Rosin-Rammler Distribution Function Research Articles

DROPLET SIZE DISTRIBUTION VARIATION OF PENDENT FIRE SPRINKLER SPRAY DEPENDING ON THE MEASUREMENT LOCATION

Droplet size of sprinkler sprays is related to the rate of evaporation and penetration of a fire plume. However, sprinkler sprays have various droplet sizes even at one location. Therefore, it is essential to examine the droplet size distribution depending on the location to predict the fire suppression performance of the sprinkler spray. To examine the droplet size distribution of spray from a pendent sprinkler head, acrylic plates were installed around the sprinkler head and a gap was made on one side of the wall. A charge-coupled device camera was installed to capture the droplet images both on a plane parallel to the sprinkler frame arm and on a plane perpendicular to the frame arm. Droplet information was obtained by deriving the image from the brightness and gradient images extracted from the original image. Large droplets, exceeding 1.5 mm in diameter, were observed in the mainstream of the spray. The probability of observing small droplets decreased as the droplets moved downstream. Spherical droplets were observed in the mainstream of the frame arm direction, while nonspherical droplets were observed in the perpendicular direction to the frame arm because of high velocity. The number-based cumulative distribution function (CDFs) fitted using the Rosin-Rammler distribution function provided the best fitting results. The volume CDFs fitted using the Rosin-Rammler distribution function yielded acceptable adjusted R<sup>2</sup> values. In this case, the coefficient m related to D<sub>v50</sub> and the coefficient n related to the width of the distribution increased with increasing radial and vertical locations.

Stiffening effect of filler on asphalt mastic composite: A new insight based on nearest surface function

This study aims to provide a new insight into the reinforcement effect of filler on stiffness of asphalt mastic through the probability theory, nearest surface function and micromechanics. To implement the consideration of microphysical mechanisms in the stiffening behavior of asphalt mastic composite, a general methodological framework was developed. A new method to calculate the filler’s critical volume fraction (CVF) in asphalt mastic was constructed through the volume fraction of penetrable transition zone (PTZ) acting as a link. Particle size distribution (PSD) of filler was tested by a laser particle size analyzer. Asphalt mastics were fabricated with different filler concentrations. Distributions of filler particles in these mastics were tested by a scanning electron microscope. Complex stiffness moduli of asphalt binder and mastics were tested by a dynamic shear rheometer. Nearest surface distance (NSD) of filler particles in asphalt mastics was analyzed by nearest surface functions. Filler’s CVF in asphalt mastics was calculated through the constructed method. Results show that the shifted Rosin-Rammler distribution function allows to describe the PSD of filler with a high accuracy. Void nearest-surface exclusion probability of filler particles allows to represent the volume fraction of free asphalt in asphalt mastic. The larger the filler volume fraction, the higher the proportion of NSD making particles intercontact. A filler particle with larger radius has more likely to contact with other filler particles, and thus large particles tend to dominate the interparticle interaction in asphalt mastic. The mean NSD of filler particles decreases with increasing the filler volume fraction. The volume fraction of PTZ has an increased first and decreased afterwards trend with the filler volume fraction. The filler’s CVF decreases with the temperature increases. The constructed method is capable of determining the filler’s CVF in asphalt mastic.

New Insights into the Drill Cutting Characteristics and Fault Distribution in Gas-Containing Coal Seams

This study is aimed at detecting small faults in coal seams. With coal seams of different buried depths in Luling Coal Mine, Yuenan Coal Mine, and Sihe Coal Mine with obvious difference in hardness and outburst hazards selected as the research objects, the morphological characteristics of a sample particle size such as the Rosin-Rammler distribution function, average particle size, cumulative mass distribution, and mechanical parameters such as particle strength and F value were statistically analyzed through drill cuttings related to sampling points at different positions of faults already known. The results show that the effect of tectonic stress reduces the strength and permeability of the coal after the borehole enters the fault damage zone, resulting in abnormal fluctuations in the morphological characteristics of the drill cuttings. Correspondingly, large-size particles account for a high percentage. The weight analysis discloses that the characteristic particle size of the Rosin-Rammler distribution function has the greatest influence on the determination of fault existence. The analysis of drill cutting characteristics conduces to detecting the distribution of small faults, helps to improve the utilization of mine information, and is of great significance for accident prevention and control.

A Validation Study for RANS Based Modelling of Swirling Pulverized Fuel Flames

A swirling pulverized coal flame is computationally investigated. A Eulerian–Lagrangian formulation is used to describe the two-phase flow. Turbulence is modelled within a RANS (Reynolds averaged numerical simulation) framework. Four turbulence viscosity- (TV) based models, namely the standard k-ε model, realizable k-ε model, renormalization group theory k-ε model, and the shear stress transport k-ω model are used. In addition, a Reynolds stress transport model (RSM) is employed. The models are assessed by comparing the predicted velocity fields with the measurements of other authors. In terms of overall average values, the agreement of the predictions to the measurements is observed to be within the range 20–40%. A better performance of the RSM compared to the TV models is observed, with a nearly twice as better overall agreement to the experiments, particularly for the swirl velocity. In the second part of the investigation, the resolution of the discrete particle phase in modelling the turbulent particle dispersion (TPD) and particle size distribution (SD) is investigated. Using the discrete random walk model for the TPD, it is shown that even five random walks are sufficient for an accuracy that is quite high, with a less than 1% mean deviation from the solution obtained by thirty random walks. The approximation of the measured SD is determined by a continuous Rosin–Rammler distribution function, and inaccuracies that can occur in its subsequent discretization are demonstrated and discussed. An investigation on the resolution of the SD by discrete particle size classes (SC) indicates that 12 SC are required for an accuracy with a less than 1% mean deviation from the solution with 18 SC. Although these numbers may not necessarily be claimed to be sufficiently universal, they may serve as guidance, at least for SD with similar characteristics.

Study on Size Distribution and Flow Characteristics of Condensed Products in Solid Rocket Motor

The size distribution of condensed products during the combustion of aluminized propellants and flow characteristics of the gas-solid two-phase flow in solid rocket motor were studied in this paper. Firstly, based on the laser scattering technology, an online detection system for condensed products in plume was established, and the size detection of condensed products in the plume of solid rocket motor is carried out. Secondly, a numerical model of two-phase flow in solid rocket motor is established by combining the real size distribution of products in the plume with discrete phase model through the Rosin-Rammler distribution function. Besides, numerical simulation research is carried out under the same experimental conditions, focusing on the influence of condensed products with real size on the characteristics of solid rocket motor. The results show that the innovation measurement system can be used to obtain the size distribution characteristic of condensed products in the plume. At the particle size of stable stage, the mean size, D v 50 , is 104 μm, which is the smallest among all stages. It is also suggested that condensed products at the end stage have the most impact on the flow behavior in solid rocket motor, in that the shock structure, Mach number, and temperature distribution in the near field of plume are significantly changed.

Rock Fragmentation Size Distribution Prediction and Blasting Parameter Optimization Based on the Muck-Pile Model

Rock fragmentation size distribution is often used as an important index to account for the blasting effect because it directly affects the subsequent loading, transportation, and secondary crushing. Due to the mismatching of explosive and rock wave impedance, high boulder yield often occurs which affects the blasting effect. In this study, methods of measuring rock acoustic impedance, rock strength point loading, and detonation wave velocity have been used to obtain more accurate input parameters. Then, in the watershed image segmentation technique, the Gates-Gaudin-Schuhmann and Rosin-Rammler distribution functions have been used to analyze and quantitatively describe the rock fragmentation size distribution in the existing muck-pile. Finally, taking the rock properties, explosive performance, blasting parameters, and system characteristic variable into consideration, support vector machine (SVM) regression model has been analyzed on the learning and prediction of samples. The results show that SVM has a good prediction accuracy, high precision, and strong generalization ability. The optimized matching coefficient of rock and explosive wave impedance K ranges from 2.50 to 2.58 times. This study has developed a series of simple, accurate methods for rock properties analysis, detonation wave velocity measurement, and muck-pile model image processing, and a basis for predicting and evaluating rock fragmentation size distribution and optimizing the matching coefficient before carrying out a blasting operation.

Bubble diameter distribution and intergroup mass transfer coefficient in flows with phase change

The intergroup mass transfer term is investigated in the multigroup two-fluid model. Past intergroup mass transfer modeling is thoroughly reviewed, highlighting the limited applicability to phase-change flows due to the closure need of the intergroup mass transfer coefficient. The intergroup mass transfer coefficient is dependent on the bubble diameter distribution. The backward transform method, which is used to transform chord length distribution data to a bubble diameter distribution, is improved with a new regularization strategy which can better reduce the inherent instability of the inverse problem. Experimental data from phase-change flows are processed with the modified backward transform method to evaluate the bubble distribution and to determine the intergroup mass transfer coefficient. Analytical correlations for the intergroup mass transfer coefficient are developed, employing the Nukiyama-Tanasawa distribution function and the Rosin-Rammler distribution function. The benchmark with the experimental data demonstrates that the new correlations for the intergroup mass transfer coefficient are accurate over a wide range of two-phase flow conditions. In addition, a new empirical correlation for the intergroup mass transfer coefficient is developed from a regression of the experimental data.

An experimental study on oil droplet size distribution in subsurface oil releases

Oil droplet size distribution (ODSD) plays a critical role in the rising velocity and transport of oil droplets in subsurface oil releases. In this paper, subsurface oil release experiments were conducted to study ODSD under different experimental conditions in a laboratory water tank observed by two high-speed cameras in March and April 2017. The correlation formulas Oh=10.2Re–1 and Oh=39.2Re–1 (Re represents Reynolds number and Oh represents Ohnesorge number) were established to distinguish the boundaries of the three instability regimes in dimensionless space based on the experimental results. The oil droplet sizes from the experimental data showed an excellent match to the Rosin–Rammler distribution function with determination coefficients ranging from 0.86 to 1.00 for Lvda 10-1 oil. This paper also explored the influence factors on and change rules of oil droplet size. The volume median diameter d50 decreased steadily with increasing jet velocity, and a sharp decrease occurred in the laminar-breakup regime. At Weber numbers (We) <100, the orifice diameter and oil viscosity appeared to have a large influence on the mean droplet diameter. At 100<We<1 000, the oil viscosity appeared to have a larger influence on the relative mean droplet diameter.

Modelling of bio-oil steam gasification in a fluidized bed reactor

This paper reports a three-dimensional CFD model for bio-oil gasification in a fluidized bed reactor. The model considered three-phase hydrodynamics, heat and mass transfer, bio-oil atomization, spray droplet vaporization and thermal decomposition in gas–solid flow. It employed a Euler-Lagrange method, in which gas and solid flow were solved using the Eulerian method and the bio-oil droplets were tracked using the Lagrangian approach. Droplet trajectory was calculated via equation of motion using discrete phase model in the Lagrangian frame, considering the interactions with flow field. Experimental data were obtained for bio-oil injection characteristics and simulations were conducted for generating the Rosin-Rammler distribution function under different injection conditions. As the droplets were injected into a fluidised-bed reactor, the depletion in bio-oil droplet size as a result of evaporation could not be described by the D2-law due to the complex composition of bio-oil. Spray penetration into the reactor increased substantially with increasing droplet size. The predictions from the CFD model for bio-oil steam gasification were in good agreement with the experimental data available in the literature, in terms of cold gas efficiency (CGE) and syngas compositions at various bed temperatures, steam-carbon molar ratios and methane equivalent gas hourly space velocity (GC1HSV) of feed. Sensitivity analyses on these key process parameters were also carried out.

Comparison of two analysis methods on bubble size distribution

The object of this work was to analyze foam bubbles’ diameter distribution. Firstly, Rosin-Rammler distribution function was used in bubble size analysis in some studies. This Rosin-Rammler distribution function should be modified to fit foam bubbles distribution curve. Secondly, coefficient of variation value was introduced in our study. This analysis method could be carried out directly without any modification. Thirdly, these two methods were compared whose characteristics were analyzed. Both analysis methods were effective to analyze foam bubbles figures with relatively obvious difference.

Numerical investigation of spray characteristics of an air-blast atomizer with dynamic mesh

In this paper, a numerical simulation of an air-blast atomizer using OpenFOAM software is performed to evaluate the effects of geometrical parameters and flow conditions on spray characteristics. The method used in this numerical simulation is discrete droplets tracking-based Eulerian–Lagrangian approach. In the primary breakup of liquid jet modeling, the Rosin–Rammler distribution function and in modeling the secondary breakup phase, the Kelvin–Helmholtz, Rayleigh–Taylor (KHRT), and the TAB models are used and compared. The simulation results show that the KHRT model has reasonable prediction of atomization characteristics and, at a specific Weber number, SMD increases with raising liquid port diameter. However, in high Weber number, this parameter has little effect on SMD. In addition, gas–liquid injection angle has an insignificant effect on the penetration depth of spray, while increasing the liquid port diameter decreases it considerably.

An engineering approach to design of dextran microgels size fabricated by water/oil emulsification

A correlation, based on fluid mechanics, has been investigated for the mean particle diameter of crosslinked dextran microgels (CDMs) prepared via a water/oil emulsification methodology conducted in a single-stirred vessel. To this end, non-dimensional correlations were developed to predict the mean particle size of CDMs as a function of Weber number, Reynolds number and viscosity number similar to ones introduced for liquid–liquid dispersions. Moreover, a Rosin–Rammler distribution function has been successfully applied to the microgel particle size distributions. The correlations were validated using experimentally obtained mean particle sizes for CDMs prepared at different stirring conditions. The validated correlation is especially applicable to medical and pharmaceutical applications where strict control on the mean particle size and size distribution of CDMs are extremely essential.

Development of the Kuz-Ram Model to Blasting in a Limestone Quarry/Opracowanie Modelu Kuz-Ram Do Wykorzystania Przy Pracach Strzałowych W Kopalni Wapienia

Abstract It is very important to know the degree of disintegration beforehand in open quarry bench blasting in terms of blasting efficiency. Kuznetsov (1973), Cunningham (1987), and Ouchterlony (2005) have developed the Rosin-Rammler distribution function for estimating the degrees of fragmentation (Rosin &amp; Rammler, 1933). However, models they developed do not give realistic results for blast surfaces where there are a lot of discontinuity characteristics with broken and fissured areas due to the difference in structural characteristics of the rocks. In this study, average fragmentative distribution of the heap formed as a result of several blasting tests in a quarry belonging to BATIÇİM have been separately determined by using a dimensional analysis program with Wipfrag image processing technique and Kuz-Ram estimation model. Average granular size correction has been carried out with the approach of accepting as fine-grain the areas that couldn’t be determined by means of image analysis programs and that were neglected in the analysis. Subsequently, the land coefficient in Kuz-Ram model was determined to be 0.0383 rather than 0.06 for the said quarry by taking the average dimension values determined by Wipfrag method as reference point.

Particle Size Distribution of Brown and White Rice during Gastric Digestion Measured by Image Analysis

The particle size distribution of foods during gastric digestion indicates the amount of physical breakdown that occurred due to the peristaltic movement of the stomach walls in addition to the breakdown that initially occurred during oral processing. The objective of this study was to present an image analysis technique that was rapid, simple, and could distinguish between food components (that is, rice kernel and bran layer in brown rice). The technique was used to quantify particle breakdown of brown and white rice during gastric digestion in growing pigs (used as a model for an adult human) over 480 min of digestion. The particle area distributions were fit to a Rosin-Rammler distribution function. Brown and white rice exhibited considerable breakdown as the number of particles per image decreased over time. The median particle area (x(50)) increased during digestion, suggesting a gastric sieving phenomenon, where small particles were emptied and larger particles were retained for additional breakdown. Brown rice breakdown was further quantified by an examination of the bran layer fragments and rice grain pieces. The percentage of total particle area composed of bran layer fragments was greater in the distal stomach than the proximal stomach in the first 120 min of digestion. The results of this study showed that image analysis may be used to quantify particle breakdown of a soft food product during gastric digestion, discriminate between different food components, and help to clarify the role of food structure and processing in food breakdown during gastric digestion.

보통 포틀랜드 시멘트 페이스트의 유동특성에 미치는 석회석 미분말의 영향

This study examines the effects of limestone’s factors on the fluidity of cement paste when of up to 15%. As the substitution ratio of limestone powder increases, the fluidity of the paste is also improved; however, it has no correlation to the CaCO3 content of the limestone, fineness of the limestone, and fluidity of the pastes. Regardless of clay content of the limestone, it showed a similar mini-slump, so there was no correlation between the clay content and the fluidity of the paste. Also, the total organic carbon content of the limestone and the fluidity of the paste showed no correlation. Regardless of the limestone’s grade or fineness, n value of powder gained by using the Rosin-Rammler distribution function showed that the fluidity of the paste increased as the n value reduced. It was also shown that particle size distribution of ordinary Portland cement with limestone powder had a major effect on the fluidity of the paste.

Experimental measurement of cooling tower emissions using image processing of sensitive papers

Cooling tower emissions are harmful for several reasons such as air polluting, wetting, icing and solid particle deposition, but mainly due to human health hazards (i.e. Legionella). There are several methods for measuring drift drops. This paper is focussed on the sensitive paper technique, which is suitable in low drift scenarios and real conditions. The lack of an automatic classification method motivated the development of a digital image process algorithm for the Sensitive Paper method. This paper presents a detailed description of this method, in which, drop-like elements are identified by means of the Canny edge detector combined with some morphological operations. Afterwards, the application of a J48 decision tree is proposed as one of the most relevant contributions. This classification method allows us to discern between stains whose origin is a drop and stains whose origin is not a drop. The method is applied to a real case and results are presented in terms of drift and PM10 emissions. This involves the calculation of the main features of the droplet distribution at the cooling tower exit surface in terms of drop size distribution data, cumulative mass distribution curve and characteristic drop diameters. The Log-normal and the Rosin–Rammler distribution functions have been fitted to the experimental data collected in the tests and it can been concluded that the first one is the most suitable for experimental data among the functions tested (whereas the second one is less suitable). Realistic PM10 calculations include the measurement of drift emissions and Total Dissolved Solids as well as the size and number of drops. Results are compared to the method proposed by the U.S. Environmental Protection Agency assessing its overestimation. Drift emissions have found to be 0.0517% of the recirculating water, which is over the Spanish standards limit (0.05%).

Fabrication and characterisation of 2NDPA-loaded poly(lactide-co-glycolide) (PLG) microspheres for explosive safety

We demonstrate the microencapsulation of a double-base (DB) rocket propellant stabiliser, 2-nitrodiphenylamine (2-NDPA), that can potentially increase the shelf life of DB rocket propellants. Poly(lactide-co-glycolide) (PLG) microspheres loaded with 2-NDPA were prepared using the oil-in-water emulsion technique. The microsphere size was found to be inversely related to the mixing rate. It was also found that a higher theoretical loading of 2-NDPA resulted in larger microspheres. In addition, a Rosin Rammler distribution function gave an accurate representation of the microsphere size distribution, and the release rate 2-NDPA from PLG microspheres was found to be size dependent. We show that parameters such as the stirring speed and the percent loading of 2-NDPA can be varied to tailor the release of 2-NDPA from PLG microspheres. In addition, we have shown that temperature has a dramatic effect on the release of 2-NDPA from PLG microcapsules.

Measurement of drop size characteristics in annular centrifugal extractors using phase Doppler particle analyzer (PDPA)

Drop size distributions have been measured in a 39mm annular centrifugal extractor using phase Doppler particle analyzer (PDPA). The power consumption and the interfacial tension have been varied in the range of 10–450kW/m3 and 13–33mN/m, respectively. The two liquid phases have been selected with different density and viscosity ratios. The results have been analyzed using Rosin–Rammler distribution function. A correlation has been developed for the drop size distribution. The same has been compared with the correlations in the literature.

CFD modeling of droplet dispersion in a Venturi scrubber

A modified two-dimensional mathematical model was developed to simulate droplet dispersion through a cylindrical Venturi scrubber based on Eulerian approach. Droplet concentration distribution was evaluated using the equation of mass balance of droplets. The velocity field of gas flow was determined using k– ɛ turbulence model. Droplet velocity distribution was calculated by means of the equations derived using momentum balance of droplets. Gas eddy diffusivity which has already been determined based on constant Peclet number in the previous models was calculated using turbulent characteristic velocity and length. Fathikalajahi et al. approach was applied to calculate eddy diffusivity of droplets (Fathikalajahi et al., 1995 [7]). The mean diameter of generated droplets was determined by Boll's correlation (Boll et al., 1974 [16]). Rosin–Rammler distribution function was used to take into account the distribution of droplet size. In order to verify the results of the new model a set of experiments was performed on a pilot-scale cylindrical Venturi scrubber with axial liquid injection. During these experiments, the flow rates of liquid droplets were measured at several points of throat section end from center line to the wall. The comparison between the results and experimental data showed that the droplet concentration distribution predicted using the present model were in better agreement with experimental data than that predicted using the previous models which were based on constant Peclet number. Also it was concluded the distribution parameter of Rosin–Rammler function, n RR , could not be considered as a constant parameter and it depended on the L/ G (gas to liquid flow rate ratio) and V g0 (gas throat velocity).

Modified Kuz—Ram fragmentation model and its use at the Sungun Copper Mine

Rock fragmentation, which is the fragment size distribution of blasted rock, is one of the most important indices for estimating the effectiveness of blast work. In this paper a new form of the Kuz—Ram model is proposed in which a prefactor of 0.073 is included in the formula for prediction of X 50. This new equation has a correlation coefficient that is greater than 0.98. In addition, a new approach is proposed to calculate the Uniformity Index, n. A Blastability Index ( BI) is used to correct the calculation of the Uniformity Index of Cunningham, where BI reflects the uniformity of the distribution. Interestingly, this correction also can be observed in the Kuznetsov—Cunningham—Ouchterlony (KCO) model, which uses In situ block size as a parameter for calculating the curve-undulation in the Swebrec function. However, it is in contrast to prediction of X 50 as the central parameter in Swebrec and Rosin–Rammler distribution functions. The new model is a two parameter fragmentation size distribution that can be easily determined in the field. However, it does not consider the timing effect, or upper limit for sizes, as does the original Kuz—Ram model. The model is used at the Sungun Mine, and it does a good job of predicting the fines produced during blasting.