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Modelling of the heating and evaporation of fuel droplets

By Tarsisius Kristyadi


The results of a comparative analysis of liquid and gas phase models for fuel droplets heating and evaporation, suitable for implementation into computational fluid dynamics (CFD) codes, are presented. Among liquid phase models, the analysis is focused on the model based on the assumption that the liquid thermal conductivity is infinitely large, and the so called effective thermal conductivity model. Seven gas phase models are compared. These are six semi-theoretical models, based on various assumptions, and a model based solely on the approximation to experimental data. It is pointed out that the gas phase model, taking into account the finite thickness of the thermal boundary layer around the droplet, predicts the evaporation time closest to the one based on the approximation to experimental data. \ud The values of the absorption coefficients of gasoline fuel (BP Pump Grade 95 RON ULG), 2,2,4-trimethylpentane (CH3)2CHCH2C(CH3)3 (iso-octane) and 3-pentanone CH3CH2COCH2(CH3)3 have been measured experimentally in the range of wavelengths between 0.2 μm and 4 μm. The values of the average absorption efficiency factor for all fuels have been approximated by a power function aRdb, where Rd is the droplet radius. a and b in turn have been approximated by piecewise quadratic functions of the radiation temperature, with the coefficients calculated separately in the ranges 2 - 5 μm, 5 - 50 μm, 50 - 100 μm and 100 - 200 μm for all fuels. This new approximation is shown to be more accurate compared with the case when a and b are approximated by quadratic functions or fourth power polynomials of the radiation temperature, with the coefficients calculated in the full range of 2 - 200 μm. \ud Results of experimental studies of heating and evaporation of monodisperse ethanol and acetone droplets in two regimes are compared with the results of modelling. It is pointed out that for relatively small droplets the experimentally measured droplet temperatures are close to the predicted average droplet temperatures, while for larger droplets the experimentally measured droplet temperatures are close to the temperatures predicted at the centre of droplets.\ud All the developed models have been implemented into the KIVA-2 CFD code and validated against available in-house experimental data referring to spray penetration and ignition delay in Diesel engines

Topics: H330 Automotive Engineering
Year: 2007
OAI identifier:

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  1. (1967). 9.800 244.0 Tetradecane Paredes et al. (2000) 6.55 454.38 n-heptane Hirschfelder
  2. (2000). A completely analytical equation of state for mixture of square-well chain fluid of variable well width, doi
  3. (1999). A finite conductivity model for diesel spray evaporation and computations, doi
  4. (1981). A Multidimensional Data Set for Diesel Combustion Model Validation: I. Initial Conditions, Pressure History and Spray Shapes, SAE doi
  5. (2000). A numerical Study of The Transient Heat Transfer from a Sphere at High Reynolds and Peclet Numbers, doi
  6. (1991). A phenomenological Model of Diesel Spray Atomization,
  7. (1998). A review of spray ignition phenomena: present status and future research, doi
  8. A Simplified Non-isothermal Model for Droplet Heating and Evaporation, doi
  9. (2002). A Spectral Model of Absorption and Scattering of Thermal radiation by diesel fuel droplets, doi
  10. (2001). A Study of The Formation and Break Up of a Diesel Spray for HSDI Diesel engine Combustion System,
  11. (1954). A Theoretical Investigation of The Heating-up Period of Injected Fuel Droplets Vaporizing in Air,
  12. (2004). Absorption of External Thermal Radiation in Asymmetrically Illuminated Droplets, doi
  13. Absorption of Thermal Radiation in a Semi-transparent Spherical Droplet: a Simplified Model, doi
  14. (2003). An Investigation of Simple Evaporation Models Used in Spray Simulations, doi
  15. (2005). Approaches to Numerical Modelling of Droplet Transient Heating and Evaporation, doi
  16. (2007). Approximate Analysis of Thermal Radiation Absorption in Fuel Droplets, doi
  17. (1989). Atomization and Sprays, doi
  18. (1993). Axisymmetric calculations of three droplet interactions, doi
  19. (1982). Burning Times of Linear Fuel Droplet Arrays: A comparison of Experiment and Theory, Combustion and Flame 45, 15 Sangiovanni J.J., doi
  20. (1980). Calculation of the Burning Rate of Interacting Fuel Droplets, doi
  21. (1985). Chemical Aspects of The Autoignition of Hydrocarbon Air Mixture, doi
  22. (1998). Chemiluminescence Imaging of Autoignition in a Diesel Engine, doi
  23. (2002). Combustion Processes in a Diesel Engine, Ph.D Thesis,
  24. (1972). Comparison of the Various Correlation for Spray Penetration, doi
  25. (1971). Concentration Fluctuations in a Round Turbulent Free Jet, doi
  26. (1950). Data Book on Hydrocarbons: Application to Process Engineering,
  27. (2006). Development in Diesel Spray Characterisation and Modelling, In:
  28. (2005). Development of a Heat Transfer Dimensionless Correlation for Sphere Immersed in a Wide Range Prandtl Number Fluids, doi
  29. (1984). Development of Phase dopller Spray Analyser for Liquid Drop Size and velocity characterisations, doi
  30. (2007). Diesel Fuel Spray Penetration, Heating, Evaporation and Ignition: Modelling Versus Experimentation, Int. Journal of Engineering Modelling and Simulation (submitted) Refereed international conferences proceeding Sazhin doi
  31. (1989). Droplet vaporization model for spray combustion calculation, doi
  32. (2005). Droplet Vaporization Model in The Presence of Thermal Radiation, doi
  33. (2000). Dynamics of Droplets, Springer-Verlag Berlin and Heidelberg GmbH Fuchs N.A.
  34. (1997). Effect of Fuel Injection Processes on the Structure of Diesel Spray, doi
  35. (1984). Effect of Multiple Particle Interactions on Burning Droplets, Combustion and Flame 57, doi
  36. (2002). Energetic Budget on an Evaporating Monodisperse Droplet Stream Using Combined Optical Methods. Evaluation of The Convective Heat Transfer, doi
  37. (2001). Evaluation of commonly used assumptions for isolated and cluster heptane drops in nitrogen at all pressures, doi
  38. (2001). Evaporating and Combusting Droplet Temperature Measurements using Two Color Laser Induced Fluorescence, doi
  39. (1990). Excess Volumes and Viscosities of Binary Systems Containing 4-methyl 3 pentanone doi
  40. (1997). Excess volumes of cyclohexane with 2-propanone, 2-butanone, 3-pentanone, 4-methyl-2-pentanone, 1-propanol, and 2-propanol and ethanoic acid + 1-propanol systems, doi
  41. (1983). Experimental Study of Droplet Evaporation in a High Temperature Air Stream, doi
  42. (1996). Experimental Study on High Pressure Droplet Evaporation Using Microgravity Conditions, doi
  43. (1999). Fluid Dynamics and Transport of Droplets and Sprays, doi
  44. (1980). Fuel Spray Characterization in Diesel Engine, Combustion Modelling in Reciprocating Engine, doi
  45. (1984). Handbook of Aviation Fuel Properties
  46. (1976). Handbook of Thermodynamic Tables and Charts,
  47. (2005). Heat and mass transfer of combusting monodisperse droplets in a linear stream, doi
  48. (2004). Heat Transfer 126, 105-109; Erratum 126, 490-491 Sazhin doi
  49. (2002). Heat Transfer, McGraw-Hill, London Hoyt C.H., Adel F.S.
  50. (2001). Heating and Evaporation of Semi Transparent Diesel Fuel Droplets in Presence of Thermal Radiation, doi
  51. (1996). Incompressible Flow, doi
  52. (1988). Induction Swirl in a Multiple Intake Valve Engine Three Dimensional numerical analysis, Proceeding of the Institution of Mechanical Engineers.
  53. (1993). Interacting, convecting, vaporizing fuel droplets with variable properties, doi
  54. (1979). Interaction of Two Burning Fuel Droplet of Arbitrary Size, doi
  55. (1988). Internal Combustion Engine Fundamentals, doi
  56. (1989). KIVA II: A Computer Program for Chemically Reactive Flows with Sprays, doi
  57. (1993). KIVA-3: A KIVA Program with Block-Structured Mesh for Complex Geometries, doi
  58. (1997). KIVA-3V: A Block-Structured KIVA program for Engines with Vertical or Canted Valves, doi
  59. (1996). Laser Diagnostics for Combustion Temperature and Species, Second Edition, Gordon and Breach, doi
  60. (1993). Modelling of Spray Droplet Deformation and Break-up,
  61. (1998). Modelling the Effects of Fuel Spray Characteristic on doi
  62. (2007). Models for Droplet Heating and Evaporation: Application to the Autoignition Process in Diesel Engines, doi
  63. (2006). Models for Droplet Transient Heating: Effects on Droplet Evaporation, Ignition, and Breakup, doi
  64. (1967). Molecular theory of gases and liquids, 4th Edition, doi
  65. (1985). Multidimensional Modelling of Knocking Combustion doi
  66. (1980). Numerical Heat Transfer and Fluid Flow, doi
  67. (1986). Numerical Simulation of Diesel Autoignition, doi
  68. (1998). Optical Diagnostics For in Cylinder Mixture Formation measurement in doi
  69. (1977). Overlapping effects and motional narrowing in molecular band shapes doi
  70. (2006). Papers published by the author International refereed journals Sazhin doi
  71. (2003). PDA Characterisation of Dense Spray Using a Common-rail Injection System, doi
  72. (1988). Physical Mechanism for Atomization of a Jet Spray: A Comparison of Models and Experiments, doi
  73. (1988). Principles of Heat Transfer, doi
  74. (1976). Problems of Laser Velocimeter Application to Combustion System and Combustion Measurement,
  75. (2004). Radiative Heating of Semi-transparent Diesel Fuel Droplets, doi
  76. (1992). Single droplet evaporation rate: experimental and numerical investigations, in:
  77. (2005). Spectrometric Identification of Organic Compounds, doi
  78. (2006). Temperature measurements of binary droplets using three color laser-induced fluorescence, doi
  79. (1985). The Internal Combustion Engine in The Theory and Practice, doi
  80. (1981). The Kinetics and Themochemistry of Chemical Oxidation with Application to Combustion and Flames, Prog. doi
  81. (1999). The Lewis number under supercritical conditions, doi
  82. (1996). The P-1 Model for Thermal Radiation Transfer: Advantages and Limitations, doi
  83. (1985). The role of the heat-up period in fuel drop evaporation, doi
  84. (1999). The Shell Autoignition Model: A New Mathematical Formulation, doi
  85. (1999). The Shell Autoignition Model: Applications to Gasoline and Diesel Fuels, doi
  86. (2001). Thermal Ignition Analysis of a Monodisperse Spray with Radiation. doi
  87. (2000). Thermal Radiation from Nonisothermal Spherical Particles a Semitransparent Material, doi
  88. (1978). Transient Heating and Liquid Phase Mass Diffusion doi
  89. (1995). Two Stage Ignition of n-Heptane Isolated Droplets, doi
  90. (2000). Unsteady vaporization and ignition of a threedimensional droplet array, doi
  91. (1977). Vapour heat capacities and heat of vaporization of ethyl ketone, ethyl propyl ketone, methyl isopropyl kethone and methyl phenyl ether, doi

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