3D numerical investigation of effects of density and surface tension on mixing time in bottom-blown gas-stirred ladles

In molten phase metallurgical processes,mixing via gas injection has a vital role in obtaining a homogeneous product.The efficiency of mixing depends on operational variables such as gas flow rate and slag height as well as physical properties of the molten phases.A numerical simulation is conducted to study the above parameters in the flow behavior of a bottom-blown bath.The molten metal and the slag are modeled by water and oil,respectively.The numerical results,particularly the mixing time,are validated against experimental data.The results show that mixing time increases as the slag height increases and decreases as the density of the slag material increases.The mixing time decreases with an increase in the density of the primary phase;however,it increases as the surface tension between air and water increases.A case with properties close to a real molten metal is also modeled.The performance of the system is influenced by the momentum rather than the dissipative forces.Thus,the effect of the density of the molten phase on the mixing process is more pronounced compared to the effect of the surface tension between the air and the molten phase.

Ultrasonic prediction of crack density using machine learning:A numerical investigation

Cracks are accounted as the most destructive discontinuity in rock, soil, and concrete. Enhancing our knowledge from their properties such as crack distribution, density, and/or aspect ratio is crucial in geo-systems. The most well-known mechanical parameter for such an evaluation is wave velocity through which one can qualitatively or quantitatively characterize the porous media. In small scales, such information is obtained using the ultrasonic pulse velocity(UPV) technique as a non-destructive test. In large-scale geo-systems, however, it is inverted from seismic data. In this paper, we take advantage of the recent advancements in machine learning(ML) for analyzing wave signals and predict rock properties such as crack density(CD) – the number of cracks per unit volume. To this end, we designed numerical models with different CDs and, using the rotated staggered finite-difference grid(RSG) technique, simulated wave propagation. Two ML networks, namely Convolutional Neural Networks(CNN) and Long Short-Term Memory(LSTM), are then used to predict CD values. Results show that, by selecting an optimum value for wavelength to crack length ratio, the accuracy of predictions of test data can reach R2> 96% with mean square error(MSE) < 25e-4(normalized values). Overall, we found that:(i) performance of both CNN and LSTM is highly promising,(ii) accuracy of the transmitted signals is slightly higher than the reflected signals,(iii) accuracy of 2D signals is marginally higher than 1D signals,(iv)accuracy of horizontal and vertical component signals are comparable,(v) accuracy of coda signals is less when the whole signals are used. Our results, thus, reveal that the ML methods can provide rapid solutions and estimations for crack density, without the necessity of further modeling.

A Study on Numerical Calculation Method of Small Cluster Density in Percolation Model

Percolation theory deals with the numbers and properties of the clusters formed in the different occupation probability. In this Paper, we study the calculation method of small clusters. We calcu-lated the small cluster density of 1, 2 and 3 in the percolation model with the exact method and the numerical method. The results of the two methods are very close, which can be verified by each other. We find that the cluster density of all three kinds of small clusters reaches the highest value when the occupation probability is between 0.1 and 0.2. It is very difficult to get the analytical formula for the exact method when the cluster area is relatively large (such as the area is more than 50), so we can get the density value of the cluster by numerical method. We find that the time required calculating the cluster density is proportional to the percolation area, which is indepen-dent of the cluster size and the occupation probability.

EXPERIMENTAL AND THEORETICAL STUDY ON NUMERICAL DENSITY EVOLUTION OF SHORT FATIGUE CRACKS

Fatigue testing was performed using a kind of triangular shaped specimen to obtain the characteristics of numerical density evolution for short cracks at the primary stage of fatigue damage. The material concerned is a structural alloy steel. The experimental results show that the numerical density of short cracks reaches the maximum value when crack length is slightly less than the average grain diameter, indicating grain boundary is the main barrier for short crack extension. Based on the experimental observations and related theory, the expressions for growth velocity and nucleation rate of short cracks have been proposed. With the solution to phase space conservation equation, the theoretical results of numerical density evolution for short cracks were obtained, which were in agreement with our experimental measurements.

Numerical simulation of hydraulic fracturing and associated microseismicity using finite-discrete element method

Hydraulic fracturing （HF） technique has been extensively used for the exploitation of unconventional oiland gas reservoirs. HF enhances the connectivity of less permeable oil and gas-bearing rock formationsby fluid injection, which creates an interconnected fracture network and increases the hydrocarbonproduction. Meanwhile, microseismic （MS） monitoring is one of the most effective approaches to evaluatesuch stimulation process. In this paper, the combined finite-discrete element method （FDEM） isadopted to numerically simulate HF and associated MS. Several post-processing tools, includingfrequency-magnitude distribution （b-value）, fractal dimension （D-value）, and seismic events clustering,are utilized to interpret numerical results. A non-parametric clustering algorithm designed specificallyfor FDEM is used to reduce the mesh dependency and extract more realistic seismic information.Simulation results indicated that at the local scale, the HF process tends to propagate following the rockmass discontinuities; while at the reservoir scale, it tends to develop in the direction parallel to themaximum in-situ stress. 2014 Institute of Rock and Soil Mechanics, Chinese Academy of Sciences. Production and hosting byElsevier B.V. All rights reserved.

Effects of drive current rise-time and initial load density distribution on Z-pinch characteristics

A two-dimensional, three-temperature radiation magneto-hydrodynamics model is applied to the investigation of evolutional trends in x-ray radiation power, energy, peak plasma temperature and density as functions of drive current rise-time and initial load density distribution by using the typical experimental parameters of tungsten wire-array Z- pinch on the Qiangguang-I generator. The numerical results show that as the drive current rise-time is shortened, x-ray radiation peak power, energy, peak plasma density and peak ion temperature increase approximately linearly, but among them the x-ray radiation peak power increases more quickly. As the initial plasma density distribution in the radial direction becomes gradually flattened, the peak radiation power and the peak ion-temperature almost exponentially increase, while the radiation energy and the peak plasma density change only a little. The main effect of shortening drive current rise-time is to enhance compression of plasma, and the effect of flattening initial load density distribution in the radial direction is to raise the plasma temperature. Both of the approaches elevate the x-ray peak radiation power

Numerical Analysis of Artificial Electron Heating Effects on Polar Mesospheric Winter Echoes

In this paper,an analytical model is used to analyze the modulated polar mesospheric winter echoes(PMWE).The winter parameters were introduced to simulate the effects of different parameters during the artificial electron heating of PMWE.The important role of the charged dust particle in the creation of PMWE is confirmed again.It is found that during the heating of PMWE,the increases of the dust size,dust charge,electron temperature,initial electron density,and ion-neutral collision frequency cause the increase of the electron density irregularity,and hence the PMWE strength.However,with increasing the dust density,the electron density irregularity and the PMWE strength decrease.

Optimization of Mo/Cu(In,Ga)Se2/CdS/ZnO Hetero-Junction Solar Cell Performance by Numerical Simulation with SCAPS-1D

The paper presents a one-dimensional simulation study of chalcopyrite Cu(In,Ga)Se2(CIGS)solar cells,where the effects of the variation of CIGS,CdS,and ZnO layers are presented.Additionlly the influence of the variation of doping and the defects density of shallow uniform donors and acceptors types are also presented.The analyse of the simulation results shows that recombination inside the space charge region(SCR)decrease more our CIGS solar cell model performance.We also found that the electrical parameters increase with increasing CIGS absorber doping density exception of JSC values that reach their maximum at 1016cm-3 and decrease due to recombination of charge carriers in the p-n junction particularly the recombination inside the SCR.We also stressed the fact that the effects of shallow uniforme donor density is very low on the performance of our CIGS solar cell model is important because it will allow to control the width of space charge region from shallow uniform acceptors defect density that has a strong influence on the different electrical parameters.Yet,good optimization of performance of the CIGS-based solar cell necessarily passes though a good control of the space charge region width and will constitute a boosting perspective for the preparation of our next paper.We contact that the results obtained of the numerical simulation with SCAPS-1D show a good agreement comparatively of the literature results.The simulation of our CIGS solar cell presents best performances if the values of the absorber layer thickness is in the range of 0.02 to 0.03μm,the buffer layer thickness is in the range of 0.02 to 0.06μm and the defects density of shallow uniform acceptors types is in the range of 1015 to 1017cm-3.

Numerical simulation of current distribution in metal pad of aluminum reduction cells

Based on the numerical calculation of 3-D potential distribution in aluminum reduction cells, current distribution in the metal pad is calculated under the following conditions: 1) pot ledge ideally formed; 2) ledge extension to below anode; 3) different metal heights; 4) AC and 5) Spike. It is found that J_y in metal pad increases first to a highest point and then decreases along anode length. At normal status, the largest J_y is about 0.4A/cm^2 and it locates at about 2/3 of anode length. With longer ledge, the maximum value of J_y decreases and its position moves center-ward. The longer the side ledge, the larger the negative current flowing center-ward at side channel. J_z in metal pad increases with anode length and it is not affected by metal height; while J_y increases with metal height. At AC, current flows toward metal under new anode. At spike, current concentrates at spike rather than evenly distributes. Normally, J_x is almost negligible in metal pad.

Numerical Simulation of Contamination Accumulation Characteristics of Composite Insulators in Salt Fog Environment

To investigate the fouling characteristics of the composite insulator surface under the salt fog environment,the FXBW-110/120-2 composite insulator was taken as the research object.Based on the field-induced charge mechanism,the multi-physical field coupling software COMSOL was used to numerically simulate the fouling characteristics,explored the calculation method of ESDD,and demonstrated its rationality.Based on this method,the pollution characteristics of the composite insulator under the pollution fog environment were studied,and the influence of wind speed,droplet size,and voltage type on the pollution characteristics of the composite insulator was analyzed.The results showed that:with the increase in wind speed,the amount of accumulated pollution of insulator increases in the range of droplet size,and the relationship between wind speed and accumulated pollution is approximately linear;at the same wind speed,the amount of accumulated pollution increases with the increase of droplet size under the action of DC voltage;when there is no voltage,the amount of dirt on the upper surface of the insulator is more than that on the lower surface,while it is the opposite under DC voltage.

Simulation Monitoring for Rainfall Infiltration in Soil Based on High Density Electrical Method

Rainfall infiltration is a porous medium flow problem with variable saturation. Based on the theoretical analysis of the flow field, electrical conductivity of rocks, the electrical field, the paper simulates the coupling relationship between the water saturation in soil and the apparent resistivity distribution. It combines the Richards equation, the Archie formula and the Laplace equation. The experiment simulates the potential field data by the Wenner setting in electrical exploration on a two-layer geologic model with continuous rainfall during 5 days, which shows that the effective saturation in soil is increasing with the rainfall time, while the apparent resistivity is decreasing. This can provide a theoretical basis for the analyzing the rainfall infiltration and porosity of the soil by using high-density electrical method in the future.

The Temperature Dependence of the Density of States in Semiconductors

The temperature dependence of the density of energy states in semiconductors is considered. With the help of mathematical modeling of the thermal broadening of the energy levels, the temperature dependence of the band gap of semiconductors is studied. In view of the non-parabolic and the temperature dependence of the effective mass of the density of states in the allowed bands, graphs of temperature dependence of the band gap are obtained. The theoretical results of mathematical modeling are compared with experimental data for Si, InAs and solid solutions of p-Bi2-xSbxTe3-ySey. The theoretical results satisfactorily explain the experimental results for Si and InAs. The new approach is investigated by the temperature dependence of the band gap of semiconductors.

Impact of Surface Potential Vorticity Density Forcing over the Tibetan Plateau on the South China Extreme Precipitation in January 2008. Part Ⅱ:Numerical Simulation

The surface air convergence on the eastern flank of the Tibetan Plateau (TP) can increase the in situ surface potential vorticity density (PVD). Since the elevated TP intersects with the isentropic surfaces in the lower troposphere, the increased PVD on the eastern flank of TP thus forms a PVD forcing to the intersected isentropic surface in the boundary layer. The influence of surface PVD forcing over the TP on the extreme freezing rain/snow over South China in January 2008 is investigated by using numerical experiments based on the Finite-volume Atmospheric Model of the IAP/LASG (FAMIL). Compared with observations, the simulation results show that, by using a nudging method for assimilating observation data in the initial flow, this model can reasonably reproduce the distribution of precipitation, atmospheric circulation, and PVD propagation over and downstream of the TP during the extreme winter precipitation period. In order to investigate the impact of the increased surface PVD over the TP on the extreme precipitation in South China, a sensitivity experiment with surface PVD reduced over the TP region was performed. Compared with the control experiment, it is found that the precipitation in the TP downstream area, especially in Southeast China, is reduced. The rainband from Guangxi Region to Shandong Province has almost disappeared. In the lower troposphere, the increase of surface PVD over the TP region has generated an anomalous cyclonic circulation over southern China, which plays an important role in increasing southerly wind and the water vapor transport in this area;it also increases the northward negative absolute vorticity advection. In the upper troposphere, the surface PVD generated in eastern TP propagates on isentropic surface along westerly wind and results in positive absolute vorticity advection in the downstream areas. Consequently, due to the development of both ascending motion and water vapor transport in the downstream place of the TP, extremely heavy precipitation occurs over southern China. Thereby, a new mechanism concerning the influence of the increased surface PVD over the eastern TP slopes on the extreme weather event occurring over southern China is revealed.

Orbital-Free Density Functional Theory for Molecular Structure Calculations

We give here an overview of the orbital-flee density functional theory that is used for modeling atoms and molecules. We review typical approximations to the kinetic energy, exchange-correlation corrections to the kinetic and Hartree energies, and constructions of the pseudopotentials. We discuss numerical discretizations for the orbital-free methods and include several numerical results for illustrations.

Numerical simulation of carbon arc discharge for graphene synthesis without catalyst

In this study, graphene sheets are prepared under a hydrogen atmosphere without a catalyst, and the growth mechanism of graphene by direct current arc discharge is investigated experimentally and numerically. The size and layer numbers of graphene sheets increase with the arc current.Distributions of temperature, velocity, and mass fraction of carbon are obtained through numerical simulations. A high current corresponds to a high saturation temperature, evaporation rate, and mass density of carbon clusters. When the carbon vapor is saturated, the saturation temperatures are 3274.9, 3313.9, and 3363.6 K, and the mass densities are 6.4×1022,8.42×1022, and 1.23×1023 m-3 under currents of 150, 200, and 250 A, respectively. A hydrogen-induced marginal growth model is used to explain the growth mechanism. Under a high current, the condensation coefficient and van der Waals force increase owing to the higher saturation temperature and mass density of carbon clusters, which is consistent with experimental results.

Study of Numerical Analysis on Smoke Exhaust Performance of Portable Smoke Exhaust Fan

In houses and general buildings of environment where smoke control equipment is not installed, or its operation is difficult, there is a need to develop and utilize a portable smoke exhaust fan that can perform emergency ventilation in case of fire suppression and rescue operations. As a part of the development process for portable smoke exhaust fans, a numerical analysis model of the portable smoke exhaust fan was derived from the building in which a fire occurred, and an analysis on the smoke and toxic gas exhaust effects was performed in this study. The numerical analysis results showed that under a condition where the height of an opening is less than 1.0 m after fire source disappears in a situation where the smoke exhaust fan does not operate, smoke does not come out well, and thus the density of smoke within the target area does not drop significantly. On the other hand, if the smoke exhaust fan operates after the fire source disappears, smoke is directly exhausted to the outside due to the operation of the smoke exhaust fan, and the smoke density within the space drops sharply in all opening height conditions, thereby getting close to zero.

Analysis of Tidal Current Energy Potential in the Major Channels of the Bohai Strait Based on Delft3D

The utilization and development of tidal current energy can help alleviate the current energy shortage,improve the global ecological environment,and maintain sustainable development.In this study,numerical simulation is carried out on a rectangular grid using Delft3D.The tidal current energy potential of the major channels in the Bohai Strait is further simulated and estimated by comparing the simulated and measured data.Results show that the flow module in Delft3D has good modeling ability for the assessment of tidal current energy potential.The average flow velocity,maximum flow velocity,and energy flow density are consistent.The Laotieshan Channel,located in the northern part of the Bohai Strait,shows a large tidal current energy potential.The maximum flow velocity of this channel can reach 2 m s-1,and the maximum energy flow density can exceed 500 W m-2.The tidal current energy in the Laotieshan Channel is more than 10 times that in other channels.Therefore,this study advocates for the continued exploration and exploitation of the tidal current energy resources in the Laotieshan Channel.

Numerical simulation of the internal wave propagation in continuously densitystratified ocean

A numerical model is proposed to simulate the internal wave propagation in a continuously density-stratified ocean, and in the model, the momentum equations are derived from the Euler equations on the basis of the Boussinesq approximation. The governing equations, including the continuity equation and the momentum equations, are discretized with the finite volume method. The advection terms are treated with the total variation diminishing （TVD） scheme, and the SIMPLE algorithm is employed to solve the discretized governing equations. After the modeling test, the suitable TVD scheme is selected. The SIMPLE algorithm is modified to simplify the calculation process, and it is easily made to adapt to the TVD scheme. The Sommerfeld＇s radiation condition combined with a sponge layer is adopted at the outflow boundary. In the water flume with a constant water depth, the numerical results are compared to the analytical solutions with a good agreement. The numerical simulations are carried out for a wave flume with a submerged dike, and the model results are analyzed in detail. The results show that the present numerical model can effectively simulate the propagation of the internal wave.

Comparison study of several numerical integration schemes used in calculations of density functional theory

Several numerical integration schemes for the evaluation of matrix elements in density functional theory calculations have been studied and compared by computational practice. The best scheme was found to be the combination of the atomic partition function proposed by Becke with the scaled generalized Gauss-Laguerre quadrature formula for radial integration suggested by Yang, which achieve the highest convergence rate to the numerical integration. With the same number of integration points, the accuracy of the calculated results by this scheme is higher by 1 to 2 orders of magnitudes than that by other schemes. The reason for achieving higher accuracy by this scheme has been proposed preliminarily.

Joint product numerical range and geometry of reduced density matrices

The reduced density matrices of a many-body quantum system form a convex set, whose three-dimensional projection is convex in R3. The boundary of may exhibit nontrivial geometry, in particular ruled surfaces. Two physical mechanisms are known for the origins of ruled surfaces： symmetry breaking and gapless. In this work, we study the emergence of ruled surfaces for systems with local Hamiltonians in infinite spatial dimension, where the reduced density matrices are known to be separable as a consequence of the quantum de Finetti＇s theorem. This allows us to identify the reduced density matrix geometry with joint product numerical range II of the Hamiltonian interaction terms. We focus on the case where the interaction terms have certain structures, such that a ruled surface emerges naturally when taking a convex hull of ∏. We show that, a ruled surface on sitting in ∏ has a gapless origin, otherwise it has a symmetry breaking origin. As an example, we demonstrate that a famous ruled surface, known as the oloid, is a possible shape of , with two boundary pieces of symmetry breaking origin separated by two gapless lines.