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A high-order finite element method was used to simulate the blood flow within an idealised aortic geometry, composed of ascending aorta, aortic arch and descending aorta. Steady-state flow of a Newtonian fluid was modelled within different geometries, which were assumed to have rigid and stationary walls. The velocity profile forced on the inlet of the pipe is the Hagen- Poiseuille fully developed profile.
First the effect of tapering on simpler straight pipe geometries was considered. Because of the mass conservation the flow accelerates along the centreline. The velocity profiles also change their shape and become more blunt than the typical developed Hagen-Poiseuille profile of a straight non-tapered pipe.
Then the physiological representative bended pipe geometry was taken in consideration. The tapering of the pipe mainly acts on the velocity in the axial direction, constantly ac- celerating the flow and, therefore locally increasing Reynolds and Dean number. All the forces and the convective accelerations in this direction increase in magnitude, moving along the centreline. The forces acting in-plane at each cross-section are also greatly enhanced, both locally and as cross-sectional averages. However, the stronger in-plane forces balance out causing only small differences to the in-plane velocity component. The secondary flow motion in the plane normal to the axial direction are not significantly modified by the taper.
An attempt to separate the effects of the tapering on the averaged forces from the effects of bending was made. The two contributions, in fact, act respectively on the axial direction and on the normal plane. However, the two effects are highly coupled because of non-linearity of the Navier-Stokes equations and a non linear interaction is always present in the forces acting on the other direction.