Time-dependent compressible extrudate-swell problem with slip at the wall

Abstract

We solve the time-dependent compressible Newtonian extrudate-swell problem with slip at the wall, in an attempt to simulate the stick-slip extrusion instability. An arbitrary nonlinear slip model relating the shear stress to the velocity at the wall is employed, such that the flow curve consists of two stable branches separated by an unstable negative-slope branch. Finite elements are used for the space discretization and a standard fully implicit scheme for the time discretization. When the volumetric flow rate at the inlet is in the unstable regime and compressibility is taken into account, self-sustained periodic oscillations of the pressure drop and of the mass flow rate at the exit are observed and the extrudate surface becomes wavy, as is the case in stick-slip instability. Results are presented for different values of the compressibility number. As compressibility is reduced, the frequency of the oscillations becomes higher, the amplitude of the pressure drop oscillations decreases, and the amplitude of the mass flow-rate oscillations decreases, whereas the amplitude and the wavelength of the free-surface waves decrease.