Final report for project ending in 1994; report dated April 1995
This program consisted of two major portions: a two-year feasibility study and a three-year investigation into the fundamentals of effervescent atornization. A number of goals were proposed and met during each portion. They are listed in Tables 1 and 2. Those goals are also discussed in the following ten paragraphs.
The primary goal of the feasibility study was to produce sub-50 µm droplets when spraying highly viscous (up to 100,000 cP) non-Newtonian fluids at process level throughputs (up to 1 kg/s). A secondary goal was to determine the spatial structure of the spray, in terms of how mean drop size and the width of the drop size distribution varied with axial and radial position throughout the spray. Work was conducted using a new type of nozzle developed at Purdue (an effervescent atomizer) because it was the only candidate likely to meet the sub-50 µm criterion. Fluids considered during the feasibility portion of the program consisted of glycerin/water/polymer and coal-water slurry/glycerin/polymer mixtures. Their consistency indices were as high as 41,500 and their flow behavior indices were as low as 0.27, Mean drop sizes as low as 28 µm were achieved when using air-liquid ratio values of less than 0.20, nozzle performance was shown to improve, i.e. mean drop size decreased, with increased throughput (in contrast to the behaviour of conventional atomizers) and polymer addition was demonstrated to have an adverse effect on the atomization of either single-phase or multi-phase feedstocks (although the extent of the increase left the mean drop size below the target value of 50 µm).
The fundamental investigation had a number of goals We first focused on spray behavior in the transition region where the two-phase flow that exits the nozzle as discrete gas bubbles in a continuous liquid is transformed into a continuous gas stream containing discrete liquid drops. Our goal was to determine the mechanism(s) controlling effervescent atomization so that a model could be developed for future design usage. Single-pulse holography was employed to observe the liquid breakup phenomena characteristic of effervescent atomization. A qualitative explanation of the mechanisms responsible for effervescent atomization was provided, based on this data.
We then broadened our efforts to include an investigation of the interactions between the spray and its surroundings. Our goal was to improve the already superior energy efficiency of effervescent atomizers by minimizing the impact of the major energy loss mechanisms. A computational study was performed to identify these major loss mechanisms and suggest methods for reducing their impact. We discovered that turbulent dissipation was the largest loss, followed by transformation of bulk kinetic energy into turbulent kinetic energy, and then entrainment of surrounding air. We concluded it was unlikely that turbulent dissipation and transformation of bulk kinetic energy into turbulent kinetic energy could be reduced, but that entrainment might be minimized.
We then focused on entrainment, with our efforts proceeding along two parallel paths. First, an entrainment model was developed for effervescent sprays that is based on the dimensional analysis performed by Ricou and Spalding [ 1961] in their work on entrainment by gas jets. This results in the entrainment number, which is the entrained gas flow rate normalized by jet momentum flux, axial distance, and entrained gas density.
Second, experimental apparatus were built to measure both the entrained mass flow rate and momentum rate for a variety of sprays. The entrainment measurements showed that entrainment increases linearly with axial distance and that it increases with &-liquid-ratio (ALR) and viscosity. By measuring momentum rate, it was possible to calculate the entrainment number directly. Comparison of entrainment numbers showed that it increases with viscosity, nozzle orifice diameter, and the combined effects of surface tension and liquid density. A dimensional scaling by liquid density and orifice diameter collapsed the majority of the entrainment number curves onto a single line. The modified version of the entrainment predictive equation describes the entrainment behavior of effervescent sprays to within 25%.
Subsequent efforts were focused on the relationship between fluid rheological properties and spray mean drop size. Our goal was to identify the fluid rheological * property that resulted in reduced spray performance upon addition of polymer to a feedstock This work was motivated by our previous study into the influence of polymer addition on nozzle performance.
One result of that study was the conclusion that spray mean drop size was independent of changes in either consistency index or flow behavior index for a power law fluid - it is fluid viscoelasticity that degrades nozzle performance. We then focused our efforts on a study of viscolelastic liquid effervescent atomixation Fluids were formulated using a Newtonian solvent into which were dissolved varying amounts of Poly(ethylene oxide). Six different polymer molecular weights were investigated between 12,000 and 900,000. Qualitative and quantitative drop size measurements were made for a range of fluid operating conditions. Liquid mass flow rate was held constant at 10 g/s while the air-liquid mass flow rate ratio varied from 2 to 10%.
Data show that the spray mean drop size decreases with increasing air-liquid ratio, that the addition of polymer increases mean drop size, and that spray mean drop size increases with polymer molecular weight and polymer concentration beyond a molecular weight of 35,000. Below 35,000 no significant variations in mean drop size were measured regardless of polymer concentration.
Holograms of the near nozzle structure indicated that the presence of polymer in the fluid serves to delay the formation of ligaments from an annular sheet as the fluid exits the nozzle. Also the breakup length and diameter of the ligaments increases with the addition of polymer. These two phenomena explain the increase in mean drop size with the addition of polymer to a pure Newtonian solvent.
Modeling of the spray formation process was carried out in the spirit of previous effervescent spray models. The analysis correctly predicts an increase in mean drop size with increases in polymer molecular weight or polymer concentration. The model predicts excellent qualitative behavior of Sauter mean diameter (SMD) versus ALR. In addition the error between the experimental data and the model predictions was as low as 10%. The maximum disagreement was never more than 50%.
Finally, a theoretical analysis was performed to describe the combined longitudinal- circumferential breakup of the annular liquid sheet present at the nozzle exit plane. The analysis considered only linear terms in the governing equations far momentum and mass conservation.
This analysis provided the correct scaling for ligament breakup length and number of ligaments formed from the annular sheet at the exit plane versus fluid viscosity, air-liquid ratio, and mass flow rate. However, the analysis did not provide the correct ligament breakup length and ligament number scaling versus surface tension, and predicted too few ligaments formed in the viscous case, as well as a fastest growing circumferential mode of order zero. Neutral stability plots indicated that the model was able to predict the combined circumferential-longitudinal breakup observed experimentally, thereby justifying a more sophisticated study that included the influence of non-linear effects. Finally, the neutral stability plots indicated that the present analysis can be used as a basis for derivation of drop size distribution functions from first principles. Such an analysis would couple classic instability theory, as presented here, with the discrete probability function (DPP) approach to incorporate contributions to the drop spectrum from all unstable modes. Fluctuations in fluid properties, such as viscosity, density and surface tension, due to inhomogeneities, as well as velocity variations due to turbulence could be incorporated. Consequently, the influence of these variations on the width of the drop size distribution could be evaluated