Comprehensive Gas Turbine Combustion Modeling Methodology Hukam Mongia GE Aviation, Cincinnati, OH, U.S.A. Sundar Krishnaswami and PSVS Sreedhar EACoE, GE Aviation, Bangalore, India ABSTRACT: A comprehensive gas turbine combustion modeling methodology must account for complex geometry, physics, and chemistry. The methodology adopted here exploits the continuously evolving suite of combustion models of FLUENT, GE Aviations User-Defined Functions (UDFs), and High-Performance Computing (HPC). As such, it provides a framework to readily incorporate advances in simulation technology. Here we document the systematic validation of submodels for turbulence, fuel injection, droplet formation, droplet breakup, and turbulence-chemistry interactions. Keywords: Gas Turbine Combustion, Modeling, Design Methodology. INTRODUCTION

In the past, CFD has been mainly used as a qualitative guiding tool rather than for the actual design of gas turbine combustors. This is primarily because of the inadequacy of the available analytical and numerical models as well as limited computing resources to predict the different performance characteristics of the combustor. Now, with advances in modeling capabilities aided by several fold increase in computing power, it is possible to work towards realizing the goal of a CFD-based analytical combustor design approach. Traditionally, a typical combustor design cycle involves conceptual, preliminary and a detailed design complimented by several sub-scale component tests along with a couple of full-scale annular rig tests and one or more full engine test(s).

The goal set for a CFD-based design cycle is to reduce dependence on the iterative analyze-build-test-refine design process with attendant reduction in the cycle time of conceptual, preliminary and detailed design stages and the number of rig tests. The readiness of CFD to be used for design is assessed by its prediction capability of certain critical performance characteristics like emissions, exit temperature profiles, wall temperatures,

International Aerospace CFD Conference (Paris, June 18 19 2007)

lean blowout (LBO) fuel-air ratio etc, within certain specifications as stated in Mongia, (2002).

For reliable aircraft gas turbine combustion calculations using CFD, the following four steps need to taken:

1. Systematic assessment of the available turbulence models

against standard benchmark cases. This exercise is required to establish the prediction capability of the solver and for appropriate selection of the turbulence model.

2. Accurate prediction of the cold flow field in and around the combustor (air flow through multiple inlet ports of the combustion chamber, pressure, velocity & turbulence distribution), as impacted by the compressor exit profiles, the diffusion system and the combustion system details.

3. State-of-the-art modeling of the fuel atomization process, resulting in an accurate estimation of the spray quality.

4. Finally an appropriate choice of the chemistry model, a turbulence chemistry interaction model and rigorously established process for exercising them, in order to predict the critical characteristics of chemically reacting flow within the combustor.

CALCULATION PROCESS In all the investigations carried out, the commercial software FLUENT has been used. Details of the four steps outlined in the introduction are described below. TURBULENCE MODELS ASSESSMENT It is well known that the choice of turbulence model is dependent upon the class of problems to be investigated. For typical combustor application, the class of problems of interest can be grouped among the un-separated flows like, the flat plate, channel, pipe and annulus and separated flows like backward facing step, sudden expansion (with and without swirl). In addition, several cooling arrangements in combustor require accurate prediction of the heat transfer characteristics, and these arrangements can be simplified as flow problems involving wall jets and impinging (single and multiple) jets.

Singh and Mongia (2007), have described in detail, in their paper, the benchmark cases investigated, the approach followed and the comparisons made. Specifically, their effort focused on four different turbulence models Standard k- (SKE) (Launder and Spalding, 1974), Realizable k- (RKE) (Shih et.al., 1995), Reynolds Stress Model (RSM) (Launder et.al., 1975) and Shear Stress Transport (SST) model (Menter, 1994), and two different near wall treatment, namely, standard wall function (swf) (Launder and Spalding, 1974) and enhanced wall treatment (ewt) (Chen and Patel, 1988). Based on their investigations, they have recommended the use of RKE-ewt model for all

combustor applications. All further investigations reported in this paper will be using the aforementioned model, unless otherwise stated. COMBUSTION SYSTEM ANALYSIS (CSA) For reliable aircraft gas turbine combustion calculations, the foremost requirement is the cold flow field in and around the combustor (air flow through multiple inlet ports of the combustion chamber, pressure, velocity & turbulence distribution), supplied by the diffusion system. A typical combustor-diffusion system consists of an annular pre-diffuser, a dump section, fuel nozzles, casing, cowlings, dome, liners, annular passages and support structure. The objectives of a combustor-diffuser system are to supply the combustion & cooling air to the combustor in prescribed amounts through various inlets of the combustor, ensure optimum static-pressure recovery (Cp) & total-pressure losses (), ensure uniformity of flow entering the annular passages around the combustor.

Combustion System Analysis (CSA) entails the CFD based prediction of the airflow distribution and pressure drop within the combustor-diffuser system. During the years 2001 through 2004, considerable attention has been devoted to the key aspects that would ensure the success of the CSA approach. In addition to the appropriate choice of the turbulence models, these include the investigation of the inlet conditions and the importance of the grid quality. The summary of the earlier investigation has been published in a series of six papers (Mongia et. al., 2004a-f). The approach has since then been further improved and applied to 11 different combustors and the results are summarized below.

Fig. 1 shows how well the approach works even for the combustor cooling ports which inject a very small fraction of combustor air through many discrete holes. Predicted airflow distribution through each axial row of the cooling holes and nuggets against measured data for 11 different combustors are presented in this figure. It can be seen that the agreement with data is excellent, the prediction capability is within 0.16%, with a sigma of around 1%.

Fig. 2 shows the comparison of coefficient of pressure (defined as static pressure recovery normalized by the inlet dynamic head) in the inner and outer passages for 11 different annular combustors. The prediction of Cp is within 5%. Clearly, from the results, one can infer that the CFD prediction with respect to pressure drop and air flow distribution is as good as the experimental results.

Fig. 1: Comparison of cooling air flow distribution for 11 different combustors

Fig. 2: Coefficient of Pressure for different combustors.

Cp at Outer and Inner passage inlets, = 0.09

y = 1.046xR2 = 0.6031

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00Measured

Pred

icte

d

Combustor1

Combustor2

Combustor3

Combustor4

Combustor5

Combustor6

Combustor7

Combustor8

Combustor9

Combustor10

Combustor11

Ideal Fit

Outer Passage: Red, Inner Passage: Magenta

Air Flow Distribution through all the holes, = 1.0%

y = 1.0016xR2 = 0.994

0%

10%

20%

30%

40%

50%

60%

70%

0% 10% 20% 30% 40% 50% 60% 70%Measured

Pred

icte

d

Combustor1

Combustor2

Combustor3

Combustor4

Combustor5

Combustor6

Combustor7

Combustor8

Combustor9

Combustor10

Combustor11

Ideal Fit

COMPREHENSIVE INJECTOR MODEL (CIM) Having satisfactorily addressed the airflow and pressure drop, the next major challenge is to establish and assess a robust fuel atomization and spray distribution model. Development of a predictive model for fuel atomization and subsequent spray distribution requires a comprehensive approach for addressing various sub processes like the proper development of the flow (in a pressure swirl atomizer), the formation of a sheet and its breakup using a model for sheet instability, followed by the influence of the aerodynamic forces to form droplets from the broken sheets, and the subsequent distribution of drops.

There are two widely used approaches for numerically predicting the sheet formation, and they are the Arbitrary Lagrangian-Eulerian (ALE) approach advocated by Jog et. al., (2000), and the Volume of Fluid (VOF) approach developed by Hirt et. al. (1981). In the current investigation, a two phase VOF technique available in FLUENT is used to simulate the flow through a fuel nozzle. The primary focus of this analysis is on the flow characteristics of the atomizer, the formation of the liquid film as it exits from the orifice, and the resulting cone angle. The turbulence model exercised is the RSM model (Launder et. al., 1975) with the coupled solver and PRESTO (PREssure STaggering Option, Patankar, 1980) scheme for pressure interpolation and modified HRIC (Muzaferija, S. et. al., 1988) for volume fraction equation.

Investigations were carried out for the range of flow numbers normally experienced by fuel atomizers in modern aviation engines. Fig. 3, below, illustrates the air-core obtained for two different flow numbers through the atomizer. One can observe that the liquid-air interface is sharply captured. The region in red is representative of the fuel (Jet-A) and the region in blue is representative of air.

Fig. 3: Air-core and liquid film for two different Flow Numbers.

Using the liquid sheet and flow field parameters obtained from VOF as inputs, a linear stability analysis has been carried out to predict the primary droplet diameter and the breakup length. This involves conducting a temporal linear stability analysis to study the primary atomization of annular liquid sheets. The approach captures the instability of a swirling annular liquid sheet subject to axi-symmetric disturbances and swirling inner and outer air

FN=2.7 FN=10.6

streams and is based on the paper by Ibrahim and Jog, 2006. The VOF simulation and linear stability analysis provide a comprehensive approach to modeling atomization from pressure-swirl and airblast atomizers.

Having obtained the mean diameter through the stability analysis, the droplet distribution is modeled using a two parameter Rosin Rammler distribution, wherein the most probable droplet size is obtained from processing the results of stability analysis, and the spread parameter is assumed to be 2.5. Key physical properties of the liquid droplet, such as surface tension, vapor pressure and thermal conductivity are obtained from piecewise linear fits. Conical injection is assumed, and the parameters relevant for setting up the injection are obtained from VOF.

The secondary breakup model used in the current investigation is the Taylor Analogy Breakup (TAB) model (Taylor, G.I, 1963). This model was chosen because the Weber number experienced for the range of conditions investigated was less than 100. Coupling of the discrete phase with the continuous phase was invoked through the discrete phase model available in FLUENT, which included accounting for the effect of instantaneous turbulent velocity fluctuations on particle trajectories through the stochastic discrete random walk model and invoking two-way turbulence coupling to account for the effect of particles on the turbulence quantities in the continuous phase.

Using the above approach, the CIM model was validated against atmospheric rig test data, and the comparisons obtained for the secondary droplet size are shown in Fig. 4. The results show very good agreement with data, thereby validating the process for comprehensive injector modeling.

Fig. 4: SMD comparison for atmospheric Rig Test.

Secondary SMD

0

50

100

150

200

0 50 100 150 200Rig data (microns)

Pred

icte

d (m

icro

ns)

REACTING FLOW MODEL With an established combustion system analysis procedure and a comprehensive injector modeling approach, the final step to successful prediction of key characteristics of a combustor is a robust and reliable reacting flow model. In most of the lean dome combustors, the fuel stream undergoes some degree of partial premixing before it is subject to chemical reaction. Therefore, the partially premixed combustion approach is most appropriate for modeling the combustion process. Because of the requirement of quick turnaround in calculations, the commonly used combustion models are relatively simple, like for example, the assumed-shape PDF (fast chemistry) and eddy-breakup. However, these models have limitations, particularly when calculating the emissions from lean dome combustors.

In contrast, the laminar flamelet approach (Peters, 1986) offers significant advantages, without adding additional calculation speed penalties. Briefly, a flamelet model assumes that the effect of turbulence on a flame can, under certain conditions, be modeled as a flame area increase. The main criterion for making this assumption is that the flame length scale is much smaller than the Kolmogorov turbulence length scale. For the combustor modeled here, that assumption is not strictly correct, and the true combustion regime is intermediate between flamelet combustion and distributed reaction. As an engineering model, however, the mean properties of the flow field can often be well-reproduced by a flamelet model even when it is not strictly valid.

In employing a single flamelet model for investigation, the key challenge is a-priori estimate of the appropriate stoichiometric scalar dissipation. In the current investigation, an iterative approach recommended by Shui-Chi Li (2003), as described below, is adopted to determine the scalar dissipation.

To start with, a nominal value of scalar dissipation is assumed and the corresponding flamelet and the PDF table is generated. The reacting flow is run to convergence. From the converged CFD solution, the stoichiometric scalar dissipation is estimated from a weighted average of the local scalar dissipation on iso-mean mixture-fraction surfaces that envelope the thin flame zone. A single flamelet is re-generated and the CFD solution is run again, until the scalar dissipation used in flamelet generation and the CFD based computed stoichiometric scalar dissipation are within 0.5% of one another.

For the range of pressures, temperatures and fuel air ratios for dome combustors investigated, a maximum of 3 iterations between the CFD solution and flamelet generation was required.

Fig. 5: Comparison of NOx Emissions.

Fig. 5, above, shows the comparison of prediction of NOx emissions against data for two different lean dome combustors, and for a range of pressures from 29 psi to 200 psi, and temperatures in the range from 330F 710F. It can be seen clearly that the predictions agree with data within 1EI.

Shown below in Fig. 6 is the comparison of prediction of CO emissions. Again, one can observe that the agreement is very good and is within 5EI. Deviations at the highest values of CO EI can be explained due to the lack of a good chemistry model to predict unburned hydrocarbons and inadequacy of the flamelet approach for thick flame brushes, and it points towards adopting the approach to solve transport equations for CO and unburned hydrocarbons.

EINOx y = 1.0038xR2 = 0.9204

3

5

7

9

11

13

15

3 5 7 9 11 13 15Data

CFD

EINOx

Ideal Fit

Ideal+1EI

Fig. 6: Comparison of CO emissions.

Fig. 7, below shows the comparison of exit temperature quality. One can observe very good agreement between data and CFD.

Fig. 7: Comparison of exit temperature quality.

EICOy = 0.9999xR2 = 0.9602

0

10

20

30

40

50

60

70

80

0 10 20 30 40 50 60 70 80Data

CFD

EICO

Ideal Fit

Ideal+5EI

RDG825-Profile Factor

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4NDT AVG

Hei

ght F

ract

ion

RDG825-DATARDG825-CFD

RDG825-Profile Factor

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4NDT AVG

Hei

ght F

ract

ion

RDG825-DATARDG825-CFD

SUMMARY A systematic investigation for the prediction of the key characteristics of combustors using CFD has been carried out. This entailed a rigorous assessment of the turbulence models for combustor applications, establishing and validating a combustion system analysis methodology for 11 different combustors, a comprehensive spray injection modeling approach, and a systematic way of exercising a single flamelet approach for reacting flow. Good agreement with data, for the key performance parameters has been demonstrated.

The authors would like to acknowledge S C Li, GE Aviation, Springdale for sharing his approach of CFD-based estimation of scalar dissipation, and the team in GE Aviation, Bangalore, for their efforts in the validation process. REFERENCES Chen, H. C., and Patel, V. C. (1988) Near wall turbulence models for complex flows including separation, AIAA Journal, 26, 641-648. Ghanshyam Singh and Mongia, H. C. (2007) Comparison of turbulence models for gas turbine applications, Workshop on Diagnostics and control of Pollutant Formation and Emission in Combustion, Jadavpur University, India. Hirt, C. W., and Nichols, B. D., (1981) Volume of Fluid (VOF) method for the dynamics of free boundaries, Journal of computational physics, 39, 201-225. Ibrahim, A. A., and Jog, M. A. (2006), Effect of liquid and air swirl strength and relative rotational direction on the instability of an annular liquid sheet, Acta Mechanica, 186, 113-133. Jog, M. A., Sakman, A. T., Jeng, S. M., and Benjamin, M. A. (2000), Parametric study of simplex fuel nozzle internal flow and performance, AIAA Journal, 38, 1214-1218. Jones, W. P., and Whitelaw, J. H. (1982) Calculation methods for reacting turbulent flows A review, Combustion and Flame 48, 1-48. Launder, B. E., and Spalding, D. B (1974) The numerical computation of turbulent flows, Computer Methods in Applied Mechanics and Engineering, 3, 269-289. Launder, B. E., Reece, G. J., and Rodi, W. (1975) Progress in the development of a Reynolds stress turbulence closure, Journal of Fluid Mechanics, 68, 537-566. Menter, F. R., (1994) Two equation eddy viscosity turbulence models for engineering applications, AIAA Journal, 32, 1598-1605.

Muzaferija, S., Peric, M., Sames, P., and Schellin, T., (1998), A two fluid Navier Stokes solver to simulate water entry, Proceedings of 22nd Symposium on Naval Hydrodynamics, 277-289. Mongia, H. C., (2002) Development of combustion chamber design tools, TRF workshop, IIT Madras. Mongia, H.C., Hsiao, G., Burrus, D., Sreedhar, PSVS, Rao, A. and Naik, P, (2004a), Combustor Diffuser Modeling Part I: Inlet Profiles & 2-D Calculations, AIAA Paper 2004-4168. 40th AIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit, Fort Lauderdale, Florida, July 11-14. Mongia, H.C., Hsiao, G., Burrus, D., Sreedhar, PSVS, Rao, A. and Ismail, S. (2004b), Combustor Diffuser Modeling Part II: Inlet Profiles and 3-D Calculations, AIAA Paper 2004-4169. 40th AIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit, Fort Lauderdale, Florida, July 11-14. Mongia, H.C., Hsiao, G., Burrus, D., Sreedhar, PSVS, (2004c), Combustor Diffuser Modeling Part III: Validation w/ Typical Separating Single Passage Diffusers Combustor Diffuser Modeling, AIAA Paper 2004-4170. 40th AIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit, Fort Lauderdale, Florida, July 11-14. Mongia, H.C., Hsiao, G and Burrus, D., Sreedhar, PSVS, Rao A and Ismail, S, (2004d), Combustor Diffuser Modeling Part IV: Effect of Cowling Geometry, Mixer Size and Nozzle Blockage, AIAA-2004-4171, 40th AIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit, Fort Lauderdale, Florida, July 11-14. Mongia, H.C., Hsiao, G., Sreedhar, PSVS, Rao, A. and Ismail, S. (2004e), Combustor Diffuser Modeling Part V: Validation with a Three Passage Diffuser Rig Data, AIAA Paper 2004-4172. 40th AIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit, Fort Lauderdale, Florida, July 11-14. Mongia, H.C., Mueller, M., Dai, Z., Sreedhar, PSVS, Rao, A. and Ismail, S. (2004f), Combustor Diffuser Modeling Part VI: Validation with a Four Passage Diffuser Rig Data, AIAA Paper 2004-4173. 40th AIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit, Fort Lauderdale, Florida, July 11-14. Patankar, S. V., 1980, Numerical Heat Transfer, Hemisphere Publication. Peters, N (1986), Laminar flamelet concepts in turbulent combustion, 21st Symposium (International) of Combustion, 1231-1250.

Peters, N., Riesmeier, E. and Honnet, S.. (2004), Flamelet modeling of pollutant formation in a gas turbine combustion chamber using detailed chemistry for a kerosene model fuel, Journal of engineering for gas turbines and power, 126, 899-905. Shih, T. H., Liou, W. W., Shabbir, A., Yang, Z., and Zhu, J. (1995) A new k-e eddy viscosity model for high Reynolds number turbulent flows Model development and validation, Computers Fluids 24, 227-238. Taylor, G. I., (1963), The shape and acceleration of a drop in a high speed air stream, Technical Report in the scientific papers of G I Taylor ed. G.K., Batchelor. Zimont, V. L., (2000) Gas premixed combustion at high turbulence. Turbulent flame closure model combustion model, Experimental thermal and fluid science, 21, 179-186.

Mongia Release IACC 07mongia_iacc_07