A computational framework for predicting laminar reactive flows with soot formation

Combustion Theory and Modelling

Volumn 14, Issue 6, 2010, Pages 793-825

  Charest, Marc R J ^a   Groth, Clinton P T ^a   Gülder, Ömer L ^a  

^a UNIVERSITY OF TORONTO   (Canada)

Author keywords

Adaptive mesh refinement; Laminar diffusion flames; Numerical modeling; Parallel computation; Soot formation

Indexed keywords

ADAPTIVE MESH REFINEMENT; LAMINAR DIFFUSION FLAMES; NUMERICAL MODELING; PARALLEL COMPUTATION; SOOT FORMATION;

ALGORITHMS; COMPUTER ARCHITECTURE; DIFFUSION; DUST; ETHYLENE; FORECASTING; METHANE; MODELS; NUMERICAL METHODS; PHASE INTERFACES; SOOT;

COMBUSTION;

EID: 78649364788     PISSN: 13647830     EISSN: 17413559     Source Type: Journal    
DOI: 10.1080/13647830.2010.512960     Document Type: Article

References (99)

1. A. Ern, C.C. Douglas, and M.D. Smooke, Detailed chemistry modeling of laminar diffusion flames on parallel computers, Int. J. Supercomput. Ap. 9 (1995), pp. 167-186.
2. M.D. Smooke, C.S. McEnally, L.D. Pfefferle, R.J. Hall, and M.B. Colket, Computational and experimental study of soot formation in a coflow, laminar diffusion flame, Combust. Flame 117 (1999),117-139.
3. C. Davies and P.W. Carpenter, A novel velocity-vorticity formulation of the Navier-Stokes equations with applications to boundary layer disturbance evolution, J. Comput. Phys. 172 (2001), pp. 119-165.
4. P. Deuflhard, A modified Newton method for the solution of ill-conditioned systems of nonlinear equations with application to multiple shooting, Numer. Math. 22 (1974), pp. 289-315.
5. R.J. Hall, M.D. Smooke, and M.B. Colket, Prediction of soot dynamics in opposed jet diffusion flames. In: F Dryer, R Sawyer (Eds.), Physical and Chemical Aspects of Combustion: A Tribute to Irvin Glassman. Amsterdam: Gordon & Breach, 1997, pp. 189-230.
6. M.D. Smooke, M.B. Long, B.C. Connelly, M.B. Colket, and R.J. Hall, Soot formation in laminar diffusion flames, Combust. Flame 143 (2005), pp. 613-628.
7. F.C. Lockwood and N.G. Shah, A new radiation solution method for incorporation in general combustion prediction procedures, Proc. Combust. Inst. 18(1) (1981), pp. 1405-1414.
8. W.L. Grosshandler, RADCAL: A narrow-band model for radiation calculations in a combustion environment, NIST Technical Note 1402 (1993).
9. S.B. Dworkin, B.A.V. Bennett, and M.D. Smooke, A mass-conserving vorticity-velocity formulation with application to nonreacting and reacting flows, J. Comput. Phys. 215 (2006), pp. 430-447.
10. S.B. Dworkin, J.A. Cooke, B.A.V. Bennett, B.C. Connelly, M.B. Long, M.D. Smooke, R.J. Hall, and M.B. Colket, Distributed-memory parallel computation of a forced, time-dependent, sooting, ethylene/air coflow diffusion flame, Combust. Theor. Model. 13 (2009), pp. 795-822.
11. A. D'Anna, A. D'Alessio, and J.H. Kent, A computational study of hydrocarbon growth and the formation of aromatics in coflowing laminar diffusion flames, Combust. Flame 125 (2001), pp. 1196-1206.
12. W.J. Minkowycz, E.M. Sparrow, G.E. Schneider, and R.H. Pletcher, Handbook of Numerical Heat Transfer, John Wiley, New York, 1988.
13. A. D'Anna and J.H. Kent, Aromatic formation pathways in non-premixed methane flames, Combust. Flame 132 (2003), pp. 715-722.
14. A. D'Anna, G. Mazzotti, and J. Kent, Modeling of particulate formation in a coflowing diffusion flame, Combust. Sci. Tech. 176 (2004), pp. 753-767.
15. A. D'Anna and J.H. Kent, A model of particulate and species formation applied to laminar, nonpremixed flames for three aliphatic-hydrocarbon fuels, Combust. Flame 152 (2008), pp. 573-587.
16. F. Liu, H. Guo, G.J. Smallwood, and Ö.L. Gülder, Effects of gas and soot radiation on soot formation in a coflow laminar ethylene diffusion flame, J. Quant. Spectrosc. Radiat. Transfer 73 (2002), pp. 409-421.
17. H. Guo, F. Liu, G.J. Smallwood, and Ö.L. Gülder, The flame preheating effect on numerical modelling of soot formation in a two-dimensional laminar ethylene-air diffusion flame, Combust. Theor. Model. 6 (2002), pp. 173-187.
18. M. Fairweather, W.P. Jones, and R.P. Lindstedt, Predictions of radiative transfer from a turbulent reacting jet in a cross-wind, Combust. Flame 89 (1992), pp. 45-63.
19. K.M. Leung, R.P. Lindstedt, and W.P. Jones, A simplified reaction mechanism for soot formation in nonpremixed flames, Combust. Flame 87 (1991), pp. 289-305.
20. B.G. Carlson and K.D. Lathrop, Transport theory - The method of discrete ordinates, in Computing Methods in Reactor Physics, H. Greenspan, C.N. Kelber, and D. Okrent, eds., Gordon and Breach, London, 1968, pp. 171-266.
21. F. Liu, G.J. Smallwood, and Ö.L. Gülder, Band lumping strategy for radiation heat transfer calculations using a narrowband model, J. Thermophys. Heat Transfer 14 (2000), pp. 278-281.
22. S.V. Patankar, Numerical Heat Transfer and Fluid Flow, Taylor & Francis, London, 1980.
23. Z. Liu, C. Liao, C. Liu, and S. McCormick, Multigrid method for multi-step finite rate combustion, AIAA paper 95-0205 (1995).
24. Q. Zhang, H. Guo, F. Liu, G.J. Smallwood, and M.J. Thomson, Implementation of an advanced fixed sectional aerosol dynamics model with soot aggregate formation in a laminar methane/air coflow diffusion flame, Combust. Theor. Model. 12 (2008), pp. 621-641.
25. M.S. Day and J.B. Bell, Numerical simulation of laminar reacting flows with complex chemistry, Combust. Theor. Model. 4 (2000), pp. 535-556.
26. R.B. Pember, L.H. Howell, J.B. Bell, P. Colella, W.Y. Crutchfield, W.A. Fiveland, and J.P. Jessee, An adaptive projection method for unsteady, low-Mach number combustion, Combust. Sci. Tech. 140 (1998), pp. 123-168.
27. J.B. Bell, A.J. Aspden, M.S. Day, and M.J. Lijewski, Numerical simulation of low Mach number reacting flows, J. Phys: Conf. Ser. 78 (2007) doi: 10.1088/1742-6596/78/1/012004.
28. rd AIAAA ero space Sciences Meeting and Exhibit, Reno, Nevada, AIAA paper 2005-0547, 10-13 January, 2005.
29. S.A. Northrup and C.P.T. Groth, Solution of laminar combusting flows using a parallel implicit adaptive mesh refinement algorithm, in Proceedings of the Fourth International Conference on Computational Fluid Dynamics, ICCFD4, Ghent, Belgium, 10-14 July, 2006, pp. 341-346.
30. K.K. Kuo, Principles of Combustion, 2nd edn, John Wiley, New Jersey, 2005.
31. J.O. Hirschfelder, C.F. Curtiss, and R.B. Byrd, Molecular Theory of Gases and Liquids, John Wiley, New York, 1969.
32. I.M. Kennedy, W. Kollmann, and J.Y. Chen, A model for the soot formation in a laminar diffusion flame, Combust. Flame 81 (1990), pp. 73-85.
33. A. Gomez and D.E. Rosner, Thermophoretic effects on particles in counterflow laminar diffusion flames, Combust. Sci. Tech. 89 (1993), pp. 335-362.
34. ◦C, in Proceedings of the Fifth Conference on Carbon, Pergamon Press, London, 1962, pp. 154-164.
35. J.B. Moss, C.D. Stewart, and K.J. Young, Modeling soot formation and burnout in a high temperature laminar diffusion flame burning under oxygen-enriched conditions, Combust. Flame 101 (1995), pp. 491-500.
36. D. Bradley, G. Dixon-Lewis, S.E. Habik, and E.M.J. Mushi, The oxidation of graphite powder in flame reaction zones, Proc. Combust. Inst. 20 (1984), pp. 931-940.
37. O.A. Ezekoye and Z. Zhang, Soot oxidation and agglomeration modeling in a microgravity diffusion flame, Combust. Flame 110 (1997), pp. 127-139.
38. R. Viskanta and M.P. Mengüç, Radiation heat transfer in combustion systems, Prog. Energy Combust. Sci. 13 (1987), pp. 97-160.
39. A.A. Lacis and V. Oinas, A description of the correlated k distribution method for modeling nongray gaseous absorption, thermal emission, and multiple scattering in vertically inhomogeneous atmospheres, J. Geophys. Res. 96 (1991), pp. 9027-9063.
40. C.P. Thurgood, A. Pollard, and H.A. Becker, TN quadrature set for the discrete ordinates method, J. Heat Transfer 117 (1995), pp. 1068-1070.
41. S. Jendoubi, H.S. Lee, and T.K. Kim, Discrete ordinates solutions for radiatively participating media in a cylindrical enclosure, J. Thermophys. Heat Transfer 7 (1993), pp. 213-219.
42. A. Soufiani and J. Taine, High temperature gas radiative property parameters of statistical narrow-band model for H2O, CO2 and CO, and correlated-K model for H2O and CO2, Int. J. Heat Mass Transfer 40 (1997), pp. 987-991.
43. F. Liu, G.J. Smallwood, and Ö.L. Gülder, Application of the statistical narrow-band correlated-k method to non-grey gas radiation in CO2-H2O mixtures: Approximate treatments of overlapping bands, J. Quant. Spectrosc. Radiat. Transfer 68 (2001), pp. 401-417.
44. V. Goutière, A. Charette, and L. Kiss, Comparative performance of nongray gas modeling techniques, Numer. Heat Transfer, Part B 41 (2002), pp. 361-381.
45. M.F. Modest, Radiative Heat Transfer, 2nd edn, Academic Press, New York, 2003.
46. S.A. Northrup and C.P.T. Groth, Parallel implicit adaptive mesh refinement algorithm for solution of laminar combusting flows, in Proceedings of the 14th Annual Conference of the CFD Society of Canada, Kingston, Ontario, Canada, paper 1106, 16-18 July 2006, pp. 221-228.
47. X. Gao and C.P.T. Groth, Parallel adaptive mesh refinement scheme for turbulent non-premixed combusting flow prediction, 44th AIAA Aerospace Sciences Meeting and Exhibit, Reno, Nevada, Vol. 23, AIAA paper 2006-1448, 9-12 January 2006, pp. 17450-17463.
48. S. Venkateswaran and C.L. Merkle, Analysis of preconditioning methods for the Euler and Navier-Stokes equations, Von Karman Institute Lecture Series, 1999.
49. J.M. Weiss and W.A. Smith, Preconditioning applied to variable and constant density flows, AIAA J. 33 (1995), pp. 2050-2057.
50. J.M. Weiss, J.P. Maruszewski, and W.A. Smith, Implicit solution of preconditioned NavierStokes equations using algebraic multigrid, AIAA J. 37 (1999), pp. 29-36.
51. Y.-H. Choi and C.L. Merkle, The application of preconditioning in viscous flows, J. Comput. Phys. 105 (1993), pp. 207-223.
52. S.K. Godunov, Fintite-difference method for numerical computations of discontinuous solutions of the equations of fluid dynamics, Mat. Sb. 47 (1959), pp. 271-306.
53. P.L. Roe, Approximate Riemann solvers, parameter vectors, and difference schemes, J. Comput. Phys. 43 (1981), pp. 357-372.
54. P.L. Roe and J. Pike, Efficient construction and utilisation of approximate Riemann solutions, in Computing Methods in Applied Science and Engineering, Vol. VI, R. Glowinski and J.L. Lions, eds., North-Holland, Amsterdam, 1984, pp. 499-518.
55. A. Harten, High resolution schemes for hyperbolic conservation laws, J. Comput. Phys. 49 (1983), pp. 357-393.
56. J.S. Shuen, Inviscid flux-splitting algorithms for real gases with non-equilibrium chemistry, J. Comput. Phys. 90 (1990), pp. 371-395.
57. R. Walters, P. Cinnella, D. Slack, and D. Halt, Characteristic-based algorithms for flows in thermochemical nonequilibrium, AIAA J. 30 (1992), pp. 1304-1313.
58. B. Engquist and S. Osher, One-sided difference approximations for nonlinear conservation laws, Math. Comp. 36 (1981), pp. 321-352.
59. B. van Leer, Towards the ultimate conservative difference scheme. V. A second-order sequel to Godunov's method, J. Comput. Phys. 32 (1979), pp. 101-136.
60. V. Venkatakrishnan, Convergence to steady state solutions of the Euler equations on unstructured grids with limiters, J. Comput. Phys. 118 (1995), pp. 120-130.
61. T.J. Barth and D.C. Jespersen, The design and application of upwind schemes on unstructured meshes, AIAA Paper 89-0366, 1989.
62. W.J. Coirier, An adaptively-refined, Cartesian, cell-based scheme for the Euler and NavierStokes equations, PhD thesis, University of Michigan, 1994.
63. W.J. Coirier and K.G. Powell, Solution-adaptive Cartesian cell approach for viscous and inviscid flows, AIAA J. 34 (1996), pp. 938-945.
64. D.W. Zingg and M. Yarrow, A method of smooth bivariate interpolation for data given on a generalized curvilinear grid, SIAM J. Sci. Stat. Comput. 13 (1992), pp. 687-693.
65. C.P.T. Groth and S.A. Northrup, Parallel implicit adaptive mesh refinement scheme for bodyfitted multi-block mesh, 17th AIAA Computational Fluid Dynamics Conference, Toronto, Ontario, Canada, AIAA paper 2005-5333, 6-9 June 2005.
66. Y. Saad and M.H. Schultz, GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems, SIAM J. Sci. Stat. Comput. 7 (1986), pp. 856-869.
67. Y. Saad, Krylov subspace methods on supercomputers, SIAM J. Sci. Stat. Comput. 10 (1989), pp. 1200-1232.
68. P.N. Brown and Y. Saad, Hybrid Krylov methods for nonlinear systems of equations, SIAM J. Sci. Stat. Comput. 11 (1990), pp. 450-481.
69. Y. Saad, Iterative Methods for Sparse Linear Systems, PWS Publishing Company, Boston, 1996.
70. D.A. Knoll and D.E. Keyes, Jacobian-free Newton-Krylov methods: A survey of approaches and applications, J. Comput. Phys. 193 (2004), pp. 357-397.
71. R.S. Dembo, S.C. Eisenstat, and T. Steihaug, Inexact Newton methods, SIAM J. Numer. Anal. 19 (1982), pp. 400-408.
72. W.A. Mulderand B. van Leer, Experiments with implicit up wind methods for the Euler equations, J. Comput. Phys. 59 (1985), pp. 232-246.
73. J.S. Sachdev, C.P.T. Groth, and J.J. Gottlieb, A parallel solution-adaptive scheme for multi-phase core flows in solid propellant rocket motors, Int. J. Comput. Fluid Dyn. 19 (2005), pp. 159-177.
74. J.S. Sachdev and C.P.T. Groth, A mesh adjustment scheme for embedded boundaries, Commun. Comput. Phys. 2 (2007), pp. 1095-1124.
75. X. Gao and C.P.T. Groth, Parallel adaptive mesh refinement scheme for three-dimensional turbulent non-premixed combustion, 46th AIAA Aerospace Sciences Meeting and Exhibit, Reno, Nevada, AIAA paper 2008-1017, 7-10 January, 2008.
76. M.J. Berger, Adaptive mesh refinement for hyperbolic partial differential equations, J. Comput. Phys. 53 (1984), pp. 484-512.
77. M.J. Berger and P. Colella, Local adaptive mesh refinement for shock hydrodynamics, J. Comput. Phys. 82 (1989), pp. 67-84.
78. M.J. Berger and J.S. Saltzman, AMR on the CM-2, Appl. Numer. Math. 14 (1994), pp. 239-253.
79. M.J. Aftomis, M.J. Berger and J.E. Melton, Robust and efficient Cartesian mesh generation for component-base geometry, AIAA J. 36 (1998), pp. 952-960.
80. J.J. Quirk, An adaptive grid algorithm for computational shock hydrodynamics, PhD thesis, Cranfield Institute of Technology, 1991.
81. D. de Zeeuw and K.G. Powell, An adaptively refined Cartesian mesh solver for the Euler equations, J. Comput. Phys. 104 (1993), pp. 56-68.
82. J.J. Quirk and U.R. Hanebutte, A parallel adaptive mesh refinement algorithm, ICASE Report 93-63, 1993.
83. W. Gropp, E. Lusk, and A. Skjellum, Using MPI, MIT Press, Cambridge, MA, 1999.
84. J. Gonçalves and P.J. Coelho, Parallelization of the discrete ordinates method, Numer. Heat Transfer, Part B 32 (1997), pp. 151-173.
85. L.H. Howell, A parallel AMR implementation of the discrete ordinates method for radiation transport, in Adaptive Mesh Refinement - Theory and Applications, Lecture Notes in Computational Science and Engineering, Vol. 41, T. Plewa, T. Linde, and V.G. Weirs, eds., Springer, Berlin, 2005, pp. 255-270.
86. M.R.J. Charest, C.P.T. Groth, and Ö.L. Gülder, Solution of the equation of radiative transfer using a Newton-Krylov approach and adaptive mesh refinement, Submitted to the Journal of Computational Physics, 2010.
87. E. Turkel, R. Radespiel, and N. Kroll, Assessment of preconditioning methods for multidimensional aerodynamics, Comput. Fluids 26 (1997), pp. 613-634.
88. D.G. Goodwin, An open-source, extensible software suite for CVD process simulation, Chemical Vapor Deposition XVI and EUROCVD 14, 2003, pp. 155-162.
89. F. Liu, H. Guo, and G.J. Smallwood, Effects of radiation model on the modeling of a laminar coflow methane/air diffusion flame, Combust. Flame 138 (2004), pp. 136-154.
90. G.P. Smith, D.M. Golden, M. Frenklach, N.W. Moriarty, B. Eiteneer, M. Goldenberg, C.T. Bowman, R.K. Hanson, S. Song, W.C. Jr. Gardiner, V.V. Lissianski, and Z. Qin, GRI-Mech 3.0, 2002. http://www.me.berkeley.edu/gri mech/.
91. D.R. Snelling, K.A. Thomson, G.J. Smallwood, and Ö.L. Gülder, Two-dimensional imaging of soot volume fraction in laminar diffusion flames, Appl. Opt. 38 (1999), pp. 2478-2485.
92. C.K. Law, Comprehensive description of chemistry in combustion modeling, Combust. Sci. Tech. 177 (2005), pp. 845-870.
93. Z. Qin, V.V. Lissianski, H. Yang, W.C. Gardiner, S.G. Davis, and H. Wang, Combustion chemistry of propane: A case study of detailed reaction mechanism optimization, Proc. Combust. Inst. 28 (2000), pp. 1663-1669.
94. R. Bustinza, G.N. Gatica, and B. Cockburn, An a posteriori error estimate for the local discontinuous Galerkin method applied to linear and nonlinear diffusion problems, J. Sci. Comput. 22-23 (2005), pp. 147-185.
95. M. Nemec, M.J. Aftosmis, and M. Wintzer, Adjoint-based adaptive mesh refinement for complex geometries, AIAA Paper 2008-0725, 2008.
96. F.N. Egolfopoulos and P.E. Dimotakis, A comparative numerical study of premixed and nonpremixed ethylene flames, Combust. Sci. Tech. 162 (2001), pp. 19-35.
97. A. Kazakov and M. Frenklach, Reduced reaction sets based on GRI-Mech 1.2, 1994. http://www.me.berkeley.edu/drm/.
98. J. Appel, H. Bockhorn, and M. Frenklach, Kinetic modeling of soot formation with detailed chemistry and physics: Laminar premixed flames of C2 hydrocarbons, Combust. Flame 121 (2000), pp. 122-136.
99. G. Amdahl, Validity of the single processor approach to achieving large-scale computing capabilities, AFIPS'67 (Spring): Proceedings of the Spring Joint Computer Conference, April 18-20, 1967, pp. 483-485.