Numerical study of Kelvin-Helmholtz instability of Newtonian and non-Newtonian fluids

Document Type : Research Article

Authors

1 Department of Mechanical Engineering, Shahrekord University, Shahrekord, Iran

2 Department of Mechanical Engineering, Shahrekord University, Shhahhrekord, Iran

Abstract

Kelvin-Helmholtz Instability (KHI) is a hydrodynamic instability generated by the relative motion of immiscible, irrotational, incompressible, and inviscid fluids. In the present study, the KHI is assessed for Newtonian and non-Newtonian fluids by solving two-dimensional Navier-Stokes equations using the finite volume method. In the case of Newtonian fluids, it was found that for t^*>1.5 the growth rate of KHI depends on the surface tension when the surface tension is in the range of 0.000192-0.000993 N/m. The results demonstrate that the critical wavenumber is enhanced by increasing the power-law index (n) for shear-thinning and shear-thickening non-Newtonian fluids; however, at a specific time, the amount of critical wavenumber for shear-thickening fluids is smaller than that for shear-thinning ones. It is also concluded that as the power-law index increases, the wave stability can be reached more rapidly. When n = 0.2 and σ = 0.004 N/m, the velocity profile is asymmetric, showing that the velocity of the lighter liquid increases significantly at a specific height of the chamber. As the surface tension decreases, the interface velocity profile exhibits symmetrical behavior.

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