Skip to main content
SpringerLink
Log in

Cycle-to-Cycle Variability

  • Chapter
  • First Online:
Quasi-Dimensional Simulation of Spark Ignition Engines

Abstract

In this chapter we shall analyze how to simulate, within a quasi-dimensional combustion model, the cyclic variability experimentally observed in spark ignition engines. Explicit qualitative comparison with experimental results will be shown. Moreover, we report a nonlinear dynamics analysis of cycle-by-cycle variations in heat release for the simulated engine with noisy components. Our approaches are based on nonlinear scaling properties of heat release fluctuations mainly, by means of correlation dimension, monofractal, and multifractal methods, and also by means of wavelet decomposition. We characterize the fluctuations for several fuel–air ratio values, \(\phi \), from lean mixtures to over stoichiometric situations by computing very long time series. Finally, we study the behavior of energetic functions when the presence of cyclic variability is considered. The fluctuating behavior of the net heat release, the power output, and the fuel conversion efficiency are simultaneously evaluated and analyzed.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    It is worth mentioning that the experiments by Beretta [2] measure the evolution of pressure during combustion with high-speed motion picture records of flame propagation. So we fit \(l_t\) with experiments on combustion and tried to recover cycle-to-cycle fluctuations by adding an stochastic behavior of a key parameter of combustion on the deterministic simulation.

  2. 2.

    An extrapolation of the laminar flame speed, \(S_L\) as a function of the fuel–air ratio, \(\phi \), was necessary for low values of \(\phi \).

  3. 3.

    See Fig. 3.20 in Chap. 3 and the \(P-\eta _{f}\) curves used with optimization purposes in Chap. 4.

References

  1. J. Keck, in Proceedings of Nineteenth Symposium (International) on Combustion (The Combustion Institute, Pittsburgh, 1982), pp. 1451–1466

    Google Scholar 

  2. G. Beretta, M. Rashidi, J. Keck, Combust. Flame 52, 217 (1983)

    Article  Google Scholar 

  3. J. Keck, J. Heywood, G. Noske, SAE Paper 870164 (1987)

    Google Scholar 

  4. C.S. Daw, M.B. Kennel, C.E.A. Finney, F.T. Connolly, Phys. Rev. E 57, 2811 (1998)

    Article  Google Scholar 

  5. G. Litak, T. Kaminski, J. Czarnigowski, D. Zukowski, M. Wendeker, Meccanica 42, 423 (2007)

    Article  MATH  Google Scholar 

  6. A. Sen, G. Litak, C. Finney, C. Daw, R. Wagner, Appl. Energ. 87, 1736 (2010)

    Article  Google Scholar 

  7. J.B.J. Green, C.S. Daw, J.S. Armfield, R.M. Wagner, J.A. Drallmeier, M.B. Kennel, P. Durbetaki, SAE Paper 1999-01-0221 (1999)

    Google Scholar 

  8. C.S. Daw, C.E.A. Finney, J.B. Green, M.B. Kennel, J.F. Thomas, F.T. Connolly, SAE Paper 962086 (1996)

    Google Scholar 

  9. E. Abdi Aghdam, A.A. Burluka, T. Hattrell, K. Liu, G.W. Sheppard, J. Neumeister, N. Crundwell, SAE Paper 2007-01-0939 (2007)

    Google Scholar 

  10. C. Stone, A. Brown, P. Beckwith, SAE Paper 960613 (1996)

    Google Scholar 

  11. P. Grassberger, I. Procaccia, Phys. Rev. Lett. 50, 346 (1983)

    Article  MathSciNet  Google Scholar 

  12. P. Grassberger, I. Procaccia, Physica D 9, 189 (1983)

    Article  MathSciNet  MATH  Google Scholar 

  13. H. Kantz, T. Schreiber, Non-Linear Time Serie Analysis (Cambridge University Press, Cambridge, 2004)

    Google Scholar 

  14. R. Hegger, H. Kantz, T. Schreiber, Chaos 9, 413 (1999)

    Article  MATH  Google Scholar 

  15. C.K. Peng, S. Havlin, H.E. Stanley, A.L. Goldberger, Phys. Rev. Lett. 70, 1343 (1995)

    Article  Google Scholar 

  16. G. Rangarajan, M. Ding, Phys. Rev. E 61(5), 4991 (2000). doi:10.1103/PhysRevE.61.4991

    Google Scholar 

  17. T. Higuchi, Physica D 46(2), 254 (1990). doi:10.1016/0167-2789(90)90039-R

  18. G. Gálvez-Coyt, A. Munoz-Diosdado, J.L. del Río-Correa, F. Angulo-Brown, Fractals 18(2), 235 (2009)

    Article  Google Scholar 

  19. D.T. Schmitt, P.C. Ivanov, Am. J. Physiol. 293(5), R1923 (2007). doi:10.1152/ajpregu.00372.2007

  20. J. Heywood, Internal Combustion Engine Fundamentals (McGraw-Hill, New York, 1988), Chap. 4, pp. 100–154

    Google Scholar 

  21. P. Curto-Risso, A. Medina, A. CalvoHernández, L. Guzmán-Vargas, F. Angulo-Brown, Appl. Energ. 88, 1557 (2011)

    Article  Google Scholar 

  22. D. Scholl, S. Russ, SAE Paper 1999-01-3513 (1999)

    Google Scholar 

  23. J. Theiler, S. Eubank, A. Longtin, B. Galdrikian, J. Doyne Farmer, Physica D 58, 77 (1992)

    Article  MATH  Google Scholar 

  24. T. Schreiber, A. Schmitz, Physica D 142(3–4), 346 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  25. J. Feder, Fractals (Plenum Press, New York, 1988)

    Book  MATH  Google Scholar 

  26. B.B. Mandelbrot, The Fractal Geometry of Nature, 2nd edn. (Freeman, San Francisco, 1982)

    MATH  Google Scholar 

  27. J.F. Muzy, E. Bacry, A. Arneodo, Phys. Rev. Lett. 67(25), 3515 (1991)

    Article  Google Scholar 

  28. P.C. Ivanov, L. Amaral, A. Goldberger, S. Havlin, M. Rosenblum, Z. Stuzik, H. Stanley, Nature 399, 461 (1999)

    Article  Google Scholar 

  29. A.L. Goldberger, L.A.N. Amaral, L. Glass, J.M. Hausdorff, P.C. Ivanov, R.G. Mark, J.E. Mietus, G.B. Moody, C.K. Peng, H.E. Stanley, Circulation 101(23), e215 (2000 (June 13)). http://circ.ahajournals.org/cgi/content/full/101/23/e215

  30. J.W. Kantelhardt, S.A. Zschiegner, E. Koscielny-Bunde, A. Bunde, S. Havlin, H.E. Stanley, Multifractal detrended fluctuation analysis of nonstationary time series (2002). http://arxiv.org/abs/physics/0202070

  31. D. Watts, S. Strogatz, Nature 393, 409 (1998)

    Article  Google Scholar 

  32. M. Newman, SIAM Rev. 45, 167 (2003). http://epubs.siam.org/doi/abs/10.1137/S003614450342480

  33. L. Lacasa, B. Luque, F. Ballesteros, J. Luque, J.C. Nun, Proc. Natl. Acad. Sci. U S A 105, 4972 (2008)

    Article  MATH  Google Scholar 

  34. L. Lacasa, B. Luque, J. Luque, J.C. Nun, Europhys. Lett. 86, 30001 (2009)

    Article  Google Scholar 

  35. P. Addison, The Illustrated Wavelet Transform Handbook (Institute of Physics Publishing, Bristol, 2002)

    Google Scholar 

  36. P. Curto-Risso, A. Medina, A. Calvo-Hernández, in 24th International Conference on Efficiency, Cost, Optimization, Simulation and Environmental Impact (Novi Sad, Serbia, 2011)

    Google Scholar 

  37. A. Sen, J. Zheng, Z. Huang, Appl. Energ. 88, 2324 (2011)

    Article  Google Scholar 

  38. A. Sen, S. Ash, B. Huang, Z. Huang, Appl. Therm. Eng. 31, 2247 (2011)

    Article  Google Scholar 

  39. A. Sen, G. Litak, K. Edwards, C. Finney, C. Daw, R. Wagner, Appl. Energ. 88, 1648 (2011)

    Google Scholar 

  40. M. Ceviz, A. Sen, A. Küleri, I. Öner, Appl. Therm. Eng. 36, 314 (2012)

    Article  Google Scholar 

  41. A. Sen, J. Wang, Z. Huang, Appl. Energ. 88, 4860 (2011)

    Article  Google Scholar 

  42. C. Torrence, G. Compo, Bull. Amer. Meteorol. Soc. 79, 61 (1998)

    Article  Google Scholar 

  43. P.L. Curto-Risso, A. Medina, A. CalvoHernández, L. Guzmán-Vargas, F. Angulo-Brown, Physica A 389, 5662 (2010)

    Article  Google Scholar 

  44. J. Heywood, Internal Combustion Engine Fundamentals (McGraw-Hill, New York, 1988)

    Google Scholar 

  45. F. Angulo-Brown, J. Appl. Phys. 69, 7465 (1991)

    Article  Google Scholar 

  46. A. CalvoHernández, A. Medina, J. Roco, J. White, S. Velasco, Phys. Rev. E. 63, 037102 (2001)

    Article  Google Scholar 

  47. P. Curto-Risso, A. Medina, A. CalvoHernández, J. Appl. Phys. 105, 094904 (2009)

    Article  Google Scholar 

  48. J. Gordon, M. Huleihil, J. Appl. Phys. 72, 829 (1992)

    Article  Google Scholar 

  49. A. Fischer, K. Hoffmann, J. Non-Equilib. Thermodyn. 29, 9 (2004)

    Article  MATH  Google Scholar 

  50. D. Descieux, M. Feidt, Appl. Therm. Eng. 27, 1457 (2007)

    Article  Google Scholar 

  51. P. Curto-Risso, A. Medina, A. CalvoHernández, Appl. Therm. Eng. 31, 803 (2011)

    Article  Google Scholar 

  52. J. Chen, J. Phys. D: Appl. Phys. 27, 1144 (1994)

    Article  Google Scholar 

  53. A. Durmayaz, O.S. Sogut, B. Sahin, H. Yavuz, Prog. Energ. Combust. 30, 175 (2004)

    Article  Google Scholar 

  54. A. CalvoHernández, A. Medina, J. Roco, J. Phys. D: Appl. Phys. 28, 2020 (1995)

    Article  Google Scholar 

  55. S. Sánchez-Orgaz, A. Medina, A. CalvoHernández, Energ. Convers. Manage. 51, 2134 (2010)

    Article  Google Scholar 

Download references

Open Access

This article is distributed under the terms of the Creative Commons Attribution License which permits any use, distribution, and reproduction in any medium, provided the original author(s) and the source are credited.

Author information

Authors and Affiliations

  1. Departamento de Física Aplicada, Universidad de Salamanca, 37008, Salamanca, Spain

    Alejandro Medina & Antonio Calvo Hernández

  2. Instituto de Ingeniería Mecánica y, Universidad de la República, Montevideo, Uruguay

    Pedro Luis Curto-Risso

  3. Unidad Profesional Interdisciplinaria en, Instituto Politécnico Nacional, Av. IPN 2580, 07340, Mexico, D.F., Mexico

    Lev Guzmán-Vargas

  4. Instituto Politécnico Nacional, Edif. 9, 07738, Mexico, D.F., Mexico

    Fernando Angulo-Brown

  5. Department of Mathematical Sciences, Richard G. Lugar Centre for Renewable Energy, Indiana University, Indianapolis, 46202, USA

    Asok K. Sen

Authors
  1. Alejandro Medina
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Pedro Luis Curto-Risso
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Antonio Calvo Hernández
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Lev Guzmán-Vargas
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Fernando Angulo-Brown
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Asok K. Sen
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Alejandro Medina .

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer-Verlag London

About this chapter

Cite this chapter

Medina, A., Curto-Risso, P.L., Hernández, A.C., Guzmán-Vargas, L., Angulo-Brown, F., Sen, A.K. (2014). Cycle-to-Cycle Variability. In: Quasi-Dimensional Simulation of Spark Ignition Engines. Springer, London. https://doi.org/10.1007/978-1-4471-5289-7_5

Download citation

  • DOI: https://doi.org/10.1007/978-1-4471-5289-7_5

  • Published:

  • Publisher Name: Springer, London

  • Print ISBN: 978-1-4471-5288-0

  • Online ISBN: 978-1-4471-5289-7

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation