Modelling of diesel spray flames under engine-like conditions using an accelerated Eulerian Stochastic Fields method

Research output: Contribution to journalArticlepeer-review


  • Kar Mun Pang
  • Mehdi Jangi
  • Xue Song Bai
  • Jesper Schramm
  • Jens Honore Walther

Colleges, School and Institutes

External organisations

  • Technical University of Denmark
  • Department of Mechanical Engineering
  • Lunds Universitet
  • HPK H27


This paper aims to simulate diesel spray flames across a wide range of engine-like conditions using the Eulerian Stochastic Field probability density function (ESF-PDF) model. The ESF model is coupled with the Chemistry Coordinate Mapping approach to expedite the calculation. A convergence study is carried out for a number of stochastic fields at five different conditions, covering both conventional diesel combustion and low-temperature combustion regimes. Ignition delay time, flame lift-off length as well as distributions of temperature and various combustion products are used to evaluate the performance of the model. The peak values of these properties generated using thirty-two stochastic fields are found to converge, with a maximum relative difference of 27% as compared to those from a greater number of stochastic fields. The ESF-PDF model with thirty-two stochastic fields performs reasonably well in producing the experimental flame development, ignition delay times and lift-off lengths. The ESF-PDF model also predicts a broader hydroxyl radical distribution which resembles the experimental observation, indicating that the turbulence-chemistry interaction is captured by the ESF-PDF model. The validated model is
subsequently used to investigate the flame structures under different conditions. Analyses based on flame index and formaldehyde distribution suggest that a triple flame, which consists of a rich premixed flame, a diffusion flame and a lean premixed flame, is established in the earlier stage of the
combustion. As the combustion progresses, the lean premixed flame weakens and diminishes with time. Eventually, only a double-flame structure, made up of the diffusion flame and the rich premixed flame, is observed. The analyses for various ambient temperatures show that the triple-flame structure remains for a longer period of time in cases with lower ambient temperatures. The present study shows that the ESF-PDF method is a valuable alternative to Lagrangian particle PDF methods.


Original languageEnglish
Pages (from-to)363-383
Number of pages21
JournalCombustion and Flame
Early online date24 Apr 2018
Publication statusPublished - 1 Jul 2018


  • Diesel engine, Eulerian Stochastic Field, Probability density function, Spray flame, Turbulent combustion