Implicit solutions of the unsteady Navier-Stokes equation for laminar flow through an orifice within a pipe

Effects of Reynolds number on physiological-type pulsatile flows in a pipe with ring-type constrictions

“…Following the studies by Coder and Buckley [18] and Durst et al [19], the flow Reynolds number is known to have significant effects on the flow field for a given bell-shaped constriction opening. Investigations are then focused here on the effects of the Reynolds number on the flow field and the maximum values of velocity (V max ), vorticity (V max ), shear stress (~m ax ), as well as the pressure loss (P loss ) across the ring-type constriction, the recirculation length (z r /D).…”

Pressure drop characteristics of viscous fluid flow across orifices

“…The plate thickness for each orifice was fixed at 0.2 times the pipe diameter and a 45-degree bevel was introduced into the downstream side of each orifice to a depth of 50 percent. Navier-Stokes equations were used as the starting point in their analysis and initial comparisons with steady flow data from Johansen (1930), Tuve and Sprenkle (1933), and Keith (1971) as presented by Coder (1973) showed good agreement with the resulting discharge coefficients. Results from the pulsating analysis were plotted as discharge coefficient vs. time for every 45 degrees, and show that the discharge coefficient initially oscillates around the discharge coefficient that would be expected for steady flow.…”