Improved Flamelet Modeling of Supersonic Combustion
Abstract
This paper has the objective of addressing a few basic issues pertaining to the use of the laminar flamelet method to model turbulence-combustion interactions in supersonic combustion. Specifically, this paper documents the way in which the use of Troe’s pressure-reaction-rate model affects the laminar flame solutions that are used in the generation of the flamelet library for supersonic combustion. For the opposed-jet model of nonpremixed flames, this study also investigates how the laminar-flamelet results obtained using the flamelet equations differ from those obtained from the canonical equations for opposed-jet flame (OJF). The differential results obtained for supersonic combustion predictions in two models of the scramjet isolator/combustor when pressure, in several formulations, is included as an independent variable of the flamelet table are also presented. Lastly, this study investigates the manner in which the use of various interpolations of the reaction progress variable from the S-curve affects turbulent supersonic combustion results. The overall goal of the various studies is to provide an improved flamelet modeling of supersonic combustion. Simulations based on linear progress variable interpolation coupled with the seven-level pressure field in the base flamelet library, using the OJF equations, appear to yield the best results.
References
[1] , “Theoretical and Experimental Investigation of Supersonic Combustion,” Aeronautical Research Laboratories Rept. 62-467, Wright-Patterson Air Force Base, Dayton, OH, 1962. doi:https://doi.org/10.1016/B978-0-08-010558-1.50011-6
[2] , “Mixing-Controlled Supersonic Combustion,” Annual Review of Fluid Mechanics, Vol. 5, No. 1, 1973, pp. 301–338. doi:https://doi.org/10.1146/annurev.fl.05.010173.001505 ARVFA3 0066-4189
[3] , “Scramjets,” The Aeronautical Journal, Vol. 111, No. 1124, 2007, pp. 605–619. doi:https://doi.org/10.1017/S0001924000004796 AENJAK 0001-9240
[4] , “Fluid Phenomenon in Scramjet Combustion Systems,” Annual Review of Fluid Mechanics, Vol. 28, No. 1, 1996, pp. 323–360. doi:https://doi.org/10.1146/annurev.fl.28.010196.001543 ARVFA3 0066-4189
[5] , “A Century of Ramjet Propulsion Technology Evolution,” Journal of Propulsion and Power, Vol. 20, No. 1, 2004, pp. 27–58. doi:https://doi.org/10.2514/1.9178 JPPOEL 0748-4658
[6] , “Methods for Prediction of High-Speed Reacting Flows in Aerospace Propulsion,” AIAA Journal, Vol. 52, No. 3, 2014, pp. 465–485. doi:https://doi.org/10.2514/1.J052283 AIAJAH 0001-1452
[7] , “Advanced Computational-Fluid-Dynamic Techniques for Scramjet Combustion Simulation,” AIAA Journal, Vol. 48, No. 3, 2010, pp. 513–514. doi:https://doi.org/10.2514/1.48989 AIAJAH 0001-1452
[8] , “Enhancements for Supersonic Combustion Simulation with VULCAN,” AIAA Paper 2010-6876, July 2010. doi:https://doi.org/10.2514/6.2010-6876
[9] , “A Critical Review of Scramjet Combustion,” AIAA Paper 2009-0036, Jan. 2009, doi:https://doi.org/10.2514/6.2009-127
[10] , “Large-Eddy Simulations of the HIFiRE Scramjet Using a Compressible Flamelet/Progress Variable Approach,” Proceedings of the Combustion Institute, Vol. 35, No. 2, 2015, pp. 2163–2172. doi:https://doi.org/10.1016/j.proci.2014.10.004
[11] , “Numerical Study of a Scramjet Combustor Fueled by an Aerodynamic Ramp Injector in a Dual-Mode Combustion,” AIAA Paper 2010-0279, Jan. 2010. doi:https://doi.org/10.2514/6.2001-379
[12] , “A Comparative Study of Flamelet and Finite Rate Chemistry LES for an Axisymmetric Dump Combustor,” Journal of Turbulence, Vol. 12, No. 24, 2011, pp. 1–20. doi:https://doi.org/10.1080/14685248.2011.582586 JTOUAO 1468-5248
[13] , “Assumed and Evolution Probability Density Functions in Supersonic Turbulent Combustion Calculations,” Journal of Propulsion and Power, Vol. 11, No. 6, 1995, pp. 1132–1138. doi:https://doi.org/10.2514/3.23951 JPPOEL 0748-4658
[14] , “Analysis of Dual-Mode Hydrocarbon Scramjet Operation at Mach 4–6.5,” Journal of Propulsion and Power, Vol. 18, No. 5, 2002, pp. 990–1002. doi:https://doi.org/10.2514/2.6047 JPPOEL 0748-4658
[15] , “Modeling Scramjet Flows with Variable Turbulent Prandtl and Schmidt Numbers,” AIAA Journal, Vol. 45, No. 6, 2007, pp. 1415–1423. doi:https://doi.org/10.2514/1.26382 AIAJAH 0001-1452
[16] , “Supersonic Combustion Simulations Using Reduced Chemical Kinetics Mechanisms and ISAT,” AIAA Paper 2003-3547, July 2003. doi:https://doi.org/10.2514/6.2003-3547
[17] , “Laminar Flamelet Concepts in Turbulent Combustion,” 21st Symposium on Combustion, The Combustion Inst., Amsterdam, The Netherlands, 1986, pp. 1231–1250.
[18] , Turbulent Combustion, 1st ed., Cambridge Univ. Press, Cambridge, England, U.K., 1994, pp. 1–261. doi:https://doi.org/10.1017/CBO9780511612701
[19] , “Flamelet Studies of Reduced and Detailed Kinetic Mechanisms for Methane/Air Diffusion Flames,” Proceedings of IGTI, ASME Turbo Expo 2000, ASME Paper 2000-GT-0144, 2000. doi:https://doi.org/10.1115/2000-GT-0144
[20] , “Performance of Sub-Grid Flamelet Model in LES of Reacting, Turbulent Flows,” DNS/LES: Progress and Challenges, edited by Liu C., Sakell L. and Beutner T., Greyden Press, Columbus, OH, 2001, pp. 299–310.
[21] , “Application of Combined LES and Flamelet Modeling to Methane, Propane, and Jet-A Combustion,” AIAA Paper 2001-0634, Jan. 2001. doi:https://doi.org/10.2514/6.2001-634
[22] , “Validation of Advanced Large Eddy Simulation Methods for Augmentor Application,” 53rd Joint Army-Navy-NASA-Air Force (JANNAF) Meeting, US Army, Navy, NASA and Air Force, Monterey, CA, 2005.
[23] , “A Combined Level-Set/Mixture Fraction/Progress-Variable Approach for Partially-Premixed Turbulent Reacting Flows,” AIAA Paper 2007-1436, Jan. 2007. doi:https://doi.org/10.2514/6.2007-1436
[24] , “An Evaluation of the Partially-Resolved Numerical Simulation Procedure for Near-Wall Performance,” AIAA Paper 2006-115, Jan. 2006.
[25] , “Level-Set Flamelet/Large-Eddy Simulation of a Premixed Augmentor Flame Holder,” AIAA Paper 2006-156, Jan. 2006. doi:https://doi.org/10.2514/6.2006-156
[26] , “An Unsteady/Flamelet Progress Variable Method for LES of Nonpremixed Turbulent Combustion,” AIAA Paper 2005-557, Jan. 2005. doi:https://doi.org/10.2514/6.2005-557
[27] , “Evaluation of an Unsteady Flamelet Progress Variable Model for Autoignition and Flame Lift-Off in Diesel Jets,” Combustion Science and Technology, Vol. 185, No. 3, 2013, pp. 454–472. doi:https://doi.org/10.1080/00102202.2012.726667 CBSTB9 0010-2202
[28] , “Steady Flamelet Progress-Variable (FPV) Modeling and Simulation of a High-Pressure Gasifier,” Energy and Fuels, Vol. 27, No. 12, 2013, pp. 7772–7777. doi:https://doi.org/10.1021/ef4014136 ENFUEH
[29] , “Large-Eddy Simulation of Turbulent Combustion,” Annual Review of Fluid Mechanics, Vol. 38, No. 1, 2006, pp. 453–482. doi:https://doi.org/10.1146/annurev.fluid.38.050304.092133 ARVFA3 0066-4189
[30] , “Studies of Hydrogen-Air Diffusion Flames and of Compressibility Effects Related to High-Speed Propulsion,” Ph.D. Dissertation, Univ. of San Diego, San Diego, CA, 1992.
[31] , “Turbulent Combustion Regimes for Hypersonic Propulsion Employing Hydrogen-Air Diffusion Flames,” Journal of Propulsion and Power, Vol. 10, No. 3, 1994, pp. 434–437. doi:https://doi.org/10.2514/3.23754 JPPOEL 0748-4658
[32] , “Comparison of Flamelet and Finite Rate Chemistry LES for Premixed Turbulent Combustion,” AIAA Paper 2007-1413, Jan. 2007. doi:https://doi.org/10.2514/6.2007-1413
[33] , “Improved Flamelet Modeling of Supersonic Combustion,” Ph.D. Thesis, Stony Brook Univ., Stony Brook, NY, May 2017.
[34] , “Pressure Treatment in the Flamelet Modeling of Turbulent Supersonic Combustion,” AIAA Paper 2017-0342, Jan. 2017.
[35] , “A RANS Flamelet-Progress-Variable Method for Computing Reacting Flows of Real-Gas Mixtures,” Computers and Fluids, Vol. 39, No. 3, 2010, pp. 485–498. doi:https://doi.org/10.1016/j.compfluid.2009.10.001 CPFLBI 0045-7930
[36] , “A Stochastic Flamelet Progerss-Variable Approach for Numerical Simulations of High-Speed Turbulent Combustion Under Chemical-Kinetic Uncertainties,” Center for Turbulence Research Annual Research Briefs, Stanford Univ., Palo Alto, CA, 2012, pp. 12–30.
[37] , “Progress-Variable Approach for Large-Eddy Simulation of Non-Premixed Turbulent Combustion,” Journal of Fluid Mechanics, Vol. 504, April 2004, pp. 73–97. doi:https://doi.org/10.1017/S0022112004008213 JFLSA7 0022-1120
[38] , “An Efficient Flamelet-Based Combustion Model for Compressible Flows,” Combustion and Flame, Vol. 162, No. 3, 2015, pp. 652–667. doi:https://doi.org/10.1016/j.combustflame.2014.08.007 CBFMAO 0010-2180
[39] , “A Priori Analysis of a Compressible Flamelet Model Using RANS Data for a Dual-Mode Scramjet Combustor,” AIAA Paper 2015-3208, June 2015. doi:https://doi.org/10.2514/6.2015-3208
[40] , “In Search of Reaction Rate Scaling Law for Supersonic Combustion,” Bulletin of the American Physical Society, Vol. 60, No. 21, 2015, Paper E6.00005. BAPSA6 0003-0503
[41] , “Scaling of Flamelet Calculation of Turbulent Supersonic Combustion,” AIAA Propulsion and Energy, AIAA Paper 2016-4567, July 2016. doi:https://doi.org/10.2514/6.2016-4567
[42] , “Pressure Treatment in the Flamelet Modeling of Turbulent Supersonic Combustion,” AIAA Paper 2017-0342, Jan. 2017. doi:https://doi.org/10.2514/6.2017-0342
[43] , “Pressure Modeling in Supersonic Combustion,” Proceedings of Asian Joint Conference on Propulsion and Power (AJCPP), The Japan Soc. of Aeronautical and Space Sciences, Tokyo, Japan, March 2016.
[44] , “FlameMaster v3.1: A C++ Computer Program for 0D Combustion and 1D Laminar Flame Calculations,” 1998, http://www.stanford.edu/group/pitsch/ [retrieved 10 Jan. 2010]
[45] , “Measured Supersonic Flame Properties-Heat-Release Patterns, Pressure Losses, Thermal Choking Limits,” Journal of Propulsion and Power, Vol. 12, No. 4, 1996, pp. 718–723. doi:https://doi.org/10.2514/3.24093 JPPOEL 0748-4658
[46] , “Combustion Oscillations in a Scramjet Engine Combustor with Transverse Fuel Injection,” Proceedings of the Combustion Institute, Vol. 30, No. 2, 2005, pp. 2851–2858. doi:https://doi.org/10.1016/j.proci.2004.08.250
[47] , “On Reduced Mechanisms for Methane-Air Combustion in Non-Premixed Flames,” Combustion and Flame, Vol. 80, No. 2, 1990, pp. 135–149. doi:https://doi.org/10.1016/0010-2180(90)90122-8 CBFMAO 0010-2180
[48] , “A Subgrid Model for Equilibrium Chemistry in Turbulent Flows,” Physics of Fluids, Vol. 6, No. 8, 1994, pp. 2868–2870. doi:https://doi.org/10.1063/1.868111
[49] , “High-Order Schemes for Navier–Stokes Equations: Algorithm and Implementation into FDL3DI,” Technical Rept. AFRL VA-WP-TR-1998-3060, Wright-Patterson Air Force Base, Dayton, OH, 1998.
[50] , “The First High-Order CFD Simulation of Aircraft: Challenges and Opportunities,” AIAA Paper 2006-1526, Jan. 2006. doi:https://doi.org/10.2514/6.2006-1526
[51] , “Chemkin-II: A Fortran Chemical Kinetics Package for the Analysis of Gas-Phase Chemical Kinetics,” Sandia National Labs. Rept. SAND-89-8009, Livermore, CA, 1989.
[52] , “A Consistent Flamelet Formulation for Non-Premixed Combustion Considering Differential Diffusion Effects,” Combustion and Flame, Vol. 114, No. 1, 1998, pp. 26–40. doi:https://doi.org/10.1016/S0010-2180(97)00278-2 CBFMAO 0010-2180
[53] , “Multicomponent Diffusion of Various Admixtures in Turbulent Flow,” Fluid Dynamics, Vol. 25, No. 3, 1990, pp. 327–334. doi:https://doi.org/10.1007/BF01049811 FLDYAH 0015-4628
[54] , “Laminar Flow Between Parallel Plates with Injection of a Reactant at High Reynolds Number,” International Journal of Heat and Mass Transfer, Vol. 21, No. 2, 1978, pp. 251–253. doi:https://doi.org/10.1016/0017-9310(78)90230-2 IJHMAK 0017-9310
[55] , “OPPDIF: A Fortran Program for Computing Opposed-Flow Diffusion Flames,” Sandia National Labs. Rept. SAND–96-8243, Livermore, CA, 1997.
[56] , “Theory of Thermal Unimolecular Reactions in the Fall-Off Range. II. Weak Collision Rate Constants,” Berichte der Bunsengesellschaft für Physikalische Chemie, Vol. 87, No. 2, 1983, pp. 169–177. doi:https://doi.org/10.1002/bbpc.19830870218
[57] , “A Comprehensive Modeling Study of Hydrogen Oxidation,” International Journal of Chemical Kinetics, Vol. 36, No. 11, 2004, pp. 603–622. doi:https://doi.org/10.1002/kin.v36:11 IJCKBO 0538-8066
[58] , “Regularization of Reaction Progress Variable for Application to Flamelet-Based Combustion Models,” Journal of Computational Physics, Vol. 231, No. 23, 2012, pp. 7715–7721. doi:https://doi.org/10.1016/j.jcp.2012.06.029
[59] , “Measured Lengths of Supersonic Hydrogen-Air Jet Flames-Compared to Subsonic Flame Lengths-and Analysis,” Combustion and Flame, Vol. 107, No. 1, 1996, pp. 176–186. doi:https://doi.org/10.1016/0010-2180(96)00048-X CBFMAO 0010-2180
[60] , The Dynamics and Thermodynamics of Compressible Fluid Flow, The Ronald Press Company, New York, 1958, pp. 190–218. doi:https://doi.org/10.1002/zamm.19550350511
[61] , “Convergence Analysis of Shock-Capturing and Shock-Fitting Solutions on Unstructured Grids,” AIAA Journal, Vol. 52, No. 7, 2014, pp. 1404–1416. doi:https://doi.org/10.2514/1.J052567 AIAJAH 0001-1452
[62] , “Comparative Advantages of High-Order Schemes for Subsonic, Transonic, and Supersonic Flows,” 45th AIAA Aerospace Sciences Meeting and Exhibit, AIAA Paper 2006-299, Jan. 2006. doi:https://doi.org/10.2514/6.2006-299
[63] , Theoretical and Numerical Combustion, RT Edwards Inc. Publ., Philadephia, PA, 2005, pp. 287–348.