Ainsley Rexford | Engineering Portfolio

This study, completed for MEAM 5360, investigates the drag force on solid bodies in low-Reynolds-number flows using both analytical and numerical approaches for Newtonian and non-Newtonian fluids. The work begins with a derivation of Stokes’ drag on a sphere in creeping flow of an incompressible Newtonian fluid. Using the stream function, analytical expressions for the velocity field, pressure, and stress are obtained. Numerically, flow past a circular disk in a 2D channel is simulated using COMSOL Multiphysics across a range of Reynolds numbers (0.1, 10, 100) to validate the analytical solution and examine inertial effects. The analysis is extended to non-Newtonian flows using the Herschel-Bulkley model to describe viscoplastic fluids exhibiting yield stress and shear-thinning behavior. To capture viscoelastic flow, both the Oldroyd-B and FENE-P constitutive models are implemented. The Oldroyd-B model, while widely used, exhibits numerical instability at Weissenberg numbers over 0.2 due to its assumption of infinite polymer extensibility. The FENE-P model addresses this limitation by incorporating finite extensibility, resulting in smoother and more stable stress distributions but failed at Weissenberg numbers above 0.25. Comparison of the two models highlights the impact of nonlinear elasticity on drag prediction and flow structure in viscoelastic media.