Computer simulation of viscoelastic flow at the entry region

Non-Newtonian flow has a nonlinear constitutive relationship with an advective nature. It was found that in highly advective (convective) problems, the Galerkin formulation “under-diffused,” resulting in divergence at low elastic numbers. The use of the Streamline-Upwinding (SU) method improved the solution, especially when used with the Phan-Thien-Tanner (PTT) model. At the boundary discontinuity, however, the stress gradient did not necessarily flow along the streamline direction, and oscillations still remained at the corner. The Discontinuity-Capturing (DC) method resolved this problem by applying control in the direction of the stress gradient rather than the stream line direction, and a smoother solution at the corner region was achieved.     

The application of an integral type constitutive equation to numerical flow analyses of viscoelastic fluid in unsteady flow

The applicability of the Wagner model to numerical flow analyses of the injection molding process is investigated under the following approximations: the strain and stress histories of the molten polymer before the injection is negligible, and the flow field in a mold cavity is treated as Hele‐Shaw flow. A comparison between the results for simple step‐strain‐rate flow calculated with the Wagner model and that calculated with the Leonov model suggests that the Wagner model is superior to the Leonov model for unsteady flow because of its stability and accuracy. Therefore, numerical flow analysis software of a viscoelastic fluid in the injection molding process is developed using the Wagner model. For the analysis, the velocity profile of a Newtonian fluid is used instead of that obtained through iterative calculation. The validity of the developed program is confirmed through a comparison of the results of the computation for two simple flow velocity histories with the analytical results from the Wagner model. Furthermore, the computation time of the developed software is only 1.4 times greater than that of the previous numerical flow analysis of a viscous fluid.     

Finite element simulation of three-dimensional viscoelastic planar contraction flow with multi-mode FENE-P constitutive model

Viscoelasticity is a characteristic of many complex fluids like polymer melts, petroleum, blood, etc. The investigation of viscoelastic flow mechanism has practical significance in both scientific and engineering field. Owing to strongly nonlinear, numerical method becomes a practical way to solve viscoelastic flow problem. In the study, the mathematical model of three-dimensional flow of viscoelastic fluids is established. The planar contraction flow as a benchmark problem for the numerical investigation of viscoelastic flow is solved by using the penalty finite element method with a decoupled algorithm. The multi-mode finitely extensible nonlinear elastic dumbbell with a Peterlin closure approximation (FENE-P) constitutive model is used to describe the viscoelastic rheological properties. The discrete elastic viscous split stress formulation in cooperating with the inconsistent streamline upwind scheme is employed to improve the computation stability. The numerical methods proposed in the study can be well used to predict complex flow patterns of viscoelastic fluids.     

制冷工质流动沸腾数值模拟中源项模型的研究进展

作为描述流动沸腾过程物理现象的核心,源项在流动沸腾的数值模拟研究中起着至关重要的作用,主要体现在：①反映流动沸腾过程的传热、传质机理;②描述沸腾传热、两相流动特征;③影响数值计算稳定性。源项模型的准确性、适用性及稳定性对于制冷工质流动沸腾机理的数值研究具有重要意义。本文通过文献综述的方法,对现有源项模型进行了梳理。首先从源项在数值模拟中的角色入手,对现有针对流动沸腾数值模拟的源项模型进行归纳;其后分别从纯工质、混合工质两方面对源项模型的研究进展进行具体综述,分析了典型模型（如动力学模型、标量场模型、扩散模型等）的优缺点;同时对源项模型的典型验证方法进行系统总结,包括标准模型验证法、实验验证法。在此基础上,指出了流动沸腾数值模拟中源项模型的发展方向。     

Cyclic deformation behavior of an epoxy polymer. Part II: Predictions of viscoelastic constitutive models

The experimental results presented in Part I of this study were used to evaluate the predictive capabilities of two viscoelastic constitutive models. One of the models, developed by Xia and Ellyin, is in a differential form. The other, which is a modified Schapery model by Lai and Bakker, is in an integral form. The results of the comparison indicate that the Xia‐Ellyin constitutive model simulated the experimental observations well. This was attributed to the existence of a general rule that delineates the loading and unloading parts of the cyclic response. The modified Schapery model was able to predict the general trends of the deformation behavior; however, it was unable to correctly simulate the unloading behavior. This difference became more pronounced when the applied cyclic stress/strain was high. At high applied loads, the material response became more nonlinear. POLYM. ENG. SCI. 45:103–113, 2005. © 2004 Society of Plastics Engineers     

Numerical simulation of three-dimensional viscoelastic flow within dies

In recent years, the development of CAE (Computer Aided Engineering) in polymer processing has been remarkable, and it is expected to be more realistic in viscoelastic numerical simulation, particularly in three-dimensional complex geometry. Because of the problems of computational memory capacity, CPU time, and the numerical convergence of viscoelastic flow simulation, three-dimensional viscoelastic simulation applicable to industrial flow behaviors has not yet been attempted. In this paper, we developed the numerical simulation of three-dimensional viscoelastic flow within dies using a decoupled method, streamwise integration, and penalty function methods to decrease memory, and the TME (“Transformation of Equation of Motion to the Elliptic Equation,” S. Tanoue, T. Kajiwara, and K. Funatsu, The Eleventh Annual Meeting, the Polymer Processing Society Seoul, Korea, Extended Abstracts p.439) method, which raises the stability of convergence. We confirmed the reliability of this simulation technique to compare simulation results with experimental data of the stress field at a downstream wall shear rate of 5.41s^?1 within a 60° angle tapered contraction die. We compared the predictions of a viscoelastic model (Phan-Thien and Tanner model) with a pure viscosity model (Carreau model) at a downstream wall shear rate of 120s^?1 and discovered a remarkable effect of viscoelasticity in the shear stress and first normal stress difference in particular in the tapered region.     

Numerical simulation of the fountain flow problem for viscoelastic fluids

Fountain flow for isothermal viscoelastic fluids is simulated by a numerical method based on a combination of a finite element method and a finite volume method. For the treatment of moving free surfaces, a fringe element generation method is used. Circulating flow and elongation in the transverse direction at the melt front are simulated well. Numerical results also suggest that circulation in fountain flow and viscoelastic retardation may give rise to symmetric V-shaped patterns of birefringence between the center-plane and wall. Such information on molecular orientation in fountain flow is important for physical properties of thick molded products.     

Fluidization with viscoelastic polymer solutions in the transition flow region

Fluidization of spherical and non-spherical particle beds with shear thinning viscoelastic polymer solutions was investigated experimentally in the transition flow region. It was observed that the influence of elasticity on the anomalous expansion course weakens with the increasing value of Reynolds number. After exceeding a critical value of Reynolds number, which depends on the measure of liquid elasticity, the effect of elasticity vanishes and the expansion curves have the same linear shape as for fluidization with Newtonian (or purely viscous non-Newtonian) fluids. Semi-empirical equations based on the Carreau viscosity model were proposed for predicting the critical value of Reynolds number and the bed expansion in the region of diminishing elasticity effects.     

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     

Simulation of Vortex growth in planar entry flow of a viscoelastic fluid

A numerical simulation of entry flow in a slit die has been undertaken for a fluid that is Newtonian in shear but exhibits normal stresses (Boger fluid). Experimentally measured normal stress and viscosity data are included in a simple rheological model. Flow patterns reveal the existence of vortices in the reservoir corners. Vortex size and intensity increase rapidly with elasticity level.     

CFD-DPM-based numerical simulation for char gasification in an entrained flow reactor: Effect of residence time distribution

The rate of conversion during gasification of char particles depends on the type of reagents, the concentration of reactants, and reactor temperature, among many other parameters; however, the overall conversion depends on the residence time distribution (RTD) of the particles in the reactor. The objective of the present work is to investigate the influence of gasifying agents, their concentration, and reactor wall temperature on the RTD of the char particles. The aim also includes studying the effect of mean residence time on the overall char conversion during gasification of Victorian brown coal in an entrained flow reactor. Two gasifying reagents, namely, CO₂ and H₂O, are selected in the present study. A discrete particle model (DPM) is coupled with computational fluid dynamics (CFD) to simulate the solid phase dynamics. Gasification is modelled using a lumped approach. The mean residence time of the solid char particles, determined using three different methods, is observed to increase with the CO₂ concentration and wall temperature but decrease in the H₂O environment. The longer residence time leads to higher overall char conversion in a CO₂ environment despite the higher reactivity of H₂O compared to CO₂ as a gasifying reagent.     

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.     

Numerical simulation of the flow in an extensional flow mixer. Effect of fluid elasticity on the flow

We discuss the viscoelastic flow of the matrix fluid in an Extensional Flow Mixer (EFM) obtained by a numerical simulation. The effect of the fluid viscoelasticity on the flow state in an EFM was considered by the comparison of the flow states of the purely viscous fluid and the viscoelastic fluid. The mixing performance of the EFM is also considered. The Phan‐Thien Tanner model was used as the constitutive equation of the viscoelastic fluid and the Carreau model was used as that of the purely viscous fluid. Results obtained are as follows: (1) Stagnation flows occur in the converging‐diverging plates (c‐d plates) in the case of viscoelastic fluid. The size of stagnation flow region becomes large when the fluid has a strain‐thickening elongational viscosity. (2) The absolute value of the extensional strain and the pressure drop in the c‐d region increase with fluid elasticity. Meanwhile, the residence time in the c‐d region decreases with that. (3) There is no stagnation region in the c‐d plates for a purely viscous fluid. The stagnation flow has an effect on the estimation value of EFM's performance. The prediction by the purely viscous fluid is not useful for the flow in an EFM because of extremely low accuracy.     

非等温黏弹流体圆柱绕流的数值模拟(英文)

A collocated finite volume method on unstructured meshes is introduced to simulate the viscoelastic flow of the polymer melt with viscous dissipation past a confined cylinder. The constitutive equation for the simulations is non-isothermal FENE-P model, which is derived from the molecular theories. The temperature effect on the macroscopic fields (e.g., velocity, stress) and microscopic fields (e.g., molecular orientation, deformation, stretch) is investigated by comparison of isothermal and non-isothermal situations. This investigation indicates that temperature rise caused by viscous dissipation should not be neglected since it has significant effect on the macroscopic and microscopic properties of the polymer melt.     

搅拌器内湍流场的CFD模拟研究

采用CFD技术研究了DT和PTU型桨叶搅拌器内的湍流场,结果表明:对于PTU和DT桨叶,理论预测速度场分布规律与LDA测试结果吻合较好,理论预测漩涡的空间位置坐标与实测值完全一致。预测速度值与实测值在桨叶叶尖附近相对误差比较大,在离旋转中心轴线2R/3处竖直线上, 对于DT桨叶搅拌器,CFD预测的速度值和LDA测试值吻合比较好,最大相对误差在11%左右。而对于PTU桨叶,在同样的空间位置上,CFD预测值与测试结果的变化趋势相吻合,速度峰值附近的误差较大,相对误差高达30%左右。     

A comparison of Newtonian and viscoelastic constitutive models for dry spinning of polymer fibers

A comparison is made of the predictions of one‐dimensional mathematical model simulations of dry spinning based on Newtonian and viscoelastic constitutive equations for the spin dope. The viscoelastic model is based upon a modified Giesekus constitutive equation with a temperature and composition‐dependent relaxation time. The simulation algorithm includes the effects of the glass transition on the expected solution viscosity and relaxation time behavior along the spinline. Predictions of axial velocity, tensile stress, and composition profiles for the two cases suggest the role of viscoelasticity in the locking‐in behavior associated with fiber solidification along the spinline. The effects of model parameters and processing conditions are also discussed. © 2003 Wiley Periodicals, Inc. J Appl Polym Sci 87: 2136–2145, 2003     

Numerical simulation of three-dimensional viscoelastic planar contraction flow using the software OpenFOAM

In this study, we have used a highly accurate and novel approach to solve numerically for true three-dimensional (3D) viscoelastic flows into sudden contractions. Motivation for this development has been for the advancement of 3D viscoelastic flows in complex geometries, where this new methodology is available as a general solver, written for the open source code OpenFOAM (Weller et al., 1998). The proposed approach is able to include the multiple relaxation times of differential constitutive equations, and has been performed using the Finite Volume Method (FVM), based on a Discrete Elastic Viscous Split Stress (DEVSS) technique (Fortin et al., 1997). In this work, both the Giesekus and Phan-Thien–Tanner (PTT) shear-thinning models were implemented to reproduce flow through a planar 4:1 contraction, where numerical convergence was achieved for a Weissenberg number (We) of 2.9. Direct comparison with experimental data and literature involving 2D and 3D numerical simulations shows this method to be both stable and effective.     

聚合物多层共挤成型离模膨胀过程的三维黏弹性数值模拟

共挤成型中,聚合物黏弹特性与过程参数波动的耦合作用会产生波动的离模膨胀,使得根据共挤制品的形状设计相应的共挤定型口模在工程上仍是一项技术挑战。基于这一技术问题,通过建立的稳态有限元数值算法,系统研究了过程参数和黏弹性流变性能参数对共挤成型离模膨胀的影响规律和机理。研究结果表明,多层共挤口模芯壳层熔体离模膨胀是由熔体的二次流动引起,主要取决于芯壳层熔体二次流动的方向与强度。熔体二次流动的方向与第二法向应力差的正负号有关,而熔体二次流动的强度则与第二法向应力差大小呈正比。芯层熔体的离模膨胀与口模出口和混合区进口处芯层熔体向外的二次流动强度呈正比,而壳层熔体的离模膨胀取决于壳层熔体内外界面向外的二次流动的相对强度。研究还表明芯、壳层熔体及口模整体的离模膨胀随着壳层熔体黏度的增大而增加,而随着壳层熔体进口流量的增大而减小。     

空化射流流场数值模拟的研究进展

空化射流因具有高效能、无污染等优点而被广泛应用,但是由于其流场结构和水动力学性能过于复杂,使得对其的应用受到限制,为进一步认识和研究空化射流流场特性,对空化射流数值模拟过程中的空化模型、数值计算方法和流场特性影响因素的研究进行了综合论述.阐述了数值模型中不同的空化模型、湍流模型和多相流模型各自的特点、适用条件及存在的问题;对比分析了拉格朗日和欧拉数值计算方法在空化射流模拟中的应用,以及空化射流自身特点对计算方法的要求;对空化射流流场特性的影响因素研究情况进行了综合概述,使复杂的空化射流流场结构有更加清晰的表现,为以后的研究与应用提供了依据.通过以上论述,对目前空化射流数值模拟研究进展中存在的问题进行了分析,并根据所提出的问题,对以后的研究方向提出展望,有助于以后在空化射流流场的数值模拟研究中取得进展.     

微通道内液-液多相流数值模拟研究进展

液滴微流控技术在化学化工、生物医学等领域具有良好的应用前景,而微通道内的液-液多相流动则是液滴微流控技术中最常见的流动现象,深入研究其机理及其内在规律对相关装置与过程的优化设计具有重要的指导意义。本文系统地综述了研究微通道液-液多相流常用数值研究方法,回顾了连续力学方法与介观动理学方法的研究进展,详细介绍了界面追踪方法与界面捕捉方法的特点以及常用模型,讨论了多种模型的应用情况,论述并对比了不同模型的优势与限制。为进一步开展微通道液-液多相流行为规律及其内在机理的研究提供有益借鉴。微通道内多相流动涉及多种流体与界面的相互耦合,应进一步深入研究在模型简化的基础上实现更精确的界面与流体动力学行为描述。