Effect of liquid sheet and gas streams characteristics on the instability of a hollow cone spray using an improved linear instability analysis

Abstract

The breakup of a liquid sheet or jet is led to atomization phenomenon. The liquid sheet surface instability controls spray formation and determines the spray characteristics. Therefore, the instability study of the liquid jet has attracted a lot of attentions so that a lot of works have been carried out on this subject. The instability study of a swirling annular liquid sheet exposed to inner and outer gas streams is represented in the paper. A three-dimensional flow for the liquid sheet and a two-dimensional flow for inner and outer gas streams have been considered. In previous studies, a cylindrical liquid sheet has been considered, but in this study, the instability theory is implemented on a conical liquid sheet for different cone angles. The effects of swirl velocity of the liquid sheet and axial velocity of the gas streams on the sheet instability and breakup length have been investigated. Results show that liquid swirl Weber number has a destabilizing effect on a conical liquid jet. Study of the effect of ambient pressure shows that disturbance growth rate increases with increasing gas-to-liquid density ratio. The effect of spray angle on the instability of the liquid sheet is a very important issue in combustion chamber design especially when the available space and/or weight is limited. Higher spray angle enhances the instability of the liquid sheet, and it leads to a shorter breakup length and larger ligaments. Sheet thickness is another parameter that has been considered. Increasing sheet thickness enhances the sheet instability. These behaviors are consistent with the experimental observations.

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“…The ultimate equation was numerically solved using Maple TM by Hosseinalipour et al (2016) The parameters of ρ i , U i , V i , ρ l , U l , V l , A l , ρ o , U o , V o , R b , R a , σ , k ¯, α , n as input parameters were utilized to solve the ultimate equation.…”

“…Mahdavi et al (2013) made an effort to estimate the breakup characteristics of a round and a hollow liquid sheet based on LI theory used by Ibrahim (2006). Hosseinalipour et al (2016) implemented LI theory on a hollow-cone liquid sheet to take into account different spray angles in the analysis and finally introduced the improved (ILI) analysis.…”

“…In this paper, to estimate the most unstable wave, happening before the breakup, on a liquid sheet, LI theory was employed. In addition to implementation of LI theory based on Ibrahim-style, a different implementation of LI theory was done based on Hosseinalipour et al ’s (2016) studies. It should be noted that in the prior studies carried out by Ibrahim (2006) and Mahdavi et al (2013), cylindrical liquid sheet has been taken into account for implementation of the LI analysis but Hosseinalipour et al (2016) implemented the LI theory on hollow-cone liquid sheet.…”

“…In addition to implementation of LI theory based on Ibrahim-style, a different implementation of LI theory was done based on Hosseinalipour et al ’s (2016) studies. It should be noted that in the prior studies carried out by Ibrahim (2006) and Mahdavi et al (2013), cylindrical liquid sheet has been taken into account for implementation of the LI analysis but Hosseinalipour et al (2016) implemented the LI theory on hollow-cone liquid sheet. This implementation has a lot of elaborations because the spray angle must be entered in the governing equations.…”