Non-Newtonian Flow: Fluid Flow Between Two Moving Eccentric Cylinders

This project simulates the two-phase flow of a non-Newtonian fluid — a mixture of drilling fluid and CMC (carboxymethyl cellulose) — in the annular gap between two eccentric cylinders with a rotating inner cylinder. Unlike a Newtonian fluid, a non-Newtonian fluid's viscosity changes with applied shear: it can thin or thicken under stress (ketchup, blood, toothpaste, starch suspensions, and many polymer and salt solutions behave this way). This makes the case directly relevant to drilling engineering, where shear-dependent muds circulate through eccentric annuli between the drill pipe and the borehole wall.

The methodology combines a Eulerian multiphase model for the two phases (drilling fluid and CMC) with the standard k-ω turbulence model, and the low-Re correction is activated to better resolve the near-wall flow patterns that dominate in a narrow, eccentric annulus. The rotation of the inner cylinder is imposed through the Moving Wall boundary condition — the key driver that sets up the shearing flow and exercises the fluid's non-Newtonian response.

Setup: the drilling–CMC mixture enters the gap between the eccentric cylinders at 0.25 m/s, while the inner cylinder rotates. Geometry and meshing are done in Gambit as a structured mesh (179,820 elements) — structured here because the regular annular geometry suits a clean, aligned grid.

What the results show: 2-D and 3-D contours of pressure, velocity, streamlines, phase volume fraction, and eddy viscosity. The phase distribution tells the central story — the drilling-fluid volume fraction peaks exactly where the CMC fraction is lowest, and vice versa — showing how the two phases separate and redistribute across the eccentric gap under rotation and shear.

You'll learn to: set up a Eulerian two-phase non-Newtonian case, apply the Moving Wall condition to drive annular shear flow, use the k-ω model with low-Re correction for near-wall resolution, and interpret phase separation from volume-fraction and eddy-viscosity contours.