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Dynamic Mode Decomposition: A Tool to Extract Structures Hidden in Massive Datasets

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Data Analysis for Direct Numerical Simulations of Turbulent Combustion

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Abstract

Dynamic Mode Decomposition (DMD) is able to decompose flow field data into coherent modes and determine their oscillatory frequencies and growth/decay rates, allowing for the investigation of unsteady and dynamic phenomena unlike conventional statistical analyses. The decomposition can be applied for the analysis of data having a broad range of temporal and spatial scales since it identifies structures that characterize the physical phenomena independently from their energy content. In this work, a DMD algorithm specifically created for the analysis of massive databases is used to analyze three-dimensional Direct Numerical Simulation of spatially evolving turbulent planar premixed hydrogen/air jet flames at varying Karlovitz number. The focus of this investigation is the identification of the most important modes and frequencies for the physical phenomena, specifically heat release and turbulence, governing the flow field evolution.

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References

  1. P.J. Schmid, J.L. Sesterhenn, Bull. Am. Phys. Soc. (2008)

    Google Scholar 

  2. P.J. Schmid, J. Fluid Mech. 656 (2010)

    Article  MathSciNet  Google Scholar 

  3. C.W. Rowley, I. Mezić, S. Bagheri, P. Schlatter, D.S. Henningson, J. Fluid Mech. 641 (2009)

    Article  MathSciNet  Google Scholar 

  4. Y. Delorme, A.E. Kerlo, K. Anupindi, M.D. Rodefeld, S. Frankel, Fluid Dyn. Res. 46 (2014)

    Article  MathSciNet  Google Scholar 

  5. J. **, W. Zhao, PloS One 14(1) (2019)

    Google Scholar 

  6. J.L. Proctor, P. Welkhoff, Int. Health 7 (2015)

    Google Scholar 

  7. L. Cui, W. Long, Phys. A: Stat. Mech. Its Appl. 461 (2016)

    Google Scholar 

  8. J. Yin, B. Liu, G. Zhu, Z. **e, Sensors 18(10) (2018)

    Article  Google Scholar 

  9. J.L. Lumley, Atmospheric turbulence and radio wave propagation (1967)

    Google Scholar 

  10. J.L. Lumley, Stochastic Tools in Turbulence (Courier Corporation, North Chelmsford, 2007)

    Google Scholar 

  11. J.L. Lumley, Transition and Turbulence (Elsevier, Amsterdam, 1981)

    Google Scholar 

  12. P. Holmes, J. Lumley, G. Berkooz, Cambridge Monographs on Mechanics (Cambridge University Press, Cambridge, 1996)

    Google Scholar 

  13. K. Pearson, LIII. On lines and planes of closest fit to systems of points in space (1901)

    Article  Google Scholar 

  14. H. Hotelling, J. Educ. Psychol. 24(6) (1933)

    Google Scholar 

  15. M. Loeve, Graduate Texts in Mathematics (1978)

    Google Scholar 

  16. E.N. Lorenz, Empirical orthogonal functions and statistical weather prediction. Massachusetts Institute of Technology, Department of Meteorology, Cambridge, 1956

    Google Scholar 

  17. M. Ilak, C.W. Rowley, Phys. Fluids 20(3) (2008)

    Google Scholar 

  18. J.R. Singler, Numer. Math. 121(1) (2012)

    Google Scholar 

  19. B.O. Koopman, Proc. Natl. Acad. Sci. 17(5) (1931)

    Google Scholar 

  20. K.K. Chen, J.H. Tu, C.W. Rowley, J. Nonlinear Sci. 22(6) (2012)

    Google Scholar 

  21. Y. Saad, Linear Algebr. Its Appl. 34 (1980)

    Google Scholar 

  22. I. Mezić, A. Banaszuk, Phys. D: Nonlinear Phenom. 197(1–2), 101 (2004)

    Google Scholar 

  23. I. Mezić, Nonlinear Dyn. 41(1–3), 309 (2005)

    Article  MathSciNet  Google Scholar 

  24. C. Penland, Mon. Weather. Rev. 117(10) (1989)

    Google Scholar 

  25. P.J. Goulart, A. Wynn, D. Pearson, in 51st IEEE Conference on Decision and Control (2012)

    Google Scholar 

  26. J.N. Kutz, X. Fu, S.L. Brunton, SIAM J. Appl. Dyn. Syst. 15(2) (2016)

    Article  MathSciNet  Google Scholar 

  27. B.R. Noack, W. Stankiewicz, M. Morzyński, P.J. Schmid, J. Fluid Mech. 809 (2016)

    Article  MathSciNet  Google Scholar 

  28. I. Mezić, Annu. Rev. Fluid Mech. 45 (2013)

    Article  MathSciNet  Google Scholar 

  29. P.J. Schmid, L. Li, M.P. Juniper, O. Pust, Theor. Comput. Fluid Dyn. 25(1) (2011)

    Google Scholar 

  30. P.J. Schmid, Exp. Fluids 50(4) (2011)

    Google Scholar 

  31. P.J. Schmid, D. Violato, F. Scarano, Exp. Fluids 52(6) (2012)

    Google Scholar 

  32. D. Duke, D. Honnery, J. Soria, J. Fluid Mech. 691 (2012)

    Article  Google Scholar 

  33. Q. Zhang, Y. Liu, S. Wang, J. Fluids Struct. 49 (2014)

    Google Scholar 

  34. S. Camarri, B.E. Fallenius, J.H. Fransson, J. Fluid Mech. 715 (2013)

    Article  MathSciNet  Google Scholar 

  35. S. Sarkar, S. Ganguly, A. Dalal, P. Saha, S. Chakraborty, Int. J. Heat Fluid Flow 44 (2013)

    Google Scholar 

  36. P.J. Schmid, K.E. Meyer, O. Pust, in 8th International Symposium on Particle Image Velocimetry-PIV09 (2009), 3

    Google Scholar 

  37. A. Seena, H.J. Sung, Int. J. Heat Fluid Flow 32(6) (2011)

    Google Scholar 

  38. A. Seena, H.J. Sung, Int. J. Heat Fluid Flow 44 (2013)

    Google Scholar 

  39. L. Massa, R. Kumar, P. Ravindran, Phys. Fluids 24(6) (2012)

    Google Scholar 

  40. R. Kumar, L. Massa, in 42nd AIAA Fluid Dynamics Conference and Exhibit (2012)

    Google Scholar 

  41. T.W. Muld, G. Efraimsson, D.S. Henningson, Comput. Fluids 57 (2012)

    Google Scholar 

  42. V. Statnikov, T. Sayadi, M. Meinke, P. Schmid, W. Schröder, Phys. Fluids 27(1) (2015)

    Google Scholar 

  43. F. Richecoeur, L. Hakim, A. Renaud, L. Zimmer (Center for Turbulence Research, Stanford University, 2012)

    Google Scholar 

  44. C. Souvick, M. Achintya, S. Swarnendu, in N3L-International Summer School and Workshop on Non-Normal and Nonlinear (2013)

    Google Scholar 

  45. S. Ghosal, in ASME 2016 Dynamic Systems and Control Conference (2016)

    Google Scholar 

  46. J.M. Quinlan, B.T. Zinn, in 50th AIAA/ASME/SAE/ASEE Joint Propulsion Conference (2014)

    Google Scholar 

  47. C. Huang, W.E. Anderson, M.E. Harvazinski, V. Sankaran, AIAA J (2016)

    Google Scholar 

  48. A. Ghani, L. Gicquel, T. Poinsot, in ASME Turbo Expo 2015: Turbine Technical Conference and Exposition (2015)

    Google Scholar 

  49. E. Motheau, F. Nicoud, T. Poinsot, J. Fluid Mech. 749 (2014)

    Article  Google Scholar 

  50. A. Abou-Taouk, S. Sadasivuni, D. Lörstad, B. Ghenadie, L.E. Eriksson, in Proceedings of the 7th European Combustion Meeting (2015)

    Google Scholar 

  51. A. Ghani, T. Poinsot, L. Gicquel, G. Staffelbach, Combust. Flame 162(11) (2015)

    Google Scholar 

  52. T. Grenga, J. MacArt, M. Mueller, Combust. Theory Model. 22(4) (2018)

    Google Scholar 

  53. J.H. Tu, C.W. Rowley, J. Comput. Phys. 231(16) (2012)

    Google Scholar 

  54. L. Sirovich, Q. Appl. Math. 45(3) (1987)

    Google Scholar 

  55. J.H. Tu, C.W. Rowley, D.M. Luchtenburg, S.L. Brunton, J.N. Kutz (2013), ar**v:1312.0041

  56. B.A. Belson, J.H. Tu, C.W. Rowley, ACM Trans. Math. Softw. 40(4) (2014)

    Article  Google Scholar 

  57. J. MacArt, T. Grenga, M. Mueller, Combust. Flame 191 (2018)

    Google Scholar 

  58. S.G. Davis, A.V. Joshi, H. Wang, F. Egolfopoulos, Proc. Combust. Inst. 30(1) (2005)

    Google Scholar 

  59. R.W. Bilger, Flow, Turbul. Combust. 72(2) (2004)

    Google Scholar 

  60. S. Zhang, C.J. Rutland, Combust. Flame 102(4) (1995)

    Google Scholar 

  61. J. MacArt, T. Grenga, M. Mueller, Proc. Combust. Inst. 37(2) (2019)

    Google Scholar 

  62. O. Desjardins, G. Blanquart, G. Balarac, H. Pitsch, J. Comput. Phys. 227 (2008)

    Google Scholar 

  63. J.F. MacArt, M.E. Mueller, J. Comput. Phys. 326 (2016)

    Google Scholar 

  64. T. Sayadi, P.J. Schmid, Theor. Comput. Fluid Dyn. 30(5), 415 (2016)

    Article  Google Scholar 

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Acknowledgements

The authors gratefully acknowledge valuable support in the form of computational time on the TIGRESS high-performance computer center at Princeton University, which is jointly supported by the Princeton Institute for Computational Science and Engineering (PICSciE) and the Princeton University Office of Information Technology’s Research Computing department.

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Authors and Affiliations

  1. RWTH Aachen University, Templegraben 64, 52062, Aachen, Germany

    T. Grenga

  2. Princeton University, Olden Street, Princeton, NJ, 08544, USA

    M. E. Mueller

Authors
  1. T. Grenga
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  2. M. E. Mueller
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Correspondence to T. Grenga .

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Editors and Affiliations

  1. Institute for Combustion Technology, RWTH Aachen University, Aachen, Germany

    Heinz Pitsch

  2. Institute for Combustion Technology, RWTH Aachen University, Aachen, Germany

    Antonio Attili

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Grenga, T., Mueller, M.E. (2020). Dynamic Mode Decomposition: A Tool to Extract Structures Hidden in Massive Datasets. In: Pitsch, H., Attili, A. (eds) Data Analysis for Direct Numerical Simulations of Turbulent Combustion. Springer, Cham. https://doi.org/10.1007/978-3-030-44718-2_8

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