Enclosed swirling flows as a bench mark for LES of gas turbine combustorsB. Wegnera, D. Bissieresb , L.Y.M. Gicquelc, B. Janusa,

A. Sadikia, A. Dreizlera,J. Janickaa

a FG Energie- und Kraftwerkstechnik, TU Darmstadt,Petersenstr. 30, D-64287 Darmstadt, Germany

b Turbomeca, DT/CP/CTE, 64511 Bordes Cedex, Francec CERFACS, 42 Av. G. Coriolis, 31057 Toulouse, France

REPORT_NUMBER : TR/CFD/05/24IntroductionFuture gas turbine technology needs improvements in terms of higher efficiency and lower NOx emis-sions. This calls for more detailed modelling to capture on the one hand complex flow dynamics suchas coherent motions and on the other hand chemical reactions in sufficient detail to predict pollutantemissions. The emergence of large eddy simulation as a fully transient approach to describe fluid mo-tion and mixing as well as its transfer to combustion related problems opened up a new perspective ofmore detailed prediction of turbulent flames.To make use of this challenging approach for gas turbine combustors suitable test cases have to bedefined and used as bench mark for state-of-the-art LES codes. For this purpose the present study re-ports on an optically accessible combustor showing features with some relevance for gas turbine com-bustion chambers. As the various optical measurement techniques that have been applied to character-ise flow and mixing field are published in (Janus, Dreizler et al. 2004), the focus in this contribution ison a comparison of two different LES codes (FASTEST and AVBP). Both codes are briefly describedin and simulation results are compared to experimental data. So far only the non-reactive case is con-sidered. More work is needed for inclusion of appropriate combustion models.

Combustor and operational conditionsA single nozzle was operated in a modular high pressure combustion rig capable of providing gas tur-bine combustor inlet conditions corresponding to pressures up to p=10bar and temperatures up toT=773K with a max. primary air flow of m&=150g/s. The combustor pressure can be continuously setby an electronically controlled back pressure valve in the exhaust duct. The compressed natural gaswas supplied by a piston compressor. It’s mass flow as well as the mixture composition of the fuelsubstitute was set and regulated by mass flow controllers. The basic design concept consisted of adouble walled, air cooled flame tube encased by a pressure vessel. Being mainly designed for the ap-plication of laser based measurement techniques, the combustor was equipped with large optical ac-cess from three sides. The flame tube cross sectional area was circular with three planar window seg-ments. It’s inner diameter was 120mm with an optical accessible length of 100mm. The height of theinward windows was 60mm.The generic type nozzle was based on a design by TURBOMECA. It consisted of a round gaseous fueljet, surrounded by a single swirled, heated combustion air flow. The swirl was generated through tan-gential vanes as can be seen from the 3-D view of the nozzle in Fig. 1. The operation point is definedin table 1.

Combustor pressure p 2barCombustion air temperature T 623KCombustion air mass flow rate m& 30g/sEquivalence ratio φ 0.8Reair 46000Refuel 40800

Figure 1

3D view of nozzle and combustion chamber

Table 1Operational point

Modeling Approach

FASTEST: The low-Mach number formulation of the Navier-Stokes equations is considered togetherwith the transport equation for mixture fraction as a conserved scalar. An implicit filtering approach isused and the unknown subgrid stress and subgrid scalar flux are modelled using the Smagorinskymodel and an eddy-diffusivity approximation, respectively. The model constant CS in the Smagorin-sky model is determined using Germano’s dynamic procedure with the modification as proposed byLilly. The turbulent diffusion coefficient of mixture fraction is set proportional to the eddy viscosityusing a turbulent Schmidt number of 0.7. Since no special wall treatment is used for the sgs stress, theboundary layer is resolved in regions of importance and we rely on the dynamic procedure to capturethe correct near-wall physical behavior.

AVBP-Turbomeca: The multi-species fully compressible Navier-Stokes equations are considered inan implicit filtering framework. Modelling of the unclosed terms is based on the Smagorinsky modelfor the sgs tensor and an eddy-diffusivity model for the sgs scalar fluxes. A turbulent Schmidt numberof 0.7 is employed for these terms regardless of the specie considered. The turbulent heat flux isclosed by means of a turbulent eddy-diffusivity concept along with a turbulent Prandtl number of 0.9.The model constant CS is set to its default value and no dynamic procedure is devised. Wall treatmentneeds in that context specific attention and the mean physical behaviour of the LES predictions is en-sured through the use of a law of the wall (cf. Prière et al 2005 for details).

Numerical Scheme

FASTEST: FASTEST-3D, the code used in Darmstadt uses a finite-volume discretization of the low-Mach number equations on collocated, hexahedral, block-structured, boundary-fitted grids. For thespatial discretization second order central schemes are used and the implicit Crank-Nicolson timemarching method is used to achieve second order accuracy also in time. An exception is the convec-tive term of the mixture fraction equation for which a higher-order flux-limited approximation is em-ployed to ensure bounded, non-oscillatory solutions for the scalar field. Pressure-velocity coupling isachieved using the SIMPLE algorithm with Rhie&Chow’s pressure-weighted interpolation. The re-sulting sets of linear equations are solved iteratively using a 9-diagonal SIP-solver according to Stone.

AVBP-Turbomeca: At Turbomeca the AVBP code from CERFACS is used. This code features anunstructered explicit solver based on hybrid grids (mixed hexahedral/tetrahedral cells) and acell/vertex finite-volume formulation. Spatial and temporal discretizations offer up to third order accu-racy (TTGC scheme). However results presented here are limited to second order accuracies (in timeand space) through the use of a finite-volume expression of the Lax-Wendroff approach. Higher orderschemes will be used at latter stages of the work. The code is fully parallel with automatic grid parti-tioning making parallelization fully transparent to the user.

Configuration and Numerical SetupFASTEST: The computational domain includes the swirler, combustion chamber, contraction sectionand the first part of the outlet duct. The swirler is included to be able to capture the common PVC-likeswirl-flow-instabilities while the part of the outlet duct is included to make sure that the outlet is farenough away from regions of actual interest. The complete grid consists of 137 blocks with approxi-mately 2.4 million control volumes. As inflow conditions, laminar uniform profiles were set for allinlets according to the prescribed mass flow rates. A perturbation of the inflow (e.g. using artificialturbulence, Klein et al. 2003) was not necessary, since the shear forces in the nozzle and main cham-ber produce the main turbulence observed in this configuration.

AVBP-Turbomeca: The computational domain considered for LES with AVBP includes: the injec-tion system, the combustion chamber, the contraction section and part of the outlet pipe. For the re-sults presented here the entire injection system is meshed. It includes: the swirler’s settling chamber inwhich air is injected, the blade passage and the exit section of the burner. This approach was able to

predict the PVC-like swirl-flow-stability without artificial forcing or interactions with a priori BCprofiles. The final mesh is fully unstructured and composed of approximately 1,25 million cells. Localrefinement is enforced in the region of potential importance and turbulence generation. Dealing with afully compressible flow solver, boundary conditions need specific attention. All entrance and exit con-ditions make use of the method of characteristics and relax parameters determined following themethod of Selle et al. 2004 Target inlet profiles are set in agreement with experimental in-flow condi-tions and follow laminar flow expressions.

Results and DiscussionFigure 2 and 3show mean and fluctuation of axial (u) and radial velocity (v) components. The overallagreement between both LES predictions and experimental data is remarkable. Both LES predictionsare capable to predict the overall structure of the flow field with the high velocity central jet sur-rounded by swirling flow correctly. Especially the spreading of the swirling flow is described in veryclose agreement to experimental values. At the upstream locations at x=1 to 10 mm, various peaks ofshear-induced turbulence are located in accordance to experimental data. However, some differencesare observed especially at the exit plane at x=1 mm. The AVPB code over-predicts the mean axialcentral jet velocity while the FASTEST code under predicts the experimental values. This is mostlikely due to different inlet conditions used for both simulations (or the difference in wall treatmentand local resolution). Notice, that the preheated swirled air preheated the central jet flow to around 400K. At x=20 mm these differences in central jet velocities levelled out.

Figure 2: Left: Radial profiles of mean axial velocity at several axial positions; Right: Profilesof mean radial velocity. (solid line – LES TM-AVBP; dashed line – LES TUD-FASTEST;symbols - Experiments TUD)

The mixing field of a passive scalar is compared in figure 4. The axial decay and broadening of themean mixture fraction is described very well by both LES codes. This is noteworthy, because rotatingvortex structures as coherent motions may play a crucial role in mixing especially nearby the nozzle(Adrian Spencer, 2004). The fluctuation levels of the mixture fraction are over predicted in the vicinityof the inner shear layers at x=1 mm but under predicted at the center. These differences at the centermight be caused by less intermittency of the fuel jet in both simulations. Further downstream up tox=15 mm the overall fluctuation level predicted by the LES approaches is too high, which may belinked to the propagation of the initial high fluctuations.

Figure 3: Left: Radial profiles of rms fluctuation of axial velocity; Right: rms value of radialvelocity. (solid line – LES TM-AVBP; dashed line – LES TUD; symbols - Exp. TUD)

Figure 4: Left: Radial profiles of mean mixture fraction; Right: Profiles of rms fluctuation ofmixture fraction. (solid line – LES TM-AVBP; dashed line – LES TUD; symbols - Exp.TUD)

Acknowledgements

The authors are grateful to the European Union through Project MOLECULES, contract no.G4RD-CT-2000-00402.

References

Janus, B., A. Dreizler, et al. (2004). Flow field and structure of swirl stabilized non-premixed naturalgas flames at elevated pressure. ASME TURBO EXPO, Vienna.

Prière, C. et al. (2005). Experimental and Numerical Studies of Dilution Systems for Low EmissionCombustors. AIAA Journal (to be published).

Selle, L. et al. (2004), The actual impedance of non-reflecting boundary conditions: implications forthe computations of resonators, AIAA Journal, Vol. 42, 33, No. 5, 2004, pp. 1-21.

Kris Midgley, Adrian Spencer, James J McGuirk, (2004) Unsteady flow structures in radial swirler fedfuel injectors, ASME Turbo Expo Vienna, GT2004-53608.