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Effectiveness of the dispersed-phase continuum model for investigating the airflow in the print gap of inkjet printers

, , , , , and . Physical Review Fluids, 8 (9): 094302 (September 2023)
DOI: 10.1103/PhysRevFluids.8.094302

Abstract

To investigate the effectiveness of the dispersed-phase continuum (DPC) approximation to model the airflow in the print gap of inkjet printers, three-dimensional simulations using the DPC model were compared against those using the classic particle-in-cell (P-in-C) approach. The DPC approximation, due to the separation of time scales, models the dispersed phase with a momentum source that depends on a predefined temporally averaged particle number density field. The results demonstrated that the steady DPC model correlated well to the time-averaged P-in-C solution when the former's formulation accounted for the droplet deceleration. The steady DPC model requires less than 0.1% of the computational resources used by the transient P-in-C approach to compute the mean flow field. Further analyses indicated that the DPC model captured a supercritical pitchfork bifurcation, where the airflow shifted from a steady spanwise uniform regime to a standing wave regime at a critical number density. The P-in-C model computed a smooth continuous transition that characterizes an excited supercritical pitchfork bifurcation. An excellent correlation between the models was observed at print densities above the transition point, but at low number densities a certain level of discrepancy was observed. This was a result of the pseudoturbulence or spottiness induced by the local and instantaneous motion of droplets that excited the standing wave solution even at low number densities. The results, thus, demonstrated that the DPC model is effective at estimating the mean flow field and approximating the bifurcation diagram, while being simultaneously more computationally efficient than the P-in-C model.

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