Investigation of the primary breakup length and instability of non-Newtonian viscoelastic liquid jets
DOI:
https://doi.org/10.21152/1750-9548.12.4.327Abstract
The temporal instability and primary breakup length of a non-Newtonian viscoelastic liquid jet moving in an inviscid gaseous environment were carried out by solving a set of linearized Navier-Stokes equations and employing the linear viscoelastic model, respectively. The dimensionless dispersion equation that governs the instability was derived and solved by a numerical method. The effects of fluid properties on the instability and primary breakup length of viscoelastic liquid jets were carried out. It could be seen that by increasing the growth rate, the instability range and the primary breakup length of the viscoelastic liquid jets could result in an increase in the liquid Weber number and the ratio of gas to liquid density. Moreover, the significant findings are that an increase in the time constant ratio, and also the Ohnesorge number reduced both of the growth rates of disturbances and primary breakup length. Though, increasing the elasticity number resulted in a higher growth rate of disturbances and enhanced the breakup mechanism.
References
Saboohi Z, Ommi F, Fakhrtabatabaei A. Development of an augmented conceptual design tool for aircraft gas turbine combustors. The International Journal of Multiphysics. 2016;10(1). https://doi.org/10.21152/1750-9548.10.1.53
RAYLEIOH L. On the instability of a cylinder of viscous liquid under capillary. 1892.
Weber C. Zum zerfall eines flüssigkeitsstrahles. ZAMM‐Journal of Applied Mathematics and Mechanics/Zeitschrift für Angewandte Mathematik und Mechanik. 1931;11(2):136-54. https://doi.org/10.1002/zamm.19310110207
Lefebvre AH, McDonell VG. Atomization and sprays: CRC press; 2017.
Lin S-P. Breakup of liquid sheets and jets: Cambridge university press; 2003.
Sirignano W, Mehring C. Review of theory of distortion and disintegration of liquid streams. Progress in energy and combustion science. 2000;26(4-6):609-55. https://doi.org/10.1016/s0360-1285(00)00014-9
Reitz R, Bracco F. Mechanism of atomization of a liquid jet. The physics of Fluids. 1982;25(10):1730-42. https://doi.org/10.1063/1.863650
Alzahabi B, Schulz K. Analysis of pressure wave dynamics in fuel rail system. The International Journal of Multiphysics. 2008;2(3). https://doi.org/10.1260/175095408786927444
Squire H. Investigation of the instability of a moving liquid film. British Journal of Applied Physics. 1953;4(6):167.
Hagerty W. A study of the stability of plane fluid sheets. J App Phys. 1955;22:509-14.
Li X, Tankin R. On the temporal instability of a two-dimensional viscous liquid sheet. Journal of Fluid Mechanics. 1991;226:425-43. https://doi.org/10.1017/s0022112091002458
Wang X-T, Ning Z, Lü M, Sun C-H. Temporal analysis of breakup for a power law liquid jet in a swirling gas. Meccanica. 2018;53(8):2067-78. https://doi.org/10.1007/s11012-017-0794-y
Yang L-j, Qu Y-y, Fu Q-f, Xu B-r, Zhang W, Du M-l. Linear stability analysis of a slightly viscoelastic liquid jet. Aerospace Science and Technology. 2013;28(1):249-56. https://doi.org/10.1016/j.ast.2012.11.005
Yang L-J, Tong M-X, Fu Q-F. Linear stability analysis of a three-dimensional viscoelastic liquid jet surrounded by a swirling air stream. Journal of Non-Newtonian Fluid Mechanics. 2013;191:1-13. https://doi.org/10.1016/j.jnnfm.2012.10.011
Yang L-j, Qu Y-y, Fu Q-f, Gu B, Wang F. Linear stability analysis of a non-Newtonian liquid sheet. Journal of Propulsion and Power. 2010;26(6):1212-25. https://doi.org/10.2514/1.50361
Yarin AL. Free liquid jets and films: hydrodynamics and rheology: Longman Publishing Group; 1993.
Rallison JM, Hinch EJ. Instability of a high-speed submerged elastic jet. Journal of Fluid Mechanics. 1995;288:311-24. https://doi.org/10.1017/s0022112095001157
Keller JB, Rubinow S, Tu Y. Spatial instability of a jet. The physics of fluids. 1973;16(12):2052-5.
Gordon M, Yerushalmi J, Shinnar R. Instability of jets of non‐Newtonian fluids. Transactions of the Society of Rheology. 1973;17(2):303-24. https://doi.org/10.1122/1.549292
Brenn G, Liu Z, Durst F. Linear analysis of the temporal instability of axisymmetrical non-Newtonian liquid jets. International journal of multiphase flow. 2000;26(10):1621-44. https://doi.org/10.1016/s0301-9322(99)00115-9
Liu Z, Brenn G, Durst F. Linear analysis of the instability of two-dimensional non-Newtonian liquid sheets. Journal of non-newtonian fluid mechanics. 1998;78(2-3):133-66. https://doi.org/10.1016/s0377-0257(98)00060-3
Guo J-P, Wang Y-B, Bai F-Q, Zhang F, Du Q. Effects of Asymmetric Gas Distribution on the Instability of a Plane Power-Law Liquid Jet. Energies. 2018;11(7):1854. https://doi.org/10.3390/en11071854
Published
How to Cite
Issue
Section
Copyright (c) 2018 H Khodayari, F Ommi, Z Saboohi
This work is licensed under a Creative Commons Attribution 4.0 International License.