A model for growth and engulfment of gas microporosity during aluminum alloy solidification process

A new coupled approach is presented for modeling the hydrogen bubble evolution and engulfment during an aluminum alloy solidification process in a micro-scale domain. An explicit enthalpy scheme is used to model the solidification process which is coupled with a level-set method for tracking the hydrogen bubble evolution. The volume averaging techniques are used to model mass, momentum, energy and species conservation equations in the chosen micro-scale domain. The interaction between the solid, liquid and gas interfaces in the system have been studied. Using an order-of-magnitude study on growth rates of bubble and solid interfaces, a criterion is developed to predict bubble elongation which can occur during the engulfment phase. Using this model, we provide further evidence in support of a conceptual thought experiment reported in literature, with regard to estimation of final pore shape as a function of typical casting cooling rates. The results from the proposed model are qualitatively compared with in situ experimental observations reported in literature. The ability of the model to predict growth and movement of a hydrogen bubble and its subsequent engulfment by a solidifying front has been demonstrated for varying average cooling rates encountered in typical sand, permanent mold, and various casting processes. (C) 2012 Elsevier B.V. All rights reserved.

An enthalpy-based model of dendritic growth in a convecting binary alloy melt

Purpose-In the present work, a numerical method, based on the well established enthalpy technique, is developed to simulate the growth of binary alloy equiaxed dendrites in presence of melt convection. The paper aims to discuss these issues. Design/methodology/approach-The principle of volume-averaging is used to formulate the governing equations (mass, momentum, energy and species conservation) which are solved using a coupled explicit-implicit method. The velocity and pressure fields are obtained using a fully implicit finite volume approach whereas the energy and species conservation equations are solved explicitly to obtain the enthalpy and solute concentration fields. As a model problem, simulation of the growth of a single crystal in a two-dimensional cavity filled with an undercooled melt is performed. Findings-Comparison of the simulation results with available solutions obtained using level set method and the phase field method shows good agreement. The effects of melt flow on dendrite growth rate and solute distribution along the solid-liquid interface are studied. A faster growth rate of the upstream dendrite arm in case of binary alloys is observed, which can be attributed to the enhanced heat transfer due to convection as well as lower solute pile-up at the solid-liquid interface. Subsequently, the influence of thermal and solutal Peclet number and undercooling on the dendrite tip velocity is investigated. Originality/value-As the present enthalpy based microscopic solidification model with melt convection is based on a framework similar to popularly used enthalpy models at the macroscopic scale, it lays the foundation to develop effective multiscale solidification.

Nonlinear preconditioning for efficient and accurate interface capturing in simulation of multicomponent compressible flows

Single fluid schemes that rely on an interface function for phase identification in multicomponent compressible flows are widely used to study hydrodynamic flow phenomena in several diverse applications. Simulations based on standard numerical implementation of these schemes suffer from an artificial increase in the width of the interface function owing to the numerical dissipation introduced by an upwind discretization of the governing equations. In addition, monotonicity requirements which ensure that the sharp interface function remains bounded at all times necessitate use of low-order accurate discretization strategies. This results in a significant reduction in accuracy along with a loss of intricate flow features. In this paper we develop a nonlinear transformation based interface capturing method which achieves superior accuracy without compromising the simplicity, computational efficiency and robustness of the original flow solver. A nonlinear map from the signed distance function to the sigmoid type interface function is used to effectively couple a standard single fluid shock and interface capturing scheme with a high-order accurate constrained level set reinitialization method in a way that allows for oscillation-free transport of the sharp material interface. Imposition of a maximum principle, which ensures that the multidimensional preconditioned interface capturing method does not produce new maxima or minima even in the extreme events of interface merger or breakup, allows for an explicit determination of the interface thickness in terms of the grid spacing. A narrow band method is formulated in order to localize computations pertinent to the preconditioned interface capturing method. Numerical tests in one dimension reveal a significant improvement in accuracy and convergence; in stark contrast to the conventional scheme, the proposed method retains its accuracy and convergence characteristics in a shifted reference frame. Results from the test cases in two dimensions show that the nonlinear transformation based interface capturing method outperforms both the conventional method and an interface capturing method without nonlinear transformation in resolving intricate flow features such as sheet jetting in the shock-induced cavity collapse. The ability of the proposed method in accounting for the gravitational and surface tension forces besides compressibility is demonstrated through a model fully three-dimensional problem concerning droplet splash and formation of a crownlike feature. (C) 2014 Elsevier Inc. All rights reserved.

T形微通道中互不相溶两相流数值模拟

采用摄动有限体积(PFV)算法和水平集(level set)技术对T形微通道内互不相溶两相流动进行了数值模拟研究。考察了两相界面张力和微通道壁面润湿性对流动的影响,精确地捕捉到了油水两相流动的界面。对一些典型的T形微通道油水两相流动进行了数值计算,模拟结果和实验结果吻合较好。分析总结出了微通道内两相流动过程中的一些基本规律,为微通道内的液液两相流动实验设计和工业应用提供了新的数值预测手段.

蒸汽-冷流体接触冷凝流动的数值模拟

介绍了关于蒸汽-冷流体直接接触冷凝流动与传热的数值计算模型与部分研究结果。用Level Set方法确定蒸汽-冷流体接触界面的位置和形状,建立了对蒸汽和冷流体普遍适用的动量、能量和质量守恒方程,在能量和质量寺恒方程中增加了部分项用于计算蒸汽冷凝所产生的影响。用有限差分法在交错网格上离散控制方程,用Runge-Kutta法-五阶WENO组合格式求解Level Set输运方程,用压力修正的迭代Projection方法求解动量方程,而用SIMPLE方法求解温度控制方程。对算例的计算结果表明,本文所建立的数值计算模型能反映物理现象的宏观特性。根据计算结果,分析了本文模型的优缺点,并指出了今后改进的方向。

气-液两相流界面迁移现象的数值模拟研究

借助于Level Set函数,建立了气-液两相的统一控制方程组,并在交错网格中进行离散.用两种格式,即Superbee-TVD格式和5阶WENO格式求解Level Set函数的输运方程,用SIMPLER算法的思想对主流场控制方程的求解方法进行改进.数值实验结果表明,在求解Level Set的控制方程时,5阶WENO方法比Superbee-TVD格式的结果更准确;用改进的数值算法可成功实现对密度比大于1 000/1的气-液两相流界面迁移问题的数值模拟.对几种典型大密度比气-液两相流问题的计算结果与实际问题的物理规律完全一致,验证了该方法的有效性和可靠性.

利用Ghost Fluid方法模拟激波与柱形界面相互作用

利用Ghost Fluid方法(后面简称Ghost方法)和γ-model方法，在同样的时空离散精度条件下，对激波与柱形界面相互作用的二维可压缩流场进行了直接模拟，并与实验结果相比较．从模拟结果看，在短时间内， Ghost方法和γ-model方法模拟的结果与实验结果基本相同，两种方法均正确地模拟出界面的位置、激波的强度和速度．但随着时间的发展，具有较大数值耗散的γ-model方法的计算结果与实验差别越来越大；而数值耗散较小的Ghost方法能较为正确地模拟界面的运动．

不同重力条件下不相溶流体层间界面波演化规律的数值模拟研究

报道了关于不相溶流体层间界面波演化规律的数值模拟研究及结果，重点考察了重力条件对界面波演化特性的影响。考虑在深度方向无限扩展的互不相容的两个流体层，上层流体比下层的轻，但比下层的运动速度快；两层流体间的界面上存在正弦波形的初始扰动，并随流体流动而不断变化。本文采用Level Set方法来实现对运动的相界面的追踪，用有限差分法来离散控制方程组。为了提高数值算法的稳定性，采用三阶的Runge-Kutta法来离散时间导数，而采用五阶的WENO（Weighted Essentially Non-oscillatory）格式来离散一阶对流输运项，并用压力修正投影法（Pressure Correction Projection Method）来实现离散控制方程组的求解。为了提高对复杂非稳态过程的解的准确度，采用了嵌套的三层迭代循环。本文对一系列工况条件下的界面波演化过程进行了计算；除了研究重力的作用之外，还考察了流体密度、粘性、表面张力、初始界面波频率、振幅及波数对界面波演化特性的影响。其中，上下流体层的最大密度比和粘性比可达3000/1，而重力加速度在0~5g0（g0=9.8m/s^2）之间变化，上下流体层间的最大速度差为8m/s。研究结果表明，随着重力、流体密度比、流体粘性比及表面张力的增加，界面波的演化受到不同程度的抑制，而界面波的传播速度也与重力及流体的密度、粘性和表面张力等因素相关。

Numerical simulation of a single fluid particle rising in non-Newtonian fluids

In this work, a level set method is developed for simulating the motion of a fluid particle rising in non-Newtonian fluids described by generalized Newtonian as well as viscoelastic model fluids. As the shear-thinning model we use a Carreau-Yasuda model, and the viscoelastic effect can be modeled with Oldroyd-B constitutive equations. The control volume formulation with the SIMPLEC algorithm incorporated is used to solve the governing equations on a staggered Eulerian grid. The level set method is implemented to compute the motion of a bubble in a Newtonian fluid as one of typical examples for validation, and the computational results are in good agreement with the reported experimental data．The level set method is also applied for simulating a Newtonian drop rising in Carreau-Yasuda and Oldroyd-B fluids．Numerical results including noticeably negative wake behind the drop and viscosity field are obtained, and compare satisfactorily with the known literature data.

An Improved Ce/Se Scheme For Multi-Material Elastic-Plastic Flows And Its Applications

In this paper, a new definition of SE and CE, which is based on the hexahedron mesh and simpler than Chang's original CE/SE method (the space-time Conservation Element and Solution Element method), is proposed and an improved CE/SE scheme is constructed. Furthermore, the improved CE/SE scheme is extended in order to solve the elastic-plastic flow problems. The hybrid particle level set method is used for tracing the interfaces of materials. Proper boundary conditions are presented in interface tracking. Two high-velocity impact problems are simulated numerically and the computational results are carefully compared with the experimental data, as well as the results from other literature and LS-DYNA software. The comparisons show that the computational scheme developed currently is clear in physical concept, easy to be implemented and high accurate and efficient for the problems considered. (C) 2008 Elsevier Ltd. All rights reserved.

New Numerical Algorithms in SUPER CE/SE and Their Applications in Explosion Mechanics

The new numerical algorithms in SUPER/CESE and their applications in explosion mechanics are studied. The researched algorithms and models include an improved CE/SE (space-time Conservation Element and Solution Element) method, a local hybrid particle level set method, three chemical reaction models and a two-fluid model. Problems of shock wave reflection over wedges, explosive welding, cellular structure of gaseous detonations and two-phase detonations in the gas-droplet system are simulated by using the above-mentioned algorithms and models. The numerical results reveal that the adopted algorithms have many advantages such as high numerical accuracy, wide application field and good compatibility. The numerical algorithms presented in this paper may be applied to the numerical research of explosion mechanics.

摄动有限体积算法及其在两相流中应用

采用一种全新的摄动有限体积(PFV)算法和水平集(Level Set)技术对液液两相系统中液滴坠落进行数值模拟,数值结果表明,PFV新算法具有节点少、精度高,效率高,编程方便等优点,能成功模拟液液两相流动,为两相流动数值模拟提供了一种新的途径.

Numerical simulation of condensation of bubbles under microgravity conditions by moving mesh method in the double-staggered grid

A numerical 2D method for simulation of two-phase flows including phase change under microgravity conditions is presented in this paper, with a level set method being coupled with the moving mesh method in the double-staggered grid systems. When the grid lines bend very much in a curvilinear grid, great errors may be generated by using the collocated grid or the staggered grid. So the double-staggered grid was adopted in this paper. The level set method is used to track the liquid-vapor interface. The numerical analysis is fulfilled by solving the Navier-Stokes equations using the SIMPLER method, and the surface tension force is modeled by a continuum surface force approximation. A comparison of the numerical results obtained with different numerical strategies shows that the double-staggered grid moving-mesh method presented in this paper is more accurate than that used previously in the collocated grid system. Based on the method presented in this paper, the condensation of a single bubble in the cold water under different level of gravity is simulated. The results show that the condensation process under the normal gravity condition is different from the condensation process under microgravity conditions. The whole condensation time is much longer under the normal gravity than under the microgravity conditions.

Influência do sistema de cimentação e do modo de ativação na resistência ao push-out de pinos de fibra de vidro

O objetivo deste estudo foi avaliar a influência do tipo de sistema de cimentação (condicionamento ácido total ou autoadesivo), do modo de ativação (autoativado ou dual), do terço do conduto radicular (cervical, médio ou apical) e da espessura do filme de cimento sobre a resistência de união de pinos de fibra de vidro cimentados em dentes humanos. Quarenta raízes foram incluídas em resina epóxi, submetidas a tratamento endodôntico e obturadas com guta percha e cimento endodôntico sem eugenol. Decorridos sete dias, os condutos foram preparados a uma profundidade de 10mm com brocas padronizadas do sistema dos pinos de fibra (WhitePost DC #2) e aleatoriamente divididos em 4 grupos, conforme o sistema de cimentação e o modo de ativação: (G1) RelyX ARC/Adper Scotchbond Multi-Purpose Plus (condicionamento ácido total), ativação dual, (G2) RelyX ARC/Adper Scotchbond Multi-Purpose Plus, autoativado, (G3) RelyX U100 (autoadesivo), dual e (G4) RelyX U100, autoativado. Após uma semana, cada raiz foi seccionada em máquina de corte, originando 6 fatias de 1 mm de espessura (n=60). Antes do ensaio de push-out cada fatia foi fotografada em ambas as faces, para determinação do raio dos pinos e da espessura do filme de cimento. Após o ensaio mecânico, novas imagens foram capturadas para determinação do modo de falha. Para automatizar a determinação da espessura de cimento, foi desenvolvida uma macro no software KS 400. Os dados foram estatisticamente analisados com ANOVA 3 fatores (resistência de união) e teste de Kruskall-Wallis (espessura do cimento). Comparações múltiplas foram realizadas com o teste Student-Newman-Keuls. Análise de regressão, modelo linear, foi empregada para verificar a correlação entre espessura do cimento e resistência de união. Todos os testes foram aplicados com α = 0,05. O fator cimento exerceu influência significativa para a resistência de união (p = 0,0402): o RelyX U100 apresentou a maior média. A ativação dual elevou os valores de resistência de união em comparação ao modo quimicamente ativado (p < 0,0001). Houve diferenças significantes entre os grupos, sendo G1 (22,4 4,0 MPa) > G3 (20,4 3,6 MPa) > G4 (17,8 5,2 MPa) > G2 (13,5 4,3 MPa). O terço do conduto não exerceu influência significativa sobre a resistência adesiva (p = 0,4749). As espessuras dos filmes de cimento foram estatisticamente diferentes nos diferentes terços: cervical (102 45 m) > médio (75 29 m) > apical (52 28m). Não foi observada forte correlação entre os valores de espessura e os de resistência ao push-out (r = - 0,2016, p = 0,0033). O tipo de falha predominante foi a mista, exceto para o G2, que apresentou 74% das falhas na interface cimento-pino. Dessa forma, o cimento autoadesivo apresentou melhor desempenho que o convencional, e ambos os sistemas duais, sobretudo o RelyX ARC, apresentaram dependência da fotoativação para atingirem maiores valores de resistência de união.

Microscopic Origin of Macroscopic Strength in Granular Media: A Numerical and Analytical Approach

Constitutive modeling in granular materials has historically been based on macroscopic experimental observations that, while being usually effective at predicting the bulk behavior of these type of materials, suffer important limitations when it comes to understanding the physics behind grain-to-grain interactions that induce the material to macroscopically behave in a given way when subjected to certain boundary conditions.

The advent of the discrete element method (DEM) in the late 1970s helped scientists and engineers to gain a deeper insight into some of the most fundamental mechanisms furnishing the grain scale. However, one of the most critical limitations of classical DEM schemes has been their inability to account for complex grain morphologies. Instead, simplified geometries such as discs, spheres, and polyhedra have typically been used. Fortunately, in the last fifteen years, there has been an increasing development of new computational as well as experimental techniques, such as non-uniform rational basis splines (NURBS) and 3D X-ray Computed Tomography (3DXRCT), which are contributing to create new tools that enable the inclusion of complex grain morphologies into DEM schemes.

Yet, as the scientific community is still developing these new tools, there is still a gap in thoroughly understanding the physical relations connecting grain and continuum scales as well as in the development of discrete techniques that can predict the emergent behavior of granular materials without resorting to phenomenology, but rather can directly unravel the micro-mechanical origin of macroscopic behavior.

In order to contribute towards closing the aforementioned gap, we have developed a micro-mechanical analysis of macroscopic peak strength, critical state, and residual strength in two-dimensional non-cohesive granular media, where typical continuum constitutive quantities such as frictional strength and dilation angle are explicitly related to their corresponding grain-scale counterparts (e.g., inter-particle contact forces, fabric, particle displacements, and velocities), providing an across-the-scale basis for better understanding and modeling granular media.

In the same way, we utilize a new DEM scheme (LS-DEM) that takes advantage of a mathematical technique called level set (LS) to enable the inclusion of real grain shapes into a classical discrete element method. After calibrating LS-DEM with respect to real experimental results, we exploit part of its potential to study the dependency of critical state (CS) parameters such as the critical state line (CSL) slope, CSL intercept, and CS friction angle on the grain's morphology, i.e., sphericity, roundness, and regularity.

Finally, we introduce a first computational algorithm to ``clone'' the grain morphologies of a sample of real digital grains. This cloning algorithm allows us to generate an arbitrary number of cloned grains that satisfy the same morphological features (e.g., roundness and aspect ratio) displayed by their real parents and can be included into a DEM simulation of a given mechanical phenomenon. In turn, this will help with the development of discrete techniques that can directly predict the engineering scale behavior of granular media without resorting to phenomenology.