Auto-ignition and combustion of diesel spray using unsteady laminar flamelet model Isares Dhuchakallaya a, * , Phadungsak Rattanadecho a , Paul Watkins b a Department of Mechanical Engineering, Thammasat University, Klong-Luang, Pathumthani 12120, Thailand b School of Mechanical, Aerospace and Civil Engineering, University of Manchester, M13 9PL, UK highlights < This model is able to capture the main features of the diesel flame structure. < The flame shapes obtained are closely related to the luminous flames. < The present model is apparently able to match the experimental results. < The lifted flame is well represented by this developed model. article info Article history: Received 29 June 2012 Accepted 18 December 2012 Available online 2 January 2013 Keywords: Auto-ignition Combustion Flamelet Modelling Spray abstract This work emphasises the modelling capabilities of the unsteady flamelet/reaction progress variable approach to implement diesel spray flames for capturing the auto-ignition and flame lift-off phenomena. The droplet size distribution based on the moment scheme characterises the poly-disperse spray model [1] employed in this work. The flamelet progress variable solutions embedded in a Reynolds-averaged NaviereStokes (RANS) framework, together with the probability density function (PDF) approach, sig- nify the turbulenceechemistry interaction. All thermochemical scalars are represented as a function of mean mixture fraction, mixture fraction variance, reaction progress variable and scalar dissipation rate. Mixture fraction is assumed to follow a beta-PDF distribution, because the reaction progress variable and scalar dissipation rate distributions are assumed to be a delta-PDF. In order to assess the capability of this developed model, the predicted results are compared with experimental data [2]. The developed model gives a reasonably good overall prediction performance in terms of auto-ignition, flame development and flame lift-off length. The flame temperature distributions are comparable with the formations of lumi- nous flames. The predicted flame growth rate is consistent with the experimental results but there is a small over-prediction. Therefore, the present approach can accurately and efficiently capture the auto- ignition and flame lift-off phenomena of diesel spray flame. Ó 2013 Elsevier Ltd. All rights reserved. 1. Introduction Due to superior fuel economy, spray combustion is utilised in a wide range of engineering devices, such as gas turbine engines and internal combustion engines. Because the fuel is injected into the high-temperature chamber, the fuel droplets are partially evaporated and then mixed with the oxidiser. The chemical reac- tion plays a key role in this period until the auto-ignition takes place. The remaining unmixed fuel is then burned more slowly due to limited oxidiser. Therefore, spray combustion can be con- sidered as a partially premixed combustion mode. Thus, standard combustion models based on the fully premixed or fully non- premixed theories are not exactly appropriate for this concern. Many studies have been performed to investigate the underly- ing physics governing partially premixed combustion [3e6]. These studies strived to capture spray combustion accurately and effi- ciently. In general, the key parameter used to predict the partially premixed lifted flames is the reaction progress variable. The method widely applied to model diffusion flame is the laminar flamelet approach proposed by Peters [7]. The formulations of the flamelet that incorporate the reaction progress variable are the steady flamelet model (SFM) and unsteady flamelet model (UFM). The basic concept of the laminar flamelet model, as introduced by Peters [7], considers that the turbulent diffusion flames behave locally as an ensemble of laminar stretched flamelets. Each laminar flamelet is subjected to the local flow field, convecting and * Corresponding author. E-mail address: dhuchakallaya@yahoo.com (I. Dhuchakallaya). Contents lists available at SciVerse ScienceDirect Applied Thermal Engineering journal homepage: www.elsevier.com/locate/apthermeng 1359-4311/$ e see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.applthermaleng.2012.12.016 Applied Thermal Engineering 52 (2013) 420e427