NUMERICAL SIMULATION OF LDI COMBUSTOR WITH DISCRETE-JET SWIRLERS USING RE-STRESS MODEL IN THE KIVA CODE S. L. Yang, C. Y. Teo, and Y. K. Siow Department of Mechanical Engineering Engineering Mechanics Michigan Technological University Houghton, Michigan R.R. Tacina and P.F. Penko Combustion Technology Branch NASA Glenn Research Center Cleveland, Ohio ABSTRACT The flowfield in a lean-direct injection (LDI) combustor with discrete-jet swirlers is described and analyzed using a computational-fluid-dynamics (CFD) code with a Reynolds Stress Turbulence Model (RSTM). The results from the RSTM are compared to time-averaged laser-doppler velocimetry (LDV) data, as well as results from the National Combustion Code (NCC) that has a cubic non-linear κ ε turbulence model. The comparison of results from the two codes indicates that the RSTM does a better job of resolving recirculation zones and high velocity-gradients than the κ ε model. This confirms that, within the Reynolds averaging approach, the higher-order RSTM is preferred for simulating complex flowfields where separations, strong anisotropy, and high swirl are present. INTRODUCTION Flame stability over a wide range of operating conditions is a basic requirement for through-flow combustion devices, such as gas turbine combustors. One common practice used to stabilize combustion is generation of swirling flow that entrains and recirculates a portion of the hot combustion products. For direct injection engine, the recirculation zones also enhance the mixing of the incoming air with fuel. This effect is readily accomplished by use of swirlers, such as discrete jet swirlers, surrounding the fuel injector. 1 Air swirlers are often used in many types of aircraft engines. In the lean direct injection (LDI) concept, a key feature is the injection of finely atomized fuel into the high-swirling airflow at the combustor dome that provides a homogenous, lean fuel-air Associate Professor Graduate Research Assistant Aerospace Engineer 1
mixture. This allows for a better combustion efficiency and the reduction of NO x and other pollutant. Another advantage of the LDI concept is that, with proper design of swirler configuration, a shorter combustor length is possible. Accordingly, to fully realize the potential of the LDI concept, a good understanding of the complex, turbulent swirling flow inside the combustor becomes essential. To effectively calculate flowfield where swirl, wall effect, flow separation and recirculation are present, a high-level turbulence model should be used. The most widely used turbulence model in current advanced CFD codes is the κ ε model, such as the cubic non-linear model 2,3 used in the National Combustion Code 4, (NCC). Its popularity is due to the relative ease of implementation and its low CPU and memory overhead. It does, however, have considerable drawbacks for use in resolving flow with high gradients of velocity and swirl. Regardless of the advantages of the κ ε model, it has a tendency to yield inconsistent and diffusive results for complex flows because of its isotropic nature in modeling eddy viscosity. Without ad-hoc modifications, the κ ε model often does not completely describe the large gradients in swirling and recirculating flows. For more accurate calculations of the complex flowfield typical of an engine, or a combustor with high degree of swirl, use of a higher-order turbulence model is more appropriate. Unlike the κ ε models, the Reynolds Stress Turbulence Model (RSTM) naturally resolves flow anisotropy, streamline curvature, sudden changes in strain rate, secondary motions, flow in rotation (swirl flow) etc. This is mainly due to the fact that each Reynolds-stress component has its own transport equation. In addition, the source terms in the RSTM are exact and need not be modeled. This greatly improves the accuracy and robustness of the solver. All in all, the RSTM represents the most comprehensive description of turbulent flows within the framework of the Reynolds averaging approach. 6 Despite the added complexity due to the number of equations in the modeling, the applicability of the RSTM has been made feasible by present-day computer capacity. In addition to obtaining a better understanding of the complex flow physics inside the combustor, the main purpose of this paper is to present cold-flow calculations of the flowfield in an LDI combustor with a discrete-jet swirler array using the KIVA-3V 7 code with an RSTM. 8,9 It also aims to compare the RSTM results to the same calculations done with the NCC that has a cubic nonlinear κ ε models, which has been tuned for swirl flow calculations. 1-13 Both calculated results are compared to laser-doppler velocimetry (LDV) data 14 for the same configuration and operating conditions. Result comparisons show that, for such a complex flow geometry and physics, the RSTM performs substantially better than the cubic non-linear κ ε turbulence model in the NCC. ACKNOWLEDGEMENT The authors would to thank NASA for their financial assistance under NASA Grant Contract #: NAG3 288. The authors also wish to thank Mr. Anthony C. Iannetti of NASA GRC for providing valuable comments, the LDV data, and the NCC results. 2
REFERENCES 1. Lefebvre, Arthur H., Gas Turbine Combustion, Hemisphere Publishing Corporation, USA, 1983. 2. Shih, T.-H., Chen, K.-H., Liu, N.-S., and Lumley, J. L., Modeling of Turbulent Swirling Flows, NASA-TM 113112, 1998. 3. Shih, T.-H., Chen, K.-H., and Liu, N.-S., A Non-Linear k-epsilon Model for Turbulent Shear Flows, AIAA Paper 98-3983, 1998. 4. Stubbs, R.M. and Liu, N.-S., Preview of the National Combustion Code, AIAA 97-3314, 33 rd AIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit, July 6-9, Seattle, WA, USA.. Quealy, A., Ryder, R., Norris, A., and Liu, N. -S., National Combustion Code: Parallel Implementation and Performance, NASA TM-2-2981, 2. 6. Hanjalic, K., Second-moment turbulence closures for CFD: needs and prospects, Int. J. Comp. Fluid Dynamics, Vol. 12, pp. 67-97, 1999. 7. Amsden, A. A., KIVA-3V, Release 2, Improvements to KIVA-3V, Los Alamos National Laboratory, LA-1368-MS, Los Alamos, NM, 1999. 8. Speziale, C. G., Sarkar, S., and Gatski, T. B., Modeling the Pressure-Strain Correlation of Turbulence: an Invariant Dynamical Systems Approach, J. of Fluid Mechanics, Vol. 227, pp. 24 272, 1991. 9. Yang, S. L., Peschke, B. D., and Hankalic, K., Second-Moment Closure Model for IC Engine Flow Simulation Using KIVA Code, ASME J. of Engineering for Gas Turbines and Power, Vol. 122, No. 2, pp. 37 36, 2. 1. Iannetti, A., Tacina, R., Jeng, S. -M., and Cai, J., Toward Accurate Prediction of Turbulence, Three-Dimensional, Recirculation Flows with the NCC, AIAA-21-89, 39 th AIAA Aerospace Sciences Meeting and Exhibit, Reno, NV, USA, January 8 11, 21. 11. Iannetti, A., Tacina, R., Cai, J., and Jeng, S.-M., Multi-Swirler Aerodynamics: CFD Predictions, AIAA 21-37, 37 th AIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit, Salt Palace, Salt Lake City, UT, USA, July 8-11, 21 12. Craft, T. J., Launder, B. E., and Suga, K., Extending the Applicability of Eddy Viscosity Models through the Use of Deformation Invariations and Non-Linear Elements, th IAHR Conference on Refined-Flow Modeling and Turbulence Measurement, Paris, September 7 1, 1993. 13. Shih, T.-H., Lumley, J. L., Remarks on Turbulent Constitutive Relations, Math. Comput. Modeling 18, 9-6, 1993. 14. Jeng, S.-M, Cai, J., Tacina, R., Multi-Swirler Aerodynamics: Experimental Measurements, AIAA 21-374, 37 th AIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit, Salt Palace, Salt Lake City, UT, USA, July 8-11, 21. 3
X Y 7.62 cm 7.62 cm Z 1.27 cm.63 cm cm.3 cm 1.3 cm 2.3 cm.3 cm Figure 1 Medium-Grid Computational Mesh X Y Z Figure 2 Orientation of the Discrete-Jet Swirler Array (Medium-Grid) 4
(a) NCC k-e result (b) RSTM result (c) LDV measurement Figure 3 Axial (W) Velocity Contours at Z =.3 cm (a) NCC k-e result (b) RSTM result (c) LDV measurement Figure 4 Axial (W) Velocity Contours at Z = 1.3 cm
1 1 4 k - e model 1 k - e model 1 4 1 3 1 3 1 2 1 2 1 1 1 1 Swirl Velocity [m/s] 1 9 8 7 6 4 Swirl Velocity [m/s] 1 9 8 7 6 4 3 3 2 2 1 1 2 3 4 6 Z Ax is a t X = 2. 4 cm, Y = -2. 4 cm (a) 1 1 2 3 4 6 Z Ax is a t X = 1.2 7 cm, Y = -1. 2 7 cm (b) Figure Swirl Velocity Line Plots 2 2 1 k - e model 2 k - e model 2 1 Axial (W) Velocity [m/s] 1 - -1 Axial(W) Velocity[m/s] 1 - - 1-1 - 1-2 - 2-2 1 2 3 4 6 Z Axis at X = 2.4 cm, Y = -2.4 cm (a) - 2 1 2 3 4 6 Z Axis at X = 1.27 cm, Y = -1.27 cm (b) Figure 6 Axial (W) Velocity Line Plots Turbulent Kinetic Energy (k) [m 2 /s 2 ] 1 6 1 4 1 2 1 8 6 4 2 1 2 3 4 6 Z Axi s a t X = 2. 4 c m, Y = -2. 4 c m (a) k- e model R ST M EX P Turbulent Kinetic Energy (k) [m 2 /s 2 ] 3 k- e m odel R STM EX P 2 7 2 2 2 2 1 7 1 1 2 1 7 2 1 2 3 4 6 Z Ax is a t X = 1. 2 7 c m, Y = -1.2 7 c m (b) Figure 7 Turbulent Kinetic Energy (k) Line Plots 6