The maximum entropy formalism and the prediction of liquid spray drop-size distribution

Entropy

Volumn 11, Issue 4, 2009, Pages 713-747

  Dumouchel, Christophe ^a  

^a UNIVERSITÉ ET INSA DE ROUEN   (France)

Author keywords

Drop Size distribution; Drop Velocity distribution; Liquid sprays; Maximum entropy formalism

Indexed keywords

EID: 77953482285     PISSN: None     EISSN: 10994300     Source Type: Journal    
DOI: 10.3390/e11040713     Document Type: Review

References (46)

1. Lefebvre, A.H. Atomization and Sprays; Hemisphere Publishing Corporation: New York, NY, USA, 1989.
2. Bayvel, L.; Orzechowski, Z. Liquid Atomization; Taylor and Francis: Washington, DC, USA, 1993.
3. Lin, S.P.; Reitz, R.D. Drop and spray formation from a liquid jet. Annu. Rev. Fluid. Mech. 1998, 30, 85-105.
4. Sirignano, W.A.; Mehring, C. Review of theory of distortion and disintegration of liquid streams. PECS 2000, 26, 609-655.
5. Dumouchel, C. On the experimental investigation on primary atomization of liquid streams. Exp. Fluids 2008, 45, 371-422.
6. Babinski, E.; Sojka, P.E. Modeling drop-size distribution. Prog. Ener. Comb. Sci. 2002, 28, 303-329.
7. Bhatia, J.C.; Dominick, J.; Durst, F.; Tropea, C. Phase-doppler-anemometry and the log-hyperbolic distribution applied to liquid sprays. Part. Part. Syst. Charact. 1988, 5, 153-164.
8. Bhatia, J.C.; Durst, F. Description of sprays using joint hyperbolic distribution in particle size and velocity. Comb. Flame 1990, 81, 203-218.
9. Paloposki, T. Drop-Size Distribution in Liquid Sprays; Acta Polytechnica Scandinavica, Mechanical Engineering Series No. 114, Helsinki, Finland, 1994.
10. Sowa, W.A. Interpreting mean drop diameters using distribution moments. Atom. Sprays 1992, 2, 1-15.
11. Mugele, R.A.; Evans, H.D. Droplet size distribution in sprays. Ind. Engng. Chem. 1951, 43, 1317-1324.
12. Sellens, R.W.; Brzustowski, T.A. A prediction of the drop-size distribution in a spray from first principles. Atom. Spray Tech. 1985, 1, 89-102.
13. Kapur, J.N. Twenty five years of maximum entropy principle. J. Math. Phys. Sci. 1983, 17, 103-156.
14. Sellens, R.W.; Brzustowski, T.A. A simplified prediction of droplet velocity distribution in a spray. Comb. Flame 1986, 65, 273-279.
15. Li, X.; Tankin, R.S. Droplet size distribution: a derivation of a nukiyama-tanasawa type distribution function. Comb. Sci. Technol. 1987, 56, 65-76.
16. Li, X.; Tankin, R.S. Derivation of droplet size distribution in sprays by using information theory. Comb. Sci. Technol. 1988, 60, 345-357.
17. Paloposki, T. The physically relevant parameter space of the nukiyama-tanasawa distribution function. Part. Part. Syst. Charact. 1991, 8, 287-293.
18. Li, X.; Tankin, R.S.; Renksizbulut, M. Calculated characteristics of droplet size and velocity in liquid sprays. Part. Part. Syst. Charact. 1990, 7, 54-59.
19. Bhatia, J.C.; Durst, F. Comparative study of some probability distributions applied to liquid sprays. Part. Part. Syst. Charact. 1989, 6, 151-162.
20. Dodge, L.G.; Rhodes, D.J.; Reitz, R.D. Drop-size measurement techniques for sprays: comparison of malvern laser-diffraction and aerometrics phase/doppler. Appl. Opt. 1987, 26, 2144-2154.
21. Sellens, R.W. Prediction of the drop size and velocity distribution in a spray based on the maximum entropy formalism. Part. Part. Syst. Charact. 1989, 6, 17-27.
22. LI, X.; Chin, L.P.; Tankin, R.S.; Jackson, T.; Stutrud, J.; Switzer, G. Comparison between experiments and predictions based on maximum entropy for sprays from a pressure atomizer. Comb. Flame 1991, 86, 73-89.
23. Li, X.; Tankin, R.S. In the prediction of droplet size and velocity distributions in sprays through maximum entropy principle. Part. Part. Syst. Charact. 1992, 9, 195-201.
24. Chin, L.P.; LaRose, P.G.; Tankin, R.S.; Jackson, T.; Stutrud, J.; Switzer, G. Droplet distributions from the breakup of a cylindrical liquid jet. Phys. Fluids A 1991, 3, 1897-1906.
25. Ahmadi, M.; Sellens, W. A simplified maximum-entropy-based drop-size distribution. Atom. Sprays 1993, 3, 291-310.
26. Van Der Geld, C.W.M.; Vermeer, H. Prediction of drop size distributions in sprays using the maximum entropy formalism: the effect of satellite formation. Int. J. Multiphase Flow 1994, 20, 363-381.
27. Chin, L.P.; Switzer, G.; Tankin, R.S.; Jackson, T.; Stutrud, J. Bi-modal size distribution predicted by maximum entropy are compared with experiments in sprays. Comb. Sci. Tech. 1995, 109, 35-52.
28. Chin, L.P.; Hsing, P.C.; Tankin, R.S.; Jackson, T. Comparisons between experiments and prediction based on maximum entropy for the breakup of a cylindrical liquid jet. Atom. Sprays 1996, 5, 603-620.
29. Mitra, S.K.; Li, X. A predictive model for droplet size distribution in sprays. Atom. Sprays 1999, 9, 29-50.
30. Dobre, M.; Bolle, L. Practical design of ultrasonic spray devices: experimental testing of several atomizer geometries. Exp. Therm. Fluid Sci. 2002, 26, 205-211.
31. Cousin, J.; Yoon, S.J.; Dumouchel, C. Coupling of classical linear theory and maximum entropy formalism for prediction of drop-size distribution in sprays: application to pressure swirl atomizers. Atom. Sprays 1996, 6, 601-622.
32. Sindayihebura, D.; Cousin, J.; Dumouchel, C. Experimental and theoretical study of sprays produced by ultrasonic atomisers. Part. Part. Syst. Charact. 1997, 14, 93-101.
33. Dumouchel, C.; Boyaval, S. Use of the maximum entropy formalism to determine drop-size distribution characteristics. Part. Part. Syst. Charact. 1999, 16, 177-184.
34. Boyaval, S.; Dumouchel, C. Investigation on the drop-size distribution of sprays produced by a high-pressure swirl injector. measurements and application of the maximum entropy formalism. Part. Part. Syst. Charact. 2001, 18, 33-46.
35. Dumouchel, C.; Malot, H. Development of a three-parameter volume-based spray drop-size distribution through the application of the maximum entropy formalism. Part. Part. Syst. Charact. 1999, 16, 220-228.
36. Malot, H.; Dumouchel, C. Analysis of the Drop-size distribution of Sprays Produced by Plain Cylindrical Jets: Application of the Maximum Entropy Formalism. In Proceedings of ILASS-Europe 2001, Zürich, Switzerland, September 2001.
37. Dumouchel, C.; Sindayihebura, D.; Bolle, L. Application of the maximum entropy formalism on sprays produced by ultrasonic atomizers. Part. Part. Syst. Charact. 2003, 20, 150-161.
38. Jaynes, E.T. Papers ion Probability, Statistics and Statistical Physics; Reidel: Dordrecht, The Netherlands, 1983; pp. 60; 210-315.
39. Kim, W.T.; Mitra, S.K.; Li, X.; Prociw, L.A.; Hu, T.C.J. A predictive model for the initial droplet size and velocity distributions in sprays and comparison with experiments. Part. Part. Syst. Charact. 2003, 20, 135-149.
40. Dumouchel, C. A new formulation of the maximum entropy formalism to model liquid spray drop-size distribution. Part. Part. Syst. Charact. 2006, 23, 468-479.
41. Griffith, L. A theory of the size distribution of particles in a comminuted system. Can. J. Res. 1943, 21, 57-64.
42. Lienhard, J.H.; Meyer, P.L. A physical basis for the generalized gamma distribution. Quart. Applied Math. 1967, 25, 330-334.
43. Lecompte, M.; Dumouchel, C. On the capability of the generalized gamma function to represent spray drop-size distribution. Part. Part. Syst. Charact. 2008, 25, 154-167.
44. Yongyingsakthavorn, P.; Cousin, J.; Dumouchel, C.; Hélie, J. Piezo-Spray Drop-Size Measurements by Laser-Diffraction Technique in the Presence of Multiple Scattering Effects. In Proceedings of the ILASS-Europe 2008, Paper ID ILASS08-070, Como Lake, Italy, September 2008.
45. Li, X.; Li, M.; Fu, H. Modeling the initial droplet size distribution in sprays based on the maximization of entropy generation. Atom. Sprays 2005, 15, 295-321.
46. Sirignano, W.A.; Mehring, C. Comments on Energy Conservation in Liquid-Stream Disintegration. In Proceedings of ICLASS 2000, Pasadena, CA, USA, July 2000.