scholarly journals Non-dissipative hydrodynamic equations based on a nonlocal collision integral

2018 ◽  
Vol 26 (1) ◽  
pp. 11-18
Author(s):  
V. N. Gorev ◽  
A. I. Sokolovsky
Keyword(s):  
Particle Number ◽  
Evolution Equations ◽  
Particle Number Density ◽  
Collision Integral ◽  
Second Order ◽  
Total System ◽  
Hydrodynamic Equations ◽  
Number Density ◽  
Total Energy Density ◽  
System Energy

We consider a slightly non-uniform one-component gas with weak potential interaction. The basis of the investigation is the known kinetic equation in the case of small interaction which is truncated up to the second order of smallness. This equation contains a nonlocal collision integral of the second order in small interaction. In this paper we consider the hydrodynamic stage of the system evolution, and, in contrast to the standard hydrodynamics, we take into account the non-locality of the collision integral. We propose the following set of the reduced description parameters which are the densities of the conserved quantities: the particle number density, the momentum density, and the total energy density. It should be stressed that in contrast to the standard hydrodynamics, the kinetic energy is not conserved, and only the total system energy is conserved if the nonlocal collision integral is used. Definitions of the system velocity and temperature are proposed; it should be stressed that the proposed temperature definition is based on the total system energy rather than on the kinetic one. The hydrodynamics in the leading order in small gradients is investigated, and it is shown that the system one-particle distribution function in the leading-in-gradients order coincides with the Maxwellian one. Particle number density, velocity and temperature time evolution equations (hydrodynamic equations) are derived in the non-dissipative case. The leading-in-interaction orders of the obtained equations coincide with the corresponding equations in the framework of the standard hydrodynamics. The corrections of the first and second order in small interaction are also obtained.

Experimentally determined particle number density statistics in an industrial-scale, pulverized-coal-fired boiler

1993 ◽  
Vol 7 (6) ◽  
pp. 842-851 ◽  
Author(s):  
M. Queiroz ◽  
M. P. Bonin ◽  
J. S. Shirolkar ◽  
R. W. Dawson
Keyword(s):  
Particle Number ◽  
Particle Number Density ◽  
Pulverized Coal ◽  
Industrial Scale ◽  
Number Density

The next step in precipitation polymerization of N-isopropylacrylamide: particle number density control by monochain globule surface charge modulation

2016 ◽  
Vol 7 (32) ◽  
pp. 5123-5131 ◽  
Author(s):  
O. L. J. Virtanen ◽  
M. Brugnoni ◽  
M. Kather ◽  
A. Pich ◽  
W. Richtering
Keyword(s):  
Particle Size ◽  
Robust Control ◽  
Surface Charge ◽  
Particle Number ◽  
Particle Number Density ◽  
Precipitation Polymerization ◽  
Number Density ◽  
Density Control ◽  
Charge Modulation

Many applications of poly(N-isopropylacrylamide) microgels necessitate robust control over particle size.

Effect of Particle Number Density on Wave Dispersion in a Two-Dimensional Yukawa System

2017 ◽  
Vol 34 (7) ◽  
pp. 075203
Author(s):  
Rang-Yue Zhang ◽  
Yan-Hong Liu ◽  
Feng Huang ◽  
Zhao-Yang Chen ◽  
Chun-Yan Li
Keyword(s):  
Particle Number ◽  
Wave Dispersion ◽  
Particle Number Density ◽  
Two Dimensional ◽  
Number Density

Simulation of Multi-Phase Glass-Melt Flows in a Glass Melter

2001 ◽  
Author(s):  
S. L. Chang ◽  
C. Q. Zhou ◽  
B. Golchert ◽  
M. Petrick
Keyword(s):  
Heat Transfer ◽  
Molten Glass ◽  
Transfer Rate ◽  
Liquid Glass ◽  
Particle Number ◽  
Particle Number Density ◽  
Number Density ◽  
Melt Flow ◽  
Glass Melter ◽  
Multi Phase

Abstract A typical glass furnace consists of a combustion space and a melter. The intense heat, generated from the combustion of fuel and air/oxygen in the combustion space, is transferred mainly by radiation to the melter where the melt sand and cullet (scrap glass) are melted, creating molten glass. The melter flow is a complex multi-phase flow including solid batches of sand/cullet and molten glass. Proper modeling of the flow patterns of the solid batch and liquid glass is a key to determining the glass quality and furnace efficiency. A multi-phase CFD code has been developed to simulate glass melter flow. It uses an Eulerian approach for both the solid batch and the liquid glass-melt flows. The mass, momentum, and energy conservation equations of the batch flow are used to solve for local batch particle number density, velocity, and temperature. In a similar manner, the conservation equations of mass, momentum, and energy of the glass-melt flow are used to solve for local liquid molten glass pressure, velocity, and temperature. The solid batch is melted on the top by the heat from the combustion space and from below by heat from the glass-melt flow. The heat transfer rate from the combustion space is calculated from a radiation model calculation while the heat transfer rate from the glass-melt flow to the solid batch is calculated from a model based on local particle number density and glass-melt temperature. Energy and mass are balanced between the batch and the glass-melt. Batch coverage is determined from local particle number density and velocity. A commercial-scale glass melter has been simulated at different operating/design conditions.

scholarly journals Diffusion of Particles, Heat and Magnetic Fields in Compressible Turbulent Media

1991 ◽  
Vol 130 ◽  
pp. 71-74
Author(s):  
A.Z. Dolginov ◽  
N.A. Silant’ev
Keyword(s):  
Magnetic Field ◽  
Magnetic Fields ◽  
Vector Fields ◽  
Particle Number ◽  
Particle Number Density ◽  
Turbulent Diffusivity ◽  
Number Density ◽  
Scalar And Vector Fields ◽  
Kinetic Coefficients ◽  
The Magnetic Field

AbstractA new method for the calculation of kinetic coefficients is presented. This method allows us to obtain the distribution of scalar and vector fields (such as the temperature, the admixture particle number density and the magnetic field) in turbulent cosmic media with any value of S = u0т0/R0. The explicit expression for the “turbulent” diffusivity DT is obtained. In some cases DT becomes negative, implying the clustering of the admixture particles in patches (a local increase of the temperature and magnetic fields). The magnetic α-effect is considered for the case S ~ 1.

Particle Deposition in a Room-Scale Chamber With Particle Injection

2005 ◽  
Author(s):  
N. Zhang ◽  
Z. Charlie Zheng ◽  
L. Glasgow ◽  
B. Braley
Keyword(s):  
Particle Deposition ◽  
Particle Number ◽  
Particle Distribution ◽  
Turbulent Transport ◽  
Distribution Patterns ◽  
Particle Number Density ◽  
Number Density ◽  
Small Particles ◽  
Particle Injection ◽  
Simulation Results

A model simulating the deposition of small particles with turbulent transport, sedimentation, and coagulation, is presented. Experimental measurements were conducted in a room-scale chamber using a specially designed sequential sampler. The measured deposition-rate data are compared with the simulation results. Distributions of particle-number density at different times are plotted in several viewing planes to facilitate discussion of the particle distribution patterns.

The Dependence of Pool Scrubbing Decontamination Factor on Particle Number Density: Modeling Based on Bubble Mass and Energy Balance

2020 ◽  
Author(s):  
Yasuteru Sibamoto ◽  
Haomin Sun ◽  
Yoshiyasu Hirose ◽  
Yutaka Kukita
Keyword(s):  
Energy Balance ◽  
Particle Number ◽  
Sharp Decrease ◽  
Particle Growth ◽  
Decontamination Factor ◽  
Particle Number Density ◽  
Vapor Condensation ◽  
Vapor Concentration ◽  
Number Density ◽  
Condensational Growth

Abstract The dependence of pool scrubbing performance on particle number density is studied through numerical simulation of experimental results. The DF values obtained from the authors’ experiments (Sun et al., Sci. Technol. Nucl. Inst., Article ID 1743982, 2019) indicate a sharp decrease with an increase in the inlet particle number density beyond 1011/m3. The mechanisms underlying such dependence is yet to be studied. In this paper, a simple model is developed to study the factors affecting the experimentally observed dependence of DF. The test results suggest that the condensational growth of particles plays an essential role in the inertial capture. The vapor condensation on the particles has an effect to deplete the vapor supersaturation in the bubble by both lowering the vapor concentration and raising the temperature. This effect will become important at high particle number densities. The bubble mass and energy balance is calculated to derive the particle growth and the inertial DF as a function of the bubble rise distance through the pool water. The balance is assumed to be quasi-steady, and the vapor concentration and the temperature to be uniform in the bubble. It is shown that the model reproduces the tendency observed in the experimental DF. The model predicts that the degree of supersaturation is affected when particle concentration exceeds 1011/m3, curbing the condensational growth of particles, and thereby retarding the inertial capture.

scholarly journals Progression of errors in morphometry. Estimation of particle number density.

1986 ◽  
Vol 34 (7) ◽  
pp. 941-944 ◽  
Author(s):  
I Hammel
Keyword(s):  
Coefficient Of Variation ◽  
Particle Number ◽  
Particle Number Density ◽  
Suitable Method ◽  
Number Density ◽  
Morphometric Data ◽  
Propagation Of Errors ◽  
Cost Of Time ◽  
Data Extrapolation

We have developed procedures whereby the progression of errors in various methods of morphometric data extrapolation may be evaluated. The analysis is straightforward and simple. We suggest that before collecting data, one should estimate the accepted fluctuations of the various parameters. Then, by calculation of propagation of errors, the most suitable method may be chosen, so that the data extracted will have an acceptable coefficient of variation. Higher precision carries a cost of time and/or money, and may not be necessary.

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