Numerical approaches for motion of dispersed particles, droplets and bubbles

Progress in Energy and Combustion Science

Volumn 26, Issue 3, 2000, Pages 161-223

  Loth, E ^a  

^a UNIVERSITY OF ILLINOIS AT URBANA CHAMPAIGN   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BUBBLES (IN FLUIDS); CONTINUUM MECHANICS; FLOW INTERACTIONS; NUMERICAL METHODS; TURBULENT FLOW;

CONTINUUM PARTICLE FLOW; INTERPHASE TRANSFER;

TWO PHASE FLOW;

EID: 0033744380     PISSN: 03601285     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0360-1285(99)00013-1     Document Type: Review

References (169)

1. Faeth G.M. Mixing transport and combustion in sprays. Progress in Energy and Combustion Science. 13:1987;293-345.
2. Soo S.L. Multiphase fluid dynamics. 1990;Gower Technical, Aldershot-Brookfield, USA.
3. Elghobashi S. On predicting particle-laden turbulent flows. Applied Scientific Research. 52:1994;309-329.
4. Shirolkar J.S., Coimbra C.F.M., Quirez McQuay M. Fundamental aspects of modeling turbulent particle dispersion in dilute flows. Progress in Energy and Combustion Science. 22:1996;363-399.
5. Crowe C.T., Sommerfeld M., Tsuji Y. Multiphase flows with droplets and particles. 1998;CRC Press, Boca Raton, FL.
6. Tomiyama A. Plenary lecture: struggle with computational bubble dynamics. International Conference on Multiphase Flow, Lyon, France, June, 1998.
7. Williams F.A. Combustion theory. 1965;Addison-Wesley, Reading, MA.
8. Oran E.S., Boris J.P. Numerical simulation of reactive flow. 1987;Elsevier, Amsterdam.
9. Kuo K.K. Principles of combustion. 1986;Wiley, New York.
10. Stock D.E. Particle dispersion in flowing gases - Freeman scholar lecture. ASME Journal of Fluids Engineering. 118:1996;4-17.
11. Crowe C., Chung J.N., Troutt T.R. Particle mixing in free shear flows. Progress in Energy and Combustion Science. 14:(3):1988;171-194.
12. Hetsroni G. Roco M.C. The Effect of Particles on the turbulence in a boundary layer, particulate two-phase flow. 1993;244-264 Butterworth-Heinemann, Boston.
13. Sirignano W.A. Fluid dynamics of sprays - Freeman scholar lecture. ASME Journal of Fluids Engineering. 115:1993;345-378.
14. Yuan H., Prosperetti A. On the in-line motion of two spherical bubbles in a viscous fluid. Journal of Fluid Mechanics. 278:1994;325-349.
15. Chen RC, Wu TL. The flow characteristics between two interactive spheres. ASME Fluids Engineering Conference, San Francisco, FEDSM99-7776, June 1999.
16. Druzhinin and Elghobashi. DNS of bubble-laden turbulent flows using a two-fluid formulation. International Conference on Multiphase Flow, Lyon, France, June 1998.
17. Yakhot V., Orzag S.A. Renormalization group analysis for turbulence. I. Basic theory. Journal of Scientific Computing. 1:1986;1.
18. Bocksell T, Loth E. Stochastic diffusion models for particles in wakes and jets. ASME Summer Fluids Engineering Meeting, FEDSM98-5017, Washington, DC, June 1998.
19. Loth E. An Eulerian model for turbulent diffusion of particles in free shear layers. AIAA Journal. 36:(1):1998;12-17.
20. Taeibi-Rahni M., Loth E., Tryggvason G. Flow modulation of a Planar free shear layer with large bubbles - direct numerical simulations. International Journal of Multiphase Flow. 20:(6):1994;1109-1128.
21. Mei R., Adrian R.J. effect of turbulence structure on the dispersion of fluid and particles gas-solid flows. ASME Fluids Engineering Division. 166:1993;131-143.
22. Hu H.H., Joseph D.D., Crochet M.J. Direct simulation of fluid particle motions. Theoretical and Compuational Fluid Dyanmics. 3:1994;285-306.
23. Gañán-Calvo A.M., Lasheras J.C. The dynamics and mixing of small spherical particles in plane, free shear layer. Physics of Fluids. 3:(5):1991;1207-1217.
24. Wang L.-P., Stock D.E. Dispersion of heavy particles by turbulent motion. Journal of Atmospheric Sciences. 50:1996;1897-1913.
25. Elghobashi S., Truesdell G.C. Direct simulation of particle dispersion in a decaying isotropic turbulence. Journal of Fluid Mechanics. 242:1984;655-700.
26. Rogers C. Tufts University, personal communication, 1992.
27. Viollet P.L., Simonin O. Modeling dispersed two-phase flows: closure, validation and software development part of mechanics USA 1994. Applied Mechanical Reviews. 47:(6):1994;s80-s84. ASME Reprint No. AMR146, 1994.
28. Young J., Leeming A. A theory of particle deposition in a turbulent pipe flow. Journal of Fluid Mechanics. 340:1997;129-159.
29. Sivier S.A., Loth E., Baum J.D., Lohner R. Unstructured adaptive remeshing finite element method for dusty shock flows. Shock Waves International Journal. 4:(1):1994;31-41.
30. Yang Y., Chung J.N., Troutt T.R., Crowe C.T. The influence of particles on the spatial stability of two-phase mixing layers. Physics Fluids A. 2:(10):1990;1839-1845.
31. Vandromme D. Introduction to the modeling of turbulence: turbulence modeling for compressible flows and acoustics. von Karman Institute for Fluid Dynamics, Lecture Series 1997-03, March 1997.
32. White F.M. Viscous fluid flow. 1991;McGraw-Hill, New York.
33. Speziale C.G., Sarkar S., Gatski T.B. Modeling the pressure-strain correlation of turbulence: an invariant dynamical systems approach. Journal of Fluid Mechanics. 227:1991;245-272.
34. Kassinos SC, Reynolds WC. Particle and one-point structure-based modeling of slow deformations of homogeneous turbulence. Proceedings of the 11th Symposium on Turbulent Shear Flows, Institut National Polytechnique, University of Joseph Fourier, 1997.
35. Moin P. Progress in large eddy simulation of turbulent flows. AIAA Aerospace Sciences Meeting, Reno, NV, AIAA-97-0749, 1997.
36. Nihei and Nadaoka. Improvement of GAL model for convective transport simulation. International Conference on Multiphase Flow, Lyon, France, June 1998.
37. Eaton JK. Local distortion of turbulence by dispersed particles. AIAA Fluid Dynamics Conference, Norfolk, VA, AIAA-99-3643, June 1999.
38. Maxey M.R., Patel B.K., Chang E.J., Wang L.-P. Simulations of dispersed turbulent multiphase flow. Fluid Dynamics Research. 20:1997;143-156.
39. Sangini A.S., Didwania A.K. Dynamic simulations of bubbly liquids at large Reynolds number. Journal of Fluid Mechanics. 250:1993;307-337.
40. Gelfand B.E. Droplet breakup phenomena in flows with velocity lag. Progress in Energy and Combustion Science. 22:1996;201-266.
41. Luo H., Svendsen H.F. Theoretical model for drop and bubble breakup in turbulent dispersions. American Institute of Chemical Engineering Journal. 42:1996;1225-1233.
42. Michaelidis E. Review - the transient equation of motion for particles bubbles, and droplets. AMSE Journal of Fluids Engineering. 119:1997;233-247.
43. Govier G.W., Aziz K. The flow of complex mixtures in pipes. 1972;Van Nostrand-Reinhold, New York.
44. Heywood H. Symposiom on interactions of fluids on particles. 1962;Institute of Chemical Engineers, London. p. 1-8.
45. Stone H.A., Samuel A.D.T. Propulsion of microorganisms by surface distortions. Physical Review Letters. 77:(19):1996;4102-4104.
46. Allen MG, Glezer A. Demonstration of robust micromachined jet technology and its application to realistic flow control problems. AFOSR Turbulence and Internal Flows/Unsteady Aerodynamics and Hypersonics Conference, August, Annapolis, MD, 1998. p. 7-12.
47. Garner F.H., Lihou D.A. DECHEMA-Monograph. 55:1965;155-178.
48. Clift R., Grace J.R., Weber M.E. Bubbles, drops and particles. 1978;Academic Press, New York.
49. Ford B., Loth E. Forces on ellipsoidal bubbles in a turbulent free shear layer. Physics of Fluids. 10:(1):1998;178-188.
50. Takagi S., Prosperetti A., Matsumoto Y. Drag coefficient of a gas bubble in an axisymmetric shear flow. Physics of Fluids. 6:(9):1994;3186-3188.
51. Ryskin G., Leal L.G. Numerical simulation of a free-boundary problems in fluid mechanics. Part 3. Bubble deformation in an axisymmetric straining flow. Journal of Fluid Mechanics. 148:(37):1983.
52. Nielsen and Zeng. Turbulence effects on the settling of heavy particles and the rise of bubbles. International Conference on Multiphase Flow, Lyon, France, June.
53. Maxey MR. Private communication, 1998.
54. Clift R., Gauvin W.H. Proceedings of the CHEMECA '70, Butterworth, Melbourne. 1:1970;14-28.
55. Eppinger K. Study of the movement of bubbles in homogeneous isotropic turbulence. PhD thesis, Institut National Polytechnique de Toulouse, France, 1995.
56. Poorte REG. On the motion of bubbles in active grid generated turbulent flows. PhD thesis, University of Twente, Netherlands, September 1988.
57. Spelt P.D.M., Biesheuvel A. On the motion of gas bubbles in homogeneous isotropic turbulence. Journal of Fluid Mechanics. 336:1997;221-244.
58. Schlichting H. Boundary layer theory. 1979;McGraw-Hill, New York.
59. Sommerfeld M. Numerical simulation of supersonic two-phase gas-particle flows. Proceedings of the 16th International Symposium on Shock Tubes and Waves, 1987. p. 235-241.
60. Cherukat P., McLaughlin J.B., Graham A.L. The inertial lift on a rigid sphere translating in a linear shear flow field. International Journal of Multiphase Flow. 20:(2):1994;339-353.
61. McLaughlin J.B. Inertial migration of a small sphere in linear shear flows. Journal of Fluid Mechanics. 224:1991;261-274.
62. Wang Q., Squires K.D., Chen M., McLaughlin J.B. On the role of the lift force in turbulence simulations of particle deposition. International Journal of Multiphase Flow. 23:1997;749-763.
63. Mei R., Klausner J.F. Unsteady force on a spherical bubble with finite Reynolds number with small fluctuations in the free-stream velocity. Physics of Fluids A. 4:(1):1992;63.
64. Mei R., Klausner J.F. Shear lift force on spherical bubbles. International Journal of Heat and Fluid Flow. 15:(1):1994;62-65.
65. Van der Geld C.W.M. Measurement and prediction of solid sphere trajectories in accelerated gas flow. International Journal of Multiphase Flow. 23:(2):1997;357-376.
66. Tsuji Y., Morikawa Y., Mizuno O. Experimental measurements of the magnus force on a rotating sphere at low Reynolds numbers bubble in an axisymmetric shear flow. Journal of Fluids Engineering. 107:(9):1985;484.
67. Tanaka T., Yonemura S., Tsuji Y. Experiments of fluid forces on a rotating sphere and spheroid. Proceedings of the Second KSME-JSME Fluids Engineering Conference. 1:1990;366.
68. Dennis S.C.R., Singh S.N., Ingham D.B. The steady flow due to a rotating sphere at low and moderate Reynolds numbers. Journal of Fluid Mechanics. 101:1980;257-279.
69. Bataille J., Lance M., Marie J.L. Hewitt G.F., Mayinger F., Riznic J.R. Some aspects of the modeling of bubbly flows, phase-interface phenomena in multiphase flow. 1991;Hemisphere Publishing Corporation.
70. Sridhar G., Katz J. Drag and lift forces on microscopic bubbles entrained by a vortex. Physics of Fluids. 7:(2):1995;389-399.
71. Kariyasaki A. Behavior of a single gas bubble in a liquid flow with a linear velocity profile. Proceedings of the 1987 ASME-JSME Thermal Engineering Joint Conference. 5:1987;261-267. ASME, New York.
72. Ervin EA. Computations of bubbles and drops in shear flow. PhD dissertation, Department of Mechanical Engineering, University of Michigan, Ann Arbor, MI, 1993.
73. Yih C.-S. Fluid mechanics. 1979;West River Press, Ann Arbor, MI. p. 98-104.
74. Auton T.R., Hunt J.C.R., Prud'Homme M. The force exerted on a body in inviscid unsteady non-uniform rotational flow. Journal of Fluid Mechanics. 197:1988;241-257.
75. Maxey M.R., Riley J.J. Equation of motion for a small rigid sphere in a non-uniform flow. Physics of Fluids. 26:(4):1983;883-889.
76. Chang E.J., Maxey M.R. Unsteady flow about a sphere at low to moderate Reynolds number. Part I. Oscillatory motion. Journal of Fluid Mechanics. 277:1994;347-379.
77. Mei R., Lawrence C.J., Adrian R.J. Unsteady drag on a sphere at finite Reynolds number with small fluctuations in the free-stream velocity. Journal of Fluid Mechanics. 233:1991;613-631.
78. Kim I, Elghobashi S, Sirignano WA. The motion of a spherical particle in unsteady flows at moderate Reynolds numbers. AIAA Aerospace Sciences Meeting, Reno NV, AIAA-96-0081, January 1996.
79. Maxey M.R. Equation of motion for a small rigid sphere in a non-uniform or unsteady flow. ASME/FED Gas-Solid Flows. 166:1993;57-62.
80. Mei R., Adrian R.J. Flow past a sphere with an oscillation in the free-stream and unsteady drag at finite Reynolds number. Journal of Fluid Mechanics. 237:1992;323-341.
81. Lovalenti P.M., Brady J.F. The force on a bubble drop or particle in arbitrary time-dependent motion at small Reynolds number. Physics Fluids A. 5:(9):1993;2104-2116.
82. Park W.C., Klausner J.F., Mei R. Unsteady forces on spherical bubbles. Experiments in Fluids. 19:1995;167-172.
83. Vojir D.J., Michaelides E.E. Effect of the history term on the motion of rigid spheres in a viscous fluid. International Journal of Multiphase Flow. 20:1994;547-556.
84. Zun I., Kljenek I., Serizaw A. Bubble coalescence and transition from wall void peaking to core void peaking in turbulent bubbly flow. Jones O.C., Michiyoshi I. Dynamics of two-phase flows. 1992;233-239 Bocca Ratan, FL:
85. Marie J.L., Moursali E., Tran-Cong S. Similarity law and turbulence intensity profiles in a bubbly boundary layer at low void fractions. International Journal of Multiphase Flow. 23:(2):1997;227-247.
86. Felton K, Loth E. Sub-millimetric bubbly flow in a vertical turbulent boundary layer. ASME Fluids Engineering Conference, San Francisco, CA, July, FEDSM-7360, 1999.
87. Young J.B., Hanratty T.J. Trapping of solid particles at a wall in a turbulent flow. AIChE Journal. 37:(10):1991;1529-1536.
88. Hallouin E, Gondret P, Lance M, Petit L. On the motion of a sphere toward a plane surface: from lubrication to bouncing regime. International Conference on Multiphase Flow, Lyon, France, June 1998.
89. Gavze E., Shapiro M. Particles in a shear flow near a solid wall: effect of nonsphericity on forces and velocities. International Journal of Multiphase Flow. 23:(1):1996;155-182.
90. Tsao H.K., Koch D.T. Observations of high Reynolds number bubbles interacting with a rigid wall. Physics of Fluids. 9:(1):1997;44-56.
91. Zenit R, Joseph G, Hunt M. The coefficient of restitution for liquid immersed collisions. ASME Summer Fluids Engineering Meeting, FEDSM99-7793, San Francisco, July, 1999.
92. Hamed A. Effect of particle characteristics on trajectories and blade impact patterns. AMSE Journal of Fluids Engineering. 110:1988;33-37.
93. Hamed A, Kuhn TP. Effects of variational particle restitution characteristics on turbomachinery erosions. ASME International Gas Turbine and Aeroengine Congress and Expo. Cincinnati, OH, 24-27 May 1993, 93-GT-124.
94. Tsirkunov YM, Panfilov SV. Modelling of particle-wall interaction in two-phase flows at moderate and high particle impact velocity. International Conference on Multiphase Flow, Lyon, France, June 1998.
95. Shrayber A.A. Euler and Lagrange methods in the theory of two-phase flows with variable particle size of the discrete phase. Fluid Mechanics - Soviet Research. 8:(5):1979;79-87.
96. Sivier S.A., Loth E., Baum J.D. Dusty shock flow with unstructured adaptive finite elements and parcels. AIAA Journal. 34:(5):1996;1078-1080.
97. Joseph D.D. Interrogation of numerical simulation for modeling of flow induced microstructure. ASME/FED Liquid-Solid Flows. 189:1994;31-40.
98. Deshpande M, Feng J, Merkle CL. Navier-Stokes analysis of 2-D cavity flows. Cavitation and Multiphase Flow Forum, Washington DC, ASME FED-vol. 153, 1993. p. 149-155.
99. Chen Y., Heister S.D. A numerical treatment for attached cavitation. Journal of Fluids Engineering, Transactions of the ASME. 116:1994;613-618.
100. Chahine GL, Delepoule E, Hauwert P. Cavitation and Multiphase Flow Forum. Washington DC, ASME FED-vol. 153, 1993. p. 39-45.
101. Sussman M., Smereka P., Osher S.J. A level-set approach for computing solutions to incompressible two-phase flow. Journal of Computational Physics. 114:1994;146-159.
102. Chen X-Q. efficient particle tracking algorithm for two-phase flows in geometries using curvilinear coordinates. Numerical Heat Transfer, 1997.
103. Barton I.E. Exponential-Lagrangian tracking schemes applied to Stokes LAW. AMSE Journal of Fluids Engineering. 118:1996;85-89.
104. Sabnis JS, de Jong FJ. Calculation of the two-phase flow in an evaporating spray using an Eulerian-Lagrangian analysis. AIAA Aerospace Sciences Meeting, Reno NV, AIAA-90-0447, January 1990.
105. Löhner R., Ambrosiano J. A vectorized particle tracer for unstructured grids. Journal of Computational Physics. 91:(1):1990;22-31.
106. Wen F., Kamalu N., Chung J.N., Crowe C.T., Troutt T.R. Particle dispersion by vortex structures in plane mixing layers. Journal of Fluids Engineering. 114:1992;657-666.
107. O'Hern T.J. An experimental investigation of turbulent shear flow cavitation. Journal of Fluid Mechanics. 215:1990;365-391.
108. Gosman AD, Ioannides E. Aspects of computer simulation of liquid-fueled combustors. Aerospace Sciences Meeting, Reno NV, AIAA-81-0323, January 1981.
109. Graham D.I., James P.W. Turbulent dispersion of particles using eddy interaction models. International Journal of Multiphase Flow. 22:(1):1996;157-175.
110. DeAngelis B.C., Loth E., Lankford D., Bartlett C.S. Computations of turbulent droplet dispersion for wind tunnel tests. AIAA Journal of Aircraft. 34:(2):1997;213-219.
111. Bocksell T, Loth E. An enhanced DRW turbulent diffusion model for free shear flows. International Conference on Multiphase Flow, Lyon, France, June 1998.
112. Kallio G.A., Reeks M.W. A numerical simulation of particle deposition in turbulent boundary layers. International Journal of Multiphase Flow. 15:(3):1989;433-446.
113. Ushijima T, Perkins RJ. Evaluation of Co and To in turbulent pipe or channel flows. ASME Summer Fluids Engineering Meeting, FEDSM99-7759, San Francisco, July 1999.
114. Csanady G.T. Turbulent diffusion for heavy particles in the atmosphere. Journal of Atmospheric Sciences. 20:1963;201-208.
115. Graham D.I. Improved Eddy interaction models with random length and time scales. International Journal of Multiphase Flow. 24:(2):1998;335-345.
116. Launay K, Huilier D, Burnage H. An improved Lagrangian method for predicting the long-time turbulent dispersion in gas-particle flows. ASME Summer Fluids Engineering Meeting, FEDSM98-5012, Washington, DC, June 1998.
117. Underwood B.Y. Random-walk modeling of turbulent impaction to a smooth wall. International Journal of Multiphase Flow. 19:(3):1993;485-500.
118. Zhou Q, Leschziner MA. A time-correlated stochastic model for particle dispersion in anisotropic turbulence. Eighth Symposium on Turbulent Shear Flows, 1991. p. 1031-1036.
119. Zhou Q, Leschziner MA. Modeling particle dispersion in turbulent recirculating flow with an anisotropy-resolving scheme. ASME Summer Fluids Engineering Meeting, FEDSM97-3643, Vancouver, Canada, June 1997.
120. Berelemont A., Desjonqueres P., Gouesbet G. Particles Lagrangian simulation in turbulent flows. International Journal of Multiphase Flow. 1990;16.
121. Chen X.-Q., Pereira J.C.F. Comparison of the various particle dispersion models in plane mixing shear layers. Numerical Methods in Multiphase Flows. FED-185:1994;217-225.
122. Loth E., Stedl J. Taylor and Lagrangian Correlations in a turbulent free shear layer. Experiments in Fluids. 26:1999;1-6.
123. Ford B., Loth E. Ellipsoidal bubble diffusion in a turbulent shear layer. International Journal of Multiphase Flow. 26:(3):2000;503-516.
124. Slater SA, Young JB. The calculation of inertial particle transport using an eulerian formulations. Proceedings of the 16th ASME Fluids Engineering Summer Meeting, June, Washington, DC, FEDSM98-5007, 1988.
125. Rudinger G. Some properties of shock relaxation in gas flows carrying small particles. Physics of Fluids. 7:(5):1964;658-663.
126. Wallis G.B. One-dimensional two-phase flow. 1969;McGraw-Hill, New York.
127. Sun T.-Y., Faeth G.M. Structure of turbulent bubbly jets. International Journal of Multiphase Flow. 12:1986;115.
128. Olim, Igra, Mond, Ben-Dor. A General attenuation law of planar shock waves propagating into dusty gases. Proceedings of the 16th International Symposium on Shock Waves And Shock Tubes, 1985. p. 217-225.
129. Collins JP, Ferguson RE, Chien K, Kuhl AL, Krispen J, Glaz HM. Simulation of shock-induced dusty gas flows using various models. AIAA Fluid Dynamics Conference, Colorado Springs, CO, AIAA-94-2309, 1994.
130. Durst F., Milojevic D., Schonung B. Eulerian and Lagrangian predictions of particulate two-phase flows: a numerical study. Applied Mathematical Modelling. 8:1984;101-112.
131. Drew D.A., Lahey R.T. Roco M.C. Analytical modeling of multiphase flow particulate two-phase flow. 1993;Butterworth-Heinemann, Boston, MA.
132. Elghobashi S., Abou-Arab T.W. A two-equation turbulence model for two-phase flows. Physics of Fluids. 26:(4):1983;931-938.
133. Vaidya N., Dionne P.J., Singhal A.K. A two-fluid model finite volume formulation for computing two-phase flows in complex geometries. Gas Liquid Flows. ASME FED-225:1995;179-191.
134. Wu B, Liu D. Modeling of lateral particle dispersion in FFB. Cavitation and Multiphase Flow Forum. ASME Fluids Engineering Division, vol. 109, 1991. p. 15-19.
135. Alonso C.V. Stochastic models of suspended-sediment dispersion. ASCE Journal of Hydraulics. 107:(HY6):1981;733-757.
136. Loth E. Dispersion of particles, droplets and bubbles in a turbulent free shear layer. ASME Summer Fluids Engineering Meeting, FEDSM97-3607, Vancouver, Canada, June 1997.
137. Reeks M.W. On the dispersion of small particles suspended in an isotropic turbulent fluid. Journal of Fluid Mechanics. 83:(3):1977;529-546.
138. Wells M.R., Stock D.E. The effects of crossing trajectories on the dispersion of particles in a turbulent flow. Journal of Fluid Mechanics. 136:1983;31-62.
139. Bocksell T, Loth E. A CRW model for diffusion of bubbles and particles. ASME Summer Fluids Engineering Meeting, San Francisco, June 1999, FEDSM99-7366, 1999.
140. Sene K.J., Hunt J.C.R., Thomas N.H. The role of coherent structures in bubble transport by turbulent shear flows. Journal of Fluid Mechanics. 259:1994;219-240.
141. Felton K. A study of spherical bubbles in a vertical turbulent boundary layer. PhD thesis, Mechanical Engineering Department, University of Illinois at Urbana-Champaign, 1999.
142. Snyder W.H., Lumley J.L. Some measurements of particle velocity autocorrelation in approximately isotropic turbulence. Journal of Fluid Mechanics. 48:1971;41.
143. Crowe C.T. Review - numerical models for dilute gas-particle flows. Journal of Fluid Engineering. 104:1982;297-303.
144. Kashiwa B.A., Gore R.A. A four equation model for multiphase turbulent flow. Proceedings of the 1987 ASME-JSME Thermal Engineering Joint Conference. 5:1987;ASME, New York. pp. 261-267.
145. Lopez de Bertodano M., Lee S.-J., Lahey R.T., Drew D.A. The prediction of two-phase turbulence and phase distribution phenomena using a Reynolds stress model. AMSE Journal of Fluids Engineering. 112:1990;107-113.
146. Reeks M.W. On the constitutive relations for dispersed particles in non-uniform flows. 1: dispersion in a simple shear flow. Physics of Fluids A. 5:1993;750-761.
147. Eaton J.K., Fessler J.R. Preferential concentrations of particles by turbulence. International Journal of Multiphase Flow. 20:1994;169-209.
148. Gañán-Calvo A.M., Lasheras J.C. The dynamics and mixing of small spherical particles in plane. Free shear layer. Physics of Fluids. 3:(5):1991;1207-1217.
149. Tio K.-K., Liñán A., Lasheras J.C., Gañán-Calvo A.M. The dynamics of bubbles in periodic vortex flows. Applied Scientific Research. 51:1993;285-290.
150. Aggarwal SK, Chen G, Yapo JB, Grinstein FF, Kailasanath K. Numerical simulation of particle dynamics in planar shear layers. Aerospace Sciences Meeting, Reno, NV, AIAA-92-0107, 1992.
151. Chung J.N., Trout T.R. Simulation of particle dispersion in an axisymmetric jet. Journal of Fluid Mechanics. 186:1988;199-222.
152. Joia I.A., Ushijima T., Perkins R.J. Numerical study of bubble and particle motion in turbulent boundary layer using proper orthogonal decomposition. Applied Science Research. 57:1997;263-277.
153. Caraeni D, Bergstrom C, Fuchs L, Hoffman S, Krebs W, Meisl K. LES of Spray in compressible flows on unstructured grids. AIAA Fluid Dynamics Conference, Reno, NV, AIAA-99-3762, 1999.
154. Eaton J.K. Experiments and simulations on turbulence modification by dispersed particles. Applied Mechanics Reviews. 46:(6):1994;S44-S48.
155. Tennekes H., Lumley J.L. A first course in turbulence. 1972;MIT Press, Cambridge, MA.
156. Spalart PR. Strategies for turbulence modeling & simulations. 4th Intl Symp. on Engng Turb. Modeling & Measurements, Corsica, France, May 1999. p. 24-26.
157. Piomelli U. Introduction to the modeling of turbulence: large Eddy and direct simulation of turbulent flows. von Karman Institute for Fluid Dynamics, Lecture Series 1997-03, March 1997.
158. Wu J.-S., Faeth G.M. Sphere wakes at moderate Reynolds numbers in a turbulent environment. AIAA Journal. 32:(3):1994;535-541.
159. Fan L.-S., Tsuchiya K. Bubble wake dynamics in liquids and liquid solid suspensions. 1989;Butterworth-Heinemann, Stoneham, MA.
160. Wang L.-P., Maxey M.R. Settling velocity and concentration distribution of heavy particles in homogeneous isotropic turbulence. Journal of Fluid Mechanics. 256:1993;27-68.
161. Nirschl H, Dwyer HA, Denk V. A chimera grid scheme for the calculation of particle flows. AIAA Aerospace Sciences Meeting, Reno, NV, AIAA-94-0519, 1994.
162. Unverdi S.O., Tryggvason G. A front-tracking method for viscous incompressible, multi-fluid flows. Journal of Computational Physics. 100:(1):1992;25-37.
163. Chang Y.C., Hou T.Y., Merriman B., Osher S. A level-set formulation of eulerian interface capturing methods for incompressible fluid flows. Journal of Computational Physics. 124:1996;449-464.
164. MacInnes J.M., Bracco F.V. Stochastic particle dispersion modeling and the tracer-particle limit. Physics Fluids A. 4:(12):1992;2809-2824.
165. Yuu S., Yasukouchi N., Hirosawa Y., Jotaki T. Particle turbulent diffusion in a dust laden round jet. AIChE Journal. 24:1978;509-519.
166. Maxey M.R., Chang E.J., Wang L.-P. Interactions of particles and microbubbles with turbulence. Experimental Thermal and Fluid Science. 126:1996;417-425.
167. Lasheras J.C. Private communication. University of California at San Diego, 1998.
168. Naciri, A. Contribution of the study of the forces exercised for a liquid over a bubble of gas. PhD thesis, L'école Centrale de Lyon, Lyon, France, 1992.
169. Amsden A.A, O'Rourke P.J., Butler T.D. KIVA-IIL a computer program for chemically reactive flows with sprays. DE89-012805, Los Alamos National Laboratory, Los Alamos, NM, 1989.