Determination of the Drop Size During Air-Blast Atomization

2019 ◽  
Vol 141 (12) ◽  
Author(s):  
T.-W. Lee ◽  
J. E. Park
Keyword(s):  
Kinetic Energy ◽  
Viscous Dissipation ◽  
High Speed ◽  
Drop Size ◽  
Integral Form ◽  
Initial Kinetic Energy ◽  
Air Blast ◽  
Dissipation Term ◽  
Wide Range ◽  
Drop Size Distributions

We have used the integral form of the conservation equations, to find a cubic formula for the drop size during in liquid sprays in coflow of air (air-blast atomization). Similar to our previous work, the energy balance dictates that the initial kinetic energy of the gas and injected liquid will be distributed into the final surface tension energy, kinetic energy of the gas and droplets, and viscous dissipation. Using this approach, the drop size can be determined based on the basic injection and fluid parameters for “air-blast” atomization, where the injected liquid is atomized by high-speed coflow of air. The viscous dissipation term is estimated using appropriate velocity and length scales of liquid–air coflow breakup. The mass and energy balances 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 velocities and fluid properties. 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 computed drop size distributions based on the gas-phase velocity distribution. This approach can be used in the estimation of the drop size for practical sprays and also as a primary atomization module in computational simulations of air-blast atomization over a wide range of injection and fluid conditions, the only caveat being that a parameter to account for the viscous dissipation needs to be calibrated with a minimal set of observational data.

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

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.

Fuel Leaking Analysis of Fuel Tank by Projectiles Impact with Mechanical Properties of Projectiles

2013 ◽  
Vol 644 ◽  
pp. 203-206
Author(s):  
Hai Liang Cai ◽  
Bi Feng Song ◽  
Yang Pei ◽  
Shuai Shi
Keyword(s):  
High Speed ◽  
Drop Size ◽  
Fuel Tank ◽  
Size Distributions ◽  
Sauter Mean Diameter ◽  
Fuel Droplets ◽  
High Speed Impact ◽  
Fuel Tanks ◽  
Rigid Projectile ◽  
Drop Size Distributions

For making sure the dry bay ignition and fire, it’s necessary to calculate the number and the sizes of the droplets and determine the mass flow rate of the fuel induced by high-speed impact and penetration of a rigid projectile into fuel tank. An analytical model is founded and the method for calculating the initial leaking velocity of the fuel is determined. It gives the equation for calculating the drop size distributions of fuel and the Sauter mean diameter (SMD) of droplets, through the Maximum Entropy Theory and the conservation for mass. Using the Harmon’s equation for SMD,the fuel droplets SMD can be calculated. Results shows that the initial leaking velocity of the fuel is about linearly increasing with the velocity of the projectile, the SMD of fuel droplets increases with the hole size of the fuel tank which induced by the penetration of the projectile and linearly decreases with the velocity of the projectile. The results can be used for the ignition and fire analysis of the dry bay adjacent to fuel tanks.

Variability in Rainfall and Kinetic Energy across scales of measurement: evaluation using disdrometers in Paris region

2020 ◽  
Author(s):  
Jerry Jose ◽  
Auguste Gires ◽  
Daniel Schertzer ◽  
Yelva Roustan ◽  
Anne Ruas ◽  
...  
Keyword(s):  
Kinetic Energy ◽  
Strong Dependence ◽  
Rainfall Data ◽  
Measurement Scales ◽  
Scale Invariant ◽  
Fall Velocity ◽  
Wide Range ◽  
Paris Area ◽  
Scales Of Measurement ◽  
Drop Size Distributions

<p>To calculate the effect of rainfall in detaching particles and initiating soil erosion, it is important to represent relationship between recorded drop size distributions (DSD) and fall velocity across various scales of measurement. Commonly used relationships between kinetic energy (KE) and rainfall rate (R) exhibit strong dependence on the temporal resolution at which analysis is carried out. Here we aim at developing a scale invariant relationship relying on the framework of Universal Multifractals (UM), which has been widely used to analyze and characterize geophysical fields that exhibit extreme variability over measurement scales.</p><p>Rainfall data is collected using three optical disdrometers working on different underlying technologies (one Campbell Scientific PWS100 and two OTT Parsivel2 instruments) and operated by Hydrology, Meteorology, and Complexity laboratory of École des Ponts ParisTech in the Paris area (France). They provide access to the size and velocity of drops falling through sampling areas of few tens of cm<sup>2</sup>. Such data enables estimation of rainfall microphysics, R and KE at various resolutions. The temporal variation of this geophysical data over wide range of scales is then characterized in the UM framework. A power law relation has been developed for describing the dependence of KE on R. The developed equation using scale invariant features of UM are valid not only at a single scale, but also across scales. The amount of uncertainty is further characterized by comparing actual data with simulated rainfall data from Sense-City climate chamber.</p><p>Keywords: rainfall intensity; rainfall kinetic energy; disdrometer; multi fractal; scale invariant</p>

Maximum Spread of Droplet on Solid Surface: Low Reynolds and Weber Numbers

2010 ◽  
Vol 132 (6) ◽  
Author(s):  
Ri Li ◽  
Nasser Ashgriz ◽  
Sanjeev Chandra
Keyword(s):  
Kinetic Energy ◽  
Viscous Dissipation ◽  
Theoretical Study ◽  
Control Volume ◽  
Reynolds Numbers ◽  
Solid Surfaces ◽  
Initial Kinetic Energy ◽  
Spherical Cap ◽  
Fundamental Physics ◽  
Single Droplets

This theoretical study proposes an analytical model to predict the maximum spread of single droplets on solid surfaces with zero or low Weber and Reynolds numbers. The spreading droplet is assumed as a spherical cap considering low impact velocities. Three spreading states are considered, which include equilibrium spread, maximum spontaneous spread, and maximum spread. Energy conservation is applied to the droplet as a control volume. The model equation contains two viscous dissipation terms, each of which has a defined coefficient. One term is for viscous dissipation in spontaneous spreading and the other one is for viscous dissipation of the initial kinetic energy of the droplet. The new model satisfies the fundamental physics of drop-surface interaction and can be used for droplets impacting on solid surfaces with or without initial kinetic energy.

Examination of the μ–Λ Relation Suggested for Drop Size Distribution Parameters

2007 ◽  
Vol 24 (5) ◽  
pp. 847-855 ◽  
Author(s):  
Dmitri N. Moisseev ◽  
V. Chandrasekar
Keyword(s):  
Gamma Distribution ◽  
Method Of Moments ◽  
Drop Size ◽  
Size Distributions ◽  
Data Filtering ◽  
Wide Range ◽  
Distribution Parameters ◽  
Raindrop Size ◽  
Drop Size Distributions ◽  
Physical Correlations

Abstract Raindrop size distributions are often assumed to follow a three-parameter gamma distribution. Since rain intensity retrieval from radar observations is an underdetermined problem, there is great interest in finding physical correlations between the parameters of the gamma distribution. One of the more common approaches is to measure naturally occurring drop size distributions (DSDs) using a disdrometer and to find DSD parameters by fitting a gamma distribution to these observations. Often the method of moments is used to retrieve the parameters of a gamma distribution from disdrometer observations. In this work the effect of the method of moments and data filtering on the relation between the parameters of the DSD is investigated, namely, the shape μ and the slope Λ parameters. For this study the disdrometer observations were simulated. In these simulations the gamma distribution parameters Nw, D0, and μ were randomly selected from a wide range of values that are found in rainfall. Then, using simulated disdrometer measurements, DSD parameters were estimated using the method of moments. It is shown that the statistical errors associated with data filtering of disdrometer measurements might produce a spurious relation between μ and Λ parameters. It is also shown that three independent disdrometer measurements can be used to verify the existence of such a relation.

scholarly journals An assessment of the laminar kinetic energy concept for the prediction of high-lift, low-Reynolds number cascade flows

2011 ◽  
Vol 225 (7) ◽  
pp. 995-1003 ◽  
Author(s):  
R Pacciani ◽  
M Marconcini ◽  
A Arnone ◽  
F Bertini
Keyword(s):  
Reynolds Number ◽  
Kinetic Energy ◽  
High Speed ◽  
Low Reynolds Number ◽  
Flow Region ◽  
Freestream Turbulence ◽  
High Lift ◽  
Numerical Predictions ◽  
Wide Range ◽  
Low Reynolds

The laminar kinetic energy (LKE) concept has been applied to the prediction of low-Reynolds number flows, characterized by separation-induced transition, in high-lift airfoil cascades for aeronautical low-pressure turbine applications. The LKE transport equation has been coupled with the low-Reynolds number formulation of the Wilcox's k − ω turbulence model. The proposed methodology has been assessed against two high-lift cascade configurations, characterized by different loading distributions and suction-side diffusion rates, and tested over a wide range of Reynolds numbers. The aft-loaded T106C cascade is studied in both high- and low-speed conditions for several expansion ratios and inlet freestream turbulence values. The front-loaded T108 cascade is analysed in high-speed, low-freestream turbulence conditions. Numerical predictions with steady inflow conditions are compared to measurements carried out by the von Kármán Institute and the University of Cambridge. Results obtained with the proposed model show its ability to predict the evolution of the separated flow region, including bubble-bursting phenomenon and the formation of open separations, in high-lift, low-Reynolds number cascade flows.

Dynamical similarity and universality of drop size and velocity spectra in sprays

2018 ◽  
Vol 860 ◽  
pp. 510-543 ◽  
Author(s):  
K. Dhivyaraja ◽  
D. Gaddes ◽  
E. Freeman ◽  
S. Tadigadapa ◽  
M. V. Panchagnula
Keyword(s):  
Nozzle Exit ◽  
High Speed ◽  
Drop Size ◽  
Residual Effect ◽  
Liquid Sheet ◽  
Mathematical Form ◽  
High Speed Imaging ◽  
Size Spectra ◽  
Wide Range ◽  
Velocity Spectra

Sprays are a class of multiphase flows which exhibit a wide range of drop size and velocity scales spanning several orders of magnitude. The objective of the current work is to experimentally investigate the prospect of dynamical similarity in these flows. We are also motivated to identify a choice of length and time scales which could lead towards a universal description of the drop size and velocity spectra. Towards this end, we have fabricated a cohort of geometrically similar pressure swirl atomizers using micro-electromechanical systems (MEMS) as well as additive manufacturing technology. We have characterized the dynamical characteristics of the sprays as well as the drop size and velocity spectra (in terms of probability density functions, p.d.f.s) over a wide range of Reynolds ($Re$) and Weber numbers ($We$) using high-speed imaging and phase Doppler interferometry, respectively. We show that the dimensionless Sauter mean diameter ($D_{32}$) scaled to the boundary layer thickness in the liquid sheet at the nozzle exit ($\unicode[STIX]{x1D6FF}_{o}$) exhibits self-similarity in the core region of the spray, but not in the outer zone. In addition, we show that global drop size spectra in the sprays show two distinct characteristics. The spectra from varying $Re$ and $We$ collapse onto a universal p.d.f. for drops of size $x$ where $x/\unicode[STIX]{x1D6FF}_{o}>1$. For $x/\unicode[STIX]{x1D6FF}_{o}<1$, a residual effect of $Re$ and $We$ persists in the size spectra. We explain this characteristic by the fact that the physical mechanisms that cause large drops is different from that which is responsible for the small drops. Similarly, with the liquid sheet velocity at the nozzle exit ($u_{s}$) as the choice of velocity scale, we show that drops moving with a velocity $u$ such that $u/u_{s}<1$ collapse onto a universal p.d.f., while drops with $u/u_{s}>1$ exhibit a residual effect of $Re$ and $We$. From these observations, we suggest that physically accurate models for drop size and velocity spectra should rely on piecewise descriptions of the p.d.f. rather than invoking a single mathematical form for the entire distribution. Finally, we show from a dynamical modal analysis that the conical liquid sheet flapping characteristics exhibit a sharp transition in Strouhal number ($St$) at a critical $Re$.

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

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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