Linear spatial instability of viscous flow of a liquid sheet through gas

• The present paper focuses on the linear spatial instability of a viscous two-dimensional liquid sheet bounded by two identical viscous gas streams. The Orr–Sommerfeld differential equations and the boundary conditions of the flow configuration are numerically solved using Chebyshev series expansions and the collocation method. The strong dependence of the instability parameters on the velocity profiles is proven by using both quadratic and error functions to define the base flow in the liquid sheet and the gas shear layer. The sensitivity of the spatial instability growth rate to changes in the dimensionless parameters of the problem is assessed. Regarding the liquid sheet Reynolds number, it has been observed that, when this parameter increases, both the most unstable growth rate and the corresponding wavenumber decrease, whereas the cutoff wavenumber increases. The results of this analysis are compared with temporal theory through Gaster transformation. The effects liquid and gas viscosity have on instability are studied by comparing the instability curves given by the presented model with those from an inviscid liquid sheet and a viscous liquid sheet in an inviscid gaseous medium. The model presented in this paper features a variation in the cutoff wavenumber with all the governing parameters of the problem, whereas that provided by cases that account for an inviscid surrounding gas depends only on the liquid sheet Weber number and the ratio of gas to liquid densities. Results provided by the presented model have been experimentally validated and show that quadratic profiles have a greater capacity to predict the disturbance wavelength.

Ämnesord

TEKNIK OCH TEKNOLOGIER  -- Maskinteknik -- Strömningsmekanik och akustik (hsv//swe)

ENGINEERING AND TECHNOLOGY  -- Mechanical Engineering -- Fluid Mechanics and Acoustics (hsv//eng)

Nyckelord

linear instability analysis

spatial instability

viscous liquid sheet

spectral methods

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