Influence of inertia and gravity on the stability of filament jet flow

Abstract

The interplay between inertia and gravity is examined for a filament jet flow. The velocity is imposed at the tube exit and jet tip downstream. Both linear and nonlinear stability analyses are carried out. The loss of stability coincides with the onset of a Hopf bifurcation. While both inertia and gravity enhance the stability of steady flow, inertia plays a more dominant role regarding critical parameters. In contrast, the disturbance frequency is more sensitive to the effect of gravity. Above criticality, finite-amplitude disturbances are amplified, and sustained oscillation is achieved. It is found that the growth rate increases with velocity ratio, but decreases with inertia and gravity, which suggests that initial transients tend to take longer to die out for a fluid with stronger inertia and gravity. Transient postcritical calculations show that the nonlinearity can be effectively halted by inertia and gravity. The oscillation frequency ͑jet radius͒ decreases ͑increases͒ with velocity ratio. However, the jet oscillates more frequently but less fiercely with stronger inertia and gravity effects. The rupture of the jet is also examined, and is found to be delayed by inertia and gravity. Although the oscillation amplitude is found to be weakest at the jet tip, it is at this location that the jet tends to rupture first. Finally, comparison is carried out between theory and experiment, leading to good agreement.

Draw ratio enhancement in nonisothermal melt spinning

“…The effects of gravity are similar to those of S. Increasing Re/Fr makes the system more unstable and also increases the value of Dr at fixed F o . However, these effects combine to produce an increase in Dr cr with Re/ Fr, similar to what was observed in prior work 22,29,32 for an isothermal MS operation. In all of the above cases, the changes in Dr cr with respect to C, S, Re/Fr are small compared with those produced by a change in Re.…”

“…Aðz; tÞ ¼ÂðzÞ þÃðzÞ expðktÞ; uðz; tÞ ¼ûðzÞ þũðzÞ expðktÞ; hðz; tÞ ¼ĥðzÞ þhðzÞ expðktÞ; (32) where hats and tildes denote steady-state and perturbation quantities, respectively, and k is the growth rate of the perturbation. After substitution of eq.…”