ORIGINAL Self-ignition of diesel spray combustion Isares Dhuchakallaya Æ A. P. Watkins Received: 28 May 2009 / Accepted: 3 September 2009 / Published online: 17 September 2009 Ó Springer-Verlag 2009 Abstract This work presents the development and implementation of auto-ignition modelling for DI diesel engines by using the probability density function-eddy break-up (PDF-EBU) model. The key concept of this approach is to combine the chemical reaction rate dealing with low-temperature mode, and the turbulence reaction rate governing the high-temperature part by a reaction progress variable coupling function which represents the level of reaction. The average reaction rate here is evalu- ated by a PDF averaging approach. In order to assess the potential of this developed model, the well-known Shell ignition model is chosen to compare in auto-ignition analysis. In comparison, the PDF-EBU ignition model yields the ignition delay time in good agreement with the Shell ignition model prediction. However, the ignition kernel location predicted by the Shell model is slightly nearer injector than that by the PDF-EBU model leading to shorter lift-off length. As a result, the PDF-EBU ignition model developed here are fairly satisfactory in predicting the auto-ignition of diesel engines with the Shell ignition model. 1 Introduction The overview of spray combustion mechanism can be described simply as follows. Liquid fuel is sprayed into the hot air by means of a high-pressure liquid injector. The liquid spray then disintegrates into small droplets which evaporate as they spread into the chamber. The resulting fuel vapour mixes with the air. The time delay during which the fuel is prepared for burning is often termed the physical delay. Precursor chemical reactions are believed to occur during and after the fuel mixing stage, causing an additional time delay referred to as the chemical delay. The fuel and air which are mixed sufficiently within combus- tible limits burn very quickly without an external source of ignition energy. This process called ‘‘auto-ignition’’ is mainly controlled by chemical reaction rate, thus this flame is namely ‘‘premixed flame’’. As reported in the experi- mental results, ignition generally occurs somewhere in the downstream portion of the vaporised cloud and this is the onset of combustion. The remaining unmixed or unevap- orated fuel is burned more slowly and it is burned only as properly prepared. The later stage of diesel combustion is described as being ‘‘mixing-controlled’’ or limited by the rate at which the fuel vapour may be mixed with air, hence this flame is called ‘‘non-premixed’’ or ‘‘diffusion flame’’. As described above, the combustion in the diesel engines is ambiguous with a mixture of premixed and non-premixed flames, therefore the theories and modelling about pre- mixed and diffusion flames are involved in the spray combustion. In addition, the interactions between phases, complicated turbulence in the gaseous phase and the chemical kinetic mechanisms of fuel also crucially raise the complexity of spray combustion simulation. Hence spray combustion modelling requires a large computational resource to simulate. 2 Self-ignition Theoretically, the auto-ignition may be considered as a continuous process of physical delay and chemical delay. I. Dhuchakallaya (&)  A. P. Watkins Energy, Environment and Climate Change Research Group, School of Mechanical, Aerospace and Civil Engineering, University of Manchester, Manchester, UK e-mail: dhuchakallaya@yahoo.com 123 Heat Mass Transfer (2009) 45:1627–1635 DOI 10.1007/s00231-009-0537-2