Identification of Coherent Structures in a Turbulent Generic Swirl Burner using Large Eddy Simulations

Transcription

1 20th AIAA Computational Fluid Dynamics Conference June 2011, Honolulu, Hawaii AIAA Identification of Coherent Structures in a Turbulent Generic Swirl Burner using Large Eddy Simulations Oliver Krüger, Katharina Göckeler, Steffen Terhaar, Christoph Strangfeld, and Christian Oliver Paschereit Berlin University of Technology, D Berlin, Germany Christophe Duwig and Laszlo Fuchs Lund University, Box 118, SE Lund, Sweden The isothermal flow dynamics of a generic swirl burner are studied employing large eddy simulation (LES). A sensitivity analysis was conducted, considering different mesh sizes and subgrid-scale models and the results were compared to experimental data. It was found that the overall influence of the computational grid and the subgrid-scale model was neglectable and the simulations were in line with the experiments. A dominant frequency was found in the turbulent kinetic energy spectrum representing a coherent structure. Moreover, by applying the proper orthogonal decomposition (POD) this structure could be identified as a convective helical instability. This helical instability and can be represented by a pair of modes, and is assumed to be triggered by a precessing vortex core (PVC). A B C 1 C 3 C s Co D h HP Q Re S ij V 0 a i (t) e i f k m n p Power law coefficient Power law exponent Constant Constant Smagorinsky constant Courant number Hydraulic diameter High-pass filter Vector of field variables Reynolds number Strain rate tensor Characteristic volume flow rate Time coefficient Solution of eigenvalue problem Frequency Turbulent kinetic energy Power law exponent Iterator Pressure Nomenclature r t u i x i Conventions Radial co-ordinate Time Velocity component Co-ordinate. Time averaging operator Low-pass filter Symbols λ ν t Φ( x) ϱ τ τ ij RR St PhD student, Chair of Fluid Dynamics, Hermann-Föttinger-Institut, TU-Berlin Professor, Chair of Fluid Dynamics, Hermann-Föttinger-Institut, TU-Berlin Associate Professor, Department of Energy Sciences, Lund University Professor, Department of Energy Sciences, Lund University Filter width Filter length scale Eigenvalue Eddy viscosity Spatial eigenfunction Density Characteristic time Subgrid scale stress tensor Recirculation rate Strouhal number 1 of 14 Copyright 2011 by the authors. Published by the, Inc., with permission.

2 I. Introduction With the increasing concern about our environment, progressively stringent emission limits have been specified. Due to these regulations the control of the pollutant emissions becomes a more and more important focus in the design of modern gas turbine systems for power generation. In order to reduce harmful emissions, the current approach often is to design combustion devices operating under lean premixed conditions. This reduces the peak temperature and therefore, NOx emissions, but may lead to flame instabilities and higher UHC/CO emissions. 1 Due to high mass flows of modern gas turbines the flame stabilization is challenging. Modern gas turbine combustors are based on an aerodynamic type of flame holding, which implies a recirculation of the hot burnt gases to constantly re-ignite the fresh gases. Recirculation in a swirling flow generally is the result of a vortex breakdown, which occurs, when the static pressure on the centerline of the vortex decreases such that the regular spiraling motion becomes unstable and develops a stagnation point on or near the axis. 2 Usually, this low-pressure region appears around the axis region, close to the expansion between the burner and the combustion chamber. If the pressure gradient is strong enough, an axial back flow is induced. Due to the constant support of thermal energy and burnt gases as well as the lower velocities in the shear layer between the recirculation zone and the outer swirling flow the flame is stabilized. Therefore, modeling and understanding the vortex breakdown and the flow field characteristics within the combustion chamber is a key issue for efficient combustion devices. Numerous experimental and numerical studies have been published on this subject, but the mechanisms of vortex breakdown are only partly understood. A comprehensive review is given by Lucca-Negro and O Doherty, 3 who summed up several different patterns, of which two, the bubble- and the spiral-type breakdown are typical for turbulent flows with high Reynolds numbers. Despite all these efforts no final explanation for the formation of a vortex breakdown is currently available. 3, 4 The large structures resulting from vortex breakdown and swirling shear-layers directly affecting the flame stabilization leading to heat release fluctuations and combustion instabilities. This unsteady behavior is the main difficulty and inhibits to assess the problem. These structures cause large deterministic fluctuations in the flow field, as presented 5, 6, 7, 8, 9 in many other works. The turbulent coherent structure dynamics is highlighted in these works and provides knowledge for the design of essential burners. To capture the motion of a coherent structure within a chaotic field is a challenging task, which demands for state-of-the art numerical and experimental techniques. A suitable approach to investigate the generation and evolution of coherent structures is in particular to use Large Eddy Simulations (LES). It allows treatment of high Reynolds number flows, has only limited sensitivity to modeling assumptions and, compared to a Direct Numerical Simulation is less demanding for computational resources. The present study focuses on the isothermal vortex breakdown in a generic swirl burner. In order to handle the anisotropic and highly dynamic character of turbulent swirling flows LES is employed. To determine the influence of grid sizes and turbulence modeling a sensitivity study was performed. For comparison, experimental data from a water tunnel facility were used. The results presented in the current study were founded within the Greenest project by the European Research Council. The first part of the paper will deal with the experimental and numerical techniques, as well as the investigated configuration. The different models will be explained in detail. The second part of the paper will show how the flow field is characterized using averaged RMS velocity fields as well as Reynolds stress components obtained from LDV, PIV and LES. Moreover, the flow field dynamics will be presented by computing the time dependent recirculation rate, as well as the turbulent energy spectrum. The third part will be dedicated to the coherent structures and the motion of the precessing vortex core (PVC) and will be analyzed employing the proper orthogonal decomposition (POD). II. Numerical Methods and Subgrid Scale Modeling A. Governing equations The incompressible Navier-Stokes equations are used to simulate the turbulent flow field. For an isothermal flow the fluid motion is described by basic equations as the conservation of momentum and mass. In LES, a low-pass filter is applied to the dependent variables so that the filtered equations only describe 2 of 14

3 the larger turbulent fluctuations. 10 The low-pass filtered (denoted by the superscript ) equations read as follows: Continuity (i = 1, 2, 3): Navier-Stokes (i = 1, 2, 3): ũ t + ũ iũ j x j (ũ i ) x i = 0. (1) = 1 p + ϱ x i [ 2ν x ] S ij + τ ij, (2) i where u i represents the velocity component, ϱ the density, p the pressure, τ ij the subgrid scale stress tensor, S ij is the tensor of the strain rate and ν the kinematic viscosity. The filtering is a linear function which is assumed to be commutative with temporal and spatial derivatives. The filtering is not commutative for non-linear terms. Therefore, these terms can not be expressed as filtered expressions and are gathered on the right-hand side. These terms are collectively called the subgrid scale (SGS) term. B. Subgrid Scale Modeling The present work uses two different subgrid scale modelings in order to analyze the sensitivity of the models on the flow field predictions. The first SGS is modeled by the classical Smagorinsky closure. 11 There the unresolved stress tensor τ ij = ũ i u j ũ i ũ j is modeled using the Boussinesq hypothesis, in which the effect of the unresolved turbulence on the large-scale flow is modeled as an increase in the viscosity: τ ij = 2 ( 3 ki 2ν t S ij 13 ) S kk δ ij, (3) where k = u i u i is the turbulent kinetic energy and ν t the turbulent kinematic viscosity. The shear strain tensor can be written as: S ij = 1 ( ũi + ũ ) j. (4) 2 x j x i The form of the subgrid-scale eddy viscosity can be derived by dimensional analysis and is: ν t = C s 2 2 S ij Sij, (5) where C s is a model parameter and is the filter length scale. The Smagorinsky constant C s was set to C s = The second approach to model the unresolved subgrid scales is based on the filtered formulations of Sagaut. 12 The advantage of this subgrid-scale model is that it is less sensitive to low-frequency modes. Accordingly, by applying a spatial high-pass filter it prevents large scales from contributing to the eddy viscosity. It describes the subgrid-scale eddy viscosity as: ( ν t = C HP (n) (ũ i ) + HP ) (n) (ũ j ). (6) 2 x j x i The filter HP (n) (ũ) is explained in detail by Sagaut in. 12 The constant C 3 can be expressed by: C 3 = C 1 B m A(3.0 m), (7) with C 1 = 1 and m = 5 /3. By Sagaut 12 it was shown that for a LES of spatially growing boundary layer it yields for the terms A = 40 n, B = 3.05 n and n = 3. 3 of 14

4 C. Proper Orthogonal Decomposition Investigating spatial and temporal resolved turbulent flow fields usually leads to high amount of data. To extract information from the collected data, the Proper Orthogonal Decomposition (POD) is employed. It is a procedure to extract a basis for a modal decomposition to find an expansion that gives fastest convergence for a given number of terms. Pioneer work has be done by Lumley, 13 who started from the idea that the most containing kinetic energy eddies/modes are of the highest interest. In other words, the aim is to project the turbulent flow field on a vector base that maximizes the turbulent kinetic energy for any subset of base. 13, 14, 15 This allows for an accurate description of the turbulent flow by using only a few modes. The POD decomposition reads as follows: Q N ( x, t) = a 0 Φ 0 ( x) + N a i (t)φ i ( x), (8) where the zero-th eigenfunction Φ 0 corresponds for the mean field. The following modes (i > 0) contain the fluctuation of the mean field, and by means of the time coefficients a i (t) one may reconstruct the given dynamics. Accordingly, this means that for a given vector Q containing the field variables, one seeks for a 13, 14 base of spatial eigenfunctions Φ. The base vectors have to satisfy the eigenvalue problem: i=1 Q( x, t) Q T ( x, t) Φ( x) = λφ( x), (9) where the transposed vector is denoted by the superscript T and the time averaging by.. The vectors Φ are the eigenvectors of the temporal autocorrelation tensor. The eigenvalue λ i stores the turbulent kinetic energy content of mode i. Solving equation 9 directly, would require to solve a eigenvalue problem represented by a matrix of the dimensions M xm where M is the number of data points. To reduce the computational cost, Sirovich s method of snapshots 16 is used instead, which reduces the cost to an equivalent eigenvalue problem of the dimensions KxK, where K is the number of snap shots used to estimate the time averaging operator.. This reduces computational cost significantly, since the spatial resolution is much higher than the temporal resolution in most cases. In Sirlovichs s method the modes are expressed as a linear combination of the samples: Φ i ( x) = 1 λ i N e i (t)q( x, t), (10) t where the coefficients e i are solutions of the eigenvalue problem. The time coefficients are computed by projecting the snapshots on the modes: a i (t) = Φ i ( x) Q( x, t). (11) Detailed information on implementing the POD method and applying it to turbulent flows may be found 13, 14, 15, 16, 17, 18, 19, 20, 21 in various other studies III. Investigated Configuration The simulations have been carried out on a cylindrical computational domain with an attached swirl generator. It is adapted from the experimental set-up as shown in in Figure 1. In order to reduce computational time the combustion chamber was truncated, since the influence of the far downstream locations are assumed to be small. The characteristic length and velocity were chosen to be the hydraulic diameter D h = 27.5 mm and the mean bulk velocity u 0 at the burner exit. Thus, a characteristic timescale τ = D h/u 0 and volume flow V 0 = (u 0 A) can be defined for normalization. The Moveable Block Burner used in this investigation is based on a design by Beér. 22 It is presented in Figure 2. As can be seen it consists of eight movable and eight fixed blocks, which are placed alternately, as shown in Figure 2(a). Due to simultaneous rotation of the movable blocks about the symmetry axis, the oblique passages are opened while the non-oblique parts are narrowed and vice versa. This yields in an 4 of 14

5 Figure 1. Visualization of the computational domain. increase or reduction of the swirl intensity. The swirl number can be derived by the geometry 23 and can be varied between 0 and 2. Air and steam are premixed before entering the swirl generator. Fuel is injected directly at the bottom plate of the swirl generator through 16 holes. The fuel mixes with the swirling flow in the annular passage to the combustion chamber. (a) (b) Figure 2. Swirl generator and Moveable Block Burner IV. Experimental Techniques A. Operating Conditions For the simulations and the experiments the same geometry was used. The latter was a cylindrical silica glass with a diameter of 0.2 m. This results in an area expansion ratio of The swirl number was set to S = 0.7. The swirl number was chosen to correspond to a high-swirling flow ensuring a vortex breakdown. As a set of operating conditions atmospheric pressure, water as fluid, inlet velocity of 0.6 m /s and an inlet temperature of 293 K was applied. This results in a Reynolds number of Re = 33, 000, corresponding to the mass flow rate used in the gas-fired tests. B. Experimental Database The flow experiments were conducted in a water tunnel facility. An unscaled Plexiglass model of the burner allowed optical access for the application of laser diagnostics. As non-intrusive techniques Laser Doppler Velocimetry (LDV) as well as Stereoscopic Particle Image Velocimetry (Stereo PIV) were applied. The setup is sketched in Figure 3. For the LDV a two-component backscatter LDV system was used to measure at various axial positions the tangential and axial velocities. A three-dimensional traverse system ensured the position- 5 of 14

6 ing of the measurement volume. Distinct refraction indexes of air, glass and water were taken into account. Depending on the position a data rate of 50 Hz to 350 Hz was achieved. The stereo PIV measurements were performed using a Nd:YAG pulse laser (18 mj per pulse) and two PCO Sensicams (Resolution: 1024x1024 pixel at 4 Hz). The laser sheet was tilted to the diagonal of the test section. This way, the cameras look almost 24, 25, 26 straight through the glass window. The experimental set-up and equipment was discussed in detail in. V. Numerical Set-up The LES simulations are performed with the open source framework OpenFOAM (version 1.7.x). In order to determine the influence of different grid sizes two different meshes are applied using the standard Smagorinsky subgrid-scale model. For the grid study a coarse unstructured polyhedral mesh with about 90 cells per hydraulic diameter with a cell size of 0.3 mm was used. The mesh exhibits around 1.7 million grid points. Thus, the smallest resolved scales are in the inertial range of the turbulent spectrum and the grid is suitable for performing LES. The second mesh exhibits about 140 cells per hydraulic diameter with a cell size of 0.2 mm in the shear-layer and it features more than 6.9 million grid points. Both meshes were locally refined where high velocity gradients were expected as it was observed in former investigations. 27 In order to determine the influence of the subgrid-scale model the filtered Smagorinsky model, as presented in 12 is additionally employed on the coarser mesh. The conditions for the three cases are listed in Figure 3. Setup for Flow Measurements Table 1. For all cases the pressure velocity coupling is performed using the PISO algorithm as described by, 28 ensuring that continuity is satisfied. A second-order central differencing scheme for all spatial derivates is applied, time derivates are treated using a second order upwind scheme and time integration is done implicitly in a sequential manner. Dirichlet boundary conditions are enforced at the inlet for all variables except pressure which uses a zero gradient condition (Neumann). Similarly, the out flow is treated using zero gradient for all variables except for pressure that uses a Neumann condition. Non slip walls (zero velocity) are used with zero gradient for the other variables. Table 1. Overview of the three conducted simulations Condition Case 1 Case 2 Case 3 Name Smagorinsky Smagorinsky 6M filtered Smagorinsky Fluid Water Water Water Inlet Velocity u in 0.6 m /s 0.6 m /s 0.6 m /s Bulk Velocity u m /s 1.3 m /s 1.3 m /s Kinematic viscosity m2 /s 1.004e e e 6 Pressure p 101, 325 Pa 101, 325 Pa 101, 325 Pa Reynolds number Re 33, , , 000 Subgrid-scale model Smagorinsky Smagorinsky filtered Smagorinsky Grid points 1.7e6 6.9e6 1.7e6 Grid faces 4.8e6 19.5e6 4.8e6 Grid elements 1.6e6 6.5e6 1.6e6 6 of 14

7 VI. Results and Discussion The performed LES computations were run with a constant time step to keep the maximum Courant number below Co = 0.2 to avoid numerical instabilities. This resulted in an averaged time step of 10 5 s. For the coarser mesh this resulted in a typical Courant number in the shear layer of Co = 8. For the finer mesh the time step had to be slightly reduced, nevertheless this resulted in a slightly higher Courant number in the shear layer. After a statistically steady state was reached averaging of the flow field was enabled. The results were time-averaged over 2.0 physical seconds. The simulations were finished after a symmetrically averaged velocity field was reached. For the following discussion, velocity plots are shown at several axial positions. These locations are presented in Figure 4. The burner exit serves as origin (x/d h = 0) and all coordinates are normalized by the hydraulic diameter D h. The coordinate in the streamwise direction will be denoted as axial component. For the latter the bulk velocity u 0 = 1.3 m /s at the contraction is used r x/d h Figure 4. Sketch of the computational domain. Profile positions are highlighted for the discussion. A. Sensitivity Analysis LES is only capable to resolve turbulent scales that are larger than the grid spacing. Therefore, it is essential to assess the influence of the incomplete resolution by conducting grid studies and applying different subgridscale models. Due to the high computational costs, it is difficult to consider large grid variations. Thus, this study focuses on changing the swirling jet resolution by exercising two grid resolutions. Moreover, an additional subgrid-scale model, denoted as filtered Smagorinsky, was used. This model is intended to prevent large scales from contributing to the eddy viscosity. Figure 5(a) gives a comparison of the measured and simulated stream wise flow at several axial locations. It can be seen that an inner recirculation zone establishes near the burner exit, due to a vortex break down. This leads to high velocity gradients in the shear layer between the inner recirculation zone and the surrounding swirling flow. The gradient decreases further downstream. Furthermore, an outer recirculation zone establishes at the corner of combustion chamber walls and the burner plenum. This outer recirculation zone has the shape of a ring vortex and is fed by the surrounding swirling flow. The experimental data of the different measurement techniques is in agreement at all axial positions and shows only small differences. For all three simulations it can be seen that the negative axial velocities within the inner recirculation zone are over estimated. The largest differences appear in the inner recirculation zone. The surrounding swirling flow is well captured. A trend which case differs the most cannot be drawn. Nevertheless, the simulations are in line with the experimental data. The RMS values of axial velocity fluctuations are also compared and shown in Figure 5(b). The measurements are in close agreement and only differ in the jet region near the burner exit. Here, one would expect the highest uncertainties. For the simulations, it can be seen, that all three cases are in general close to the measurements, especially in the surrounding jet. The highest differences appear in the shear-layer and the inner recirculation zone. Near the burner exit the filtered Smagorinsky model underestimates the fluctuation level in the inner recirculation zone. Further downstream this behavior changes and the fluctuation level in the reverse flow is slightly overestimated. Moreover, it predicts a faster decay of the turbulence in the inner recirculation zone. The Smagorinsky and the Smagorinsky 6M case are close to the measurements, 7 of 14

8 u x /u x/d h = 2.0 u x RMS/u x/d h = 2.0 u x /u x/d h = 1.0 u x RMS/u x/d h = 1.0 u x /u x/d h = 0.5 Smagorinsky Smagorinsky 6M filtered Smagorinsky LDV PIV r/d h u x RMS/u x/d h = 0.5 Smagorinsky Smagorinsky 6M filtered Smagorinsky r/d h LDV PIV (a) Streamwise velocity u x/u 0 profiles at different axial positions downstream of the burner exit. All three cases are compared to the experimental data. (b) RMS of the fluctuations of the streamwise velocity component for three different axial positions for all three cases. Figure 5. Axial velocity and turbulence profiles at different axial positions. but the latter predicts some local aberration, especially near the center line at x/d h = 2. However, the influence of these discrepancies on the flow field was found to be low. Nevertheless, the differences between the three simulations are rather low and all three cases predict the central recirculation zone both in terms of magnitude and size. Therefore, the coarsest grid (denoted as Smagorinsky ) was used to investigating the flow field dynamics. B. Flow Dynamics Figure 7 depicts an instantaneous snapshot of the axial velocity. The flow is highly turbulent and asymmetric. To investigate the flow dynamics of the inner recirculation zone the recirculation rate RR is assessed. The recirculation rate RR is defined as the negative velocity flux in a cross section Ω of the combustion chamber: S=0.7 RR(x = cst.) = u x dy dz. (12) Ω ux<0 Figure 6 shows the recirculation rate plotted versus time for different axial positions. The markers are only plotted to indicate the lines and do not represent the sampling points. Thr recirculation rate is low near the burner outlet and increases with x /D h up to x /D h = 2 where it reaches the maximum. Further downstream it decreases. The recirculation rate shows slow fluctuations and it can be seen that the fluctuations that appear at x /D h = 2 propagate upand downstream. Nevertheless, a periodically correlation could not be found. Hence, no relation to the motion of a precessing vortex core can be drawn. RR/ V 0 (-) x/d h =1 x/d h =2 x/d h =3 x/d h =4 x/d h =5 x/d h = t/τ Figure 6. Recirculation rate (RR) versus time at 6 different locations downstream of the burner exit (x/d h = 0). 8 of 14

9 To assess this highly unsteady behavior the turbulent kinetic energy spectrum was computed for three points as shown in Figure 7. Point A is located in the shear layer, point B in the region where the vortex break down establishes and strong fluctuations appear, and point C was set downstream in the inner recirculation zone. The energy spectrum describes the energy cascade, thus the energy transfer between large scales and small scales. The spectrum for the three points is plotted in Figure 8. The frequency is normalized by the hydraulic diameter and the bulk velocity, which results in the Strouhal number St = f D h/u 0. A comparison with the Kolmogorov- 5 /3 power law yields that the simulation is able to predict the characteristic of the inertial subrange reasonably. Moreover, a dominant frequency (St 0.19) is seen at all three locations, which implies the existence of a coherent structure. Using a similar configuration García-Villalba 29 observed that a recessing vortex core(pvc) is related to a dominant frequency. 1. POD analysis of the PVC As discussed previously a dominant frequency was found in the turbulent energy spectrum that can be linked to a helical instability caused by a PVC. To assess coherent structures only considering averaged quantities is inadequate, but the flow velocities can decomposed into average, coherent and random turbulent fluctuations. Turbulent fluctuations can be isolated from the strong coherent structures by applying a proper orthogonal decomposition (POD). The POD was processed for the PIV and LES in a longitudinal planar cross section. In Figure 9 the time coefficients of the first two modes were plotted. The circle that is formed by the coefficients indicates a phase shift of π /2 of the two modes. Hence, a superposition of these modes likely describes the periodic coherent structure that was observed in Figure 8. Figure 11 shows the time coefficients represented in Fourier space. The two modes exhibit a clear peak at the PVC frequency St The phase angle between both modes is π /2, indicating that both modes are orthogonal in time and space. The similarity becomes more evident since the power density spectrum PDS of the mode coefficients, shown in Figure 7. Instantaneous snapshot of the axial velocity component. Three points are marked, where the turbulent kinetic energy spectrum was determined. E(f) A slope -5/ St (-) B slope -5/ St (-) C slope -5/ St (-) Figure 8. Turbulent kinetic energy spectrum determined for three different points located on the longitudinal cross-section downstream of the burner exit Figure 11, yields the same Strouhal number as 8. As can be seen the results of the LES are comparable to the PIV. The axial and radial velocity modes are plotted for the PIV and the LES in Figure 12. For the PIV results it can be seen that the axial modes exhibit an anti-symmetric pattern. The blue and the red structures are located pairwise and are caused by vortices. To point this out, the vector field computed by the axial and radial component of the modes are superimposed on the color coded velocity component. The plot shows a cut through a helical structure. In order to highlight this, three points are shown, each in the vortex center. These three points are part of the same helix. This helix is accompanied by a second helix which is co-winding. The radial mode seems to be symmetric, but due to the change of signs when transforming 9 of 14

10 40 40 Mode 2 0 Mode Mode 1 (a) PIV Mode 1 (b) LES Figure 9. Scatter plots of time coefficients (a 1 (t) vs a 2 (t)) for the PIV (left) and LES (right) from a cartesian to a cylindrical co-ordinate system it is anti-symmetric. Furthermore, the highest energy content is kept in the vortices near the burner exit, indicating a structure rotating around the center body. The LES shows similar results as the PIV. However, a faster energy decay for the vortices in axial direction is predicted the same pattern. The faster decay of the energy amplitudes could be the explanation for the underestimation of the turbulence levels downstream of the burner. Furthermore, it was shown by Oberleithner 19 that the PVC triggers convective instabilities in the shear layer inducing strong vortices that entrain fluid to the jet center. This would result in lower entrainment rate predicted by the LES. 15 LES PIV Energy captured (%) Mode Figure 10. Energy content of the first 20 modes for experiment (PIV) and simulation (LES) Figure 10 shows, that by far the most energy is captured in the first two POD modes. This indicates that the coherent structure, that was linked to the PVC contains a large share of the total turbulent energy. In order to visualize the coherent structure García-Villalba 29 pointed out that the PVC is marked by a minimum in the pressure fluctuation distribution of the swirling flow. That coherent structures are associated 10 of 14

11 A PDS Φ/π A PDS1.2 1e4 Mode e4 Mode Phase Angle St (-) Figure 11. Fourier analysis of the POD time coefficients a i (t), PDS vs St. for the first two modes of the LES. 30, 31 with local minimum of the pressure field were furthermore shown in. Figure 13 shows the helical instability through an isosurface of the pressure. By subtracting the current pressure field from the mean field a second structure appears, which is just the virtual counterpart of the structure. Three time steps with a phase angle of π were chosen to highlight the rotation of the helical structure. García-Villalba 29 described furthermore that the motion of the PVC can be decomposed into two components: The rotation of the vortex core around the symmetry axis and a spinning of the vortex around its own axis; the latter was not observed in our simulations. 11 of 14

12 (a) PIV (b) LES Figure 12. First two POD velocity modes of the PIV (top) and LES (bottom) in the axial cross-section for axial and radial components. The vector field is calculated by the axial and radial components of the modes. 12 of 14

13 (a) Pressure isosurface at t/τ = 152 (b) Pressure isosurface at t/τ = (c) Pressure isosurface at t/τ = 157 Figure 13. Visualization of a half-period rotation of the coherent structure. Structure is represented by a iso-pressure contour. VII. Conclusion The present paper employs Large Eddy Simulations of an isothermal flow in a generic swirl burner undergoing vortex breakdown. The results were compared to experimental data obtained with PIV and LDV. In a first step a sensitivity analysis was conducted to determine the influence of grid resolution and the subgrid-scale model on the flow pattern. Though some minor discrepancies between the simulations and the experiments were found. However, the overall influence of the computational grid and the subgrid-scale model were found to be low. In general, the simulations showed a good agreement with the experimental data. In a second step the flow field dynamics were determined. The recirculation rate was the strongest within the first three burner diameters and exhibits high fluctuations. The turbulent kinetic energy spectrum showed a dominant frequency which could be identified as the motion of a coherent structure. Performing a POD analysis allowed for isolating large-scale coherent structures. from the velocity fluctuations. The POD analysis decomposes the field in a mean, coherent and turbulent fraction, leading to an accurate representation of the flow dynamics. In the present study a convective helical instability triggered by a PVC is identified and represented by a pair of modes. In conclusion it was shown, that flow dynamics of a swirling flow can be excellently captured by using LES. Acknowledgments The research leading to these results has received funding from the European Research Council under the ERC grant agreement n , GREENEST. A part of the computations have been performed at HLRN (North-German Supercomputing Alliance) facilities within the allocation program Nasse Verbrennung. The authors would like to thank the CONFET for the helpful discussions. References 1 Lefebvre, A. H., The Role of Fuel-Preparation in Low-Emission Combustion, Journal of Engineering for Gas Turbines and Power, Vol. 117, 1995, pp Leibovich, S., Vortex stability and breakdown: Survey and extension, AIAA Journal, Vol. 22, No. 1192, Lucca-Negro, O. and O Doherty, T., Vortex breakdown: A review, Progress in Energy and Combustion Science, Vol. 27, 2001, pp 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, 2006, pp Anacelto, P. M., Fernandes, E. C., Heitor, M. V., and Shtork, S. I., Swirl flow structure and flame charateristics in a model model lean premixed combustor, Combustion Science and Technology, Vol. 175, 2003, pp of 14

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