A numerical study of the particle size distribution of an aerosol undergoing turbulent coagulation

2000 ◽  
Vol 415 ◽  
pp. 45-64 ◽  
Author(s):  
WALTER C. READE ◽  
LANCE R. COLLINS
Keyword(s):  
Particle Size ◽  
Standard Deviation ◽  
Particle Size Distribution ◽  
Size Distribution ◽  
Radial Distribution ◽  
Isotropic Turbulence ◽  
Numerical Study ◽  
Functional Dependence ◽  
Stokes Number ◽  
Final Particle

Coagulation and growth of aerosol particles subject to isotropic turbulence has been explored using direct numerical simulations. The computations follow the trajectories of 262 144 initial particles as they are convected by the turbulent flow field. Collision between two parent particles leads to the formation of a new daughter particle with the mass and momentum (but not necessarily the energy) of the parent particles. The initially monodisperse population of particles will develop a size distribution over time that is controlled by the collision dynamics. In an earlier study, Sundaram & Collins (1997) showed that collision rates in isotropic turbulence are controlled by two statistics: (i) the radial distribution of the particles and (ii) the relative velocity probability density function. Their study considered particles that rebound elastically; however, we find that the formula that they derived is equally valid in a coagulating system. However, coagulation alters the numerical values of these statistics from the values they attain for the elastic rebound case. This difference is substantial and must be taken into consideration to properly predict the evolution of the size distribution of a population of particles. The DNS results also show surprising trends in the relative breadth of the particle size distribution. First, in all cases, the standard deviation of the particle size distribution of particles with finite Stokes numbers is much larger than the standard deviation for either the zero-Stokes-number or infinite-Stokes-number limits. Secondly, for particles with small initial Stokes numbers, the standard deviation of the final particle size distribution decreases with increasing initial particle size; however, the opposite trend is observed for particles with slightly larger initial Stokes numbers. An explanation for these phenomena can be found by carefully examining the functional dependence of the radial distribution function on the particle size and Stokes number.

scholarly journals Grinding Kinetics of Slag and Effect of Final Particle Size on the Compressive Strength of Alkali Activated Materials

Minerals ◽  
2019 ◽  
Vol 9 (11) ◽  
pp. 714 ◽  
Author(s):  
Evangelos Petrakis ◽  
Vasiliki Karmali ◽  
Georgios Bartzas ◽  
Konstantinos Komnitsas
Keyword(s):  
Particle Size ◽  
Compressive Strength ◽  
Particle Size Distribution ◽  
Size Distribution ◽  
Ageing Time ◽  
Reduction Rate ◽  
Curing Temperature ◽  
Alkali Activation ◽  
Final Particle ◽  
Alkali Activated

This study aims to model grinding of a Polish ferronickel slag and evaluate the particle size distributions (PSDs) of the products obtained after different grinding times. Then, selected products were alkali activated in order to investigate the effect of particle size on the compressive strength of the produced alkali activated materials (AAMs). Other parameters affecting alkali activation, i.e., temperature, curing, and ageing time were also examined. Among the different mathematical models used to simulate the particle size distribution, Rosin–Rammler (RR) was found to be the most suitable. When piecewise regression analysis was applied to experimental data it was found that the particle size distribution of the slag products exhibits multifractal character. In addition, grinding of slag exhibits non-first-order behavior and the reduction rate of each size is time dependent. The grinding rate and consequently the grinding efficiency increases when the particle size increases, but drops sharply near zero after prolonged grinding periods. Regarding alkali activation, it is deduced that among the parameters studied, particle size (and the respective specific surface area) of the raw slag product and curing temperature have the most noticeable impact on the compressive strength of the produced AAMs.

Assessment of Lost Circulation Material Particle-Size Distribution on Fracture Sealing: A Numerical Study

2022 ◽  
pp. 1-15
Author(s):  
Lu Lee ◽  
Arash Dahi Taleghani
Keyword(s):  
Particle Size ◽  
Particle Size Distribution ◽  
Size Distribution ◽  
Numerical Study ◽  
Fluid Loss ◽  
Material Particle ◽  
Lost Circulation ◽  
Fracture Sealing ◽  
Discrete Element Methods ◽  
Lost Circulation Materials

Summary Lost circulation materials (LCMs) are essential to combat fluid loss while drilling and may put the whole operation at risk if a proper LCM design is not used. The focus of this research is understanding the function of LCMs in sealing fractures to reduce fluid loss. One important consideration in the success of fracture sealing is the particle-size distribution (PSD) of LCMs. Various studies have suggested different guidelines for obtaining the best size distribution of LCMs for effective fracture sealing based on limited laboratory experiments or field observations. Hence, there is a need for sophisticated numerical methods to improve the LCM design by providing some predictive capabilities. In this study, computational fluid dynamics (CFD) and discrete element methods (DEM) numerical simulations are coupled to investigate the influence of PSD of granular LCMs on fracture sealing. Dimensionless variables were introduced to compare cases with different PSDs. We validated the CFD-DEM model in reproducing specific laboratory observations of fracture-sealing experiments within the model boundary parameters. Our simulations suggested that a bimodally distributed blend would be the most effective design in comparison to other PSDs tested here.

scholarly journals An experimental and numerical study of particle size distribution effects on the sintering of porous ceramics

2003 ◽  
Vol 348 (1-2) ◽  
pp. 76-83 ◽  
Author(s):  
Ken Darcovich ◽  
Floyd Toll ◽  
Pierre Hontanx ◽  
Virginie Roux ◽  
Kazunari Shinagawa
Keyword(s):  
Particle Size ◽  
Particle Size Distribution ◽  
Size Distribution ◽  
Numerical Study ◽  
Porous Ceramics

scholarly journals Application of Multistep Inversion Method for Online Monitoring Aerosol Particle Size Distribution and Aerosol Concentration

2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Zhenzong He ◽  
Liang Xu ◽  
Junkui Mao ◽  
Xingsi Han ◽  
Biao Zhang
Keyword(s):  
Particle Size ◽  
Standard Deviation ◽  
Particle Size Distribution ◽  
Size Distribution ◽  
Sampling Time ◽  
Aerosol Concentration ◽  
Inversion Method ◽  
Time Interval ◽  
Aerosol Particle Size ◽  
Sampling Time Interval

Aerosol concentration in the flow is usually time varying, and aerosol particle size distribution (PSD) is considered to be unchanged, which increases the difficulty of the measurement of aerosol PSD and concentration online. To solve these problems, a kind of multistep inversion method based on the angular light-scattering (ALS) signals is proposed. First, the aerosol PSD is estimated using shuffled frog-leaping algorithms (SFLAs) from relative ALS signals. Then, with aerosol PSD as priori information, the aerosol concentration is obtained by the Kalman filter (KF) algorithm, widely used in the real-time control system of industrial facilities for its ability of fast predictions. The result reveals that the performance of the improved SFLA is better than that of the original SFLA in solving the aerosol PSD. Moreover, in studying the aerosol concentration, more accurate results can be obtained with larger standard deviation of process noise or smaller standard deviation of measurement noise, while decreasing sampling time interval can improve the accuracy of retrieval results and reduce time delay to a certain degree. So, to improve retrieval accuracy, the noise should be controlled, and appropriate sampling time interval should be selected. All the numerical simulations confirm that the methodology provides effective and reliable results in real-time estimating.

scholarly journals Statistical estimation of stratospheric particle size distribution by combining optical modelling and lidar scattering measurements

2008 ◽  
Vol 8 (17) ◽  
pp. 5435-5448 ◽  
Author(s):  
J. Jumelet ◽  
S. Bekki ◽  
C. David ◽  
P. Keckhut
Keyword(s):  
Particle Size ◽  
Refractive Index ◽  
Standard Deviation ◽  
Particle Size Distribution ◽  
Size Distribution ◽  
Optical Model ◽  
Solid Particles ◽  
Spherical Particles ◽  
Lidar Measurements ◽  
Distribution Parameters

Abstract. A method for estimating the stratospheric particle size distribution from multiwavelength lidar measurements is presented. It is based on matching measured and model-simulated backscatter coefficients. The lidar backscatter coefficients measured at the three commonly used wavelengths 355, 532 and 1064 nm are compared to a precomputed look-up table of model-calculated values. The optical model assumes that particles are spherical and that their size distribution is unimodal. This inverse problem is not trivial because the optical model is highly non-linear with a strong sensitivity to the size distribution parameters in some cases. The errors in the lidar backscatter coefficients are explicitly taken into account in the estimation. The method takes advantage of the statistical properties of the possible solution cluster to identify the most probable size distribution parameters. In order to discard model-simulated outliers resulting from the strong non-linearity of the model, solutions farther than one standard deviation of the median values of the solution cluster are filtered out, because the most probable solution is expected to be in the densest part of the cluster. Within the filtered solution cluster, the estimation algorithm minimizes a cost function of the misfit between measurements and model simulations. Two validation cases are presented on Polar Stratospheric Cloud (PSC) events detected above the ALOMAR observatory (69° N – Norway). A first validation is performed against optical particle counter measurements carried out in January 1996. In non-depolarizing regions of the cloud (i.e. spherical particles), the parameters of an unimodal size distribution and those of the optically dominant mode of a bimodal size distribution are quite successfully retrieved, especially for the median radius and the geometrical standard deviation. As expected, the algorithm performs poorly when solid particles drive the backscatter coefficient. A small bias is identified in modelling the refractive index when compared to previous works that inferred PSC type Ib refractive indices. The accuracy of the size distribution retrieval is improved when the refractive index is set to the value inferred in the reference paper. Our results are then compared to values retrieved with another similar method that does not account for the effect of the measurements errors and the non-linearity of the optical model on the likelihood of the solution. The case considered is a liquid PSC observed over northern Scandinavia on January 2005. An excellent agreement is found between the two methods when our algorithm is applied without any statistical filtering of the solution cluster. However, the solution for the geometrical standard deviation appears to be rather unlikely with a value close to unity (σ≈1.04). When our algorithm is applied with solution filtering, a more realistic value of the standard deviation (σ≈1.27) is found. This highlights the importance of taking into account the non linearity of the model together with the lidar errors, when estimating particle size distribution parameters from lidar measurements.

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