1932

Abstract

This review focuses on direct numerical simulations (DNS) of turbulent flows laden with droplets or bubbles. DNS of these flows are more challenging than those of flows laden with solid particles due to the surface deformation in the former. The numerical methods discussed are classified by whether the initial diameter of the bubble/droplet is smaller or larger than the Kolmogorov length scale and whether the instantaneous surface deformation is fully resolved or obtained via a phenomenological model. Also discussed are numerical methods that account for the breakup of a single droplet or bubble, as well as multiple droplets or bubbles in canonical turbulent flows.

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2019-01-05
2024-05-05
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Literature Cited

  1. Albernaz DL, Do-Quang M, Hermanson JC, Amberg G 2017. Droplet deformation and heat transfer in isotropic turbulence. J. Fluid Mech. 820:61–85
    [Google Scholar]
  2. Anderson DM, McFadden GB, Wheeler AA 1998. Diffuse-interface methods in fluid mechanics. Annu. Rev. Fluid Mech. 30:139–65
    [Google Scholar]
  3. Auton T 1987. The lift force on a spherical body in a rotational flow. J. Fluid Mech. 183:199–218
    [Google Scholar]
  4. Auton T, Hunt J, Prud'homme M 1988. The force exerted on a body in inviscid unsteady non-uniform rotational flow. J. Fluid Mech. 197:241–57
    [Google Scholar]
  5. Balachandar S, Eaton J 2010. Turbulent dispersed multiphase flow. Annu. Rev. Fluid Mech. 42:111–33
    [Google Scholar]
  6. Beard K 1976. Terminal velocity and shape of cloud and precipitation drops aloft. J. Atmos. Sci. 33:851–64
    [Google Scholar]
  7. Bhatnagar PL, Gross EP, Krook M 1954. A model for collision processes in gases. I. Small amplitude processes in charged and neutral one-component systems. Phys. Rev. 94:511–25
    [Google Scholar]
  8. Biferale L, Meneveau C, Verzicco R 2014. Deformation statistics of sub-Kolmogorov-scale ellipsoidal neutrally buoyant drops in isotropic turbulence. J. Fluid Mech. 754:184–207
    [Google Scholar]
  9. Cahn JW, Hilliard JE 1959. Free energy of a nonuniform system. III. Nucleation in a two-component incompressible fluid. J. Chem. Phys. 31:688–99
    [Google Scholar]
  10. Carl M, Behrendt T, Fleing C, Frodermann M, Heinze J et al. 2001. Experimental and numerical investigation of a planar combustor sector at realistic operating conditions. J. Eng. Gas Turbines Power 123:811–16
    [Google Scholar]
  11. Chen M, Kontomaris K, McLaughlin J 1998. Direct numerical simulation of droplet collisions in a turbulent channel flow. Part II: collision rates. Int. J. Multiph. Flow 24:1105–38
    [Google Scholar]
  12. Clift R, Grace J, Weber ME 1978. Bubbles, Drops, and Particles Mineola, NY: Dover
  13. Cristini V, Blawzdziewicz J, Loewenberg M 2001. An adaptive mesh algorithm for evolving surfaces: simulations of drop breakup and coalescence. J. Comput. Phys. 168:445–63
    [Google Scholar]
  14. Cristini V, Blawzdziewicz J, Loewenberg M, Collins L 2003. Breakup in stochastic stokes flows: sub-Kolmogorov drops in isotropic turbulence. J. Fluid Mech. 492:231–50
    [Google Scholar]
  15. de Tullio M, Pascazio G 2016. A moving-least-squares immersed boundary method for simulating the fluid–structure interaction of elastic bodies with arbitrary thickness. J. Comput. Phys. 325:201–25
    [Google Scholar]
  16. Desjardins O, Moureau V, Pitsch H 2008. An accurate conservative level set/ghost fluid method for simulating turbulent atomization. J. Comput. Phys. 227:8395–416
    [Google Scholar]
  17. d'Humières D, Ginzburg I, Krafczyk M, Lallemand P, Luo L 2002. Lattice Boltzmann multiple-relaxation-time models in three dimensions. Proc. R. Soc. A 360:427–51
    [Google Scholar]
  18. Dodd M, Ferrante A 2014. A fast pressure-correction method for incompressible two-fluid flows. J. Comput. Phys. 273:416–34
    [Google Scholar]
  19. Dodd M, Ferrante A 2016. On the interaction of Taylor length scale size droplets and isotropic turbulence. J. Fluid Mech. 806:356–412
    [Google Scholar]
  20. Dong S, Shen J 2012. A time-stepping scheme involving constant coefficient matrices for phase-field simulations of two-phase incompressible flows with large density ratios. J. Comput. Phys. 231:5788–804
    [Google Scholar]
  21. Druzhinin O, Elghobashi S 1998. Direct numerical simulations of bubble-laden turbulent flows using the two-fluid formulation. Phys. Fluids 10:685–97
    [Google Scholar]
  22. Druzhinin O, Elghobashi S 2001. Direct numerical simulation of a spatially-developing three-dimensional bubble-laden mixing layer with two-way coupling. J. Fluid Mech. 429:23–61
    [Google Scholar]
  23. Elghobashi S 1994. On predicting particle-laden turbulent flows. Appl. Sci. Res. 52:309–29
    [Google Scholar]
  24. Elghobashi S, Prosperetti A 2009. Preface. Int. J. Multiph. Flow 35:791
    [Google Scholar]
  25. Elghobashi S, Truesdell G 1993. On the two-way interaction between homogeneous turbulence and dispersed solid particles. I: turbulence modification. Phys. Fluids 5:1790–801
    [Google Scholar]
  26. Ferrante A, Elghobashi S 2003. On the physical mechanisms of two-way coupling in particle-laden isotropic turbulence. Phys. Fluids 15:315–29
    [Google Scholar]
  27. Ferrante A, Elghobashi S 2004. On the physical mechanisms of drag reduction in a spatially-developing turbulent boundary layer laden with microbubbles. J. Fluid Mech. 503:345–55
    [Google Scholar]
  28. Ferrante A, Elghobashi S 2007. On the effects of microbubbles on the Taylor–Green vortex flow. J. Fluid Mech. 572:145–77
    [Google Scholar]
  29. Gueyffier D, Li J, Nadim A, Scardovelli R, Zaleski S 1999. Volume-of-fluid interface tracking with smoothed surface stress methods for three-dimensional flows. J. Comput. Phys. 152:423–56
    [Google Scholar]
  30. Guido S, Minale M, Maffettone P 2000. Drop shape dynamics under shear-flow reversal. J. Rheol. 44:1385–99
    [Google Scholar]
  31. Gurtin ME, Fried E, Anand L 2010. The Mechanics and Thermodynamics of Continua Cambridge, UK: Cambridge Univ. Press
  32. Gurtin ME, Polignone D, Vinals J 1996. Two-phase binary fluids and immiscible fluids described by an order parameter. Math. Models Methods Appl. Sci. 6:815–31
    [Google Scholar]
  33. Hinze J 1955. Fundamentals of the hydrodynamic mechanism of splitting in dispersion processes. AIChE J. 1:289–95
    [Google Scholar]
  34. Jacqmin D 1999. Calculation of two-phase Navier–Stokes flows using phase-field modeling. J. Comput. Phys. 155:96–127
    [Google Scholar]
  35. Kareem WA, Izawa S, Xiong AK, Fukunishi Y 2009. Lattice Boltzmann simulations of homogeneous isotropic turbulence. Comput. Math. Appl. 58:1055–61
    [Google Scholar]
  36. Keestra B, Van Puyvelde P, Anderson P, Meijer HEH 2003. Diffuse interface modeling of the morphology and rheology of immiscible polymer blends. Phys. Fluids 15:2567–75
    [Google Scholar]
  37. Kolmogorov A 1949. On the disintegration of drops in turbulent flow. Dokl. Akad. Nauk 66:825–28
    [Google Scholar]
  38. Komrakova AE, Eskin D, Derksen JJ 2015. Numerical study of turbulent liquid-liquid dispersions. AIChE J. 61:2618–33
    [Google Scholar]
  39. Kuerten J 2006. Subgrid modeling in particle-laden channel flow. Phys. Fluids 18:025108
    [Google Scholar]
  40. Kuerten J, Vreman A 2015. Effect of droplet interaction on droplet-laden turbulent channel flow. Phys. Fluids 27:053304
    [Google Scholar]
  41. Kupershtokh A, Medvedev D 2006. Lattice Boltzmann equation method in electrohydrodynamic problems. J. Electrost. 64:581–85
    [Google Scholar]
  42. Lallemand P, Luo LS 2003. Hybrid finite-difference thermal lattice Boltzmann equation. Int. J. Mod. Phys. 17:41–47
    [Google Scholar]
  43. Landau L, Lifshitz E 1959. Fluid Mechanics Oxford: Pergamon
  44. Leclercq P, Bellan J 2005. Direct numerical simulation of gaseous mixing layers laden with multicomponent-liquid drops: liquid-specific effects. J. Fluid Mech. 533:57–94
    [Google Scholar]
  45. Lu J, Biswas S, Tryggvason G 2006. A DNS study of laminar bubbly flows in a vertical channel. Int. J. Multiph. Flow 32:643–60
    [Google Scholar]
  46. Lu J, Fernandez A, Tryggvason G 2005. The effect of bubbles on the wall drag in a turbulent channel flow. Phys. Fluids 17:095102
    [Google Scholar]
  47. Lu J, Tryggvason G 2006. Numerical study of turbulent bubbly downflows in a vertical channel. Phys. Fluids 18:103302
    [Google Scholar]
  48. Lu J, Tryggvason G 2008. Effect of bubble deformability in turbulent bubbly upflow in a vertical channel. Phys. Fluids 20:040701
    [Google Scholar]
  49. Lu J, Tryggvason G 2013. Dynamics of nearly spherical bubbles in a turbulent channel upflow. J. Fluid Mech. 732:166–89
    [Google Scholar]
  50. Lundgren T 2003. Linearly forced isotropic turbulence. Annual Research Briefs 2003461–73 Stanford, CA: Cent. Turbul. Res.
    [Google Scholar]
  51. Madavan N, Deutsch S, Merkle C 1984. Reduction of turbulent skin friction by microbubbles. Phys. Fluids 27:356–63
    [Google Scholar]
  52. Maffettone P, Minale M 1998. Equation of change for ellipsoidal drops in viscous flow. J. Non-Newton. Fluid Mech. 78:227–41
    [Google Scholar]
  53. Mashayek F 1998. Droplet-turbulence interactions in low-Mach-number homogeneous shear two-phase flows. J. Fluid Mech. 367:163–203
    [Google Scholar]
  54. Maxey MR 2017. Simulation methods for particulate flows and concentrated suspensions. Annu. Rev. Fluid Mech. 49:171–93
    [Google Scholar]
  55. Maxey MR, Riley J 1983. Equation of motion for a small rigid sphere in a nonuniform flow. Phys. Fluids 26:883–89
    [Google Scholar]
  56. Mazzitelli I, Lohse D, Toschi F 2003. On the relevance of the lift force in bubbly turbulence. J. Fluid Mech. 488:283–313
    [Google Scholar]
  57. Miller R, Bellan J 1999. Direct numerical simulation of a confined three-dimensional gas mixing layer with one evaporating hydrocarbon-droplet-laden stream. J. Fluid Mech. 384:293–338
    [Google Scholar]
  58. Njobuenwu DO, Fairweather M 2015. Dynamics of single, non-spherical ellipsoidal particles in a turbulent channel flow. Chem. Eng. Sci. 123:265–82
    [Google Scholar]
  59. Osher S, Fedkiw R 2001. Level set methods: an overview and some recent results. J. Comput. Phys. 169:463–502
    [Google Scholar]
  60. Prosperetti A 1981. Motion of two superposed viscous fluids. Phys. Fluids 24:1217–23
    [Google Scholar]
  61. Prosperetti A 2017. Vapor bubbles. Annu. Rev. Fluid Mech. 49:221–48
    [Google Scholar]
  62. Qian D, McLaughlin J, Sankaranarayanan K, Sundaresan S, Kontomaris K 2006. Simulation of bubble breakup dynamics in homogeneous turbulence. Chem. Eng. Comm. 193:1038–63
    [Google Scholar]
  63. Qian YH, d'Humières D, Lallemand P 1992. Lattice BGK models for Navier-Stokes equation. Europhys. Lett. 17:479–84
    [Google Scholar]
  64. Reeks MW 1983. The transport of discrete particles in inhomogeneous turbulence. J. Aerosol Sci. 14:729–39
    [Google Scholar]
  65. Risso F, Fabre J 1998. Oscillations and breakup of a bubble immersed in a turbulent field. J. Fluid Mech. 806:323–55
    [Google Scholar]
  66. Roccon A, Paoli MD, Zonta F, Soldati A 2017. Viscosity-modulated breakup and coalescence of large drops in bounded turbulence. Phys. Rev. Fluids 2:083603
    [Google Scholar]
  67. Russo E, Kuerten JGM, van der Geld CWM, Geurts BJ 2014. Water droplet condensation and evaporation in turbulent channel flow. J. Fluid Mech. 749:666–700
    [Google Scholar]
  68. Saffman PG 1965. The lift on a small sphere in a slow shear flow. J. Fluid Mech. 22:385–400
    [Google Scholar]
  69. Saffman PG, Turner J 1956. On the collision of drops in turbulent clouds. J. Fluid Mech. 1:16–30
    [Google Scholar]
  70. Sankaranarayanan K, Kevrekidis I, Sundaresan S, Lu J, Tryggvason G 2003. A comparative study of lattice Boltzmann and front-tracking finite-difference methods for bubble simulations. Int. J. Multiph. Flow 29:109–16
    [Google Scholar]
  71. Scarbolo L, Bianco F, Soldati A 2015. Coalescence and breakup of large droplets in turbulent channel flow. Phys. Fluids 27:073302
    [Google Scholar]
  72. Scarbolo L, Bianco F, Soldati A 2016. Turbulence modification by dispersion of large deformable droplets. Eur. J. Mech. B 55:294–99
    [Google Scholar]
  73. Scarbolo L, Molin D, Perlekar P, Sbragaglia M, Soldati A, Toschi F 2013. Unified framework for a side-by-side comparison of different multicomponent algorithms: Lattice Boltzmann versus phase field model. J. Comput. Phys. 234:263–79
    [Google Scholar]
  74. Scarbolo L, Soldati A 2013. Turbulence modulation across the interface of a large deformable drop. J. Turbul. 14:27–43
    [Google Scholar]
  75. Scardovelli R, Zaleski S 1999. Direct numerical simulation of free-surface and interfacial flow. Annu. Rev. Fluid Mech. 31:567–603
    [Google Scholar]
  76. Shan X, Chen H 1993. Lattice Boltzmann model for simulating flows with multiple phases and components. Phys. Rev. E. 47:1815–19
    [Google Scholar]
  77. Shardt O, Derksen J, Mitra S 2013. Simulations of droplet coalescence in simple shear flow. Langmuir 29:6201–12
    [Google Scholar]
  78. Snyder M, Knio O, Katz J, Le Maître O 2007. Statistical analysis of small bubble dynamics in isotropic turbulence. Phys. Fluids 19:065108
    [Google Scholar]
  79. Spandan V, Lohse D, Verzicco R 2016. Deformation and orientation statistics of neutrally buoyant sub-Kolmogorov ellipsoidal droplets in turbulent Taylor–Couette flow. J. Fluid Mech. 809:480–501
    [Google Scholar]
  80. Spandan V, Meschini V, Ostilla-Mónico R, Lohse D, Querzoli G et al. 2017.a A parallel interaction potential approach coupled with the immersed boundary method for fully resolved simulations of deformable interfaces and membranes. J. Comput. Phys. 348:567–90
    [Google Scholar]
  81. Spandan V, Verzicco R, Lohse D 2017.b Deformable ellipsoidal bubbles in Taylor-Couette flow with enhanced Euler-Lagrangian tracking. Phys. Rev. Fluids 2:104304
    [Google Scholar]
  82. Spandan V, Verzicco R, Lohse D 2018. Physical mechanisms governing drag reduction in turbulent Taylor-Couette flow with finite-size deformable bubbles. J. Fluid Mech. 849:R3
    [Google Scholar]
  83. Sugiyama K, Calzavarini E, Lohse D 2008. Microbubbly drag reduction in Taylor-Couette flow in the wavy vortex regime. J. Fluid Mech. 608:21–41
    [Google Scholar]
  84. Sun Y, Beckermann C 2007. Sharp interface tracking using the phase-field equation. J. Comput. Phys. 220:626–53
    [Google Scholar]
  85. Sussman M, Puckett E 2000. A coupled level set and volume-of-fluid method for computing 3D and axisymmetric incompressible two-phase flows. J. Comput. Phys. 162:301–37
    [Google Scholar]
  86. Sussman M, Smereka P, Osher S 1994. A level set approach for computing solutions to incompressible two-phase flow. J. Comput. Phys. 114:146–59
    [Google Scholar]
  87. Swift M, Orlandini E, Osbornand WR, Yeomans JM 1996. Lattice Boltzmann simulations of liquid-gas and binary fluid systems. Phys. Rev. E 54:5041–52
    [Google Scholar]
  88. Tryggvason G, Bunner B, Esmaeeli A, Juric D, Al-Rawahi N et al. 2001. A front-tracking method for the computations of multiphase flow. J. Comput. Phys. 169:708–59
    [Google Scholar]
  89. Tryggvason G, Dabiri S, Aboulhasanzadeh B, Lu J 2013. Multiscale considerations in direct numerical simulations of multiphase flows. Phys. Fluids 25:031302
    [Google Scholar]
  90. Tryggvason G, Esmaeeli A, Lu J, Homma S, Biswas S 2006. Recent progress in computational studies of disperse bubbly. Multiph. Sci. Technol. 18:231–49
    [Google Scholar]
  91. Unverdi S, Tryggvason G 1992. A front-tracking method of viscous incompressible, multi-fluid flows. J. Comput. Phys. 100:25–37
    [Google Scholar]
  92. van der Veen R, Huisman S, Merbold S, Harlander U, Egbers C et al. 2016. Taylor–Couette turbulence at radius ratio η=0.5: scaling, flow structures and plumes. J. Fluid Mech. 799:334–51
    [Google Scholar]
  93. Vanella M, Balaras E 2009. A moving-least-squares reconstruction for embedded-boundary formulations. J. Comput. Phys. 228:6617–28
    [Google Scholar]
  94. Wang LP, Maxey MR 1993. The motion of microbubbles in a forced isotropic and homogeneous turbulence. Appl. Sci. Res. 51:291–96
    [Google Scholar]
  95. Yue P, Zhou C, Feng J 2007. Spontaneous shrinkage of drops and mass conservation in phase-field simulations. J. Comput. Phys. 223:1–9
    [Google Scholar]
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