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Evaluation of Flame Area Based on Detailed Chemistry DNS of Premixed Turbulent Hydrogen-Air Flames in Different Regimes of Combustion

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Abstract

Precise evaluation of flame surface area plays a pivotal role in the fundamental understanding and accurate modelling of turbulent premixed flames. This necessity is reflected in the requirement for the instantaneous flame area evaluation of the turbulent burning velocity (by making use of Damköhler’s first hypothesis). Moreover, the information regarding flame area is required in the context of flame surface density based modelling, and for determining the wrinkling factor or estimating the efficiency function. Usually flame surface areas in experiments and Direct Numerical Simulation (DNS) analyses are evaluated differently and the present analysis aims at comparing these approaches by making use of a detailed chemistry DNS database of turbulent, statistically planar flames. It has been found that the flame surface area evaluation is sensitive to the choice of scalar quantity and the isosurface level, and this holds particularly true for two-dimensional evaluations. The conditions, which provide a satisfactory agreement between experimental and numerical approaches in the flame area evaluation, have been identified by a detailed comparative analysis of the usual postprocessing techniques.

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References

  1. Peters, N.: Turbulent Combustion. Cambridge University Press (2000)

  2. Poinsot T. and Veynante D., Theoretical and Numerical Combustion, R T Edwards, (2005)

    Google Scholar 

  3. Creta, F., Matalon, M.: Propagation of wrinkled turbulent flames in the context of hydrodynamic theory. J. Fluid Mech. 680, 225–264 (2011)

    Article  MathSciNet  Google Scholar 

  4. Fogla, N., Creta, F., Matalon, M.: The turbulent flame speed for low-to-moderate turbulence intensities: hydrodynamic theory vs. experiments. Combustion and Flame. 175, 155–169 (2017)

    Article  Google Scholar 

  5. Boger, M., Veynante, D., Boughanem, H., Trouvé, A.: Direct numerical simulation analysis of flame surface density concept for large eddy simulation of turbulent premixed combustion. Proc. Combust. Inst. 27, 917–925 (1998)

    Article  Google Scholar 

  6. Driscoll, J.F.: Turbulent premixed combustion: Flamelet structure and its effect on turbulent burning velocities. Prog. Energy Combust. Sci. 34, 91–134 (2008)

    Article  Google Scholar 

  7. Chakraborty, N., Alwazzan, D., Klein, M., Cant, R.S., On the validity of Damköhler’s first hypothesis in turbulent Bunsen burner flames: A computational analysis, Proc. Combust. Inst., 37 (2018)

    Article  Google Scholar 

  8. Hawkes, E.R., and Cant, R.S., Implications of a flame surface density approach to large eddy simulation of premixed turbulent combustion. Combust. Flame, 126(3), 1617–1629. 590 https://doi.org/10.1016/S0010-2180(01)00273-5, (2001)

    Article  Google Scholar 

  9. Nivarti G., Cant S., Direct Numerical Simulation of the bending effect in turbulent premixed flames. Proc. Combust. Inst., 36. 1903–1910, (2017)

    Article  Google Scholar 

  10. Ahmed, U., Chakraborty, N. and Klein, M., Insights into the Bending Effect in Premixed Turbulent Combustion Using the Flame Surface Density Transport, Combust. Sci. Technol., accepted, (2019)

  11. Gülder, O.: Contribution of small scale turbulence to burning velocity of flamelets in the thin reaction zone regime. Proc. Combust. Inst. 31, 1369–1375 (2007)

    Article  Google Scholar 

  12. Sabelnikov, V.A., Yu, R., Lipatnikov, A.N.: Thin reaction zones in constant-density turbulent flows at low Damköhler numbers: theory and simulations. Phys. Fluids. 31, 055104 (2019)

    Article  Google Scholar 

  13. Hult, J., Gashi, S., Chakraborty, N., Klein, M., Jenkins, K.W., Cant, S., Kaminski, C.: Measurement of flame surface density for turbulent premixed flames using PLIF and DNS. Proc. Combust. Inst. 31, 1319–1326 (2007)

    Article  Google Scholar 

  14. Pope, S.B.: The evolution of surfaces in turbulence. Int. J. Eng. Sci. 26, 445–469 (1988)

    Article  MathSciNet  Google Scholar 

  15. Im, H.G., Arias, P.G., Chaudhuri, S., Uranakara, H.A.: Direct Numerical Simulations of Statistically Stationary Turbulent Premixed Flames, 10th Asia-Pacific Conference on Combustion, Topical Review, July 19–22. Beijing, China (2015)

    Google Scholar 

  16. Burke, M.P., Chaos, M., Ju, Y., Dryer, F.L., Klippenstein, S.J.: Comprehensive H2-O2 kinetic model for high-pressure combustion. I. J. Chem. Kin. 444-472, (2012)

  17. Im, H.G., Chen, J.H.: Preferential diffusion effects on the burning rate of interacting turbulent premixed hydrogen-air flames, combust. Flame. 126, 246 (2002)

    Article  Google Scholar 

  18. Klein, M., Chakraborty, N., Ketterl, S.: A Comparison of Strategies for Direct Numerical Simulation of Turbulence Chemistry Interaction in Generic Planar Turbulent Premixed Flames. Flow Turb, Combust (2017). https://doi.org/10.1007/s10494-017-9843-9

    Book  Google Scholar 

  19. Yoo, C.S., Wang, Y., Trouve, A., Im, H.G.: Characteristic boundary conditions for direct simulations of turbulent counterflow flames. Combust. Theor. Model. 9, 617–646 (2005)

    Article  MathSciNet  Google Scholar 

  20. Rogallo, R.S.: Numerical experiments in homogeneous turbulence. NASA Ames Research Center Report No. 81315, (1981)

  21. Passot, T., Pouquet, P.: Numerical simulation of compressible homogeneous flows in the turbulent regime. J. Fluid Mech. 181, 441 (1987)

    Article  Google Scholar 

  22. Chakraborty, N., Wang, L., Klein, M.: Streamline segment statistics of premixed flames with non-unity Lewis numbers. Phys. Rev. E. E89, 033015 (2014)

    Article  Google Scholar 

  23. Chaudhuri, S., Wu, F., Law, C.K.: Scaling of turbulent flame speed for expanding flames with Markstein diffusion considerations. Phys. Rev. E. 88, 033005 (2013)

    Article  Google Scholar 

  24. Chakraborty, N., Klein, M.: Influence of Lewis number on the surface density function transport in the thin reaction zones regime for turbulent premixed flames. Phys. Fluids. 20, 065102 (2008)

    Article  Google Scholar 

  25. Chakraborty, N., Klein, M., Cant, S.: Effects of turbulent Reynolds number on the displacement speed statistics in the thin reaction zones regime of turbulent premixed combustion. J. Comb. 2011, 1–19 (2011). https://doi.org/10.1155/2011/473679

    Article  Google Scholar 

  26. Klein, M., Chakraborty, N., Jenkins, K.W., Cant, R.S.: Effects of initial radius on the propagation of premixed flame kernels in a turbulent environment. Phys. Fluids. 18, 055102 (2006)

    Article  MathSciNet  Google Scholar 

  27. Wu, F., Liang, W., Chen, Z., Ju, Y., Chung, K.: Law, uncertainty in stretch extrapolation of laminar flame speed from expanding spherical flames. Proc. Combust. Inst. 35, 663–670 (2015)

    Article  Google Scholar 

  28. Giannakopoulos, G.K., Gatzoulis, A., Frouzakis, C.E., Matalon, M., Tomboulides, A.G.: Consistent definitions of “flame displacement speed” and “Markstein length” for premixed flame propagation, combustion and flame. Combust. Flame. 162, 1249–1264 (2015)

    Article  Google Scholar 

  29. Sandeep, A., Proch, F., Kempf, A.M., Chakraborty, N.: Statistics of strain rates and surface density function in a flame-resolved high-fidelity simulation of a turbulent premixed bluff body burner, Phys. Fluids. 30, 065101 (2018)

    Article  Google Scholar 

  30. Haworth, D.C.: Applications of turbulent combustion modelling, turbulent combustion, lecture series 2003-04, von Karman Institute for Fluid Dynamics. March. 17-21, (2003)

  31. Chakraborty, N., Klein, M.: A priori direct numerical simulation assessment of algebraic flame surface density models for turbulent premixed flames in the context of large eddy simulation. Fluids. 20, 065102 (2008)

    Article  Google Scholar 

  32. Utkarsh, A.: The ParaView Guide: a Parallel Visualization Application, pp. 978–1930934306. Kitware, ISBN (2015)

    Google Scholar 

  33. Pareja, J., Johchi, A., Li, T., Dreizler, A., Böhm, B.: A study of the spatial and temporal evolution of auto-ignition kernels using time-resolved tomographic OH-LIF. Proc. Combust. Inst. 37, 1321–1328 (2019)

    Article  Google Scholar 

  34. Donbar, J.M., Driscoll, J.F., Carter, C.D.: Reaction zone structure in turbulent non-premixed jet flames from CH-OH PLIF images. Combust. Flame. 122, 1–19 (2000)

    Article  Google Scholar 

  35. Jainski, C., Rißmann, M., Böhm, B., Dreizler, A.: Experimental investigation of flame surface density and mean reaction rate during flame–wall interaction. Proc. Combust. Inst. 36, 1827–1834 (2017)

    Article  Google Scholar 

  36. Canny, J.: A computational approach to edge detection. Readings in Computer Vision, Morgan Kaufmann Publishers. 184-203, (1987)

  37. Jainski, C., Rißmann, M., Böhm, B., Janicka, J., Dreizler, A.: Sidewall quenching of atmospheric laminar premixed flames studied by laser-based diagnostics. Combustion and Flame. 183, 271–282 (2017)

    Article  Google Scholar 

  38. Peterson, B., Baum, E., Böhm, B., Dreizler, A.: Early flame propagation in a spark-ignition engine measured with quasi 4D-diagnostics. Proc. Combust. Inst. 35, 3829–3837 (2015)

    Article  Google Scholar 

  39. Hawkes, E.R., Sankaran, R., Chen, J.H.: Estimates of the three-dimensional flame surface density and every term in its transport equation from two-dimensional measurements. Proc. Combust. Inst. 33, 1447–1454 (2011)

    Article  Google Scholar 

  40. Chakraborty, N., Hawkes, E.R.: Determination of 3D flame surface density variables from 2D measurements: validation using direct numerical simulation, Phys. Fluids. 23, 065113 (2011)

    Article  Google Scholar 

  41. Lorensen, W.E., Cline, H.E.: Marching cubes: a high resolution 3D surface construction algorithm. Comput. Graph. 21, 163–169 (1987)

    Article  Google Scholar 

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Funding

The authors are grateful to EPSRC, UK, the German Research Foundation (DFG, KL1456/5–1; DFG 237267381 – TRR 150) and competitive research funding from King Abdullah University of Science and Technology (KAUST) for financial support. Computational support by ARCHER, Rocket HPC, KAUST Supercomputing Laboratory is also gratefully acknowledged.

Author information

Authors and Affiliations

  1. Department of Aerospace Engineering, Bundeswehr University Munich, Neubiberg, Germany

    M. Klein, A. Herbert & J. Hasslberger

  2. Institute of Reactive Flows and Diagnostics, Technische Universität Darmstadt, Darmstadt, Germany

    H. Kosaka, B. Böhm & A. Dreizler

  3. School of Engineering, Newcastle University, Newcastle-Upon-Tyne, NE1 7RU, UK

    N. Chakraborty & V. Papapostolou

  4. Clean Combustion Research Center, KAUST, Thuwal, Saudi Arabia

    H. G. Im

Authors
  1. M. Klein
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  2. A. Herbert
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  3. H. Kosaka
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  4. B. Böhm
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  5. A. Dreizler
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  6. N. Chakraborty
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  7. V. Papapostolou
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  8. H. G. Im
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  9. J. Hasslberger
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Correspondence to M. Klein.

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Ethics Statement

This work did not involve any active collection of human data.

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We have no competing interests.

Appendix

Appendix

The Software Paraview has been used for postprocessing the isosurfaces based flame surface areas [32]. In this respect, piecewise planar interface reconstructions (more precisely a triangulation) have been employed. The very famous “Marching cube” algorithm [41] has been used in order to calculate the isosurfaces. The evaluation of surface areas for our application has been verified in the following manner: The DNS data fields specified in the paper have been filtered and subsequently sampled on grids coarsened by a factor of 2 and 4 in each direction (denoted as DNS2 and DNS4, respectively). The DNS resolution is used as a reference and the relative errors have been calculated and are reported in the Table 4 below. Results indicate that a sufficiently small error is obtained for all cases. Furthermore, as the grid is coarsened by a factor two and four respectively, it demonstrates nearly quadratic convergence of flame areas with increasing resolution (except for case C).

Table 4 Relative error in % for isosurface based flame area determination (cT = 0.5) using Paraview for cases A,B,C. DNS2 and DNS4 refer to the DNS solution filtered and sampled on a two respectively four times coarser grid
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Klein, M., Herbert, A., Kosaka, H. et al. Evaluation of Flame Area Based on Detailed Chemistry DNS of Premixed Turbulent Hydrogen-Air Flames in Different Regimes of Combustion. Flow Turbulence Combust 104, 403–419 (2020). https://doi.org/10.1007/s10494-019-00068-2

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