Numerical Filling Simulation of Injection Molding Using Three-Dimensional Model

1 Introduction During injection moulding, the rheological response of polymer melts is generally non-Newtonian and nonisothermal with the position of the moving flow front. Because of these inherent factors, it is difficult to analyze the filling process. Therefore, simplifications usually are used. For example, in middle-plane technique and dual domain technique [1], because the most injection molded parts have the characteristic of being thin but generally of complex shape, the Hele-Shaw …     

Numerical Filling Simulation of Injection Molding Using Three-Dimensional Model

Most injection molded parts are three-dimensional, with complex geometrical configurations and thick/thin wall sections. A 3D simulation model will predict more accurately the filling process than a 2.5D model. This paper gives a mathematical model and numeric method based on 3D model, in which an equal-order velocity-pressure interpolation method is employed successfully. The relation between velocity and pressure is obtained from the discretized momentum equations in order to derive the pressure equation. A 3D control volume scheme is employed to track the flow front. The validity of the model has been tested through the analysis of the flow in cavity.     

有限单元法在塑料注射充模流动模拟中的应用

对塑料熔体注射成型充模流动过程的流变方程进行了熔体充模过程流变方程参数基于3维有限单元法的数值求解研究,得到基于形函数的压力刚度矩阵、温度刚度矩阵的方程式,进而得出压力场、速度场、温度场数值解的方程式。据此完成了注射熔体流动充模过程由M atlab编程实现的有限元分析本体程序。用具体的注射成型塑料制品作为检验实例,用2种不同的塑料进行注射成型模拟,其结果与国际著名的M old flow商品化软件和文献数据进行比较,表明本研究的设计软件算法正确、程序运行速度快。     

Coupled solid (FVM)–fluid (DSMC) simulation of micro-nozzle with unstructured-grid

The flow field and temperature distributions of free molecular micro-electro-thermal resist jet (FMMR) were studied resorting to DSMC–FVM coupled method. Direct simulation Monte Carlo (DSMC) method is the most useful tool to simulate the flow field of FMMR and unstructured grid is suitable for the flow simulation in a complicated region with tilted wall surface. DSMC code based on unstructured grid system was developed and the result was compared with that of structured grid and analytical solution to validate the reliability of the developed code. The DSMC method was then used to simulate the fluid flow in the micro-nozzle (Kn > 0.01) and the temperature distribution in the nozzle wall was obtained by the finite volume method (FVM). The Dirichlet–Neumann method was used to couple the wall heat flux and temperature between flow field and solid area. The effect of different income pressure was studied in detail and the results showed that the temperature of solid area changed drastically at different income pressure, so the commonly-adopted method of pre-setting boundary temperature before simulation was unreasonable.     

Pressure field evaluation in microchannel junction flows through μPIV measurement

An experimental method for evaluating pressure fields in a microchannel flow was studied using μPIV measurement in conjunction with the pressure Poisson equation. The pressure error due to the influence of numbers of measurement planes, computational grids for solving pressure Poisson equation, and an experimental error in μPIV measurement was evaluated with respect to the exact solution of Navier–Stokes equation for straight microchannel flow. The mean velocity field in microchannel junction flows with bifurcation and confluence was measured by a μPIV system, which consists of a CCD camera and a microscope with an in-line illumination of white light from stroboscopes. The planar velocity fields at various cross-sections of the microchannel flow were measured by traversing the focal plane within a depth of focus of the microscope. The pressure contour in the microchannel flow was evaluated by solving the pressure Poisson equation with the experimental velocity data. The results indicate that the pressure field in the microchannel junction flow agrees closely with the numerical simulation of laminar channel flow, which suggests the validity of the present method.     

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 met...     

ANSYS二次开发在PIM充模流动模拟中的应用

论文介绍了ANSYS所具有的针对不同需求、特点和应用范围的多种二次开发技术;根据PIM充模喂料流体的幂律模型,基于ANSYS用户可编程特性中对其FLOTRAN模块流体特性中的粘度模型进行了二次开发,用所开发的幂律模型对I型拉伸试样的PIM充模二维流动进行了数值模拟,模拟结果与实验结果吻合很好;并将二次开发的方法推广到PIM喂料的密度、导热系数、比热等的修改,为将ANSYS强大的计算流体力学功能广泛应用于PIM充模流动模拟的研究奠定了基础。     

Analysis of combined pressure-driven electroosmotic flow through square microchannels

In this paper three-dimensional single-phase liquid flow through microchannels with a square-shaped cross-section driven by simultaneous application of pressure gradient and electroosmotic pumping mechanism is studied. The governing system of equations consists of the electric potential field and flow field equations. The solution procedure involves three steps. First, the net charge distribution on the cross-section of the microchannel is computed by solving two-dimensional Poisson–Boltzmann equation using the finite element method. Then, using the computed fluid’s charge distribution, the magnitude of the resulting body force due to interaction of an external electric field with the charged fluid particles is calculated along the microchannel. In the third step, the flow equations are solved by considering three-dimensional Navier–Stokes equations with an electrokinetic body force. The computations reveal that the flow pattern in the microchannel is significantly different from the parabolic velocity profile of the laminar pressure-driven flow. The effect of the liquid bulk ionic concentration and the external electric field strength on flow patterns through the square-shaped microchannels is also investigated.     

Experiment and simulation of mixed flows in a trapezoidal microchannel

This paper presents experimental and numerical results of mixed electroosmotic and pressure driven flows in a trapezoidal shaped microchannel. A micro particle image velocimetry (μPIV) technique is utilized to acquire velocity profiles across the microchannel for pressure, electroosmotic and mixed electroosmotic-pressure driven flows. In mixed flow studies, both favorable and adverse pressure gradient cases are considered. Flow results obtained from the μPIV technique are compared with 3D numerical predictions, and an excellent agreement is obtained between them. In the numerical technique, the electric double layer is not resolved to avoid expensive computation, rather a slip velocity is assigned at the channel surface based on the electric field and electroosmotic mobility. This study shows that a trapezoidal microchannel provides a tapered-cosine velocity profile if there is any pressure gradient in the flow direction. This result is significantly different from that observed in rectangular microchannels. Our experimental results verify that velocity distribution in mixed flow can be decomposed into pressure and electroosmotic driven components.     

内置转子换热管强化传热数值模拟

为分析内置转子换热管的传热效果,建立光管和内置转子换热管的三维模型,对换热管内流场、温度场、压力场以及传热过程进行模拟,得到管内流体的阻力特性和传热特性.模拟结果表明:内置转子换热管内的三维流动比较复杂,转子与管壁之间缝隙内的流体有明显的环绕流动,切向速度和径向速度也增大到一定范围;相同雷诺数条件下,内置转子换热管压降...     

Capillary filling with the effect of pneumatic pressure of trapped air

This article presents an investigation into the effects of pneumatic pressure of trapped air on the dynamics of capillary filling. Controlled experiments were carried out in horizontal closed-end capillaries with diameters of 200–700 μm. Glycerol–DI water mixture solutions having viscosities ranging from 8 to 80 mPa s were used as the filling liquids. The pneumatic air backpressure is built up as a result of the air compressed at the closed end of the capillary. A model is presented based on the conventional theory of capillary filling (i.e., Washburn’s equation) with consideration of the effect of air backpressure force on the advancing meniscus. The molecular kinetics theory of Blake and De Coninck’s model (Adv Colloid Interface Sci 96:21–36, 2002) is also incorporated in the model to account for the dependence of dynamic contact angle on wetting velocity. The model predictions agree reasonably well with the experimental data. It is observed that due to the presence of air backpressure, the smaller the capillary diameter, the longer the length that the liquid fills the capillary, regardless of the liquid viscosity. It is also shown that the increased pneumatic air backpressure reduces the equilibrium contact angle (θ ⁰). A relation is then proposed among liquid penetration, capillary length and radius, and contact angle. In addition, a dimensionless analysis is performed on experimental data, and the power law dependence of dimensionless meniscus position on dimensionless time is obtained.     

Pressure drop of gas–liquid Taylor flow in round micro-capillaries for low to intermediate Reynolds numbers

In this paper, a model is presented that describes the pressure drop of gas–liquid Taylor flow in round capillaries with a channel diameter typically less than 1 mm. The analysis of Bretherton (J Fluid Mech 10:166–188, 1961) for the pressure drop over a single gas bubble for vanishing liquid film thickness is extended to include a non-negligible liquid film thickness using the analysis of Aussillous and Quéré (Phys Fluids 12(10):2367–2371, 2000). This result is combined with the Hagen–Poiseuille equation for liquid flow using a mass balance-based Taylor flow model previously developed by the authors (Warnier et al. in Chem Eng J 135S:S153–S158, 2007). The model presented in this paper includes the effect of the liquid slug length on the pressure drop similar to the model of Kreutzer et al. (AIChE J 51(9):2428–2440, 2005). Additionally, the gas bubble velocity is taken into account, thereby increasing the accuracy of the pressure drop predictions compared to those of the model of Kreutzer et al. Experimental data were obtained for nitrogen–water Taylor flow in a round glass channel with an inner diameter of 250 μm. The capillary number Ca _gl varied between 2.3 × 10⁻³ and 8.8 × 10⁻³ and the Reynolds number Re _gl varied between 41 and 159. The presented model describes the experimental results with an accuracy of ±4% of the measured values.     

旋风除尘器流场仿真分析

为分析旋风除尘器的速度场和分离效率,通过计算流体力学(Computational Fluid Dynamics,CFD)方法研究典型的旋风除尘器的强旋流场.用ANSYS Workbench提供的Geometry和Mesh软件进行三维几何建模和非结构网格划分,以高炉煤气的除尘为例进行流场仿真.湍流模拟采用雷诺应力模型,分离效率预测采用基于拉格朗日方法的离散相模型(Discrete Phase Model,DPM).通过分析压力场和速度场的分布,得到旋风除尘器中的内、外旋流结构;该结构并非完全稳定,涡轴存在一定的摆动.仿真结果表明选用的旋风除尘器模型对高炉煤气有良好的除尘效率.     

Dynamic aspects of electroosmotic flow

This article presents an analysis of the frequency and time dependent electroosmotic flow in open-end and closed-end microchannels of arbitrary cross-section shape. In the numerical model, the modified Navier–Stokes equation governing the AC electroosmotic flow is solved using the control volume method. The iterative approach is used to determine the induced backpressure gradient. The potential distribution of the EDL in the channel is obtained by solving the non-linear 2D Poisson–Blotzmann equation. The comparison between the control volume formulation and the Green’s function method for the case of a rectangular microchannel shows a good agreement. The time evolution of the electroosmotic flow and the effect of a frequency-dependent AC electric field on the oscillating electroosmotic flow are also examined. The effect of the induced backpressure gradient with the frequency of the applied electric field is also shown.     

Quadratic divergence-free finite elements on Powell–Sabin tetrahedral grids

Given a tetrahedral grid in 3D, a Powell–Sabin grid can be constructed by refining each original tetrahedron into 12 subtetrahedra. A new divergence-free finite element on 3D Powell–Sabin grids is constructed for Stokes equations, where the velocity is approximated by continuous piecewise quadratic polynomials while the pressure is approximated by discontinuous piecewise linear polynomials on the same grid. To be precise, the finite element space for the pressure is exactly the divergence of the corresponding space for the velocity. Therefore, the resulting finite element solution for the velocity is pointwise divergence-free, including the inter-element boundary. By establishing the inf-sup condition, the finite element is stable and of the optimal order. Numerical tests are provided.     

Multi-scale study of liquid flow in micro/nanochannels: effects of surface wettability and topology

The paper reports parametric study, using a molecular dynamics–continuum hybrid simulation method, of liquid flow in micro/nanochannels with surface nanostructures. The effects of channel height, shape of roughening element, ratio of pitch to length of roughening element and liquid–solid bonding strengths (representing surface wettability) on the velocity and temperature boundary conditions are investigated. The velocity boundary condition is found to shift from significant slip to locking due to the blocking of the surface nanostructure. The blocking appears weak for small pitch ratio and weak liquid–solid bonding. Distorted streamlines, small random eddies and appreciable density oscillations are seen in the vicinity of the wall for small pitch ratio and strong liquid–solid bonding. On the other hand, smooth streamlines and weak density oscillations are seen for large pitch ratio and weak liquid–solid bonding. Results also reveals that: relative slip length, relative Kapitza length and minus pressure gradient vary with channel height and pitch ratio in functions of power law and approximately linear, respectively; relative slip and Kapitza lengths vary with liquid–solid bonding strength as approximately decreasing power functions (except for the strongest case), whereas minus pressure gradient varies with liquid–solid bonding strength as approximately a logarithm-like function. The effect of shape of roughening element is found to be much less significant compared with the other factors studied.     

A molecular dynamics study of perturbed Poiseuille flow in a nanochannel

This paper reports the results from a nonequilibrium molecular dynamics (NEMD) simulation and analytical solution of Poiseuille flow through a nanochannel. Two kinds of external perturbing forces, sinusoidal and step pulse, have been applied on the flow passing through a nanochannel. A total number of 2,000 particles of simple fluid interacting with one another, according to the Week–Chandler–Anderson (WCA) potential model between two parallel plates, has been considered in this study. The flow is bounded by horizontal walls in one direction and periodic boundary conditions are imposed in the other two directions. The velocity profile predicted by molecular dynamics is a second-order polynomial and is in good agreement with the analytical solution based on the Navier–Stokes equations. The temperature profile obtained from the molecular dynamics simulation also conforms to the overall continuum predictions of a fourth-order polynomial energy equation. Moreover, in the vicinity of the boundaries, a jump in temperature profile has been observed.     

煤矿膏体充填测控系统与RBF神经网络建模

通过对充填实验工艺的研究,设计了可靠的充填实验过程计算机测控系统,实现对试验过程的监测与控制。煤矿现场井下管路的出口压力是主要的控制参量,它必须满足变化的射程。而现场井下环境极其恶劣,难以测量。采用RBF神经网络建模方法,获得了膏体容重、塌落度、质量浓度、平均流速与出口压力值之间的多变量非线性函数模型。经模拟实验系统检验,模型预报的出口压力满足精度要求,且具有快速性和实时性的特点,解决了现场实测困难的问题,为现场工程应用推广打好了基础。     

Simulations of unsteady cavitating turbulent flow in a Francis turbine using the RANS method and the improved mixture model of two-phase flows

This paper reports the simulation results for the unsteady cavitating turbulent flow in a Francis turbine using the mixture model for cavity–liquid two-phase flows. The RNG k–ε turbulence model is employed in the Reynolds averaged Navier–Stokes equations in this study. In the mixture model, an improved expression for the mass transfer is employed which is based on evaporation and condensation mechanisms with considering the effects of the non-dissolved gas, the turbulence, the tension of interface at cavity and the effect of phase change rate and so on. The computing domain includes the guide vanes, the runner, and the draft tube, which is discretized with a full three-dimensional mesh system of unstructured tetrahedral shapes. The finite volume method is used to solve the governing equations of the mixture model and a full coupled method is combined into the algorithm to accelerate the solution. The computing results with the mixture model have been compared with those by the single-phase flow model as well as the experimental data. The simulation results show that the cavitating flow computation based on the improved mixture model agrees much better with experimental data than that by the single-phase flow calculation, in terms of the amplitude and dominated frequency of the pressure fluctuation. It is also observed from the present simulations that the amplitude of the pressure fluctuation at small flow rate is larger than that at large flow rate, which accords with the experimental data.     

乙烯裂解炉反应管数学模拟新方法

综述了不同类型的乙烯裂解炉反应管数学模型，分析了各类模型的缺点。为此提出了一种进行反应管数学模拟的新方法。即应用CFD方法对反应管内流体流动、传热、传质及裂解反应过程，不经任何简化直接进行数值求解，得到了管内的流场、温度场和浓度场等详细信息。模拟计算得到了反应管长度方向上的温度、速度、压力和组分浓度的变化规律；在反应管径向上存在着明显的速度和温度分布，而组分浓度变化程度不如速度和温度明显；计算结果为提出结焦抑制方法提供了依据。