Quantitative Parametrization of Mixture Distribution in GDI Engines: A CFD Analysis

Original Paper


This paper presents an objective classification of mixture distribution in the combustion chamber of a gasoline direct injection (GDI) engine into homogeneous and non-homogeneous types. The non-homogeneous mixture distribution is further classified as properly stratified, improperly stratified and mal-distributed types. Based on this classification, four types of properly stratified mixture distributions viz., random, linear, Gaussian and parabolic are virtually simulated in the combustion chamber of a GDI engine using computational fluid dynamics to identify the mixture that results in maximum indicated mean effective pressure (IMEP). It is found that the IMEP is highest for the parabolic mixture distribution which is followed by Gaussian, linear and random types. The performance and emission characteristics of the virtual mixture distributions are compared with a late fuel injection case at different over all equivalence ratios ranging from 0.3 to 0.7. Then the variation of mixture equivalence ratio with the distance from the spark plug is parametrized for different virtual mixture distribution cases and expressed using a parameter called the “stratification index”. It is found that the stratification index based on Gaussian variation gives maximum information about the mixture distribution in the combustion chamber. Finally the stratification index of different virtual mixture distributions is compared with the late fuel injection case at various overall equivalence ratios. It is found that the late fuel injection case tends to produce highest IMEP when the stratification index is close to unity.



Bottom dead center


Crank angle degree


Computational fluid dynamics


Courant Fredrich and Lewis


Direct injection spark ignition


Equivalence ratio


Exhaust valve closing


Exhaust valve opening


Gasoline direct injection


Hydro carbons


Internal combustion


Indicated mean effective pressure


Intake valve closing


Intake valve opening


Kelvin Helmholtz–Rayleigh–Taylor


Nitric oxides


Port fuel injection


Pressure implicit with the splitting of operators


Renormalized group


Stratification index


Successive over relaxation


Top dead center


Turbulent kinetic energy



Authors would like to acknowledge the support of Mr. Phaninder Injeti, Convergent Science who helped to develop the python script for different calculations used in this study. Authors also acknowledge the high-performance computing facility at Indian Institute of Technology Madras, which was used to perform numerical simulations.

Compliance with Ethical Standards

Conflict of interest

On behalf of all authors, the corresponding author states that there is no conflict of interest.


  1. 1.
    Guo H, Ma X, Li Y, Liang S, Wang Z, Xu H, Wang J (2017) Effect of flash boiling on microscopic and macroscopic spray characteristics in optical GDI engine. Fuel 190:79–89.  https://doi.org/10.1016/j.fuel.2016.11.043 CrossRefGoogle Scholar
  2. 2.
    Irimescu A, Merola SS, Di Iorio S, Vaglieco BM (2018) Investigation on the effects of butanol and ethanol fueling on combustion and PM emissions in an optically accessible DISI engine. Fuel 216:121–141.  https://doi.org/10.1016/j.fuel.2017.11.116 CrossRefGoogle Scholar
  3. 3.
    Li B, Li Y, Wang D (2012) Fuel spray dynamic characteristics of GDI high pressure injection system. Chin J Mech Eng 25(2):355–361.  https://doi.org/10.3901/CJME.2012.02.355 CrossRefGoogle Scholar
  4. 4.
    Yang J, Dong X, Wu Q, Xu M (2018) Influence of flash boiling spray on the combustion characteristics of a spark-ignition direct-injection optical engine under cold start. Combust Flame 188(Supplement C):66–76.  https://doi.org/10.1016/j.combustflame.2017.09.019 CrossRefGoogle Scholar
  5. 5.
    Moxey BG, Cairns A, Zhao H (2016) A comparison of butanol and ethanol flame development in an optical spark ignition engine. Fuel 170(Supplement C):27–38.  https://doi.org/10.1016/j.fuel.2015.12.008 CrossRefGoogle Scholar
  6. 6.
    Costa M, Sorge U, Sementa P, Vaglieco BM (2015) CFD modeling of a mixed mode boosted GDI engine and performance optimization for the avoidance of knocking. In: Simulation and modeling methodologies, technologies and applications. Springer, Cham, pp 195–215.  https://doi.org/10.1007/978-3-319-26470-7_10
  7. 7.
    Costa M, Sorge U, Allocca L (2012) CFD optimization for GDI spray model tuning and enhancement of engine performance. Adv Eng Softw 49(Supplement C):43–53.  https://doi.org/10.1016/j.advengsoft.2012.03.004 CrossRefGoogle Scholar
  8. 8.
    Banerjee R, Kumar S (2016) Numerical investigation of stratified air/fuel preparation in a GDI engine. Appl Therm Eng 104(Supplement C):414–428.  https://doi.org/10.1016/j.applthermaleng.2016.05.050 CrossRefGoogle Scholar
  9. 9.
    Montanaro A, Allocca L, Costa M, Sorge U (2016) Assessment of a 3D CFD model for GDI spray impact against wall through experiments based on different optical techniques. Int J Multiph Flow 84(Supplement C):204–216.  https://doi.org/10.1016/j.ijmultiphaseflow.2016.05.007 CrossRefGoogle Scholar
  10. 10.
    Haworth DC (2005) A review of turbulent combustion modeling for multidimensional in-cylinder CFD.  https://doi.org/10.4271/2005-01-0993
  11. 11.
    Xu Z, Yi J, Curtis EW, Wooldridge S (2009) Applications of CFD modeling in GDI engine piston optimization. SAE Int J Engines 2(1):1749–1763.  https://doi.org/10.4271/2009-01-1936 CrossRefGoogle Scholar
  12. 12.
    Reddy AA, Mallikarjuna JM (2017) Parametric study on a gasoline direct injection engine: a CFD analysis.  https://doi.org/10.4271/2017-26-0039
  13. 13.
    Rakopoulos CD, Kosmadakis GM, Dimaratos AM, Pariotis EG (2011) Investigating the effect of crevice flow on internal combustion engines using a new simple crevice model implemented in a CFD code. Appl Energy 88(1):111–126.  https://doi.org/10.1016/j.apenergy.2010.07.012 CrossRefGoogle Scholar
  14. 14.
    Komninos NP (2009) Modeling HCCI combustion: modification of a multi-zone model and comparison to experimental results at varying boost pressure. Appl Energy 86(10):2141–2151.  https://doi.org/10.1016/j.apenergy.2009.01.026 CrossRefGoogle Scholar
  15. 15.
    Sjerić M, Kozarac D, Ormuž K (2016) Cycle-simulation turbulence modelling of IC engines. Int J Automot Technol 17(1):51–61.  https://doi.org/10.1007/s12239-016-0004-2 CrossRefGoogle Scholar
  16. 16.
    Rakowski S, Merker GP, Spicher U (2008) Gasoline evaporation as a CFD model for spark-ignition engines. MTZ Worldw 69(9):70–77.  https://doi.org/10.1007/BF03227919 CrossRefGoogle Scholar
  17. 17.
    Torre AD, Montenegro G, Onorati A (2017) Coupled 1D-quasi3D fluid dynamic models for the simulation of IC engine intake and exhaust systems. In: 17. Internationales Stuttgarter Symposium. Springer, Wiesbaden, pp 1461–1476.  https://doi.org/10.1007/978-3-658-16988-6_111
  18. 18.
    Versteeg H, Malalasekera W (2007) An introduction to computational fluid dynamics: the finite volume method, 2nd edn. PHI, New YorkGoogle Scholar
  19. 19.
    Krishna AS, Mallikarjuna JM, Kumar D (2016) Effect of engine parameters on in-cylinder flows in a two-stroke gasoline direct injection engine. Appl Energy 176:282–294.  https://doi.org/10.1016/j.apenergy.2016.05.067 CrossRefGoogle Scholar
  20. 20.
    Keskinen K, Kaario O, Nuutinen M, Vuorinen V, Künsch Z, Liavåg LO, Larmi M (2016) Mixture formation in a direct injection gas engine: numerical study on nozzle type, injection pressure and injection timing effects. Energy 94:542–556.  https://doi.org/10.1016/j.energy.2015.09.121 CrossRefGoogle Scholar
  21. 21.
    Kubach H, Gindele J, Spicher U (2001) Investigations of mixture formation and combustion in gasoline direct injection engines.  https://doi.org/10.4271/2001-01-3647
  22. 22.
    Jiang C, Xu H, Srivastava D, Ma X, Dearn K, Cracknell R, Krueger-Venus J (2017) Effect of fuel injector deposit on spray characteristics, gaseous emissions and particulate matter in a gasoline direct injection engine. Appl Energy 203(Supplement C):390–402.  https://doi.org/10.1016/j.apenergy.2017.06.020 CrossRefGoogle Scholar
  23. 23.
    Graves BM, Koch CR, Olfert JS (2017) Morphology and volatility of particulate matter emitted from a gasoline direct injection engine fuelled on gasoline and ethanol blends. J Aerosol Sci 105(Supplement C):166–178.  https://doi.org/10.1016/j.jaerosci.2016.10.013 CrossRefGoogle Scholar
  24. 24.
    Park C, Lee S, Yi U (2016) Effects of engine operating conditions on particle emissions of lean-burn gasoline direct-injection engine. Energy 115(Part 1):1148–1155.  https://doi.org/10.1016/j.energy.2016.09.051 CrossRefGoogle Scholar
  25. 25.
    Zhao F-Q, Lai M-C, Harrington DL (1997) A review of mixture preparation and combustion control strategies for spark-ignited direct-injection gasoline engines.  https://doi.org/10.4271/970627
  26. 26.
    Stan C, Guenther S, Martorano L, Tarantino C (2000) Aspects of mixture formation and combustion in GDI engines.  https://doi.org/10.4271/2000-01-0648
  27. 27.
    Stanglmaier RH, Hall MJ, Matthews RD (1998) Fuel-spray/charge–motion interaction within the cylinder of a direct-injected, 4-valve. SI Engine.  https://doi.org/10.4271/980155 Google Scholar
  28. 28.
    Lake TH, Stokes J, Whitaker PA, Crump JV (1998) Comparison of direct injection gasoline combustion systems.  https://doi.org/10.4271/980154
  29. 29.
    Khalilarya S, Jafarmadar S, Khatamnezhad H, Javadirad G, Pourfallah M (2012) Simultaneously reduction of NOx and soot emissions in a DI heavy duty diesel engine operating at high cooled EGR rates. Int J Aerosp Mech Eng 6(1):1020–1028Google Scholar
  30. 30.
    Yao M, Zheng Z, Liu H (2009) Progress and recent trends in homogeneous charge compression ignition (HCCI) engines. Prog Energy Combust Sci 35(5):398–437.  https://doi.org/10.1016/j.pecs.2009.05.001 CrossRefGoogle Scholar
  31. 31.
    Choi S, Park W, Lee S, Min K, Choi H (2011) Methods for in-cylinder EGR stratification and its effects on combustion and emission characteristics in a diesel engine. Energy 36(12):6948–6959.  https://doi.org/10.1016/j.energy.2011.09.016 CrossRefGoogle Scholar
  32. 32.
    Bendu H, Murugan S (2014) Homogeneous charge compression ignition (HCCI) combustion: Mixture preparation and control strategies in diesel engines. Renew Sustain Energy Rev 38(Supplement C):732–746.  https://doi.org/10.1016/j.rser.2014.07.019 CrossRefGoogle Scholar
  33. 33.
    Saxena S, Bedoya ID (2013) Fundamental phenomena affecting low temperature combustion and HCCI engines, high load limits and strategies for extending these limits. Prog Energy Combust Sci 39(5):457–488.  https://doi.org/10.1016/j.pecs.2013.05.002 CrossRefGoogle Scholar
  34. 34.
    Salmani MH, Rehman S, Zaidi K, Hasan AK (2015) Study of ignition characteristics of microemulsion of coconut oil under off diesel engine conditions. Eng Sci Technol Int J 18(3):318–324.  https://doi.org/10.1016/j.jestch.2014.12.002 CrossRefGoogle Scholar
  35. 35.
    Elfasakhany A (2015) Investigations on the effects of ethanol–methanol–gasoline blends in a spark-ignition engine: performance and emissions analysis. Eng Sci Technol Int J 18(4):713–719.  https://doi.org/10.1016/j.jestch.2015.05.003 CrossRefGoogle Scholar
  36. 36.
    Millo F, Badami M, Bianco A, Delogu E (2011) CFD diagnostic methodology for the assessment of mixture formation quality in GDI engines. SAE Int J Engines 4(2):2461–2476.  https://doi.org/10.4271/2011-24-0151 CrossRefGoogle Scholar
  37. 37.
    Costa M, Marchitto L, Merola SS, Sorge U (2014) Study of mixture formation and early flame development in a research GDI (gasoline direct injection) engine through numerical simulation and UV-digital imaging. Energy 77(Supplement C):88–96.  https://doi.org/10.1016/j.energy.2014.04.114 CrossRefGoogle Scholar
  38. 38.
    Raj ARGS, Mallikarjuna JM, Ganesan V (2013) Energy efficient piston configuration for effective air motion: a CFD study. Appl Energy 102:347–354.  https://doi.org/10.1016/j.apenergy.2012.07.022 CrossRefGoogle Scholar
  39. 39.
    Rhie CM, Chow WL (1983) Numerical study of the turbulent flow past an airfoil with trailing edge separation. AIAA J 21(11):1525–1532.  https://doi.org/10.2514/3.8284 MATHCrossRefGoogle Scholar
  40. 40.
    Yakhot V, Orszag SA, Thangam S, Gatski TB, Speziale CG (1992) Development of turbulence models for shear flows by a double expansion technique. Phys Fluids A 4(7):1510–1520.  https://doi.org/10.1063/1.858424 MathSciNetMATHCrossRefGoogle Scholar
  41. 41.
    Harshavardhan B, Mallikarjuna JM (2015) Effect of piston shape on in-cylinder flows and air–fuel interaction in a direct injection spark ignition engine: a CFD analysis. Energy 81:361–372.  https://doi.org/10.1016/j.energy.2014.12.049 CrossRefGoogle Scholar
  42. 42.
    Verma I, Bish E, Kuntz M, Meeks E, Puduppakkam K, Naik C, Liang L (2016) CFD modeling of spark ignited gasoline engines. Part 2: modeling the engine in direct injection mode along with spray validation.  https://doi.org/10.4271/2016-01-0579
  43. 43.
    Imaoka Y, Shouji K, Inoue T, Noda T (2015) A study of a multistage injection mechanism for improving the combustion of direct-injection gasoline engines. SAE Int J Engines.  https://doi.org/10.4271/2015-01-0883 Google Scholar
  44. 44.
    Benajes J, García A, Pastor JM, Monsalve-Serrano J (2016) Effects of piston bowl geometry on reactivity controlled compression ignition heat transfer and combustion losses at different engine loads. Energy 98:64–77.  https://doi.org/10.1016/j.energy.2016.01.014 CrossRefGoogle Scholar
  45. 45.
    Amsden AA, Orourke PJ, Butler TD (1989) KIVA-2: a computer program for chemically reactive flows with sprays. Los Alamos National Laboratory Technical Report LA-11560-MSGoogle Scholar
  46. 46.
    Schmidt DP, Rutland CJ (2000) A new droplet collision algorithm. J Comput Phys 164(1):62–80.  https://doi.org/10.1006/jcph.2000.6568 MATHCrossRefGoogle Scholar
  47. 47.
    O’Rourke PJ, Amsden AA (2000) A spray/wall interaction submodel for the KIVA-3 wall film model.  https://doi.org/10.4271/2000-01-0271
  48. 48.
    Givler SD, Raju M, Pomraning E, Senecal PK, Salman N, Reese R (2013) Gasoline combustion modeling of direct and port-fuel injected engines using a reduced chemical mechanism.  https://doi.org/10.4271/2013-01-1098
  49. 49.
    Yakhot V, Orszag SA (1986) Renormalization group analysis of turbulence. I. Basic theory. J Sci Comput 1(1):3–51.  https://doi.org/10.1007/BF01061452 MathSciNetMATHCrossRefGoogle Scholar
  50. 50.
    Rodi W (1991) Experience with two-layer models combining the k-epsilon model with a one-equation model near the wall. Am Inst Aeronaut Astronaut.  https://doi.org/10.2514/6.1991-216 Google Scholar
  51. 51.
    Reitz R, Bracco FV (1986) Mechanisms of breakup of round liquid jets. Encycl Fluid Mech 3:233–249Google Scholar
  52. 52.
    Senecal PK, Pomraning E, Richards KJ, Briggs TE, Choi CY, Mcdavid RM, Patterson MA (2003) Multi-dimensional modeling of direct-injection diesel spray liquid length and flame lift-off length using CFD and parallel detailed chemistry.  https://doi.org/10.4271/2003-01-1043
  53. 53.
    Yajia E, Xu M, Zeng W, Zhang Y, Cleary DJ (2009) An experimental and numerical investigation on characteristics of methanol and ethanol sprays from a multi-hole DISI injector. In: The 13th annual conference on liquid atomization and spray systems, Wuxin, P. R. China, Asia, 15–17 Oct 2009Google Scholar
  54. 54.
    Spicher U, Kölmel A, Kubach H, Töpfer G (2000) Combustion in spark ignition engines with direct injection.  https://doi.org/10.4271/2000-01-0649

Copyright information

© CIMNE, Barcelona, Spain 2018

Authors and Affiliations

  1. 1.Internal Combustion Engine Laboratory, Department of Mechanical EngineeringIndian Institute of Technology, MadrasChennaiIndia

Personalised recommendations