Numerical study of steady laminar flow through tubes with multiple constrictions using curvilinear co-ordinates

The flow field through tubes with multiple axisymmetric constrictions in tubes was studied numerically. Two practical problem cases were considered and the numerical scheme was developed for both. In the first case there are one, two, three and four constrictions in the tube. The effects of the number of constrictions on wall shear stress, pressure drop, streamline, vorticity and velocity distributions as the flow passes through the tube were studied and the development of the periodicity characteristics was investigated. In the second case there were multiple constrictions in the tube equidistant from each other. For this case the governing equations were reformulated for a module at a sufficient distance downstream from the inlet where the entrance region effects could be ignored and flow field is assumed to repeat itself. The flow field solutions were obtained in this region. The governing equations were formulated in curvilinear co-ordinates and a finite volume discretization procedure was used to solve the problem. The computations were carried out over a range of Reynolds numbers between 50 to 250 for constrictions with 75 percent area reduction. The method is validated by comparing some of the solutions with experimental results.