Numerical Study of Kelvin-Helmholtz Instability of Newtonian and Non-Newtonian Fluids

Kelvin-Helmholtz instability is a hydrodynamic instability generated by the relative motion of immiscible, irrotational, incompressible, and inviscid fluids. In the present study, the Kelvin-Helmholtz instability is assessed for Newtonian and non-Newtonian fluids by solving two-dimensional Navier-Stokes equations using the finite volume method. ANSYS FLUENT software is used to simulate the two-phase flow field. The numerical method is the finite volume method. Using the semi-implicit method for pressure-linked equations algorithm, the velocity and pressure fields are coupled and the Navier-Stokes equations are solved. The second-order upwind method is used to discretize the convection terms in Navier-Stokes equations and the central difference method is employed to approximate the time derivative. In the case of Newtonian fluids, it was found that for  the growth rate of Kelvin-Helmholtz instability 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.