Simulation of Non-isothermal Injection Molding for a Non-Newtonian Fluid by Level Set Method

A non-isothermal injection molding process for a non-Newtonian viscous pseudoplastic fluid is simulated.A conservative interface capturing technique and the flow field solving method are coupled to perform a dynamic simulation.The validity of the numerical method is verified by a benchmark problem.The melt interface evolution versus time is captured and the physical quantities such as temperature,velocity and pressure at each time step are obtained with corresponding analysis.A"frozen skin"layer with the thickness increasing versus time during the injection process is found.The fact that the"frozen skin"layer can be reduced by increasing the injection velocity is numerically verified.The fountain flow phenomenon near the melt interface is also captured.Moreover,comparisons with the non-isothermal Newtonian case show that the curvatures of the interface arcs and the pressure contours near the horizontal mid-line of the cavity for the non-Newtonian pseudoplastic case is larger than that for the Newtonian case.The velocity profiles are different at different positions for the non-Newtonian pseudoplastic case,while in the case of Newtonian flow the velocity profiles are parabolic and almost the same at different positions.

New numerical algorithm of gas-liquid two-phase flow considering characteristics of liquid metal during mold filling

A new program is developed for gas-liquid two-phase mold filling simulation in casting. The gas fluid, the superheated liquid metal and the liquid metal containing solid grains are assumed to be governed by Navier-Stokes equations and solved through Projection method. The Level set method is used to track the gas-liquid interface boundary. In order to demonstrate the correctness of this new program for simulation of gas-liquid two-phase mold filling in casting, a benchmark filling experiment is simulated （this benchmark test is designed by XU and the filling process is recorded by a 16-mm film camera）. The simulated results agree very well with the experimental results, showing that this new program can be used to properly predicate the gas-liquid two-phase mold filling simulation in casting.

A Simple Weighted Integration Method for Calculating Surface Tension Force to Suppress Parasitic Flow in the Level Set Approach

Parasitic flows may occur in the numerical simulation of incompressible multiphase flow due to errors in the calculation of surface tension terms, specifically for the curvature and unit normal vector. An improved method for calculating the surface tension based on the level set approach is proposed, in which the contribution of not only the center node but also the rest area of a control volume to the calculation of surface tension is considered in a balanced manner. The weighted integration method (WIM) is more consistent with the concept of a banded interface in the level set method. It is applied to the temporal evolution of a two-dimensional neutrally buoyant liquid drop and a buoyancy driven deformable bubble in an immiscible fluid for the validation of WIM. The results show that the parasitic flows are evidently suppressed by the weighted integration method. The weight factors for WIM in 3-D cases are also suggested.

A Simple Weighted Integration Method for Calculating Surface Tension Force to Suppress Parasitic Flow in the Level Set Approach

Parasitic flows may occur in the numerical simulation of incompressible multiphase flow due to errors in the calculation of surface tension terms, specifically for the curvature and unit normal vector. An improved method for calculating the surface tension based on the level set approach is proposed, in which the contribution of not only the center node but also the rest area of a control volume to the calculation of surface tension is considered in a balanced manner. The weighted integration method (WIM) is more consistent with the concept of a banded in- terface in the level set method. It is applied to the temporal evolution of a two-dimensional neutrally buoyant liquid drop and a buoyancy driven deformable bubble in an immiscible fluid for the validation of WIM. The results show that the parasitic flows are evidently suppressed by the weighted integration method. The weight factors for WIM in 3-D cases are also suggested.

Simulation of Hydrophobicity Evaluation and Structural Optimization Design Method for Micro-Array Units

In recent years, researches published on hydrophobic materials increase rapidly, wherein the method for changing hydrophobicity by modifying a micro-array structure on the surface of the material also has been proposed. Of course, if it is possible for us to quantitatively analyse and evaluate hydrophobicity of different structures of one certain material at first, this task will greatly optimize the design of actual structures. In this work, we used the algorithm for Laminar Two-Phase Flow, Horizontal-set method integrated in COMSOL to build two single-pore simulation structures in different shapes and simulated the behaviour of the liquid transition from Cassie-state to Wenzel-state during the impregnation process. After that, the intrinsic contact angle of Structure T (a porous structure with a T-shaped sectional profile) was obtained under a certain pressure which maintained liquids in Cassie-state. Meanwhile, two equilibrium states of the liquid-air interface as well as two different patterns of the equilibrium state disrupting were found in Structure R (a porous structure with a Chamfered T-shaped sectional profile). Simulation results show that the modelling method can be applied for simulating the hydrophobicity of different porous structures and optimizing the procedures for the design of the micro-array efficiently.

追踪不可压缩两相流相界面的CLSVOF方法

根据CLSVOF方法的基本思想,将VOF和Level Set两种方法结合起来,用于追踪不可压缩两相流相界面的计算。通过对经典的两相流流动问题的计算,研究了CLSVOF方法对对流输运方程和动量输运方程计算精度的影响,并与VOF方法和Level Set方法进行了对比。研究结果表明:求解对流输运方程时,CLSVOF方法的计算精度明显高于Level Set方法;求解动量输运方程时,CLSVOF方法产生的虚假速度接近于0,基本克服了利用VOF方法求解动量输运方程时的虚假速度势问题。

求解不可压缩两相流的复合Level Set-VOF方法

目前,不可压缩两相流问题的数值求解方法主要有VOF方法和Level Set方法等.根据CLSVOF方法基本思想,通过将VOF和Level Set两种方法结合,实现了复合Level Set-VOF方法追踪不可压缩两相流相界面的模拟计算;对比分析了VOF、Level Set和复合Level Set-VOF方法计算经典两相流问题的结果.研究结果表明,复合Level Set-VOF方法继承了VOF方法精确构造相界面和Level Set方法精确计算表面张力的优点,能够有效削弱两相流求解过程中出现的虚假流动问题,因此可以更加精确地求解不可压缩两相流问题.

基于CLSVOF方法的多介质流运动界面追踪(英文)

根据Level-Set方法和VOF方法各自的优缺点,耦合生成一种Level-Set和VOF的耦合界面追踪方法,简称CLSVOF(Coupled Level Set and Volume Of Fluid Method)方法。CLSVOF方法利用Level-Set函数计算VOF体积份额,克服了VOF方法难以准确计算界面的法向量和曲率的缺点;同时又利用VOF体积份额修正Level-Set函数,克服了Lev-el-Set方法在计算过程中有物理量的损失的缺点。用旋转流场和剪切流场的数值算例验证了CLSVOF方法相比VOF方法提高了运动界面追踪的分辨率,相比Level-Set方法实现了计算过程中的物理量守恒。运用CLSVOF方法数值模拟了两个多介质流运动界面算例,分别是自由剪切层问题和气泡在静止水体中上升问题.对比数值模拟结果与理论分析和实验结果可知CLSVOF方法能精确地追踪多介质流运动界面。

PARALLEL ADAPTIVE SIMULATION OF A PLUNGING LIQUID JET

This paper is concerned with three-dimensional numerical simulation of a plunging liquid jet. The transient processes of forming an air cavity around the jet, capturing an initially large air bubble, and the break-up of this large toroidal-shaped bubble into smaller bubbles were analyzed. A stabilized finite element method （FEM） was employed under parallel numerical simulations based on adaptive, unstructured grid and coupled with a level-set method to track the interface between air and liquid. These simulations show that the inertia of the liquid jet initially depresses the pool＇s surface, forming an annular air cavity which surrounds the liquid jet. A toroidal liquid eddy which is subse- quently formed in the liquid pool results in air cavity collapse, and in turn entrains air into the liquid pool from the unstable annular air gap region around the liquid jet.

一类广义Kirchhoff方程基态变号解的存在性

研究了一类广义Kirchhoff方程-a+b∫R^(3)|u|2 d x△u+V(x)u=g(u)其中a,b>0是常数.由于在方程中出现了非局部项b∫R^(3)|u|2 d x△u,所以,方程的变分泛函与b=0时方程的变分泛函具有不同的性质.与相关文献相比,g不需要满足单调性条件,并且非线性项g包含g(t)=|t|^(p-2) t(2<p≤4)这种情况,V也不需要满足强制性条件.首先引入辅助算子,构造伪梯度向量场,证明了下降流不变集的存在性.其次,由于4超线性AR条件不成立,所以引入了一种非局部扰动方法,即增加了一个高阶项β|u|^(r-2)u和另一个非局部扰动.对于扰动问题,通过改进的AR条件和下降流不变集下的极大极小参数得到了扰动问题的变号解,进而得到了原方程的变号解.最后,证明了该变号解是原方程的基态变号解.

Formation of radially expanding liquid sheet by impinging two round jets

A thin circular liquid sheet can be formed by impinging two identical round jets against each other. The liquid sheet expands to a certain critical radial distance and breaks. The unsteady process of the formation and breakup of the liquid sheet in the ambient gas is simulated numerically. Both liquid and gas are treated as incompressible Newtonian fluids. The flow considered is axisymmetric. The liquid-gas interface is modeled with a level set function. A finite difference scheme is used to solve the governing Navier-Stokes equations with physical boundary conditions. The numerical results show how a thin circular sheet can be formed and break at its circular edge in slow motion. The sheet continues to thin as it expands radially. Hence, the Weber number decreases radially. The Weber number is defined as ρu 2 h/σ, where ρ and σ are, respectively, the liquid density and the surface tension, and u and h are, respectively, the average velocity and the half sheet thickness at a local radial location in the liquid sheet. The numerical results show that the sheet indeed terminates at a radial location, where the Weber number reaches one as observed in experiments. The spatio-temporal linear theory predicts that the breakup is initiated by the sinuous mode at the critical Weber number We c =1, below which the absolute instability occurs. The other independent mode called the varicose mode grows more slowly than the sinuous mode according to the linear theory. However, our numerical results show that the varicose mode actually overtakes the sinuous mode during the nonlinear evolution, and is responsible for the final breakup. The linear theory predicts the nature of disturbance waves correctly only at the onset of the instability, but cannot predict the exact consequence of the instability.

一类含凹项的分数阶Kirchhoff方程变号解的存在性和多重性

研究了一类含凹项的分数阶Kirchhoff方程变号解的存在性和多重性,利用下降流不变集方法验证了变号解的存在性,借助属和相对属得到了变号解的多重性,并且确定了节点域数界.研究结果改进并推广了已知结果.

Modeling OH transport phenomena in cold plasma discharges using the level set method

Cold atmospheric plasmas(CAPs)have attracted considerable interest in the field of plasma medicine.Generated reactive species such as hydroxyl(OH)species play an important role in applications of CAPs.Transportation of OH species towards the target and distribution of these OH species in the plasma plume play an important role in the applications of plasma medicine.In the present work,a computational model was built to simulate the transportation and distribution of OH species in CAP discharges,which was based on the level set method to dynamically track the propagation of plasma carrier gas in air.A reaction term was incorporated for the OH species.The OH species tended to diffuse around the main stream of the carrier gas,and thus covered larger radial and axial distances.A CAP discharge onto a skin layer led to the largest accumulation of OH species at the central part of the exposed area.The distribution of OH species on the skin was asymmetric,which agreed with experiments.The computational model itself and the obtained results would be useful for future development of plasma medicine.

A Low Mach Number IMEX Flux Splitting for the Level Set Ghost Fluid Method

Considering droplet phenomena at low Mach numbers,large differences in the magnitude of the occurring characteristic waves are presented.As acoustic phenomena often play a minor role in such applications,classical explicit schemes which resolve these waves suffer from a very restrictive timestep restriction.In this work,a novel scheme based on a specific level set ghost fluid method and an implicit-explicit(IMEX)flux splitting is proposed to overcome this timestep restriction.A fully implicit narrow band around the sharp phase interface is combined with a splitting of the convective and acoustic phenomena away from the interface.In this part of the domain,the IMEX Runge-Kutta time discretization and the high order discontinuous Galerkin spectral element method are applied to achieve high accuracies in the bulk phases.It is shown that for low Mach numbers a significant gain in computational time can be achieved compared to a fully explicit method.Applica-tions to typical droplet dynamic phenomena validate the proposed method and illustrate its capabilities.

Existence and Concentration of Sign-Changing Solutions of Quasilinear Choquard Equation

In this paper, we study the following quasilinear equation of choquard type: where A(x,t) is given real functions on RN × R and with N ≥ 3, 1 p N, max{N-2p,1} α N, , and ε > 0 is a small parameter, Iα is the Riesz potential. We establish for small ε the existence of a sequence of sign-changing solutions concentrating near a given local minimum point of the bounded potential function V by using the method of invariant sets of descending flow, perturbation method and truncation technique. .

Liquid-Gas Two-Phase Flow Simulation in Mold Filling Process with Level Set Method

Air entrapped in liquid metal during the mold filling process seriously affects the casting quality, thus it is important to track its behavior in the mold cavity. A liquid-gas two-phase flow model is developed to describe the mold filling process and predict the air entrapment defect. The model is based on the combination of SOLA and Level Set Method. The pressure and velocity fields are calculated by SOLA,and the interface movement is simulated by Level Set method as the most common interface tracking method in recent years.In order to validate the feasibility of the model,the liquid-gas two-phase simulation results were tested by the broken dam problem and the S-shaped experiment. Comparison between the experiments and simulation results show that Level Set method might be a very promising tool in two-phase flow simulation during the mold filling process.

A LEVEL SET METHOD FOR STRUCTURAL TOPOLOGY OPTIMIZATION WITH MULTI-CONSTRAINTS AND MULTI-MATERIALS

Combining the vector level set model,the shape sensitivity analysis theory with the gradient projection technique,a level set method for topology optimization with multi-constraints and multi-materials is presented in this paper.The method implicitly describes structural material in- terfaces by the vector level set and achieves the optimal shape and topology through the continuous evolution of the material interfaces in the structure.In order to increase computational efficiency for a fast convergence,an appropriate nonlinear speed mapping is established in the tangential space of the active constraints.Meanwhile,in order to overcome the numerical instability of general topology opti- mization problems,the regularization with the mean curvature flow is utilized to maintain the interface smoothness during the optimization process.The numerical examples demonstrate that the approach possesses a good flexibility in handling topological changes and gives an interface representation in a high fidelity,compared with other methods based on explicit boundary variations in the literature.

LEVEL SET METHOD FOR TOPOLOGICAL OPTIMIZATION APPLYING TO STRUCTURE, MECHANISM AND MATERIAL DESIGNS

Based on a level set model, a topology optimization method has been suggestedrecently. It uses a level set to express the moving structural boundary, which can flexibly handlecomplex topological changes. By combining vector level set models with gradient projectiontechnology, the level set method for topological optimization is extended to a topologicaloptimization problem with multi-constraints, multi-materials and multi-load cases. Meanwhile, anappropriate nonlinear speed, mapping is established in the tangential space of the activeconstraints for a fast convergence. Then the method is applied to structure designs, mechanism andmaterial designs by a number of benchmark examples. Finally, in order to further improvecomputational efficiency and overcome the difficulty that the level set method cannot generate newmaterial interfaces during the optimization process, the topological derivative analysis isincorporated into the level set method for topological optimization, and a topological derivativeand level set algorithm for topological optimization is proposed.

An explicit finite volume element method for solving characteristic level set equation on triangular grids

Level set methods are widely used for predicting evolutions of complex free surface topologies,such as the crystal and crack growth,bubbles and droplets deformation,spilling and breaking waves,and two-phase flow phenomena.This paper presents a characteristic level set equation which is derived from the two-dimensional level set equation by using the characteristic-based scheme.An explicit finite volume element method is developed to discretize the equation on triangular grids.Several examples are presented to demonstrate the performance of the proposed method for calculating interface evolutions in time.The proposed level set method is also coupled with the Navier-Stokes equations for two-phase immiscible incompressible flow analysis with surface tension.The Rayleigh-Taylor instability problem is used to test and evaluate the effectiveness of the proposed scheme.

Robust positively invariant sets of discrete-time convex polyhedral system family

Certain problems concerning state constraints and control constraints can often be reduced to the study of positive invariance of some subsets of the state space of dynamical systems. The robust positive invariance of given linear state constraint sets of uncertain discrete-time systems is studied by the mixed monotone decomposition method. Necessary and suffi-