Unsteady sheet fragmentation: droplet sizes and speeds

2018 ◽  
Vol 848 ◽  
pp. 946-967 ◽  
Author(s):  
Y. Wang ◽  
L. Bourouiba
Keyword(s):  
Drop Size ◽  
Size Distributions ◽  
Single Drop ◽  
Population Mean ◽  
Droplet Sizes ◽  
Precision Tracking ◽  
Drop Size Distributions ◽  
Detachment Time ◽  
Ligament Size ◽  
Comparable Size

Understanding what shapes the drop size distributions produced from fluid fragmentation is important for a range of industrial, natural and health processes. Gilet & Bourouiba (J. R. Soc. Interface, vol. 12, 2015, 20141092) showed that both the size and speed of fragmented droplets are critical to transmission of pathogens in the agricultural context. In this paper, we study both the size and speed distributions of droplets ejected during a canonical unsteady sheet fragmentation from drop impact on a target of comparable size to that of the drop. Upon impact, the drop transforms into a sheet which expands in the air bounded by a rim on which ligaments grow, continuously shedding droplets. We developed high-precision tracking algorithms that capture all ejected droplets, measuring their size and speed, as well as the detachment time from, and link to, their ligament of origin. Both size and speed distributions of all ejected droplets are skewed. We show that the polydispersity and skewness of the distributions are inherently due to the unsteadiness of the sheet expansion. We show that each ligament sheds a single drop at a time throughout the entire sheet expansion by a mechanism of end-pinching. The droplet-to-ligament size ratio $R\approx 1.5$ remains constant throughout the unsteady fragmentation, and is robust to change in impact Weber number. We also show that the population mean speed of the fragmented droplets at a given time is equal to the population mean speed of ligaments one necking time prior to detachment time.

Experimental Study of Binary Drop Collisions for Drops of Greatly Unequal Size

2007 ◽  
Author(s):  
S. L. Post ◽  
A. M. Hales
Keyword(s):  
Drop Size ◽  
Size Distributions ◽  
Liquid Drops ◽  
High Injection ◽  
Order Of Magnitude ◽  
Water Drops ◽  
Drop Collision ◽  
The Mean ◽  
Drop Size Distributions ◽  
Comparable Size

The collisions and coalescence of liquid drops is important in many spraying applications. Those sprays with high injection velocities tend to generate a very turbulent flow field, which induces relative velocities between the spray drops leading to collisions. If those collisions result in frequent coalescence, this will increase the mean drop size of the spray and reduce the overall vaporization rate, and generally result in poorer spray performance. Multi-dimensional spray simulation codes are commonly used in computational simulations of spray. These codes have sub-models for the drop collision rate and coalescence efficiency. The model that is most commonly used for the coalescence efficiency was developed more than thirty years ago, and was validated with binary drop collision experiments for water drops of comparable size to each other. This model is used in simulations with many different spray liquids, and in sprays that have a wide drop size distributions. The experimental results presented here show that the commonly used model is not valid for collisions between drops whose sizes differ by an order of magnitude.

Drop-size distributions from pneumatic atomizers

AIChE Journal ◽  
1971 ◽  
Vol 17 (3) ◽  
pp. 575-584 ◽  
Author(s):  
K. Y. Kim ◽  
W. R. Marshall
Keyword(s):  
Drop Size ◽  
Size Distributions ◽  
Drop Size Distributions

scholarly journals Raindrop Size Distribution and Rain Characteristics during the 2013 Great Colorado Flood

2015 ◽  
Vol 17 (1) ◽  
pp. 53-72 ◽  
Author(s):  
Katja Friedrich ◽  
Evan A. Kalina ◽  
Joshua Aikins ◽  
Matthias Steiner ◽  
David Gochis ◽  
...  
Keyword(s):  
Drop Size ◽  
Doppler Radar ◽  
Liquid Water Content ◽  
Size Distributions ◽  
Intense Rainfall ◽  
Wind Fields ◽  
Raindrop Size Distribution ◽  
Median Volume ◽  
Drop Size Distributions ◽  
Analysis System

Abstract Drop size distributions observed by four Particle Size Velocity (PARSIVEL) disdrometers during the 2013 Great Colorado Flood are used to diagnose rain characteristics during intensive rainfall episodes. The analysis focuses on 30 h of intense rainfall in the vicinity of Boulder, Colorado, from 2200 UTC 11 September to 0400 UTC 13 September 2013. Rainfall rates R, median volume diameters D0, reflectivity Z, drop size distributions (DSDs), and gamma DSD parameters were derived and compared between the foothills and adjacent plains locations. Rainfall throughout the entire event was characterized by a large number of small- to medium-sized raindrops (diameters smaller than 1.5 mm) resulting in small values of Z (<40 dBZ), differential reflectivity Zdr (<1.3 dB), specific differential phase Kdp (<1° km−1), and D0 (<1 mm). In addition, high liquid water content was present throughout the entire event. Raindrops observed in the plains were generally larger than those in the foothills. DSDs observed in the foothills were characterized by a large concentration of small-sized drops (d < 1 mm). Heavy rainfall rates with slightly larger drops were observed during the first intense rainfall episode (0000–0800 UTC 12 September) and were associated with areas of enhanced low-level convergence and vertical velocity according to the wind fields derived from the Variational Doppler Radar Analysis System. The disdrometer-derived Z–R relationships reflect how unusual the DSDs were during the 2013 Great Colorado Flood. As a result, Z–R relations commonly used by the operational NEXRAD strongly underestimated rainfall rates by up to 43%.

scholarly journals On the Shape–Slope Relation of Drop Size Distributions in Convective Rain

2005 ◽  
Vol 44 (7) ◽  
pp. 1146-1151 ◽  
Author(s):  
Axel Seifert
Keyword(s):  
Size Distribution ◽  
Gamma Distribution ◽  
Drop Size ◽  
Empirical Relation ◽  
Size Distributions ◽  
Shape Parameters ◽  
Raindrop Size Distribution ◽  
Raindrop Size ◽  
Drop Size Distributions ◽  
Good Agreement

Abstract The relation between the slope and shape parameters of the raindrop size distribution parameterized by a gamma distribution is examined. The comparison of results of a simple rain shaft model with an empirical relation based on disdrometer measurements at the surface shows very good agreement, but a more detailed discussion reveals some difficulties—for example, deviations from the gamma shape and the overestimation of collisional breakup.

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.

scholarly journals Modeling the Variability of Drop Size Distributions in Space and Time

2007 ◽  
Vol 46 (6) ◽  
pp. 742-756 ◽  
Author(s):  
Gyu Won Lee ◽  
Alan W. Seed ◽  
Isztar Zawadzki
Keyword(s):  
Drop Size ◽  
Temporal Structure ◽  
Space Time ◽  
Cascade Model ◽  
Time Variability ◽  
Size Distributions ◽  
Precipitation Field ◽  
Stochastic Fluctuations ◽  
Taylor Hypothesis ◽  
Drop Size Distributions

Abstract The information on the time variability of drop size distributions (DSDs) as seen by a disdrometer is used to illustrate the structure of uncertainty in radar estimates of precipitation. Based on this, a method to generate the space–time variability of the distributions of the size of raindrops is developed. The model generates one moment of DSDs that is conditioned on another moment of DSDs; in particular, radar reflectivity Z is used to obtain rainfall rate R. Based on the fact that two moments of the DSDs are sufficient to capture most of the DSD variability, the model can be used to calculate DSDs and other moments of interest of the DSD. A deterministic component of the precipitation field is obtained from a fixed R–Z relationship. Two different components of DSD variability are added to the deterministic precipitation field. The first represents the systematic departures from the fixed R–Z relationship that are expected from different regimes of precipitation. This is generated using a simple broken-line model. The second represents the fluctuations around the R–Z relationship for a particular regime and uses a space–time multiplicative cascade model. The temporal structure of the stochastic fluctuations is investigated using disdrometer data. Assuming Taylor hypothesis, the spatial structure of the fluctuations is obtained and a stochastic model of the spatial distribution of the DSD variability is constructed. The consistency of the model is validated using concurrent radar and disdrometer data.

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