Abstract
An existing droplets size distribution function, which was established based on the maximum entropy principle, momentum conservation law and energy conservation law, was used to predict the characteristics of spray field of a swirl injector with small geometry characteristics constant. The experimental system for spray characteristics was built, and an experimental study on the spray characteristics of swirl injectors with different geometries was conducted with phase Doppler particle analyzer (PDPA). It shows a coincidence between the experimental results and the spray characteristics predicted with the maximum entropy principle. The maximum entropy method can be a useful tool for the design of this type of injector.
Similar content being viewed by others
References
Ayres D, Caldas M, Semiao V, da Graca Carvalho M (2001) Prediction of the droplet size and velocity joint distribution for sprays. Fuel 80:383–394
Babinsky E, Sojka PE (2002) Modeling droplet size distributions. Prog Energy Combust Sci 28:303–329
Chu CC, Chou SF, Lin HI, Liann YH (2008) An experimental investigation of swirl atomizer sprays. Heat Mass Transf 45:11–22
Cousin J, Yoon SJ, Dumouchel C (1996) Coupling of classical linear theory and maximum entropy formalism for prediction of drop size distribution in sprays: application to pressure-swirl atomizers. At Sprays 6:601–622
Fan WH, Ling ZY, Fu QF, Yang J (2011) Numerical simulation of minor geometry characteristics and small orifice water mist swirl injector. J Beijing Univ Aeronaut Astronaut 37:538–544 (in Chinese)
Fu QF, Yang LJ, Qu YY, Gu B (2010) Linear stability analysis of a conical liquid sheet. J Propuls Power 26:955–968
Fu QF, Yang LJ, Zhang W, Cui KD (2012) Spray characteristics of an open-end swirl injector. At Sprays 22:431–445
Kim WT, Mitra SK, Li X, Prociw LA, Hu TCJ (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
Kim S, Khil T, Kim D, Yoon Y (2009) Effect of geometric parameters on the liquid film thickness and air core formation in a swirl injector. Meas Sci Technol 20:015403
Li X, Chin LP, Tankin RS, Jackson T, Stutrud J, Switzer G (1991) Comparison between experiments and predictions based on maximum entropy for spray from a pressure atomizer. Combust Flame 86:73–89
Li T, Nishida K, Hiroyasu H (2011) Droplet size distribution and evaporation characteristics of fuel spray by a swirl type atomizer. Fuel 90:2367–2376
Liu J, Zhang XQ, Li QL, Wang ZG (2013) Effect of geometric parameters on the spray cone angle in the pressure swirl injector. J Aerosp Eng 227:342–353
Mani M, Dadkhah M (2002) The measurement of oxidant/fuel ratio in injector plate of liquid propellant rocket engine before combustion, with an experimental method and its comparison with a theoretical method. Iran J Sci Technol 26:507–514
Mitra SK, Li X (1999) A predictive model for droplet size distribution in sprays. At Sprays 9:29–50
Mizutani Y, Fuchihata M, Takada H (2001) Effects of velocity, turbulence and wall collision on the ignition of fuel sprays injected across a high-temperature air stream. Iran J Sci Technol 25:221–230
Moghiman M, Maneshkarimi MR (2001) On the dependence of spray evaporation and combustion on atomization techniques. Iran J Sci Technol 25:241–252
Mondal D, Datta A, Sarkar A (2003) Prediction of drop size distribution in a spray from a pressure swirl atomizer using maximum entropy formalism. J Mech Eng Sci 217:831–838
Moon S, Abo-Serie E, Bae C (2008) The spray characteristics of a pressure-swirl injector with various exit plane tilts. Int J Multiph Flow 34:615–627
Movahednejad E, Ommi F, Hosseinalipour SM, Chen CP, Mahdavi SA (2011) Application of maximum entropy method for droplet size distribution prediction using instability analysis of liquid sheet. Heat Mass Transfer 47:1591–1600
Nath S, Datta A, Nukhopadhyay A, Sen S, Tharakan TJ (2011) Prediction of size and velocity distributions in sprays formed by the breakup of planar liquid sheets using maximum entropy formalism. At Sprays 21:483–501
Park H, Heister SD (2006) Nonlinear simulation of free surfaces and atomization in pressure swirl atomizers. Phys Fluids 18:052103
Rizk NK, Lefebvre AH (1985) Internal flow characteristics of simplex swirl atomizers. J Propuls Power 1:193–199
Santangelo PE (2012) Experiments and modeling of discharge characteristics in water-mist sprays generated by pressure-swirl atomizers. J Therm Sci 21:539–548
Sellens RW, Brzustowski TA (1986) A simplified prediction of droplet velocity distribution in a spray. Combust Flame 65:273–279
Siamas GA, Jiang X, Wrobel LC (2009) Numerical investigation of a perturbed swirling annular two-phase jet. Int J Multiph Flow 30:481–493
Wang XF, Lefebvre AH (1987) Mean drop sizes from pressure swirl nozzles. J Propuls Power 3:11–18
Yang LJ, Ge MH, Zhang MZ, Fu QF, Cai GB (2008) Spray characteristics of a recessed gas-liquid coaxial swirl injector. J Propuls Power 24:1332–1339
Yang LJ, Fu QF, Qu YY, Zhang W, Du ML, Xu BR (2012) Spray characteristics of gelled propellants in swirl injectors. Fuel 97:253–261
Acknowledgements
The financial support of China National Nature Science Funds (Support Number: 11302013) is gratefully acknowledged.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Fu, Qf., Wang, Jj. & Yang, Lj. Application of Maximum Entropy Principle to Predict Droplet Size Distribution for Swirl Injectors. Iran J Sci Technol Trans Mech Eng 41, 305–313 (2017). https://doi.org/10.1007/s40997-016-0065-x
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s40997-016-0065-x