Power law fluid flow over a bundle of cylinders at intermediate Reynolds numbers

Abstract

Extensive theoretical estimates of pressure, friction and total drag coefficients for the cross flow of power law fluids normal to an array of long circular cylinders are reported in this paper. The equations of continuity and of momentum have been solved numerically for the unknown velocities and pressure which, in turn, have been processed further to infer the values of drag coefficients. The inter-cylinder interactions have been approximated by the two commonly employed "concentric cylinders" cell models. The results reported herein embrace the following ranges of physical and kinematic conditions: power law flow behaviour index: 0.5, 0.6, 0.8 and 1; Reynolds number, 1-500 and the voidage of 0.4 and 0.5, albeit limited results are also presented for voidage values of 0.6 and 0.9. The accuracy of the numerical solution procedure has been established by carrying out extensive comparisons with the previously available analytical and/or numerical results for the flow of Newtonian and power law fluids. Similarly, the applicability of this simple approach of the cell model has been demonstrated by presenting detailed comparisons between the present predictions and the limited experimental results available in the literature for the flow of shear-thinning polymer solutions over banks of cylinders.