Numerical study of the combined effects of inertia, slip, and compressibility in extrusion of yield stress fluids

The axisymmetric extrudate swell flow of a compressible Herschel–Bulkley fluid with wall slip is solved numerically. The Papanastasiou-regularized version of the constitutive equation is employed, together with a linear equation of state relating the density of the fluid to the pressure. Wall slip is assumed to obey Navier’s slip law. The combined effects of yield stress, inertia, slip, and compressibility on the extrudate shape and the extrudate swell ratio are analyzed for representative values of the power-law exponent. When the Reynolds number is zero or low, swelling is reduced with the yield stress and eventually the extrudate contracts so that the extrudate swell ratio reaches a minimum beyond which it starts increasing asymptotically to unity. Slip suppresses both swelling and contraction in this regime. For moderate Reynolds numbers, the extrudate may exhibit necking and the extrudate swell ratio initially increases with yield stress reaching a maximum; then, it decreases till a minimum corresponding to contraction, and finally, it converges asymptotically to unity. In this regime, slip tends to eliminate necking and may initially cause further swelling of the extrudate, which is suppressed if slip becomes stronger. Compressibility was found to slightly increase swelling, this effect being more pronounced for moderate yield stress values and wall slip.