Numerical simulation of spray coalescence in an Eulerian framework: Direct quadrature method of moments and multi-fluid method

Journal of Computational Physics

Volumn 227, Issue 6, 2008, Pages 3058-3088

  Fox, R O ^a   Laurent, F ^b   Massot, M ^b  

^a Iowa State University of Science and Technology   (United States)

^b ECOLE CENTRALE PARIS   (France)

Author keywords

Coalescence; Direct quadrature method of moments; Liquid sprays; Multi fluid model; Number density function; Spray equation

Indexed keywords

DELTA FUNCTIONS; DROP FORMATION; LAGRANGE MULTIPLIERS; METHOD OF MOMENTS; NUMERICAL MODELS; SPRAY NOZZLES; STOCHASTIC SYSTEMS;

DIRECT QUADRATURE METHOD OF MOMENTS; EULERIAN MODELS; LIQUID SPRAY; MULTI-FLUIDS; MULTIFLUID MODEL; NUMBER DENSITY; NUMBER DENSITY FUNCTION; POLYDISPERSES; SPRAY EQUATION; WILLIAMS;

NUMERICAL METHODS;

EID: 38949186410     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2007.10.028     Document Type: Article

References (37)

1. Alexander F.J., and Garcia A.L. The direct simulation Monte Carlo method. Comput. Phys 11 6 (1997) 588-593
2. A.A. Amsden, P.J. O'Rourke, T.D. Butler, Kiva II, a computer program for chemically reactive flows with sprays, Technical Report LA-11560-MS, Report Los Alamos National Laboratory, Los Alamos, New Mexico, 1989.
3. Aulisa E., Manservisi S., Scardovelli R., and Zaleski S. A geometrical area-preserving volume-of-fluid method. J. Comput. Phys. 192 (2003) 355-364
4. Bird G.A. Molecular gas dynamics and the direct simulation of gas flows. Oxford Science Publications 42 (1994)
5. Bracco A., Chavanis P.H., Provenzale A., and Spiegel A. Particle aggregation in a turbulent Keplerian flow. Phys. Fluids 11 (1999) 2280-2286
6. Chavanis P.H. Trapping of dust by coherent vortices in the solar nebula. Astron. Astrophys. 356 (2000) 1089-1111
7. G. Dufour, Modélisation multi-fluide eulérienne pour les écoulements diphasiques à inclusions dispersées, Ph.D. Thesis, Université Paul Sabatier Toulouse III, 2005.
8. Dufour G., and Villedieu P. A second-order multi-fluid model for evaporating sprays. M2AN Math. Model. Numer. Anal. 39 5 (2005) 931-963
9. Dukowicz J.K. A particle-fluid numerical model for liquid sprays. J. Comput. Phys 35 2 (1980) 229-253
10. J. Dupays, Y. Fabignon, P. Villedieu, G. Lavergne, J.L. Estivalezes, Some aspects of two-phase flows in solid-propellant rocket motors, in: Progress in Astronautics and Aeronautics, vol. 185 Solid Propellant Chemistry, Combustion, and Motor Interior Ballistics, AIAA, 2000.
11. Fox R.O. Computational Models for Turbulent Reacting Flows (2003), Cambridge University Press, Cambridge
12. Greenberg J.B., Albagli D., and Tambour Y. An opposed jet quasi-monodisperse spray diffusion flame. Combust. Sci. Technol. 50 (1986) 255-270
13. Greenberg J.B., Silverman I., and Tambour Y. On the origin of spray sectional conservation equations. Combust. Flame 93 (1993) 90-96
14. Hairer E., and Wanner G. Stiff and differential-algebraic problems. Solving Ordinary Differential Equations II (1991), Springer-Verlag, Berlin
15. Herrmann M. A Eulerian level set/vortex sheet method for two-phase interface dynamics. J. Comput. Phys 203 2 (2005) 539-571
16. Hindmarsh A.C. ODEPACK, a systematized collection of ODE solvers. Scientific computing (Montreal, Que., 1982) (1983), IMACS, New Brunswick, NJ 55-64
17. J. Hylkema. Modélisation cinétique et simulation numérique d'un brouillard dense de gouttelettes. Application aux propulseurs à poudre, Ph.D. Thesis, ENSAE, 1999.
18. J. Hylkema, P. Villedieu, A random particle method to simulate coalescence phenomena in dense liquid sprays, in: Proceedings of the 16th International Conference on Numerical Methods in Fluid Dynamics, Lecture Notes in Physics, vol. 515, Arcachon, France, 1998, pp. 488-493.
19. Josserand C., Lemoyne L., Troeger R., and Zaleski S. Droplet impact on a dry surface: triggering the splash with a small obstacle. J. Fluid Mech. 524 (2005) 47-56
20. Laurent F. Numerical analysis of Eulerian multi-fluid models in the context of kinetic formulations for dilute evaporating sprays. M2AN Math. Model. Numer. Anal. 40 3 (2006) 431-468
21. Laurent F., and Massot M. Multi-fluid modeling of laminar poly-dispersed spray flames: origin, assumptions and comparison of the sectional and sampling methods. Combust. Theory Modell. 5 (2001) 537-572
22. Laurent F., Massot M., and Villedieu P. Eulerian multi-fluid modeling for the numerical simulation of coalescence in polydisperse dense liquid sprays. J. Comput. Phys 194 (2004) 505-543
23. Laurent F., Santoro V., Noskov M., Gomez A., Smooke M.D., and Massot M. Accurate treatment of size distribution effects in polydispersed spray diffusion flames: multi-fluid modeling, computations and experiments. Combust. Theory Modell. 8 (2004) 385-412
24. Marchisio D.L., and Fox R.O. Solution of population balance equations using the direct quadrature method of moments. J. Aerosol Sci. 36 (2005) 43-73
25. Marchisio D.L., Vigil R.D., and Fox R.O. Quadrature method of moments for aggregation-breakage processes. J. Colloid Interface Sci. 258 2 (2003) 322-334
26. McGraw R. Description of aerosol dynamics by the quadrature method of moments. Aerosol Sci. Technol. 27 (1997) 255-265
27. Miller R.S., and Bellan J. Direct numerical simulation of a confined three-dimensional gas mixing layer with one evaporating hydrocarbon-droplet-laden stream. J. Fluids Mech. 384 (1999) 293-338
28. Miller R.S., and Bellan J. Direct numerical simulation and subgrid analysis of a transitional droplet laden mixing layer. Phys. Fluid 12 3 (2000) 650-671
29. J.-B. Mossa. Extension polydisperse pour la description euler-euler des écoulements diphasiques réactifs - TH/CFD/05/74, Ph.D. Thesis, Institut National Polytechnique de Toulouse, 2005.
30. P.J. O'Rourke, Collective drop effects on vaporizing liquid sprays, Ph.D. Thesis, Princeton University, 1981.
31. Press W.H., Teukolsky S.A., Vetterling W.T., and Flannery B.P. Numerical Recipes in Fortran 77 (1992), Cambridge University Press, Cambridge
32. Réveillon J., Péra C., Massot M., and Knikker R. Eulerian analysis of the dispersion of evaporating polydispersed sprays in a statistically stationary turbulent flow. J. Turbulence 5 1 (2004) 1-27
33. Rüger M., Hohmann S., Sommerfeld M., and Kohnen G. Euler/Lagrange calculations of turbulent sprays: the effect of droplet collisions and coalescence. Atom. Sprays 10 1 (2000) 47-81
34. Schmidt D.P., and Rutland C.J. A new droplet collision algorithm. J. Comput. Phys. 164 1 (2000) 62-80
35. Tanguy S., and Berlemont A. Development of a level set method for interface tracking: application to droplet collisions. Int. J. Multiphase Flows 31 9 (2005) 1015-1035
36. Tsuji Y., Tanaka T., and Yonemura S. Cluster patterns in circulating fluidized beds predicted by numerical simulation (discrete particle versus two-fluid models. Powder Technol. 95 (1998) 254-264
37. Williams F.A. Spray combustion and atomization. Phys. Fluids 1 (1958) 541-545