinal acoustic excitation, as well as excitation of fluid mechanic instabilities sensitive to both longitudinal and transverse flow perturbations.

2. Different disturbance mechanisms manifest themselves in different portions of the flow. Axial velocity fluctuations are dominant in the shear layers, while vorticity fluctuations and transverse velocity fluctuations are dominant in the jet core.

3. Transverse acoustic excitation leads to a multi-dimensional velocity disturbance field. The velocity fluctuations near the base of the flame are multi-directional, while the velocity fluctuations near the tip of the flame are almost completely transverse.

Future work will include tracking of the flame edge and vortex motion with simultaneous chemiluminescence measurements. These measurements will allow for correlation between vortex motion, flame disturbance, and heat release fluctuations.

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.

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