Skip to main content
SpringerLink
Log in

A Comparative Study of Conditional Moment Closure Modelling for Ignition of iso-octane and n-heptane in Thermally Stratified Mixtures

  • Published:
Flow, Turbulence and Combustion Aims and scope Submit manuscript

Abstract

This paper presents a comparative study of the premixed conditional moment closure (CMC) model for modelling ignition of thermally stratified mixtures under homogeneous charge compression ignition (HCCI) conditions. For this purpose, the CMC model is applied to two sets of direct numerical simulations (DNSs) modelling ignition of lean n-heptane/air and iso-octane/air mixtures with various levels of thermal stratification. The results show excellent agreement for all n-heptane cases with thermal stratification of 15-60 K. However, an advanced ignition is predicted by the CMC model for the iso-octane case with thermal stratification of 60 K in comparison with the DNS data. Inspection of homogeneous ignition delay demonstrates that the ignition delay time fluctuations are much higher in the iso-octane cases compared with the n-heptane cases having same level of temperature inhomogeneities. This is because of the differing ignition responses to temperature between these two fuels. The observed discrepancies in the iso-octane case with \({T}^{\prime }=60\) K are due to the dominance of deflagration mode of combustion resulting in large conditional fluctuations, which occurs in the iso-octane case and not the n-heptane case because the temperature dependence of ignition delay is stronger for iso-octane. To further investigate the reasons for the observed discrepancies, a transport equation for the conditional variance is derived for premixed combustion. Assessment of the conditional variance equation using the DNS data shows that correlations between dissipation and conditional fluctuation and correlations between reaction and conditional fluctuations are the dominant sources of conditional fluctuations.

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

Similar content being viewed by others

References

  1. Dec, J.E.: Advanced compression-ignition engines-understanding the in-cylinder processes. Proc. Combust. Inst. 32(2), 2727–2742 (2009)

    Article  Google Scholar 

  2. Premier, A.: HCCI could cut fuel consumption by 15 %. Adv. Mater. Process., 27 (2007)

  3. Dec, J.E., Hwang, W., Sjöberg, M.: An investigation of thermal stratification in HCCI engines using chemiluminescence imaging. SAE Paper 2006-01-1518 (2006)

  4. Liu, H., Yao, M., Zheng, Z., Wang, Y.: An investigation of different ported fuel injection strategies and thermal stratification in HCCI engines using chemiluminescence imaging. SAE Paper 2010-01-0163 (2010)

  5. Snyder, J., Dronniou, N., Dec, J., Hanson, R.: PLIF measurements of thermal stratification in an HCCI engine under fired operation. SAE Int. J. Engines 5(1), 1669–1688 (2011)

    Article  Google Scholar 

  6. Yang, Y., Dec, J.E., Dronniou, N., Sjöberg, M.: Tailoring HCCI heat-release rates with partial fuel stratification: Comparison of two-stage and single-stage-ignition fuels. Proc. Combust. Inst. 33(2), 3047–3055 (2011)

    Article  Google Scholar 

  7. Krasselt, J., Foster, D., Ghandhi, J., Herold, R., Reuss, D., Najt, P.: Investigations into the effects of thermal and compositional stratification on HCCI combustion part I: Metal engine results. SAE Paper 2009-01-1105 (2009)

  8. Chen, J.H., Hawkes, E.R., Sankaran, R., Mason, S.D., Im, H.G.: Direct numerical simulation of ignition front propagation in a constant volume with temperature inhomogeneities: I. Fundamental analysis and diagnostics. Combust. Flame 145(12), 128–144 (2006)

    Article  Google Scholar 

  9. Hawkes, E.R., Sankaran, R., Pébay, P.P., Chen, J.H.: Direct numerical simulation of ignition front propagation in a constant volume with temperature inhomogeneities: II. Parametric study. Combust. Flame 145(12), 145–159 (2006)

    Article  Google Scholar 

  10. Bansal, G., Im, H.G.: Autoignition and front propagation in low temperature combustion engine environments. Combust. Flame 158(11), 2105–2112 (2011)

    Article  Google Scholar 

  11. Yu, R., Bai, X.S.: Direct numerical simulation of lean hydrogen/air auto-ignition in a constant volume enclosure. Combust. Flame 160(9), 1706–1716 (2013)

    Article  Google Scholar 

  12. Talei, M., Hawkes, E.R.: Ignition in compositionally and thermally stratified n-heptane/air mixtures: A direct numerical simulation study. Proc. Combust. Inst. 35(3), 3027–3035 (2015)

  13. Yoo, C.S., Lu, T., Chen, J.H., Law, C.K.: Direct numerical simulations of ignition of a lean n-heptane/air mixture with temperature inhomogeneities at constant volume: Parametric study. Combust. Flame 158(9), 1727–1741 (2011)

    Article  Google Scholar 

  14. Yoo, C.S., Luo, Z., Lu, T., Kim, H., Chen, J.H.: A DNS study of ignition characteristics of a lean iso-octane/air mixture under HCCI and SACI conditions. Proc. Combust. Inst. 34(2), 2985–2993 (2013)

    Article  Google Scholar 

  15. Zhang, H., Hawkes, E.R., Chen, J.H., Kook, S.: A numerical study of the autoignition of dimethyl ether with temperature inhomogeneities. Proc. Combust. Inst. 34(1), 803–812 (2013)

    Article  Google Scholar 

  16. El-Asrag, H.A., Ju, Y.: Direct numerical simulations of exhaust gas recirculation effect on multistage autoignition in the negative temperature combustion regime for stratified HCCI flow conditions by using H2O2 addition. Combust. Theor. Model 17(2), 316–334 (2013)

    Article  Google Scholar 

  17. Aceves, S.M., Flowers, D.L., Espinosa-Loza, F., Martinez-Frias, J., Dec, J.E., Sjöberg, M., Dibble, R.W., Hessel, R.P.: Spatial analysis of emissions sources for HCCI combustion at low loads using a multi-zone model. SAE Paper 2004-01-1910 (2004)

  18. Krisman, A., Hawkes, E.R., Kook, S., Sjöberg, M., Dec, J.E.: On the potential of ethanol fuel stratification to extend the high load limit in stratified-charge compression-ignition engines. Fuel 99(0), 45–54 (2012)

    Article  Google Scholar 

  19. Cook, D.J., Pitsch, H., Chen, J.H., Hawkes, E.R.: Flamelet-based modeling of auto-ignition with thermal inhomogeneities for application to HCCI engines. Proc. Combust. Inst. 31(2), 2903–2911 (2007)

    Article  Google Scholar 

  20. Hu, B., Rutland, C.J., Shethaji, T.A.: Combustion modeling of conventional diesel-type and HCCI-type diesel combustion with large eddy simulations. SAE Paper 2008-01-0958 (2008)

  21. Cook, D.J., Pitsch, H.: Enthalpy-based flamelet model for HCCI applied to a rapid compression machine. SAE Paper 2005-01-3735 (2005)

  22. Cook, D.J., Pitsch, H., Nentwig, G.: Numerical investigation of unburnt hydrocarbon emissions in a homogeneous-charge late-injection diesel-fueled engine. SAE Paper 2008-01-1666 (2008)

  23. Dahms, R., Felsch, C., Röhl, O., Peters, N.: Detailed chemistry flamelet modeling of mixed-mode combustion in spark-assisted HCCI engines. Proc. Combust. Inst. 33(2), 3023–3030 (2011)

    Article  Google Scholar 

  24. Colin, O., da Cruz, A.P., Jay, S.: Detailed chemistry-based auto-ignition model including low temperature phenomena applied to 3-D engine calculations. Proc. Combust. Inst. 30(2), 2649–2656 (2005)

    Article  Google Scholar 

  25. Pera, C., Colin, O., Jay, S.: Development of a FPI detailed chemistry tabulation methodology for internal combustion engines. Oil & Gas Science and Technology - Rev. IFP 64(3), 243–258 (2009)

    Article  Google Scholar 

  26. Jay, S., Colin, O.: Modeling of pollutant emissions using combined tabulated detailed kinetics and reduced kinetics. SAE Paper 2010-01-0628 (2010)

  27. Bisetti, F., Chen, J.Y., Hawkes, E.R., Chen, J.H.: Probability density function treatment of turbulence chemistry interactions during the ignition of a temperature-stratified mixture for application to HCCI engine modeling. Combust. Flame 155(4), 571–584 (2008)

    Article  Google Scholar 

  28. Zhang, Y., Kung, E., Haworth, D.: A PDF method for multidimensional modeling of HCCI engine combustion: effects of turbulence/chemistry interactions on ignition timing and emissions. Proc. Combust. Inst. 30(2), 2763–2771 (2005)

    Article  Google Scholar 

  29. Salehi, F., Talei, M., Hawkes, E.R., Yoo, C.S., Lucchini, T., D’Errico, G., Kook, S.: Conditional moment closure modelling for HCCI with temperature inhomogeneities. Proc. Combust. Inst. 35(3), 3087–3095 (2015)

    Article  Google Scholar 

  30. Klimenko, A.Y.: Multicomponent diffusion of various admixtures in turbulent flow. Fluid Dyn. 25(3), 327–334 (1990)

    Article  MATH  Google Scholar 

  31. Bilger, R.: Conditional moment closure for turbulent reacting flow. Phys. Fluids A 5(2), 436–444 (1993)

    Article  MATH  Google Scholar 

  32. Navarro-Martinez, S., Kronenburg, A.: LES-CMC simulations of a turbulent bluff-body flame. Proc. Combust. Inst. 31(2), 1721–1728 (2007)

    Article  Google Scholar 

  33. Kim, G., Kang, S., Kim, Y., Bilger, R.W., Cleary, M.J.: Conditional moment closure and transient flamelet modelling for detailed structure and NOx formation characteristics of turbulent nonpremixed jet and recirculating flames. Combust. Theor. Model 11(4), 527–552 (2007)

    Article  MATH  Google Scholar 

  34. Richardson, E., Mastorakos, E.: Conditional moment closure modelling for spark ignition in a turbulent n-heptane spray. 5th Mediterranean combustion symposium (2007)

  35. Navarro-Martinez, S., Kronenburg, A.: LES-CMC simulations of a lifted methane flame. Proc. Combust. Inst. 32(1), 1509–1516 (2009)

    Article  Google Scholar 

  36. Devaud, C., Bray, K.: Assessment of the applicability of conditional moment closure to a lifted turbulent flame: first order model. Combust. Flame 132(12), 102–114 (2003)

    Article  Google Scholar 

  37. El Sayed, A., Devaud, C.B.: Conditional moment closure (CMC) applied to autoignition of high pressure methane jets in a shock tube. Combust. Theor. Model 12(5), 943–972 (2008)

    Article  MATH  Google Scholar 

  38. Buckrell, A., Devaud, C.: Investigation of mixing models and conditional moment closure applied to autoignition of hydrogen jets. Flow Turbul. Combust. 90(3), 621–644 (2013)

    Article  Google Scholar 

  39. Cleary, M.J., Kent, J.H., Bilger, R.W.: Prediction of carbon monoxide in fires by conditional moment closure. Proc. Combust. Inst. 29(1), 273–279 (2002)

    Article  Google Scholar 

  40. Cleary, M., Kent, J.: Modelling of species in hood fires by conditional moment closure. Combust. Flame 143(4), 357–368 (2005)

    Article  Google Scholar 

  41. Wright, Y.M., Paola, G.D., Boulouchos, K., Mastorakos, E.: Simulations of spray autoignition and flame establishment with two-dimensional CMC. Combust. Flame 143(4), 402–419 (2005)

    Article  Google Scholar 

  42. De Paola, G., Mastorakos, E., Wright, Y.M., Boulouchos, K.: Diesel engine simulations with multi-dimensional conditional moment closure. Combust. Sci. Technol. 180(5), 883–899 (2008)

    Article  Google Scholar 

  43. Wright, Y.M., Boulouchos, K., Paola, G.D., Mastorakos, E.: Multi-dimensional conditional moment closure modelling applied to a heavy-duty common-rail diesel engine. SAE. Int. J. Engines 2, 714–726 (2009)

    Article  Google Scholar 

  44. Seo, J., Lee, D., Huh, K.Y., Chung, J.: Combustion simulation of a diesel engine in the pHCCI mode with split injections by the spatially integrated CMC model. Combust. Sci. Tech. 182(9), 1241–1260 (2010)

    Article  Google Scholar 

  45. Borghesi, G., Mastorakos, E., Devaud, C.B., Bilger, R.W.: Modeling evaporation effects in conditional moment closure for spray autoignition. Combust. Theor. Model 15(5), 725–752 (2011)

    Article  MATH  Google Scholar 

  46. Bolla, M., Wright, Y.M., Boulouchos, K., Borghesi, G., Mastorakos, E.: Soot formation modeling of n-heptane sprays under diesel engine conditions using the conditional moment closure approach. Combust. Sci. Tech. 185(5), 766–793 (2013)

    Article  Google Scholar 

  47. Swaminathan, N., Bilger, R.W.: Analyses of conditional moment closure for turbulent premixed flames. Combust. Theor. Model. 5(2), 241–260 (2001)

    Article  MATH  Google Scholar 

  48. Amzin, S., Swaminathan, N., Rogerson, J.W., Kent, J.H.: Conditional moment closure for turbulent premixed flames. Combust. Sci. Tech. 184(10-11), 1743–1767 (2012)

    Article  Google Scholar 

  49. Thornber, B., Bilger, R.W., Masri, A.R., Hawkes, E.R.: An algorithm for LES of premixed compressible flows using the conditional moment closure model. J. Comput. Phys. 230(20), 7687–7705 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  50. Klimenko, A.Y., Bilger, R.W.: Conditional moment closure for turbulent combustion. Prog. Energ. Combust. Sci. 25(6), 595–687 (1999)

    Article  Google Scholar 

  51. Zeldovich, Y.B.: Regime classification of an exothermic reaction with nonuniform initial conditions. Combust. Flame 39(2), 211–214 (1980)

    Article  Google Scholar 

  52. Klimenko, A.: On the relation between the conditional moment closure and unsteady flamelets. Combust. Theor. Model. 5(3), 275–294 (2001)

    Article  MATH  Google Scholar 

  53. Sankaran, R., Hawkes, E.R., Chen, J.H., Lu, T., Law, C.K.: Direct numerical simulations of turbulent lean premixed combustion. J. Phys. Conf. Ser. 46(1), 38 (2006)

    Article  Google Scholar 

  54. Hawkes, E.R., Sankaran, R., Chen, J.H., Kaiser, S.A., Frank, J.H.: An analysis of lower-dimensional approximations to the scalar dissipation rate using direct numerical simulations of plane jet flames. Proc. Combust. Inst. 32(1), 1455–1463 (2009)

    Article  Google Scholar 

  55. 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(1), 1447–1454 (2011)

    Article  Google Scholar 

  56. Chen, J.H.: Petascale direct numerical simulation of turbulent combustion-fundamental insights towards predictive models. Proc. Combust. Inst 33(1), 99–123 (2011)

    Article  Google Scholar 

  57. Gruber, A., Chen, J.H., Valiev, D., Law, C.K.: Direct numerical simulation of premixed flame boundary layer flashback in turbulent channel flow. J. Fluid Mech. 709, 516–542 (2012)

    Article  MATH  Google Scholar 

  58. Kolla, H., Grout, R.W., Gruber, A., Chen, J.H.: Mechanisms of flame stabilization and blowout in a reacting turbulent hydrogen jet in cross-flow. Combust. Flame 159(8), 2755–2766 (2012)

    Article  Google Scholar 

  59. Chatakonda, O., Hawkes, E.R., Aspden, A.J., Kerstein, A.R., Kolla, H., Chen, J.H.: On the fractal characteristics of low Damköhler number flames. Combust. Flame 160(11), 242–2433 (2013)

    Google Scholar 

  60. Pope, S.: Turbulent Flowes. Cambridge (2000)

  61. Kronenburg, A., Bilger, R., Kent, J.: Second-order conditional moment closure for turbulent jet diffusion flames. Proc. Combust. Inst. 27(1), 1097–1104 (1998)

    Article  Google Scholar 

  62. Swaminathan, N., Bilger, R.W.: Study of the conditional covariance and variance equations for second order conditional moment closure. Phys. Fluids 11(9), 2679–2695 (1999)

    Article  MATH  Google Scholar 

  63. Kim, S.H., Huh, K.Y.: Second-order conditional moment closure modeling of turbulent piloted jet diffusion flames. Combust. Flame 138(4), 336–352 (2004)

    Article  Google Scholar 

  64. Richardson, E., Yoo, C., Chen, J.: Analysis of second-order conditional moment closure applied to an autoignitive lifted hydrogen jet flame. Proc. Combust. Inst. 32(2), 1695–1703 (2009)

    Article  Google Scholar 

  65. Paola, G., Kim, I., Mastorakos, E.: Second-order conditional moment closure simulations of autoignition of an n-heptane plume in a turbulent coflow of heated air. Flow Turbul. Combust. 82(4), 455–475 (2009)

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Photovoltaic and Renewable Energy Engineering, The University of New South Wales, Sydney, NSW, 2052, Australia

    Fatemeh Salehi

  2. Department of Mechanical Engineering, University of Melbourne, Parkville, VIC, 3010, Australia

    Mohsen Talei

  3. School of Photovoltaic and Renewable Energy Engineering, School of Mechanical and Manufacturing Engineering, The University of New South Wales, Sydney, NSW, 2052, Australia

    Evatt R. Hawkes

  4. School of Mechanical and Nuclear Engineering, Ulsan National Institute of Science and Technology, Ulsan, 689-798, Republic of Korea

    Chun Sang Yoo

  5. Department of Energy, Politecnico di Milano, Milan, 20156, Italy

    Tommaso Lucchini & Gianluca D’Errico

  6. School of Mechanical and Manufacturing Engineering, The University of New South Wales, Sydney, NSW, 2052, Australia

    Sanghoon Kook

Authors
  1. Fatemeh Salehi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Mohsen Talei
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Evatt R. Hawkes
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Chun Sang Yoo
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Tommaso Lucchini
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Gianluca D’Errico
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. Sanghoon Kook
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Fatemeh Salehi.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Salehi, F., Talei, M., Hawkes, E.R. et al. A Comparative Study of Conditional Moment Closure Modelling for Ignition of iso-octane and n-heptane in Thermally Stratified Mixtures. Flow Turbulence Combust 95, 1–28 (2015). https://doi.org/10.1007/s10494-015-9604-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10494-015-9604-6

Keywords

Search

Navigation