TIME-DEPENDENT COMPRESSIBLE EXTRUDATE-SWELL PROBLEM WITH SLIP AT THE WALL

We solve the time-dependent compressible Newtonian extrudate-swell pro blem with slip at the wall, in an attempt to simulate the stick-dip ex trusion instability. An arbitrary nonlinear slip model relating the sh ear stress to the velocity at the wall is employed, such that the flow curve consists of two stable branches separated by an unstable negati ve-slope branch. Finite elements are used for the space discretization and a standard fully implicit scheme for the time discretization. Whe n the volumetric flow rate at the inlet is in the unstable regime and compressibility is taken into account, self-sustained periodic oscilla tions of the pressure drop and of the mass flow rate at the exit are o bserved and the extrudate surface becomes wavy, as is the case in stic k-dip instability. Results are presented for different values of the c ompressibility number. As compressibility is reduced, the frequency of the oscillations becomes higher, the amplitude of the pressure drop o scillations decreases, and the amplitude of the mass flow-rate oscilla tions decreases, whereas the amplitude and the wavelength of the free- surface waves decrease.