On the generalisation of the mixture fraction to a monotonic mixing-describing variable for the flamelet formulation of spray flames

References

• G.M. Faeth, Evaporation and combustion of sprays, Prog. Energy Combust. Sci. 9 (1983), pp. 1–76.
   Web of Science ®Google Scholar
• R. Borghi, Background on droplets and sprays, in Combustion and Turbulence in Two Phase Flows, Lecture Series 1996–2002, Von Karman Institute for Fluid Dynamics, Sint-Genesius-Rode, Belgium, 1996.
   Google Scholar
• W.A. Sirignano, Fluid dynamics and transport of droplets and sprays, 2nd ed., Cambridge University Press, Cambridge, 2010.
   Google Scholar
• P. Jenny, D. Roekaerts, and N. Beishuizen, Modeling of turbulent dilute spray combustion, Prog. Energy Combust. Sci. 38 (2012), pp. 846–887.
   Web of Science ®Google Scholar
• W.A. Sirignano, Advances in droplet array combustion theory and modeling, Prog. Energy Combust. Sci. 42 (2014), pp. 54–86.
   Web of Science ®Google Scholar
• A.L. Sanchez, J. Urzay, and A. Liñán, The role of separation of scales in the description of spray combustion, Proc. Combust. Inst. 35 (2014), pp. 1549–1577.
   Web of Science ®Google Scholar
• G. Continillo and W.A. Sirignano, Counterflow spray combustion modeling, Combust. Flame 81 (1990), pp. 325–340.
   Web of Science ®Google Scholar
• C. Hollmann and E. Gutheil, Diffusion flames based on a laminar spray flame library, Combust. Sci. Technol. 135 (1998), pp. 175–192.
   Web of Science ®Google Scholar
• S. Russo and A. Gomez, The extinction behavior of small interacting droplets in cross-flow, Combust. Flame 130 (2002), pp. 215–224.
   Web of Science ®Google Scholar
• S. Russo and A. Gomez, Physical characterization of laminar spray flames in the pressure range 0.1–0.9 MPa, Combust. Flame 145 (2006), pp. 339–356.
   Web of Science ®Google Scholar
• S. Lerman and J.B. Greenberg, Spray diffusion flames – an asymptotic theory, Atomiz. & Sprays 20 (2010), pp. 1047–1064.
   Web of Science ®Google Scholar
• S.C. Li, P.A. Libby, and F.A. Williams, Experimental and theoretical studies of counterflow spray diffusion flames, Symp. (Int.) Combust. 24 (1992), pp. 1503–1512.
   Google Scholar
• N. Darabiha, F. Lacas, J.C. Rolon, and S. Candel, Laminar counterflow spray diffusion flames: A comparison between experimental results and complex chemistry calculations, Combust. Flame 95 (1993), pp. 261–275.
   Web of Science ®Google Scholar
• M. Massot, M. Kumar, M.D. Smooke, and A. Gomez, Spray counterflow diffusion flames of heptane: Experiments and computations with detailed kinetics and transport, Proc. Combust. Inst. 27 (1998), pp. 1975–1983.
   Google Scholar
• E. Gutheil and W.A. Sirignano, Counterflow spray combustion modeling with detailed transport and detailed chemistry, Combust. Flame 113 (1998), pp. 92–105.
   Web of Science ®Google Scholar
• E. Gutheil, Multiple solutions for structures of laminar counterflow spray flames, Prog. Comput. Fluid Dyn. 5 (2005), pp. 414–419.
   Web of Science ®Google Scholar
• H. Watanabe, R. Kurose, S.M. Hwang, and F. Akamatsu, Characteristics of flamelets in spray flames formed in a laminar counterflow, Combust. Flame 148 (2007), pp. 234–248.
   Web of Science ®Google Scholar
• J.B. Greenberg and N. Sarig, Coupled evaporation and transport effects in counterflow spray diffusion flames, Combust. Sci. Technol. 92 (1993), pp. 1–33.
   Web of Science ®Google Scholar
• A. Dvorjetski and J.B. Greenberg, Steady-state and extinction analyses of counterflow spray diffusion flames with arbitrary finite evaporation rate, Combust. Sci. Technol. 174 (2002), pp. 187–208.
   Web of Science ®Google Scholar
• A. Dvorjetski and J.B. Greenberg, Analysis of steady state polydisperse counterflow spray diffusion flames in the large Stokes number limit, Proc. Combust. Inst. 32 (2009), pp. 2205–2214.
   Web of Science ®Google Scholar
• V.S. Santoro, D.C. Kyritsis, and A. Gomez, An experimental study of vortex–flame interaction in counterflow spray diffusion flames, Proc. Combust. Inst. 28 (2000), pp. 1023–1030.
   Web of Science ®Google Scholar
• V.S. Santoro and A. Gomez, Extinction and reignition in counterflow spray diffusion flames interacting with laminar vortices, Proc. Combust. Inst. 29 (2002), pp. 585–592.
   Web of Science ®Google Scholar
• A. Vié, B. Franzelli, Y. Gao, T. Lu, H. Wang, and M. Ihme, Analysis of segregation and bifurcation in turbulent spray flames: A 3D counterflow configuration, Proc. Combust. Inst. 35 (2014), pp. 1675–1683.
   Web of Science ®Google Scholar
• N. Peters, Laminar diffusion flamelet models in non-premixed turbulent combustion, Prog. Energy Combust. Sci. 10 (1984), pp. 319–339.
   Web of Science ®Google Scholar
• R. Borghi, The links between turbulent combustion and spray combustion and their modelling, in 8th International Symposium on Transport Phenomena in Combustion, 1996, pp. 1–18.
   Google Scholar
• F. Demoulin and R. Borghi, Assumed PDF modeling of turbulent spray combustion, Combust. Sci. Technol. 158 (2000), pp. 249–271.
   Web of Science ®Google Scholar
• H. Olguin and E. Gutheil, Influence of evaporation on spray flamelet structures, Combust. Flame 161 (2014), pp. 987–996.
   Web of Science ®Google Scholar
• A. Vié, B. Franzelli, B. Fiorina, N. Darabiha, and M. Ihme, On the description of spray flame structure in the mixture fraction space, Annual Research Briefs, Center for Turbulence Research, Stanford University, 2013, pp. 93–106.
   Google Scholar
• W.A. Sirignano, A general superscalar for the combustion of liquid fuels, Proc. Combust. Inst. 29 (2002), pp. 535–542.
   Web of Science ®Google Scholar
• R.W. Bilger, A mixture fraction framework for the theory and modeling of droplets and sprays, Combust. Flame 158 (2011), pp. 191–202.
   Web of Science ®Google Scholar
• N.S.A. Smith, C.M. Cha, H. Pitsch, and J.C. Oefelein, Simulation and modeling of the behavior of conditional scalar moments in turbulent spray combustion, Proceedings of the Summer Program 2000, Center for Turbulence Research, Stanford University, 2000, pp. 207–218.
   Google Scholar
• K. Luo, F. Jianren, and K. Cen, New spray flamelet equations considering evaporation effects in the mixture fraction space, Fuel 103 (2014), pp. 1154–1157.
   Web of Science ®Google Scholar
• H. Olguin and E. Gutheil, Theoretical and numerical study of evaporation effects in spray flamelet model, in Experiments and Numerical Simulations of Turbulent Combustion of Diluted Sprays, B. Merci and E. Gutheil, eds., Springer, Switzerland, 2014, pp. 79–106.
   Google Scholar
• D. Maionchi and F. Fachini, Simple spray–flamelet model: Influence of ambient temperature and fuel concentration, vaporisation source and fuel injection position, Combust. Theory Model. 17 (2013), pp. 522–542.
   Web of Science ®Google Scholar
• F.A. Williams, Combustion Theory, Benjamin Cummings, Menlo Park, CA, 1985.
   Google Scholar
• A. Liñán, The asymptotic structure of counterflow diffusion flames for large activation energies, Acta Astronautica 1 (1974), pp. 1007–1039.
   Web of Science ®Google Scholar
• T. Poinsot and D. Veynante, Theoretical and Numerical Combustion, 3rd ed., Thierry Poinsot, 2012.
   Google Scholar
• K. Seshadri and N. Peters, Simulation of a turbulent spray flame using coupled PDF gas phase and spray flamelet modeling, Combust. Flame 73 (1988), pp. 24–44.
   Web of Science ®Google Scholar
• M. Maxey and J. Riley, Equation of motion for a small rigid sphere in a non uniform flow, Phys. Fluids 26(4) (1983), pp. 2883–2889.
   Web of Science ®Google Scholar
• R.W. Bilger, S.H. Starner, and R.J. Kee, On reduced mechanisms for methane–air combustion in nonpremixed flames, Combust. Flame 80 (1990), pp. 135–149.
   Web of Science ®Google Scholar
• J. Urzay, D. Martìnez-Ruiz, A.L. Sánchez, A. Liñán, and F.A. Williams, Flamelet structures in spray ignition, Annual Research Briefs, Center for Turbulence Research, Stanford University, 2014, pp. 107–122.
   Google Scholar
• B. Franzelli, E. Riber, M. Sanjosé, and T. Poinsot, A two-step chemical scheme for large eddy simulation of kerosene–air flames, Combust. Flame 157 (2010), pp. 1364–1373.
   Web of Science ®Google Scholar
• F. Laurent and M. Massot, Multi-fluid modeling of laminar poly-dispersed spray flames: Origin, assumptions and comparison of the sectional and sampling methods, Combust. Theory Model. 5 (2001), pp. 537–572.
   Web of Science ®Google Scholar
• D. Kah, F. Laurent, L. Fréret, S. de Chaisemartin, R. Fox, J. Reveillon, and M. Massot, Eulerian quadrature-based moment models for dilute polydisperse evaporating sprays, Flow Turbul. Combust. 85 (2010), pp. 649–676.
   Web of Science ®Google Scholar
• J. Ferry and S. Balachandar, A fast Eulerian method for disperse two-phase flow, Int. J. Multiphase Flow 27 (2001), pp. 1199–1226.
   Web of Science ®Google Scholar
• H. Pitsch and N. Peters, A consistent flamelet formulation for non-premixed combustion considering differential diffusion effects, Combust. Flame 114 (1998), pp. 26–40.
   Web of Science ®Google Scholar