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Spray Interface Drag Modeling Based on the Power-Law Droplet Velocity Using the Moment Theory

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Abstract

Interphase momentum exchange of a polydispersed two-phase flow is numerically studied by using a model based on interfacial drag effects of a bulk liquid, ligaments, and droplets entrained in the air flow. A power-law relation is proposed between the droplet velocity and its diameter. The dispersed phase is modeled using the methodology of spray moments of the drop size distribution. All the equations are solved in a Eulerian framework using the finite volume approach, and the phases are coupled with the source terms. The proposed dependence accurately simulates the droplet behavior because droplets with larger diameters experience a higher drag and generally have higher velocities than smaller droplets. The model shows reasonable agreement with experimental and numerical data on the spray tip penetration and Sauter mean radius.

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References

  1. J. Beck and A. Watkins, “On the Development of a Spray Model Based on Drop-Size Moments,” Proc. Roy. Soc. London, Ser. A: Math. Phys. Eng. Sci. 459, 1365–1394 (2003).

    Article  ADS  MathSciNet  Google Scholar 

  2. P. Moin and S. V. Apte, “Large-Eddy Simulation of Realistic Gas Turbine Combustors,” AIAA J. 44 (4), 698–708 (2006).

    Article  ADS  Google Scholar 

  3. B. Mohan, W. Yang, K. L. Tay, and W. Yu, “Macroscopic Spray Characterization under High Ambient Density Conditions,” Exp. Therm. Fluid Sci. 59, 109–117 (2014).

    Article  Google Scholar 

  4. V. K. Champagne, D. J. Helfritch, S. P. G. Dinavahi, and P. F. Leyman, “Theoretical and Experimental Particle Velocity in Cold Spray,” J. Therm. Spray Technol. 20 (3), 425–431 (2011).

    Article  ADS  Google Scholar 

  5. M. Karimi, A. Fartai, G. Rankin, et al., “Numerical Simulation of the Cold Gas Dynamic Spray Process,” J. Therm. Spray Technol. 15 (4), 518–523 (2006).

    Article  ADS  Google Scholar 

  6. H. Katanoda, M. Fukuhara, and N. Iino, “Numerical Study of Combination Parameters for Particle Impact Velocity and Temperature in Cold Spray,” J. Therm. Spray Technol. 16 (5/6), 627–633 (2007).

    Article  ADS  Google Scholar 

  7. B. Samareh, O. Stiek, V. Lüthen, and A. Dolatabadi, “Assessment of CFD Modeling via Flow Visualization in Cold Spray Process,” J. Therm. Spray Technol. 18 (5/6), 934–943 (2009).

    Article  ADS  Google Scholar 

  8. F. Payri, R. Payri, M. Bardi, and M. Garreres, “Engine Combustion Network: Influence of the Gas Properties on the Spray Penetration and Spreading Angle,” Experiment. Therm. Fluid Sci. 53, 236–243 (2014).

    Article  Google Scholar 

  9. A. Amoresano, C. Allouis, M. Di Santo, P. Fodice, et al., “Experimental Characterization of a Press Pure Swirl Spray by Analyzing the Half Cone Angle Fluctuation,” Experiment. Therm. Fluid Sci. 94, 122–133 (2018).

    Article  Google Scholar 

  10. F. Li, J. Li, F. Song, et al., “MP-PIC Simulation of CFB Riser with EMMS-Based Drag Model,” Chem. Eng. Sci. 82, 104–113 (2012).

    Article  Google Scholar 

  11. P. Porombka and T. Höhne, “Drag and Turbulence Modelling for Free Surface Flows within the Two-Fluid Euler-Euler Framework,” Chem. Eng. Sci. 134, 348–359 (2015).

    Article  Google Scholar 

  12. F. Cello, A. Di Renzo, and F. P. Di Maio, “A Semi-Empirical Model for the Drag Force and Fluid-Particle Interaction in Polydisperse Suspensions,” Chem. Eng. Sci. 65 (10), 3128–3139 (2010).

    Article  Google Scholar 

  13. S. Lacour, F. Raoult, C. Tinet, L. Fournaison, et al., “A Modal Analysis of the Size Distribution for an Hollow-Cone Spray in Cross-Flow,” Exp. Therm. Fluid Sci. 104, 164–174 (2019).

    Article  Google Scholar 

  14. F. Li, V. Fu, B. Yi, et al., “Comparison of Macroscopic Spray Characteristics between Biodiesel-Pentanol Blends and Diesel,” Exp. Therm. Fluid Sci. 98, 523–533 (2018).

    Article  Google Scholar 

  15. A. Gosman and E. Loannides, “Aspects of Computer Simulation of Liquid-Fueled Combustors,” J. Energy 7 (6), 482–490 (1983).

    Article  ADS  Google Scholar 

  16. G. B. Wallis and S. Makkenchery, “The Hanging Film Phenomenon in Vertical Annular Two-Phase Flow,” J. Fluids Eng. 96 (3), 297–298 (1974).

    Article  Google Scholar 

  17. H. Hiroyasu and T. Kadota, “Fuel Droplet Size Distribution in Diesel Combustion Chamber,” Bull. JSME 19, 1064–1072 (1976).

    Article  Google Scholar 

  18. S. Sazhin, G. Feng, and M. Heikal, “A Model for Fuel Spray Penetration,” Fuel 80, 2171–2180 (2001).

    Article  Google Scholar 

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Correspondence to A. A. Majhool.

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Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 61, No. 1, pp. 71–81, January–February, 2020.

Original Russian Text © A.A. Majhool, N.H. Hamza, N.M. Jasim.

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Majhool, A.A., Hamza, N.H. & Jasim, N.M. Spray Interface Drag Modeling Based on the Power-Law Droplet Velocity Using the Moment Theory. J Appl Mech Tech Phy 61, 61–69 (2020). https://doi.org/10.1134/S0021894420010071

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  • DOI: https://doi.org/10.1134/S0021894420010071

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