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Application of Maximum Entropy Principle to Predict Droplet Size Distribution for Swirl Injectors

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Iranian Journal of Science and Technology, Transactions of Mechanical Engineering Aims and scope Submit manuscript

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.

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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

    Article  Google Scholar 

  • Babinsky E, Sojka PE (2002) Modeling droplet size distributions. Prog Energy Combust Sci 28:303–329

    Article  Google Scholar 

  • Chu CC, Chou SF, Lin HI, Liann YH (2008) An experimental investigation of swirl atomizer sprays. Heat Mass Transf 45:11–22

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • 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)

    Google Scholar 

  • Fu QF, Yang LJ, Qu YY, Gu B (2010) Linear stability analysis of a conical liquid sheet. J Propuls Power 26:955–968

    Article  Google Scholar 

  • Fu QF, Yang LJ, Zhang W, Cui KD (2012) Spray characteristics of an open-end swirl injector. At Sprays 22:431–445

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Google Scholar 

  • 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

    Google Scholar 

  • Mitra SK, Li X (1999) A predictive model for droplet size distribution in sprays. At Sprays 9:29–50

    Article  Google Scholar 

  • 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

    Google Scholar 

  • Moghiman M, Maneshkarimi MR (2001) On the dependence of spray evaporation and combustion on atomization techniques. Iran J Sci Technol 25:241–252

    Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • Park H, Heister SD (2006) Nonlinear simulation of free surfaces and atomization in pressure swirl atomizers. Phys Fluids 18:052103

    Article  Google Scholar 

  • Rizk NK, Lefebvre AH (1985) Internal flow characteristics of simplex swirl atomizers. J Propuls Power 1:193–199

    Article  Google Scholar 

  • Santangelo PE (2012) Experiments and modeling of discharge characteristics in water-mist sprays generated by pressure-swirl atomizers. J Therm Sci 21:539–548

    Article  Google Scholar 

  • Sellens RW, Brzustowski TA (1986) A simplified prediction of droplet velocity distribution in a spray. Combust Flame 65:273–279

    Article  Google Scholar 

  • Siamas GA, Jiang X, Wrobel LC (2009) Numerical investigation of a perturbed swirling annular two-phase jet. Int J Multiph Flow 30:481–493

    Google Scholar 

  • Wang XF, Lefebvre AH (1987) Mean drop sizes from pressure swirl nozzles. J Propuls Power 3:11–18

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

Download references

Acknowledgements

The financial support of China National Nature Science Funds (Support Number: 11302013) is gratefully acknowledged.

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Correspondence to Li-jun Yang.

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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

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  • DOI: https://doi.org/10.1007/s40997-016-0065-x

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