Role of Azimuthal Flow Fluctuations on Flow Dynamics and Global Flame Response of Axisymmetric Swirling Flames

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1 Role of Azimuthal Flow Fluctuations on Flow Dynamics and Global Flame Response of Axisymmetric Swirling Flames Vishal Acharya 1 and Tim Lieuwen 2 Georgia Institute of Technology, Atlanta, GA, 3332 Recent studies have clearly shown the important role of swirl fluctuations in the response of premixed flames to flow oscillations. An important implication of this mechanism is that the axial location of the swirler plays a key role in the phase between the acoustic flow excitation source, and the resulting axial vorticity fluctuation at the flame. Similar to the previously well recognized role of azimuthal vorticity fluctuations, these swirl fluctuations are vortical and convect at the mean flow velocity, unlike the acoustic flow fluctuations. However, there is a fundamental difference between axial and azimuthal vorticity disturbances in terms of the flow oscillations they induce on the flame. Specifically, azimuthal vorticity disturbances excite radial and axial flow disturbances, while axial vorticity oscillations only directly excite azimuthal flow fluctuations. However, the axial vorticity fluctuations do indirectly excite axial and radial velocity fluctuations when the vortex tube is tilted off-axis, such as at locations of area expansion. This difference is significant because axisymmetric flames are disturbed only by the velocity component normal to it which stem from axial and radial velocity components only. This implies that axisymmetric mean flames are not directly affected by azimuthal flow fluctuations, since they are tangential to it. Thus, it is the extent to which the axial vorticity is tilted and rotated that controls the strength of the flow oscillations normal to the flame and, in turn, lead to heat release oscillations. This coupling process is not easily amenable to analytical calculations and, as such, we report here a computational study of the role of these different flow fluctuations on the flame response in an axisymmetric framework. The results indicate that the swirl fluctuations act as a secondary, but still very significant source of flame heat release disturbances, relative to shear-generated azimuthal vorticity disturbances. A D G H L f Nomenclature = Spatially integrated ("global") flame area = Outer diamater of the swirler-annulus nozzle = Level set function (or) iso-contour variable = Length of the annulus between the swirler exit and the combustor dump-plane = Characteristic flame length scale (flame height) Re = Reynolds number, = U D ν St = Strouhal number, = fd U T = Time period of acoustic forcing, = 1 f = 2π ω U = Characteristic velocity scale s T = Turbulent flame speed u = Velocity vector ε = Ratio of amplitude of excitation and characteristic mean velocity scale ν = Kinematic viscosity ω = Acoustic forcing frequency ( ) r, z, x ( ) * = Dimensional quantity,θ = Radial, azimuthal, axial component, respectively 1 Research Engineer-II, School of Aerospace Engineering, 27 Ferst Dr. 2 Professor, School of Aerospace Engineering, 27 Ferst Dr, Senior AIAA Member. 1

2 ( ) = Fluctuating component ( ) = Mean component ( ) = Frequency domain representation of corresponding time domain quantity Abbreviations IVM = Inlet Velocity Modulation LES = Large Eddy Simulation FTF = Flame Transfer Function FTF swirl = Flame Transfer Function for the swirl only forcing at the inlet FTF axial = Flame Transfer Function for the axial only forcing at the inlet FTF both = Flame Transfer Function for both components forced at the inlet RANS = Reynolds Averaged Navier Stokes SSG = Speziale-Sarkar-Gatski closure for RANS turbulence modeling. URANS = Unsteady RANS I. Introduction Combustion instabilities have long been a source of significant problems for premixed combustion systems 1-7. These instabilities occur when unsteady heat release couples with one or more of the acoustic modes in the combustor, potentially causing high amplitude pressure and velocity oscillations 8. These oscillations then in turn lead to component fatigue and failure, that eventually reduce combustor operability and increases overall operating costs. The focus of this paper is on combustors with swirl-stabilized flames. Swirling flows are subject to several shear and centrifugal flow instability mechanisms, leading to a variety of unsteady flow features, such as the precessing vortex core and helical shear layer disturbances The dominant mechanisms leading to heat release oscillations are fuel/air ratio fluctuations and flow velocity fluctuations The focus of this study is on the latter mechanism, which leads to flame surface wrinkling and surface area oscillations. The flow oscillations are comprised of both acoustic and vortical disturbances 2. The direct excitation of the flame by these flow disturbances has previously been treated in detail by both experimental and modeling studies Acoustic waves are directly excited by the flame and reverberate in the combustor system. Vortical disturbances are generated by modulation of the separating shear layer, which organize themselves into concentrated regions of vorticity through the Kelvin-Helmholtz instability. In addition, there exists an additional, indirect mechanism that is unique to swirl flows. In this mechanism, acoustic waves propagating through swirlers excite axial vortical disturbances, leading to modulations in swirl number The focus of this paper is to understand this indirect mechanism and its significance relative to shear generated vorticity. The first study we are aware of that indirectly suggested the importance of this mechanism was performed by Straub and Richards 31, who noted the importance of swirler vane position on combustion instability limits in their facility. This mechanism was explicitly noted in the computations of Wang et al. 19, 32, 33. Hirsch et al. 34 similarly reported experiments showing the effect of swirler vane location on the flame transfer function (FTF). They also showed that the flame shape was unaffected by these swirl vane location changes, an important observation as time averaged changes in flame shape (such as induced by changes in swirl) would also lead to changes in flame response and stability limits. They argued that axial acoustic flow fluctuations excited an azimuthal flow disturbance which is non-acoustic, and therefore convected by the flow. They suggested that this azimuthal flow disturbance induces an axial velocity fluctuation, which then causes a modulation of the heat release. This basic idea was made further rigorous by Palies et al. 36, using results from Cumpsty and Marble 35 developed for pulsating flow over an airfoil, showing how acoustic flow fluctuations lead to axial vorticity fluctuations. They also reported experiments in both axial and radial swirlers 37. In both swirlers, they showed that the incident acoustic wave generated both a transmitted acoustic wave, as well as a convective vorticity wave. They showed that the mode conversion process for both swirlers were quite similar and produced similar effects on the flame dynamics. The effect of swirler geometry was also investigated by Bourgouin et al. 38, drawing similar conclusions. Experiments by Durox et al. 39 used a radial swirler with variable vane angle. They showed that dynamic variation of the blade angle can be used to control the flame dynamics in the combustor through swirl fluctuations, similar to earlier computations by Stone and Menon 4. 2

3 Several computational studies of this phenomenon have also been reported. Garcia-Villalba et al. 3 investigated the effect of swirl fluctuations in non-reacting flows using Large Eddy Simulations (LES) of a model combustor. They excited different velocity components at the inlet of the combustion chamber (post-swirler) and examined the differences in flow-field in the combustion chamber. They showed that the instantaneous structures were mainly influenced by the azimuthal velocity oscillations at the inlet. For a fixed azimuthal velocity however, the structures rotate at a constant rate. These results were based on non-reacting simulations, however, and did not illustrate the impact on flame response. Work by Komarek and Polifke 29 considered both experiments and unsteady Reynolds averaged Navier-Stokes (URANS) simulations of a reacting swirling flow in a model combustor. They investigated the effect of swirl number fluctuations for different upstream axial positions of their axial swirl generator. They showed that the axial position of the swirler affected the time-lag of the swirl number fluctuations and hence the flame response. Figure 1 Disturbance pathways leading to heat release oscillations. To summarize, it is clear that axial vortical disturbances, and not only the familiar azimuthal vortical disturbances associated with vortex roll-up of the shear layers, have significant influences on the flame response. However, there is a fundamental difference between axial and azimuthal vorticity disturbances in terms of the flow oscillations they induce on the flame. In order to better understand this, consider the disturbance pathways shown in Figure 1, which show how an acoustic disturbance leads to heat release oscillations. The familiar azimuthal vortical disturbances due to vortex roll-up are shown in pathway (2a). These then cause axial and radial flow fluctuations in the combustor via pathway (2b). The presence of the swirler causes axial vorticity fluctuations (path 1a) which then induce azimuthal flow fluctuations (path 1b) only. These azimuthal flow fluctuations indirectly excite axial and radial velocity fluctuations, due to bending/rotation of the axial vortex tube (1c). For example, the oscillatory azimuthal flow in the injector nozzle induces an oscillatory radial flow component at the rapid expansion point where the swirling nozzle flow enters the combustor. This differentiation between azimuthal flow disturbances on one hand, and radial/axial disturbances on the other, is significant because the flame itself is disturbed only by the velocity component normal to it (3a). This implies that axisymmetric mean flames are not directly affected by azimuthal flow fluctuations, since they are tangential to it. Thus, it is the indirect azimuthal to radial/axial mechanism (1c) that controls the strength of the flow oscillations normal to the flame that lead to heat release oscillations in axisymmetric flames, as indicated by pathways (1a-1b-1c-3a), which is boxed in red in the figure under the heading of I. This coupling process is not easily amenable to analytical calculations and, as such, we report here a computational study of the role of these different flow fluctuations on the flame response in an axisymmetric framework. In this paper, we present computations of a forced model combustor to understand the role played by these axial vorticity fluctuations relative to azimuthal ones, in affecting the global flame response. In other words, we compare 3

4 the relative strengths of the cumulative path I and path II indicated in the figure. This global flame response is quantified by means of the Flame Transfer Function (FTF) 27, 29, and defined as: ( Qˆ ( ω ) Q ) FTF( ω) = (1) uˆ ( ω) U ( ) ref Here, Q ˆ ( ω) Q is the normalized heat release rate fluctuations and uˆ ( ω) U is the normalized reference ref velocity fluctuations chosen to be those at the inflow to the combustor dump (exit plane of the swirler). This paper is organized as follows. First we present the simulation framework used for the different model geometries and discuss their flow features respectively. Following this, the FTFs calculated from each simulation are compared for variations in input control parameters, to illustrate the differences in global flame response due to azimuthal flow fluctuations. Figure 2 Schematic of complete model combustor. II. Computational Simulations The model combustor configuration used in this work is shown in Figure 2. It consists of an annular flow passage with a 45 degree, 8 vane swirler, connected to a larger combustor. The dimensions of this geometry are detailed in Table 1. Table 1 Dimensions of the model combustor shown in Figure 2. Detail Dimension Outer diameter of nozzle D Inner diameter of nozzle.57 D Outer diameter of combustor dump 2.75 D Combustor Length 11. D Swirler location upstream of dump 2.84 D Length of nozzle 6.25 D An unsteady RANS approach is used (similar to work by Komarek and Polifke 29 ), implemented with the C++ toolbox OpenFOAM ( Open-Field-Operations-and-Manipulations). This toolbox is an open-source collection of finite volume solvers and numerical methods tailored for CFD simulations 56. The non-reacting steady state flow fields are computed using the simplefoam solver which uses the SIMPLE 62 pressure-coupling method in an incompressible framework. The forced unsteady simulations are performed using the pisofoam solver which uses the PISO method for pressure-velocity coupling. For the flow forcing at the inlet, the inlet velocity modulation (IVM) technique is adopted, as outlined by Kaufmann et al. 61. An SSG (Speziale-Sarkar-Gatski) closure model 57 is 4

5 used for turbulence closure, following the recommendations of Shamami et al. 58 based on their assessment of different RANS models for swirling flows in can-combustors. The flame surface is assumed to be thin and captured using the G-equation 4, 59 with Zimont and Lipatnikov s turbulent flame speed closure 6. The reacting cases are handled using a user modified version of the XiFoam module in OpenFOAM. The original XiFoam module makes use of a progress variable approach with a turbulent Schmidt number based diffusion of the progress variable. This was modified to accommodate the G-equation based front tracking, without any diffusion, in a finite volume framework with reinitialization. The module was further modified to use the in-built 2D Cartesian solver and add the required terms and momentum equation for the swirl flow component. A second order backward Euler scheme was used with a time-step that is 1/1 th the time-period of acoustic forcing. The simulations were run for a total of 1 time-steps, corresponding to 1 acoustic time-periods. The spatial discretization is performed using a second order scheme. The Reynolds number for the flow, defined as Re = U D ν is 87,. The configuration shown in Figure 2 is split into two separate domains for the CFD simulations, in order to understand different aspects of the physics. These are detailed in the next 2 sub-sections. A. Generation of Azimuthal Flow Fluctuations In order to understand the generation of azimuthal flow fluctuations at the swirler, we consider simulations of the non-reacting flow in the swirler-annulus section only for the geometry shown in Figure 2. The swirler annulus simulation was performed for an inlet axial velocity of 3 m/s. The swirler-annulus geometry is solved for a single blade passage, with rotational periodic boundary conditions. It is meshed into 1 million body-fitted hexagonal volume elements. Figure 3 Instantaneous streamline pattern in the Swirler-Annulus section of the combustor. Typical streamlines are shown in Figure 3. The streamlines are colored by the swirl component of velocity. This figure clearly shows the change in flow direction across the swirler. The downstream evolution of the mean axial and tangential flow components are shown in Figure 4. Note that the flow is uniform upstream of the swirler and accelerates as the flow traverses the swirler vanes. This is due to the volume constriction created by the swirler vanes within the annulus cross-section. Since the swirler has 8 vanes, the immediate downstream region of the swirler is spatially periodic. However, this profile becomes uniform downstream, as indicated in the figure. Next, consider the flow dynamics in the swirler annulus section when the axial flow at the inlet is forced. The axial forcing was performed with amplitude of 1% at frequencies 25Hz, 3Hz, 35Hz and 4Hz. The timeseries of the axial and azimuthal flow at different locations downstream of the swirler is shown in Figure 5, for the 25Hz forcing case. Note that there is negligible phase difference across the different locations for the axial component, as shown in Figure 5(a). This is an artifact of incompressible simulations where the speed of the wave is infinite. However, notice the axial dependence of the azimuthal flow phase, as shown in Figure 5(b). The axial phase variation is shown in Figure 5(c) from which an axial phase speed is extracted. Note that the mean axial flow velocity from this phase speed corresponds to that measured at the mid-annular location of r =.39D. Due to the acceleration of the flow in the annulus past the swirler, this velocity (~4 m/s) is higher than the uniform velocity (3 m/s) imposed at the upstream inlet. This plots clearly indicates how the swirler converts the axial, incompressible disturbance, into an azimuthal, convecting (vortical) flow disturbance, as previously described by Hirsch et al. 34, Komarek and Polifke 29 and Palies et al. 27, 36. 5

6 (a) (b) Figure 4 Downstream evolution of the (a) mean axial velocity and (b) mean azimuthal velocity, shown in transverse cut-planes perpendicular to the axial direction. The inlet axial mean flow is 3 m/s (from the bottom). (a) (b) (c) Figure 5 Time-series evolution of the mid-annular (r =.39D) (a) axial flow and (b) azimuthal flow components at different axial locations downstream of the swirler for the 25Hz forcing case. (c) Spatial phase variation of the azimuthal flow velocity fluctuation. H is the axial length of the annular section downstream of the swirler ( = 2.84D), h is the location downstream of the swirler where the time-series is shown. 6

7 The differences in wave propagation speed of the axial and azimuthal components also imply that their relative phase difference evolves axially. In fact, these components of the flow fluctuations are not in phase at the exit of the swirler. This phase difference at the swirler exit is a function of the forcing frequency, as shown in Figure 6. The relative phase exhibits a monotonically increasing trend (roughly linear) with an increase in forcing frequency. This relative phasing is incorporated in the parameter ϕ shown later in Eq.(4), and is a very important parameter for the FTF. Figure 6 Variation of relative phase between the axial and azimuthal flow fluctuations, with forcing frequency, at the exit of the swirler. B. Flow-field coupling In this section, we consider the conversion of axial vorticity into azimuthal and radial vorticity, with particular focus on the flow field in the combustor section itself. Attention here is confined to flows that are axisymmetric, so that all calculations are axisymmetric. This post-swirler axisymmetric geometry shown in Figure 7 is meshed into structured.5 million quad elements. Figure 7 Schematic of the post-swirler section showing the 2D axisymmetric configuration used for the combustion cases. Conditions for which the post-swirler simulations were performed are detailed in Table 2. For all of these cases, the average axial velocity at the INFLOW to the annulus is U = 3 m/s. Note that in the swirler annulus simulations described in the previous section, the swirl number and mean swirl velocity are controlled by the vane angle and vane geometry. However, for the simulations shown in this section, the swirl number and mean swirl inlet velocity are freely chosen. Table 2 Mean operating conditions used for the post-swirler simulations in Figure 7. Case φ T u U z, U θ, 1.7 5K 3 m/s 3 m/s 2.7 5K 3 m/s 26.1 m/s 7

8 In order to understand the role played by azimuthal flow fluctuations, the simulations are performed using 3 different inlet forcing configurations: (a) Axial flow forcing only: u ( z =, t) = ε U ( z = ) sin( ωt) z z z, (2) u ( z =, t) = u ( z =, t) = θ r (b) Swirl flow forcing only: u ( z =, t) = ε U ( z = ) sin( ωt) θ θ θ, (3) u ( z =, t) = u ( z =, t) = z r (c) Both axial and swirl flow components forced: u ( z =, t) = ε U ( z = ) sin( ωt) z z z, u ( z =, t) = ε U ( z = ) sin( ωt + ϕ) θ θ θ, u ( z =, t) = r Here, ϕ is the relative phase difference between the two flow components at the inlet (from the exit of the swirler). These different inlet pulsations were also performed by Garcia-Villalba et al. 3 for the full 3D post-swirler section of their model combustor in a LES framework. We next consider the unsteady flow-field coupling for this configuration. (4) Figure 8 Steady state computations for case (1) in Table 2 showing the Axial velocity. The black curve denotes the flame location represented by the G = contour. For case (1), the steady state axial flow and flame are shown in Figure 8. The steady state solution for each case is used as the initial condition for the respective forced simulations. The different flow forcing configurations are shown in Eqs.(2)-(4). The axial flow forcing amplitude was kept fixed: ε =.1. The amplitude of forcing for the z azimuthal flow was chosen based on the mean inlet swirl velocity and swirl number. The forcing frequency, f, is varied from 15Hz to 1Hz. This corresponds to.27 < St < 1.85, where St = fd U. The simulations are performed for 1 acoustic time periods and the time signal of the heat release rate fluctuations is obtained. After the initial transient, the steady-oscillating state is reached and the time-signal from this set is used for further analysis. The aim of these simulations is to understand the role played by azimuthal flow fluctuations in dictating global flame response. As mentioned earlier, this role is an indirect one, since axisymmetric flames are directly affected only by the radial and axial flow fluctuations. Note that for the axisymmetric flame case, only the local normal velocity fluctuations cause heat release rate fluctuations 54. The generation of radial and axial flow fluctuations due to azimuthal flow fluctuations at the inlet is best understood by considering simulations that use the boundary conditions described in Eq.(3), where only the azimuthal flow component is forced at the inlet. First consider the generation of axial and radial flow fluctuations in the annulus section. These are shown in Figure 9. The plots show the spatial evolution of the disturbances at different instances in an acoustic cycle. Note that since only the azimuthal flow is forced at the inlet, the axial and radial fluctuations are zero at the inlet, z H =. Thus, the disturbances grow from an initially zero value at the inlet section. The axial component has a maximum amplitude of about 25% of the inlet forcing amplitude while the radial component reaches a maximum of about 5%. These correspond to the transfer of fluctuations from the azimuthal component to the axial and radial components due to vortex tube re-orientation. The plots also clearly indicate the convective nature of the 8

9 disturbance. Based on the Strouhal number for this example ( St = 1.2 ) and the disturbance wavelength, the disturbance convection speed is 1.4U. The velocity corresponds to the center-line mean axial velocity in the annulus. These fluctuations further evolve in the combustor dump due to changes in the geometry and since the flame is located in this region, it is important to consider the evolution of these disturbances along the flame. (a) (b) Figure 9 Spatial evolution of (a) axial and (b) radial flow fluctuations along the center-line of the annulus section (corresponds to r/d =.4) at different instances in an acoustic cycle (indicated by t/t). H is the axial length of the annular section downstream of the swirler (=2.84D). Baseline conditions correspond to case (1) in Table 2, with purely azimuthal velocity forcing at the inlet at St = 1.2. Figure 1 shows the spatial evolution of the normalized axial velocity fluctuations along the mean flame position shown in Figure 8 for case (1) in Table 2, using BCs in Eq.(3). The plots are shown separately for the upper and lower branches of the flame. There are 2 important features to notice from these plots. First, they show the presence of radial and axial velocity disturbances, although neither of them are forced at the inflow point. These velocity disturbances are a superposition of the vortical nature of the source disturbance (azimuthal flow fluctuations) and the vortical fluctuations generated at the shear layer as the flow enters the combustor dump from the annulus. The maximum fluctuation on both flame branches reach about 6% of the forcing amplitude at the inlet. (a) (b) Figure 1 Axial velocity fluctuation (normalized by the inlet forcing amplitude) along the (a) lower and (b) upper branches of the flame, at different instances in an acoustic time-period. Baseline conditions correspond to case (1) in Table 2, with purely azimuthal velocity forcing at the inlet at St =

10 Similar qualitative features can be seen for the radial flow fluctuations shown in Figure 11. The radial flow fluctuations reach a maximum amplitude of 125% of the inlet forcing amplitude, indicating that they are the primary contributor to the unsteady flame response and dominate relative to the axial fluctuations. Note that these maximum amplitudes and the wavelength of the disturbances are a function of forcing Strouhal number. An important takeaway from this example is that, despite the presence of only azimuthal flow fluctuations at the inlet, the axial and radial flow fluctuations affecting the flame are not negligible and can even exceed the forcing amplitude at the inlet. Their importance is dictated by the frequency of forcing and this shall be discussed in the context of the global flame response, presented next. (a) (b) Figure 11 Radial velocity fluctuation (normalized by the inlet forcing amplitude) along the (a) lower and (b) upper branches of the flame, at different instances in an acoustic time-period. Baseline conditions correspond to case (1) in Table 2, with purely azimuthal velocity forcing at the inlet at St = 1.2. III. Flame Transfer Function In this section, we shall discuss the impact of azimuthal flow fluctuations on the global flame response using the Flame Transfer Function (FTF) defined earlier in Eq.(1). The instantaneous heat release rate is calculated as: Q( t) = ρust hrda (5) Here, ρ is the unburnt gas density, u flame G= h R is the heat of reaction, T s is the turbulent flame front speed and A is the flame surface area. The flame front speed is obtained from a closure model 6 as mentioned earlier and the area is obtained from the instantaneous G = contour. The reference velocity fluctuation is chosen at the inlet. Using these quantities, the FTF is obtained as defined in Eq.(1). First consider the effects of the different forcing configurations (Eqs.(2)-(4)) on the FTF. For convenience of notation, we shall denote the FTFs using the axial only forcing BC in Eq.(2) as, using the swirl only forcing BC in Eq.(3) as FTF swirl and using BCs in Eq.(4) as FTF both FTF axial. Figure 12 shows the variation in amplitude and phase of the FTF for the different inlet forcing configurations, for case (1) from Table 2. As discussed earlier, the presence of swirl-only forcing at the inlet can generate significant axial and radial flow disturbances depending on the frequency of forcing. This is reflected in the finite non-negligible value of FTF dominates FTF swirl for most part, however there Strouhal number values where swirl FTF swirl. axial FTF dominates. This can be attributed to interference phenomena in the flow-field coupling effects at those frequencies. Finally, the combined effect of both forcing components of the inlet shows that FTF both takes values that oscillate about the FTF axial curve. 1

11 Figure 12 FTF comparison for Case (1) in Table 2 showing (a) amplitude and (b) phase. Figure 13 FTF comparison for different relative phasing (φ) between the axial and tangential forcing at the inlet, showing (a) amplitude and (b) phase. Mean operating conditions correspond to Case (1) in Table 2. Next, consider the effect of the relative phasing between the axial and swirl component at the inlet on the FTF. It was mentioned earlier, in the context of Figure 6, that this relative phase was a function of forcing frequency. However, in that geometry, this relative phasing is a function of the swirler vane design as well. In the post-swirler simulations, since the swirler is not included, we have the freedom to vary the relative phase so as to indirectly account for the effect of differences in swirler vane design, as well as location of the swirler upstream of the combustor. For this comparison, we use the inlet BCs from Eq.(4). The simulations are performed for ϕ varying between degrees and 27 degrees, in steps of 9 degrees. The amplitude and phase of the FTF are shown in Figure 13. Notice that as the relative phase is changed, the qualitative nature of the FTFs remains the same but the interference locations are shifted in Strouhal number space. This indicates that the relative phasing has a strong control over the frequencies at which the FTF are a minima or maxima. This is also reflected in the phase variation wherein the qualitative nature remains the same but the locations of phase jump are changed. A second comparison is shown in Figure 14 for a different set of control parameters. 11

12 Figure 14 FTF comparison for different relative phasing (φ) between the axial and tangential forcing at the inlet, showing (a) amplitude and (b) phase. Mean operating conditions correspond to Case (2) in Table 2. IV. Conclusions In this work, we used numerical simulations to understand the role played by azimuthal flow fluctuations on the global FTF for different mean operating conditions. Specifically, we considered axisymmetric mean flame configurations, where the azimuthal flow fluctuations do not have a direct influence on the flame response, but rather an indirect one, through coupling with other flow components. The post-swirler axisymmetric part of the combustor was considered, where we had the freedom to keep or remove the azimuthal flow fluctuations at the inlet. This allowed for understanding the coupling between different flow components and how swirl flow fluctuations could change axial and radial flow fluctuations, thus causing heat release rate fluctuations. Specifically, the azimuthal flow fluctuations generate significant radial and axial flow fluctuations, whose values are quite sensitive to the Strouhal number. The global flame response was higher for these Strouhal numbers indicating that the azimuthal flow fluctuations have varying effects on the FTF. This effect was analyzed for differences in swirl number and relative phasing. Acknowledgments This work has been partially supported by the US Department of Energy under contract DE-NT554, contract monitor Mark Freeman, as well as the National Science Foundation through contract CBET , contract monitor Prof. Ruey-Hung Chen. The numerical simulations were performed on the Georgia Tech PACE cluster and the Kraken, Stampede, Nautilus and Blacklight cluster systems offered through the NSF XSEDE program, under Charge numbers TG-CTS1316 and TG-DMS131. References 1 Lieuwen, T., and Yang, V. Combustion Instabilities in Gas Turbine Engines: Operational Experience, Fundamental Mechanisms, and Modeling. Reston, VA, USA: American Institute of Aeronautics and Astronautics, Thumuluru, S. K., and Lieuwen, T. "Characterization of acoustically forced swirl flame dynamics," Proceedings of the Combustion Institute Vol. 32, No. 2, 29, pp Bellows, B., Bobba, M., Forte, A., Seitzman, J., and Lieuwen, T. "Flame transfer function saturation mechanisms in a swirl-stabilized combustor," Proceedings of the Combustion Institute Vol. 31, No. 2, 27, pp Nagaraja, S., Kedia, K., and Sujith, R. I. "Characterizing energy growth during combustion instabilities: Singularvalues or eigenvalues?," Proceedings of the Combustion Institute Vol. 32, 29, pp Kang, D., Culick, F., and Ratner, A. "Combustion dynamics of a low-swirl combustor," Combustion and Flame Vol. 151, No. 3, 27, pp

13 6 Yilmaz, I., Ratner, A., Ilbas, M., and Huang, Y. "Experimental investigation of thermoacoustic coupling using blended hydrogen methane fuels in a low swirl burner," International Journal of Hydrogen Energy Vol. 35, No. 1, 21, pp Rodriguez-Martinez, V., Dawson, J., O'Doherty, T., and Syred, N. "Low-frequency combustion oscillations in a swirl burner/furnace," Journal of Propulsion and Power Vol. 22, No. 1, 26, pp Rayleigh, B. J. W. S. The Theory of Sound, Syred, N. "A review of oscillation mechanisms and the role of the precessing vortex core (PVC) in swirl combustion systems," Progress in Energy and Combustion Science Vol. 32, No. 2, 26, pp Cala, C. E., Fernandes, E. C., Heitor, M. V., and S.I., S. "Coherent structures in unsteady swirling jet flow," Experiments in Fluids Vol. 4, No. 2, 26, pp Jochmann, P., Sinigersky, A., Hehle, M., Schafer, O., Koch, R., and Bauer, H. J. "Numerical simulation of a precessing vortex breakdown," International Journal of Heat and Fluid Flow Vol. 27, No. 2, 26, pp Fick, W., Griffiths, A. J., and O'Doherty, T. "Visualisation of the Precessing Vortex Core in an unconfined Swirling flow," Optical Diagnostics in Engineering Vol. 2, No. 1, 1997, pp Shtork, S. I., Vieira, N. F., and Fernandes, E. C. "On the identification of helical instabilities in a reacting swirling flow," Fuel Vol. 87, No. 1-11, 28, pp Ducruix, S., Schuller, T., Durox, D., and Candel, S. "Combustion Dynamics and Instabilities: Elementary Coupling and Driving Mechanisms," Journal of Propulsion and Power Vol. 19, No. 5, 23, pp Lee, J. G., Kim, K., and Santavicca, D. A. "Measurement of equivalence ratio fluctuation and its effect on heat release during unstable combustion," Proceedings of the Combustion Institute Vol. 28, No. 1, 2, pp Poinsot, T. J., Trouve, A. C., Veynante, D. P., Candel, S. M., and Esposito, E. J. "Vortex-driven acoustically coupled combustion instabilities," Journal of Fluid Mechanics Vol. 177, 26, pp Ghoniem, A. F., Annaswamy, A., Wee, D., Yi, T., and Park, S. "Shear flow-driven combustion instability: Evidence, simulation, and modeling," Proceedings of the Combustion Institute Vol. 29, No. 1, 22, pp Schadow, K. C., and Gutmark, E. "Combustion instability related to vortex shedding in dump combustors and their passive control," Progress in Energy and Combustion Science Vol. 18, No. 2, 1992, pp Wang, S., Yang, V., Hsiao, G., Hsieh, S. Y., and Mongia, H. C. "Large-eddy simulations of gas-turbine swirl injector flow dynamics," Journal of Fluid Mechanics Vol. 583, 27, pp Lieuwen, T. C. Unsteady Combustor Physics: Cambridge University Press, Balachandran, R., Ayoola, B., Kaminski, C., Dowling, A., and Mastorakos, E. "Experimental investigation of the nonlinear response of turbulent premixed flames to imposed inlet velocity oscillations," Combustion and Flame Vol. 143, No. 1-2, 25, pp Armitage, C., Balachandran, R., Mastorakos, E., and Cant, R. "Investigation of the nonlinear response of turbulent premixed flames to imposed inlet velocity oscillations," Combustion and Flame Vol. 146, No. 3, 26, pp Ducruix, S., Schuller, T., Durox, D., and Candel, S. "Combustion dynamics and instabilities: Elementary coupling and driving mechanisms," J. Propul. Power Vol. 19, No. 5, 23, pp Dowling, A. "A kinematic model of a ducted flame," Journal of Fluid Mechanics Vol. 394, No. -1, 1999, pp Schuller, T., Durox, D., and Candel, S. "A unified model for the prediction of laminar flame transfer functions comparisons between conical and V-flame dynamics," Combust. Flame Vol. 134, No. 1-2, 23, pp Preetham, Hemchandra, S., and Lieuwen, T. "Dynamics of Laminar Premixed Flames Forced by Harmonic Velocity Disturbances," Journal of Propulsion and Power Vol. 24, No. 6, 28, pp Palies, P., Schuller, T., Durox, D., and Candel, S. "Modeling of premixed swirling flames transfer functions," Proceedings of the Combustion Institute Vol. 33, No. 2, 211, pp Fanaca, D., Alemela, P. R., Hirsch, C., and Sattelmayer, T. "Comparison of the Flow Field of a Swirl Stabilized Premixed Burner in an Annular and a Single Burner Combustion Chamber," Journal of Engineering for Gas Turbines and Power Vol. 132, No. 7, 21, p

14 29 Komarek, T., and Polifke, W. "Impact of Swirl Fluctuations on the Flame Response of a Perfectly Premixed Swirl Burner," Journal of Engineering for Gas Turbines and Power Vol. 132, No. 6, 21, pp Garcia-Villalba, M., Frohlich, J., and Rodi, W. "Large Eddy Simulation of an Annular Swirling Jet With Pulsating Inflow," Turbulence and Shear Flow Phenomena. Vol. 4, Williamsburg, VA, Straub, D., and Richards, G. "Effect of Axial Swirl Vane Location on Combustion Dynamics," ASME Turbo Expo. Indianpolis, IN, Wang, S., Hsieh, S. Y., and Yang, V. "Unsteady Flow Evolution in Swirl Injectors, Part I: Stationary Conditions," Physics of Fluids Vol. 17, 25, pp (1-13). 33 Wang, S., and Yang, V. "Unsteady Flow Evolution in Swirl Injectors, Part II: External Excitations," Physics of Fluids Vol. 17, 25, pp (1-12). 34 Hirsch, C., Fanaca, D., Reddy, P., Polifke, W., and Sattelmayer, T. "Influence of Swirler Design on the Flame Transfer Function of Premixed Flames," ASME Turbo Expo. ASME, Cumpsty, N., and Marble, F. "The Interaction of Entropy Fluctuations with Turbine Blade Rows; A Mechanism of Turbojet engine Noise," Proceedings of the Royal Society London A Vol. 357, 1977, pp Palies, P., Durox, D., Schuller, T., and Candel, S. "Acoustic-convective mode conversion in an aerofoil cascade," Journal of Fluid Mechanics Vol. 672, 211, pp Palies, P., Durox, D., Schuller, T., and Candel, S. "Experimental Study on the Effect of Swirler Geometry and Swirl Number on Flame Describing Functions," Combustion Science and Technology Vol. 183, No. 7, 211, pp Bourgouin, J.-F., Moeck, J., Durox, D., Schuller, T., and Candel, S. "Sensitivity of swirling flows to small changes in the swirler geometry," Comptes Rendus Mecanique Vol. 341, 213, pp Durox, D., Moeck, J., Bourgouin, J.-F., Morenton, P., Viallon, M., Schuller, T., and Candel, S. "Flame Dynamics of a Variable Swirl Number System and Instability Control," Combustion and Flame Vol. 16, 213, pp Stone, C., and Menon, S. "Swirl Control of Combustion Instabilities in a Gas Turbine Combustor," Proceedings of the Combustion Institute Vol. 29, No. 1, 22, pp Merck, H. "An analysis of unstable combustion of premixed gases," Symposium (International) on Combustion Vol. 6, 1957, pp Fleifil, M., Annaswamy, A. M., Ghoneim, Z. A., and Ghoniem, A. F. "Response of a laminar premixed flame to flow oscillations: A kinematic model and thermoacoustic instability results," Combustion and Flame Vol. 16, No. 4, 1996, pp Ducruix, S., Durox, D., and Candel, S. "Theoretical and experimental determination of the transfer function of a laminar premixed flame," Proceedings of the Combustion Institute Vol. 28, 2, pp Lieuwen, T. Unsteady Combustor Physics. New York, NY, USA: Cambridge University Press, Lacarelle, A., Faustmann, T., Greenblatt, D., Paschereit, C. O., Lehmann, O., Luchtenburg, D. M., and Noack, B. R. "Spatiotemporal Characterization of a Conical Swirler Flow Field Under Strong Forcing," Journal of Engineering for Gas Turbines and Power Vol. 131, 29, p Paschereit, C. O., Gutmark, E., and Weisenstein, W. "Excitation of thermoacoustic instabilities by interaction of acoustics and unstable swirling flow," AIAA Journal Vol. 38, No. 6, 2, pp Steinberg, A. M., Boxx, I., Stohr, M., Carter, C. D., and Meier, W. "Flow flame interactions causing acoustically coupled heat release fluctuations in a thermo-acoustically unstable gas turbine model combustor," Combustion and Flame Vol. 157, No. 12, 21, pp Stohr, M., Boxx, I., Carter, C. D., and Meier, W. "Experimental study of vortex-flame interaction in a gas turbine model combustor," Combustion and Flame Vol. 159, No. 8, 212, pp Moeck, J. P., Bourgouin, J.-F., Durox, D., Schuller, T., and Candel, S. "Nonlinear interaction between a precessing vortex core and acoustic oscillations in a turbulent swirling flame," Combustion and Flame Vol. 159, No. 8, 212, pp O'Connor, J., and Lieuwen, T. "Disturbance Field Characteristics of a Transversely Excited Burner," Combustion Science and Technology Vol. 183, No. 5, 211, pp

15 51 O'Connor, J., and Lieuwen, T. "Recirculation Zone Dynamics of a Transversely Excited Swirl Flow and Flame," Physics of Fluids Vol. 24, No. 7, 212, p Loiseleux, T., Chomaz, J., and Huerre, P. "The effect of swirl on jets and wakes: Linear instability of the Rankine vortex with axial flow," Physics of Fluids Vol. 1, 1998, p Worth, N., and Dawson, J. "Self-excited Circumferential Instabilities in a Model Annular Gas Turbine Combustor: Global Flame Dynamics," Proceedings of the Combustion Institute Vol. 34, 213, p. In Press. 54 Acharya, V., and Lieuwen, T. "Premixed Flames excited by Helical Disturbances: Flame Wrinkling and Heat Release Oscillations," Journal of Propulsion and Power Vol. In Press, Susan-Resiga, R., Muntean, S., Tanasa, C., and Bosioc, A. "Three-Dimensional Versus Two-Dimensional Axisymmetric Analysis For Decelerated Swirling Flows," Conference on Modeling Fluid Flow. Budapest, Hungary, Jasak, H., Jemcov, A., and Tukovic, Z. "OpenFOAM: A C++ Library for Complex Physics Simulations," International Workshop on Coupled Methods in Numerical Dynamics. Dubrovnik, Croatia, Speziale, C., Sarkar, S., and Gatski, T. "Modelling the pressure-strain correlation of turbulence: An invariant dynamical systems approach," Journal of Fluid Mechanics Vol. 227, 1991, pp Shamami, K., and Birouk, M. "Assessment of the Performance of RANS models for Simulating Swirling Flows in a Can-Combustor," The Open Aerospace Engineering Journal Vol. 1, 28, pp Wang, P., and Bai, X. "Large Eddy Simulation of Turbulent Premixed Flames using Level-set G-equation," Proceedings of the Combustion Institute Vol. 3, No. 1, 25, pp Zimont, V., and Lipatnikov, A. "A Numerical Model of Premixed Turbulent Combustion of Gases," Chem. Phys. Rep. Vol. 14, No. 7, 1995, pp Kaufmann, A., Nicoud, F., and Poinsot, T. J. "Flow Forcing Techniques for Numerical Simulation of Combustion Instabilities," Combustion and Flame Vol. 131, 22, pp Patankar, S., and Spalding, D. "A Calculation Procedure for Heat, Mass and Momentum Transfer in Threedimensional Parabolic Flows," International Journal of Heat and Mass Transfer Vol. 15, No. 1, 1972, pp Issa, R. "Solution of the implicitly discretized fluid flow equations by operator-splitting," Journal of Computational Physics Vol. 62, No. 1, 1986, pp