Effect of constitutive models on the numerical simulation of viscoelastic flow at an entry region

The poor solutions of numerical simulations at a contraction has often been attributed to the numerical scheme used. However, the solution of a numerical simulation is also highly dependent on the constitutive equation. A study of various constitutive equations on the simulation of the 4:1 contraction flow is made in this paper, and their effects on the results analyzed. The constitutive models considered include the Upper Convected Maxwell model, the Oldroyd-B model, the White-Metzner model, the Phan-Thien-Tanner model and the Giesekus-Leonov model. It was found that although the Phan-Thien-Tanner model gave the best results, the solution at higher shear rates were still not satisfactory.     

Computer simulation of injection mold filling for viscoelastic melts with fountain flow

The ultimate properties of a molded article arc directly related In the microstructure of the article and are consequently influenced by the thermomechanical history experienced by the melt during processing. The mold filling behavior of thermopalastic polymer melts has been analyzed quantitatively by means of a computer simulation. The mathematical model is based on the equations of continuity, motion, and energy, along with appropriate constitutive relations and relevant initial and boundary conditions. The governing system of equations is solved numerically by means of a Marker-and-Cell computational scheme. One to the significant implications for microstructure development, the fountain effect at the advancing free surface is explicitly taken into consideration in the simulation. The model yields data on filling time and melt front position as well as velocity, temperature, pressure, and shear stress distributions within the mold cavity. The rearrangement of the velocity and temperature profiles in the vicinity of the melt front are considered in detail. Experimental studies have also been undertaken in order to verify the predictions of the computer Simulation.     

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.     

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.     

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.     

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.     

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.     

LDPE熔体在挤出口模流动时入口区流型的观测

应用毛细管流变仪测量了在接近实际挤出工艺条件下低密度聚乙烯熔体的流变性质，应用流动可视化技术，观测了试样熔体流经突然收缩的轴对称口模时的入口收敛流型，发现，在口模入口前区的两侧存在明显的环流区，环流区长度随着挤出速率和流道收缩比的增加而增大，而随着温度的升高而减小，采用环流区长度的公式估算了实验条件下试样的环流区长度值，结果表明，预测值与实测值之间有较好的一致性。     

Particle motion in the fountain flow region during filling of a tube with a viscoelastic fluid

We present the results of an investigation of particle motion behind the advancing free surface during the filling of an initially empty tube with a viscoelastic fluid. Particle motion in the vicinity of an advancing free surface (the fountain flow region) is of significance in a number of processes used to form composite materials, notably injection and compression molding. This motion determines, to a large extent, the distribution of the reinforcing phase in the molded part. We show experimentally that an isolated spherical particle moves behind the interface in characteristic orbits, remaining in close proximity to the advancing free surface. This is in stark contrast to what happens in a Newtonian fluid. In that case, the particle is deposited on the tube walls by the fountain flow and never again reaches the faster moving free surface. The particle motion behind the interface is modeled with a combination of equations that describe the advection of the particle due to convective/fountain flow and its lateral migration due to viscoelasticity. This model neglects the finite size of the particle and is thus unable to capture the full details of the observed motion. However, the qualitative agreement between the experimental results and the modeling predictions suggests that the observed particle motion is the result of the combined effect of viscoelasticity and fountain flow.     

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.     

Unsteady flow of viscoelastic fluids

Theoretical solutions for unsteady flow of a three constant Oldroyd fluid and a second order fluid under several different flow conditions of practical interest are obtained. The response of these fluids to suddenly applied external force is investigated in each case. Without using the stick-slip boundary condition at the wall, it is possible to show that pressure oscillation occurs with both fluids under a certain case.     

Flow behavior of stratified viscoelastic laminar flow at junctions with different angles

Detailed study was carried out in order to investigate flow phenomena occurring at the junction of two incoming stratified flow layers with junction angles. Various combinations of fluids with Newtonian and non‐Newtonian rheological characteristics were tested in a relatively high‐speed stratification where the inertia of flow cannot be neglected. The flow characteristics at the junctions were classified into six main flow modes, which were arranged in mode maps by use of generalized Reynolds numbers and viscous ratios. From the resultant mode maps it was found that a mutual relation of inertial and viscous effects is essential for the determination of flow modes in the stratified flows.     

Entrance — region flow of viscoelastic fluids examined by means of jet thrust method

Tube entrance-region flow is examined by measuring the thrust of jets of liquid emerging from capillary tubes of different lengths. The liquids used are water, toluene, n-pentanol and two aqueous polyacrylamide solutions possessing viscoelastic properties. The jet thrust behavior of each liquid is compared with the behavior calculated on the assumption that the liquid is Newtonian in character. Several facts emerge (a) the water behavior is near-Newtonian. (b) for other liquids, the entry region is much more extensive than that predicted by Newtonian theory. (c) there is a striking peak in the jet thrust for intermediate values of L/D. (d) the steady state thrust levels are generally lower than those predicted by Newtonian theory. (e) for n-pentanol and the more dilute polymer solution, these reduced thrust levels are consistent with previously published normal stress data. Possible reasons for the presence of a peak in jet thrust are discussed; this may well depend on shear elasticity possessed by the liquids. If so, the controversial suggestion that simple organic liquids possess shear elasticity is supported. It is shown that, in some cases, L/D ratios in excess of 350 are required for the establishment of steady laminar flow in the tubes.     

变截面导流筒换热器入口流场均化性能数值仿真

采用变截面导流筒真实三维实体模型,通过数值模拟的方法,以流体流动均匀性和压降作为综合衡量依据,研究了变截面导流筒装置中关键结构参数的变化对其内部流体流动均匀性和流体流动阻力的影响规律,得出了导流筒的结构参数L,H,θ与壳程进口处流体流动状况的对应关系,证实了在适当范围内调整上述结构参数,不仅可以提高壳程进口处流体流动均匀性,而且可以有效降低壳程流体的压力损失。从导流筒换热器的流体流动均匀性和壳程压降角度出发,推荐L,θ,H的取值范围分别是:L=50~70 mm,θ=7°~12.5°,H=50~100 mm。研究结果为变截面导流筒换热器优化设计提供了参考依据。     

Time-dependent flow of quasi-linear viscoelastic fluids

Transient flow behavior of an incompressible quasi-linear viscoelastic fluid under suddenly applied constant pressure as well as under a periodic pressure gradient was investigated using a three-parameter relaxation function. In the light of these solutions, the roll of viscoelastic relaxation in the overshooting of volumetric flow rate and the effect of viscoelastic parameters on the mean square velocity profile are discussed.     

Turbulent flow properties of viscoelastic fluids

The abnormally high resistance of viscoelastic fluids to sudden deformations and to stretching may be expected to cause the structure of turbulent velocity fields in these systems to differ appreciably from those of Newtonian fluids. An analysis based on these considerations is presented and supported using friction factor data for three concentrations of a water soluble polymer. Pressure losses predicted by use of this correlation are within 15% or less of the experimental values, but as all dimensionless groups which influence the results were not varied independently, the correlation developed may not be universally applicable to all fluids. Suggestions for further and more more specific analyses are made.     

Computer simulation and analysis of fountain flow in filling process of injection molding

The viscous flow in the filling stage of injection molding can be described in terms of an one-dimensional fully developed main flow and a complex two-dimensional flow near the advancing front, which is often termed the fountain flow. The transport characteristics in the front region of the mold flow are of increasing importance in injection process of composite materials such as resin injection molding (RIM). By using of finite element method, the simulation of non-isothermal viscous flow between two isothermal parallel plates with the generalized newtonian fluid is presented in detail. The un-folding of the fluid particles towards the mold wall directly affects transport characteristics such as the distribution of temperature, the orientation and the concentration of molecule near the front in filling stage.