Annular Extrudate Swell of Newtonian Fluids: Effects of Compressibility and Slip at the Wall

Numerical simulations have been undertaken for the benchmark problem of annular extrudate swell present in pipe extrusion and parison formation in blow molding. The effects of weak compressibility and slip at the wall are studied through simple linear laws. The finite element method is used to provide numerical results for different inner/outer diameter ratios $κ$ under steady-state conditions for Newtonian fluids. The present results provide the shape of the extrudate, and, in particular, the thickness and diameter swells, as a function of the dimensionless compressibility and slip coefficients, $B$ and $Bsl$⁠, respectively. The pressures from the simulations have been used to compute the excess pressure losses in the flow field (exit correction). Weak compressibility slightly affects the thickness swell (about 1% in the range of simulations $0⩽B⩽0.02$⁠) mainly by a swell reduction, while slip drastically reduces the swelling to 1–2% for obvious slip $(Bsl≈1)$ and to 0 for perfect slip $(Bsl>10)$⁠. The exit correction increases with increasing compressibility levels and is highest for the tube $(κ=0)$ and lowest for the slit $(κ=1)$⁠. It decreases monotonically to 0 as the dimensionless slip coefficient reaches its asymptotic limit of perfect slip. All results are ordered with the diameter ratio $κ$⁠, between the limits of tube $(κ=0)$ and slit $(κ=1)$⁠.