A quadrature-based moment method for the evolution of the joint size-velocity number density function of a particle population

2021 ◽  
pp. 108072
Author(s):  
J.C. Heylmun ◽  
Rodney O. Fox ◽  
Alberto Passalacqua
Keyword(s):  
Density Function ◽  
Moment Method ◽  
Number Density ◽  
Particle Population

A General Theory on Media with Randomly Distributed Inclusions: Part I—The Average Field Behaviors

1990 ◽  
Vol 57 (4) ◽  
pp. 857-862 ◽  
Author(s):  
B. Wang
Keyword(s):  
Field Equation ◽  
General Theory ◽  
Density Function ◽  
Strain Field ◽  
Statistical Information ◽  
Ensemble Average ◽  
Average Field ◽  
Number Density ◽  
Average Strain ◽  
Uniform Distributions

In this paper, a theory is developed to calculate the average strain field in the materials with randomly distributed inclusions. Many previous researches investigating the average field behaviors were based upon Mori and Tanaka’s idea. Since they were restricted to studying those materials with uniform distributions of inclusions they did not need detailed statistical information of random microstructures, and could use the volume average to replace the ensemble average. To study more general materials with randomly distributed inclusions, the number density function is introduced in formulating the average field equation in this research. Both uniform and nonuniform distributions of inclusions are taken into account in detail.

scholarly journals Fractal aggregation and breakup of fine particles

2016 ◽  
Vol 20 (3) ◽  
pp. 797-801 ◽  
Author(s):  
Bingru Li ◽  
Feifeng Cao ◽  
Zhanhong Wan ◽  
Zhigang Feng ◽  
Honghao Zheng
Keyword(s):  
Fluid Dynamics ◽  
Moment Method ◽  
Taylor Expansion ◽  
Fine Particles ◽  
Size Distributions ◽  
Number Density ◽  
Dynamics Modeling ◽  
Particle Size Distributions ◽  
Particle Volume ◽  
Computational Fluid Dynamics Modeling

Breakup may exert a controlling influence on particle size distributions and particles either are fractured or are eroded particle-by-particle through shear. The shear-induced breakage of fine particles in turbulent conditions is investigated using Taylor-expansion moment method. Their equations have been derived in continuous form in terms of the number density function with particle volume. It suitable for future implementation in computational fluid dynamics modeling.

scholarly journals DETERMINATION OF WEIBULL PARAMETERS FOR WIND APPLICATIONS IN TWO DIFFERENT REGIONS

2018 ◽  
Vol 17 (2) ◽  
pp. 12
Author(s):  
W. F. A. Borges ◽  
A. M. Araújo ◽  
O. D. Q. de Oliveira Filho ◽  
J. S. Rohatgi ◽  
G. F. Pinto
Keyword(s):  
Probability Density Function ◽  
Numerical Methods ◽  
Probability Density ◽  
Density Function ◽  
Moment Method ◽  
Graphical Method ◽  
Empirical Method ◽  
Weibull Parameters ◽  
Wind Regimes

In this work, the main objective is to determine the shape (k) and scale (c) parameters of the Weibull probability density function through four numerical methods, known as graphical method (GM), empirical method of Justus (EMJ), empirical method of Lysen (EML), and moment method (MM) in two distinct cities, Gravatá-PE and Osório-RS, under the influence of two wind regimes. To do that, it will be used the hourly wind data obtained through NASA's Meteonorm database, from 2006 to 2015. Statistical analyzes also will be used to determine the best method used to determine these parameters.

scholarly journals The verification of the Taylor-expansion moment method in solving aerosol breakage

2012 ◽  
Vol 16 (5) ◽  
pp. 1424-1428 ◽  
Author(s):  
Ming-Zhou Yu ◽  
Kai Zhang
Keyword(s):  
Moment Method ◽  
Taylor Expansion ◽  
High Efficiency ◽  
Population Balance ◽  
Moment Equation ◽  
Method Of Moment ◽  
Balance Equations ◽  
Particle Population ◽  
The Moment ◽  
Linear Integral

The combination of the method of moment, characterizing the particle population balance, and the computational fluid dynamics has been an emerging research issue in the studies on the aerosol science and on the multiphase flow science. The difficulty of solving the moment equation arises mainly from the closure of some fractal moment variables which appears in the transform from the non-linear integral-differential population balance equation to the moment equations. Within the Taylor-expansion moment method, the breakage-dominated Taylor-expansion moment equation is first derived here when the symmetric fragmentation mechanism is involved. Due to the high efficiency and the high precision, this proposed moment model is expected to become an important tool for solving population balance equations.

Mass Determination by Direct Measurement of Electron Scattering

1975 ◽  
Vol 33 ◽  
pp. 240-241
Author(s):  
M. K. Lamvik ◽  
A. V. Crewe
Keyword(s):  
Cross Section ◽  
Electron Scattering ◽  
Mass Density ◽  
Variable Mass ◽  
Scattering Cross Section ◽  
Mass Determination ◽  
Number Density ◽  
Cross Sectional ◽  
Thin Slice ◽  
Scattering Cross

If a molecule or atom of material has molecular weight A, the number density of such units is given by n=Nρ/A, where N is Avogadro's number and ρ is the mass density of the material. The amount of scattering from each unit can be written by assigning an imaginary cross-sectional area σ to each unit. If the current I0 is incident on a thin slice of material of thickness z and the current I remains unscattered, then the scattering cross-section σ is defined by I=IOnσz. For a specimen that is not thin, the definition must be applied to each imaginary thin slice and the result I/I0 =exp(-nσz) is obtained by integrating over the whole thickness. It is useful to separate the variable mass-thickness w=ρz from the other factors to yield I/I0 =exp(-sw), where s=Nσ/A is the scattering cross-section per unit mass.

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