A numerical comparison of one-dimensional fluid jet models applied to drop-on-demand printing

This paper presents a numerical simulation of capillary jets motivated by the study of dropon-demand ink-jet printing. Two sets of 1-dimensional equations for an inviscid axisymmetric fluid jet are integrated using a numerical scheme suggested by MacCormack's predictor-corrector algorithm. The difference between the two sets of equations is the inclusion or exclusion of the terms that account for radial inertia. When these terms are included the numerical scheme necessary to solve the equations is more complicated. The results from both schemes are, presented for three Weber numbers with a simplified nozzle entry pressure history that has been converted to a velocity history at the nozzle exit by a momentum integral applied to the nozzle region. The results indicate that at higher Weber numbers the omission of radial inertia has a greater effect on the drop profiles than at lower Weber numbers. The conditions under which each numerical scheme might be a useful simulation are also discussed.