American Institute of Mathematical Sciences

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

Mesh convergence for turbulent combustion

Xiaoxue Gong 1, , Ying Xu 1, , Vinay Mahadeo 1, , Tulin Kaman 2, , Johan Larsson 3, and  James Glimm 1,

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.
Keywords: Finite rate chemistry, turbulent combustion, reduced reaction mechanism, mesh convergence., scramjet.
Mathematics Subject Classification: Primary: 76N, 76.
Citation: Xiaoxue Gong, Ying Xu, Vinay Mahadeo, Tulin Kaman, Johan Larsson, James Glimm. Mesh convergence for turbulent combustion. Discrete & Continuous Dynamical Systems - A, 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.  doi: 10.1017/jfm.2011.164.  Google Scholar

[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.  doi: 10.1016/0010-2180(95)00031-Z.  Google Scholar

[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.  doi: 10.1016/j.proci.2012.07.046.  Google Scholar

[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.  doi: 10.1016/j.combustflame.2010.10.023.  Google Scholar

[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.  doi: 10.1016/j.combustflame.2008.04.013.  Google Scholar

[6]

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

[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.   Google Scholar

[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).  doi: 10.2514/6.2012-612.  Google Scholar

[9]

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

[10]

X. Gong, Turbulent Combustion Study of Scramjet Problem,, PhD thesis, (2015).   Google Scholar

[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.), (1983), 55.   Google Scholar

[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.  doi: 10.1016/j.combustflame.2010.10.002.  Google Scholar

[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, (1988).   Google Scholar

[14]

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

[15]

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

[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.   Google Scholar

[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.  doi: 10.1016/j.combustflame.2014.09.017.  Google Scholar

[18]

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

[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).   Google Scholar

[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.  doi: 10.1063/1.858164.  Google Scholar

[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.  doi: 10.1017/S0022112004000266.  Google Scholar

[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).   Google Scholar

[23]

N. Peters, Turbulent Combustion,, Cambridge university press, (2000).  doi: 10.1017/CBO9780511612701.  Google Scholar

[24]

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

[25]

T. Poinsot and D. Veynante, Theoretical and Numerical Combustion,, Edwards, (2005).   Google Scholar

[26]

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

[27]

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

[28]

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

[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, (1999).   Google Scholar

[30]

V. Terrapon, F. Ham, R. Pecnik and H. Pitsch, A flamelet-based model for supersonic combustion,, Annual Research Briefs, (): 47.   Google Scholar

[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.  doi: 10.1007/s00162-009-0103-z.  Google Scholar

[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.  doi: 10.1063/1.1785131.  Google Scholar

[33]

F. Williams et al., Chemical-kinetic Mechanisms for Combustion Applications,, University of California, ().   Google Scholar

[34]

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

[35]

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

[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.  doi: 10.1080/00102209108951759.  Google Scholar

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.  doi: 10.1017/jfm.2011.164.  Google Scholar

[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.  doi: 10.1016/0010-2180(95)00031-Z.  Google Scholar

[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.  doi: 10.1016/j.proci.2012.07.046.  Google Scholar

[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.  doi: 10.1016/j.combustflame.2010.10.023.  Google Scholar

[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.  doi: 10.1016/j.combustflame.2008.04.013.  Google Scholar

[6]

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

[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.   Google Scholar

[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).  doi: 10.2514/6.2012-612.  Google Scholar

[9]

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

[10]

X. Gong, Turbulent Combustion Study of Scramjet Problem,, PhD thesis, (2015).   Google Scholar

[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.), (1983), 55.   Google Scholar

[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.  doi: 10.1016/j.combustflame.2010.10.002.  Google Scholar

[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, (1988).   Google Scholar

[14]

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

[15]

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

[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.   Google Scholar

[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.  doi: 10.1016/j.combustflame.2014.09.017.  Google Scholar

[18]

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

[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).   Google Scholar

[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.  doi: 10.1063/1.858164.  Google Scholar

[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.  doi: 10.1017/S0022112004000266.  Google Scholar

[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).   Google Scholar

[23]

N. Peters, Turbulent Combustion,, Cambridge university press, (2000).  doi: 10.1017/CBO9780511612701.  Google Scholar

[24]

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

[25]

T. Poinsot and D. Veynante, Theoretical and Numerical Combustion,, Edwards, (2005).   Google Scholar

[26]

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

[27]

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

[28]

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

[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, (1999).   Google Scholar

[30]

V. Terrapon, F. Ham, R. Pecnik and H. Pitsch, A flamelet-based model for supersonic combustion,, Annual Research Briefs, (): 47.   Google Scholar

[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.  doi: 10.1007/s00162-009-0103-z.  Google Scholar

[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.  doi: 10.1063/1.1785131.  Google Scholar

[33]

F. Williams et al., Chemical-kinetic Mechanisms for Combustion Applications,, University of California, ().   Google Scholar

[34]

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

[35]

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

[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.  doi: 10.1080/00102209108951759.  Google Scholar

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