Paul E. Sojka

Modeling drop size distributions

There is abundant literature discussing the prediction of a representative drop diameter in a spray. However, there are relatively few publications discussing prediction of a drop size distribution in sprays. In the present paper, we review the three available methods for modeling drop size distributions: the maximum entropy method, the discrete probability function method, and the empirical method.

On the three‐dimensional instability of a swirling, annular, inviscid liquid sheet subject to unequal gas velocities

A linear model describing the instability behavior of annular, swirling, inviscid sheets subject to inner and outer gas flows of differing velocities is presented. The model considers three‐dimensional disturbances and contains previous flat sheet, cylindrical jet, and annular jet analyses as limiting cases. Model predictions show that, in the absence of swirl, (i) an increase in axial Weber number causes the range of unstable axial disturbance modes to increase, (ii) when the axial Weber numbers are small (<8), inner gas flows lead to slightly faster growing axial instability modes than outer gas flows at equivalent inner and outer Weber numbers, but inner and outer gas flows have the same effect when Weber numbers are high (≳10), (iii) the wavenumber for the axial mode having the highest growth rate decreases with a decrease in axial Weber number, (iv) an increase in the density of the atomizing gas results in a slight increase in the wavenumber of the axial disturbance mode having the highest growth ra...

Spatial droplet velocity and size profiles in effervescent atomizer-produced sprays

Effervescent atomizer produced sprays were studied for application to rotary kiln incinerators. The sprays were characterized by their number averaged droplet velocity profiles, Sauter mean diameter (SMD) profiles, and size-velocity correlations. Spray mass flow rates ranged from 30 to 120 g/s. Air-liquid-ratios by mass (ALRs) were between 2% and 10%. Data were obtained at seven to ten radial positions across the diameter of the spray at three separate axial locations, all in the far-field (or dilute region) of the spray. The number averaged droplet velocity profiles were bell-shaped across any diameter, irrespective of ALR, liquid mass flow rate, or axial location. Velocity magnitudes were found to increase with an increase in either liquid mass flow rate or ALR, and to decrease with an increase in axial distance from the atomizer exit. SMD was found to be nearly constant across any spray diameter. On the basis of velocity-size-number flux contour plots, it was determined that the droplet size-velocity correlation is minimal. This observation, coupled with the minimal variation in SMD across a diameter, indicates that the spray can be modeled as a variable-density single-phase jet. A model was developed, based on previous gas-phase studies, to explain the development of the drop velocity profiles in the dilute spray region. Agreement between the measured drop velocities and model predictions was within 30% in all cases.

Quantitative, three-dimensional diagnostics of multiphase drop fragmentation via digital in-line holography

Quantitative application of digital in-line holography (DIH) to characterize multiphase fragmentation is demonstrated. DIH is applied to record sequential holograms of the breakup of an ethanol droplet in an aerodynamic flow field. Various stages of the breakup process are recorded, including deformation, bag growth, bag breakup, and rim breakup. A recently proposed hybrid method is applied to extract the three-dimensional (3D) location and size of secondary droplets as well as the 3D morphology of the rim. Particle matching between sequential frames is used to determine the velocity. Coincidence with the results obtained from phase Doppler anemometry measurement demonstrates the accuracy of measurement by DIH and the hybrid method.

Design and atomization properties for an inside-out type effervescent atomizer.

Atomization of aqueous polymer solutions is a key step in the formulation of several pharmaceutical products. Droplet size control is essential in order to produce pharmaceutical products with the desired properties. The purpose of this paper is to investigate design issues for an inside‐out type of effervescent atomizer used to spray water and aqueous solutions of polyvinylpyrrolidone (Kollidon® K‐30) and hydroxypropyl methylcellulose (Pharmacoat® 603). The atomizer was operated at air‐to‐liquid mass ratios of 0.1, 0.3, and 0.5 and a feed pressure of 1172 kPa. Fluid viscosities ranged from 1 to 47 mPa.s. The influence of several atomizer design features was considered, including exit orifice length‐to‐diameter ratio, exit orifice diameter, the total area of the air injection holes, the distance between the air injection point and the exit orifice, the diameter of the mixing chamber, and the orientation of both air and liquid flows. Droplet size distributions were shown to vary significantly with the atomizers exit orifice diameter, air injector design, and air injector distance to the exit orifice. In all cases air‐to‐liquid mass ratio played a key role in the mean droplet size. The design of the atomizer was shown to have the most pronounced effect on the mean droplet size at the lowest air‐to‐liquid mass ratios. Optimization of the atomizer design is very important in order to obtain small droplet sizes in pharmaceutical processes where the amount of air/gas should be minimized, e.g., closed‐cycle spray drying and agglomeration processes.

Effervescent Atomization of Aqueous Polymer Solutions and Dispersions

The purpose of this paper is to characterize the performance of effervescent atomizers via the effects of Air-to-Liquid-Mass-Ratio, (ALMR), feed pressure, and liquid viscosity on spray droplet size. Water and aqueous solutions having varying concentrations of polyvinylpyrrolidone, (PVP), (Kollidon® 30, 90, and the copolymer VA 64), hydroxypropyl methylcellulose, (HPMC), (Pharmacoat® 603, 606, and 615), and aqueous polymethacrylate dispersions, (Eudragit® RS 30 D, RL 30 D, and L 30 D-55) were sprayed over a range of ALMRs from approximately 0.1 to 0.8 at feed pressures ranging from approximately 550 to 1590 kPa. Fluid viscosities ranged from 1 to 228 mPa.s. The ALMR of the spray was shown to be the most important factor influencing the Sauter mean diameter (SMD) of the droplets, while feed pressure was shown to have only a minor effect on droplet size. Sprays with SMDs between 7 and 12 μm were produced for the polymethacrylates, 13 to 24 μm for the PVPs, and 15 to 20 μm for the HPMCs, all at an ALMR of 0.4 and a feed pressure of 1172 kPa. A higher liquid viscosity lead to larger droplets. The correlation between viscosity and droplet size was found to be dependent on the type of polymer.

Focused-image holography as a dense-spray diagnostic.

The denser regions of sprays need to be probed for us to understand further the basic phenomena of the breakup of a bulk liquid into droplets and the subsequent drop dynamics. The instruments currently available to spray diagnosticians, the Malvern spray analyzer and the phase/Doppler particle analyzer, cannot be used in the denser regions of the spray and in regions where ligaments or nonspherical droplets exist. Holography, as applied in the past, has permitted the interrogation of nonspherical drops but in general has been applied to droplet-dominated dilute regions of sprays. Using a focused-image holographic system, with the advantages of an imaging lens and side lighting, we can probe highly complex regions of sprays, such as those that include bubble explosions and complex ligament formation at the nozzle exit. In this paper we present components of a focused-image holographic system for spray analysis, advantages and limitations of that system, and how the longitudinal magnification varies as a funct on of the length of the object along the optical path.

Entrainment by ligament-controlled effervescent atomizer-produced sprays

Abstract Entrainment of ambient air into sprays produced by a new type of effervescent atomizer is reported. Entrainment data were obtained using a device similar to that described previously. Entrainment data were analyzed using a previous model, together with measured momentum rate data that were also acquired as part of this study. The analysis shows that entrainment by sprays produced using this type of atomizer is predicted to within about 35% by the expression E = m e /x√ρ e M o , where me, is the entrained gas mass flow rate, x is the distance along the spray axis measured from the dispenser exit orifice, ϱe is the density of the entrained air, Mo is the spray momentum rate at the exit orifice, and E is the experimentally determined entrainment number whose value is 0.15 ± 0.056 (2σ).

Holographic particle diagnostics

Abstract Holography is now an accepted method of interrogating particle fields and multiphase flows. Yet, holography systems are not produced in a commercially available form due to the complexity and variety of systems needed for different applications. As such, individual researchers must design and construct their own systems, systems which are usually tailored to specific applications. The process of designing and constructing a holographic system is complex and, to our knowledge, there is only one summary of the issues to be considered during this procedure. Consequently, holography is not as widely used as it might be. In addition, while several excellent reviews of holographic particle diagnostic systems have been published in the past, an updated review is overdue. Two contributions worthy of special note are “Selected Papers on Holographic Particle Diagnostics” (an SPIE publication) edited by C. Vikram, and the recent book entitled Particle Field Holography by C. Vikram. The SPIE publication is an excellent source of early papers on holographic particle diagnostics. The book is an excellent and thorough description of the foundations of holography and is highly recommended reading for anyone interested in the field. The purpose of this review article is therefore twofold. First, we hope to inform engineers and scientists of the issues to be considered and the options available to them when designing and constructing a holographic particle diagnostic system. Second, we hope to provide them with a history of previous efforts in the field so that if work has been done in an area similar to theirs they will be able to locate it and use it to facilitate their own research. Types of holographic techniques discussed in this paper include in-line, in-line Fraunhofer (far-field), and off-axis, using either diffracted or reflected light. Film types and light sources are also briefly noted. Some of the applications discussed are: spray injection systems (including rocket engine injection, aerosols, and coal injection), combustion processes, cavitation studies and internal two-phase flows, bubble chamber studies, and microbiology. Finally, a number of papers are discussed that describe innovations in the field of automated analysis of particle field holograms. This area must be pursued if holography is to become a time efficient diagnostic tool.

Indeterminate-origin nozzles to control jet structure and evolution

An indeterminate-origin (IO) nozzle consisting of a four-point tapered crown geometry is used to control jet structure and evolution. The near-field structure and flow field of round water jets were studied with particle image velocimetry (PIV) and laser-induced fluorescence (LIF) techniques. Typical jet Reynolds numbers (based on the nozzle diameter) are 5 000–10 000. The jet structures for IO nozzles are compared with those produced by conventional round nozzles. The IO nozzles introduce strong streamwise vortex pairs, which influence the near-nozzle structure and spreading by deforming the Kelvin–Helmholtz vortex rings. A pair of counter-rotating vortices forms at each valley plane, within the interior of the jet. Adjacent vortex pairs reorganize themselves and form another set of counter-rotating vortex pairs that propagate radially outwards from the jet. The evolution of these effects with streamwise distance and their implications are discussed.