Numerical study of flow in a constricted curved annulus: An application to flow in a catheterised artery (Q5950206)

The authors investigate numerically the flow of an incompressible Newtonian fluid in a curved annulus with a local constriction at the outer wall. The governing equations are simplified by use of small curvature and mild constriction approximations. Finite difference method described by \textit{W. M. Collins} and \textit{S. C. R. Dennis} [Q. J. Mech. Appl. Math. 28, 133-156 (1975; Zbl 0324.76018)] is employed to solve the locally two-dimensional elliptic equation at each cross-section, and solutions are given valid for all Dean numbers \(D\) in the entire laminar flow regime. Then the authors apply the results obtained to investigate the effects of Dean number \(D\) and the radii ratio \(k\) on various flow characteristics. It is shown that, for higher value of \(k\), the pressure gradient, pressure drop and frictional resistance increase considerably, and that the variation across the constricted length is also significant. The results are also applied to the study of an important clinical problem, namely to the flow in a stenosed artery with an inserted catheter. The authors are able to estimate numerically the increase in frictional resistance in this arterial flow.