Hostname: page-component-cd9895bd7-q99xh Total loading time: 0 Render date: 2024-12-28T21:40:49.108Z Has data issue: false hasContentIssue false
  • English
  • Français

Evaporation and breakup effects in the shock-driven multiphase instability

Published online by Cambridge University Press:  03 December 2020

Vasco Duke-Walker ,
W. Curtis Maxon ,
Sahir R. Almuhna  and
Jacob A. McFarland Open the ORCID record for Jacob A. McFarland [Opens in a new window]
Vasco Duke-Walker
Affiliation:
Department of Mechanical Engineering, Texas A&M University, College Station, TX77843, USA
W. Curtis Maxon
Affiliation:
Department of Mechanical and Aerospace Engineering, University of Missouri, Columbia, MO65211, USA
Sahir R. Almuhna
Affiliation:
Department of Mechanical and Aerospace Engineering, University of Missouri, Columbia, MO65211, USA
Jacob A. McFarland*
Affiliation:
Department of Mechanical Engineering, Texas A&M University, College Station, TX77843, USA
*
†Email address for correspondence: mcfarlandja@tamu.edu
Get access Rights & Permissions [Opens in a new window]

Abstract

Evaporation and breakup of liquid droplets are common in many applications of the shock-driven multiphase instability (SDMI), such as in liquid-fuelled detonation engines, multiphase ejector pumps and turbines and explosive dispersal of liquid particles (i.e. chemical or biological agents). In this paper, the effects of evaporation and breakup of droplets on the mixing induced by the SDMI are considered through simulations and compared with experimental results. The evaporation model is validated against previous experimental data. The capabilities of the simulations and particle models are then demonstrated through a qualitative comparison with experimental results where breakup effects are negligible (i.e. small droplets). The simulation results are explored further to quantify the effects of evaporation (i.e. mixing enhancement) in the SDMI, providing further insight into the experimental results. A new breakup model, derived from previous works, is then presented for low Reynolds number (below 500), low Weber number (below 100) droplets in a shock-driven multiphase instability. The breakup model capabilities are then demonstrated through a comparison with experimental results where breakup effects are significant (larger droplet sizes). Finally, the simulation results are used to highlight the importance of breakup parameters on the evaporation rate and large-scale mixing in the SDMI. Overall, it is shown that evaporation is enhanced by the large-scale hydrodynamics instability, the SDMI, and that breakup of the droplets significantly increases the strength of the instability, and rate of droplet evaporation.

JFM classification

Drops and Bubbles: Breakup/coalescence Multiphase and Particle-laden Flows: Multiphase flow Multiphase and Particle-laden Flows: Particle/fluid flow
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 908 , 10 February 2021 , A13
Check for updates
Copyright
© The Author(s), 2020. Published by Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Abramzon, B. & Sirignano, W. A. 1989 Droplet vaporization model for spray combustion calculations. Intl J. Heat Mass Transfer 32 (9), 1605–1618.CrossRefGoogle Scholar
Aggarwal, S. K. & Mongia, H. C. 2002 Multicomponent and high-pressure effects on droplet vaporization. Trans. ASME: J. Engng Gas Turbines Power 124 (2), 248–255.Google Scholar
Aggarwal, S. K. & Peng, F. 1995 A review of droplet dynamics and vaporization modeling for engineering calculations. Trans. ASME: J. Engng Gas Turbines Power 117 (3), 453–461.Google Scholar
Andrews, M. J. & O'Rourke, P. J. 1996 The multiphase particle-in-cell (mp-pic) method for dense particulate flows. Intl J. Multiphase Flow 22 (2), 379–402.CrossRefGoogle Scholar
Black, W. J., Denissen, N. A. & McFarland, J. A. 2017 Evaporation effects in shock-driven multiphase instabilities. Trans. ASME: J. Fluids Engng 139 (7), 071204.Google Scholar
Cheatham, S. & Kailasanath, K. 2005 Numerical modelling of liquid-fuelled detonations in tubes. Combust. Theor. Model. 9 (1), 23–48.CrossRefGoogle Scholar
Chou, W. H. & Faeth, G. M. 1998 Temporal properties of secondary drop breakup in the bag breakup regime. Intl J. Multiphase Flow 24 (6), 889–912.CrossRefGoogle Scholar
Crowe, C. T., Schwarzkopf, J. D., Sommerfeld, M. & Tsuji, Y. 2011 Multiphase Flows with Droplets and Particles. CRC Press.CrossRefGoogle Scholar
Dahal, J. & McFarland, J. A. 2017 A numerical method for shock driven multiphase flow with evaporating particles. J. Comput. Phys. 344, 210–233.CrossRefGoogle Scholar
Dai, Z. & Faeth, G. M. 2001 Temporal properties of secondary drop breakup in the multimode breakup regime. Intl J. Multiphase Flow 27 (2), 217–236.CrossRefGoogle Scholar
Feng, M., Li, F., Wang, W. & Li, J. 2018 Parametric study for mp-pic simulation of bubbling fluidized beds with geldart a particles. Powder Technol. 328, 215–226.CrossRefGoogle Scholar
Flash Center for Computational Science University of Chicago 2016 ASC FLASH 2016 Flash user's guide–version 4.4. Chicago: University of Chicago.Google Scholar
Fryxell, B., Olson, K., Ricker, P., Timmes, F. X., Zingale, M., Lamb, D. Q., MacNeice, P., Rosner, R., Truran, J. W. & Tufo, H. 2000 Flash: an adaptive mesh hydrodynamics code for modeling astrophysical thermonuclear flashes. Astrophys. J. Suppl. 131 (1), 273–334.Google Scholar
Godsave, G. A. E. 1953 Studies of the combustion of drops in a fuel spray–the burning of single drops of fuel. In Symposium (International) on Combustion, vol. 4, pp. 818–830.Google Scholar
Goossens, H. W. J., Cleijne, J. W., Smolders, H. J. & van Dongen, M. E. H. 1988 Shock wave induced evaporation of water droplets in a gas-droplet mixture. Exp. Fluids 6 (8), 561–568.CrossRefGoogle Scholar
Guildenbecher, D. R., López-Rivera, C. & Sojka, P. E. 2009 Secondary atomization. Exp. Fluids 46 (3), 371–402.CrossRefGoogle Scholar
Hanson, T. C., Davidson, D. F. & Hanson, R. K. 2007 Shock-induced behavior in micron-sized water aerosols. Phys. Fluids 19 (5), 056104.CrossRefGoogle Scholar
Hsiang, L.-P. & Faeth, G. M. 1992 Near-limit drop deformation and secondary breakup. Intl J. Multiphase Flow 18 (5), 635–652.CrossRefGoogle Scholar
Kailasanath, K. 2006 Liquid-fueled detonations in tubes. J. Propul. Power 22 (6), 1261–1268.CrossRefGoogle Scholar
Liu, A. B., Mather, D. & Reitz, R. D. 1993 Modeling the effects of drop drag and breakup on fuel sprays. In SAE International Congress and Exposition, SAE Transactions 930072, pp. 1–13.Google Scholar
Liu, Z., Zhou, J. & Wu, H. 2018 New correlations for slip flow and heat transfer over a micro spherical particle in gaseous fluid. Powder Technol. 338, 129–139.Google Scholar
Marble, F. E. 1970 Dynamics of dusty gases. Annu. Rev. Fluid Mech. 2 (1), 397–446.CrossRefGoogle Scholar
McFarland, J. A, Black, W. J, Dahal, J. & Morgan, B. E. 2016 Computational study of the shock driven instability of a multiphase particle-gas system. Phys. Fluids 28 (2), 024105.CrossRefGoogle Scholar
Middlebrooks, J. B., Avgoustopoulos, C. G., Black, W. J., Allen, R. C. & McFarland, J. A. 2018 Droplet and multiphase effects in a shock-driven hydrodynamic instability with reshock. Exp. Fluids 59 (98), 1–16.Google Scholar
Nicholls, J. A. & Ranger, A. A. 1969 Aerodynamic shattering of liquid drops. AIAA J. 7 (2), 285–290.Google Scholar
O'Rourke, P. & Amsden, A. 1987 The TAB method for numerical calculation of spray droplet breakup. Tech. Rep. LA-UR-2105. Los Alamos National Laboratory.CrossRefGoogle Scholar
Paudel, M., Dahal, J. & McFarland, J. 2018 Particle evaporation and hydrodynamics in a shock driven multiphase instability. Intl J. Multiphase Flow 101, 137–151.CrossRefGoogle Scholar
Pilch, M. & Erdman, C. A. 1987 Use of breakup time data and velocity history data to predict the maximum size of stable fragments for acceleration-induced breakup of a liquid drop. Intl J. Multiphase flow 13 (6), 741–757.CrossRefGoogle Scholar
Ranz, W. E. & Marshall, W. R. 1952 Evaporation from drops. Chem. Engng Prog. 48 (3), 141–146.Google Scholar
Sazhin, S. S., Kristyadi, T., Abdelghaffar, W. A. & Heikal, M. R. 2006 Models for fuel droplet heating and evaporation: comparative analysis. Fuel 85 (12), 1613–1630.CrossRefGoogle Scholar
Snider, D. M. 2001 An incompressible three-dimensional multiphase particle-in-cell model for dense particle flows. J. Comput. Phys. 170 (2), 523–549.CrossRefGoogle Scholar
Snider, D. M., ORourke, P. J. & Andrews, M. J. 1997 An incompressible two-dimensional multiphase particle-in-cell model for dense particle flows. Tech. Rep. Los Alamos National Lab.CrossRefGoogle Scholar
Syahdan, I. M. 2015 On the mach number effects on droplet breakup in laminar flow. PhD thesis, University of Washington.Google Scholar
Tanner, F. X. 1997 Liquid jet atomization and droplet breakup modeling of non-evaporating diesel fuel sprays. SAE Trans J Eng 106, 127–140.Google Scholar
Theofanous, T. G. 2011 Aerobreakup of Newtonian and viscoelastic liquids. Annu. Rev. Fluid Mech. 43 (1), 661–690.Google Scholar
Wert, K. 1995 A rationally-based correlation of mean fragment size for drop secondary breakup. Intl J. Multiphase Flow 21 (6), 1063–1071.CrossRefGoogle Scholar
Zhao, H., Liu, H.-F., Xu, J.-L., Li, W.-F. & Lin, K.-F. 2013 Temporal properties of secondary drop breakup in the bag-stamen breakup regime. Phys. Fluids 25 (5), 054102.CrossRefGoogle Scholar