Numerical modelling and simulation of blood flow through a multi-irregular stenosed artery

Abstract

The blood flow problem in a multi-irregular stenosed artery is important from the physiological considerations in view of many clinical situations. For instance, the patient is found to have multiple stenoses in the same arterial segment and the geometry of the stenosis is irregular. In this study, numerical modelling of blood flow through a multi-irregular stenosed artery is developed. Experimental investigations have also revealed that blood exhibits non-Newtonian properties at low shear rate. This research deals with both Newtonian and non-Newtonian models of blood flow. Such effects have been studied in the form of generalized Newtonian fluid, where apparent viscosity decreases by increasing shear rate. Two external factors namely periodic body acceleration and magnetic field have been considered. Numerical solutions are established under the assumptions that the flow is axisymmetric, unsteady, laminar, fully developed and two-dimensional. Numerical computation by finite difference Marker and Cell (MAC) method has been used to discretize the governing equations of motion for unsteady flow in the cylindrical polar co-ordinate system. The obtained pressure-Poisson equation was then solved through the successive-over-relaxation (S.O.R.) method. The obtained numerical results show good agreement with the experiments. It is found that under the influence of body acceleration, the velocity and flow rate are increased. The pressure drop gives higher values and the separation region is found to be larger in the case of blood flowing through a flexible artery having multiple irregular stenoses when compared to blood flowing through a single irregular stenosed artery. Furthermore, when magnetic field is increased, the velocity gradient near the wall and the wall shear stress will also be increased. With a sufficiently large magnetic field, the flow separations completely disappeared. The generalized Newtonian model results in a higher pressure drop with a smaller separation region in comparison to the Newtonian fluid.