Bird’s total collision energy model: 4 decades and going strong

2019 ◽  
Vol 31 (7) ◽  
pp. 076101 ◽  
Author(s):  
Sergey F. Gimelshein ◽  
Ingrid J. Wysong
Keyword(s):  
Collision Energy ◽  
Energy Model ◽  
Total Collision

scholarly journals Multi-layer kinematics and collision energy in a large-scale grinding mill-the largest semi-autogenous grinding mill in China

2016 ◽  
Vol 8 (12) ◽  
pp. 168781401668137 ◽  
Author(s):  
Tongqing Li ◽  
Yuxing Peng ◽  
Zhencai Zhu ◽  
Shengyong Zou ◽  
Songyong Liu ◽  
...  
Keyword(s):  
Large Scale ◽  
Collision Energy ◽  
Tangential Velocity ◽  
Speed Ratio ◽  
Collision Velocity ◽  
Kinematic Equation ◽  
Steel Balls ◽  
Mill Speed ◽  
Total Collision ◽  
Grinding Mill

Using the largest semi-autogenous grinding mill in China as a model, collision energy was analyzed on the basis of the multi-layer kinematics of the steel balls. First, the kinematic equation of the steel balls was obtained by considering the multi-layer characteristics of the steel balls. Second, the collision energy of the inner-layer steel balls was addressed according to its kinematic characteristics. Finally, the total collision energy per unit time was obtained. Results show that the leaving angle decreases as the mill speed ratio increases and as the radius ratio increases, but the leaving velocity increases linearly. Moreover, a discontinuity point of the tangential collision velocity occurs at an angle factor β = 0, and the angle factor β is divided into two intervals: [−3, 0] and [0, 1.5]. The leaving angles corresponding to a tangential velocity equal to zero are calculated to be 1.185 and 0.7854 rad in the two intervals. In addition, the sum collision velocity increases when β is less than zero, but it decreases sharply above zero. The maximum total collision energy per unit time occurs at 84.2% of the mill speed corresponding to the optimal mill speed ratio.

scholarly journals Simulation of Particle Motion Behavior in Fluidized Bed Opposed Jet Mill

2021 ◽  
Vol 2125 (1) ◽  
pp. 012040
Author(s):  
Kangwei Yang ◽  
Xuewen He
Keyword(s):  
Flow Field ◽  
Fluidized Bed ◽  
High Speed ◽  
Collision Energy ◽  
Inlet Pressure ◽  
Acceleration Process ◽  
Total Collision ◽  
Motion Behavior ◽  
Opposed Jet ◽  
Nozzle Spacing

Abstract In order to study the influence of the internal flow field of the fluidized bed opposed jet mill on the motion behavior of particles, Computational Fluid Dynamics (CFD) and Discrete Dlement Method (DEM) are used for coupling calculations. By adjusting the nozzle spacing and inlet pressure, Numerical simulation is carried out on the process of particles collisions with each other after accelerating under the high-speed jet produced by the nozzle. The trajectory of the particles in the flow field of the collision area and the change of the collision state of the particles are analyzed. Finally, the best parameters are selected based on the total collision energy. The results show that the particles will gradually shift and spread during the acceleration process. The reduction of the nozzle spacing is beneficial to increase the probability of particle collisions. However, if the spacing is too small, the particles cannot be fully accelerated; the increase in inlet pressure will increase the kinetic energy of the particles, and number of collisions is almost unaffected. By comparing the total collision energy, the best-simulated preparation conditions are selected as 110mm and 1.1MPa.

Hydrogen Atom Transfer Reaction Free Energy as a Predictor of Abiotic Nitroaromatic Reduction Rate Constants: A Comprehensive Analysis

2019 ◽  
Author(s):  
Dominic Di Toro ◽  
Kevin P. Hickey ◽  
Herbert E. Allen ◽  
Richard F. Carbonaro ◽  
Pei C. Chiu
Keyword(s):  
Free Energy ◽  
Hydrogen Atom ◽  
Hydrogen Atom Transfer ◽  
Energy Model ◽  
Second Order ◽  
Transfer Model ◽  
Atom Transfer ◽  
Order Rate ◽  
Linear Free Energy ◽  
Free Energy Model

<div>A linear free energy model is presented that predicts the second order rate constant for the abiotic reduction of nitroaromatic compounds (NACs). For this situation previously presented models use the one electron reduction potential of the NAC reaction. If such value is not available, it has been has been proposed that it could be computed directly or estimated from the electron affinity (EA). The model proposed herein uses the Gibbs free energy of the hydrogen atom transfer (HAT) as the parameter in the linear free energy model. Both models employ quantum chemical computations for the required thermodynamic parameters. The available and proposed models are compared using second order rate constants obtained from five investigations reported in the literature in which a variety of NACs were exposed to a variety of reductants. A comprehensive analysis utilizing all the NACs and reductants demonstrate that the computed hydrogen atom transfer model and the experimental one electron reduction potential model have similar root mean square errors and residual error probability distributions. In contrast, the model using the computed electron affinity has a more variable residual error distribution with a significant number of outliers. The results suggest that a linear free energy model utilizing computed hydrogen transfer reaction free energy produces a more reliable prediction of the NAC abiotic reduction second order rate constant than previously available methods. The advantages of the proposed hydrogen atom transfer model and its mechanistic implications are discussed as well.</div>

scholarly journals Simulation of Self-Consumption Photovoltaic Installations: Profitability Thresholds

2021 ◽  
Vol 11 (14) ◽  
pp. 6517
Author(s):  
Marta Varo-Martínez ◽  
Luis Manuel Fernández-Ahumada ◽  
Rafael López-Luque ◽  
José Ramírez-Faz
Keyword(s):  
Systematic Study ◽  
Peak Power ◽  
Net Present Value ◽  
Energy Model ◽  
Present Value ◽  
Lower Power ◽  
Design Variables ◽  
Sunshine Hours ◽  
Optimal Value ◽  
Renewable Technology

PV self-consumption can contribute positively to the spread of PV and, therefore, to the progress of renewable energies as a key element in a decarbonized energy model. However, the policies of each country regarding the promotion of this type of renewable technology is fundamental for their growth. Despite the high number of sunshine hours registered in Spain, self-consumption in this country has not been authorized until recently. In this new context, this work presents a systematic study of the profitability limits of a self-consumption PV installation under different conditions of installed peak power, orientation and inclination of the PV panels and level of obstruction of the installation. It was proved that, for the case of study (Córdoba, Spain), the maximum profitability was achieved for PV panels oriented to the south and with an inclination of 15° whereas the most unfavourable conditions are those of PV panels with an orientation and inclination of 180° and 90°, respectively. Furthermore, when the level of obstruction increases the maximum of the Net Present Value of self-consumptions PV installations decreases and this optimal value is achieved for installations with lower power. Finally, empirical adjustment equations have been developed to estimate the profitability parameters of self-consumptions PV installations as a function of their design variables.

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