Spray Formation and Penetration

Chapter

Abstract

The conventional understanding of spray formation when liquid leaves the nozzle is based on the analysis of the following stages: development of a jet, conversion of a jet into liquid sheets and ligaments, disintegration of ligaments into relatively large droplets (primary break-up) and break-up of large droplets into smaller ones (secondary break-up). The following stages of spray formation are considered in this chapter: instability of a jet emerging from the nozzle, break-up of droplets, and spray penetration, taking and not taking into account the effect of turbulence. In the case of gasoline direct injection engines the development of sprays is typically accompanied by the formation of vortex ring-like structures. Some new approaches to modelling these structures are discussed. The predicted velocities of displacement of the regions of maximal vorticity in typical gasoline engines are compared with available experimental data where possible.

Keywords

Combustion Vortex Diesel Dimethyl Vorticity 

References

  1. 1.
    Abdelghaffar, W. A., Elwardany, A. E., & Sazhin, S. S. (2010). Modeling of the processes in diesel engine-like conditions: Effects of fuel heating and evaporation. Atomization Sprays, 20, 737–737.CrossRefGoogle Scholar
  2. 2.
    Afanasyev, Y. D., & Korabel, V. N. (2004). Starting vortex dipoles in a viscous fluid: Asymptotic theory, numerical simulation, and laboratory experiments. Physics of Fluids, 16(11), 3850–3858.CrossRefMathSciNetGoogle Scholar
  3. 3.
    Allocca, L., Belardini, P., Bertoli, C., Corcione, F. E., & de Angelis, F. (1992). Experimental and numerical analysis of a diesel spray. SAE report 920576.Google Scholar
  4. 4.
    Arienti, M., & Sussman, M. (2014). An embedded level set method for sharp-interface multiphase simulations of diesel injectors. International Journal of Multiphase Flow, 59, 1–14.CrossRefGoogle Scholar
  5. 5.
    Begg, S., Kaplanski, F., Sazhin, S. S., Hindle, M., & Heikal, M. (2009). Vortex ring structures in gasoline engines under cold-start conditions. International Journal of Engine Research, 10, 195–214.CrossRefGoogle Scholar
  6. 6.
    Bellman, R., & Pennington, R. H. (1954). Effects of surface tension and viscosity on Taylor instability. Quarterly of Applied Mathematics, 12, 151–162.Google Scholar
  7. 7.
    Berezovski, A., & Kaplanski, F. (1995). Vorticity distributions for thick and thin vortex pairs and rings. Archives of Mechanics, 47(6), 1015–1026 (in Russian).Google Scholar
  8. 8.
    Borman, G. L., & Ragland, K. W. (1998). Combustion engineering. New York: McGraw-Hill.Google Scholar
  9. 9.
    Cantwell, B. (2002). Introduction to symmetry analysis. Cambridge: Cambridge University Press.Google Scholar
  10. 10.
    Cebeci, T., & Smith, A. M. O. (1974). Analysis of turbulent boundary layers. Applied mathematics and mechanics (Vol. 15). NY: Academic Press.Google Scholar
  11. 11.
    Chehroudi, B., & Bracco, F. V. (1988). Structure of a transient hollow cone spray. SAE report 880522.Google Scholar
  12. 12.
    Chesnel, J., Menard, T., Reveillon, J., & Demoulin, F. -X. (2011). Subgrid analysis of liquid jet atomization. Atomization Sprays, 21, 41–67.Google Scholar
  13. 13.
    Chigier, N., & Reitz, R. D. (1998). Regimes of jet breakup and breakup mechanisms (physical aspects). In Kuo, K. K. (Ed.), Recent advances in spray combustion: Spray atomization and drop burning phenomena ( pp. 109–135). Reston: American Institute of Aeronautics and Astronautics Inc.Google Scholar
  14. 14.
    Chryssakis, C., & Assamis, D. N. (2008). A unified fuel spray breakup model for internal combustion engine applications. Atomization Sprays, 18, 375–426.CrossRefGoogle Scholar
  15. 15.
    Cossali, G. E. (2001). An integral model for gas entrainment into full cone sprays. Journal of Fluid Mechanics, 439, 353–366.CrossRefMATHGoogle Scholar
  16. 16.
    Crua, C., Shoba, T., Heikal, M., Gold, M., & Higham, C. (2010). High-speed microscopic imaging of the initial stage of Diesel spray formation and primary breakup. SAE Technical, Report 2010–01-2247.Google Scholar
  17. 17.
    Csanady, G. T. (1973). Turbulent diffusion in the environment. Dordrecht-Holland: D. Reidel Publishing Comp.Google Scholar
  18. 18.
    Dai, Z., & Faith, G. M. (2001). Temporal properties of secondary drop breakup in the multimode breakup regime. International Journal of Multiphase Flow, 27, 217–236.CrossRefMATHGoogle Scholar
  19. 19.
    Dent, J. C. (1971). A basic for the comparison of various experimental methods for studying spray penetration. SAE report 710571.Google Scholar
  20. 20.
    Desantes, J. M., Payri, R., Salvador, F. J., & Gil, A. (2006). Development and validation of a theoretical model for diesel spray penetration. Fuel, 85, 910–917.CrossRefGoogle Scholar
  21. 21.
    Desantes, J. M., Payri, R., Garcia, J. M., & Salvador, F. J. (2007). A contribution to the understanding of isothermal diesel spray dynamics. Fuel, 86, 1093–1101.Google Scholar
  22. 22.
    Desantes, J. M., Payri, R., Salvador, F. J., & de la Morena, J. (2010). Influence of cavitation phenomenon on primary break-up and spray behavior at stationary conditions. Fuel, 89, 3033–3041.Google Scholar
  23. 23.
    Devassy, B.M., Habchi, C., & Daniel, E. (2013). A new atomization model for high speed liquid jets using a turbulent, compressible, two-phase flow model and a surface density approach. Proceedings of ILASS—Europe 2013, 25th European Conference on Liquid Atomization and Spray Systems, Chania, Greece, 1–4 September 2013, paper 32.Google Scholar
  24. 24.
    Dombrowski, N., & Johns, W. R. (1963). The aerodynamic instability and disintegration of viscous liquid sheets. Chemical Engineering Science, 18, 203–214.CrossRefGoogle Scholar
  25. 25.
    Douglas, J. F., Gasiorek, J. M., Swaffield, J. A., & Jack, L. B. (2005). Fluid mechanics (5\(^{\rm th}\) ed.). Singapore: Pearson.Google Scholar
  26. 26.
    Drazin, P. G., & Reid, W. H. (2004). Hydrodynamic stability (2\(^{\rm nd}\) ed.), Cambridge: Cambridge University Press.Google Scholar
  27. 27.
    Dumouchel, C., & Grout, S. (2009). Application of the scale entropy diffusion to describe a liquid atomization process. International Journal of Multiphase Flow, 35, 952–962.CrossRefGoogle Scholar
  28. 28.
    Dumouchel, C., & Grout, S. (2011). On the scale diffusivity of a 2-D liquid atomization process analysis. Physica A, 390, 1811–1825.CrossRefGoogle Scholar
  29. 29.
    Dumouchel, C., & Blaisot, J. -B. (2013) Multi-scale analysis of liquid atomization processes and sprays. Proceedings of ILASS—Europe 2013, 25th European Conference on Liquid Atomization and Spray Systems, Chania, Greece, 1–4 September 2013, paper 25.Google Scholar
  30. 30.
    Duret, B., Menard, T., Reveillon, J., & Demoulin, F. X. (2013) Improving primary atomization modelling through DNS of two-phase flows. Proceedings of ILASS—Europe 2013, 25th European Conference on Liquid Atomization and Spray Systems, Chania, Greece, 1–4 September 2013, paper 110.Google Scholar
  31. 31.
    Dyson, F. W. (1893). The potential of an anchor ring-part ii. Philosophical transactions of the Royal Society of London, A184, 1041–1106.CrossRefGoogle Scholar
  32. 32.
    Eggers, J., & Villermaux, E. (2008). Physics of liquid jets. Reports on Progress in Physics 616, 79 p.Google Scholar
  33. 33.
    Faeth, G. M., Hsiang, L. -P., & Wu, P. -K. (1995). Structure and breakup properties of sprays. International Journal of Multiphase Flow, 21, Suppl., 99–127.Google Scholar
  34. 34.
    Fraenkel, L. E. (1972). Examples of steady vortex rings of small cross-section in an ideal fluid. Journal of Fluid Mechanics, 51, 119–135.CrossRefMATHGoogle Scholar
  35. 35.
    Fukumoto, Y., & Kaplanski, F. (2008). Global time evolution of an axisymmetric vortex ring at low Reynolds numbers. Physics of Fluids, 20, 053103.Google Scholar
  36. 36.
    Fukumoto, Y., & Moffatt, H. K. (2008). Kinematic variational principle for motion of vortex rings. Physica D, 237, 2210–2217.CrossRefMATHMathSciNetGoogle Scholar
  37. 37.
    Fuster, D., Bagué, A., Boeck, T., Le Moyne, L., Leboissetier, A., Popinet, S., et al. (2009). Simulation of primary atomization with an octree adaptive mesh refinement and VOF method. International Journal of Multiphase Flow, 35, 550–565.Google Scholar
  38. 38.
    Ghasemi, A., Barron, R. M., & Balachandar, R. (2014). Spray-induced air motion in single and twin ultra-high injection diesel sprays. Fuel, 121, 284–297.CrossRefGoogle Scholar
  39. 39.
    Ghosh, S., & Hunt, J. C. R. (1994). Induced air velocity within droplet driven sprays. Proceedings of the Royal Society of London, A444, 105–127.CrossRefGoogle Scholar
  40. 40.
    Ghosh, S., & Hunt, J. C. R. (1998). Spray jets in a cross-flow. Journal of Fluid Mechanics, 365, 109–136.CrossRefMATHMathSciNetGoogle Scholar
  41. 41.
    Giannadakis, E., Gavaises, M., & Arcoumanis, C. (2006). Modelling of cavitation in diesel injector nozzles. Journal of Fluid Mechanics, 616, 153–193.CrossRefGoogle Scholar
  42. 42.
    Girin, A. G. (2012). On the mechanism of inviscid drop breakup at relatively small Weber numbers. Atomization Sprays, 22, 921–934.CrossRefGoogle Scholar
  43. 43.
    Girin, A. G. (2013). Deformation and acceleration of drop. Proceedings of ILASS—Europe 2013, 25th European Conference on Liquid Atomization and Spray Systems, Chania, Greece, 1–4 September 2013, paper 43.Google Scholar
  44. 44.
    Girin, A. G., & Ivanchenko, Y. A. (2012). Model of liquid film disintegration at ‘bag’ mode of drop breakup. Atomization Sprays, 22, 935–949.CrossRefGoogle Scholar
  45. 45.
    Glezer, A., & Coles, D. (1990). An experimental study of a turbulent vortex ring. Journal of Fluid Mechanics, 211, 243–283.CrossRefGoogle Scholar
  46. 46.
    Gorokhovski, M. A., & Saveliev, V. L. (2003). Analysis of Kolmogorov’s model of breakup and its application into Lagrangian computation of liquid sprays under air-blast atomisation. Physics of Fluids, 15, 184–192.CrossRefGoogle Scholar
  47. 47.
    Gorokhovski, M., & Herrmann, M. (2008). Modeling primary atomization. Annual Review of Fluid Mechanics, 40(1), 343–366.Google Scholar
  48. 48.
    Gorokhovski, M. A., & Saveliev, V. L. (2008). Statistical universalities in fragmentation under scaling symmetry with a constant frequency of fragmentation. Journal of Physics D: Applied Physics, 41, 085405.Google Scholar
  49. 49.
    Grout, S., Dumouchel, C., Cousin, J., & Nuglisch, H. (2007). Fractal analysis of atomizing liquid flows. International Journal of Multiphase Flow, 33, 1023–1044.CrossRefGoogle Scholar
  50. 50.
    Günther, A., & Wirth, K. -E. (2013). Evaporation phenomena in superheated atomization and its impact on the generated spray. International Journal of Heat and Mass Transfer, 64, 952–965.Google Scholar
  51. 51.
    Habchi, C. (2011). The energy spectrum analogy breakup (SAB) model for the numerical simulation of sprays. Atomization Sprays, 21, 1033–1057.CrossRefGoogle Scholar
  52. 52.
    Habchi, C. (2013). A Gibbs free energy relaxation model for cavitation simulation in Diesel injectors. Proceedings of ILASS—Europe 2013, 25th European Conference on Liquid Atomization and Spray Systems, Chania, Greece, 1–4 September 2013, paper 93.Google Scholar
  53. 53.
    Healy, D. P., & Young, J. B. (2005). Full Lagrangian methods for calculating the particle concentration and velocity fields in dilute gas-particle flows. Proceedings of the Royal Society of London. Series A, 461, 2197–2225.CrossRefMATHMathSciNetGoogle Scholar
  54. 54.
    Helmholtz, H. (1858) On integrals of the hydrodynamical equations which express vortex-motion. P. G. Tait, Trans. with a letter by Lord Kelvin (W. Thompson) in London Edinburgh and Dublin Philosophy Magazine and Journal of Science, 33, 485–512 (Fourth series).Google Scholar
  55. 55.
    Herrmann, M. (2011). On simulating primary atomization using the refined level set grid method. Atomization Sprays, 21, 283–301.CrossRefGoogle Scholar
  56. 56.
    Herrmann, M. (2013). On simulating primary atomization. Atomization and Sprays, 23(11–12), v–ix.Google Scholar
  57. 57.
    Heywood, J. B. (1988). Internal combustion engines fundamentals. New York: McGraw-Hill Book Company.Google Scholar
  58. 58.
    Hiroyasu, H. & Kadota, T. (1974). Fuel droplet size distribution in a diesel combustion chamber. SAE Paper 740715.Google Scholar
  59. 59.
    Hong, J. G., Ku, K. W., & Lee, C. -W. (2011). Numerical simulation of the cavitating flow in an elliptical nozzle. Atomization Sprays, 21, 237–248.Google Scholar
  60. 60.
    Hsiang, L. -P., & Faeth, G. M. (1993). Drop properties after secondary breakup. International Journal of Multiphase Flow, 19, 721–735.Google Scholar
  61. 61.
    Huh, K. Y., Lee, E., & Koo, J. -Y. (1998). Diesel spray atomization model considering nozzle exit turbulence conditions. Atomization Sprays, 8, 453–459.Google Scholar
  62. 62.
    Jiang, X., Siamas, G. A., Jagus, K., & Karayiannis, T. G. (2010). Physical modelling and advanced simulations of gas-liquid two-phase jet flows in atomization and sprays. Progress in Energy Combustion Science, 36, 131–167.CrossRefGoogle Scholar
  63. 63.
    Juniper, M. P. (2008). The effect of confinement on the stability of non-swirling round jet/wake flows. Journal of Fluid Mechanics, 605, 227–252.CrossRefMATHMathSciNetGoogle Scholar
  64. 64.
    Kaltaev, A. (1982). Investigation of dynamic characteristics of a vortex ring of viscous fluid. Continuum dynamics (pp. 63–70). Alma-Ata: Kazah State University (in Russian).Google Scholar
  65. 65.
    Kambe, T., & Oshima, Y. (1975). Generation and decay of viscous vortex rings. Journal of the Physical Society of Japan, 38, 271–280.CrossRefGoogle Scholar
  66. 66.
    Kaplanski, F., Fukumoto, Y., & Rudi, U. (2012). Reynolds-number effects on vortex ring evolution in a viscous fluid. Physics Fluids, 24, 033101.Google Scholar
  67. 67.
    Kaplanski, F., & Rudi, U. (1999). Dynamics of a viscous vortex ring. International Journal of Fluid Mechanics Research, 26, 618–630.MathSciNetGoogle Scholar
  68. 68.
    Kaplanski, F., & Rudi, Y. (2005). A model for the formation of ‘optimal’ vortex rings taking into account viscosity. Physics of Fluids, 17, 087101.CrossRefMathSciNetGoogle Scholar
  69. 69.
    Kaplanski, F., Sazhin, S. S., Fukumoto, Y., Begg, S., & Heikal, M. (2009). A generalised vortex ring model. Journal of Fluid Mechanics, 622, 233–258.CrossRefMATHMathSciNetGoogle Scholar
  70. 70.
    Kaplanski, F., Sazhin, S. S., Begg, S., Fukumoto, Y., & Heikal, M. (2010). Dynamics of vortex rings and spray induced vortex ring-like structures. European Journal of Mechanics - B/Fluids, 29(3), 208–216.CrossRefMATHMathSciNetGoogle Scholar
  71. 71.
    Karimi, K. (2007). Characterisation of multiple-injection diesel sprays at elevated pressures and temperatures. Ph.D. Thesis, University of Brighton, Brighton, United Kingdom.Google Scholar
  72. 72.
    Kolakaluri, R., Li, Y., & Kong, S. -C. (2010). A unified spray model for engine spray simulation using dynamic mesh refinement. International Journal of Multiphase Flow, 36, 858–869.Google Scholar
  73. 73.
    Kolmogorov, A. N. (1941). On the log-normal distribution of particle sizes during the breakup process. Doklady Akademii Nauk SSSR, 31, 99.Google Scholar
  74. 74.
    Kostas, J., Honnery, D., & Soria, J. (2009). Time resolved measurements of the initial stages of fuel spray penetration. Fuel, 88, 2225–2237.CrossRefGoogle Scholar
  75. 75.
    Kasyap, T. V., Sivakumar, D., & Raghunandan, B. N. (2009). Flow and breakup characteristics of elliptical liquid jets. International Journal of Multiphase Flow, 35, 8–19.CrossRefGoogle Scholar
  76. 76.
    Kovasznay, L. S. G., Fujita, H., & Lee, R. L. (1974). Unsteady turbulent puffs. Advances in Geophysics, 18B, 253–263.Google Scholar
  77. 77.
    Lamb, H. (1932). Hydrodynamics. New York: Dover Publishers.Google Scholar
  78. 78.
    Lavrentiev, M. A., & Shabat, B. V. (1973). Problems of hydrodynamics and mathematical models. Moscow: Nauka Publishing House. (in Russian).Google Scholar
  79. 79.
    Lebas, R., Menard, T., Beau, P. A., Berlemont, A., & Demoulin, F. X. (2009). Numerical simulation of primary break-up and atomization: DNS and modelling study. International Journal of Multiphase Flow, 35, 247–260.CrossRefGoogle Scholar
  80. 80.
    Lebedeva, N. A., Osiptsov, A. N., & Sazhin, S. S. (2013). A combined fully Lagrangian approach to mesh-free modelling of transient two phase flows. Atomization Sprays, 23, 47–69.CrossRefGoogle Scholar
  81. 81.
    Lee, C. H., & Reitz, R. D. (2013). CFD simulations of diesel spray tip penetration with multiple injections and with engine compression ratios up to 100:1. Fuel, 111, 289–297.CrossRefGoogle Scholar
  82. 82.
    Lee, C. S., & Park, S. W. (2002). An experimental and numerical study on fuel atomization characteristics of high-pressure diesel injection sprays. Fuel, 81, 2417–2423.CrossRefGoogle Scholar
  83. 83.
    Lefebvre, A. H. (1989). Atomization and sprays. Bristol, PA: Taylor & Francis.Google Scholar
  84. 84.
    Li, X. (1995). Mechanism of atomisation of a liquid jet. Atomization Sprays, 5, 89–105.Google Scholar
  85. 85.
    Li, Y., & Umemura, A. (2014). Two-dimensional numerical investigation on the dynamics of ligament formation by Faraday instability. International Journal of Multiphase Flow, 60, 64–75.CrossRefGoogle Scholar
  86. 86.
    Lightfoot, M. (2009). Fundamental classification of atomization processes. Atomization Sprays, 19, 1065–1104.CrossRefGoogle Scholar
  87. 87.
    Lim, T., & Nickels, T. (1995). Vortex rings. In S. I. Green (Ed.), Fluid vortices (pp. 95–153). Dordrecht: Kluwer.Google Scholar
  88. 88.
    Lin, S. P., & Rietz, R. D. (1998). Droplet and spray formation from a liquid jet. Annual Review of Fluid Mechanics, 30, 85–105.CrossRefGoogle Scholar
  89. 89.
    Liu, F. -S., Zhou, L., Sun, B. -G., Li, Z. -J., & Schock, H. J. (2008). Validation and modification of wave spray model for diesel combustion simulation. Fuel, 87, 3420–3427.Google Scholar
  90. 90.
    Liu, Z., & Liu, Z. (2006). Linear analysis of three-dimensional instability of non-newtonian liquid jets. Journal of Fluid Mechanics, 559, 451–459.CrossRefMATHMathSciNetGoogle Scholar
  91. 91.
    Lozano, A., Barreras, F., Hauke, G., & Dopazo, C. (2001). Longitudinal instabilities in an air-blasted liquid sheet. Journal of Fluid Mechanics, 437, 143–173.CrossRefMATHGoogle Scholar
  92. 92.
    Lugovtsov, B. A. (1970). On the motion of a turbulent vortex ring and its role in the transport of passive contaminant. In Some problems of mathematics and mechanics (dedicated to the 70th anniversary of M.A. Lavrentiev) (pp. 182–187), Leningrad: Nauka Publishing House (in Russian).Google Scholar
  93. 93.
    Lugovtsov, B. A. (1976). On the motion of a turbulent vortex ring. Archives of Mechanics, 28, 759–766.MATHGoogle Scholar
  94. 94.
    Malaguti, S., Fontanesi, S., Cantore, G., Montanaro, A., & Allocca, L. (2013). Modelling of primary breakup process of a gasoline direct engine multi-hole spray. Atomization and Sprays, 23, 861–888.CrossRefGoogle Scholar
  95. 95.
    Marmottant, P., & Villermauz, E. (2004). On spray formation. Journal of Fluid Mechanics, 498, 73–111.CrossRefMATHGoogle Scholar
  96. 96.
    Martinez, L., Benkenida, A., & Cuenot, B. (2010). A model for the injection boundary conditions in the context of 3D simulation of diesel spray: methodology and validation. Fuel, 89, 219–228.CrossRefGoogle Scholar
  97. 97.
    Martynov, S. B., Mason, D. J., & Heikal, M. R. (2006). Numerical simulation of cavitation flows based on their hydrodynamic similarity. International Journal of Engine Research, 7, 1–14.CrossRefGoogle Scholar
  98. 98.
    MATHEMATICA (2007). Book version 6.0.0, Wolfram Research Inc. Available at http://functions.wolfram.com. Retrieved July 25, 2008.
  99. 99.
    Ménard, T., Tanguy, S., & Berlemont. A. (2007). Coupling level set/VOF/ghost fluid methods: Validation and application to 3D simulation of the primary break-up of a liquid jet. International Journal of Multiphase Flow, 33, 510–524.Google Scholar
  100. 100.
    Narasimha, R., & Sreenivasan, K. R. (1979). Relaminarization of fluid flows. Advances in Applied Mechanics, 19, 221–301.CrossRefGoogle Scholar
  101. 101.
    Nichols, J. (1972). Stream and droplet breakup by shock waves. In D.T. Harrje & F.H. Reardon (Eds.), Liquid propellant rocket combustion instability (pp. 126–128), NASA SP-194, Washington, DC.Google Scholar
  102. 102.
    Nordin, N. (2001). Complex chemistry modeling of Diesel spray combustion, Ph.D. Thesis, Chalmers University of Technology, Gothenburg, Sweden.Google Scholar
  103. 103.
    O’Rourke, P. J. (1981). Collective drop effects on vaporizing liquid sprays. Ph.D. thesis, Princeton University.Google Scholar
  104. 104.
    O’Rourke, P. J., & Amsden, A. A. (1987). The TAB method for numerical calculation of spray droplet breakup. SAE report 872089.Google Scholar
  105. 105.
    Panton, R. L. (1996). Incompressible flow. New York, Chichester: John Wiley & Sons Inc.Google Scholar
  106. 106.
    Park, K. S., & Heister, S. D. (2010). Nonlinear modeling of drop size distributions produced by pressure-swirl atomizers. International Journal of Multiphase Flow, 36, 1–12.CrossRefGoogle Scholar
  107. 107.
    Pastor, J. V., López, J. J., García, J. M., & Pastor, J. M. (2008). A 1D model for the description of mixing-controlled inert diesel sprays. Fuel, 87, 2871–2885.CrossRefGoogle Scholar
  108. 108.
    Pastor, J. V., Garca-Oliver, J. M., Nerva, J.-G., & Giménez, B. (2011). Fuel effect on the liquid-phase penetration of an evaporating spray under transient diesel-like conditions. Fuel, 90, 3369–3381.CrossRefGoogle Scholar
  109. 109.
    Patterson, M. A., & Reitz, R. D. (1998). Modelling of the effects of fuel spray characteristics on Diesel engine combustion and emission. SAE report 980131.Google Scholar
  110. 110.
    Payri, R., Salvador, F. J., Gimeno, J., & Zapata, L. D. (2008). Diesel nozzle geometry influence on spray liquid-phase fuel penetration in evaporative conditions. Fuel, 87, 1165–1176.CrossRefGoogle Scholar
  111. 111.
    Phillips, O. M. (1956). The final period of decay of non-homogeneous turbulence. Proceedings of the Cambridge Philosophical Society, 252, 135–151.CrossRefGoogle Scholar
  112. 112.
    Poole, D. R., Barenghi, C. F., Sergeev, Y. A., & Vinen, W. F. (2005). The motion of tracer particles in helium II. Physical Review B, 71, 064514-1-16.Google Scholar
  113. 113.
    Postrioti, L., Mariani, F., & Battistoni, M. (2012). Experimental and numerical momentum flux evaluation of high pressure diesel spray. Fuel, 98, 149–163.CrossRefGoogle Scholar
  114. 114.
    Pozorski, J., & Minier, J.-P. (1998). On the Lagrangian turbulent dispersion models based on the Langevin equation. International Journal of Multiphase Flow, 24, 913–945.CrossRefMATHGoogle Scholar
  115. 115.
    Pozorski, J., & Minier, J.-P. (1999). PDF modeling of dispersed two-phase turbulent flows. Physical Review E, 59, 855–863.CrossRefGoogle Scholar
  116. 116.
    Pozorski, J., Sazhin, S. S., Wacławczyk, M., Crua, C., Kennaird, D., & Heikal, M. R. (2002). Spray penetration in a turbulent flow. Flow, Turbulence and Combustion, 68(2), 153–165.CrossRefMATHGoogle Scholar
  117. 117.
    Ranger, A. A., & Nicholls, J. A. (1969). The aerodynamic shattering of liquid drops. AIAA Journal, 3, 285–290.Google Scholar
  118. 118.
    Reitz, R. D. (1987). Modelling atomization processes in high-pressure vaporizing sprays. Atomisation and Spray Technology, 3, 309–337.Google Scholar
  119. 119.
    Reitz, R. D., & Bracco, F. V. (1982). Mechanism of atomization of a liquid jet. Physics of Fluids, 25, 1730–1742.CrossRefMATHGoogle Scholar
  120. 120.
    Reitz, R. D., & Bracco, F. V. (2009). Mechanisms of breakup of round jets. In N. Cheremisnoff (Ed.), Encyclopedia of fluid mechanics (Vol. 3, pp. 012101). Houston: Gulf Publishing (Chapter 10).Google Scholar
  121. 121.
    Reitz, R. D., & Diwakar, R. (1986). Effect of drop breakup on fuel sprays. SAE report 860469.Google Scholar
  122. 122.
    Reitz, R. D., & Diwakar, R. (1987). Structure of high-pressure fuel sprays. SAE report 870598.Google Scholar
  123. 123.
    Rewse-Davis, Z., Nouri, J., Gavaises, M., & Arcoumanis, C. (2013). Near-nozzle instabilities in gasoline direct injection sprays. Proceedings of ILASS—Europe 2013, 25th European Conference on Liquid Atomization and Spray Systems, Chania, Greece, 1–4 September 2013, paper 141.Google Scholar
  124. 124.
    Rimbert, N. (2010). Simple model for turbulence intermittencies based on self-avoiding random vortex stretching. Physical Review E, 81, 056315.Google Scholar
  125. 125.
    Rimbert, N., Séro-Guillaume, O. (2004). Log-stable laws as asymptotic solutions to a fragmentation equation: Application to the distribution of droplets in a high Weber-number spray. Physical Review E, 69, 056316.Google Scholar
  126. 126.
    Roisman, I. V., Araneo, L., & Tropea, C. (2007). Effect of ambient pressure on penetration of a diesel spray. International Journal of Multiphase Flow, 33, 904–920.CrossRefGoogle Scholar
  127. 127.
    Rotondi, R., Bella, G., Grimaldi, C., & Postrioti, L. (2001). Atomization of high-pressure Diesel spray: experimental validation of a new breakup model. SAE report 2001–01-1070.Google Scholar
  128. 128.
    Rott, N., & Cantwell, B. (1993). Vortex drift. i: Dynamic interpretation. Physics of Fluids, A5, 1443–1450.CrossRefMathSciNetGoogle Scholar
  129. 129.
    Rott, N., & Cantwell, B. (1993). Vortex drift. ii: The flow potential surrounding a drifting vortical region. Physics of Fluids, A5, 1451–1455.CrossRefMathSciNetGoogle Scholar
  130. 130.
    Ruo, A. C., Chen, F., & Chang, M. H. (1992). Linear instability of compound jets with nonaxisymmetric disturbances. Physics of Fluids, 21, 681–689.Google Scholar
  131. 131.
    Saffman, P. G. (1970). The velocity of viscous vortex rings. Studies in Applied Mathematics, 49, 371–380.MATHGoogle Scholar
  132. 132.
    Saffman, P. G. (1992). Vortex dynamics. Cambridge: Cambridge University Press.Google Scholar
  133. 133.
    Sarimeseli, A., & Kelbaliev, G. (2004). Modelling of the break-up of deformable particles in developed turbulent flow. Chemical Engineering Science, 59, 1233–1240.CrossRefGoogle Scholar
  134. 134.
    Sakaguchi, D., Yamamoto, S., Ueki, H., & Ishdia, M. (2010). Study of heterogeneous structure in diesel fuel spray by using micro-probe L2F. Journal of Fluid Science and Technology, 5, 75–85.CrossRefGoogle Scholar
  135. 135.
    Savich, S. (2001). Spray dynamics and in-cylinder air motion. Ph.D. Thesis, The University of Brighton.Google Scholar
  136. 136.
    Sazhin, S. S., Feng, G., & Heikal, M. R. (2001). A model for fuel spray penetration. Fuel, 80(15), 2171–2180.CrossRefGoogle Scholar
  137. 137.
    Sazhin, S. S., Kaplanski, F., Feng, G., Heikal, M. R., & Bowen, P. J. (2001). A fuel spray induced vortex ring. Fuel, 80(13), 1871–1883.CrossRefGoogle Scholar
  138. 138.
    Sazhin, S. S., Crua, C., Kennaird, D., & Heikal, M. R. (2003). The initial stage of fuel spray penetration. Fuel, 82(8), 875–885.CrossRefGoogle Scholar
  139. 139.
    Sazhin, S. S., Crua, C., Hwang, J. -S., No, S. -Y., & Heikal, M. (2005). Models of fuel spray penetration. Proceedings of the Estonian Academy of Sciences: Engineering 11(2), 154–160.Google Scholar
  140. 140.
    Sazhin, S. S., Martynov, S. B., Kristyadi, T., Crua, C., & Heikal, M. R. (2008). Diesel fuel spray penetration, heating, evaporation and ignition: Modelling versus experimentation. International Journal of Engineering Systems Modelling and Simulation, 1, 1–19.Google Scholar
  141. 141.
    Sazhin, S. S., Kaplanski, F., Begg, S., & Heikal, M. (2009). Vortex ring-like structures in gasoline fuel sprays, Proceedings of the JUMV International Automotive Conference and Exhibition (XXII Science and Motor Vehicles 2009), Belgrade 14–16 April 2009, paper 31 (CD). Published by the Society of Automotive Engineers of Serbia.Google Scholar
  142. 142.
    Schugger, C., Meingast, U., & Renz, U. (2000). Time-resolved velocity measurements in the primary breakup zone of a high pressure diesel injection nozzle. Proceedings of ILASS-Europe, Darmstadt, Germany (2000).Google Scholar
  143. 143.
    Senecal, P. K., Schmidt, D. P., Nouar, I., Rutland, C. J., Reitz, R. D., & Corradini, M. L. (1999). Modeling high-speed viscous liquid sheet atomization. International Journal of Multiphase Flow, 25, 1073–1097.CrossRefMATHGoogle Scholar
  144. 144.
    Shariff, K., & Leonard, A. (1992). Vortex rings. Annual Review of Fluid Mechanics, 24, 235–279.CrossRefMathSciNetGoogle Scholar
  145. 145.
    Sher, I., & Sher, E. (2011). Analytical criterion for droplet breakup. Atomization and Sprays, 21, 1059–1063.CrossRefGoogle Scholar
  146. 146.
    Shinjo, J., & Umemura, A. (2004). Simulation of liquid jet primary breakup: Dynamics of ligament and droplet formation. International Journal of Multiphase Flow, 36, 513–532.CrossRefGoogle Scholar
  147. 147.
    Snegirev, A., Talalov, V., Sheinman, I., & Sazhin, S. S. (2011). An enhanced spray model for flame suppression simulations. Proceedings of the Fifth European Combustion Meeting ECM, Cardiff, 29th June to 1st July 2011 paper 072–1 (CD).Google Scholar
  148. 148.
    Som, S., & Aggarwal, S. K. (2009). Assessment of atomization models for diesel engine simulations. Atomization and Sprays, 19, 885–903.CrossRefGoogle Scholar
  149. 149.
    Som, S., & Aggarwal, S. K. (2010). Effects of primary breakup modeling on spray and combustion characteristics of compression ignition engines. Combustion and Flame, 157, 1179–1193.CrossRefGoogle Scholar
  150. 150.
    Som, S., Ramirez, A. I., Longman, D. E., & Aggarwal, S. K. (2011). Effect of nozzle orifice geometry on spray, combustion, and emission characteristics under diesel engine conditions. Fuel, 90, 1267–1276.CrossRefGoogle Scholar
  151. 151.
    Squire, H. B. (1933). On the stability for three-dimensional disturbances of viscous fluid flow between parallel walls. Proceedings of the Royal Society of London, 142, 621–628.CrossRefMATHGoogle Scholar
  152. 152.
    Srinivasan, V., Salazar, A. J., & Saito, K. (2008). Numerical investigation on the disintegration of round turbulent liquid jets using LES/VOF techniques. Atomization and Sprays, 18, 571–617.CrossRefGoogle Scholar
  153. 153.
    Stanaway, S., Cantwell, B. J., & Spalart, P. R. (1988). A numerical study of viscous vortex rings using a spectral method, NASA Technical Memorandum 101041.Google Scholar
  154. 154.
    Stapper, B. E., Sowa, W. A., & Samuelson, G. S. (1992). An experimental study of the effects of liquid properties on the breakup of a two-dimensional liquid sheet. ASME Journal of Engineering for Gas Turbines and Power, 114, 39–45.Google Scholar
  155. 155.
    Su, T. F., Patterson, M. A., Reitz, R. D., & Farrell, P. V. (1996). Experimental and numerical studies of high pressure multiple injection sprays. SAE report 960861.Google Scholar
  156. 156.
    Tanner, F. X. (2004). Development and validation of a cascade atomization and drop breakup model for high-velocity dense sprays. Atomization and Sprays, 14, 211–242.CrossRefGoogle Scholar
  157. 157.
    Turner, M. R., Healey, J. J., Sazhin, S. S., & Piazzesi, R. (2011). Stability analysis and break-up length calculations for steady planar liquid jets. Journal of Fluid Mechanics, 668, 384–411.CrossRefMATHMathSciNetGoogle Scholar
  158. 158.
    Turner, M. R., Healey, J. J., Sazhin, S. S., & Piazzesi, R. (2012). Wave packet analysis and break-up length calculations for accelerating planar liquid jets. Fluid Dynamics Research, 44(1), article number: 015503, DOI: 10.1088/0169-5983/44/1/015503.Google Scholar
  159. 159.
    Turner, M. R., Sazhin, S. S., Healey, J. J., Crua, C., & Martynov, S. B. (2012). A breakup model for transient diesel fuel sprays. Fuel, 97, 288–305.CrossRefGoogle Scholar
  160. 160.
    Uchiyama, M. (2009). Numericall simulation of non-evaporating spray jet by the vortex method. Atomization and Sprays, 19, 917–928.CrossRefGoogle Scholar
  161. 161.
    Versteeg, H. K., & Malalasekera, W. (2007). An introduction to computational fluid dynamics. The finite volume method (2\(^{\rm nd}\) ed.). Harlow: Pearson Prentice Hall.Google Scholar
  162. 162.
    Vogel, T., Rie\(\beta \), S., Lutz, M., Wenzing, M., & Leipertz, A. (2011). Comparison of current spray models under high pressure and high temperature engine relevant conditions. Proceedings of the 24th European Conference on Liquid Atomization and Spray Systems (ILASS)—Europe 2011, Estoril, Portugal, 5–7 September 2011.Google Scholar
  163. 163.
    Weigand, A., & Gharib, M. (1997). On the evolution of laminar vortex rings. Experiments in Fluids, 22, 447–457.CrossRefGoogle Scholar
  164. 164.
    Yang, H. Q. (1992). Asymmetric instability of a liquid jet. Physics of Fluids, A4, 681–689.CrossRefGoogle Scholar
  165. 165.
    Yi, Y., & Reitz, R. D. (2004). Modelling the primary breakup of high-speed jets. Atomization and Sprays, 14, 53–80.CrossRefGoogle Scholar
  166. 166.
    Zhao, H., Liu, H. -F., Cao, X, -K., Li, W. -F., & Xu, J. -L. (2011). Breakup characteristics of liquid drops in bag regime by a continuous and uniform air jet flow. International Journal of Multiphase Flow, 37, 530–534.Google Scholar
  167. 167.
    Zhang, K., Wang, Z., Wang, J., & Wang, Z. (2012). Spray model based on step response theory. Fuel, 95, 499–503.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag London 2014

Authors and Affiliations

  1. 1.School of Computing, Engineering and MathematicsUniversity of BrightonBrightonUK

Personalised recommendations