Experiments in Fluids

, 46:371 | Cite as

Secondary atomization

  • D. R. Guildenbecher
  • C. López-Rivera
  • P. E. Sojka
Review Article

Abstract

When a drop is subjected to a surrounding dispersed phase that is moving at an initial relative velocity, aerodynamic forces will cause it to deform and fragment. This is referred to as secondary atomization. In this paper, the abundant literature on secondary atomization experimental methods, breakup morphology, breakup times, fragment size and velocity distributions, and modeling efforts is reviewed and discussed. Focus is placed on experimental and numerical results which clarify the physical processes that lead to breakup. From this, a consistent theory is presented which explains the observed behavior. It is concluded that viscous shear plays little role in the breakup of liquid drops in a gaseous environment. Correlations are given which will be useful to the designer, and a number of areas are highlighted where more work is needed.

List of symbols

Dimensional

a

drop acceleration (m/s2)

c

velocity of sound (m/s)

D10

drop or fragment arithmetic mean diameter (m)

D30

drop or fragment volume mean diameter (m)

D32

drop or fragment Sauter mean diameter (m)

D43

drop or fragment de Brouckere mean diameter (m)

d0

drop initial spherical diameter (m)

dcore

diameter of drop core at end of sheet-thinning breakup (m)

dcro

drop cross-stream diameter (m)

dstr

drop stream-wise diameter (m)

FD

aerodynamic drag force (kg m/s2)

Fsurf

net surface force (kg m/s2)

Fμ

shear force (kg m/s2)

f0(D)

fragment number PDF (1/m)

f3(D)

fragment volume PDF (1/m)

K

power-law fluid consistency index (kg/m s(2−n))

k

wave number; 2π/λ (1/m)

MMD

drop or fragment mass median diameter (m)

q

net electrostatic charge (C)

qRa

Rayleigh charge limit (C)

t

time (s)

U0

initial relative velocity between drop and ambient fluid in main flow direction (m/s)

Ucore

velocity of drop core relative to ambient fluid (m/s)

\( \bar{U}_{\text{f}} \)

mean relative velocity of fragments in main flow direction (m/s)

V0

initial relative velocity between drop and ambient fluid perpendicular to main flow direction (m/s)

\( \bar{V}_{\text{f}} \)

mean relative velocity of fragments in cross-stream direction (m/s)

δ

boundary layer thickness (m)

εa

electrical permittivity of ambient (C2/N m2)

λ

wavelength (m)

λ(1)

elastic fluid relaxation time (s)

μa

ambient viscosity (kg/m s)

μd

drop viscosity (kg/m s)

μeff

power-law effective viscosity (kg/m s)

μsol

solvent shear viscosity (kg/m s)

ρa

ambient density (kg/m3)

ρd

drop density (kg/m3)

σ

surface tension (kg/s2)

Non-dimensional

CD

instantaneous coefficient of drag based on drop cross-stream diameter

\( \bar{C}_{\text{D}} \)

average coefficient of drag based on initial spherical diameter

CD-sphere

coefficient of drag of a solid sphere at a given Reynolds number

Eocr

Eötvös number at end of sheet-thinning breakup; \( {{a\left| {\rho_{\rm d} - \rho_{\rm a} } \right|d_{\text{core}}^{2} } \mathord{\left/ {\vphantom {{a\left| {\rho_{\rm d} - \rho_{\rm a} } \right|d_{\text{core}}^{2} } \sigma }} \right. \kern-\nulldelimiterspace} \sigma } \)

La

Laplace number; La = Oh−2

Ma

Mach number

N

viscosity ratio; μd/μa

n

power-law fluid flow behavior index

Oh

Ohnesorge number; \( {{\mu_{\rm d} } \mathord{\left/ {\vphantom {{\mu_{\rm d} } {\sqrt {\rho_{\rm d} d_{0} \sigma } }}} \right. \kern-\nulldelimiterspace} {\sqrt {\rho_{\rm d} d_{0} \sigma } }} \)

Re

gas-phase Reynolds number; \( {{\rho_{\rm a} U_{0} d_{0} } \mathord{\left/ {\vphantom {{\rho_{\rm a} U_{0} d_{0} } {\mu_{\rm a} }}} \right. \kern-\nulldelimiterspace} {\mu_{\rm a} }} \)

ReNN

Reynolds number for a power-law fluid; ρU02−nd0n/K

T

dimensionless time; \( tU_{0} \varepsilon^{{{{ - 1} \mathord{\left/ {\vphantom {{ - 1} 2}} \right. \kern-\nulldelimiterspace} 2}}} d_{0}^{ - 1} \)

Tini

breakup initiation time

Ttot

total breakup time

We

Weber number; \( {{\rho_{\rm a} U_{0}^{2} d_{0} } \mathord{\left/ {\vphantom {{\rho_{\rm a} U_{0}^{2} d_{0} } \sigma }} \right. \kern-\nulldelimiterspace} \sigma } \)

Wec

critical Weber number

WecOh→0

critical Weber number at low Ohnesorge number

Wecore

Weber number of drop core at end of sheet-thinning breakup

Wee−

electrostatic Weber number; \( {{\rho_{\rm a} U_{0} d_{0}^{2} } \mathord{\left/ {\vphantom {{\rho_{\rm a} U_{0} d_{0}^{2} } {\left( {\sigma - {{q^{2} } \mathord{\left/ {\vphantom {{q^{2} } {8\pi^{2} \varepsilon_{\rm a} d_{0}^{3} }}} \right. \kern-\nulldelimiterspace} {8\pi^{2} \varepsilon_{\rm a} d_{0}^{3} }}} \right)}}} \right. \kern-\nulldelimiterspace} {\left( {\sigma - {{q^{2} } \mathord{\left/ {\vphantom {{q^{2} } {8\pi^{2} \varepsilon_{\rm a} d_{0}^{3} }}} \right. \kern-\nulldelimiterspace} {8\pi^{2} \varepsilon_{\rm a} d_{0}^{3} }}} \right)}} \)

Wi

Weissenberg number; \( {{\lambda^{(1)} U_{0} } \mathord{\left/ {\vphantom {{\lambda^{(1)} U_{0} } {d_{0} }}} \right. \kern-\nulldelimiterspace} {d_{0} }} \)

y

non-dimensional displacement of drop equator; 1 − (d0/dcro)2

ε

density ratio; ρd/ρa

ω

exponential growth factor

References

  1. Aalburg C, van Leer B, Faeth GM (2003) Deformation and drag properties of round drops subjected to shock-wave disturbances. AIAA J 41(12):2371–2378CrossRefGoogle Scholar
  2. Apte SV, Gorokhovski M, Moin P (2003) LES of atomizing spray with stochastic modeling of secondary breakup. Int J Multiphase Flow 29:1503–1522MATHCrossRefGoogle Scholar
  3. Arcoumanis C, Khezzar L, Whitelaw DS, Warren BCH (1994) Breakup of Newtonian and non-Newtonian Fluids in air jets. Exp Fluids 17(6):405–414CrossRefGoogle Scholar
  4. Arcoumanis C, Whitelaw DS, Whitelaw JH (1996) Breakup of droplets of Newtonian and non-Newtonian fluids. Atomization Spray 6:245–256Google Scholar
  5. Babinsky E, Sojka PE (2002) Modeling drop size distributions. Prog Energ Combust 28:303–329CrossRefGoogle Scholar
  6. Berthoumieu P, Carentz H, Villedieu P, Lavergne G (1999) Contribution to droplet breakup analysis. Int J Heat Fluid 20:492–498CrossRefGoogle Scholar
  7. Bird RB, Armstrong RRC, Hasseger O (1987) Dynamics of polymeric liquids. Wiley, New YorkGoogle Scholar
  8. Brodkey, RS (1967) Formation of drops and bubbles. In: The phenomena of fluid motions. Addison-Wesley, ReadingGoogle Scholar
  9. Cao XK, Sun ZG, Li WF, Liu HF, Yu ZH (2007) A new breakup regime for liquid drops identified in a continuous and uniform air jet flow. Phys Fluids 19(5):057103CrossRefGoogle Scholar
  10. Chandrasekhar S (1961) Hydrodynamic and hydromagnetic stability. Oxford University Press, LondonMATHGoogle Scholar
  11. Chang CH, Liou MS (2007) A Robust and accurate approach to computing compressible multiphase flow: stratified flow model and AUSM+-up scheme. J Comput Phys 225:840–873MATHCrossRefMathSciNetGoogle Scholar
  12. Chou WH, Faeth GM (1998) Temporal properties of secondary drop breakup in the bag breakup regime. Int J Multiphase Flow 24:889–912MATHCrossRefGoogle Scholar
  13. Chou WH, Hsiang LP, Faeth GM (1997) Temporal properties of drop breakup in the shear breakup regime. Int J Multiphas Flow 23(4):651–669MATHCrossRefGoogle Scholar
  14. Chryssakis CA, Assanis DN (2005) A secondary atomization model for liquid droplet deformation and breakup under high weber number conditions. In: ILASS Americas 18th annual conference on liquid atomization and spray systems, Irvine, CA, USAGoogle Scholar
  15. Clift R, Grace JR, Weber ME (1978) Bubbles, drops, and particles. Academic Press, New YorkGoogle Scholar
  16. Cohen RD (1994) Effect of viscosity on drop breakup. Int J Multiphase Flow 20(1):211–216CrossRefGoogle Scholar
  17. Cousin J, Yoon SJ, Dumouchel C (1996) Coupling of classical linear theory and maximum entropy formalism for prediction of drop size distribution in sprays: application to pressure-swirl atomizers. Atomization Spray 6:601–622Google Scholar
  18. Dai Z, Faeth GM (2001) Temporal properties of secondary drop breakup in the multimode breakup regime. Int J Multiphase Flow 27:217–236MATHCrossRefGoogle Scholar
  19. Duan RQ, Koshizuka S, Oka Y (2003a) Numerical and theoretical investigation of effect of density ratio on the critical weber number of droplet breakup. J Nucl Sci Technol 40(7):501–508CrossRefGoogle Scholar
  20. Duan RQ, Koshizuka S, Oka Y (2003b) Two-dimensional simulation of drop deformation and breakup at around the critical Weber number. Nucl Eng Des 225:37–48CrossRefGoogle Scholar
  21. Dumouchel C (2006) A new formulation of the maximum entropy formalism to model liquid spray drop-size distribution. Part Part Syst Char 23:468–479CrossRefGoogle Scholar
  22. Dumouchel C, Boyaval S (1999) Use of the maximum entropy formalism to determine drop size characteristics. Part Part Syst Char 16:177–184CrossRefGoogle Scholar
  23. Faeth GM, Hsiang LP, Wu PK (1995) Structure and breakup properties of sprays. Int J Multiphase Flow 21(Suppl): 99–127MATHCrossRefGoogle Scholar
  24. Gelfand BE (1996) Droplet breakup phenomena in flows with velocity lag. Prog Energ Combust 22:201–265CrossRefGoogle Scholar
  25. Gelfand BE, Gubin SA, Kogarko SM, Komar SP (1975) Singularities of the breakup of viscous liquid droplets in shock waves. J Eng Phys 25(3):1140–1142CrossRefGoogle Scholar
  26. Gökalp I, Chauveau C, Morin C, Vieille B, Birouk M (2000) Improving droplet breakup and vaporization models by including high pressure and turbulence effects. Atomization Spray 10:475–510Google Scholar
  27. Gorokhovski M (2001) The stochastic Lagrangian model of drop breakup in the computation of liquid sprays. Atomization Spray 11:505–519Google Scholar
  28. Gorokhovski MA, Saveliev VL (2003) Analyses of Kolmogorov’s model of breakup and its application into Lagrangian computation of liquid sprays under air-blast atomization. Phys Fluids 15(1):184–192CrossRefGoogle Scholar
  29. Guildenbecher DR, Sojka PE (2007) Secondary breakup of electrically charged Newtonian drops. In: Proceedings of IMECE2007, IMECE2007–4189Google Scholar
  30. Han J, Tryggvason G (1999) Secondary breakup of axisymmetric liquid drops. I. Acceleration by a constant body force. Phys Fluids 11(12):3650–3667MATHCrossRefGoogle Scholar
  31. Han J, Tryggvason G (2001) Secondary breakup of axisymmetric liquid drops. II. Impulsive acceleration. Phys Fluids 13(6):1554–1565CrossRefGoogle Scholar
  32. Helenbrook BT, Edwards CF (2002) Quasi-steady deformation and drag of uncontaminated liquid drops. Int J of Multiphas Flow 28(10):1631–1657MATHCrossRefGoogle Scholar
  33. Hinze JO (1955) Fundamentals of the hydrodynamic mechanism of splitting in dispersion processes. AIChE J 1(3):289–295CrossRefGoogle Scholar
  34. Hsiang LP, Faeth GM (1992) Near-limit drop deformation and secondary breakup. Int J Multiphas Flow 18(5):635–652MATHCrossRefGoogle Scholar
  35. Hsiang LP, Faeth GM (1993) Drop properties after secondary breakup. Int J Multiphase Flow 19(5):721–735MATHCrossRefGoogle Scholar
  36. Hsiang LP, Faeth GM (1995) Drop deformation and breakup due to shock wave and steady disturbances. Int J Multiphase Flow 21(4):545–560MATHCrossRefGoogle Scholar
  37. Hwang SS, Liu Z, Reitz RD (1996) Breakup mechanisms and drag coefficients of high-speed vaporizing liquid drops. Atomization Spray 6:353–376Google Scholar
  38. Ibrahim EA, Yang HQ, Przekwas AJ (1993) Modeling of spray droplets deformation and breakup. J Propul Power 9(4):651–654CrossRefGoogle Scholar
  39. Igra D, Ogawa T, Takayama K (2002) A parametric study of water column deformation resulting from shock wave loading. Atomization Spray 12:577–591CrossRefGoogle Scholar
  40. Igra D, Takayama K (2001) Investigation of aerodynamic breakup of a cylindrical water droplet. Atomization Spray 11(2):167–185Google Scholar
  41. Joseph DD, Beavers GS, Funada T (2002) Rayleigh–Taylor instability of viscoelastic drops at high Weber numbers. J Fluid Mech 453:109–132MATHCrossRefGoogle Scholar
  42. Joseph DD, Belanger J, Beavers GS (1999) Breakup of a liquid drop suddenly exposed to a high-speed airstream. Int J Multiphase Flow 25:1263–1303MATHCrossRefGoogle Scholar
  43. Kalashnikov VN, Askarov AN (1989) Relaxation time of elastic stresses in liquids with small additions of soluble polymers of high molecular weights. J Eng Phys Thermophys 57:874–878Google Scholar
  44. Khosla S, Smith CE, Throckmorton RP (2006) Detailed understanding of drop atomization by gas crossflow using the volume of fluid method. Inl: ILASS Americas, 19th annual conference on liquid atomization and spray systems, Toronto, CanadaGoogle Scholar
  45. Koshizuka A, Oka Y (1996) Moving-particle semi-implicit method for fragmentation of incompressible fluid. Nucl Sci Eng 123:421Google Scholar
  46. Lasheras JC, Villermaux E, Hopfinger EJ (1998) Break-up and atomization of a round water jet by a high-speed annular air jet. J Fluid Mech 357:351–379CrossRefGoogle Scholar
  47. Lee CH, Reitz RD (1999) Modeling the effects of gas density on the drop trajectory and breakup size of high-speed liquid drops. Atomization Spray 9:497–517Google Scholar
  48. Lee CH, Reitz RD (2000) An experimental study of the effect of gas density on the distortion and breakup mechanism of drops in high speed gas stream. Int J Multiphase Flow 26:229–244MATHCrossRefGoogle Scholar
  49. Lee CS, Kim HJ, Park SW (2004) Atomization characteristics and prediction accuracies of hybrid break-up models for a gasoline direct injection spray. P I Mech Eng D-J Aut 218(D9):1041–1053CrossRefGoogle Scholar
  50. Lee CS, Reitz RD (2001) Effect of liquid properties on the breakup mechanism of high-speed liquid drops. Atomization Spray 11:1–19Google Scholar
  51. Li X, Li M, Fu H (2005) Modeling the initial droplet size distribution in sprays based on the maximization of entropy generation. Atomization Spray 15:295–321CrossRefGoogle Scholar
  52. Liu AB, Mather D, Reitz RD (1993) Modeling the effect of drop drag and breakup on fuel sprays. In: SAE International congress and exposition, SAE 930072Google Scholar
  53. Liu AB, Reitz RD (1993) Mechanisms of air-assisted liquid atomization. Atomization Spray 3:55–75Google Scholar
  54. Liu Z, Reitz RD (1997) An analysis of the distortion and breakup mechanisms of high speed liquid drops. Int J Multiphas Flow 23(4):631–650MATHCrossRefGoogle Scholar
  55. López-Rivera C, Sojka PE (2008) Secondary breakup of non-Newtonian liquid drops. In: ILASS Europe 22nd European conference on liquid atomization and spray dystems, Como Lake, ItalyGoogle Scholar
  56. Matta JE, Tytus RP (1982) Viscoelastic breakup in a high velocity airstream. J Appl Polymer Sci 27:397–405CrossRefGoogle Scholar
  57. Matta JE, Tytus RP, Harris JL (1983) Aerodynamic atomization of polymeric solutions. Chem Eng Commun 19:191–204CrossRefGoogle Scholar
  58. Mugele RA, Evans HD (1951) Droplet size distribution in sprays. Ind Eng Chem 43:1317–1324CrossRefGoogle Scholar
  59. Nomura K, Koshizuka S, Oka Y, Obata H (2001) Numerical analysis of droplet breakup behavior using particle method. J Nucl Sci Technol 38(12):1057–1064CrossRefGoogle Scholar
  60. O’Donnell BJ, Helenbrook BT (2005) Drag on ellipsoids at finite Reynolds numbers. Atomization Spray 15:363–375CrossRefGoogle Scholar
  61. O’Rourke PJ, Amsden AA (1987) The TAB method for numerical calculation of spray droplet breakup. SAE Paper No 872089Google Scholar
  62. Ortiz C, Joseph DD, Beavers GS (2004) Acceleration of a liquid drop suddenly exposed to a high-speed airstream. Int J Multiphas Flow 30:217–224MATHCrossRefGoogle Scholar
  63. Park JH, Yoon Y, Hwang SS (2002) Improved TAB model for prediction of spray droplet deformation and breakup. Atomization Spray 12:387–401CrossRefGoogle Scholar
  64. Park SW, Kim S, Lee CS (2006) Effect of mixing ratio of biodiesel on breakup mechanisms of monodispersed droplets. Energy Fuels 20(4):1709–1715CrossRefGoogle Scholar
  65. Park SW, Lee CS (2004) Investigation of atomization and evaporation characteristics of high-pressure injection diesel spray using Kelvin–Helmholtz instability/droplet deformation and break-up competition model. P I Mech Eng D-J Aut 218:767–777CrossRefGoogle Scholar
  66. Pham TL, Heister SD (2002) Spray modeling using Lagrangian droplet tracking in a homogeneous flow model. Atomization Spray 12:687–707CrossRefGoogle Scholar
  67. Pilch M, Erdman CA (1987) Use of breakup time data and velocity history data to predict the maximum size of stable fragments for acceleration-induced breakup of a liquid drop. Int J Multiphase Flow 13(6):741–757CrossRefGoogle Scholar
  68. Prevish TD, Santavicca DA (1998) Turbulent breakup of hydrocarbon droplets at elevated pressures. In: ILASS Americas, 11th annual conference on liquid atomization and spray systems, Sacramento, CA, USAGoogle Scholar
  69. Quan S, Schmidt DP (2006) Direct numerical study of a liquid droplet impulsively accelerated by gaseous flow. Phy Fluids 18(10):102103Google Scholar
  70. Ranger AA, Nicholls JA (1969) Aerodynamic shattering of liquid drops. AIAA J 7(2):285–290CrossRefGoogle Scholar
  71. Rayleigh L (1882) On the equilibrium of liquid conducting masses charged with electricity. Philos Magaz 14:184–186Google Scholar
  72. Schmelz F, Walzel P (2003) Breakup of liquid droplets in accelerated gas flows. Atomization Spray 13:357–372CrossRefGoogle Scholar
  73. Sehgal BR, Nourgaliev RR, Dinh TN (1999) Numerical simulation of droplet deformation and break-up by Lattice–Boltzmann method. Prog Nucl Energ 34(4):471–488CrossRefGoogle Scholar
  74. Shibata K, Koshizuka S, Oka Y (2004) Numerical analysis of jet breakup behavior using particle method. J Nucl Sci Technol 41(7):715–722CrossRefGoogle Scholar
  75. Shraiber AA, Podvysotsky AM, Dubrovsky VV (1996) Deformation and breakup of drops by aerodynamic forces. Atomization Spray 6:667–692Google Scholar
  76. Shrimpton JS, Laoonual Y (2006) Dynamics of electrically charged transient evaporating sprays. I J Numer Meth Eng 67:1063–1081MATHCrossRefGoogle Scholar
  77. Simmons HC (1977a) The correlation of drop-size distributions in fuel nozzle sprays part I: the drop-size/volume-fraction distribution. J Eng Power-T ASME 99(3):309–314Google Scholar
  78. Simmons HC (1977b) The correlation of drop-size distributions in fuel nozzle sprays part II: the drop-size/number distribution. J Eng Power-T ASME 99(3):315–319Google Scholar
  79. Sussman M, Smereka P, Osher S (1994) A level set approach for computing solutions to incompressible two-phase flow. J Comp Phys 114:146–159MATHCrossRefGoogle Scholar
  80. Tanner FX (1997) Liquid jet atomization and droplet breakup modeling of non-evaporating diesel fuel sprays. SAE Trans J Eng 106:127–140Google Scholar
  81. Tarnogrodzki A (1993) Theoretical prediction of the critical Weber number. Int J Multiphase Flow 19(2):329–336MATHCrossRefGoogle Scholar
  82. Taylor GI (1950) The The instability of liquid surfaces when accelerated in a direction perpendicular to their planes. I. P Royal Soc A Math Phys 201:192–196MATHCrossRefGoogle Scholar
  83. Taylor GI (1963) The shape and acceleration of a drop in a high-speed air stream. In: Batchelor GK (ed) The scientific papers of GI Taylor, vol III. University Press, CambridgeGoogle Scholar
  84. Theofanous TG, Li GJ, Dinh TN (2004) Aerobreakup in rarefied supersonic gas flows. J Fluid Eng T ASME 126:516–527CrossRefGoogle Scholar
  85. Trinh HP, Chen CP (2006) Development of liquid jet atomization and breakup models including turbulence effects. Atomization Spray 16:907–932CrossRefGoogle Scholar
  86. Trinh HP, Chen CP, Balasubramanyam MS (2007) Numerical simulation of liquid jet atomization including turbulence effects. J Eng Gas Turb Power 129:920–928CrossRefGoogle Scholar
  87. Tryggvason G (1997) Computational investigation of atomization. Contract Number F49620-96-1-0356, Report Number A915353Google Scholar
  88. Wadhwa AR, Abraham J, Magi V (2005) Hybrid compressible-incompressible numerical method for transient drop-gas flows. AIAA J 43(9):1974–1983CrossRefGoogle Scholar
  89. Wadhwa AR, Magi V, Abraham J (2007) Transient deformation and drag of decelerating drops in axisymmetric flows. Phys Fluids 19Google Scholar
  90. Weber C (1931) The breakup of liquid jets. Zeits Angew Math Mech 11:136–154MATHCrossRefGoogle Scholar
  91. Wert KL (1995) A rationally-based correlation of mean fragment size for drop secondary breakup. Int J Multiphase Flow 21(6):1063–1071MATHCrossRefGoogle Scholar
  92. Wierzba A, Takayama K (1988) Experimental investigation of the aerodynamic breakup of liquid drops. AAIA J 26(11):1329–1335CrossRefGoogle Scholar
  93. Wilcox JD, June RK, Brown HA, Kelley RC (1961) The retardation of drop breakup in high-velocity airstreams by polymeric modifiers. J Appl Polymer Sci 5(13):1–6CrossRefGoogle Scholar
  94. Zaleski S, Li J, Succi S (1995) Two-dimensional Navier–Stokes simulation of deformation and breakup of liquid patches. Phys Rev Lett 75(2):244–247CrossRefGoogle Scholar
  95. Zhou W, Zhao T, Wu T, Yu Z (2000) Application of fractal geometry to atomization process. Chem Eng J 78:193–197CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  • D. R. Guildenbecher
    • 1
  • C. López-Rivera
    • 1
  • P. E. Sojka
    • 1
  1. 1.Maurice J. Zucrow Laboratories, School of Mechanical EngineeringPurdue UniversityWest LafayetteUSA

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