ABSTRACT In this study, a Rolls-Royce production gas turbine combustor was analyzed using 3D Large Eddy Simulation (LES). The objective of the study was to evaluate the LES modeling approach for predicting emissions (CO and NOx) and pattern factor in liquid-fueled combustors at practical engine conditions. Experimental data from Rolls-Royce, at high and low power conditions, were used to evaluate the model. Combustion LES and Reynolds Averaged Navier-Stokes (RANS) calculations were performed using a compressible, pressure-based, unstructured-grid flow solver within the CFD-ACE+ commercial software. LES solves the general transport equations for mass, momentum, energy, and chemical species at the grid- and time-resolved scales of the flow. The Localized Dynamic subgrid Kinetic energy Model (LDKM) was used to model the unresolved (subgrid) turbulence and a 2-variable (mixture fraction and progress variable) assumed probability density function (PDF) method, with decoupled NOx, was used to model the unresolved turbulence-chemistry interactions. A two-step chemistry model (JETA → CO → equilibrium products) was utilized. Lagrangian tracking of spray parcels with source/sink terms for the Eulerian gas-phase was included. LES produced unsteady turbulent structures that enhanced mixing compared to RANS. LES, at high power conditions, produced lower CO and NOx and better agreement with exit emissions data compared to RANS. At low power, the LES emissions of CO were improved over RANS, but were still poor due to simplifications in the CO mechanism. Improvements in the filtered (mean) CO reaction rate could be achieved by including turbulent fluctuations of
CO. LES computational times on a 15 Personal Computer (PC) cluster were ~10 days. Application of the software to high fuel-air ratio combustors will be conducted in the future to investigate methods for reducing emissions.
INTRODUCTION Low emissions of pollutants, such as CO, NOx, unburned hydrocarbons (UHC), and smoke, are becoming a requirement for today's and future military gas turbine engines. Advanced, high performance gas turbines will feature higher inlet temperatures and pressures, and will require new fuel injector and combustor designs if lower emissions are to be realized. These low emissions gas turbine combustors will operate at near stoichiometric overall fuel-air ratios at full power, and will have many emissions design challenges, including how to minimize residence times for high-temperature, thermal NOx producing regions. To meet these challenges in a cost- and time-effective manner, improved combustor design systems are needed that include accurate models of chemical kinetics, turbulent mixing, and their interaction. Current steady-state RANS (Reynolds Averaged Navier Stokes) CFD combustion codes lack the quantitative accuracy needed for reliable predictions of emissions. The limitations of the current CFD codes are mainly due to deficiencies in the treatment of the turbulent fluid motion and its interaction with the chemical kinetics. This is because turbulent combustion is inherently unsteady (including vortex shedding, shear layer mixing, and acoustic wave propagation), and RANS codes cannot capture counter-gradient diffusion and other unsteady phenomena seen in gas turbine combustors. A more accurate, higher fidelity way to model combustor flows is combustion Large Eddy Simulation (LES). In this method, the larger scales of turbulent motion are captured numerically (without the need of
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39th AIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit20-23 July 2003, Huntsville, Alabama
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physical models), and only small (subgrid) scales need to be modeled. It has been previously shown (e.g. Spencer and Adumitroaie, 2003) that LES captures mixing better than RANS analysis, and turbulent-combustion interaction is significantly improved. In addition, the effect of the transient nature of the combustor flow, i.e., combustion dynamics, and its effect on mixing and reaction is only captured with combustion LES. Practical combustion LES calculations (1-2 million cells) can now be performed in ten days on a Beowolf cluster of 16 PCs, and in five years, the run time will be less than a day as computers become substantially faster. It is important to further develop/demonstrate combustion LES methods so that these high fidelity solutions can be used in the design environment in the years ahead. Such a design tool will dramatically reduce test costs and produce improved, low emissions combustor designs. In this paper, the feasibility of using LES for predicting emissions (CO and NOx) in advanced liquid-spray combustors is shown. Previoius combustion LES studies at CFDRC have focused on gaseous-fueled combustion (e.g. Cannon et al., 2003, and Cannon et al., 2002). In this paper, combustion LES and steady-state RANS calculations of a Rolls-Royce production combustor were performed. Comparisons of predictions to available experimental data at the combustor exit plane were made. The LES model strengths and weaknesses as well as recommendations for further work are presented.
EXPERIMENTAL RESULTS AND PROCEDURE Combustor exit temperature and emissions measurements were provided by Rolls-Royce for the annular combustor of a production gas turbine engine. The combustor liners are effusion cooled with several rows of primary, intermediate, and dilution holes. Figure 1 shows a cross-section of the combustor with the important features of the geometry. Experimental data from the combustor included average exit measurements of radial temperature profiles, and overall, global CO and NOx emissions at the combustor exit. Measurements were available for both low and high power conditions. The exit emissions measurements were obtained by averaging 7 tangentially-spaced multi-point probes with 5 radial sampling holes in each probe. The exit temperatures were measured with two rotating probes (360° sweep) with 5 elements in each probe.
LES MODELING The general conservation equations for mass, momentum, energy, and chemical species are filtered to obtain equations for the large-scale (energy containing) variables needed for LES. The filtered equations contain unknown terms such as a subgrid turbulence stress tensor and a subgrid reaction rate that must be modeled. Unlike typical steady-state turbulence models, the subgrid models for LES are a function of the local grid (or filter) size.
Figure 1. Cross-section of the Rolls-Royce Production Combustor
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The subgrid turbulence was approximated with the Localized Dynamic subgrid Kinetic energy Model (LDKM - Kim and Menon, 1997). Within the LDKM, the eddy viscosity is computed as a function of the local grid size ( ∆ ) and the subgrid turbulent kinetic energy
(ksgs): 21
sgst kC ∆=ν τ . A transport equation for the ksgs is solved and requires terms that are obtained from velocity gradients at a test filter level. The test filter width is taken to be ~2 times the grid filter width. The LDKM has no adjustable constants and is widely applicable to a large range of turbulent flow conditions. The subgrid chemistry was described with a 2-step assumed PDF method. The PDF is a 2-dimensional function of the mixture fraction and progress variable (fuel mass fraction), where these variables are assumed to be independent of each other. Top-hat and tri-delta PDF shapes were assumed for the mixture fraction and reaction progress variables, respectively. The top-hat and tri-delta pdf shapes were chosen since they are relatively inexpensive to compute and since they have given reasonable results for previous RANS combustor calculations (Liever et al., 1998). Filtered transport equations for the mean and variance of the mixture fraction and reaction progress are solved. The subgrid reaction rate is obtained by integrating the instantaneous fuel reaction rate over the 2-D PDF. Source terms in the transport equations for the mixture fraction and progress variable variance are obtained from the subgrid turbulent kinetic energy and dissipation rate. A 2-step chemical mechanism was used, where the fuel oxidizes to CO and then the CO oxidizes to equilibrium products at finite rates. The fuel oxidation rates were obtained by matching laminar flamespeeds and ignition delay times over a range of inlet temperature, pressure, and equivalence ratios. The fuel oxidation rate is expressed as
[ ] [ ] cba
2312POHCeATw 22312
RTEnHC
−=� ,
where A=6.5E11, n=0, E/R=24,000, a=0.5, b=1.0, and c=0.25, with units in kmol, m, K, sec, and atm. The CO oxidation reaction is assumed to be CO+OH ↔ CO2+H and the destruction of CO is expressed as:
[ ] [ ] [ ][ ] [ ] [ ]( )e
e2
eei COCO
COCO
1OHkdtCOd −
��
���
��
���
+−=
where the reaction rate is determined by Warnatz (1984) from ki = ATnexp(E/(RT)) with A = 4.4e3, n = 1.5, and E/R = -373 in units of kmol, m, K, and sec.
A transport equation for the filtered CO mass fraction is solved, but the influence of fluctuations in CO mass fraction were not included in the PDF. The thermal NOx mechanism (Miller and Bowman, 1989) was also included at each time-step by solving a separate transport equation for NOx. The influence of mixture fraction and progress variable fluctuations were included in the filtered NOx and CO rates. The spray model utilizes a Lagrangian approach for solving the conservation equations of droplet mass, motion, and energy. For computational efficiency, the numerical solution of these equations is obtained for a certain number of droplet parcels, where each parcel is representative of the behavior of a large number of droplets. The droplet solutions are used to calculate the source/sink terms for the gas phase equations. This LES methodology was used in the unstructured compressible CFD-ACE+ code. The computational details included a co-located, fully implicit and strongly conservative finite-volume formulation, pressure-based solution algorithm (SIMPLEC), 2nd-order Crank-Nicholson temporal differencing, 2nd-order upwind (with limiter) differencing for all variables except pressure correction and 2nd-order central spatial differencing for pressure correction. The CFD-ACE+ solver has been parallelized for distributed and SMP architectures using the MPI message passing library and domain decomposition. A parallel cluster of 15 Linux-based PCs was used for the LES calculations. Each PC includes a 2200 MHz AMD Athlon chip, 1 Gbyte of DDR-PC2100 RAM and 100-Base-T networking. The ~2.3 million cell LES cases required 10 days of wall-clock time. The computational grid included ~2.3 million cells and resolved the flow passages in and around the fuel nozzle, dome swirler, splash plate, heat shield, and combustor liner orifices. Figures 2 and 3 show the computational grid and domain. External flowpath plenums were included to eliminate the need of assuming velocity profiles and discharge coefficients at the liner holes. The CFD model is a 22.5° sector (corresponding to one fuel nozzle) with cyclic boundary conditions. Inlet boundary conditions with a fixed mass flow rate are applied at the swirlers, splash plate, heat shield, inner and outer starter films, inner and outer transition films, and inner and outer plenums that feed the primary, intermediate, and dilution holes in the liner. Fixed mass boundaries are also applied along the combustor liner to simulate the effusion cooling flow. A fixed static pressure is applied at the combustor exit.
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Figure 2. Computational Grid and Domain
Figure 3. Computational Grid Near Fuel Injector and Dome
HIGH POWER RESULTS
Steady-state RANS calculations were first performed using the standard k-ε turbulence model, the assumed, two variable (mixture fraction and progress variable) PDF model, and Lagrangian tracking of spray parcels. Turbulent Schmidt and Prandtl numbers of 0.5 were assumed. LES predictions were performed at a time-step of 5x10-6 seconds and starting from a converged steady-state solution. LES computations were carried
out for 3 flow-through times, while mean and rms statistics were collected for most of the predicted flow-field variables. Monitor points were placed throughout the combustor to track the time-history of velocity pressure, and temperature. The locations of monitor points near the fuel nozzle and primary jet shear layers are shown (Figure 4), as well as a point in the dilution zone at the combustor centerline.
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Figure 4. Monitor Point Locations for LES
Time series and Fourier transform plots of the monitor points are shown in Figure 5. The time-series plots indicate turbulent fluctuations were resolved in the simulations with peak pressure fluctuations near the nozzle of +/- 0.5% of the combustor exit pressure. The near-nozzle location indicated preferred frequencies of 1200 and 2250 Hz. These higher frequencies were due to a fluid-dynamic instability at the fuel nozzle shear layer. An 800 Hz frequency was also detected for all three monitor point locations, indicating the excitement of a bulk mode. This transient simulation data can be valuable when trying to understand the causes of instability and potential methods for controlling damaging instabilities. Complete flowfield predictions are now shown for LES and RANS at high power conditions. Figures 6 and 7 show snapshots and time-averaged predictions of velocity magnitude and temperature. The velocity predictions indicate stronger penetration of the primary jets using LES. This stronger penetration closes off the central recirculation zone, making it more compact for the LES predictions. The temperature predictions in Figure 7 again show the effect of stronger mixing with LES. The peak temperature is reduced using LES and the hot temperatures spread out over a greater area in the intermediate zone. This higher mixing in the intermediate zone is due to the strong primary jets that create stronger wakes and mixing behind the jets. It is clear that the exit temperature profile is less peaked and the pattern factor is substantially less for the LES case, compared to RANS. A comparison of the predicted temperature profile with measurements at the combustor exit is shown in Figure 8. The LES exit
temperature predictions shown here are in good agreement with data.
Figure 5. Time History and Fourier Transform of Pressure at High Power Conditions
Fuel Nozzle Primary Jet
Dilution Zone
Fuel Nozzle Primary Jet
Dilution Zone
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LES Snapshot
LES Time-Average
RANS
Figure 6. LES and RANS Predictions of Velocity Magnitude at High Power Conditions
LES Snapshot
LES Time-Average
RANS
Figure 7. LES and RANS Predictions of Temperature and Spray Trajectories at High Power Conditions
Figure 8. Comparison of Measured and Predicted Radial Temperature Profiles at Combustor Exit for High Power
Conditions
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The emissions of CO and NOx are shown in Figure 9. Very little CO exits a well-designed combustor at high power conditions (at least for modest combustor exit fuel-air ratios). At the high exit temperatures of high power, CO is generally at its equilibrium value. Thus, high CO only occurs if local fuel-air ratios are much higher than the average fuel-air ratio. Thus, mixing generally controls CO at high power, and not kinetics. It can be seen in Figure 9 that a large amount of CO is formed in the primary and intermediate zones of the combustor, and oxidation of the CO occurs as the dilution air mixes with the hot products. For LES, the mixing is sufficient to eliminate any pockets of high fuel-air ratio at the exit, and thus there is little CO. For RANS, high fuel-air ratio pockets exit the combustor, producing high CO emissions.
LES Snapshot
RANS
Figure 9. Comparison of CO Predictions for LES and RANS at High Power Conditions Figure 10 presents the NOx emissions predictions. Most NOx forms at high power conditions (compared to NOx forming at other power conditions). NOx is formed at high temperature locations when there is excessive oxygen, typically at local equivalence ratios around 0.8 – 0.9. The NOx emissions in Figure 10 show that NOx is formed sooner and over a larger volume for the LES, particularly out towards the inner and outer liner of the intermediate zone. However,
higher peak values are predicted for the RANS along the centerline of the dilution zone, most likely due to the higher peak temperatures in this region. Overall, more NOx is predicted for RANS at the combustor exit.
LES Snapshot
LES Time-Average
RANS
Figure 10. Comparison of NOx Predictions for LES and RANS at High Power Conditions Spatially-averaged CO and NOx emissions at the combustor exit plane were recorded at every 100 timesteps. A total of 10 instants (over 2 flow-through times) were averaged to obtain the overall exit CO,
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NOx, and temperature. Table 1 shows comparisons of the predictions and measurements at the high power conditions. Overall, LES provides a better prediction of emissions compared to the RANS. The improved results can be largely attributed to the stronger mixing of primary and dilution air with the combustor core flow for the LES and the mixing produced by combustor unsteadiness. The RANS did not capture the higher jet penetration as observed in the LES. The CO emissions show the largest differences between the two predictions and measurements. However, this is not of much concern since the CO emissions were relatively low anyway, at these high power conditions.
Low Power Results Computations were next carried out for low power conditions. The low power pressure and temperature were ~1/6 and 2/3 of the levels at high power conditions, respectively. The overall equivalence ratio at low power was ~2/3 of the high power equivalence ratio. Only the primary fuel circuit was used at low power. LES predictions were performed at a time-step of 5 X 10-6 seconds and starting from the converged steady-state solution. Computations were carried out for 3 flow-through times, while mean and rms statistics were collected for most of the predicted flow-field variables. Figures 11 and 12 show a comparison between the LES and RANS at low power for velocity and temperature. The low power results again show the stronger penetration of the primary jets for the LES. The central recirculation zone is more compact with the LES, similar to the results at high power conditions. The high temperature gas becomes more evident near the inner and outer liners downstream of the primary holes for the LES. The combustor exit temperatures appear to be only slightly more uniform for the LES. It is clear that a small amount of fuel spray hits the liner for these low power conditions, compared to high power. The lower combustor temperatures produce lower evaporation rates. The fuel droplets that run along the walls are relatively small and do not contribute much to the overall heat release.
LES Snapshot
LES Time-Average
RANS
Figure 11. Comparison of Velocity Magnitude for LES and RANS at Low Power Conditions
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LES Snapshot
LES Time-Average
RANS
Figure 12. Comparison of Temperature and Spray Trajectories for LES and RANS at Low Power Conditions The CO and NOx emissions predictions are shown in Figures 13 and 14. The CO emissions at low power conditions can be significant, since quenching for CO oxidation reactions can occur at the lower combustor temperatures. In the CFD predictions, a large amount of CO is predicted in the primary zone, and some oxidation occurs in the intermediate zone. However, complete oxidation does not occur in the intermediate zone, and the dilution air quenches the CO at nonequilibrium values in the dilution zone. The
expected cause of high CO at lower power, i.e. liner cooling quenching, is not evident in these calculations, probably because the high CO in the mainstream masks any quenching that may occur along the liner. The CO predictions in Figure 13 seem to indicate that the LES with stronger mixing reduces the CO emissions at the combustor exit compared to RANS. This is most likely due to the shortened slightly fuel-rich primary zone predicted in the LES case. The exit CO emissions for LES are ~20% less than the RANS predictions. Table 2 shows comparisons of the predictions with experimental data. Despite the improvement for LES, both RANS and LES overpredict the combustor exit CO emissions by substantial amounts. It is thought that improvements to the chemical kinetics mechanism should help the low power CO predictions. The current CO oxidation model assumes equilibrium levels of OH and does not include finite-rate kinetics of other minor species. Previous gas turbine combustor modeling studies by Correa et al. (1984) and Correa (1985) have pointed out the importance of correctly predicting H and OH in order to obtain accurate CO predictions. The use of a more advanced multi-step JP8 chemical kinetics model should improve CO oxidation rates at low power conditions. It is also important to remember that the filtered (mean) CO reaction rate only included turbulent fluctuations in the minor equilibrium species and temperature. The actual fluctuations in CO itself were not included. The effect of CO fluctuations on the filtered (mean) rates should be considered to accurately predict low power CO. Figure 15 shows fluid particle CO rate and temperature from a lean premixed Partially Stirred Reactor (PaSR) simulation. The CO rate for each fluid particle was computed using the mean (ensemble) CO and using the instantaneous particle CO. Use of the mean CO produces overpredicted formation rates and underpredicted oxidation rates. Therefore, lower CO emissions would be expected if turbulent fluctuations in CO were considered.
Table 2. Predicted and Measured CO, NOx, and Temperature for the Low Power Conditions
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LES Snapshot
LES Time-Average
RANS
Figure 13. Comparison of CO Emissions Predictions for LES and RANS at Low Power Conditions
LES Snapshot
LES Time-Average
RANS
Figure 14. Comparison of NOx Emissions Predictions for LES and RANS at Low Power Conditions
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Figure 15. CO Reaction Rate Using Instantaneous CO (exact) and Mean CO (current model) The predicted NOx emissions are shown in Figure 14. NOx emissions at low power are substantially lower than at high power conditions because combustor temperatures are significantly reduced. The difference between the LES and RANS NOx emissions at low power was relatively small. It can be seen that the NOx is less at the combustor exit for the LES. The lower predicted NOx for LES is due to the better mixing and reduction in peak temperature for the LES. The comparison with data in Table 2 indicates that the RANS is ~12% higher than data and the LES is ~15% lower than the measurements. Since the measured NOx is quite low, these small discrepancies are not too serious and both LES and RANS essentially provide equally good predictive capabilities for low power NOx.
SUMMARY AND CONCLUSIONS
Combustion LES software was developed and applied as a tool for the design of low emissions, high performance, gas turbine combustors. This time-accurate CFD code includes models for turbulent mixing (LDKM) and turbulence-chemistry interactions (assumed PDF) at the subgrid level. A 2-step chemical model that included finite rates for fuel and CO oxidation as well as NOx formation was tested. The LES results were compared with RANS predictions and with available experimental data for a Rolls-Royce production combustor at high and low power conditions. The LES results provided stronger penetration of primary jets into the combustor core flow and thus better mixing. The unsteadiness of the flowfield and its effect on mixing was also captured with LES. The averaged exit values of temperature, CO, and NOx were
better predicted with the LES at high power conditions. The LES results were only slightly better than RANS at low power. Both RANS and LES need to be improved for predicting CO emissions at low power. Both methods over-predicted CO emissions at low power by approximately one order of magnitude. The most likely reason for the poor low power CO emissions predictions are: 1. The simplified CO oxidation rate assumes
equilibrium levels of OH and all other minor species; and
2. The filtered (mean) CO rate did not include turbulent fluctuations in CO concentrations.
These chemical kinetics and turbulence/chemistry interaction models need to be improved in the LES combustion code. The development and use of a multi-step reduced JP8 chemical kinetics model that includes super-equilibrium levels of minor species, particularly H and OH, is needed for better low power CO predictions. An improved PDF method that includes CO fluctuations as a function of mixture fraction and reaction progress fluctuations is needed for filtered (mean) CO rates. These new models are currently being developed and applied. The computational time required by the combustion LES code was ~10 days on 16 Linux-based processors (2.3 GHz AMD Athlon Processors) for the 2.3 million cell combustor. This time could be cut to 4-5 days if 64 processors were used, and down to 1 day within 3 years as processor speeds double every 18 months. This work has shown the overall feasibility of using this LES method, with sufficient parallel processing, as a design tool to minimize emissions in practical high-performance combustors.
ACKNOWLEDGEMENTS The authors wish to acknowledge the support of the US Navy, under SBIR Contract No. N00421-03-P-0063 (Technical Monitor, Mr. Marc Richman), for the CFDRC LES validation. We are also grateful for the use of production combustor rig test results from Rolls-Royce.
REFERENCES
Cannon, S., Zuo, B., and Smith, C., (2003), “LES Prediction of Combustor Emissions From a Practical Industrial Fuel Injector,” GT2003-38200, presented at the 48th ASME Gas Turbine and Aeroengine Technical Congress, Atlanta, GA, June 16-19, 2003.
Cannon, S., Zuo, B., Adumitroiae, V., and Smith, C., (2002), “Linear Eddy Subgrid Modeling of Lean
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Premixed Methane-Air Combustion,” presented at Natural Gas Technologies, Orlando, FL, Sept 29 – Oct. 2, 2002.
Correa, S.M., (1985), “A Model for Non-Premixed Turbulent Combustion of CO/H2 Jets,” Archivum Comubstionis, Vol. 5, pp. 223-243.
Correa, S.M., Drake, M.C., Pitz, R.W., and Shyy, W., (1984), “Prediction and Measurement of a Non-Equilibrium Turbulent Diffusion Flame,” Twentieth Symposium (International) on Combustion/The Combustion Institute, Pittsburgh, PA, pp. 337-343.
Kim, W. and Menon, S., (1997), “Application of the Localized Dynamic Subgrid-Scale Model to Turbulent Wall-Bounded Flows,” AIAA paper 97-0210.
Liever, P.A., Smith, C.E., Myers, J.D., and Griffith, T., (1998), “CFD Assessment of a Wet, Low-NOx Combustion System for a 3MW-Class Industrial Gas Turbine,” 98-GT-292, presented at the International Gas Turbine & Aeroengine Congress & Exhibition, Stockholm, Sweden, June 2-5, 1998.
Miller, J.A. And Bowman, C.T., (1989), “Mechanism and Modeling of Nitrogen Chemistry in Combustion,” Progress in Energy and Combustion Science, 15, pp. 287.
Spencer, A. and Adumitroiae, V., (2003), “Large Eddy Simulation of Impinging Jets in Crossflow,” GT2003-38754, presented at the 48th ASME Gas Turbine and Aeroengine Technical Congress, Atlanta, GA, June 16-19, 2003.
Warnatz, J., (1984), “Rate Coefficients in the C/H/O System,” Combustion Chemistry, W.C. Gardiner, Jr., Editor, Springer-Verlag, New York, pp. 197-360.
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