塑料熔体三维流动的数值模拟

塑料熔体是具有记忆性的非线性黏弹性流体，为了准确分析板材挤出模具中熔体的流动，采用了积分型本构方程描述熔体的流变行为，同时给出熔体在狭缝流道中的控制方程。根据控制方程的特殊性，提出了把有限元半解析法应用于求解黏弹性流体流动问题这一思想，从而建立了有限单元体法，同时给出求解非线性有限元方程组的迭代方法，并采用以上方法对熔体在狭缝流道中的流动进行求解分析，将结果与三维有限元解法的结果相比较，证明结果是精确的，表明采用上述方法模拟熔体在狭缝中的流动是简便可行的。     

夹套管端板强度分析探讨

通过对夹套管结构进行分析,建立了端板力学模型,用板理论求解与内管连接处的应力,给出中心点作用力的求解方程,建立了一套各种应力的评判方法,使得端板的强度分析更加方便、科学。     

基于观测器的受正弦扰动MIMO系统最优跟踪控制

研究具有外界正弦扰动作用下MIMO系统的最优跟踪控制问题.根据扰动特点,假设拉格朗日算子化简求解系统两点边值问题,通过求解Riccati方程和矩阵方程分别在有限时域和无限时域得到系统前馈反馈最优跟踪控制律.证明了最优跟踪控制律的存在唯一性条件,并给出了最优跟踪控制律的实现算法.构造降维参考输入观测器解决了控制律中前馈项物理不可实现问题.仿真结果表明了该方法的有效性.     

超临界反溶剂过程传质数学模型

建立了有机溶剂(甲苯)液滴与超临界反溶剂(超临界CO2)之间的传质模型,用于模拟超临界反溶剂制备微纳米粉体材料的传质过程。该模型考虑了双向传质过程,既有反溶剂向溶液的扩散过程,又有溶液中的溶剂向反溶剂的“汽化”过程。液滴的传质行为是影响颗粒形态和尺寸分布的关键因素。假定传质是在一个孤立的微小液滴与包围着它的反溶剂连续相间进行的,利用描述液滴内和液滴外某一点行为的连续方程、扩散方程、能量方程和动量方程,及界面上的守恒条件进行耦合,从而建立传质过程的数学模型,并给出求解方程和求解的边界条件和初始条件,进行数值求解。     

滚筒造粒过程建模与控制策略的发展与展望

介绍滚筒造粒过程控制的建模方法和控制策略两个方面的发展现状，造粒过程数学建模的发展趋势是集合平衡模型，因此建模部分主要是集合平衡模型的建立、降阶及求解等；控制部分根据控制方法分为优化控制、预测控制、容错控制及智能控制等。最后通过现状分析，给出可能的发展方向。     

板类制件水辅助注射成型流动过程的数值模拟研究

基于Hde-Shaw流动模型，采用广义牛顿流体本构方程，建立了三维薄壁制件的水辅助注射成型充填阶段的数学模型，采用黏性、可压缩非牛顿流体基本方程，建立了水辅助注射成型保压补缩阶段的数学模型。采用有限元／有限差分／控制体积法数值求解。最后对一具有梯形截面水道的薄壁平板零件的水辅助注射成型流动过程进行了模拟，模拟所得到的熔体前沿位置与前人实验结果吻合较好，浇口处压力变化、水的厚度分布及平均温度分布合理。     

梭式窑内卫生瓷烧成过程热应力场的三维有限元分析

本文依据传热学和弹性力学理论,建立了梭式窑内卫生瓷烧成过程的数学模型.给出了求解理论模型的有限元法.推导了热传导有限元方程和热弹性运动有限元方程.以实例进行了模拟计算,并对输出结果进行了可视化处理.     

Benney方程的对称和群不变解

主要讨论Benney方程的一些对称以及与这些对称相应的单参数不变群的群不变解。Benney方程直接求解较困难,这里将其某些类型的求解转化为常微分方程,首先讨论了Benney方程的一些对称及其李代数,接着给出了与这些对称相应的单参数不变群,然后利用对称约化给出Benney方程的相应于这些单参数不变群的群不变解。对于Benney方程这一不易直接求解的高阶偏微分方程,文章利用了对称约化这种与微分几何密切相关的方法,给出了其一些特殊的解。     

采用Adomian逆算符方法对环流循环除尘系统分离柱内旋风流场的分析

由柱坐标系下的Navier-Stokes方程出发,建立了环流循环除尘系统分离柱内旋风流场的数学模型,利用对求解非线性微分方程非常有效的Adomian分解法——逆算符方法对流场进行求解,给出了三维流速(径向、切向和轴向)的解析表达式。     

注塑成型充填过程数值模拟的隐式算法

应用有限元 /控制体积方法 ,基于熔体在控制体积内的质量守恒 ,以结点压力和充填分数为未知量 ,建立了熔体在充填阶段流动的控制方程 ,并对方程进行隐式求解 ,完成了对注塑成型充填过程的数值模拟 .算例分析证明算法是正确的     

注塑模典型截面温度场的数值分析

通过二维典型截面简化模具的三维结构,建立了注塑模典型截面温度场的边界积分方程,并进行数值求解。将模具温度分为稳态和波动两部分,稳态部分是采用循环平均假设,推导出求解模具典型截面二维稳态温度场的边界积分方程。然后利用边界元法,分别对动模和定模进行传热分析,根据分型面边界相容性条件进行耦合;波动部分是在给出温度波动的微分方程后,利用有限差分法结合传热学对型腔表面温度波动进行数值求解。最后通过实例验证了文中算法的正确性与有效性。     

Equal Low-Order Finite Element Simulation of the Planar Contraction Flow for Branched Polymer Melts

The rheological characteristics of branched polymer melts is described by the modified XPP model, which is discretized by inconsistent streamline-upwind method. A finite increment calculus procedure is introduced to reformulate the mass equation and to overcome oscillations of the pressure field. Moreover, the governing equations are discretized and solved by the iterative fractional step algorithm. Thus the equal low-order finite elements for velocity-pressure-stress variables are adopted to calculate the planar contraction viscoelastic flows. The influences of the Weissenberg number and the amount of branched-arms on the rheological behavior of the Pom-Pom molecule are discussed. Results demonstrate good agreement with those given in the literatures.     

MODELING VACUUM-CONTACT DRYING OF WOOD: THE WATER POTENTIAL APPROACH

ABSTRACT

A two-dimensional mathematical model for vacuum-contact drying of wood is presented. The moisture and heat equations are based on the water potential concept whereas the pressure equation is formulated considering unsteady state conservation equation of dry air. Most of the model parameters were determined during independent experiments. The set of equations is then solved in a coupled form using the finite element method. The validation of the model is performed using experimental results obtained during vacuum-contact drying of sugar maple sapwood. The experimental and calculated data are in good agreement. Nevertheless, some discrepancies are observed which can be attributed to the boundary conditions used and to the fact that heat transfer by convection was neglected.     

Viscous flow in a channel partially filled with a porous medium and with wall suction

In this paper, we consider a coupled two-dimensional flow of a Newtonian fluid, both above and through a porous medium. In the fluid-only region, the two-dimensional flow field is governed by the Navier-Stokes equation. We consider the Brinkman-extended Darcy law relationship in the porous medium. Inertial terms are retained in the formulation and the interface conditions between the two domains are those as outlined by Ochoa-Tapia and Whitaker (Int. J. Heat Mass Transfer 38 (1995) 2635). It should be noted that these interface conditions are formulated with an empirical constant β that is unknown a priori. The model equations were solved using two independent methods. In the first method, we pose a similarity variable and reduce the governing equations to two, coupled, non-linear ordinary differential equations. In the second approach, the governing equations were re-posed as a one-domain problem, using the procedure outlined by Basu and Khalili (Phys. Fluids 11 (1999) 1031), so that the conditions at the interface need not be considered. The resulting equation was solved directly, in primitive variable form, using a finite volume formulation. This enabled us to determine β by comparing the resulting solutions.     

Coupled analysis of injection molding filling and fiber orientation,including in-plane velocity gradient effect

On injection molding of short fiber reinforced plastics, fiber orientation during mold filling is determined by the flow field and the interactions between the fibers. The flow field is, in turn, affected by the orientation of fibers. The Dinh and Armstrong rheological equation of state for semiconcentrated fiber suspensions was incorporated into the coupled analysis of mold filling flow and fiber orientation. The viscous shear stress and extra shear stress due to fibers dominate the momentum balance in the coupled Hele-Shaw flow approximation, but the extra in-plane stretching stress terms could be of the same order as those shear stress terms, for large in-plane stretching of suspensions of large particle number. Therefore, a new pressure equation, governing the mold filling process, was derived, including the stresses due to the in-plane velocity gradients. The mold filling simulation was then performed by solving the new pressure equation and the energy equation via a finite element/finite difference method, as well as evolution equations for the second-order orientation tensor via the fourth-order Runge-Kutta method. The effects of stresses due to the in-plane velocity gradient on pressure, velocity, and fiber orientation fields were investigated in the center-gated radial diverging flow in the cases of both an isothermal Newtonian fluid matrix and a nonisothermal polymeric matrix. In particular, the in-plane velocity gradient effect on the fiber orientation was found to be significant near the gate, and more notably for the case of a nonisothermal polymer matrix.     

塑料熔体在注塑模中的三维流动模拟

建立了非等温条件下黏性、不可压缩、非牛顿流体流动的控制方程.为了避免同时求解耦合的压力场、速度场,通过修改传统方法的变分方程导出了关于压力场的拟Poisson方程,用迭代法独立求解连续性方程、动量方程,并进行速度场-黏度迭代求出最终的压力场、温度场.这种方法可以减少内存,提高数值方法的稳定性,避免了Hele-Shaw模型中容易引起争议的“中面”概念,并能模拟中面方法不能模拟的一些物理现象.算例表明数值结果与实验结果吻合较好,这种方法可以成功地预测注射成型流动过程中的重要特征.     

矩形电渗流道中焦耳热效应的数值模拟研究

对玻璃和聚二甲基硅氧烷(PDMS)制成的矩形微流道中电渗流(EOF)的温度场进行了数值模拟研究。焦耳热效应的数学模型包括控制电势场的Poisson-Boltzm ann方程,控制流场的修正Navier-Stokes方程和控制温度场的能量方程。电势场、流场和温度场通过与温度有关的流体属性耦合在一起,将耦合的控制方程简化之后,应用有限元方法完成了矩形电渗流道中温度场的仿真计算。数值模拟结果表明,相同条件下,PDMS制成的微流道中的溶液温度明显高于玻璃制成的微流道中的溶液温度,且尺寸较大的PDMS流道中(h=48μm,b=96μm)的溶液温度明显高于尺寸较小的PDMS流道(h=32μm,b=96μm)中的溶液温度。     

VELOCITY AND TEMPERATURE DISTRIBUTIONS BETWEEN PARALLEL POROUS PLATES WITH HALL EFFECT AND VARIABLE PROPERTIES

Unsteady hydromagnetic flow and heat transfer between two parallel porous plates is studied with the Hall effect and temperature-dependent properties. The fluid is acted upon by a constant pressure gradient and an external uniform magnetic field, and uniform suction and injection are applied perpendicular to the parallel plates. A numerical solution for the governing nonlinear equations of motion and the energy equation is obtained. The effects of the Hall term and the temperature-dependent viscosity and thermal conductivity on both the velocity and temperature distributions are examined.     

VELOCITY AND TEMPERATURE DISTRIBUTIONS BETWEEN PARALLEL POROUS PLATES WITH HALL EFFECT AND VARIABLE PROPERTIES

Unsteady hydromagnetic flow and heat transfer between two parallel porous plates is studied with the Hall effect and temperature-dependent properties. The fluid is acted upon by a constant pressure gradient and an external uniform magnetic field, and uniform suction and injection are applied perpendicular to the parallel plates. A numerical solution for the governing nonlinear equations of motion and the energy equation is obtained. The effects of the Hall term and the temperature-dependent viscosity and thermal conductivity on both the velocity and temperature distributions are examined.