A Numerical Analysis of Pulsating Laminar Flow Through a Pipe Orifice

A study of laminar pulsating flow through a 45 degree bevel pipe orifice was performed using finite-difference approximations to the governing stream function and vorticity transport equations. The distance from (−∞) to (+∞) was transformed into the region from (−1) to (+1) for the streamwise coordinate. Solutions were obtained for orifice bore/pipe diameter ratios of 0.2 and 0.5 for bore Reynolds numbers in the range from 0.8 to 64 and Strouhal numbers from 10⁻⁵ to 10². Stream and vorticity function plots were generated for all cases and the time-dependent discharge coefficient waws computed and averaged over a cycle of pulsation. The numerical solutions agree closely with available experimental data for steady flow discharge coefficients. The results show that the effects of pulsation on the discharge coefficient can be correlated by using the product of the orifice bore Reynolds and Strouhal numbers.