Comparison of the stochastic fields method and DQMoM-IEM as turbulent reaction closures

Chemical Engineering Science

Volumn 65, Issue 20, 2010, Pages 5429-5441

  Akroyd, Jethro ^a   Smith, Alastair J ^a   McGlashan, Laurence R ^a   Kraft, Markus ^a  

^a UNIVERSITY OF CAMBRIDGE   (United Kingdom)

Author keywords

CFD; Chemical reactors; DQMoM IEM; SF; Simulation; Turbulence

Indexed keywords

AXISYMMETRIC; CFD; COMMON FEATURES; COMPUTATIONAL FLUID DYNAMICS CODES; DIRECT QUADRATURE METHOD OF MOMENTS; DQMOM-IEM; INTERACTION BY EXCHANGE WITH THE MEANS; MATHEMATICAL FRAMEWORKS; MICRO-MIXING; SF; SIMULATION; STOCHASTIC FIELD; SUB-GRIDS; SYSTEMATIC INVESTIGATIONS; TURBULENT REACTING FLOWS; TURBULENT REACTION; VARIANCE REDUCTION TECHNIQUES;

CHEMICAL REACTORS; CHEMICALS; METHOD OF MOMENTS; NUMERICAL METHODS; PROBABILITY DENSITY FUNCTION; REACTION RATES; STOCHASTIC MODELS; STOCHASTIC SYSTEMS; TURBULENCE;

COMPUTATIONAL FLUID DYNAMICS;

EID: 77956420410     PISSN: 00092509     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ces.2010.06.039     Document Type: Article

References (47)

1. Ahrens J.H., Dieter U. Extensions of Forsythe's method for random sampling from the normal distribution. Mathematics of Computation 1973, 27(124):927-937.
2. Akroyd J., Smith A., McGlashan L.R., Kraft M. Numerical investigation of DQMoM-IEM as a turbulent reaction closure. Chemical Engineering Science 2010, 65(6):1915-1924.
3. Bhave A., Kraft M. Partially stirred reactor model: analytical solutions and numerical convergence study of a PDF/Monte Carlo method. SIAM Journal on Scientific Computing 2004, 25(5):1798-1823.
4. Boyle P., Brodie M., Glassernan P. Monte Carlo methods for security pricing. Journal of Economic Dynamics and Control 1997, 21(8-9):1267-1321.
5. CD-adapco, 2008. Star-CD v4.08.006. http://www.cd-adapco.com/.
6. Cheng R.C.H. The use of antithetic variates in computer simulations. Journal of the Operational Research Society 1982, 33(3):229-237.
7. Fishman G.S. Monte Carlo: Concepts, Algorithms and Applications 1996, Springer-Verlag, New York.
8. Fishman G.S., Huang B.D. Antithetic variates revisited. Communications of the ACM 1983, 26(11):964-971.
9. Fox R.O. Computational Models for Turbulent Reacting Flows 2003, Cambridge University Press, Cambridge.
10. Gardiner C.W. Handbook of Stochastic Methods 2004, Springer, Berlin. third ed.
11. Garmory, A., 2007. Micromixing effects in atmospheric reacting flows. Ph.D. Thesis, University of Cambridge.
12. Garmory A., Kim I.S., Britter R.E., Mastorakos E. Simulations of the dispersion of reactive pollutants in a street canyon, considering different chemical mechanisms and micromixing. Atmospheric Environment 2009, 43(31):4670-4680.
13. Garmory A., Mastorakos E. Aerosol nucleation and growth in a turbulent jet using the stochastic fields method. Chemical Engineering Science 2008, 63(26):4078-4089.
14. Garmory A., Richardson E.S., Mastorakos E. Micromixing effects in a reacting plume by the stochastic fields method. Atmospheric Environment 2006, 40(6):1078-1091.
15. Gavi E., Marchisio D.L., Baressi A.A. CFD modelling and scale-up of confined impinging jet reactors. Chemical Engineering Science 2007, 62(8):2228-2241.
16. Gavi E., Rivautella L., Marchisio D.L., Vanni M., Baressi A.A., Baldi G. CFD modelling of nano-particle precipitation in confined impinging jet reactors. Chemical Engineering Research and Design 2007, 85(A5 Special Issue: 12th European Conference on Mixing):1-10.
17. Geweke J. Antithetic acceleration of Monte Carlo integration in Bayesian inference. Journal of Econometrics 1988, 38(1-2):73-89.
18. Hairer, E., Wanner, G., 1996. Solving Ordinary Differential Equations II. Stiff and Differential-Algebraic Problems, second revised ed. Springer Series in Computational Mathematics, vol. 14. Springer Verlag, Berlin.
19. Hammersley J.M., Handscomb D.C. Proof of the antithetic variates theorem for n>2. Mathematical Proceedings of the Cambridge Philosophical Society 1958, 54(2):300-301.
20. Hammersley J.M., Mauldon J.G. General principles of antithetic variates. Mathematical Proceedings of the Cambridge Philosophical Society 1956, 52(3):476-481.
21. Hammersley J.M., Morton K.W. A new Monte Carlo technique: antithetic variates. Mathematical Proceedings of the Cambridge Philosophical Society 1956, 52(3):449-475.
22. Hauke G., Valiño L. Computing reactive flows with a field Monte Carlo formulation and multi-scale methods. Computer Methods in Applied Mechanics and Engineering 2004, 193(15-16):1455-1470.
23. Haworth D.C. Progress in probability density function methods for turbulent reacting flows. Progress in Energy and Combustion Science 2010, 36(2):168-259.
24. Jones W.P., Navarro-Martinez S. Large eddy simulation of autoignition with a subgrid probability density function method. Combustion and Flame 2007, 150(3):170-187.
25. Jones W.P., Navarro-Martinez S. Numerical study of n-heptane auto-ignition using LES-PDF methods. Flow, Turbulence and Combustion 2009, 83(3):407-423.
26. Jones W.P., Navarro-Martinez S., Röhl O. Large eddy simulation of hydrogen auto-ignition with a probability density function method. Proceedings of the Combustion Institute 2007, 31(2):1765-1771.
27. Kloeden P.E., Platen E. Numerical Solution of Stochastic Differential Equations 1995, Springer, Berlin. second corrected printing ed.
28. Kraft M., Fey H. Some analytic solutions for stochastic reactor models based on the joint composition PDF. Combustion Theory and Modelling 1999, 3(2):343-358.
29. Li K.T., Toor H.L. Turbulent reactive mixing with a series-parallel reaction: effect of mixing on yield. AIChE Journal 1986, 32(8):1312-1320.
30. Libby P.A., Williams F.A. Turbulent Reacting Flows 1980, Springer, Berlin.
31. Lui Y., Fox R.O. CFD predictions for chemical processing in a confined impinging-jets reactor. AIChE Journal 2006, 52(2):731-744.
32. Matsumoto M., Nishimura T. Mersenne Twister: a 623-dimensionally equidistributed uniform pseudo-random number generator. ACM Transactions on Modeling and Computer Simulation 1998, 8(1):3-30.
33. Mustata R., Valiño L., Jiménez C., Jones W.P., Bondi S. A probability density function Eulerian Monte Carlo field method for large eddy simulations: application to a turbulent piloted methane/air diffusion flame (Sandia D). Combustion and Flame 2006, 145(1-2):88-104.
34. Paskov S., Traub J. Faster valuation of financial derivatives. The Journal of Portfolio Management 1995, 22(1):113-123.
35. Peters N. Turbulent Combustion 2000, Cambridge University Press, Cambridge.
36. Pope S.B. PDF methods for turbulent reacting flows. Progress in Energy and Combustion Science 1985, 11(2):119-192.
37. Raman V., Pitsch H., Fox R.O. Eulerian transported probability density function sub-filter model for large-eddy simulations of turbulent combustion. Combustion Theory and Modelling 2006, 10(3):439-548.
38. Sabel'nikov V., 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 2005, 72(1). Article No. 016301.
39. Strang G. On the construction and comparison of difference schemes. SIAM Journal on Numerical Analysis 1968, 5(3):506-517.
40. Tang Q., Zhao W., Bockelie M., Fox R.O. Multi-environment probability density function method for modelling turbulent combustion using realistic chemical kinetics. Combustion Theory and Modelling 2007, 11(6):889-907.
41. Tsai K., Fox R.O. PDF simulation of a turbulent series-parallel reaction in an axisymmetric reactor. Chemical Engineering Science 1994, 49(24B):5154-5158.
42. Tsai K., Gillis P.A., Sen S., Fox R.O. A finite-mode PDF model for turbulent reacting flows. Journal of Fluids Engineering 2002, 124(1):102-107.
43. Valiño L. A field Monte Carlo formulation for calculating the probability density function of a single scalar in a turbulent flow. Flow, Turbulence and Combustion 1998, 60(2):157-172.
44. Villermaux J., Devillon J.C. Représentation de la coalescence et de la redispersion des domaines de ségrégation dans un fluide par un modèle d'interaction phénoménologique. Proceedings of the 2nd International Symposium on Chemical Reaction Engineering 1972, 1-13. Elsevier, New York.
45. Wang L., Fox R.O. Comparison of micromixing models for CFD simulation of nanoparticle formation. AIChE Journal 2004, 50(9):2217-2232.
46. Wilson J.R. Proof of the antithetic-variates theorem for unbounded functions. Mathematical Proceedings of the Cambridge Philosophical Society 1979, 86(03):477-479.
47. Wilson J.R. Antithetic sampling with multivariate inputs. American Journal of Mathematical and Management Sciences 1983, 3:121-144.