Abstract
The linear instability of an annular liquid jet with a radial temperature gradient in an inviscid gas steam is investigated theoretically. A physical model of an annular liquid jet with a radial temperature gradient is established, dimensionless governing equations and boundary conditions are given, and numerical solutions are obtained using the spectral collocation method. The correctness of the results is verified to a certain extent. The liquid surface tension coefficient is assumed to be a linear function of temperature. The effects of various dimensionless parameters (including the Marangoni number/Prandtl number, Reynolds number, temperature gradient, Weber number, gas-to-liquid density ratio and velocity ratio) on the instability of the annular liquid jet are discussed. A decreasing Weber number destabilizes the annular liquid jet when the Weber number is lower than a critical value. It is found that the effects of the Marangoni effect are related to the Weber number. The Marangoni effect enhances instability when the Weber number is small, while the Marangoni effect weakens instability when the Weber number is large. In addition, because the thermal effect is considered, a decreasing Reynolds number enhances the instability when the Weber number is lower than a critical value, which is similar to the results of a viscous liquid sheet with a temperature difference between two planar surfaces. Furthermore, the effects of other dimensionless parameters are also investigated.
Highlights
The breakup of a liquid jet is encountered in various applications, such as liquid rocket engines and gas turbines [1]
Shen and Li [4] studied the sinusoidal mode and the varicose mode of the flat liquid film and proposed the “para-sinuous mode” and “para-varicose mode”; they found that the outer and inner amplitude ratio is not an invariant, which was opposite to the assumption made by Meyer and Weihs [5]
They found that the liquid sheet becomes more unstable when a temperature difference exists, and liquid viscosity destabilizes the sheet under this condition
Summary
The breakup of a liquid jet is encountered in various applications, such as liquid rocket engines and gas turbines [1]. Crapper et al [3] studied the instability of an inviscid annular jet injecting into a stationary gas medium. They obtained the dispersion equation and numerically solved it. The compressibility of gas plays a significant role in the instability of the gas–liquid interface [14,15]; a higher gas Mach number is a destabilizing parameter and enhances the breakup process of an annular liquid jet [16,17]. Due to the temperature difference between the inner and outer gas–liquid interface, there is a temperature gradient in the liquid phase.
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