Annular Extrudate Swell of Newtonian Fluids Revisited: Extended Range of Compressible Simulations

In a recent article (Mitsoulis, 2007, “Annular Extrudate Swell of Newtonian Fluids: Effects of Compressibility and Slip at the Wall,” ASME J. Fluids Eng., 129, pp. 1384–1393), numerical simulations were undertaken for the benchmark problem of annular extrudate swell of Newtonian fluids. The effects of weak compressibility and slip at the wall were studied through simple linear laws. While slip was studied in the full range of parameter values, compressibility was confined within a narrow range of values for weakly compressible fluids, where the results were slightly affected. This range is now markedly extended (threefold), based on a consistent finite element method formulation for the continuity equation. Such results correspond to foam extrusion, where compressibility can be substantial. The new extended numerical results are given for different inner/outer diameter ratios $κ$ under steady-state conditions for Newtonian fluids. They provide the shape of the extrudate, and, in particular, the thickness and diameter swells, as a function of the dimensionless compressibility coefficient $B$⁠. The pressures from the simulations have been used to compute the excess pressure losses in the flow field (exit correction). As before, weak compressibility slightly affects the thickness swell (about 1% in the range of $0≤B≤0.02$⁠) mainly by a swell reduction, after which a substantial and monotonic increase occurs for $B>0.02$⁠. The exit correction increases with increasing compressibility levels in the lower $B$-range and is highest for the tube $(κ=0)$ and lowest for the slit $(κ=1)$⁠. Then it passes through a maximum around $B≈0.02$⁠, after which it decreases slowly. This decrease is attributed to the limited length of the flow channel (here chosen to be eight die gaps).