Droplet Formation from a Pulsed Vibrating Nozzle

Abstract Droplet formation from a passive vibrating nozzle driven by a pulsed pressure wave is numerical simulated. The nozzle is an orifice in a thin walled plate which is allowed to vibrate due to the pressure loading on the plate. The analysis couples the fluid flow from the nozzle and the resultant droplet formation with the nozzle vibration calculated using large deflection theory. A onedimensional fluid flow model is used where droplet formation is driven by a short step change in applied pressure. The problem is made nondimensional based on the capillary parameters of time, velocity and pressure. The nozzle material properties are varied to alter the vibration characteristics of the orifice plate used to form the nozzle. It is determined that the vibration of the nozzle only weakly affects the droplet break-off time and size, but greatly affects the droplet velocity. The resultant filament after drop break-off is also significantly affected by the nozzle vibration, resulting in variations in satellite droplet formation. Higher vibration amplitudes, which correspond to more flexible plates, result in larger total satellite volume

Flow structures and their contribution to turbulent dispersion in a randomly packed porous bed based on particle image velocimetry measurements

An experimental study was undertaken to explore the evolution of flow structures and their characteristics within a randomly packed porous bed with particular attention to evaluating turbulent scalar dispersion. A low aspect ratio bed of 4.67 (bed width to spherical solid phase particle diameter) with fluid phase refractive index matched to that of the solid phase was used in order to obtain time resolved two component particle image velocimetry data. Results are based on detailed velocity vector maps obtained at selected pores near the bed center. Pore, or large scale, regions that are associated with the mean flow were identified based on Reynolds decomposed velocity fields, while smaller scale structures embedded within pore scale regions were identified and quantified by combining large eddy scale decomposition and swirling strength analysis. The velocity maps collected in distinctive pore geometries showed presence of three types of flow regions that display very different mean flow conditions, described as regions with tortuous channel like flow, high fluid momentum jet like regions, and low fluid momentum recirculating regions. The major portion of pore space is categorized as tortuous channel flow. Time series of instantaneous velocity field maps were used to identify mean and turbulent flow structures based on their spatial scales in the different regions. Even though regions exhibit varied Eulerian statistics, they show very similar eddy characteristics such as spinning rate and number density. The integral scale eddy structures show nearly a linear rate of increase in their rotation rate with increasing pore Reynolds number, indicating a linear decrease in their time scales. The convective velocities of these eddies are shown to reach an asymptotic limit at high pore Reynolds numbers, unique for each flow region. Detailed Eulerian statistics for the identified flow regions are presented and are used to predict mechanical dispersion through the use of estimated Lagrangian statistics. Contributions from each of the flow regions are presented and the recirculating regions are shown to contribute most to the overall longitudinal dispersion, whereas the tortuous channel regions contribute most to the transverse dispersion. The overall dispersion estimates agree well with global data in the limit of high Schmitt number

Turbulent flow characteristics in a randomly packed porous bed based on particle image velocimetry measurements

An experimental study was undertaken to better understand the turbulent flow characteristics within a randomly packed porous bed. A relatively low aspect ratio bed (bed width to spherical solid phase particle diameter of 4.67) with the fluid phase refractive index matched to that of the solid phase was used to obtain time resolved particle image velocimetry data. Care was taken to assure that data were outside of the wall affected region, and results are based on detailed time dependent velocity vector maps obtained at selected pores. In particular, four pores were identified that display a range of very disparate mean flow conditions which resemble channel-like flow, impinging flow, recirculating flow, and jet like flow. Velocity data were used for a range of pore Reynolds numbers, Re[subscript pore], from 418 to 3964 to determine the following turbulence measures: (i) turbulent kinetic energy components, (ii) turbulent shear production rate, (iii) integral Eulerian length and time scales, and (iv) energy spectra. The pore Reynolds number is based on the porous bed hydraulic diameter, D[subscript H] = φD[subscript B]/(1 − φ) where φ is bed porosity and D[subscript B] is solid phase bead diameter and average bed interstitial velocity, V[subscript int] = V[subscript Darcy]/φ, where V[subscript Darcy] = Q/A[subscript bed], with Q being the volumetric flow rate and A[subscript bed] the bed cross section normal to the flow. Results show that when scaled with the bed hydraulic diameter, D[subscript H], and average interstitial velocity, V[subscript int], these turbulence measures all collapse for Re[subscript pore], beyond approximately 2800, except that the integral scales collapse at a lower value near 1300–1800. These results show that the pore turbulence characteristics are remarkably similar from pore to pore and that scaling based on bed averaged variables like D[subscript H] and V[subscript int] characterizes their magnitudes despite very different mean flow conditions.This is the publisher’s final pdf. The published article is copyrighted by the American Institute of Physics and can be found at: http://pof.aip.org/ Copyright (2013) American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics

Optical Measurement Uncertainties due to Refractive Index Mismatch for Flow in a Porous Media

Application of optical techniques such as PIV, PTV and LDA for velocity field estimation in porous media requires matching of refractive indices of the liquid phase to that of the solid matrix, including the channel walls. The methods most commonly employed to match the refractive indices have been to maximize the transmitted intensity through the bed or to rely on direct refractometer measurements of the indices of the two phases. Mismatch of refractive indices leads to error in estimation of particle position, ε[subscript PD], due to refraction at solid-liquid interfaces. Analytical ray tracing applied to a model of solid beads placed randomly along the optical path is used to estimate ε[subscript PD]. The model, after validating against experimental results, is used to generate expression for ε[subscript PD] as a function of refractive index mismatch for a range of bead diameters, bed widths, bed porosity, and optical magnification. The estimate of ε[subscript PD], which is found to be unbiased, is connected to errors in PIV measurement using the central limit theorem. Mismatch in refractive indices can also lead to reduction in particle density, N[subscript s], detected light flux, J, and degrade the particle image. The model, verified through experiments, is used to predict the reduction in N[subscript s] and J, where it is found that particle defocusing caused by spherical beads in refractive index mismatched porous bed is the primary contributor to reductions of N[subscript s] and J. In addition, the magnitude of ε[subscript PD] is determined for the use of fluorescent dye emission for particle detection due to wavelength dependent index of refraction

Flow Regime Characteristics in Porous Media Flows at High Reynolds Numbers

An experimental study on the turbulent flow characteristics in a randomly packed porous bed is presented and discussed. Time resolved PIV measurements, taken in specific pore spaces are used to evaluate transitional and developed turbulent flow statistics for pore Reynolds numbers from 54 to 3964. Three different regimes of steady laminar, transitional and turbulent flow are presented. Small scale coherent vortical structures are examined, using large eddy scale (LES) decomposition, for pore Reynolds number of greater than 1000. Integral length scales were found to reach asymptotic values of approximately 0.1 times the hydraulic diameter of the bed. The integral Eulerian time scales are found to reach an asymptotic value of approximately 0.3 times the convective time scale in the bed. Mean velocity vector maps show flattening of the velocity distribution due to increased momentum mixing. Turbulent stresses show increasing level of homogeneity at higher pore Reynolds numbers.</jats:p

Refractive Index Matching With Distortion Measurements in a Bed of Irregularly Packed Spheres

Experimental flow visualization in porous media is often conducted using optical techniques such as PIV and PTV for velocity field estimation and LIF for concentration field measurements. The porous bed is made optically accessible to laser light and imaging by matching refractive indices of the liquid phase to that of the solid matrix, including the channel walls. The methods most commonly employed to match the refractive indices have been to maximize the transmitted intensity through the bed or to rely on refractometers for measurement of the liquid and solid phases. Refractometers with sensitivity of 0.001 could still cause refraction problems in a porous bed, while accuracy and sensitivity of transmission based methods are limited by the camera resolution and noise scattered by impurities and stray light caused by reflections at interfaces. Both these methods fail to provide uncertainty estimates for particle position determination due to slight refractive index mismatching. This work presents a method for assessing the matching of refractive indices that relies on measuring distortion of a target when imaged through a porous bed. The target used is a grid of 250 μm dots irradiated with light at the necessary wavelength at which refractive indices are to be matched. Two principle types of distortion are quantified, distortion of the image centroid due to interface refraction and intensity distortion within the image for index mismatching as low as 0.0005.</jats:p