Pulsatile flow of a shear-thinning model for blood through a two-dimensional stenosed channel

Abstract

The effects of percentage stenosis and Reynolds number (Re) on steady flow, and Womersley number (Wo) on pulsatile flow, of blood through a two-dimensional channel with stenosis are investigated, and the results are compared with the Newtonian case. We model blood using the shear-thinning relation proposed by Yeleswarapu, while the stenosis is approximated using a cosine-shaped taper. The vorticity–streamfunction formulation of the flow equations is solved using a finite difference scheme in conjunction with a full-multigrid algorithm that reduces computational time. The presence of stenosis leads to a recirculation zone immediately downstream of the stenosis. In steady flow, the shear-thinning fluid predicts higher peak wall shear stress than the Newtonian fluid: the difference between the predictions, expressed as a percentage of the Newtonian wall shear stress, decreases as percentage stenosis and Reynolds number increase. For a given percentage stenosis and Reynolds number, the percentage difference between the shear-thinning fluid and Newtonian fluid decreases, and remains negligible, as the Womersley number increases (corresponding to increasing pulsatile nature of the flow). This suggests that the Newtonian approximation can accurately model wall shear stress in the aortic flow of blood; however, for other variables (e.g. mean velocity) the shear-thinning model is more appropriate.