纤维悬浮聚合物熔体中纤维影响的数值模拟

采用一种多尺度模型研究了纤维悬浮聚合物熔体的流动过程,通过宏观流体的流动状态、纤维所在尺度上的纤维取向表征和聚合物溶液大分子哑铃模型尺度上的哑铃概率分布三尺度信息,实现了纤维悬浮聚合物熔体流动控制方程和本构关系的三尺度共同表征。使用SIMPLER-FDMS算法对多尺度控制方程组进行了求解,并通过4∶1等温平板收缩流的数值模拟验证了该多尺度模型的有效性。通过对纤维浓度、纤维间相互作用以及纤维长径比的分析,研究了纤维参数对聚合物基熔体悬浮体系及纤维取向的影响。     

聚合物稀溶液的微观-宏观确定性模拟

采用确定性方法数值求解了聚合物稀溶液的微观-宏观模型,其中,宏观尺度上用有限体积法求解守恒方程,介观尺度上用谱方法求解Fokker-Planck方程和聚合物对偏应力张量的贡献,模拟了聚合物稀溶液FENE哑铃模型的平板Couette流动,给出了速度随时间变化的剖面图,分析了移动平板速度、哑铃的量纲1有限拉伸参数和Deborah数对流动的影响,同时也验证了有限体积法与谱方法结合求解聚合物微观-宏观模型的有效性。     

聚合物流动分子水平的数值模拟

提出一种新的聚合物流动分子水平的模拟方法,即将流线有限元与分子模型的Brown动力学模拟相结合,求解聚合物复杂流动问题。编写了相应的计算程序,成功地对平行平板间的绕圆柱流进行了模拟。研究的流体介质为Oldroyd-B流体,该流体对应虎克哑铃分子模型的牛顿溶剂稀溶液。通过和采用本构方程的计算结果对比,对这一新方法进行了评价。     

圆管聚合物热流中黏性耗散分析的无网格模拟

以与温度相关的指数定律作为本构方程,应用无网格方法模拟了外表面为恒温时的圆管内具有黏性耗散的聚合物流动热传导问题,给出了离入口不同位置处的温度分布。计算结果表明：根据黏性耗散模型计算的温度比无黏性耗散模型高出64℃,从而说明了黏性耗散在聚合物流动热传导问题中具有举足轻重的作用。并且, 无论是无黏性耗散模型,还是黏性耗散模型,其极限温度与壁面温度有很大的关系,但与入口温度无关。     

单螺杆挤出过程熔体输送段数值模拟方法

综述了应用于螺杆挤出成型过程熔体输送段数值模拟的各种计算方法，根据挤出过程聚合物流场控制方程，介绍了几种有代表性的聚合物本构关系，包括线性黏弹性和非线性黏弹性本构方程。概述了有限差分法、有限元法、有限体积法和边界元法等数值计算方法的特点和应用范围，并针对聚合物熔体流动模拟中的迭代收敛性和稳定性、耦合和解耦合、高Weissenberg数等问题进行了讨论，指出应该根据研究目的和实际情况选择适宜的本构方程和数值方法。     

聚合物材料力学性能的计算机模拟

聚合物材料的宏观力学性能与其微观结构具有密切的关系,计算机模拟是研究这种结构与性能关系的重要手段之一,近年来国内外学者已经发展了多种模拟方法并从不同尺度来模拟聚合物材料的力学性能。本文综述了不同方法在聚合物材料力学性能模拟研究中的应用,重点介绍了Monte Carlo模拟、分子动力学模拟和基于弹簧格子模型的多尺度模拟这3种常见模拟方法的应用情况,如在分子动力学模拟中重点关注无定形聚合物玻璃态、结晶聚乙烯和部分非均质体系,而在多尺度模拟中则重点关注复杂的非均质聚合物体系,并讨论了各种方法的应用前景及亟待解决的问题。     

基于两相模型的聚合物流动诱导结晶数值模拟

基于两相流动诱导结晶模型,采用谱方法分别计算无定形相的构象张量分布函数和半晶相的取向张量分布函数,进而根据Avrami方程和晶核成核速率与第一法向应力差的关系计算成核速率和结晶度。预测剪切对体系结晶速度的影响,并模拟了活化晶核数目和晶体取向的演化。计算结果表明,剪切对聚合物的结晶动力学性能有显著的影响,但是剪切对聚合物结晶的加速作用不是无限制的,随着剪切强度的增加,对结晶加速作用会变得不再明显。     

惰性气体对分子蒸馏过程的影响

本文采用基于Bohzmann方程的Bhatnagar—Gross—Krook模型方程，建立了计算多组分稀薄气体流动的数学模型和求解方法。应用该模型对一维蒸发和冷凝问题进行了数值模拟，考察了惰性气体存在对该过程的影响，着重讨论了蒸发温度、冷凝温度、惰性气体分压以及蒸发面和冷凝面之间的距离等因素对分离因数的影响。     

注塑模充填过程动态模拟

本文基于注塑模型腔内充填机理和流体力学基本方程，视聚合物熔体在型腔中的流动为平行板中的流动，在浇注系统中的流动为等效圆柱管内的流动，在此假定的基础上进行合理简化，建立了三维薄壁型腔的基于非弹性、非牛顿流体在非等温下的Ｈｅｌｅ－Ｓｈａｗ流动的数学模型及浇注系统的数学模型，并采用混合有限元／有限差分数值方法耦合求解压力方程和能量方程，采用控制体积法自动跟踪熔体前峰面，从而实现充填过程的动态模拟。模拟结     

REV尺度多孔介质格子Boltzmann方法的数学模型及应用的研究进展

综述了多孔介质表征体元尺度(REV)格子Boltzmann模型的研究进展,根据对多孔介质处理方式主要分为部分反弹模型和阻力模型两类,分析归纳了各类模型的优缺点。由于阻力模型中渗流的广义格子Boltzmann方程(GLBE)的作用力是基于GUO等的作用力模型,可以准确得到宏观方程,不存在离散误差,且模型的平衡分布函数和作用力项中都包含反应介质特性的孔隙率,因而应用最为广泛。本文还重点介绍了REV尺度多孔介质LBE模型在流动、传热、传质、化学反应及相变等过程中的具体应用,认为REV尺度多孔介质内的三传一反数学模型中需要加入孔隙尺度因素,在更大工程尺度上应该考虑过程参数的各向异性,展望了REV尺度多孔介质LBE模型的发展和应用前景。     

聚合物溶液哑铃分子模型的数值研究

本文描述用数值方法从分子模型出发计算聚合物溶液的流变性质,并对几种哑铃式分子模型作了计算,解决了若干理论方法无法正确解答的问题     

Bead-spring model of dilute polymer solutions: Continuum modifications and an explicit constitutive equation

A continuum modification of the bead-spring (elastic dumbbell) theory of dilute solutions of linear macromolecules, recently introduced by Gordon and Schowalter, is used to obtain explicit constitutive equations for the stress and polarizability tensors. The stress constitutive equation, closely related to a semiempirical result obtained earlier by Spriggs, is superior in predictive capability to the constitutive equation obtained from the elastic dumbbell theory. Results are presented for steady shearing flow, large-amplitude oscillatory shearing, and stress relaxation following cessation of steady shearing and are compared with the results of the elastic and rigid dumbbell theories. In general, predictions are similar to those of the rigid dumbbell and thus are in qualitative agreement with experiment.     

黏弹性复杂流动的微观-宏观确定性模拟

Deterministic simulation approach was applied to simulating viscoelastic complex flows,in which,the SIMPLE algorithm based on collocated grid was used to solve the conservation equations on the macroscopic level and the spectral method was used to solve the Fokker-Planck equation on the mesoscopic level.Here,the transient 4∶1 planar contraction flow for dilute polymer solution was computed by using the coupled technique and the calculated polymeric stress distributions at steady state were identical with the results of continuum approach as well as the corresponding references.Therefore,the presented results indicated that the SIMPLE algorithm based on collocated grid coupled with the spectral method can be used to simulate viscoelastic complex flows effectively.Moreover,the influence of Deborah number and viscosity ratio on polymeric stress was also investigated.     

A two-fluid model for non-equilibrium two-phase critical discharge

A general two-fluid model is developed to predict critical (choked) flow of initially saturated or subcooled flow from pipes and nozzles. The model contains improvements in the basic formulation, constitutive relations and solution technique over previously published models. It consists of six conservation equations as well as a seventh equation representing bubble growth in bubbly flow. It allows for hydrodynamic as well as thermal non-equilibrium. The model considers the development of three flow regimes, namely, bubbly, churn and annular flow regimes. The model predictions were compared with the limited available experimental data for which the axial pressure distributions were recorded. Excellent agreement was obtained.     

Constitutive modeling for mechanical behavior of PMMA microcellular foams

Constitutive equations for nonlinear tensile behavior of PMMA foams were studied. Five viscoelastic models composed of elastic and viscous components were accounted for the modeling of the constitutive equations. The developed constitutive equations are expressed in terms of material properties and foam properties such as strain, strain rate, elastic modulus, relative density of foam, and relaxation time constant. It was found that the stress-strain behaviors by Generalized Maxwell model, Three Element model and Burgers model could be described by the constitutive equation obtained from the Maxwell model. For the verification of the constitutive model, poly(methyl methacrylate) (PMMA) microcellular foams were manufactured using batch process method, and then uniaxial tensile tests were performed. The stress-strain curves by experiment were compared with the theoretical results by the constitutive equation. It was demonstrated that nonlinear tensile stress-strain behaviors of PMMA foams were well described by the constitutive equation.     

Prediction and experimental verification of bubble and processing characteristics in blown‐film extrusion

Blown‐film modeling is useful to the flexible packaging industry for predicting process and bubble characteristics, such as freeze line height (FLH), bubble diameter, and film thickness. The use of a suitable rheological equation to describe material properties is critical in simulating the blown‐film process. In this article, we present an improved rheological constitutive equation, which incorporates more realistic parameters of stress and deformation properties of the materials by combining the Hookean model with the Phan‐Thien Tanner (PTT) model. The proposed PTT–Hookean model is aimed at enhancing the viscoelastic behavior of the melt during biaxial stretching in the blown‐film extrusion. Predictions of the blown‐film bubble characteristics and FLH obtained with the PTT–Hookean model agreed well with the experimental data of this study and previous studies with different materials and different die geometries. The justification for combining the Hookean model with the PTT model in the blown‐film process is also reported here. © 2008 Wiley Periodicals, Inc. J Appl Polym Sci, 2009     

Finite element modeling of the flow of a rubber compound through an axisymmetric die using the CEF viscoelastic constitutive equation

This work is devoted to the simulation of the flow of a high viscosity NR/SBR rubber compound through the die of a single screw extruder with axisymmetric geometry. An in-house developed computer code based on the use of continuous penalty finite element method was employed. Three constitutive equations including two generalized Newtonian models namely; power-law and Carreau and an explicit viscoelastic model named CEF (Criminale-Ericksen-Fillbey) were used to reflect the rheological behavior of the material. Using the parameters of the rheological models determined by a slit die rheometry technique, the flow of the compound was simulated through the die and results were compared with experimentally measured mass flow rates. It is shown that for high viscosity rubber compounds the use of generalized Newtonian models which do not take the normal stress in simple shear flow into consideration gives rise to significant errors in prediction of mass flow rates. On the other hand, comparing the simulations results using the CEF equation with experimental data revealed that this model is the best compromise between generalized Newtonian and full viscoelastic models which need high computational costs and effort. © 2012 Wiley Periodicals, Inc. J Appl Polym Sci, 2012