A NUMERICAL STUDY OF PULSATILE LAMINAR FLOWS IN A PIPE WITH A RING-TYPE CONSTRICTION

Numerical simulations have been carried out to study pulsatile laminar flows in a pipe with an axisymmetric ring-type constriction. Three ty pes of pulsatile flows were investigated, namely a physiological flow a pure sinusoidal flow and a non-zero mean velocity sinusoidal flow. T he laminar flow governing equations were solved by the SIMPLE algorith m on a non-staggered grid and a modified Crank-Nicolson approximation was used to discretrize the momentum equations with respect to time. T he maximum flow Reynolds number (Re) is 100. The Womersley number (N-w ) ranges from 0 to 50, with the corresponding Strouhal number (St) ran ging from 0 to 3 . 98. The constriction opening ratio (d/D) and thickn ess ratio (h/D) are fixed at 0 . 5 and 0 . 1 respectively. Within the time period investigated, all these pulsatile flows include both forwa rd and backward flows. The unsteady recirculation region and the recir culation points change in size and location with time. For N-w less th an or equal to 1 and St less than or equal to 1 . 56 x 10(-3) the thre e pulsatile flows have the same simple relation between the instantane ous flow rate and pressure loss (Delta p) across the constriction and the pressure gradient in the axial direction (dp/dz) in the fully deve loped flow region. The phase angles between the flow rate and pressure loss and the pressure gradient are equal to zero. With increasing N-w and St, the phase angle between the flow rate and the dp/dz becomes l arger and has its maximum value of 90 degrees at N-w = 50 and St = 3 . 98. The three pulsatile flows also show different relations between t he flow rate and the pressure gradient. The pure sinusoidal flow has t he largest maximum pressure gradient and the non-zero mean velocity si nusoidal flow has the smallest. For larger N-w and St the fully develo ped velocity profiles in the fully developed flow region have a smalle r velocity gradient along the radial direction in the central region. The maximum recirculation length increases for N-w ranging from 0 to 4 . 2, while this length becomes very small at N-w= 50 and St = 3 . 98. The deceleration tends to enlarge the recirculation region and this e ffect appears for N-w greater than or equal to 3 and St greater than o r equal to 1 . 43 x 10(-2). Linear relations exist between the flow ra te and the instantaneous maximum values of velocity vorticity and shea r stress.