Transported probability density function modelling of the vapour phase of an n-heptane jet at diesel engine conditions

Abstract

An n-heptane spray injected into a constant volume chamber at conditions representative of diesel engines is modelled with the probability density function (PDF) approach. The composition PDF transport is solved by a Lagrangian Monte Carlo method in conjunction with a standard Reynolds-averaged k−ϵ turbulence model to simulate transient fuel injection into a high temperature and high density ambient fluid in a constant volume chamber. Non-reacting cases are first considered with the focus on the ability of the method to predict the statistics of mixture fraction in the gas phase. The predictions are compared quantitatively against experimental measurements of mixture fraction and its variance obtained by Rayleigh scattering. The effects of mixing model and mixing constant (Cϕ) are examined. Good agreement for the mean mixture fraction is demonstrated. The mixture fraction variance is predicted well in the downstream region further than 20mm from the injector, given an appropriate choice of the mixing constant. In the region upstream of 20mm, the model variance is larger than the experimental variance, suggesting a problem with either the model or experiment. Cases are then simulated for chamber environments containing oxidiser. These cases feature transient ignition and combustion. A skeletal chemical mechanism is implemented with the PDF model and predictions of lift-off length and ignition delay are compared to experiment and to a set of results from a well-mixed model that ignores turbulence-chemistry interactions, as oxygen concentration in the chamber is varied. The results from the PDF model are noticeably different from the well-mixed model and quantitatively better in most cases.