PDF method for population balance in turbulent reactive flow

Chemical Engineering Science

Volumn 62, Issue 23, 2007, Pages 6865-6878

  Rigopoulos, Stelios ^a  

^a UNIVERSITY OF MANCHESTER   (United Kingdom)

Author keywords

Population balance; Turbulent reactive flow

Indexed keywords

COAGULATION; CONCENTRATION (PROCESS); NUCLEATION; NUMERICAL METHODS; PARTICLE SIZE ANALYSIS; POPULATION DYNAMICS; PRECIPITATION (CHEMICAL); TURBULENCE;

KINETIC LAWS; POPULATION BALANCE EQUATION; TURBULENT REACTIVE FLOWS;

TURBULENT FLOW;

COAGULATION; CONCENTRATION (PROCESS); NUCLEATION; NUMERICAL METHODS; PARTICLE SIZE ANALYSIS; POPULATION DYNAMICS; PRECIPITATION (CHEMICAL); TURBULENCE; TURBULENT FLOW;

EID: 35348929941     PISSN: 00092509     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ces.2007.05.039     Document Type: Article

References (51)

1. 2 hydrocarbons. Combustion and Flame 121 (2000) 122
2. Astarita G. Mass Transfer with Chemical Reaction (1967), Elsevier, Amsterdam
3. Baldyga J., and Orciuch W. Closure problem for precipitation. Transactions of the IChemE 75 Part A (1997) 160
4. Balthasar M., Mauss F., Knobel A., and Kraft M. Detailed modeling of soot formation in a partially stirred plug flow reactor. Combustion and Flame 128 395 (2002)
5. Chen J.Y. Stochastic modeling of partially stirred reactors. Combustion Science and Technology 122 (1997) 63
6. Dopazo C. Probability density function approach for a turbulent axisymmetric heated jet. Centreline evolution. Physics of Fluids 18 4 (1975) 397
7. Drake, R.L., 1972. A general mathematical survey of the coagulation equation. In: Hidy, G.M., Brock, J.R. (Eds.), Topics in Current Aerosol Research. vol. 3 (Part 2), 202.
8. Fox R.O. Computational Models for Turbulent Reacting Flows (2003), Cambridge University Press, Cambridge
9. Friedlander S. Smoke, Dust and Haze: Fundamentals of Aerosol Dynamics. second ed (2000), Oxford University Press, Oxford
10. Gardiner C.W. Handbook of Stochastic Methods. third ed (2004), Springer, Berlin
11. Gelbard F., and Seinfeld J.H. Simulation of multicomponent aerosol dynamics. Journal of Colloid and Interface Science 78 2 (1980) 485
12. Hounslow M.J., Ryall R.L., and Marshal V.R. Discretized population balance for nucleation, growth, and aggregation. A.I.Ch.E. Journal 34 11 (1988) 1821
13. Hulburt H.M., and Katz S. Some problems in particle technology: a statistical mechanical formulation. Chemical Engineering Science 19 (1964) 555
14. Jones, W.P., 2001. The joint scalar probability density function method. In: Launder, B.E., Sandham, N.D. (Eds.), Closure strategies for turbulent and transitional flows, vol. 582.
15. Jones W.P., and Sheen D.H. A probability density function method for modelling liquid fuel sprays. Flow Turbulence and Combustion 63 (1999) 379
16. Kazakov A., and Frenklach M. Dynamic modeling of soot particle coagulation and aggregation: implementation with the method of moments and application to high-pressure laminar premixed flames. Combustion and Flame 114 (1998) 484
17. Kollmann, W., 1995. Probability density function (PDF) closures for scalar transport in turbulent flows. In: Habashi, W.G., Hafez, M.M. (Eds.), Computational Fluid Dynamics Techniques, Section VII: Computational Techniques for Turbulent Flows, vol. 621.
18. Kollmann W., Kennedy I.M., Metternich M., and Chen J.-Y. Application of a soot model to a turbulent ethylene diffusion flame. In: Bockhorn H. (Ed). Soot Formation in Combustion-Mechanisms and Models (1994), Springer, Berlin vol. 503
19. Kumar D., and Ramkrishna D. On the solution of population balance equations by discretization-I. A fixed pivot technique. Chemical Engineering Science 51 8 (1996) 1311
20. Levin L.M., and Sedunov Y.S. The theoretical model of the drop spectrum formation process in clouds. Pure and Applied Geophysics 69 (1968) 320
21. Lindstedt R.P., Louloudi S.A., Pitsch H., and Gore J.P. Joint-scalar transported PDF modeling of soot formation and oxidation. Proceedings of the Combustion Institute 30 1 (2005) 775
22. Lundgren T.S. Distribution functions in the statistical theory of turbulence. Physics of Fluids 10 5 (1967) 969
23. Manjunath S., Gandhi K.S., Kumar R., and Ramkrishna D. Precipitation in small systems-I. Stochastic analysis. Chemical Engineering Science 49 9 (1994) 1451
24. Manjunath S., Gandhi K.S., Kumar R., and Ramkrishna D. Mean field equations more effective than population balance. Chemical Engineering Science 51 19 (1996) 4423
25. Marchisio D.L., and Fox R.O. Solution of population balance equations using the direct quadrature method of moments. Journal of Aerosol Science 36 1 (2005) 43
26. Marchisio D.L., Pikturna J.T., Fox R.O., Vigil R.D., and Barresi A.A. Quadrature method of moments for population balance equations. A.I.Ch.E. Journal 49 5 (2003) 1266
27. Mashayek F., and Pandya R.V.R. Analytical description of particle/droplet-laden turbulent flows. Progress in Energy and Combustion Science 29 (2003) 329
28. McGraw R. Description of aerosol dynamics by the quadrature method of moments (QMOM). Aerosol Science and Technology 27 (1997) 155
29. Minier J.P., and Peirano E. The PDF approach to turbulent polydispersed two-phase flows. Physics Reports 352 (2001) 11
30. Nere N.K., and Ramkrishna D. Solution of population balance equation with pure aggregation in a fully developed turbulent pipe flow. Chemical Engineering Science 61 (2006) 96
31. O'Brien, E.E., 1980. The probability density function pdf approach to reacting turbulent flows. In: Libby, P., Williams, F.A. (Eds.), Turbulent Reacting Flows, vol. 185.
32. Pope S.B. A Monte Carlo method for the PDF equations of turbulent reactive flow. Combustion Science and Technology 25 (1981) 159
33. Pope S.B. PDF methods for turbulent reactive flows. Progress in Energy and Combustion Science 11 2 (1985) 119-192
34. Pratsinis S.E. Flame aerosol synthesis of ceramic powders. Progress in Energy and Combustion Science 24 (1998) 197
35. Ramkrishna D. Population Balances: Theory and Applications to Particulate Systems in Engineering (2000), Academic Press, New York
36. Randolph A.D., and Larson M.A. Theory of Particulate Processes: Analysis and Techniques of Continuous Crystallization. second ed (1988), Academic Press, New York
37. Reade W.C., and Collins L.R. A numerical study of the particle size distribution of an aerosol undergoing turbulent coagulation. Journal of Fluid Mechanics 415 (2000) 45
38. Reeks M.W. On a kinetic equation for the transport of particles in turbulent flows. Physics of Fluids A 3 3 (1991) 446
39. Rigopoulos S., and Jones A.G. Finite-element scheme for solution of the dynamic population balance equation. A.I.Ch.E. Journal 49 5 (2003) 1127
40. Sabel'nikov V., and Soulard O. Rapidly decorrelating velocity-field model as a tool for solving one-point Fokker-Planck equations for probability density functions of turbulent reactive scalars. Physical Review E 72 1 (2005) 1
41. Saffman P.G., and Turner J.S. On the collision of drops in turbulent clouds. Journal of Fluid Mechanics 1 (1956) 16
42. Schwarzer H.C., and Peukert W. Combined experimental/numerical study on the precipitation of nanoparticles. A.I.Ch.E. Journal 50 12 (2004) 3234
43. Scott W.T. Poisson statistics in distributions of coalescing droplets. Journal of the Atmospheric Sciences 24 (1967) 221
44. Sirignano W.A. Fluid Dynamics and Transport of Droplets and Sprays (1999), Cambridge University Press, Cambridge
45. Valiño. Field Monte Carlo formulation for calculating the probability density function of a single scalar in a turbulent flow. Flow Turbulence and Combustion 60 (1998) 157
46. Van Kampen N.G. Stochastic Processes in Physics and Chemistry (2001), North-Holland, Amsterdam
47. Wang L., Wexler A., and Zhou Y. On the collision rate of small particles in isotropic turbulence. I. Zero-inertia case. Physics of Fluids 10 (1998) 266
48. Warshaw M. Cloud droplet coalescence: statistical foundations and a one-dimensional sedimentation model. Journal of the Atmospheric Sciences 24 (1967) 278
49. Williams F.A. Spray combustion and atomization. Physics of Fluids 1 6 (1958) 541
50. Wooldridge M. Gas-phase combustion synthesis of particles. Progress in Energy and Combustion Science 24 (1998) 63
51. Wright D., McGraw R., and Rosner D.E. Bivariate extension of the quadrature method of moments for modeling simultaneous coagulation and sintering of particle populations. Journal of Colloid and Interface Science 236 (2001) 242