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Three-phase (solid, melt, and gas) and two-phase (solid and melt) models of horizontal ribbon growth were compared to identify the significance of different gas effects. The boundary conditions at the melt–gas and solid–gas interfaces for two-phase simulations were obtained from decoupled simulations of the gas phase. The results showed that the gas shear stress strongly changes the flow and temperature fields and the position of the triple-phase line. Also, the gas pressure distribution determined the vertical position of the triple-phase line. In the absence of growth angle effects, the results of the two-phase model with specified convective heat transfer coefficient, shear stress, and pressure as boundary conditions along the gas phase interface closely matched that of the three-phase model. Even with non-zero growth angle effects, the two-phase model with all the boundary conditions agreed well with three-phase simulation results, despite increased deviations at higher pull speeds. Finally, the results indicated that gas-induced velocities are significant compared to the Marangoni and buoyancy velocities, which could lead to flow instabilities and the variations in solid shape as observed in HRG experiments.more » « lessFree, publicly-accessible full text available August 1, 2025
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Three-phase (solid, melt, and gas) and two-phase (solid and melt) models of horizontal ribbon growth were compared to identify the significance of different gas effects. The boundary conditions at the melt-gas and solid-gas interfaces for two-phase simulations were obtained from decoupled simulations of the gas phase. The results showed that the gas shear stress strongly changes the flow and temperature fields and the position of the triple-phase line. Also, the gas pressure distribution determined the vertical position of the triple-phase line. In the absence of growth angle effects, the results of the two-phase simulation with convective heat transfer coefficient, shear stress, and pressure specified closely matched that of the three-phase model. Even with non-zero growth angle effects the two-phase model with all the boundary conditions applied, agreed well with three-phase simulation results despite increased deviations at higher pull speeds. Finally, the results indicated that gas-induced velocities are significant compared to the Marangoni and buoyancy velocities, which could lead to flow instabilities and the variations in solid shape as observed in HRG experiments.more » « lessFree, publicly-accessible full text available May 1, 2025
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The local temperature solution near the triple-phase line of a solidifying front, its melt, and a surrounding inert phase was obtained analytically including all three phases and solidification kinetics. This analytical solution was validated using a three-phase numerical model of the horizontal ribbon growth of silicon and compared to a two-phase analysis that models the effect of the third phase (e.g. the gas) as an applied heat flux. Although the three-phase solutions have additional modes to represent the gas behavior, for many conditions the two-phase and three-phase models predicted consistent behaviors. However, introduction of a non-zero growth angle causes the gas phase heat fluxes to have strong gradients near the triple-phase line. Even with zero growth angle, there are conditions in which the two-phase and three-phase solutions are very different; one predicting infinite heat fluxes while the other predicts finite fluxes. This depended on the ratios of thermal conductivities, and the angle at which the solid-melt interface intersected the free surface. In particular, when the thermal conductivity of the inert phase was comparable to the melt or solid phases there were significant differences.more » « less
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Abstract The significance of respiratory droplet transmission in spreading respiratory diseases such as COVID-19 has been identified by researchers. Although one cough or sneeze generates a large number of respiratory droplets, they are usually infrequent. In comparison, speaking and singing generate fewer droplets, but occur much more often, highlighting their potential as a vector for airborne transmission. However, the flow dynamics of speech and the transmission of speech droplets have not been fully investigated. To shed light on this topic, two-dimensional geometries of a vocal tract for a labiodental fricative [f] were generated based on real-time MRI of a subject during pronouncing [f]. In these models, two different curvatures were considered for the tip tongue shape and the lower lip to highlight the effects of the articulator geometries on transmission dynamics. The commercial ANSYS-Fluent CFD software was used to solve the complex expiratory speech airflow trajectories. Simultaneously, the discrete phase model of the software was used to track submicron and large size respiratory droplets exhaled during [f] utterance. The simulations were performed for high, normal, and low lung pressures to explore the influence of loud, normal, and soft utterances, respectively, on the airflow dynamics. The presented results demonstrate the variability of the airflow and droplet propagation as a function of the vocal tract geometrical characteristics and loudness.