The instability of liquid jets subjected to small perturbations
Gritzo, Louis Alan
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Numerous theories have been developed since the late 1800's in an attempt to predict jet behavior. However, the results of such theories have been difficult to apply to the physical problem. Existing theories require an accurate characterization of the flow at the nozzle exit for use as a boundary or initial condition. Furthermore, present methods of analyzing jet response only describe the nature of the flow near the breakup point, a location where jet behavior is highly nonline2Lr, and therefore most theories become increasingly inaccurate. For the purposes of examining the response of liquid jets to small naturally occurring disturbances inherent in a flow system, a new optical tool is developed. This non-intrusive technique allows the behavior of the jet to be examined near the nozzle exit, and upstream of the breakup point. Application of this tool allows the spatial growth rates and temporal variation of small naturally produced disturbances to be measured with significantly improved resolution and increased sampling rates. The development of this tool includes a derivation of the intensity distribution resulting from the incidence of collimated coherent monochromatic light on a dielectric cylinder. Two separate approaches are presented, the region of applicability being determined by the jet radius to light wavelength ratio. Using this tool, the stability of a vertical liquid jet exiting from a simple nozzle with a fully developed laminar velocity profile into ambient air is investigated. The magnitude 2uid frequency of temporal jet diameter variations are obtained at points along the axis of the jet. Spatial growth rates are also analyzed and compared to the predictions of existing theories. From these results, it was possible to conclude that liquid jet instability is not well represented by the transformed predictions of temporal instability analyses. Furthermore, two separate spatial regions of jet behavior were identified. For the conditions of this investigation, approximately the first 35% of the jet is dominated by the influence of velocity profile relaxation and appears to be characterized by the slow spatial growth of disturbances associated with low frequency variations in jet diameter. The results indicate that these low frequency disturbances are related to the formation of the smooth sinusoidal disturbances which are visible in photographs slightly upstream of the breakup point. The last 25% of the jet appears to be governed by the exponential growth of high frequency temporal disturbances. These high frequency changes in jet diameter are associated with the small short bulges which appear near the breakup point. The above two regions are separated by a transitional region which exhibits behavior indicative of the interference between disturbances corresponding to low and high frequency temporal variations in jet diameter.