Fully developed pulsatile flow in a curved pipe

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Abstract
The fully developed region of periodic flows through curved pipes of circular cross-section and arbitrary curvature has been simulated numerically. The volumetric flow rate, prescribed by a cosine function, remains positive throughout the entire cycle. Such flows are characterized by three parameters: the frequency parameter α, the amplitude ratio γ and the mean Dean number κm. We use the Projection Method to solve the finite-difference approximation of the Navier–Stokes equations in their primitive form. The effect of κm on the flow has been extensively studied for the range 0.7559 [les ] κm [les ] 756 for α = 15 and γ = 1, and the curvature ratio, δ, equal to . Interactions between the Stokes layer and the interior are noted and a variety of pulsatile motions along with reversal of the axial-flow direction are revealed. The manner in which the secondary motions evolve with increasing Dean number, and how they change direction from outward to inward ‘centrifuging’ at the centre, is also explained. Reversal in the axial flow is observed for all values of Dean number studied and occupies a region ranging from the area immediately adjacent to the entire wall for low values of Dean number to the entire inner half of the cross-section for larger values. When reversal of the axial flow is present, the local maximum axial shear stress is found at the inner bend where the backflow region is located. The values of circumferential shear stress for κm = 0.7559 and 151.2 confirm the existence of a single-vortex structure in the half-cross-section, whereas the values for larger values of mean Dean number are indicative of more complicated vortical structures.