scholarly journals Numerical Simulation of Three-Dimensional Dendrite Movement Based on the CA–LBM Method

Crystals ◽  
2021 ◽  
Vol 11 (9) ◽  
pp. 1056
Author(s):  
Qi Wang ◽  
Yingming Wang ◽  
Shijie Zhang ◽  
Binxu Guo ◽  
Chenyu Li ◽  
...  
Keyword(s):  
3D Model ◽  
Three Dimensional ◽  
Solidification Process ◽  
Movement Direction ◽  
Liquid Boundary ◽  
Alloy Microstructure ◽  
The Difference ◽  
Boltzmann Method ◽  
Solid Liquid ◽  
2D Model

At present, the calculation of three-dimensional (3D) dendrite motion using the cellular automata (CA) method is still in its infancy. In this paper, a 3D dendrite motion model is constructed. The heat, mass, and momentum transfer process in the solidification process of the alloy melt are calculated using a 3D Lattice–Boltzmann method (LBM). The growth process for the alloy microstructure is calculated using the CA method. The interactions between dendrites and the melt are assessed using the Ladd method. The solid–liquid boundary of the solute field in the movement process is assessed using the solute extrapolation method. The translational velocity of the equiaxed crystals in motion is calculated using the classical mechanical law. The rationality of the model is verified and the movement of single and multiple 3D equiaxed crystals is simulated. Additionally, the difference between 3D dendrite movement and two-dimensional (2D) dendrite movement is analyzed. The results demonstrate that the growth of moving dendrites is asymmetric. The growth velocity and falling velocity of the dendrite in the 3D model are faster than that in 2D model, while the simulation result is more realistic than that of the 2D model. When multiple dendrites move, the movement direction of the dendrites will change due to the merging of flow fields and other factors.

scholarly journals Numerical Network Modeling of Heat and Moisture Transfer through Capillary-Porous Building Materials

Materials ◽  
2021 ◽  
Vol 14 (8) ◽  
pp. 1819
Author(s):  
Borys Basok ◽  
Borys Davydenko ◽  
Anatoliy M. Pavlenko
Keyword(s):  
Building Materials ◽  
Moisture Transfer ◽  
Three Dimensional ◽  
Total Pore Volume ◽  
Equivalent Diameter ◽  
Average Pore ◽  
The Difference ◽  
Three Dimensional Coordinate ◽  
Solid Liquid ◽  
Heat And Moisture

The article presents the modeling of the dynamics of the vapor-gas mixture and heat and mass transfer (sorption-desorption) in the capillary structure of the porous medium. This approach is underpinned by the fact that the porous structure is represented by a system of linear microchannels oriented along the axes of a three-dimensional coordinate system. The equivalent diameter of these channels corresponds to the average pore diameter, and the ratio of the total pore volume to the volume of the entire porous material corresponds to its porosity. The entire channel area is modeled by a set of cubic elements with a certain humidity, moisture content, pressure and temperature. A simulation is carried out taking into account the difference in temperatures of each of the phases: solid, liquid and gas.

Segregation Patterns and the Phase-Field 3D-Model for Adiabatic Phase Transition in Al-Cu Alloys

2013 ◽  
Vol 668 ◽  
pp. 870-874
Author(s):  
Heng Min Ding ◽  
Tie Qiao Zhang ◽  
Lv Chun Pu
Keyword(s):  
Dendritic Growth ◽  
3D Model ◽  
Three Dimensional ◽  
Cartesian Grid ◽  
Solute Diffusion ◽  
Solute Redistribution ◽  
Cu Alloys ◽  
Solid Phases ◽  
Solid Liquid ◽  
Liquid And Solid Phases

In the paper, a model basing on solute conservative in every unit is developed for solving the solute diffusion equation during solidification. The model includes time-dependent calculations for temperature distribution, solute redistribution in the liquid and solid phases. Three-dimensional computations are performed for Al-Cu dendritic growth into an adiabatic and highly supersaturated liquid phase. A numerical algorithm was developed to explicitly track the sharp solid/liquid (S/L) interface on a fixed Cartesian grid. Three-dimensional mesoscopic calculations were performed to simulate the evolution of equiaxed dendritic morphologies.

scholarly journals Mathematical Modelling for Micropiles Embedded in Salt Rock

2016 ◽  
Vol 12 (1) ◽  
pp. 23-35
Author(s):  
Georgiana Rădan (Toader) ◽  
Nicoleta Rădulescu ◽  
Gheorghe Oancea
Keyword(s):  
Mathematical Modelling ◽  
3D Model ◽  
Three Dimensional ◽  
Salt Rock ◽  
In Situ Tests ◽  
Calibration And Validation ◽  
Plaxis 3D ◽  
2D Model ◽  
Computing Models

Abstract This study presents the results of the mathematical modelling for the micropiles foundation of an investement objective located in Slanic, Prahova county. Three computing models were created and analyzed with software, based on Finite Element Method. With Plaxis 2D model was analyzed the isolated micropile and the three-dimensional analysis was made with Plaxis 3D model, for group of micropiles. For the micropiles foundation was used Midas GTS-NX model. The mathematical models were calibrated based with the in-situ tests results for axially loaded micropiles, embedded in salt rock. The paper presents the results obtained with the three software, the calibration and validation models.

Fetal weight estimation by automated three-dimensional limb volume model in late third trimester compared to two-dimensional model: a cross-sectional prospective observational study

2021 ◽  
Author(s):  
Xining Wu ◽  
Zihan Niu ◽  
Zhonghui Xu ◽  
Yuxin Jiang ◽  
Yixiu Zhang ◽  
...  
Keyword(s):  
Birth Weight ◽  
3D Model ◽  
Three Dimensional ◽  
Fetal Weight ◽  
Percentage Error ◽  
Limb Volume ◽  
Third Trimester ◽  
Volume Model ◽  
Estimated Error ◽  
2D Model

Abstract Background: Accurate estimation of fetal weight is important for prenatal care and for detection of fetal growth abnormalities. Prediction of fetal weight entails the indirect measurement of fetal biometry by ultrasound that is then introduced into formulae to calculate the estimated fetal weight. The aim of our study was to evaluate the accuracy of the automated three-dimensional(3D) fractional limb volume model to predict fetal weight in the third trimester.Methods: Prospective 2D and 3D ultrasonography were performed among women with singleton pregnancies 7 days before delivery to obtain 2D data, including fetal biparietal diameter, abdominal circumference and femur length, as well as 3D data, including the fractional arm volume (AVol) and fractional thigh volume (TVol). The fetal weight was estimated using the 2D model and the 3D fractional limb volume model respectively. Percentage error = (estimated fetal weight - actual birth weight) ÷ actual birth weight × 100. Systematic errors (accuracy) were evaluated as the mean percentage error (MPE). Random errors (precision) were calculated as±1 SD of percentage error.Results: Ultrasound examination was performed on 56 fetuses at 39.6 ± 1.4 weeks gestation. The average birth weight of the newborns was 3393 ± 530 g. The average fetal weight estimated by the 2D model was 3478 ± 467 g, and the MPE was 3.2 ± 8.9. The average fetal weights estimated by AVol and TVol of the 3D model were 3268 ± 467 g and 3250 ± 485 g, respectively, and the MPEs were -3.3 ± 6.6 and -3.9 ± 6.1, respectively. For the 3D TVol model, the proportion of fetuses with estimated error ≤ 5% was significantly higher than that of the 2D model (55.4% vs. 33.9%, p < 0.05). For fetuses with a birth weight < 3500 g, the accuracy of the AVol and TVol models were better than the 2D model (-0.8 vs. 7.0 and -2.8 vs. 7.0, both p < 0.05). Moreover, for these fetus, the proportions of estimated error ≤ 5% of the AVol and TVol models were 58.1% and 64.5%, respectively, significantly higher than that of the 2D model (19.4%) (both p < 0.05). The consistency of different examiners measuring fetal AVol and TVol were satisfactory,with the intraclass correlation coefficients of 0.921 and 0.963, respectively.Conclusion: In this cohort,the automated 3D fractional limb volume model improves the accuracy of weight estimation in most third-trimester fetuses. In particular, the 3D model estimation accuracy for fetuses with weight < 3500 g is significantly higher than that of the traditional 2D model.

For the Growth of 3 Inch D-Shaped GaAs Crystals by a Modified Horizontal Bridgman Process

1993 ◽  
Vol 207 (3) ◽  
pp. 185-195 ◽  
Author(s):  
M H Hsieh ◽  
C C Chieng ◽  
K H Lie ◽  
Y D Guo
Keyword(s):  
Dopant Concentration ◽  
Three Dimensional ◽  
Solidification Process ◽  
Temperature Fields ◽  
Liquid Interfaces ◽  
Axial Distribution ◽  
Mass Transfer Mechanism ◽  
Finite Volume Approach ◽  
Silicon Doped ◽  
Solid Liquid

Doped with silicon or zinc, 3 inch D-shaped GaAs crystals were grown by the modified two-temperature horizontal Bridgman (M2T-HB) technique. Then (1&10) wafers were sliced axially from the chunk of silicon-doped 3 inch GaAs crystals and chemically etched to reveal the growth striations of solid/liquid interfaces. Three-dimensional, numerical simulations of the solidification process for growing 3 inch crystals by the M2T-HB system were performed and compared with the etched (110) wafers from experiments. The heat- and mass-transfer mechanism through the melt is the combination of convection, conduction and radiation. The finite volume approach and the continuum model are employed to determine the position and shape of the interface of the solid/melt, dopant concentration and the temperature field in the crystal and melt. Two methods for computing the dopant concentration are (a) solving the transport equation of full mass concentration and (b) using the simplified model of equilibrium. The computed solidification fronts and the dopant distributions agree successfully with the experimental data, and the axial distribution of dopant concentration as well as flow and temperature fields are computed for information of the crystal quality.

scholarly journals Influence of Electric Field Coupling Model on the Simulated Performances of a GaN Based Planar Nanodevice

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
K. Y. Xu ◽  
Z. N. Wang ◽  
Y. N. Wang ◽  
J. W. Xiong ◽  
G. Wang
Keyword(s):  
Electric Field ◽  
3D Model ◽  
Second Harmonic ◽  
Strong Electric Field ◽  
Three Dimensional ◽  
Harmonic Oscillation ◽  
Two Dimensional ◽  
Dc Bias ◽  
Simulation Results ◽  
2D Model

The performances of a two-dimensional electron gas (2DEG) based planar nanodevice are studied by a two-dimensional-three-dimensional (2D-3D) combined model and an entirely 2D model. In both models, 2DEGs are depicted by 2D ensemble Monte Carlo (EMC) method. However electric field distributions in the devices are obtained by self-consistently solving 2D and 3D Poisson equations for the 2D model and the 2D-3D model, respectively. Simulation results obtained by both models are almost the same at low bias while showing distinguished differences at high bias. The 2D model predicts larger output current and slightly higher threshold voltage of Gunn oscillations. Although the fundamental frequencies of current oscillations obtained by both models are similar, the deviation of wave shape from sinusoidal waveform obtained by the 2D model is more serious than that obtained by 2D-3D model. Moreover, results obtained by the 2D model are more sensitive both to the bias conditions and to the change of device parameters. Interestingly, a look-like second harmonic oscillation has been observed at DC bias. We contribute the origin of divergences in simulation results to the different coupling path of electric field in the two models. And the second-harmonic oscillations at DC bias should be the result of the appearance of concomitant oscillations beside the channel excited by strong electric-field effects.

On the Two-Dimensional Simplification of Three-Dimensional Cementless Hip Stem Numerical Models

2017 ◽  
Vol 139 (3) ◽  
Author(s):  
Fernando J. Quevedo González ◽  
Michael Reimeringer ◽  
Natalia Nuño
Keyword(s):  
Cortical Thickness ◽  
Variable Thickness ◽  
3D Model ◽  
Numerical Models ◽  
Computational Cost ◽  
Three Dimensional ◽  
Symmetry Plane ◽  
Stair Climbing ◽  
Side Plate ◽  
2D Model

Three-dimensional (3D) finite element (FE) models are commonly used to analyze the mechanical behavior of the bone under different conditions (i.e., before and after arthroplasty). They can provide detailed information but they are numerically expensive and this limits their use in cases where large or numerous simulations are required. On the other hand, 2D models show less computational cost, but the precision of results depends on the approach used for the simplification. Two main questions arise: Are the 3D results adequately represented by a 2D section of the model? Which approach should be used to build a 2D model that provides reliable results compared to the 3D model? In this paper, we first evaluate if the stem symmetry plane used for generating the 2D models of bone-implant systems adequately represents the results of the full 3D model for stair climbing activity. Then, we explore three different approaches that have been used in the past for creating 2D models: (1) without side-plate (WOSP), (2) with variable thickness side-plate and constant cortical thickness (SPCT), and (3) with variable thickness side-plate and variable cortical thickness (SPVT). From the different approaches investigated, a 2D model including a side-plate best represents the results obtained with the full 3D model with much less computational cost. The side-plate needs to have variable thickness, while the cortical bone thickness can be kept constant.

Behaviors of Spherical and Nonspherical Particles in a Square Pipe Flow

2011 ◽  
Vol 9 (5) ◽  
pp. 1179-1192 ◽  
Author(s):  
Takaji Inamuro ◽  
Hirofumi Hayashi ◽  
Masahiro Koshiyama
Keyword(s):  
Polar Angle ◽  
Immiscible Fluids ◽  
Solid Particles ◽  
Spherical Particles ◽  
Nonspherical Particles ◽  
Fluid Mixture ◽  
Spherical Droplet ◽  
Liquid Boundary ◽  
Boltzmann Method ◽  
Solid Liquid

AbstractThe lattice Boltzmann method (LBM) for multicomponent immiscible fluids is applied to the simulations of solid-fluid mixture flows including spherical or non-spherical particles in a square pipe at Reynolds numbers of about 100. A spherical solid particle is modeled by a droplet with strong interfacial tension and large viscosity, and consequently there is no need to track the moving solid-liquid boundary explicitly. Nonspherical (discoid, flat discoid, and biconcave discoid) solid particles are made by applying artificial forces to the spherical droplet. It is found that the spherical particle moves straightly along a stable position between the wall and the center of the pipe (the Segré-Silberberg effect). On the other hand, the biconcave discoid particle moves along a periodic helical path around the center of the pipe with changing its orientation, and the radius of the helical path and the polar angle of the orientation increase as the hollow of the concave becomes large.

Comparison of Two-Dimensional and Three-Dimensional Thermal Models of the LENS® Process

2008 ◽  
Vol 130 (10) ◽  
Author(s):  
H. Yin ◽  
L. Wang ◽  
S. D. Felicelli
Keyword(s):  
Thermal Behavior ◽  
Molten Pool ◽  
3D Model ◽  
Dynamic Control ◽  
Three Dimensional ◽  
Element Model ◽  
Two Dimensional ◽  
3D Effects ◽  
Net Shaping ◽  
2D Model

A new two-dimensional (2D) transient finite element model was developed to study the thermal behavior during the multilayer deposition by the laser engineered net shaping rapid fabrication process. The reliability of the 2D model was evaluated by comparing the results obtained from the 2D model with those computed by a previously developed three-dimensional (3D) model. It is found that the predicted temperature distributions and the cooling rates in the molten pool and its surrounding area agree well with the experiment data available in literature and with the previous results calculated with the 3D model. It is also concluded that, for the geometry analyzed in this study, the 2D model can be used with good accuracy, instead of the computationally much more expensive 3D model, if certain precautions are taken to compensate for the 3D effects of the substrate. In particular, a 2D model could be applied to an in situ calculation of the thermal behavior of the deposited part during the fabrication, allowing dynamic control of the process. The 2D model is also applied to study the effects of substrate size and idle time on the thermal field and size of the molten pool.

scholarly journals A comparison of a two-dimensional depth averaged flow model and a three-dimensional RANS model for predicting tsunami inundation and fluid forces

2018 ◽  
Author(s):  
Xinsheng Qin ◽  
Michael Motley ◽  
Randall LeVeque ◽  
Frank Gonzalez ◽  
Kaspar Mueller
Keyword(s):  
Built Environment ◽  
3D Model ◽  
Computational Cost ◽  
Three Dimensional ◽  
Vertical Direction ◽  
3D Models ◽  
Tsunami Inundation ◽  
Model Based ◽  
Fine Mesh ◽  
2D Model

Abstract. The numerical modeling of tsunami inundation that incorporates the built environment of coastal communities is challenging for both depth-integrated 2D and 3D models, not only in modeling the flow, but also in predicting forces on coastal structures. For depth-integrated 2D models, inundation and flooding in this region can be very complex with variation in the vertical direction caused by wave breaking on shore and interactions with the built environment and the model may not be able to produce enough detail. For 3D models, a very fine mesh is required to properly capture the physics, dramatically increasing the computational cost and rendering impractical the modeling of some problems. In this paper, comparisons are made between GeoClaw, a depth-integrated 2D model based on the nonlinear shallow water equations (NSWE), and OpenFOAM, a 3D model based on Reynolds Averaged Navier-Stokes (RANS) equation for tsunami inundation modeling. The two models were first validated against existing experimental data of a bore impinging onto a single square column. Then they were used to simulate tsunami inundation of a physical model of Seaside, Oregon. The resulting flow parameters from the models are compared and discussed, and these results are used to extrapolate tsunami-induced force predictions. It was found that the 2D model did not accurately capture the important details of the flow near initial impact due to the transiency and large vertical variation of the flow. Tuning the drag coefficient of the 2D model worked well to predict tsunami forces on structures in simple cases but this approach was not always reliable in complicated cases. The 3D model was able to capture transient characteristic of the flow, but at a much higher computational cost; it was found this cost can be alleviated by subdividing the region into reasonably sized subdomains without loss of accuracy in critical regions.

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