Multiple Inlet Sudden Expansion Flow of Power-Law Fluids

The flow of power-law fluids through two-dimensional planar sudden expansion geometries with multiple inlets was simulated numerically using an in-house finite volume code. The fluids are modelled using the power-law model, and a range of power-law index values (0.4 < n < 1.4) was investigated to cover shearthinning, Newtonian and shear-thickening inelastic behaviour. The effect of the generalised Reynolds number and the spacing between inlets on the flow behaviour and stability was analysed. The main characteristics of the vortices formed near the wall are similar to those found in single inlet sudden expansions, with symmetric wall vortices forming at low Reynolds numbers, with transitions to steady asymmetric, third eddy flow regimes and time-dependent flow at higher generalised Reynolds numbers. In some cases, the steady asymmetric and third eddy regimes are absent and the flow transitions directly from symmetric flow to time dependent flow (as seen for the geometry with the largest spacing). The stabilising nature of shear-thinning behaviour was observed while the opposite effect was seen for shear-thickening behaviour. In addition, intermediate vortices were seen to form between inlets which grow in size within the symmetric regime as the generalised Reynolds number is increased. New scalings which help collapse the data are introduced and a strong effect of inlet spacing on all flow transitions is shown, with the ratio of the wall distance to inlet height being a determining factor on the corner vortices length when the spacing between inlets is sufficiently large.