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Fully and sparsely supported radial basis functions 完全和稀疏支持的径向基函数
Pub Date : 2020-08-25 DOI: 10.2495/cmem-v8-n3-208-219
E. Kansa, P. Holoborodko
The central idea of this paper is that computer mathematics is not identical to ideal mathematics because computer numbers only have finite precision. All functions, especially the positive definite transcendental functions, are truncated and the expansion coefficients have finite precision and all branching operations require time to complete. Of all the known methods used to obtain numerical solutions to integral and partial differential equations, the global continuously differential radial basis functions (RBFs) that are implemented on computers closely resemble many aspects of ideal mathematics. The global RBFs have the attributes required to obtain very accurate numerical results for a variety of partial differential and integral equations with smooth solutions. Without the need for extremely fine discretization, the global RBFs have their spline properties and exponential convergence rates. The resulting system of full equations can be executed very rapidly on graphical processing units and fieldprogrammable gate arrays because, with full systems, there is no branching and full systems solvers are very highly vectorized, optimizing the usage of very fast processors.
本文的中心思想是计算机数学不等同于理想数学,因为计算机数字只有有限的精度。所有函数,特别是正定超越函数,都被截断,展开系数精度有限,所有分支操作都需要时间才能完成。在所有已知的用于获得积分和偏微分方程数值解的方法中,在计算机上实现的全局连续微分径向基函数(rbf)与理想数学的许多方面非常相似。全局rbf具有对各种具有光滑解的偏微分方程和积分方程获得非常精确的数值结果所需的属性。在不需要极精细离散化的情况下,全局rbf具有样条性质和指数收敛速度。由此产生的完整方程系统可以在图形处理单元和现场可编程门阵列上非常快速地执行,因为完整系统没有分支,并且完整系统求解器非常高度矢量化,从而优化了快速处理器的使用。
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引用次数: 1
Visualization of stratified flows aro und a vertical plate: laboratory experiment and numerical simulation 垂直板周围分层流动的可视化:实验室实验和数值模拟
Pub Date : 2020-04-07 DOI: 10.2495/cmem-v8-n2-148-161
Y. Chashechkin, Ya. V. Zagumennyi
On the basis of the fundamental system, which includes equations of continuity, momentum, and substance transfer with a linearized equation of state, methods of experimental and numerical study are developed for visualizing the flow perturbation fields generated by uniform horizontal movement of a vertical plate in a stratified medium. The stratified flows were visualized in the laboratory tank by the high-sensitive and high-resolution Schlieren instrument Iab-458 at the stand ‘laboratory Mobile Tank’ of the unique research facility ‘hPC IPMech raS’ and numerically calculated within the frame of the open source CfD utility OpenfOaM using computing resources of cluster systems and supercomputers. both the computation results and the laboratory visualization data show that a vertical plate uniformly moving in a stratified fluid generates flow patterns which contain complex systems of internal waves, including upstream, attached and short ones, and thin interfaces, such as ligaments, formed due to the combined influence of the stratification and dissipation effects. Increase in the velocity of the plate movement leads to an essential restructuring of the wake flow past the plate, where typical vortex elements, such as vortex dipoles and ‘vortex bubbles’, are formed in the divergence zones of the phase surfaces of internal waves. all the flow structural components evolve and actively interact with each other and with the free stream. The observation and calculation results are in a good qualitative and quantitative agreement with each other.
在包括连续性方程、动量方程和线性化状态方程的物质传递方程的基本系统的基础上,发展了实验和数值研究的方法来可视化在分层介质中垂直板均匀水平运动所产生的流动扰动场。在独特的研究设施“hPC IPMech raS”的“实验室移动槽”展台上,通过高灵敏度和高分辨率的纹影仪lab -458在实验室槽中可视化分层流动,并在开源CfD实用程序OpenfOaM框架内使用集群系统和超级计算机的计算资源进行数值计算。计算结果和实验室可视化数据均表明,垂直板在分层流体中均匀运动产生的流型包含复杂的内波系统,包括上游、附着和短内波系统,以及由于分层和耗散效应的共同影响而形成的薄界面,如韧带。板块运动速度的增加导致经过板块的尾流发生本质上的重构,其中典型的涡旋元素,如涡旋偶极子和“涡旋气泡”,在内波相面发散区形成。所有流的结构成分都在不断演化,并与自由流相互作用。观测结果与计算结果在定性和定量上有很好的一致性。
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引用次数: 4
Development of unified framework for microstr ucture, residual stress, and crack propensity prediction using phase-field simulations 利用相场模拟开发显微组织、残余应力和裂纹倾向预测的统一框架
Pub Date : 2020-04-07 DOI: 10.2495/cmem-v8-n2-111-122
A. Staroselsky, Ranadip Acharya, B. Cassenti
The approach to obtain a specific user-defined/as-desired or conformal/epitaxial microstructure in additive manufacturing (aM) is a challenging and expensive iterative process. Modeling and validation of solidification microstructure and residual stresses can be leveraged to reduce iteration cost in obtaining as-desired microstructure, minimize residual stress and prevent hot cracking. In the present study, computational fluid dynamics analysis is used to predict melt pool characteristics, and phase-field modeling is employed to simulate solidification with corresponding microstructure evolution in the as-deposited state for laser powder bed fusion (lPBf) process. Different features of lPBf microstructure such as segregation of secondary elements, dendrite sizes, dendritic orientation and dendritic morphology are predicted. The methods are further extended to predict orientation change as a function of number of layers. a constitutive materials model coupled to solidification is used to predict the stress in as-built part as well as the effect of stress on microstructural features. The model encompasses the effect of thermo-mechanical and shrinkage stresses and considers creep flow due to the presence of liquid phases in the mushy region. a phase-field-based methodology is proposed that can solve for hot cracking starting from the intrinsic defects such as porosity in lPBf process. Depending on the residual stress, crack propagation can be predicted from the unified model. The model was incorporated in a finite element code and used to predict crack growth phenomena such as values of critical stress, crack path, etc. Phase-field models of crack growth reduce the computational complications associated with singularities and allow finite element predictions of crack propagation without remeshing. This work intends to develop a unified phase-field framework that can sequentially predict solidification microstructure, residual stresses and structural cracking.
在增材制造(aM)中获得特定的用户定义/期望或保形/外延微观结构的方法是一个具有挑战性和昂贵的迭代过程。利用凝固组织和残余应力的建模和验证可以减少获得所需组织的迭代成本,最小化残余应力并防止热裂。本研究采用计算流体动力学方法预测熔池特性,采用相场模拟方法模拟激光粉末床熔合(lPBf)过程在沉积状态下的凝固及相应的组织演变。预测了二次元素偏析、枝晶尺寸、枝晶取向和枝晶形貌等lPBf微观结构的不同特征。该方法进一步扩展到预测取向变化作为层数的函数。采用凝固耦合的本构材料模型预测了成形件的应力以及应力对微观组织特征的影响。该模型考虑了热机械应力和收缩应力的影响,并考虑了由于在糊状区域存在液相而引起的蠕变流动。提出了一种基于相场的方法,可以从lPBf工艺中气孔等固有缺陷入手解决热裂问题。根据残余应力,可以从统一模型中预测裂纹扩展。该模型被纳入有限元程序中,用于预测临界应力值、裂纹路径等裂纹扩展现象。裂纹扩展的相场模型减少了与奇点相关的计算复杂性,并允许在不重新网格化的情况下对裂纹扩展进行有限元预测。本工作旨在建立一个统一的相场框架,可以依次预测凝固组织、残余应力和组织开裂。
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引用次数: 2
Experimental investigation of fire resistance of GLT beams GLT梁耐火性能试验研究
Pub Date : 2020-04-07 DOI: 10.2495/cmem-v8-n2-99-110
Lucie Kucíková, T. Janda, M. Šejnoha, J. Sýkora
Mechanical and fire loading play together with geometric and material properties of glued laminated timber beams a decisive role in theoretical investigation into the time-dependent fire resistance of these elements. This is a multidisciplinary problem including heat conduction, water evaporation, internal gas pressure evolution, pyrolysis, volume change, etc. If properly calibrated, such complex models should allow us to forecast the evolution and shape of the charred or zero strength layer. It is doubtless that the calibration and validation steps require experiments. In particular, the results of large-scale fire experiment are discussed in this contribution focusing on the influence of fire intensity and duration on the temperature and the charred layer evolution. The influence of fire on stiffness and strength will also be addressed through the results of Pilodyn measurements of wood elastic modulus and three-point bending tests of original and fire-exposed beams.
机械载荷和火灾载荷以及胶合层合木梁的几何和材料性能对这些构件随时间变化的耐火性能的理论研究起着决定性作用。这是一个多学科的问题,包括热传导、水蒸发、内部气体压力演变、热解、体积变化等。如果校准得当,这种复杂的模型应该允许我们预测烧焦或零强度层的演变和形状。毫无疑问,校准和验证步骤需要实验。本文特别讨论了大规模火灾实验的结果,重点讨论了火灾强度和持续时间对温度和烧焦层演变的影响。火灾对刚度和强度的影响也将通过木材弹性模量的Pilodyn测量结果和原始梁和火暴露梁的三点弯曲试验来解决。
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引用次数: 4
Oil/water flow in a horizontal pipe—dispersed flow regime 油水在水平管道分散流动状态下的流动
Pub Date : 2020-04-07 DOI: 10.2495/cmem-v8-n2-123-134
D. S. Sanstos, F. Garcia, M. Rasteiro, P. Faia
In multiphase fluid flow, the formation of dispersed patterns, where one of the phases is completely dispersed in the other (continuous medium) is common, for example, in crude oil extraction, during the transport of water/oil mixture. In this work, experimental and numerical studies were carried out for the flow of an oil/water mixture in a horizontal pipe, the dispersed liquid being a paraffin (oil with density 843 kg m−3 and viscosity 0.025 Pa s) and the continuous medium a water solution doped with NaCl (1000 μS. cm−1). The tests were made for oil concentrations of 0.01, 0.13 and 0.22 v/v and velocities between 0.9 and 2.6 ms−1 of the mixture. Experimental work was performed in a pilot rig equipped with an electrical impedance tomography (EIT) system. Information on pressure drop, EIT maps, volumetric concentrations in the vertical diameter of the pipe and flow images were obtained. Simulations were performed in 2dimensional geometry using the Eulerian–Eulerian approach and the k-ε model for turbulence modelling. The model was implemented in a computational fluid dynamics platform with the programme COMSOL Multiphysics version 5.3. The simulations were carried out using the Schiller–Neumann correlation for the drag coefficient and two equations for the viscosity calculation: Guth and Simba (1936) and Pal (2000). For the validation of the simulations, the pressure drop was the main control parameter. The simulations predicted the fully dispersed flow patterns and the pressure drop calculated when using the Pal (2000) equation for the viscosity calculation showed the best fit. The results of the images of the flows obtained by the photographs and simulations were in good agreement.
在多相流体流动中,一相完全分散在另一相(连续介质)中的分散模式的形成是常见的,例如,在原油开采中,在水/油混合物的运输过程中。本文对油水混合物在水平管内的流动进行了实验和数值研究,分散液体为石蜡(密度为843 kg m−3,粘度为0.025 Pa s),连续介质为掺入NaCl (1000 μS)的水溶液。厘米−1)。试验条件为油浓度为0.01、0.13和0.22 v/v,混合速度为0.9和2.6 ms−1。实验工作在配备电阻抗层析成像(EIT)系统的中试钻机上进行。获得了压降、EIT图、管道垂直直径内的体积浓度和流动图像等信息。利用欧拉-欧拉方法和k-ε湍流模型在二维几何结构中进行了模拟。该模型在计算流体动力学平台上使用COMSOL Multiphysics version 5.3程序实现。模拟采用了阻力系数的席勒-诺伊曼关系式和粘度计算的两个方程:Guth和Simba(1936)和Pal(2000)。为了验证仿真结果,以压降为主要控制参数。模拟结果表明,采用Pal(2000)公式计算的压降最适合于完全分散的流型。通过照片和模拟得到的流场图像吻合较好。
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引用次数: 1
Correction of wet gas flow measurements applying standard orifice 使用标准孔板校正湿气流量测量
Pub Date : 2020-04-07 DOI: 10.2495/cmem-v8-n2-175-185
Barbara Tomaszewska-Wach, M. Rząsa
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引用次数: 2
SO2 and NO2 simulation and validation in Metropolitan Lima using WRF-Chem model WRF-Chem模式对利马市区SO2和NO2的模拟与验证
Pub Date : 2020-04-07 DOI: 10.2495/cmem-v8-n2-135-147
A. Luna, H. Navarro, A. Moya
In recent times, air pollution in Peru is attracting the attention of the population and the government as well, who finally makes the policies that help us to preserve good air quality. In this research, we used the chemical-meteorological model Weather research and Forecasting coupled with Chemical (WrF-Chem v3.8) to predict pollution scenarios. We studied and analyzed three 2017 months of summer (January, February and March) and three months of winter (July, august and September) to evaluate and forecast two pollutants concentration, sulfur dioxide (SO2) and nitrogen dioxide (NO2) over the city of lima. We also considered the meteorological variables such as the wind speed and its direction, average temperature, relative humidity and atmospheric pressure. besides, we used fixed industrial sources inventory as emission data and the global Forecast System (gFS) as border data for the meteorological components. Within the WrF-Chem model, we implemented the grell-Freitas parameterization of convection to represent the clouds; we used rrTMg for the shortwave/longwave radiation scheme, and the Monin-Obukhov for the processes in the surface layer, among others. On the other hand, for the gas phase chemistry, we used the raDM2 scheme, for the aerosol module we utilized the MaDE-SOrgaM, and finally, we employed the Fast-j photolysis scheme. We finally compared the results with the data provided by the ten monitoring stations that belong to the National Service of Meteorology and hydrology (SENaMhI) which are located in strategic zones in lima. lastly, we showed that the variables studied are within the environmental quality standard authorized by the Ministry of the Environment, and we also demonstrated that the simulations given by the model are, in general, overlapping the values measured experimentally in all of the monitoring stations evaluated.
最近,秘鲁的空气污染引起了民众和政府的关注,他们最终制定了帮助我们保持良好空气质量的政策。在本研究中,我们使用化学-气象模式Weather research and Forecasting coupled with Chemical (WrF-Chem v3.8)来预测污染情景。我们研究和分析了2017年夏季的三个月(1月、2月和3月)和冬季的三个月(7月、8月和9月),以评估和预测利马市的两种污染物浓度,二氧化硫(SO2)和二氧化氮(NO2)。我们还考虑了风速和风向、平均温度、相对湿度和大气压力等气象变量。此外,我们使用固定工业源清单作为排放数据,全球预报系统(gFS)作为气象成分的边界数据。在WrF-Chem模型中,我们实现对流的grell-Freitas参数化来表示云;我们将rrTMg用于短波/长波辐射方案,并将Monin-Obukhov用于表面层的过程,等等。另一方面,对于气相化学,我们使用了raDM2方案,对于气溶胶模块,我们使用了MaDE-SOrgaM,最后,我们使用了Fast-j光解方案。最后,我们将结果与位于利马战略区域的国家气象和水文局(SENaMhI)的十个监测站提供的数据进行了比较。最后,我们证明了所研究的变量在环境部授权的环境质量标准范围内,并且我们还证明了模型给出的模拟结果总体上与所有评估监测站的实验测量值重叠。
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引用次数: 1
Corrosion of historic grey cast irons: indicative rates , significance, and protection 历史灰铸铁的腐蚀:指示率,意义和保护
Pub Date : 2020-04-07 DOI: 10.2495/cmem-v8-n2-162-174
M. Sýkora, K. Kreislová, P. Pokorný
In Europe many buildings and machinery in industrial sites are recognised as cultural heritage. These structures, often made from various types of irons or historic steels, have been for decades or centuries exposed to aggressive atmospheric environments and suffered from corrosion attack. The contribution discusses corrosion rates, the effects of corrosion on structural reliability, and the efficiency of surface treatments. The model for corrosion rates of historic metals cannot be based on the degradation model for mild steels even though specific features of historic alloys such as increased content of carbon and different chemical composition would be taken into account. realistic estimates of corrosion rates need additionally account for different micro-structure with inputs and different surface properties of historic alloys. This is why the presented model is based on a limited experimental data, considering the corrosivity of environment. The model assumes no corrosion during first seven years of service life and the same type of regression function for the progress period as is provided in ISO 9224 for mild steels and other metals. The effects of repeated applications of paintings are discussed. four principal strategies to the corrosion protection of industrial heritage structures include ‘leave as it is’, apply temporary protection to reduce degradation progress, apply long term protection, or undertake a complex restoration with replacement of damaged elements. Numerical example indicates that corrosion is normally insignificant for load-bearing iron structures, but may lead to severe problems for thin secondary structural and non-structural members such as railing or decorative elements. The proposed model estimates degradation progress in a mid-term perspective and supports decisions on maintenance of industrial heritage structures.
在欧洲,许多工业场所的建筑和机械被认定为文化遗产。这些结构通常由各种类型的铁或历史悠久的钢制成,几十年或几个世纪以来一直暴露在具有腐蚀性的大气环境中,并遭受腐蚀。该贡献讨论了腐蚀速率,腐蚀对结构可靠性的影响,以及表面处理的效率。即使考虑到历史合金的特定特征,如碳含量的增加和化学成分的不同,历史金属的腐蚀速率模型也不能以低碳钢的降解模型为基础。对腐蚀速率的实际估计还需要考虑不同的微观结构和不同的表面性能。这就是为什么所提出的模型是基于有限的实验数据,考虑到环境的腐蚀性。该模型假设在前七年的使用寿命内没有腐蚀,并且在进展期间采用与ISO 9224中为低碳钢和其他金属提供的相同类型的回归函数。讨论了绘画重复应用的效果。工业遗产结构腐蚀保护的四种主要策略包括“保持原状”,采用临时保护以减少退化进程,采用长期保护,或进行复杂的修复,更换损坏的元素。数值算例表明,通常情况下,腐蚀对承重铁结构来说是微不足道的,但对薄的二次结构和非结构构件(如栏杆或装饰构件)可能会导致严重的问题。提出的模型从中期角度估计退化进程,并支持有关工业遗产结构维护的决策。
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引用次数: 1
Reduced order model of glass plate loaded by low-velocity impact 玻璃板受低速冲击载荷的降阶模型
Pub Date : 2020-01-01 DOI: 10.2495/cmem-v8-n1-36-46
T. Janda, A. Zemanová, P. Hála, Petr Konrád, Jaroslav Schmidt
This article concerns a reduced order model of unconstrained glass plate exposed to low-velocity impact. First, three-parametric model consisting of two masses connected with elastic spring is introduced, its calibration procedure is described, and the simulation of its response to force impulses with different duration is shown. Then a five-parametric variant of the reduced order model is presented, calibrated and tested. Combined with the Hertzian theory of non-adhesive contact, the model allows us to determine the time evolution of contact force for arbitrary mass, stiffness and initial velocity of the impactor. The simulated results are compared to experimentally obtained data and observations about the model properties and accuracy are made.
本文研究无约束玻璃板受低速冲击时的降阶模型。首先,介绍了由两个质量体与弹性弹簧连接组成的三参数模型,描述了该模型的标定过程,并对其在不同持续时间的力脉冲下的响应进行了仿真。然后提出了降阶模型的五参数变体,并对其进行了校准和测试。结合赫兹非粘着接触理论,该模型可以确定任意质量、刚度和初始速度下冲击器接触力的时间演化。将模拟结果与实验数据进行了比较,并对模型的性能和精度进行了观察。
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引用次数: 6
CFD based determination of sublimation mass flux for lyophilization inside a vial 基于CFD的小瓶内冻干升华质量通量的测定
Pub Date : 2020-01-01 DOI: 10.2495/CMEM-V8-N1-47-60
M. Zadravec, J. Ravnik, Ziga Casar, M. Hriberšek
In the case of computational models of lyophilization in a vial, the intensity of drying is to a large extent controlled by the pressure conditions above the drying surface, as the drying driving force is the pressure difference between the saturation vapour pressure at the sublimation interface and the vapour partial pressure above the drying substance. In majority of studies, the effect of the vial and the rubber stopper geometry on the pressure conditions inside the vial is either neglected or taken into account by an estimated additional vapour pressure increase inside the vial. As the pressure conditions depend on the flow of sublimated solvent inside the vial-stopper conduit geometry, but are experimentally difficult to determine, a dedicated CFD analysis of flow conditions inside the vial-stopper channel was performed. The influence of imposing of the no-slip and slip conditions on the solid surfaces on the pressure drop in the system was studied and the effect of the increased partial pressure of the solvent on the sublimation rate was evaluated for the starting phase of the lyophilization by implementing the Stefan’s one sided diffusion model. The computational results show, that the effect of the additional flow resistance due to the vial conduit and the stopper is most significant at lowest system temperatures, with as much as 30% increase in vapour pressure inside the vial.
在小瓶冻干计算模型中,干燥强度在很大程度上由干燥表面上方的压力条件控制,因为干燥驱动力是升华界面处的饱和蒸汽压与干燥物质上方的蒸汽分压之间的压差。在大多数研究中,小瓶和橡胶塞几何形状对小瓶内压力条件的影响要么被忽略,要么被估计的小瓶内额外蒸汽压力增加考虑在内。由于压力条件取决于升华溶剂在小塞管内的流动几何形状,但在实验上难以确定,因此对小塞管内的流动条件进行了专门的CFD分析。采用Stefan单侧扩散模型,研究了固体表面施加无滑移和滑移条件对系统压降的影响,并评估了溶剂分压的增加对冻干起始阶段升华速率的影响。计算结果表明,在最低的系统温度下,由于小瓶导管和瓶塞造成的额外流动阻力的影响最为显著,小瓶内的蒸汽压力增加了30%。
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引用次数: 1
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THE INTERNATIONAL JOURNAL OF COMPUTATIONAL METHODS AND EXPERIMENTAL MEASUREMENTS
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