A numerical study of pulsatile laminar flows in a pipe with a ring‐type constriction

Abstract

AbstractNumerical simulations have been carried out to study pulsatile laminar flows in a pipe with an axisymmetric ringtype constriction. Three types of pulsatile flows were investigated, namely a physiological flow, a pure sinusoidal flow and a non‐zero mean velocity sinusoidal flow. The laminar flow governing equations were solved by the SIMPLE algorithm on a non‐staggered grid and a modified Crank‐Nicolson approximation was used to discretrize the momentum equations with respect to time. The maximum flow Reynolds numer (Re) is 100. The Womersley number (Nw) ranges from 0 to 50, with the corresponding Strouhal number (St) ranging from 0 to 3·98. The constriction opening ratio (d/D) and thickness ratio (h/D) are fixed at 0·5 and 0·1 respectively. Within the time period investigated, all these pulsatile flows include both forward and backward flows. The unsteady recirculation region and the recirculation points change in size and location with time. For Nw ≤ 1 and St≤ 1·56 x 10−3 the three pulsatile flows have the same simple relation between the instantaneous flow rate and pressure loss (Δp) across the constriction and the pressure gradient in the axial direction (dp/dz) in the fully developed flow region. The phase angles between the flow rate and pressure loss and the pressure gradient are equal to zero. With increasing Nw and St, the phase angle between the flow rate and the dp/dz becomes larger and has its maximum value of 90° at Nw = 50 and St = 3·98. The three pulsatile flows also show different relations between the flow rate and the pressure gradient. The pure sinusoidal flow has the largest maximum pressure gradient and the non‐zero mean velocity sinusoidal flow has the smallest. For larger Nw and St the fully developed velocity profiles in the fully developed flow region have a smaller velocity gradient along the radial direction in the central region. The maximum recirculation length increases for Nw ranging from 0 to 4·2, while this length becomes very small at Nw = 50 and St = 3·98. The deceleration tends to enlarge the recirculation region and this effect appears for Nw ≥ 3 and St ≥ 1·43×10−2. Linear relations exist between the flow rate and the instantaneous maximum values of velocity, vorticity and shear stress.