On creeping flow of a Bingham plastic fluid past a square cylinder

Abstract

In this work, the 2-D creeping flow of Bingham plastic fluids past a cylinder of square cross-section has been studied numerically. The governing differential equations (continuity and momentum) have been solved over a wide range of Bingham number as 1⩽Bn⩽105. Similar to the case of a circular cylinder, three zones of unyielded regions are seen to be present in the vicinity of the submerged cylinder, namely, caps attached to the top and bottom surfaces of the square cylinder, two sectors situated on the lateral sides undergoing rigid-body like motion and the usual far away unyielded regions. The influence of the Bingham number on their size and on the stress (normal and shear components) field in the vicinity of the cylinder is discussed in detail. In addition, the corresponding rate of strain, pressure and stress contours are also presented to facilitate the visualization of the structure of the flow field for scores of values of Bingham number. Also, the present numerical drag results have been correlated with the Bingham number via a simple expression thereby enabling their interpolation for the intermediate values of Bingham numbers.