Steady flow of Bingham plastic fluids past an elliptical cylinder

Abstract

In the present work, the flow of Bingham plastic fluids past an elliptical cylinder has been investigated numerically elucidating the effect of yield stress and fluid inertia on the momentum transfer characteristics at finite Reynolds numbers for a 100-fold variation in the aspect ratio. The governing differential equations have been solved over wide ranges of Reynolds number (0.01⩽Re⩽40) and Bingham number (0.01⩽Bn⩽100) in the laminar flow regime employing the finite element method. Furthermore, the effect of the aspect ratio (E) of the elliptical cylinder on the detailed flow characteristics has been studied by varying it from E=0.1 to E=10 thereby spanning varying levels of streamlining of the submerged object. In particular, new extensive results on streamline contours, shape and size of yielded/unyielded regions, shear rate profiles, surface pressure distribution and drag coefficient as functions of the Reynolds number, Bingham number and aspect ratio are presented and discussed. The functional dependence of the individual and total drag coefficients on the governing dimensionless parameters, aspect ratio, Reynolds number and Bingham number, is explored. The present results reveal a significant influence of the shape of the cylinder, i.e., aspect ratio on the detailed flow patterns and the overall hydrodynamic flow behavior of elliptical cylinders.