Prediction of Spray Droplet Size Distribution Based on Maximum Entropy
The spray process relies heavily on the droplet size distribution, which plays a crucial role in mass, momentum and energy transport. Currently, determining the droplet size distribution is a major scientific problem, which is represented by distribution functions classified into empirical and theoretical distribution methods. Empirical methods which derive droplet size distribution formulae from statistical analysis of experimental data lack practical physical significance and rely too heavily on empirical data. In contrast, theoretical approaches mainly use the maximum entropy approach, which originates from physical conservation laws but faces challenges in accurately predicting the droplet size distribution under complex conditions. To address these challenges, a maximum entropy model of droplet size distribution was proposed based on the maximum entropy principle, with an average diameter constraint condition used for constructing three and four-parameter maximum entropy models. The optimal model was selected based on the comparison of Akaike information criterion numbers, and the three-parameter maximum entropy model using the average diameter was found to be the best in predicting droplet number distribution. Air-blast nozzle atomization experimental data were used to optimize the proposed model, and the results showed that the correlation coefficient between predicted and experimental droplet number differential distribution values was above 0.96, with a mean square error lower than 0.135. Moreover, the three-parameter maximum entropy model accurately predicted the number and distribution of spray droplets. The proposed model was also tested against experimental data on atomized droplet size distribution from different nozzle types, yielding a good match with the experimental data. Finally, the selected model was applied to predict the particle size distribution of spray droplets from pressure nozzles manufactured by Pratt & Whitney Canada, demonstrating its accuracy in predicting the spray droplet size and quantity distribution despite the complexity of the working conditions. In conclusion, the research result can provide a significant contribution to accurately predicting droplet size distribution and quantity, and the proposed three-parameter maximum entropy model had great potential in improving spray droplet size and quantity distribution prediction accuracy.
Keywords: spray, droplet size distribution, mean diameter, maximum entropy
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WEI Yanju, ZHANG Xudong, DENG Shengcai, el al. Diffusion characteristics of diesel spray in swirl flows field [ J]. Transactions of the Chinese Society for Agricultural Machinery ,2019 ,50( 8) :394 -399. (in Chinese)
FAN Guiju, NIU Chengqiang, ZHANG Zhenming, et al. Design and experiment of V-shaped orchard anti-drift spray device with multi-airflow cooperation [J], Transactions of the Chinese Society for Agricultural Machinery, 2022 ,53(3 ) : 138 - 147. (in Chinese)
HU Yu, CHEN Xuyang, LIU Bin, et al. Optimized design and performance test of axial flow orchard sprayer air delivery system [J ]. Transactions of the Chinese Society for Agricultural Machinery ,2022 ,53(5) : 147 - 157. (in Chinese)
ZHOU Sanping, ZHANG Zhan. Study on effect of geometric size on ejector performance of air ejector [ J ]. Technology & Development of Chemical Industry,2020,49( 1 1 ) :68 —71. (in Chinese)
DU Zhe, HU Yongguang, QIU Shucheng, et al. Optimization design and experiment of air duct on spray cooling fan [ J ]. Transactions of the Chinese Society for Agricultural Machinery ,2020,51 ( 8 ) : 1 1 8 — 125,151. (in Chinese)
HAN Wenting, CAO Pei, LIU Wenshuai. Raindrop characteristics of sprinklers for artificial rainfall system [J ]. Transactions of the Chinese Society for Agricultural Machinery ,2014 ,45 ( 12) ;56 -61. ( in Chinese)
LI Hong, REN Zhiyuan, TANG Yue, et al. Measurement and amelioration of the test to raindrop size of sprinklers [J]. Transactions of the Chinese Society for Agricultural Machinery ,2005 ,36 ( 10) :50 -53. (in Chinese)
ZHANG Jun, MICHAEL W Reeks. Prediction of droplet size distribution for electrostatic spray[J]. Transactions of the CSAE, 2008,24( 12) :89 -92. (in Chinese)
NUKIYAMA S, TANASAWA Y. Experiments on the atomization of liquids in an air stream reports3: on the droplet-size distribution in an atomized jet[ J ]. Transactions of the Japan Society of Mechanical Engineers, 1939, 5: 62 -67.
ROSIN P, RAMMLER E. The laws governing the fineness of powdered coal [ J ]. Journal of the Institute of Fuel, 1933, 7; 29 -36.
BHATIA J C, DURST F. Comparative study of some probability distributions applied to liquid sprays[ J ]. Particle & Particle Systems Characterization, 1989, 6(1 -4); 151 -162.
XU T H, DURST F, TROPEA C. The three-parameter log-hyperbolic distribution and its application to particle sizing [J ]. Atomization and Sprays, 1993, 3(1): 109 - 124.
LIANG Zhao, FAN Guoqiang, WANG Guangming, et al. Distribution model of wind-stressed droplet deposition based on bimodal distribution [ J ]. Transactions of the Chinese Society for Agricultural Machinery ,2020,5 1 (4 ) :28 -37. (in Chinese)
LI Xianguo, TANKIN R. Droplet size distribution: a derivation of a Nukiyama — Tanssawa type distribution function [J ]. Combustion Science and Technology, 1987, 56: 65 -76.
SELLENS R W, BRZUSTOWSKI T A. A simplified prediction of droplet velocity distributions in a spray [j]. Combustion & Flame, 1986, 65(3) :273 -279.
SELLENS R W. Prediction of the drop size and velocity distribution in a spray based on the maximum entropy formalism [ J]. Particle and Particle System Characterization , 1989,6( 1 -4) ;17 -27.
CAO Jianming. On the theoretical prediction of fuel droplet size distribution in nonreactive diesel sprays [J ]. Journal of Fluids Engineering, 2002, 124( 1 ) ;182 — 185.
WANG Jie, YU Yonggang, LIU Kun. Simplified model on droplet size distribution in the spray field of HAN-based liquid propellant[J ]. Chinese Journal of Explosives & Propellants, 2016, 39(3) ;84 -88. (in Chinese)
SHANNON E C. A mathematical theory of communication [J ]. The Bell System Technical Journal, 1948, 27(4) : 379 -423.
RIZK N K, LEFEBVRE A H. Spray characteristics of spill-return atomizers [ J ]. Journal of Propulsion and Power, 1985,
ELKOTB M M. Fuel atomization for spray modelling [ J]. Progress in Energy & Combustion Science, 1982, 8(1) ;61 -91.
WOOTAE K, MITRA S K, LI Xianguo, et al. A predictive model for the initial droplet size and velocity distributions in sprays and comparison with experiments[ J ]. Particle & Particle Systems Characterization, 2003, 20(2) ; 135 - 149.
DUMOUCHEL C, BOYAVAL S. Use of the maximum entropy formalism to determine drop size distribution characteristics[ J]. Particle & Particle Systems Characterization, 1999, 16(4) ; 177 - 184.
FU F. Experimental characterization of sprays from an air-blast annular research nozzle[ D]. University of Waterloo,2003.
MITRA S K, Breakup process of plane liquid sheets and prediction of initial droplet size and velocity distributions in sprays [D]. University of Waterloo, 2001.
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