Large eddy simulation of a medium-scale methanol pool fire using the extended eddy dissipation concept Zhibin Chen a , Jennifer Wen b,⇑ , Baopeng Xu a , Siaka Dembele a a Centre for Fire and Explosion Studies, School of Mechanical and Automotive Engineering, Kingston University, Friars Avenue, London SW15 3DW, UK b School of Engineering, University of Warwick, Library Road, Coventry CV4 7AL, UK article info Article history: Received 14 July 2013 Received in revised form 3 November 2013 Accepted 5 November 2013 Keywords: Eddy dissipation concept Large eddy simulation FireFOAM Pool fire abstract The eddy dissipation concept (EDC) is extended to the large eddy simulation (LES) framework following the same logic of the turbulent energy cascade as originally proposed by Magnussen but taking into account the distinctive roles of the sub-grid scale turbulence. A series of structure levels are assumed to exist under the filter width ‘‘D’’ in the turbulent energy cascade which spans from the Kolmogorov to the integral scale. The total kinetic energy and its dissipation rate are expressed using the sub-grid scale (SGS) quantities. Assuming infinitely fast chemistry, the filtered reaction rate in the EDC is con- trolled by the turbulent mixing rate between the fine structures at Kolmogorov scales and the surround- ing fluids. The newly extended EDC was implemented in the open source FireFOAM solver, and large eddy simulation of a 30.5 cm diameter methanol pool fire was performed using this solver. Reasonable agree- ment is achieved by comparing the predicted heat release rate, radiative fraction, velocity and its fluctu- ation, temperature and its fluctuation, turbulent heat flux, SGS and total dissipation rate, SGS and total kinetic energy, time scales, and length scales with the corresponding experimental data. Ó 2013 Elsevier Ltd. All rights reserved. 1. Introduction The eddy dissipation concept (EDC) originally developed by Magnussen [1,2] assumes that chemical reactions take place in fine structures which have similar magnitudes as the Kolmogorov scales and that the reaction rate is determined from the turbulent mixing rate between the fine structures and surrounding fluids. Thus, the turbulent effect on combustion is embedded in the reac- tion rate of EDC. The EDC is well established for the Reynolds Aver- aged Navier–Stokes (RANS) approach, but its extension to the large eddy simulation (LES) framework has been problematic partly be- cause the eddy characteristic time scale cannot be easily deter- mined in LES. Fureby and co-workers [3,4] proposed a procedure to calculate the turbulent reaction rate by directly replacing the to- tal kinetic energy and its dissipation rate with the sub-grid scale (SGS) properties. This approach has been adopted by some com- mercial CFD codes like FLUENT [5]. However, it was reported that the predicted reaction rate is strongly dependent on grid size [3]. This was thought to be likely caused by the replacement of the to- tal kinetic energy with the SGS kinetic energy. Note that in LES the SGS kinetic energy represents the unresolved turbulent energy to be modeled and this energy should be much less than the total ki- netic energy. In the present study, a new approach will be developed to ex- tend the EDC from RANS to LES, from which the characteristic time scales and length scales are derived. Numerical simulation of a 30.5 cm diameter methanol pool fire will be performed to evaluate the development. 2. Extention of the eddy dissipation concept 2.1. Turbulent energy cascade The essence of the EDC assumes that a stepwise turbulent en- ergy cascade exists from the mean flow down to the Kolmogorov scale, and the heat generation resulting from the dissipation of tur- bulence energy mainly occurs on the small scales where produc- tion and dissipation balance [6]. This assumption is believed to be independent of the chosen turbulence models, either RANS or LES, but it does neglect backscatter and upscale transfer which ex- ist in real physics but would only have marginal influence on the present applications where the interests are more focused on the mean and fluctuating flow variables and radiative heat emissions from fires. Given the fact that the filter width of LES generally falls between the Kolmogorov and integral length scale, we assume that there is a series of structure levels below the filter width D in the stepwise turbulent cascade as shown in Fig. 1. As properties on this ‘D’ level can be determined directly from a SGS turbulence model, we can derive expressions for the characteristic variables on other 0017-9310/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ijheatmasstransfer.2013.11.010 ⇑ Corresponding author. Tel.: +44 24 7657 3365. E-mail address: j.x.wen@eng.warwick.ac.uk (J. Wen). International Journal of Heat and Mass Transfer 70 (2014) 389–408 Contents lists available at ScienceDirect International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt