Development of Maximum Entropy Method for Prediction of Droplet-size Distribution in Primary Breakup Region of Spray
Droplet size distributions in the cold spray of a fuel
are important in observed combustion behavior. Specification of
droplet size and velocity distributions in the immediate downstream
of injectors is also essential as boundary conditions for advanced
computational fluid dynamics (CFD) and two-phase spray transport
calculations. This paper describes the development of a new model to
be incorporated into maximum entropy principle (MEP) formalism
for prediction of droplet size distribution in droplet formation region.
The MEP approach can predict the most likely droplet size and
velocity distributions under a set of constraints expressing the
available information related to the distribution.
In this article, by considering the mechanisms of turbulence
generation inside the nozzle and wave growth on jet surface, it is
attempted to provide a logical framework coupling the flow inside the
nozzle to the resulting atomization process. The purpose of this paper
is to describe the formulation of this new model and to incorporate it
into the maximum entropy principle (MEP) by coupling sub-models
together using source terms of momentum and energy. Comparison
between the model prediction and experimental data for a gas turbine
swirling nozzle and an annular spray indicate good agreement
between model and experiment.
[1] Jones WP, Sheen DH (1999) A Probability Density Function Method for
Modeling Liquid Fuel Sprays. Flow, Turbulence and Combustion 63:
379-394
[2] Fritsching U (2004) Spray Simulation. Cambridge University Press
[3] Babinsky E, Sojka PE (2002) Modeling Droplet Size Distributions.
Progress in Energy and Combustion Science 28: 303-329
[4] Lefebvre AH (1989) Atomization and Sprays. Hemisphere Publishing
[5] Sellens RW, Brzustowski TA (1985) A Prediction of Drop-Size
Distribution in a Spray from First Principles. Atomization and Spray
Technology 1: 89-102
[6] Li X, Tankin RS (1987) Derivation of Droplet Size Distribution in
Sprays by Using Information Theory. Combustion Science and
Technology 60: 345-357
[7] Sellens RW (1989) Prediction of the Drop Size and Velocity
Distribution in a Spray Based on the Maximum Entropy Formalism.
Particle and Particle Systems Characterization 6: 17-27
[8] Ahmadi M, Sellens RW (1993) A Simplified, Maximum Entropy Based
Drop Size Distribution. Atomization and Sprays 3: 291-310
[9] Dumouchel C (2006) A New Formulation of the Maximum Entropy
Formalism to Model Liquid Spray Drop-Size Distribution. Part. Part.
Syst. Charact. 23: 468-479
[10] Sirignano WA, Mehring C, Comments on Energy Conservation in
Liquid-Stream Disintegration, Proceedings of ICLASS, Pasadena,
California, USA, 2000
[11] Ibrahim AA, Jog MA (2008) Nonlinear instability of an annular liquid
sheet exposed to gas flow. International Journal of Multiphase Flow 34:
647-664
[12] Chu CC, Chou SF, Lin H, Liann YH (2007) Theoretical analysis of heat
and mass transfer in swirl atomizers. Heat Mass Transfer (2007)
43:1213-1224
[13] L. Rayleigh (1878) On the stability of jets. Proc Lond Math Soc 10: 4-
13
[14] Sirignano WA, Mehring C (2000) Review of theory of distortion and
disintegration of liquid streams. Prog. Energy Combustion Sci. 26: 609-
655
[15] Lin SP (1999) Breakup of liquid sheets and jets. Cambridge University
Press, 2003
[16] Kim WT, Mitra SK, Li X (2003) A Predictive Model for the Initial
Droplet Size and Velocity Distributions in Sprays and Comparison with
Experiments. Part. Part. Syst. Charact. 20: 135-149
[17] K.Y. Huh, E. Lee, J.Y. Koo, Diesel Spray Atomization Model
Considering Nozzle Exit Turbulence Conditions, Atomization and
Sprays. 1998,8, 453-469.
[18] Chu CC, Chou SF, Lin H, Liann YH (2008) An experimental
investigation of swirl atomizer sprays. Heat Mass Transfer 45, 11-22
[19] Ommi F, Nekofar K, Movahednejad E (2009) Designing and
Experimental Investigation of Characteristics of a Double-Base Swirl
Injector in a Liquid Rocket Propellant Engine. Journal of Applied
Sciences Research 5(8): 955-968
[20] Liao, Y., Jeng, S.M., Jog, M.A., Benjamin, M.A., 2001. Advanced submodel
for airblast atomizers. J. Prop. Power 17, 411-417.
[21] Movahednejad E, Ommi F, Hosseinalipour SM, Chen C, Mahdavi A
(2011) Application of maximum entropy method for droplet size
distribution prediction using instability analysis of liquid sheet. Heat and
Mass Transfer (2 June 2011), pp. 1-10.
[22] Dombrowski N, Johns WR (1963) The Aerodynamic Instability and
Disintegration of Vicious Liquid Sheets. Chem. Eng. Science 18: 203-
214
[23] Shen J, Li X (1996) Instability of an annular viscous liquid jet. Acta
Mech. 114: 167-183
[24] Bruce CA (1976) Dependence of ink jet dynamics on fluid
characteristics. IBM J. Res. Dev. 1: 258-270
[25] Movahednejad E, Ommi F, Hosseinalipour SM (2010) Prediction of
Droplet Size and Velocity Distribution in Droplet Formation Region of
Liquid Spray. Entropy 12, ISSN 1099-4300
[26] C. Dumouchel, The Maximum Entropy Formalism and the Prediction of
Liquid Spray Drop-Size Distribution. 2009, Entropy 11, 713-747
[27] Sallam KA, Dai Z, Faeth GM (2002) Liquid breakup at the surface of
turbulent round liquid jets in still gases. International Journal of
Multiphase Flow 28: 427-449
[28] J. Cousin, S.J. Yoon, C. Dumouchel, Coupling of classical linear theory
and maximum entropy formalism for prediction of drop size distribution
in sprays: application to pressure-swirl atomizers. Atomization and
Sprays. 1996, 6,
601-622.
[29] White FM (1991) Viscous fluid flow, second edition. McGrow-Hill
[30] Li, X.; Chin, L. P.; Tankin, R. S.; Jackson, T.; Stutrud, J.; Switzer, G.
Comparison between Experiments and Predictions Based on Maximum
Entropy for Sprays from a Pressure Atomizer. Combustion and Flame
1991, 86, 73-89.
[31] Mitra S K (2001) Breakup Process of plane liquid sheets and prediction
of initial droplet size and velocity distributions in sprays. PhD Thesis ,
University of Waterloo
[1] Jones WP, Sheen DH (1999) A Probability Density Function Method for
Modeling Liquid Fuel Sprays. Flow, Turbulence and Combustion 63:
379-394
[2] Fritsching U (2004) Spray Simulation. Cambridge University Press
[3] Babinsky E, Sojka PE (2002) Modeling Droplet Size Distributions.
Progress in Energy and Combustion Science 28: 303-329
[4] Lefebvre AH (1989) Atomization and Sprays. Hemisphere Publishing
[5] Sellens RW, Brzustowski TA (1985) A Prediction of Drop-Size
Distribution in a Spray from First Principles. Atomization and Spray
Technology 1: 89-102
[6] Li X, Tankin RS (1987) Derivation of Droplet Size Distribution in
Sprays by Using Information Theory. Combustion Science and
Technology 60: 345-357
[7] Sellens RW (1989) Prediction of the Drop Size and Velocity
Distribution in a Spray Based on the Maximum Entropy Formalism.
Particle and Particle Systems Characterization 6: 17-27
[8] Ahmadi M, Sellens RW (1993) A Simplified, Maximum Entropy Based
Drop Size Distribution. Atomization and Sprays 3: 291-310
[9] Dumouchel C (2006) A New Formulation of the Maximum Entropy
Formalism to Model Liquid Spray Drop-Size Distribution. Part. Part.
Syst. Charact. 23: 468-479
[10] Sirignano WA, Mehring C, Comments on Energy Conservation in
Liquid-Stream Disintegration, Proceedings of ICLASS, Pasadena,
California, USA, 2000
[11] Ibrahim AA, Jog MA (2008) Nonlinear instability of an annular liquid
sheet exposed to gas flow. International Journal of Multiphase Flow 34:
647-664
[12] Chu CC, Chou SF, Lin H, Liann YH (2007) Theoretical analysis of heat
and mass transfer in swirl atomizers. Heat Mass Transfer (2007)
43:1213-1224
[13] L. Rayleigh (1878) On the stability of jets. Proc Lond Math Soc 10: 4-
13
[14] Sirignano WA, Mehring C (2000) Review of theory of distortion and
disintegration of liquid streams. Prog. Energy Combustion Sci. 26: 609-
655
[15] Lin SP (1999) Breakup of liquid sheets and jets. Cambridge University
Press, 2003
[16] Kim WT, Mitra SK, Li X (2003) A Predictive Model for the Initial
Droplet Size and Velocity Distributions in Sprays and Comparison with
Experiments. Part. Part. Syst. Charact. 20: 135-149
[17] K.Y. Huh, E. Lee, J.Y. Koo, Diesel Spray Atomization Model
Considering Nozzle Exit Turbulence Conditions, Atomization and
Sprays. 1998,8, 453-469.
[18] Chu CC, Chou SF, Lin H, Liann YH (2008) An experimental
investigation of swirl atomizer sprays. Heat Mass Transfer 45, 11-22
[19] Ommi F, Nekofar K, Movahednejad E (2009) Designing and
Experimental Investigation of Characteristics of a Double-Base Swirl
Injector in a Liquid Rocket Propellant Engine. Journal of Applied
Sciences Research 5(8): 955-968
[20] Liao, Y., Jeng, S.M., Jog, M.A., Benjamin, M.A., 2001. Advanced submodel
for airblast atomizers. J. Prop. Power 17, 411-417.
[21] Movahednejad E, Ommi F, Hosseinalipour SM, Chen C, Mahdavi A
(2011) Application of maximum entropy method for droplet size
distribution prediction using instability analysis of liquid sheet. Heat and
Mass Transfer (2 June 2011), pp. 1-10.
[22] Dombrowski N, Johns WR (1963) The Aerodynamic Instability and
Disintegration of Vicious Liquid Sheets. Chem. Eng. Science 18: 203-
214
[23] Shen J, Li X (1996) Instability of an annular viscous liquid jet. Acta
Mech. 114: 167-183
[24] Bruce CA (1976) Dependence of ink jet dynamics on fluid
characteristics. IBM J. Res. Dev. 1: 258-270
[25] Movahednejad E, Ommi F, Hosseinalipour SM (2010) Prediction of
Droplet Size and Velocity Distribution in Droplet Formation Region of
Liquid Spray. Entropy 12, ISSN 1099-4300
[26] C. Dumouchel, The Maximum Entropy Formalism and the Prediction of
Liquid Spray Drop-Size Distribution. 2009, Entropy 11, 713-747
[27] Sallam KA, Dai Z, Faeth GM (2002) Liquid breakup at the surface of
turbulent round liquid jets in still gases. International Journal of
Multiphase Flow 28: 427-449
[28] J. Cousin, S.J. Yoon, C. Dumouchel, Coupling of classical linear theory
and maximum entropy formalism for prediction of drop size distribution
in sprays: application to pressure-swirl atomizers. Atomization and
Sprays. 1996, 6,
601-622.
[29] White FM (1991) Viscous fluid flow, second edition. McGrow-Hill
[30] Li, X.; Chin, L. P.; Tankin, R. S.; Jackson, T.; Stutrud, J.; Switzer, G.
Comparison between Experiments and Predictions Based on Maximum
Entropy for Sprays from a Pressure Atomizer. Combustion and Flame
1991, 86, 73-89.
[31] Mitra S K (2001) Breakup Process of plane liquid sheets and prediction
of initial droplet size and velocity distributions in sprays. PhD Thesis ,
University of Waterloo
@article{"International Journal of Chemical, Materials and Biomolecular Sciences:57803", author = "E. Movahednejad and F. Ommi", title = "Development of Maximum Entropy Method for Prediction of Droplet-size Distribution in Primary Breakup Region of Spray", abstract = "Droplet size distributions in the cold spray of a fuel
are important in observed combustion behavior. Specification of
droplet size and velocity distributions in the immediate downstream
of injectors is also essential as boundary conditions for advanced
computational fluid dynamics (CFD) and two-phase spray transport
calculations. This paper describes the development of a new model to
be incorporated into maximum entropy principle (MEP) formalism
for prediction of droplet size distribution in droplet formation region.
The MEP approach can predict the most likely droplet size and
velocity distributions under a set of constraints expressing the
available information related to the distribution.
In this article, by considering the mechanisms of turbulence
generation inside the nozzle and wave growth on jet surface, it is
attempted to provide a logical framework coupling the flow inside the
nozzle to the resulting atomization process. The purpose of this paper
is to describe the formulation of this new model and to incorporate it
into the maximum entropy principle (MEP) by coupling sub-models
together using source terms of momentum and energy. Comparison
between the model prediction and experimental data for a gas turbine
swirling nozzle and an annular spray indicate good agreement
between model and experiment.", keywords = "Droplet, instability, Size Distribution, Turbulence, Maximum Entropy", volume = "5", number = "11", pages = "1001-7", }
