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.