August  2016, 36(8): 4383-4402. doi: 10.3934/dcds.2016.36.4383

Mesh convergence for turbulent combustion

1. 

Department of Applied Mathematics and Statistics, Stony Brook University, Stony Brook, NY 11794-3600, United States, United States, United States, United States

2. 

Department of Computer Science, ETH Zurich, Switzerland

3. 

Department of Mechanical Engineering, University of Maryland, College Park, MD 20742, United States

Received  June 2015 Revised  October 2015 Published  March 2016

Our central result is a methodology for predicting mesh convergence for three dimensional (3D) turbulent combustion simulations, based on less expensive one dimensional (1D) and two dimensional (2D) simulations. We verify the prediction by comparison to a 3D finite rate chemistry simulation based on a reduced reaction mechanism, and we further verify it by comparison to a completely independent simulation of the same problem. We validate our simulation by comparison to experiment. Additionally, we assess grid requirements for finite rate chemistry with more detailed chemical reaction mechanism. In both cases, the test problem is an engineering scale study of a model scramjet combustor designed by Gamba et al. We find that the mesh requirements are not feasible for finite rate chemistry simulations of engineering scale problems with detailed reaction mechanism, as expected, but these criteria are less severe than the Kolmogorov scale.
Citation: Xiaoxue Gong, Ying Xu, Vinay Mahadeo, Tulin Kaman, Johan Larsson, James Glimm. Mesh convergence for turbulent combustion. Discrete and Continuous Dynamical Systems, 2016, 36 (8) : 4383-4402. doi: 10.3934/dcds.2016.36.4383
References:
[1]

A. Aspden, M. Day and J. Bell, Turbulence-flame interactions in lean premixed hydrogen: Transition to the distributed burning regime, Journal of Fluid mechanics, 680 (2011), 287-320. doi: 10.1017/jfm.2011.164.

[2]

G. Balakrishnan, M. Smooke and F. Williams, A numerical investigation of extinction and ignition limits in laminar nonpremixed counterflowing hydrogen-air streams for both elementary and reduced chemistry, Combustion and Flame, 102 (1995), 329-340. doi: 10.1016/0010-2180(95)00031-Z.

[3]

J. Bell, M. Day and M. Lijewski, Simulation of nitrogen emissions in a premixed hydrogen flame stabilized on a low swirl burner, Proceedings of the Combustion Institute, 34 (2013), 1173-1182. doi: 10.1016/j.proci.2012.07.046.

[4]

P. Boivin, C. Jiménez, A. L. Sánchez and F. A. Williams, A four-step reduced mechanism for syngas combustion, Combustion and Flame, 158 (2011), 1059-1063. doi: 10.1016/j.combustflame.2010.10.023.

[5]

G. Boudier, L. Gicquel and T. Poinsot, Effects of mesh resolution on large eddy simulation of reacting flows in complex geometry combustors, Combustion and Flame, 155 (2008), 196-214. doi: 10.1016/j.combustflame.2008.04.013.

[6]

R. S. Brokaw, Viscosity of Gas Mixtures, vol. 4496, National Aeronautics and Space Administration, 1968.

[7]

O. Colin, F. Ducros, D. Veynante and T. Poinsot, High-order finite-volume adaptive methods on locally rectangular grids, Physics of Fluids, 12 (2000), 1843-1863.

[8]

M. Gamba, V. A. Miller, M. G. Mungal and R. K. Hanson, Combustion characteristics of an inlet/supersonic combustor model, in 50th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition (American Institute of Aeronautics and Astronautics, 2012), paper AIAA, vol. 0612, American Institute of Aeronautics and Astronautics, 2012. doi: 10.2514/6.2012-612.

[9]

M. Germano, U. Piomelli, P. Moin and W. H. Cabot, A dynamic subgrid scale eddy viscosity model, Phys. Fluids A, 3 (1991), 1760-1765. doi: 10.1063/1.857955.

[10]

X. Gong, Turbulent Combustion Study of Scramjet Problem, PhD thesis, State University of New York at Stony Brook, 2015.

[11]

A. C. Hindmarsh, ODEPACK, A systematized collection of ODE solvers, in Scientific Computing: Applications of Mathematics and Computing to the Physical Sciences (ed. R. S. Stepleman et al.), North-Holland, Amsterdam, 1983, 55-64.

[12]

Z. Hong, D. F. Davidson and R. K. Hanson, An improved h 2/o 2 mechanism based on recent shock tube/laser absorption measurements, Combustion and Flame, 158 (2011), 633-644. doi: 10.1016/j.combustflame.2010.10.002.

[13]

C. J. Jachimowski, An Analytical Study of the Hydrogen-Air Reaction Mechanism with Application to Scramjet Combustion, vol. 2791, National Aeronautics and Space Administration, Scientific and Technical Information Division, 1988.

[14]

G. Jiang and C.-W. Shu, Efficient implementation of weighted ENO schemes, J. Comput. Phys., 126 (1996), 202-228.

[15]

S. Kawai and J. Larsson, Wall-modeling in large eddy simulation: Length scales, grid resolution and accuracy, Phys. Fluids, 24 (2012), 015105. doi: 10.1063/1.3678331.

[16]

M. Klein, A. Sadiki and J. Janicka, A digital filter based generation of inflow data for spatially developing direct numerical or large eddy simulations, J. Comput. Phys., 186 (2003), 652-665.

[17]

J. Larsson, S. Laurence, I. Bermejo-Moreno, J. Bodart, S. Karl and R. Vicquelin, Incipient thermal choking and stable shock-train formation in the heat-release region of a scramjet combustor. part ii: Large eddy simulations, Combustion and Flame, 162 (2015), 907-920. doi: 10.1016/j.combustflame.2014.09.017.

[18]

D. K. Lilly, A proposed modification of the germano subgrid-scale closure method, Physics of Fluids A: Fluid Dynamics (1989-1993), 4 (1992), 633-635. doi: 10.1063/1.858280.

[19]

J. Melvin, P. Rao, R. Kaufman, H. Lim, Y. Yu, J. Glimm and D. H. Sharp, Turbulent transport at high reynolds numbers in an ICF context, Journal of Fluids Engineering, 136 (2014), 091206.

[20]

P. Moin, K. Squires, W. Cabot and S. Lee, A dynamic subgrid-scale model for compressible turbulence and scalar transport, Phys. Fluids A, 3 (1991), 2746-2757. doi: 10.1063/1.858164.

[21]

C. Pantano, Direct simulation of non-premixed flame extinction in a methane-air jet with reduced chemistry, Journal of Fluid Mechanics, 514 (2004), 231-270. doi: 10.1017/S0022112004000266.

[22]

P. Pepiot and H. Pitsch, Systematic reduction of large chemical mechanisms, in 4th joint meeting of the US Sections of the Combustion Institute, 2005.

[23]

N. Peters, Turbulent Combustion, Cambridge university press, 2000. doi: 10.1017/CBO9780511612701.

[24]

H. Pitsch, Flamemaster v3. 1: A c++ computer program for 0d combustion and 1d laminar flame calculations, 1998.

[25]

T. Poinsot and D. Veynante, Theoretical and Numerical Combustion, Edwards, Philadelphia, 2005.

[26]

S. B. Pope, Turbulent Flows, Cambridge University Press, 2000. doi: 10.1017/CBO9780511840531.

[27]

B. Rogg, Reduced Kinetic Mechanisms for Applications in Combustion Systems, Springer Science and Business Media, 1993.

[28]

C. Segal, The Scramjet Engine: Processes and Characteristics, vol. 25, Cambridge University Press, 2009. doi: 10.1017/CBO9780511627019.

[29]

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. Gardiner Jr et al., GRI-Mech Homepage, Gas Research Institute, Chicago, 1999, URL http://www.me.berkeley.edu/gri_mech/.

[30]

V. Terrapon, F. Ham, R. Pecnik and H. Pitsch, A flamelet-based model for supersonic combustion, Annual Research Briefs, 47-58.

[31]

E. Touber and N. D. Sandham, Large-eddy simulation of low-frequency unsteadiness in a turbulent shock-induced separation bubble, Theoretical and Computational Fluid Dynamics, 23 (2009), 79-107. doi: 10.1007/s00162-009-0103-z.

[32]

A. Vreman, An eddy-viscosity subgrid-scale model for turbulent shear flow: Algebraic theory and applications, Physics of Fluids (1994-present), 16 (2004), 3670-3681. doi: 10.1063/1.1785131.

[33]

F. Williams et al., Chemical-kinetic Mechanisms for Combustion Applications, University of California, San Diego http://maeweb. uscd. edu/~ combustion/cermech, URL http://web.eng.ucsd.edu/mae/groups/combustion/mechanism.html.

[34]

F. A. Williams, Reduced chemistry for hydrogen combustion and detonation, A lecture presented at the First European Summer School on Hydrogen Safety, 2006.

[35]

Z.-T. Xie and I. P. Castro, Efficient generation of inflow conditions for large eddy simulation of street-scale flows, Flow, turbulence and combustion, 81 (2008), 449-470. doi: 10.1007/s10494-008-9151-5.

[36]

R. Yetter, F. Dryer and H. Rabitz, A comprehensive reaction mechanism for carbon monoxide/hydrogen/oxygen kinetics, Combustion Science and Technology, 79 (1991), 97-128. doi: 10.1080/00102209108951759.

show all references

References:
[1]

A. Aspden, M. Day and J. Bell, Turbulence-flame interactions in lean premixed hydrogen: Transition to the distributed burning regime, Journal of Fluid mechanics, 680 (2011), 287-320. doi: 10.1017/jfm.2011.164.

[2]

G. Balakrishnan, M. Smooke and F. Williams, A numerical investigation of extinction and ignition limits in laminar nonpremixed counterflowing hydrogen-air streams for both elementary and reduced chemistry, Combustion and Flame, 102 (1995), 329-340. doi: 10.1016/0010-2180(95)00031-Z.

[3]

J. Bell, M. Day and M. Lijewski, Simulation of nitrogen emissions in a premixed hydrogen flame stabilized on a low swirl burner, Proceedings of the Combustion Institute, 34 (2013), 1173-1182. doi: 10.1016/j.proci.2012.07.046.

[4]

P. Boivin, C. Jiménez, A. L. Sánchez and F. A. Williams, A four-step reduced mechanism for syngas combustion, Combustion and Flame, 158 (2011), 1059-1063. doi: 10.1016/j.combustflame.2010.10.023.

[5]

G. Boudier, L. Gicquel and T. Poinsot, Effects of mesh resolution on large eddy simulation of reacting flows in complex geometry combustors, Combustion and Flame, 155 (2008), 196-214. doi: 10.1016/j.combustflame.2008.04.013.

[6]

R. S. Brokaw, Viscosity of Gas Mixtures, vol. 4496, National Aeronautics and Space Administration, 1968.

[7]

O. Colin, F. Ducros, D. Veynante and T. Poinsot, High-order finite-volume adaptive methods on locally rectangular grids, Physics of Fluids, 12 (2000), 1843-1863.

[8]

M. Gamba, V. A. Miller, M. G. Mungal and R. K. Hanson, Combustion characteristics of an inlet/supersonic combustor model, in 50th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition (American Institute of Aeronautics and Astronautics, 2012), paper AIAA, vol. 0612, American Institute of Aeronautics and Astronautics, 2012. doi: 10.2514/6.2012-612.

[9]

M. Germano, U. Piomelli, P. Moin and W. H. Cabot, A dynamic subgrid scale eddy viscosity model, Phys. Fluids A, 3 (1991), 1760-1765. doi: 10.1063/1.857955.

[10]

X. Gong, Turbulent Combustion Study of Scramjet Problem, PhD thesis, State University of New York at Stony Brook, 2015.

[11]

A. C. Hindmarsh, ODEPACK, A systematized collection of ODE solvers, in Scientific Computing: Applications of Mathematics and Computing to the Physical Sciences (ed. R. S. Stepleman et al.), North-Holland, Amsterdam, 1983, 55-64.

[12]

Z. Hong, D. F. Davidson and R. K. Hanson, An improved h 2/o 2 mechanism based on recent shock tube/laser absorption measurements, Combustion and Flame, 158 (2011), 633-644. doi: 10.1016/j.combustflame.2010.10.002.

[13]

C. J. Jachimowski, An Analytical Study of the Hydrogen-Air Reaction Mechanism with Application to Scramjet Combustion, vol. 2791, National Aeronautics and Space Administration, Scientific and Technical Information Division, 1988.

[14]

G. Jiang and C.-W. Shu, Efficient implementation of weighted ENO schemes, J. Comput. Phys., 126 (1996), 202-228.

[15]

S. Kawai and J. Larsson, Wall-modeling in large eddy simulation: Length scales, grid resolution and accuracy, Phys. Fluids, 24 (2012), 015105. doi: 10.1063/1.3678331.

[16]

M. Klein, A. Sadiki and J. Janicka, A digital filter based generation of inflow data for spatially developing direct numerical or large eddy simulations, J. Comput. Phys., 186 (2003), 652-665.

[17]

J. Larsson, S. Laurence, I. Bermejo-Moreno, J. Bodart, S. Karl and R. Vicquelin, Incipient thermal choking and stable shock-train formation in the heat-release region of a scramjet combustor. part ii: Large eddy simulations, Combustion and Flame, 162 (2015), 907-920. doi: 10.1016/j.combustflame.2014.09.017.

[18]

D. K. Lilly, A proposed modification of the germano subgrid-scale closure method, Physics of Fluids A: Fluid Dynamics (1989-1993), 4 (1992), 633-635. doi: 10.1063/1.858280.

[19]

J. Melvin, P. Rao, R. Kaufman, H. Lim, Y. Yu, J. Glimm and D. H. Sharp, Turbulent transport at high reynolds numbers in an ICF context, Journal of Fluids Engineering, 136 (2014), 091206.

[20]

P. Moin, K. Squires, W. Cabot and S. Lee, A dynamic subgrid-scale model for compressible turbulence and scalar transport, Phys. Fluids A, 3 (1991), 2746-2757. doi: 10.1063/1.858164.

[21]

C. Pantano, Direct simulation of non-premixed flame extinction in a methane-air jet with reduced chemistry, Journal of Fluid Mechanics, 514 (2004), 231-270. doi: 10.1017/S0022112004000266.

[22]

P. Pepiot and H. Pitsch, Systematic reduction of large chemical mechanisms, in 4th joint meeting of the US Sections of the Combustion Institute, 2005.

[23]

N. Peters, Turbulent Combustion, Cambridge university press, 2000. doi: 10.1017/CBO9780511612701.

[24]

H. Pitsch, Flamemaster v3. 1: A c++ computer program for 0d combustion and 1d laminar flame calculations, 1998.

[25]

T. Poinsot and D. Veynante, Theoretical and Numerical Combustion, Edwards, Philadelphia, 2005.

[26]

S. B. Pope, Turbulent Flows, Cambridge University Press, 2000. doi: 10.1017/CBO9780511840531.

[27]

B. Rogg, Reduced Kinetic Mechanisms for Applications in Combustion Systems, Springer Science and Business Media, 1993.

[28]

C. Segal, The Scramjet Engine: Processes and Characteristics, vol. 25, Cambridge University Press, 2009. doi: 10.1017/CBO9780511627019.

[29]

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. Gardiner Jr et al., GRI-Mech Homepage, Gas Research Institute, Chicago, 1999, URL http://www.me.berkeley.edu/gri_mech/.

[30]

V. Terrapon, F. Ham, R. Pecnik and H. Pitsch, A flamelet-based model for supersonic combustion, Annual Research Briefs, 47-58.

[31]

E. Touber and N. D. Sandham, Large-eddy simulation of low-frequency unsteadiness in a turbulent shock-induced separation bubble, Theoretical and Computational Fluid Dynamics, 23 (2009), 79-107. doi: 10.1007/s00162-009-0103-z.

[32]

A. Vreman, An eddy-viscosity subgrid-scale model for turbulent shear flow: Algebraic theory and applications, Physics of Fluids (1994-present), 16 (2004), 3670-3681. doi: 10.1063/1.1785131.

[33]

F. Williams et al., Chemical-kinetic Mechanisms for Combustion Applications, University of California, San Diego http://maeweb. uscd. edu/~ combustion/cermech, URL http://web.eng.ucsd.edu/mae/groups/combustion/mechanism.html.

[34]

F. A. Williams, Reduced chemistry for hydrogen combustion and detonation, A lecture presented at the First European Summer School on Hydrogen Safety, 2006.

[35]

Z.-T. Xie and I. P. Castro, Efficient generation of inflow conditions for large eddy simulation of street-scale flows, Flow, turbulence and combustion, 81 (2008), 449-470. doi: 10.1007/s10494-008-9151-5.

[36]

R. Yetter, F. Dryer and H. Rabitz, A comprehensive reaction mechanism for carbon monoxide/hydrogen/oxygen kinetics, Combustion Science and Technology, 79 (1991), 97-128. doi: 10.1080/00102209108951759.

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