Significance of including lid thickness and particle shape factor in numerical modeling for prediction of particle trap efficiency of invert trap

Sediment accumulation on the bed of open sewers and drains reduces hydraulic efficiency and can cause localized flooding.Slotted invert traps installed underneath the bed of open sewers and drains can eliminate sediment build-up by catching sediment load.Previous three-dimensional(3D)computational studies have examined the particle trapping performance of invert traps of different shapes and depths under varied sediment and flow conditions,considering particles as spheres.For two-dimensional and 3D numerical modeling,researchers assumed the lid geometry to be a thin line and a plane,respectively.In this 3D numerical study,the particle trapping efficiency of a slotted irregular hexagonal invert trap fitted at the flume bottom was examined by incorporating the particle shape factor of non-spherical sewage solid particles and the thicknesses of upstream and downstream lids over the trap in the discrete phase model of the ANSYS Fluent 2020 R1 software.The volume of fluid(VOF)and the realizable k-turbulence models were used to predict the velocity field.The two-dimensional particle image velocimetry(PIV)was used to measure the velocity field inside the invert trap.The results showed that the thicknesses of upstream and downstream lids affected the velocity field and turbulent kinetic energy at all flow depths.The joint impact of the particle shape factor and lid thickness on the trap efficiency was significant.When both the lid thickness and particle shape factor were considered in the numerical modeling,trap efficiencies were underestimated,with relative errors of-8.66%to-0.65%in comparison to the experimental values of Mohsin and Kaushal(2017).They were also lower than the values predicted by Mohsin and Kaushal(2017),which showed an overall overestimation with errors of-2.3%to 17.4%.

Optimal Shape Factor and Fictitious Radius in the MQ-RBF:Solving Ill-Posed Laplacian Problems

To solve the Laplacian problems,we adopt a meshless method with the multiquadric radial basis function(MQRBF)as a basis whose center is distributed inside a circle with a fictitious radius.A maximal projection technique is developed to identify the optimal shape factor and fictitious radius by minimizing a merit function.A sample function is interpolated by theMQ-RBF to provide a trial coefficient vector to compute the merit function.We can quickly determine the optimal values of the parameters within a preferred rage using the golden section search algorithm.The novel method provides the optimal values of parameters and,hence,an optimal MQ-RBF;the performance of the method is validated in numerical examples.Moreover,nonharmonic problems are transformed to the Poisson equation endowed with a homogeneous boundary condition;this can overcome the problem of these problems being ill-posed.The optimal MQ-RBF is extremely accurate.We further propose a novel optimal polynomial method to solve the nonharmonic problems,which achieves high precision up to an order of 10^(−11).

Study on shape factor of the fusion-solidification zone of electron beam weld

The concept of shape factors of the fusion-solidification zone is proposed to describe the weld cross section geometry. According to these shape factors, the electron beam weld fusion-solidification zone is divided into four typical shapes and the classification criterion for these typical shapes is suggested. An integrated parameter n, combining the line power density of electron beam and material thermal properties is proposed to describe the relative power input, and another integrated parameter n2 combing the accelerating voltage and focusing current is proposed to reflect the power distribution in the keyhole. A series of new expressions, which can reflect the influence of focusing current, accelerating voltage, beam current, and material thermal properties, are developed to predict the fusion-solidification zone shape based on experimental results nonlinear fitting of n1 and n2.

A Perfect Shape Factor Corresponding States Principle for Pure Non-Polar and Polar Fluids

In the two-parameter corresponding states principle(CSP), the critical compressibility factors of the fluid under study(called 'a' fluid) and the reference fluid(called 'o' fluid) must be identical. This is not generally observed in nature. To overcome this limitation, a perfect shape factor CSP is proposed in which the compressibility factors of 'a' and 'o' fluids are corresponded perfectly by introducing a new pressure shape factor 8. Using methane as the 'o' fluid, the shape factors of many fluids are calculated from PVT properties at saturation state and the second virial coefficients. Models are also formulated for the shape factors with the assumption of is a function of temperature and volume while 6 and 5 are temperature dependent only. The models described the shape factors satisfactorily in whole region including vapor, liquid and their co-existing phases. The perfect shape factor CSP could be applied for both polar and non-polar fluids.

The influence of joint geometric parameters on shape factor of butt joint with center through crack

In this research, the influence of such joint geometric parameters as weld width and reinforcement on shape ~actor of butt joint with center crack subjected to static loading was investigated by finite element analyses method. According to the analytical resuhs, a well fracture resistant joint shape of butt joint with center crack has been approved.

Shape factor for regular and irregular matrix blocks in fractured porous media

Describing matrix–fracture interaction is one of the most important factors for modeling natural fractured reservoirs.A common approach for simulation of naturally fractured reservoirs is dual-porosity modeling where the degree of communication between the low-permeability medium(matrix)and high-permeability medium(fracture)is usually determined by a transfer function.Most of the proposed matrix–fracture functions depend on the geometry of the matrix and fractures that are lumped to a factor called shape factor.Unfortunately,there is no unique solution for calculating the shape factor even for symmetric cases.Conducting fine-scale modeling is a tool for calculating the shape factor and validating the current solutions in the literature.In this study,the shape factor is calculated based on the numerical simulation of fine-grid simulations for single-phase flow using finite element method.To the best of the author’s knowledge,this is the first study to calculate the shape factors for multidimensional irregular bodies in a systematic approach.Several models were used,and shape factors were calculated for both transient and pseudo-steady-state(PSS)cases,although in some cases they were not clarified and assumptions were not clear.The boundary condition dependency of the shape factor was also investigated,and the obtained results were compared with the results of other studies.Results show that some of the most popular formulas cannot capture the exact physics of matrix–fracture interaction.The obtained results also show that both PSS and transient approaches for describing matrix–fracture transfer lead to constant shape factors that are not unique and depend on the fracture pressure(boundary condition)and how it changes with time.

Numerical investigation of the influence of kinetics and shape factor on barium sulfate precipitation in a continuous stirred tank

The effect of kinetics and shape factor on barium sulfate precipitation in a continuous stirred tank has been investigated numerically through solving the standard momentum and mass transport equations in combination with the moment equations for crystal population balance.The numerical method was validated with the literature data.The simulated results include the distribution of the local supersaturation ratio in the reactor,the mean crystal size,and the coefficient of variation.The simulation results show that the value of shape factor used in the model affected greatly the mean crystal size and the moments of the crystal size distribution.The influence of the kinetic expressions on the simulation is also analyzed.It is important to investigate the relationship of the shape factor with the precipitator type and other operation conditions to obtain reliable simulation results and suitable kinetic equations of crystal nucleation and growth rates.

Velocity profiles description and shape factors inclusion in a hyperbolic,one-dimensional,transient two-fluid model for stratified and slug flow simulations in pipes

In a previous work it has been shown that a one-dimensional,hyperbolic,transient five equations twofluid model is able to numerically describe stratified,wavy,and slug flow in horizontal and nearhorizontal pipes.Slug statistical characteristics can be numerically predicted with results in good agreement with experimental data and well-known empirical relations.In this model some approximated and simplified assumptions are adopted to describe shear stresses at wall and at phase interface.In this paper,we focus on the possibility to account for the cross sectional flow by inserting shape factors into the momentum balance equations of the aforementioned model.Velocity profiles are obtained by a pre-integrated model and they are computed at each time step and at each computational cell.Once that the velocity profiles are known,the obtained shape factors are inserted in the numerical resolution.In this way it is possible to recover part of the information lost due to the one-dimensional flow description.Velocity profiles computed in stratified conditions are compared against experimental profiles measured by PIV technique;a method to compute the velocity profile during slug initiation and growth has been developed and the computed velocity distribution in the liquid phase was compared against the one-seventh power law.

Assessment of Dependent Performance Shaping Factors in SPAR-H Based on Pearson Correlation Coefficient

With the improvement of equipment reliability,human factors have become the most uncertain part in the system.The standardized Plant Analysis of Risk-Human Reliability Analysis(SPAR-H)method is a reliable method in the field of human reliability analysis(HRA)to evaluate human reliability and assess risk in large complex systems.However,the classical SPAR-H method does not consider the dependencies among performance shaping factors(PSFs),whichmay cause overestimation or underestimation of the risk of the actual situation.To address this issue,this paper proposes a new method to deal with the dependencies among PSFs in SPAR-H based on the Pearson correlation coefficient.First,the dependence between every two PSFs is measured by the Pearson correlation coefficient.Second,the weights of the PSFs are obtained by considering the total dependence degree.Finally,PSFs’multipliers are modified based on the weights of corresponding PSFs,and then used in the calculating of human error probability(HEP).A case study is used to illustrate the procedure and effectiveness of the proposed method.

Factors Affecting Transformation Temperatures in Fe-Mn-Si-Cr-Ni Shape Memory Alloy

The effects of prestrain and annealing temperature on phase transformation temperatures in Fel4Mn5Si8Cr4Ni shape memory alloy have been studied. The results showed that when the annealing temperature was 673 K, both the At and the Ms temperatures increased appreciably as the prestrain increased, the As temperature increased slightly with increasing prestrain; the resistivity difference at 303 K between the heating and cooling curve also increased with increasing prestrain, which agreed with the recovery strain. The shape memory effect in Fe-Mn-Si-Cr-Ni shape memory alloy is caused by the stress-induced γ→ε martensite transformation and its reverse transformation. When the prestrain was 10%, the Ms temperature decreased remarkably as the annealing temperature increased.

Modified Sadowski formula-based model for the slope shape amplification effect under multistage slope blasting vibration

Blasting operations,which are crucial to open-pit mine production due to their simplicity and efficiency,require precise control through accurate vibration velocity calculations.The conventional Sadowski formula mainly focuses on blast center distance but neglects the amplification effect of blasting vibration waves by terraced terrain,from which the calculated blasting vibration velocities are smaller than the actual values,affecting the safety of the project.To address this issue,our model introduces the influences of slope and time into Sadowski formula to measure safety through blast vibration displacement.In the northern section of the open-pit quartz mine in Jinchang City,Gansu Province,China,the data of a continuous blasting slope project are referred to.Our findings reveal a noticeable vibration amplification effect during blasting when a multi-stage slope platform undergoes a sudden cross-sectional change near the upper overhanging surface.The amplification vibration coefficient increases with height,while vibration waves within rocks decrease from bottom to top.Conversely,platforms without distinct crosssectional changes exhibit no pronounced amplification during blasting.In addition,the vibration intensity decreases with distance as the rock height difference change propagates.The results obtained by the proposed blast vibration displacement equation incorporating slope shape influence closely agree with real-world scenarios.According to Pearson correlation coefficient(PPMCC)analysis,the average accuracy rate of our model is 88.84%,which exceeds the conventional Sadowski formula(46.92%).

基于k-shape_STL的用户短期用电负荷预测模型

为挖掘复杂环境因素对电力负荷预测效果的影响,提高电力负荷预测精确度,提出了一种基于k-shape时间序列聚类与STL季节趋势分解算法相结合的负荷曲线聚类预测模型(k-shape-seasonal and trend decomposition using loess-gradient boosting decision tree,k-shape-STL-GBDT)。首先分析用户用电时序特征,利用k-shape时间序列聚类算法根据负荷曲线划分用户聚类,其次,使用STL算法将不同簇的负荷数据划分为季节项、趋势项与随机项。然后,结合温度、湿度等影响因素搭建预测模型,以麻省大学smart*可再生能源项目的公开数据集为例进行分析,并与多种主流聚类分解预测模型进行对比。结果表明新提出的模型框架MAPE减少了4%以上,针对短期负荷预测表现出了较好的性能与预测精度。

STUDY OF THE STRESS INTENSITY FACTOR OF PREFORMED V SHAPE FRACTURE TIP

In order to make the fracture cross-section of rock smooth in controlled cutting-blast, generally, two V-shape-notches on the inner wall of a shot hole are notched in symmetry along the design direction. A V-shape notch approximately be considered as V-shape-fracture under certain condition. This paper gave the complex stress function of preformed V-shape-fracture under a blasting load. The stress field and displacement field at the tip of a preformed V-shape-fracture were derived with Westergaard's method, hence its stressintensity factor was obtained. To verify the derived results, blasting tests were made with concrete samples of 400mm×400mm×300mm, and all having, in the center, a drilled hole of 25mm in diameter and 200mm in height. The test result showed that the formulas derived are correct and effective.

Digital Image Correlation Using Specific Shape Function for Stress Intensity Factor Measurement

The stress intensity factor (SIF) is a critical parameter associated with the fracture behaviour of materials. In this paper, we select the displacement function around a crack tip as the shape function of the digital image correlation (DIC), which makes it possible to directly calculate the SIF by the correlation scheme. Moreover, we use a non-rectangular subset, which can reduce the influence of plastic deformation and crack width on the DIC measurement accuracy. We measured the SIF of a mode I crack in a super-hard aluminium alloy specimen to verify the performance of the proposed method. Our experimental results show that a DIC with a specific shape function can be used to accurately and efficiently calculate the SIF. Furthermore, we also present a practical application of our proposed method for determining the SIF, crack propagation angle and crack tip displacement. © 2017, Tianjin University and Springer-Verlag Berlin Heidelberg.

Influence of Soft Filler on Stress Concentration Factor of Elliptic Holes in a Rectangular Plate

Finite element models were established to analyze the influence of soft filler on stress concentration for a rectangular plate with an elliptic hole in the center. The influence was quantified by means of stress concentration factor (SCF). Seven shape factors of the elliptic hole and three levels of elasticity modulus of the soft filler were considered. The reduction coefficient and sensitivity index of SCF are the two indicators in evaluating the influence of soft filler. It was found that the reduction coefficient of SCF increases significantly as the shape factor and the elasticity modulus of the filler increase, indicating that soft filler can reduce the concentrated stress effectively, especially when the shape factor is great. Analysis for the sensitivity index of SCF indicates that SCF is more sensitive to materials with small elasticity modulus than to materials with large one.

Analysis of dynamic stress intensity factors of thick-walled cylinder under internal impulsive pressure

Dynamic stress intensity factors are evaluated for thick-walled cylinder with a radial edge crack under internal impulsive pressure. Firstly, the equation for stress intensity factors under static uniform pressure is used as the reference case, and then the weight function for a thick-walled cylinder containing a radial edge crack can be worked out. Secondly, the dynamic stresses in uncracked thick-walled cylinders are solved under internal impulsive pressure by using mode shape function method. The solution consists of a quasi-static solution satisfying inhomogeneous boundary conditions and a dynamic solution satisfying homogeneous boundary condi- tions, and the history and distribution of dynamic stresses in thick-walled cylinders are derived in terms of Fourier-Bessel series. Finally, the dynamic stress intensity factor equations for thick-walled cylinder containing a radial edge crack sub- jected to internal impulsive pressure are given by dynamic weight function method. The finite element method is utilized to verify the results of numerical examples, showing the validity and feasibility of the proposed method.

Mechanical Behavior and Shape Optimization of Lining Structure for Subsea Tunnel Excavated in Weathered Slot

Subsea tunnel lining structures should be designed to sustain the loads transmitted from surrounding ground and groundwater during excavation. Extremely high pore-water pressure reduces the effective strength of the country rock that surrounds a tunnel, thereby lowering the arching effect and stratum stability of the structure. In this paper, the mechanical behavior and shape optimization of the lining structure for the Xiang＇an tunnel excavated in weathered slots are examined. Eight cross sections with different geometric parameters are adopted to study the mechanical behavior and shape optimization of the lining structure. The hyperstatic reaction method is used through finite element analysis software ANSYS. The mechanical behavior of the lining structure is evidently affected by the geometric parameters of crosssectional shape. The minimum safety factor of the lining structure elements is set to be the objective function. The efficient tunnel shape to maximize the minimum safety factor is identified. The minimum safety factor increases significantly after optimization. The optimized cross section significantly improves the mechanical characteristics of the lining structure and effectively reduces its deformation. Force analyses of optimization process and program are conducted parametrically so that the method can be applied to the optimization design of other similar structures. The results obtained from this study enhance our understanding of the mechanical behavior of the lining structure for subsea tunnels. These results are also beneficial to the optimal design of lining structures in general.

Theoretical studies on particle shape classification based on simultaneous small forward angle light scattering and aerodynamic sizing

Particle shape contributes to understanding the physical and chemical processes of the atmosphere and better ascer- taining the origins and chemical compositions of the particles. The particle shape can be classified by the aspect ratio. which can be estimated through the asymmetry factor measured with angularly resolved light scattering. An experimental method of obtaining the asymmetry factor based on simultaneous small forward angle light scattering and aerodynamic size measurements is described briefly. The near forward scattering intensity signals of three detectors in the azimuthal angles at 120° offset are calculated using the methods of T-matrix and discrete dipole approximation. Prolate spheroid particles with different aspect ratios are used as the shape models with the assumption that the symmetry axis is parallel to the flow axis and perpendicular to the incident light. The relations between the asymmetry factor and the optical size and aerodynamic size at various equivalent sizes, refractive indices, and mass densities are discussed in this paper. The numerically calculated results indicate that an elongated particle may be classified at diameter larger than 1.0 μm, and may not be distinguished from a sphere at diameter less than 0.5 μm. It is estimated that the lowest detected aspect ratio is around 1.5： I in consideration of the experimental errors.

基于shapely分解法的宁夏卫生总费用影响因素研究

[目的]研究宁夏卫生总费用的影响因素,为宁夏地区控制卫生总费用的不合理增长提供政策建议。[方法]运用相关性分析、多元线性回归分析、逐步回归分析以及shapely分解法对宁夏2003-2017年卫生总费用影响因素进行分析。[结果]每千人口医疗技术人员数对宁夏卫生总费用的贡献率为26.29%,其后依次是公立医院住院病人人均医药费用、农村居民人均医疗保健支出和城镇居民人均医疗保健支出,其贡献率分别为25.21%、25.18%和23.32%。[结论]每千人口卫生技术人员数、医疗技术水平和城乡居民医疗保健支出是引起宁夏卫生总费用上涨的重要因素。应加大对卫生技术人员的引进和培养力度,将医疗技术进步转向低价高效,合理分流病人,控制宁夏地区的卫生总费用不合理增长。

A PENNY-SHAPED CRACK IN A MAGNETOELECTROELASTIC LAYER UNDER RADIAL SHEAR IMPACT LOADING

This paper analyzes the dynamic magnetoelectroelastic behavior induced by a pennyshaped crack in a magnetoelectroelastic layer. The crack surfaces are subjected to only radial shear impact loading. The Laplace and Hankel transform techniques are employed to reduce the problem to solving a Fredholm integral equation. The dynamic stress intensity factor is obtained and numerically calculated for different layer heights. And the corresponding static solution is given by simple analysis. It is seen that the dynamic stress intensity factor for cracks in a magnetoelectroelastic layer has the same expression as that in a purely elastic material. And the influences of layer height on both the dynamic and static stress intensity factors are insignificant as h/a 〉 2.