Computational Protocol for Spray Flow Simulations Including Primary Atomization

Abstract Primary atomization is the key element in spray flow simulations. We have, in our previous work, used and validated the integral form of the conservation equations, leading to the “quadratic formula” for determination of the drop size during spray atomization in various geometry. A computational protocol has been developed where this formulation is adapted to existing computational frameworks for continuous and dispersed (droplet) liquid phase, for simulations of pressure-atomized sprays with and without swirl. In principle, this protocol can be applied to any spray geometry, with appropriate modifications in the atomization criterion. The preatomization continuous liquid motion (e.g., liquid column or sheet) is computed using volume-of-fluid (VOF) or similar methods, then the velocity data from this computation is input to the quadratic formula for determination of the local drop size. This initial drop size, along with the local liquid velocities from VOF, is then used in a Lagrangian tracking algorithm for the postatomization dispersed droplet calculations. This protocol can be implemented on coarse-grid, time-averaged simulations of spray flows, and produces convincing results when compared with experimental data for pressure-atomized sprays with and without swirl. This approach is general, and can be adapted in any spray geometries for complete and efficient computations of spray flows.

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Computational Simulations of Liquid Sprays in Crossflows with an Algorithmic Module for Primary Atomization

Journal of Engineering for Gas Turbines and Power ◽

10.1115/1.4049380 ◽

2020 ◽

Author(s):

Taewoo Lee ◽

Benjamin Greenlee ◽

Jung Eun Park ◽

Hana Bellerova ◽

Miroslav Raudensky

Keyword(s):

Drop Size ◽

Initial Conditions ◽

Energy State ◽

Integral Form ◽

Computational Procedure ◽

Fluid Simulation ◽

Liquid Jets ◽

Quadratic Formula ◽

Initial Drop ◽

Drop Size Distributions

Abstract For simulations of liquid jets in crossflows, the primary atomization can be treated with the quadratic formula, which has been derived from integral form of conservation equations of mass and energy in our previous work. This formula relates the drop size with the local kinetic energy state, so that local velocity data from the volume-of-fluid simulation prior to the atomization can be used to determine the initial drop size. This initial drop size, along with appropriately sampled local gas velocities, are used as the initial conditions in the dispersed-phase simulation. This procedure has been performed on a coarse-grid platform, with good validation and comparison with available experimental data at realistic Reynolds and Weber numbers, representative of gas-turbine combustor flows. The computational procedure produces all the relevant spray characteristics: spatial distributions of drop size, velocities, and volume fluxes, along with global drop size distributions. The primary atomization module is based on the conservation principles, and is generalizable and implementable to any combustor geometries for accurate and efficient computations of spray flows.

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Determination of line tension from the drop size dependence of contact angles

Colloids and Surfaces ◽

10.1016/0166-6622(90)80288-f ◽

1990 ◽

Vol 43 (2) ◽

pp. 195-206 ◽

Cited By ~ 97

Author(s):

D. Li ◽

A.W. Neumann

Keyword(s):

Drop Size ◽

Size Dependence ◽

Line Tension ◽

Contact Angles ◽

Drop Size Dependence

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Factors affecting the stability and estimation of carotene in artificially dried grass and hays

The Journal of Agricultural Science ◽

10.1017/s0021859600048267 ◽

1940 ◽

Vol 30 (4) ◽

pp. 622-638 ◽

Cited By ~ 16

Author(s):

S. K. Kon ◽

S. Y. Thompson

Keyword(s):

Chromatographic Analysis ◽

Accurate Determination ◽

Total Loss ◽

Carotene Content ◽

Factors Affecting ◽

Ordinary Temperature ◽

Initial Drop ◽

The Difference ◽

The Stability

1. The influence of storage in the light and in the dark at ordinary temperature and in a heated room at 70–80° F. on the carotene content of finely ground artificially dried grass stored in paper sacks and jute sacks was studied. There was an initial drop in carotene content from 61·1 to 46·5 mg./100 g., i.e. 23·9%, in the first month, and a total loss of 31·4% during 6 months' storage (August to February). No difference could be detected either between treatments or types of containers.2. There was a marked loss of carotene during 13 months' storage of baled artificially dried grass and of hays, amounting to 30–40% of the original value.3. Two methods of estimating carotene were compared. The method of Ferguson & Bishop (1936) gave higher results than the method of Peterson, Hughes & Freéman (1937). The difference is probably due to incomplete extraction in the latter method.4. Chromatographic analyses of “carotene” fractions from the above grasses showed the presence of coloured impurities amounting to 20·5–33·8% of the total recovered pigments.5. As these impurities are biologically inactive, chromatographic analysis or the use of special solvents are probably necessary for the accurate determination of carotene in forage.

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Dependence of rainfall interception on drop size: 2. Experimental determination of the wetting functions and two-layer stochastic model parameters for five tropical tree species

Journal of Hydrology ◽

10.1016/0022-1694(95)02999-0 ◽

1996 ◽

Vol 185 (1-4) ◽

pp. 379-388 ◽

Cited By ~ 55

Author(s):

Ian R. Calder ◽

Robin L. Hall ◽

Paul T.W. Rosier ◽

Heidi G. Bastable ◽

K.T. Prasanna

Keyword(s):

Stochastic Model ◽

Experimental Determination ◽

Tree Species ◽

Drop Size ◽

Tropical Tree ◽

Model Parameters ◽

Rainfall Interception ◽

Tropical Tree Species

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Influence of Downstream Distance on the Drop Size Characteristics of an Evaporative Liquid Spray in a Convective Gaseous Medium

Journal of Energy Resources Technology ◽

10.1115/1.2905923 ◽

1992 ◽

Vol 114 (1) ◽

pp. 70-74 ◽

Cited By ~ 2

Author(s):

S. P. Sengupta ◽

A. K. Mitra ◽

S. K. Dash ◽

S. K. Som

Keyword(s):

Drop Size ◽

Free Stream ◽

Axial Distance ◽

Numerical Studies ◽

Spray Axis ◽

Mean Diameter ◽

Liquid Spray ◽

Initial Drop ◽

The Mean ◽

Light Scattering Technique

Numerical studies have been made to evaluate the interdependence of drop size characteristics and evaporation histories of an atomized liquid spray in a convective medium of uniform free stream at high temperature. With the help of a discrete droplet evaporation model, both the actual drop size distribution and the apparent one, that could have been obtained in practice by light-scattering technique, have been determined numerically at different downstream locations perpendicular to the spray axis. Variations of actual and apparent mass mean diameter and the evaporation rate with the axial distance of the spray have been established. Finally, the influences of pertinent input parameters, namely, the initial Reynolds number of the spray, the ratio of free stream to initial drop temperature and the ratio of free stream to initial drop velocity on the mean diameter and evaporation histories have been recognized.

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Laboratory determination of potential interception of young deciduous trees during low-intense precipitation

Folia Forestalia Polonica ◽

10.2478/ffp-2014-0001 ◽

2014 ◽

Vol 56 (1) ◽

pp. 3-8

Author(s):

Anna Klamerus-Iwan ◽

Maciej Sporysz

Keyword(s):

Drop Size ◽

Deciduous Trees ◽

Simulated Rainfall ◽

Deciduous Species ◽

Exponential Equation ◽

Individual Level ◽

Ecological Criteria ◽

Fagus Sylvatica L ◽

Simulated Rain

Abstract The research issue focuses on potential interception, which is the maximum amount of water that can be stored on plant surface. Tests under controlled conditions remain the best way to enhance knowledge on interception determinants in forest communities. Such tests can provide data for identification of mathematical models based on ecological criteria. The study presented in this paper concerned tree interception under simulated rain in a range from 2 to 11 mm/h. To perform the experiment a set of sprinklers was designed and built. The study included two deciduous species: beech (Fagus sylvatica L.) and oak (Quercus robur L.). Descriptive characteristic and nonlinear estimation were suggested for the obtained data. Interdependence of potential interception, the intensity of rain and the size of raindrops were described using exponential equation. The intensity and drop size of simulated rainfall significantly influence the obtained values of potential interception. Data analysis shows a decrease of interception value with an increase of intensity of simulated rainfall for both analysed species. Every run of the experiment that differed in the intensity and size of raindrops reached an individual level of potential interception and time needed to realize it. The formation of ability of plants to intercept water depends both on the dynamics and the time of spraying.

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Cubic Formula for Determination of the Drop Size During Atomization of Liquid Jets in Co- and Cross-Flow of Air

Volume 8A: Heat Transfer and Thermal Engineering ◽

10.1115/imece2018-86372 ◽

2018 ◽

Author(s):

T.-W. Lee ◽

Jung Eun Park ◽

Ryoichi Kurose

Keyword(s):

Energy Balance ◽

Kinetic Energy ◽

Drop Size ◽

Cross Flow ◽

Liquid Jets ◽

Initial Kinetic Energy ◽

Practical Applications ◽

Relevant Variables ◽

Drop Size Distributions

Using the integral formulation of the conservation equations as in our previous work, we can determine the drop size and its distributions in liquid sprays in co- and cross flow of air. The energy balance dictates that the initial kinetic energy of the gas and injected liquid be distributed into the final surface tension energy, kinetic energy of the gas and droplets, and viscous dissipation incurred. The mass and energy balance for the spray flows render to an expression that relates the drop size to all of the relevant parameters, including the gas- and liquid-phase properties and velocities. The results agree well with experimental data and correlations for the drop size. The solution also provides for drop size-velocity cross-correlation, leading to drop size distributions based on the gas-phase velocity distributions. These aspects can be used in estimating the drop size for practical applications, in synthesizing the data as a function of relevant variables, and also in integration into CFD for atomization algorithm.

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Abstract 2211: Large Differences in Efficiency Among Fontan Patients Demonstrated In Patient Specific Models of Blood Flow Simulations

Circulation ◽

10.1161/circ.116.suppl_16.ii_480-b ◽

2007 ◽

Vol 116 (suppl_16) ◽

Author(s):

Alison L Marsden ◽

Adam J Bernstein ◽

Ryan L Spilker ◽

Frandics P Chan ◽

Charles A Taylor ◽

...

Keyword(s):

Patient Specific ◽

Additional Tool ◽

Flow Simulations ◽

Flow Features ◽

Computational Fluid Dynamics Simulations ◽

Diagnostic Modalities ◽

Hemodynamic Performance ◽

Dynamics Simulations ◽

Fontan Patients

Background: Not all Fontan patients are “equal” despite similar hemodynamics using current diagnostic modalities. Recent advances in imaging and computational fluid dynamics simulations (CFDS) enable the evaluation of both previously unmeasurable parameters (e.g. efficiency (either at rest or with exercise)) and in patient-specific scenarios. We hypothesize CFDS at rest and simulated exercise will demonstrate large differences in pressure and efficiency among Fontan patients. Methods: Using MRI-obtained anatomy and flow, time-dependent, 3-D simulations were performed using a custom finite element solver in 4 patient-specific Fontan models. Flow features, pressure, and energy efficiency were analyzed at rest and with increasing flow to simulate light, moderate and heavy exercise. Resistance boundary conditions enabled simulation at physiologic pressures and vasodilation with “exercise.” Results: Large variations in geometry, efficiency (96 – 87% at rest, 90–75% with exercise) and mean SVC pressure were seen (figure ). Efficiency did not correlate with Fontan pressures and did not decrease linearly with increased exercise. The most efficient among these four particular patients was a traditional t-junction connection though it had one of the highest SVC pressures. Conclusions: Geometries, efficiency and pressure levels vary dramatically among Fontan patients. Patients may have similar hemodynamic performance at rest, but large differences in both efficiency and pressure can be demonstrated during simulated exercise. CFDS and determination of patient specific efficiency may provide an additional tool for risk stratification among patients.

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