Abstract
An investigation has been performed to reveal the breakup mechanism of three-dimensional power-law cylindrical jets with different mode disturbances. It is observed experimentally that the asymmetric mode disturbances could prevail over the counterpart of symmetric mode under special conditions. The dispersion equation characterizing the instability of three-dimensional cylindrical jets of power-law fluids is deduced. The effects of the Weber number, generalized Reynolds number, power-law exponent, and gas–liquid density ratio on the jet instability are studied in detail. It is found that the maximum growth rates of asymmetric mode disturbances are usually larger than those of symmetric mode disturbances under high Weber numbers and low generalized Reynolds numbers, which implies that the former are more likely to be responsible for the breakup of power-law fluids. Meanwhile, the large gas–liquid interaction could trigger more short, unstable waves. Interestingly, with the increase of jet velocity, the interaction between liquid and gas phases plays an increasingly leading role on the breakup of power-law cylindrical jets, whereas the viscous force and the power-law exponent have less significant impacts. Theoretical analysis results give a better comprehensive understanding for the power-law jets.
Highlights
The transformation of liquid into spray is important in clean energy combustion, agriculture, meteorology, and many industrial processes
The dispersion equation with both symmetric and asymmetric mode disturbances is derived according to linear instability theory to reveal the breakup mechanism of the power-law fluid
The temporal instability analysis is used to obtain the complex solutions of S = Sr + iSi from the dispersion relation in Equation (38) at any real wavenumber α, when other parameters such as We, Ren, Q, and n are set to certain values
Summary
The transformation of liquid into spray is important in clean energy combustion, agriculture, meteorology, and many industrial processes. Ruo [10] carried out a temporal linear stability analysis for cylindrical liquid jets, and showed that the conditions in the non-axisymmetric mode would dominate the instability of the liquid jets These researchers have obtained many interesting results, it should be pointed out that all of the above studies are only for Newtonian fluids. Yang [20] obtained a linearly unstable dispersion equation of the power-law fluid cylindrical jet with symmetric mode. The dispersion equation with both symmetric and asymmetric mode disturbances is derived according to linear instability theory to reveal the breakup mechanism of the power-law fluid. The effects of dimensionless parameters, e.g., Weber number, the generalized Reynolds number, power-law exponent, and the gas–liquid density ratio, on the instability of a power-law liquid jet, are studied
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