On the Use of Fractional-Order Quadrature-Based Moment Closures for Predicting Soot Formation in Laminar Flames

References

• Akih-Kumgeh, B. 2013. Comparison of detailed and reduced models for syngas and ethanol. Canada: Alternative Fuels Laboratory, Department of Mechanical Engineering, McGill University.
   Google Scholar
• Appel, J., H. Bockhorn, and M. Frenklach. 2000. Kinetic modeling of soot formation with detailed chemistry and physics: Laminar premixed flames of c2 hydrocarbons. Combust. Flame 121 (1–2):122–36. doi:10.1016/S0010-2180(99)00135-2.
   Web of Science ®Google Scholar
• Balthasar, M., and M. Kraft. 2003. A stochastic approach to calculate the particle size distribution function of soot particles in laminar premixed flames. Combust. Flame 133:289–98. doi:10.1016/S0010-2180(03)00003-8.
   Web of Science ®Google Scholar
• Bhatt, J. S., and R. P. Lindstedt. 2009. Analysis of the impact of agglomeration and surface chemistry models on soot formation and oxidation. Proceedings of the Combustion Institute, vol. 32, 713–20. McGill University, Canada.
   Google Scholar
• Blacha, T., M. D. Domenico, P. Gerlinger, and M. Aigner. 2012. Soot predictions in premixed and non- premixed laminar flames using a sectional approach for pahs and soot. Combust. Flame 159:181–93. doi:10.1016/j.combustflame.2011.07.006.
   Web of Science ®Google Scholar
• Blanquart, G., and H. Pitsch. 2009. Analyzing the effects of temperature on soot formation with a joint volume-surface-hydrogen model. Combust. Flame 156:1614–26. doi:10.1016/j.combustflame.2009.04.010.
   Web of Science ®Google Scholar
• Buffo, A., M. Vanni, and D. L. Marchisio. 2012. Multidimensional population balance model for the simulation of turbulent gas-liquid systems in stirred tank reactors. Chem. Eng. Sci. 70:31–44. doi:10.1016/j.ces.2011.04.042.
   Web of Science ®Google Scholar
• Celnik, M., R. Patterson, M. Kraft, and W. Wagner. 2007. Coupling a stochastic soot population balance to gas-phase chemistry using operator splitting. Combust. Flame 148:158–76. doi:10.1016/j.combustflame.2006.10.007.
   Web of Science ®Google Scholar
• Chalons, C., R. O. Fox, and M. Massot. 2010. A multi-gaussian quadrature method of moments for gas- particle flows in a les framework. In Proceedings of the summer program 2010, 347–58. Palo Alto, California.
   Google Scholar
• Charest, M. R., C. P. Groth, and Ö. L. Gülder. 2010. A computational framework for predicting laminar reactive flows with soot formation. Combust. Theor. Model. 14:793–825. doi:10.1080/13647830.2010.512960.
   Web of Science ®Google Scholar
• Charest, M. R., C. P. Groth, and Ö. L. Gülder. 2011. Effects of gravity and pressure on laminar coflow methane–Air diffusion flames at pressures from 1 to 60 atmospheres. Combust. Flame 158 (5):860–75. doi:10.1016/j.combustflame.2011.01.019.
   Web of Science ®Google Scholar
• Charest, M. R., Ö. L. Gülder, and C. P. Groth. 2014. Numerical and experimental study of soot formation in laminar diffusion flames burning simulated biogas fuels at elevated pressures. Combust. Flame 161 (10):2678–91. doi:10.1016/j.combustflame.2014.04.012.
   Web of Science ®Google Scholar
• Charest, M. R., H. I. Joo, Ö. L. Gülder, and C. P. Groth. 2011. Experimental and numerical study of soot formation in laminar ethylene diffusion flames at elevated pressures from 10 to 35 atm. Proc. Combust. Inst. 33 (1):549–57. doi:10.1016/j.proci.2010.07.054.
   Google Scholar
• Clarke, A. D., K. J. Noone, J. Heintzenberg, S. G. Warren, and D. S. Covert. 1967. Aerosol light absorption measurement techniques: Analysis and intercomparisons. Atmos. Environ. 21:1455–65. doi:10.1016/0004-6981(67)90093-5.
   Google Scholar
• D’Anna, A., and J. H. Kent. 2006. Modeling of particulate carbon and species formation in coflowing diffusion flames of ethylene. Combust. Flame 144:249–60. doi:10.1016/j.combustflame.2005.07.011.
   Web of Science ®Google Scholar
• Frenklach, M. 2002. Method of moments with interpolative closure. Chem. Eng. Sci. 57:2229–39. doi:10.1016/S0009-2509(02)00113-6.
   Web of Science ®Google Scholar
• Frenklach, M., and S. J. Harris. 1987. Aerosol dynamics modeling using the method of moments. J. Colloid Interface Sci. 118:252–61. doi:10.1016/0021-9797(87)90454-1.
   Web of Science ®Google Scholar
• Goodson, M., and M. Kraft. 2002. An efficient stochastic algorithm for simulating nano-particle dynamics. J. Comput. Phys. 183:210–32. doi:10.1006/jcph.2002.7192.
   Web of Science ®Google Scholar
• Gordon, R. G. 1968. Error bounds in equilibrium statistical mechanics. J. Math. Phys. 9:655–63. doi:10.1063/1.1664624.
   Web of Science ®Google Scholar
• Griffin, E. A., M. Christensen, and Ö. L. Gülder. 2018. Effect of ethanol addition on soot formation in laminar methane diffusion flames at pressures above atmospheric. Combust. Flame 193:306–12. doi:10.1016/j.combustflame.2018.04.001.
   Web of Science ®Google Scholar
• Kennedy, I. M. 2007. The health effects of combustion-generated aerosols. Proc. Comb. Inst. 31:2757–70. doi:10.1016/j.proci.2006.08.116.
   Web of Science ®Google Scholar
• Köylü, Ü. Ö., G. Faeth, T. L. Farias, and M. G. Carvalho. 1995. Fractal and projected structure properties of soot aggregates. Combust. Flame 100 (4):621–33. doi:10.1016/0010-2180(94)00147-K.
   Web of Science ®Google Scholar
• Kumar, S., and D. Ramkrishna. 1996. On the solution of population balance equations by discretization i: A fixed pivot technique. Chem. Eng. Sci. 51:1311–32. doi:10.1016/0009-2509(96)88489-2.
   Web of Science ®Google Scholar
• Leung, K. M., R. P. Lindstedt, and W. P. Jones. 1991. A simplified reaction mechanism for soot formation in nonpremixed flames. Combust. Flame 87:289–305. doi:10.1016/0010-2180(91)90114-Q.
   Web of Science ®Google Scholar
• Liu, F., H. Guo, G. J. Smallwood, and Ö. L. Gülder. 2002. Effects of gas and soot radiation on soot formation in a coflow laminar ethylene diffusion flame. J. Quant. Spectrosc. Radiat. Transf. 73:409–21. doi:10.1016/S0022-4073(01)00205-9.
   Web of Science ®Google Scholar
• Madadi-Kandjani, E., and A. Passalacqua. 2015. An extended quadrature-based moment method with log-normal kernel density functions. Chem. Eng. Sci. 131:323–39. doi:10.1016/j.ces.2015.04.005.
   Web of Science ®Google Scholar
• Marchisio, D. L., J. T. Pikturna, R. O. Fox, R. D. Vigil, and A. A. Barresi. 2003. Quadrature method of moments for population-balance equations. AIChE J. 49:1266–76. doi:10.1002/(ISSN)1547-5905.
   Web of Science ®Google Scholar
• McGraw, R. 1997. Description of aerosol dynamics by the quadrature method of moments. Aerosol Sci. Technol. 27:255–65. doi:10.1080/02786829708965471.
   Web of Science ®Google Scholar
• McGraw, R., and D. L. Wright. 2003. Chemically resolved aerosol dynamics for internal mixtures by the quadrature method of moments. J. Aerosol Sci. 34:189–209. doi:10.1016/S0021-8502(02)00157-X.
   Web of Science ®Google Scholar
• Menon, S., J. Hansen, L. Nazarenko, and Y. Luo. 2002. Climate effects of black carbon aerosols in china and india. Science 297:2255–2253. doi:10.1126/science.1075159.
   Web of Science ®Google Scholar
• Mueller, M. E., G. Blanquart, and H. Pitsch. 2009. Hybrid method of moments for modeling soot formation and growth. Combust. Flame 156:1143–55. doi:10.1016/j.combustflame.2009.01.025.
   Web of Science ®Google Scholar
• Patterson, R. I. A., J. Singh, M. Balthasar, M. Kraft, and W. Wagner. 2006. Extending stochastic soot simulation to higher pressures. Combust. Flame 145:638–42. doi:10.1016/j.combustflame.2006.02.005.
   Web of Science ®Google Scholar
• Pope, C. A., R. Burnett, M. Thun, E. Calle, D. Krewski, K. Ito, and G. Thurston. 2002. Lung cancer, cardiopulmonary mortality, and long-term exposure to fine particulate air pollution. JAMA 287:1132–41. doi:10.1001/jama.287.9.1132.
   PubMed Web of Science ®Google Scholar
• Qamar, S., M. Elsner, I. Angelov, G. Warnecke, and A. Seidel-Morgenstern. 2006. A comparative study of high resolution schemes for solving population balances in crystallization. Chem. Eng. Sci. 30:1119–31.
   Google Scholar
• Salenbauch, S., A. Cuoci, A. Frassoldati, C. Saggese, and T. Faravelli. 2015. Modeling soot formation in premixed flames using an extended conditional quadrature method of moments. Combust. Flame 162:2529–43. doi:10.1016/j.combustflame.2015.03.002.
   Web of Science ®Google Scholar
• Smooke, M. D., M. B. Long, B. C. Connelly, M. B. Colket, and R. J. Hall. 2005. Soot formation in laminar diffusion flames. Combust. Flame 143:613–28. doi:10.1016/j.combustflame.2005.08.028.
   Web of Science ®Google Scholar
• Sung, Y., V. Raman, H. Koo, M. Mehta, and R. O. Fox. 2014. Large eddy simulation modeling of turbulent flame synthesis of titania nanoparticles using a bivariate particle description. AIChE J. 60:459–72. doi:10.1002/aic.14279.
   Web of Science ®Google Scholar
• Wheeler, J. C. 1974. Modified moments and gaussian quadratures. Rocky Mt. J. Math. 4:287–96. doi:10.1216/RMJ-1974-4-2-287.
   Google Scholar
• Wick, A., I.-T.-T. Nguyen, F. Laurent, R. O. Fox, and H. Pitsch. 2017. Modeling soot oxidation with the extended quadrature method of moments. Proc. Comb. Inst. 36:789–97. doi:10.1016/j.proci.2016.08.004.
   Web of Science ®Google Scholar
• Wright, D. L., R. McGraw, and D. E. Rosner. 2001. Bivariate extension of the quadrature method of moments for modeling simultaneous coagulation and sintering of particle populations. J. Colloid Interface Sci. 236:242–51. doi:10.1006/jcis.2000.7409.
   PubMed Web of Science ®Google Scholar
• Yuan, C., and R. O. Fox. 2011. Conditional quadrature method of moments for kinetic equations. J. Comput. Phys. 230:8216–46.
   Web of Science ®Google Scholar
• Yuan, C., F. Laurent, and R. O. Fox. 2012. An extended quadrature method of moments for population balance equations. J. Aerosol Sci. 51:1–23. doi:10.1016/j.jaerosci.2012.04.003.
   Web of Science ®Google Scholar
• Zhang, Q., H. Guo, F. Liu, G. J. Smallwood, and M. J. Thompson. 2008. Implementation of an advanced fixed sectional aerosol dynamics model with soot aggregate formation in a laminar methane/air coflow diffusion flame. Combust. Theor. Model. 12:621–41. doi:10.1080/13647830801966153.
   Web of Science ®Google Scholar
• Zhao, B., Z. Yang, Z. Li, M. V. Johnston, and H. Wang. 2005. Particle size distribution function of incipient soot in laminar premixed ethylene flames: Effect of flame temperature. Proceedings of the Combustion Institute, vol. 30, 1441–48. University of Illinois at Chicago, United States.
   Google Scholar
• Zucca, A., D. L. Marchisio, A. A. Barresi, and R. O. Fox. 2006. Implementation of the population balance equation in cfd codes for modelling soot formation in turbulent flames. Chem. Eng. Sci. 61:87–95. doi:10.1016/j.ces.2004.11.061.
   Web of Science ®Google Scholar