Skip to main content
SpringerLink
Log in

Nonlinear dynamics of cycle-to-cycle variations in a lean-burn natural gas engine with a non-uniform pre-mixture

  • Original paper
  • Published:
Nonlinear Dynamics Aims and scope Submit manuscript

Abstract

The cycle-to-cycle variations (CCVs) in reciprocating internal combustion engines may cause negative influence on diving performance, fuel economy, and emissions. Especially, lean-burn technology or exhaust gas recirculation (EGR) was used to improve engine combustion efficiency and reduce NOx, and the combustion boundary was limited by increased CCVs. Therefore, it was important to identify the complex dynamics of CCVs and to take measures for inhibiting them. The CCVs based on indicated mean effective pressure (IMEP) time series were examined in a lean-burn natural gas engine with a non-uniform pre-mixture based on statistical and multifractal theories. Tests were conducted at an engine speed of 1000 rpm and low loads of 10% and 25%, and combustion data at an engine load of 10% were analysed in detail because the CCVs are less sensitive to changes of gas injection timing (GIT) at the higher engine load. The nonlinear dynamics of the CCVs was revealed at the different GIT from 1° to 120°CA ATDC. The statistical properties of IMEP time series were characterised by distributions of probability density functions (PDF), the multifractal complexities of the combustion fluctuations were quantitatively analysed by the singularity spectra in terms of the Hölder exponent based on the theory of wavelet transform modulus maxima, and the primary source leading to the increased CCVs and complex dynamics in a natural gas engine with a non-uniform pre-mixture was identified using 3D-computational fluid dynamics simulations. Results show that as the GIT increased, the kurtosis of the IMEP time series systematically decreased from 592 to 1.8, the fast dynamics transitions from super-Gaussian to quasi-Gaussian distributions in combustion system were revealed, and the lower value of kurtosis implied the lower degree of intermittency. Except for the GIT of 60°CA ATDC, the value of the Hölder exponent \(h_{0} > 0.5\), which implies that the CCVs for the other GITs behaved like a persistent walk or positive correlation. For GITs of 60° and 90°CA ATDC, the narrow broadness of the singularity spectrum implicated a monofractality, while the obvious multifractal properties could be identified for the other GITs. The transitions of the dynamic behaviours may be caused by the degree of mixture in-homogeneity combined with a new mechanism of “prior-cycle effects” proposed in this paper, and the effect mechanism was not only associated with the residual gas in the cylinder but also with the residual gas fuel in the intake port, rather than independent effect of residual gas in cylinder reported in previous researches. Our research results provided the deeper understanding on the dynamics of combustion system in multi-point injection natural gas engines and may be beneficial to achieve nonlinear prediction and to develop improved control strategies for inhibiting the CCVs.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14

Similar content being viewed by others

References

  1. Liu, J.L., Dumitrescu, C.E.: Optical analysis of flame inception and propagation in a lean-burn natural-gas spark-ignition engine with a bowl-in-piston geometry. Int. J. Engine Res. 21, 1584–1596 (2020)

    Article  Google Scholar 

  2. Gong, C.M., Yi, L., Zhang, Z.L., Sun, J.Z., Liu, F.H.: Assessment of ultra-lean burn characteristics for a stratified-charge direct-injection spark-ignition methanol engine under different high compression ratios. Appl. Energy 261, 114478 (2020)

    Article  Google Scholar 

  3. Fu, J.Q., Shu, J., Zhou, F., Zhong, L.H., Liu, J.P., Deng, B.L.: Quantitative analysis on the effects of compression ratio and operating parameters on the thermodynamic performance of spark ignition liquefied methane gas engine at lean burn mode. Fuel 263, 116692 (2020)

    Article  Google Scholar 

  4. Zhang, Z.M., Wang, L., Yuan, X.N., Duan, Q.M., Yang, B., Zeng, K.: Experimental investigation on performance and combustion characteristics of spark-ignition dual-fuel engine fueled with methanol/natural gas. Appl. Therm. Eng. 150, 164–174 (2019)

    Article  Google Scholar 

  5. Chen, H., He, J.J., Zhong, X.L.: Engine combustion and emission fuelled with natural gas: A review. J. Energy Inst. 92, 1123–1136 (2019)

    Article  Google Scholar 

  6. Caton, J.: A comparison of lean operation and exhaust gas recirculation: thermodynamic reasons for the increases of efficiency. SAE Paper No. 2013-01-0266 (2013)

  7. Zheng, J.B., Wang, J.H., Zhao, Z.B., Wang, D.D., Huang, Z.H.: Effect of equivalence ratio on combustion and emissions of a dual-fuel natural gas engine ignited with diesel. Appl. Therm. Eng. 146, 738–751 (2019)

    Article  Google Scholar 

  8. Hutter, R., Libero, L.D., Elbert, P., Onder, C.H.: Catalytic methane oxidation in the exhaust gas after treatment of a lean-burn natural gas engine. Chem. Eng. J. 349, 156–167 (2018)

    Article  Google Scholar 

  9. Liu, J.L., Dumitrescu, C.E.: Lean-burn characteristics of a heavy-duty diesel engine retrofitted to natural-gas spark ignition. J. Eng. Gas Turbines Power 141, 071013 (2019)

    Article  Google Scholar 

  10. Song, E.Z., Liu, Z.T., Yang, L.P., Yao, C., Sun, J., Dong, Q.: Effects of nozzle structure on the gas mixture uniformity of marine gas engine. Ocean Eng. 142, 507–520 (2017)

    Article  Google Scholar 

  11. Zhang, M.M., Hong, W., Xie, F.X., et al.: Effects of diluents on cycle-by-cycle variations in a spark ignition engine fueled with methanol. Energy 182, 1132–1140 (2019)

    Article  Google Scholar 

  12. Chen, Y., Wang, Y., Raine, R.: Correlation between cycle-by-cycle variation, burning rate, and knock: a statistical study from PFI and DISI engines. Fuel 206, 210–218 (2017)

    Article  Google Scholar 

  13. Ozdor, N., Dulger, M., Sher, E.: Cyclic variability in spark-ignition engines: a literature survey, SAE Paper No. 940987 (1994)

  14. Finney, C.E.A., Green, Jr. J.B., Daw, C.S.: Symbolic time-series analysis of engine combustion measurements. SAE Paper No.9806244 (1998)

  15. Martin, J.K., Plee, S.L., Remboski, Jr. D.J.: Burn modes and prior-cycle effects on cyclic variations in lean burn spark-ignition engine combustion. SAE Paper No. 880201 (1988)

  16. Yang, L.P., Zare, A., Bodisco, T.A., Nabi, N., Liu, Z.T., Brown, R.J.: Analysis of cycle-to-cycle variations in a common-rail compression ignition engine fuelled with diesel and biodiesel fuels. Fuel 290, 120010 (2021)

    Article  Google Scholar 

  17. Daw, C.S., Finney, C.E.A., Green, J.B., Kennel, M.B.: A simple model for cyclic variations in a spark-ignition engine. SAE Paper No.962086 (1996)

  18. Wagner, R.M., Drallmeier, J.A., Daw, C.S.: Characterization of lean combustion instability in pre-mixed charge spark ignition engines. Int. J. Eng. Res. 1, 301–320 (2001)

    Article  Google Scholar 

  19. Wendeker, M., Litak, G., Czarnigowski, J., Szabelski, K.: Nonperiodic oscillations of pressure in a spark ignition engine. Int. J. Bifurcat. Chaos 14, 1801–1806 (2004)

    Article  MATH  Google Scholar 

  20. Litak, G., Taccani, R., Radu, R., Urbanowicz, K.: Estimation of a noise level using coarse-grained entropy of experimental time series of internal pressure in a combustion engine. Chaos Soliton Fract. 23, 1695–1701 (2005)

    Article  MATH  Google Scholar 

  21. Gao, J., Zhang, Y., Shen, T.: Anon-board calibration scheme for map-based combustion phase control of spark-ignition engines. IEEE-ASME Trans. Mech. 22, 1485–1496 (2017)

    Article  Google Scholar 

  22. Sen, A.K., Litak, G., Litak, C., Finney, C.E.A., Daw, C.S., Wagner, R.M.: Analysis of heat release dynamics in an internal combustion engine using multifractals and wavelets. Appl. Energy 87, 1736–1743 (2010)

    Article  Google Scholar 

  23. Sen, A.K., Zheng, J.J., Huang, Z.H.: Dynamics of cycle-to-cycle variations in natural gas direct-injection spark-ignition. Appl. Energy 88, 2324–2334 (2011)

    Article  Google Scholar 

  24. Reyes, M., Tinaut, F.V., Giménez, B., Pérez, A.: Characterization of cycle-to-cycle variations in a natural gas spark ignition engine. Fuel 140, 752–761 (2015)

    Article  Google Scholar 

  25. Yang, L.P., Ding, S.L., Litak, G., Song, E.Z., Ma, X.Z.: Identification and quantification analysis of nonlinear dynamics properties of combustion instability in a diesel engine. Chaos 25, 013105 (2015)

    Article  Google Scholar 

  26. Yang, L.P., Song, E.Z., Ding, S.L., Brown, R.J., Marwan, N., Ma, X.Z.: Analysis of the dynamic characteristics of combustion instabilities in a pre-mixed lean-burn natural gas engine. Appl. Energy 183, 746–759 (2016)

    Article  Google Scholar 

  27. Marseglia, G., Costa, M., Catapano, F., Sementa, P., Vaglieco, B.M.: Study about the link between injection strategy and knock onset in an optically accessible multi-cylinder GDI engine. Energ. Convers. Manag. 134, 1–19 (2017)

    Article  Google Scholar 

  28. Wang, L.Y., Yang, L.P., Song, E.Z., Yao, C., Ma, X.Z.: Effect of port gas injection on the combustion instabilities in a spark-ignition lean-burn natural gas engine. Int. J. Bifurcat. Chaos 28(10), 1850124 (2018)

    Article  MathSciNet  Google Scholar 

  29. Sen, A.K., Litak, G., Yao, B.F., Li, G.X.: Analysis of pressure fluctuations in a natural gas engine under lean burn conditions. Appl. Therm. Eng. 30, 776–779 (2010)

    Article  Google Scholar 

  30. Sen, A.K., Ash, S.K., Huang, B., Huang, Z.H.: Effect of exhaust gas recirculation on the cycle-to-cycle variations in a natural gas spark ignition engine. Appl. Therm. Eng. 31, 2247–2253 (2011)

    Article  Google Scholar 

  31. Litak, G., Rusinek, R., Czarnigowski, J., Wendeker, M.: Patterns in the combustion process in a spark ignition engine. Chaos Solitons Fract. 35, 578–585 (2008)

    Article  Google Scholar 

  32. Di, H.Y., Zhang, Y.H., Shen, T.L.: Chaos theory-based time series analysis of in-cylinder pressure and its application in combustion control of SI engines. J Therm. Sci. Tech. 15, 1–15 (2020)

    Article  Google Scholar 

  33. Finney, C.E.A., Kaul, B.C., Daw, C.S., Wagner, R.M., Edwards, K.D., Green, J.B., Jr.: A review of deterministic effects in cyclic variability of internal combustion engines. Int. J. Eng. Res. 16(3), 366–378 (2016)

    Article  Google Scholar 

  34. Chew, L., Hoekstra, R., Nayfeh, J.F., Navedo, J.: Chaos analysis on in-cylinder pressure measurements. SAE Paper No. 942486 (1994)

  35. Daily, J.W.: Cycle-to-cycle variations: a chaotic process? Combust. Sci. Technol. 57, 149–162 (1988)

    Article  Google Scholar 

  36. Foakes, A.P., Pollard, D.C.: Investigation of a chaotic mechanism for cycle-to-cycle variations. Combust. Sci. Technol. 90, 281–287 (1993)

    Article  Google Scholar 

  37. Wendeker, M., Czarnigowski, J., Litak, G., Szabelski, K.: Chaotic combustion in spark ignition engines. Chaos Soliton Fract. 18, 8035–8806 (2003)

    Article  MATH  Google Scholar 

  38. Wagner, R.M., Drallmeier, J.A.: Prior-cycle effects in lean spark ignition combustion—fuel/air charge considerations. SAE Paper No.981047 (1998)

  39. Sen, A.K., Litak, G., Kaminski, T., Wendeker, M.: Multifractal and statistical analyses of heat release fluctuations in a spark ignition engine. Chaos 18, 033115 (2008)

    Article  Google Scholar 

  40. Curto-Risso, P.L., Medina, A., Hernández, A.C., Guzmán-Vargas, L., Angulo-Brownd, F.: Monofractal and multifractal analysis of simulated heat release fluctuations in a spark ignition heat engine. Phys. A 389, 5662–5670 (2010)

    Article  Google Scholar 

  41. Ji, S.B., Lan, X., Cheng, Y., et al.: Cyclic variation of large-bore multi point injection engine fuelled by natural gas with different types of injection systems. Appl. Therm. Eng. 102, 1241–1249 (2016)

    Article  Google Scholar 

  42. Cho, H.M., He, B.Q.: Spark ignition natural gas engines—a review. Energy Convers. Manag. 48, 608–618 (2007)

    Article  Google Scholar 

  43. Awad, O.I., Zhang, Z., Kamil, M., Ma, X., Ali, O.M., Shuai, S.: Wavelet analysis of the effect of injection strategies on cycle to cycle variation GDI optical engine under clean and fouled injector. Processes 7, 817-1-11 (2019)

  44. Heydaria, M.H., Avazzadeh, Z., Haromi, M.F.: A wavelet approach for solving multi-term variable-order time fractional diffusion-wave equation. Appl. Math. Comput. 341, 215–228 (2019)

    MathSciNet  MATH  Google Scholar 

  45. Sen, A.K., Litak, G., Edwards, K.D., Finney, C.E.A., Daw, C.S., Wagner, R.M.: Characteristics of cyclic heat release variability in the transition from spark ignition to HCCI in a gasoline engine. Appl. Energy 88, 1649–1655 (2011)

    Article  Google Scholar 

  46. Sen, A.K., Litak, G., Taccani, R., Radu, R.: Wavelet analysis of cycle-to-cycle pressure variations in an internal combustion engine. Chaos Soliton Fract. 38, 886–893 (2008)

    Article  Google Scholar 

  47. Yang, L.P., Bodisco, T.A., Zare, A., Marwan, N., Chu-Van, T., Brown, R.J.: Analysis of the nonlinear dynamics of inter-cycle combustion variations in an ethanol fumigation-diesel dual-fuel engine. Nonlinear Dyn. 95, 2555–2574 (2019)

    Article  Google Scholar 

  48. Sen, A.K., Longwic, R., Litak, G.K., Gorski, K.: Analysis of cycle-to-cycle pressure variations in a spark-ignition engine. Mech. Syst. Signal Process 22, 362–373 (2008)

    Article  Google Scholar 

  49. Mallat, S.: A Wavelet Tour of Signal Processing. Academic Press, New York (1998)

    MATH  Google Scholar 

  50. Muzy, J.F., Bacry, E., Arneodo, A.: The multifractal formalism revisited with wavelets. Int. J. Bifurc. Chaos 4, 245–302 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  51. Arneodo, A., Audit, B., Kestener, P., Roux, S.: Wavelet-based multifractal analysis. Scholarpedia 3, 4103 (2008)

    Article  Google Scholar 

  52. Gerasimova, E., Audit, B.S., Roux, G. et al.: Wavelet-based multifractal analysis of dynamic infrared thermograms to assist in early breast cancer diagnosis. Front. Physiol. 5, 176–1–11 (2014).

  53. Dupont, S., Argoul, F., Gerasimova-Chechkina, E., Irvine M.R., Arneodo, A.: Experimental evidence of a phase transition in the multifractal spectra of turbulent temperature fluctuations at a forest canopy top. J. Fluid Mech. 896, A15-1-24 (2020)

  54. Ord, A., Hobbs, B., Dering, G., Gessner, K.: Nonlinear analysis of natural folds using wavelet transforms and recurrence plots. Philos. Trans. R. Soc. B. 376, 1–20 (2018)

    Google Scholar 

  55. Pavlova, O.N., Abdurashitov, A.S., Ulanova, M.V., Shushunova, N.A., Pavlov, A.N.: Effects of missing data on characterization of complex dynamics from time series. Commun. Nonlinear Sci. Numer. Simul. 66, 31–40 (2019)

    Article  MATH  Google Scholar 

  56. Muzy, J.F., Bacry, E., Arneodo, A.: Wavelets and multifractal formalism for singular signals: application to turbulence data. Phys. Rev. Lett. 67, 3515–3518 (1991)

    Article  Google Scholar 

  57. Delour, J., Muzy, J.F., Arneodo, A.: Intermittency of 1D velocity spatial profiles in turbulence: a magnitude cumulant analysis. Eur. Phys. J. B 23, 243–248 (2001)

    Article  Google Scholar 

  58. Sen, A.K.: Multifractality as a Measure of complexity in solar flare activity. Solar Phys. 241, 67–76 (2007)

    Article  Google Scholar 

Download references

Acknowledgements

This research was supported by the National Natural Science Foundation of China (51306041) and the Key Projects of the Natural Science Foundation of Heilongjiang Province of China (ZD2019E003).

Author information

Authors and Affiliations

  1. College of Power and Energy Engineering, Harbin Engineering University, No. 145-1, Nantong Street, Nangang District, Harbin, 150001, China

    Li-Ping Yang, Li-Yuan Wang & Jia-Qi Wang

  2. School of Engineering, Deakin University, Waurn Ponds, VIC, 3216, Australia

    Ali Zare

  3. Biofuel Engine Research Facility, Queensland University of Technology, Brisbane, QLD, 4000, Australia

    Richard J. Brown

Authors
  1. Li-Ping Yang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Li-Yuan Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Jia-Qi Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Ali Zare
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Richard J. Brown
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Li-Yuan Wang.

Ethics declarations

Conflict of interest

The authors declare that they have no conflicts of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Yang, LP., Wang, LY., Wang, JQ. et al. Nonlinear dynamics of cycle-to-cycle variations in a lean-burn natural gas engine with a non-uniform pre-mixture. Nonlinear Dyn 104, 2241–2258 (2021). https://doi.org/10.1007/s11071-021-06377-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11071-021-06377-4

Keywords

Search

Navigation