Development of Maximum Entropy Method for Prediction of Droplet-size Distribution in Primary Breakup Region of Spray
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Development of Maximum Entropy Method for Prediction of Droplet-size Distribution in Primary Breakup Region of Spray

Authors: E. Movahednejad, F. Ommi


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

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[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