Non-isothermal Polymer Melt Flow Research Articles

A multivariate piecewise interpolation model for viscosity representation and its application to the numerical simulation of non-isothermal polymer melt flow

In this study, a multivariate piecewise interpolation model is introduced to represent melt viscosity based on temperature and shear rate. The model does not require a predefined functional form for the entire data range, instead finding a suitable line between adjacent measured viscosity data points to obtain viscosity as a function of shear rate and temperature. To assess the effect of viscosity representation on polymer melt flow, a two-dimensional (2D) flow past a cylinder problem and a three-dimensional (3D) single screw extruder problem are numerically solved using different viscosity models. The pressure drop (ΔP) from the shift-factor model deviates by more than 10% at an average velocity (Uav) of 1 m/s due to overestimation of viscosity in the high shear rate region. The dimensionless thicknesses of the thermal boundary layer near the channel wall (δT/H) at wall temperature (Tw) of 210 °C are also misevaluated by more than 4% using both the shift-factor model and the Klein model, reflecting their poor viscosity evaluation. It is noteworthy that in all viscosity models, a high Tw leads to the formation of a thin thermal boundary layer, which adversely affects the heat transfer. In single screw extruder applications, viscosity misevaluation in high shear rate regions causes issues in pure drag flow cases, while misevaluation in low shear rate regions causes issues in pure back-pressure flow cases. These analyses highlight the accuracy and versatility of our multivariate piecewise interpolation model compared to existing viscosity models.

Modeling of Non-Isothermal Polymer Melt Flow in a Conical Annular Channel of a Disk Extruder

Purpose. The homogenization zone consists of various channels with different configurations, for each of which it is necessary to determine the passage of the melt flow process, and on its basis - the velocity fields, which determine the quality of mixing and distribution of components in the melt. To ensure a flexible and controllable homogenization process with the possibility of improving the quality of the melt, it is necessary to study the flow processes in the channels of a disk extruder. Therefore, the main objective of this work is to perform hydrodynamic modeling of processes during melt flow in a conical channel. Methodology. To achieve this goal, we propose a methodology for determining the flow processes in a conical channel, and find out which zones are convenient to consider in a special conical orthogonal coordinate system. For this purpose, the change in the radial coordinate , which has the same meaning in both the straight and the conical gap, was described - it is a coordinate along the width of the gap. This makes it possible to further apply this coordinate for the width of the disk gap - between the moving and stationary disks. Findings. A method has been proposed that describes the flow processes in the conical channel of the homogenization zone of a disk extruder. The calculation procedure is presented in an analytical form, and graphical dependences of the distribution of tangential and longitudinal velocities and shear velocities of the melt flow along the width of the annular channel at the nominal and maximum disk speeds and at the nominal and maximum disk gap are also given. Originality. For the first time, a methodology for calculating the conical channel of the homogenization zone of a disk extruder is presented, which describes the flow processes in a conical orthogonal coordinate system, which allows taking into account the common coordinate for the entire homogenization zone. The general procedure for calculating the channels of the homogenization zone has been supplemented. Practical value. The procedure for calculating the channels of the homogenization zone, which was started earlier, was extended and applied to the flow in a conical annular channel. This coordinate allows us to describe the flow processes along the width of the channel for all channels of the homogenization zone of a disk extruder, which greatly simplifies the calculations. Important results of hydrodynamic and thermal processes were obtained for the annular channel, which makes it possible to design disk extruders with greater accuracy and calculate their optimal operating modes.

Improving mixing characteristics with a pitched tip in kneading elements in twin‐screw extrusion

In twin‐screw extrusion, the geometry of a mixing element mainly determines the basic flow pattern, which eventually affects the mixing ability as well as the dispersive ability of the mixing element. The effects of geometrical modification, with both forward and backward pitched tips, of a conventional forward kneading disks element (FKD) in the pitched‐tip kneading disks element on the flow pattern and mixing characteristics are discussed. Numerical simulations of fully filled, nonisothermal polymer melt flow in the melt‐mixing zone were performed, and the flow pattern structure and the tracer trajectories were investigated. The pitched tips largely affect the inter‐disk fluid transport, which is mainly responsible for mixing. These changes in the local flow pattern are analyzed by the distribution of the strain‐rate state. The distribution of the finite‐time Lyapunov exponent reveals a large inhomogeneity of the mixing in FKD is suppressed both by the forward and backward tips. By the forward tips on FKD, the mixing ability is relatively suppressed compared to FKD, whereas for the backward tips on FKD, the mixing ability is enhanced while maintaining the same level of dispersion efficiency as FKD. From these results, the pitched tips on the conventional KD turn out to be effective at reducing the inhomogeneity of the mixing and tuning the overall mixing performance. © 2017 American Institute of Chemical Engineers AIChE J, 64: 1424–1434, 2018

Influence of die geometric structure on flow balance in complex hollow plastic profile extrusion

The unbalanced flow problem often occurs at die exit in the extrusion process of plastic profile, which directly influences the performance of final products. For the lack of corresponding theoretical basis, reasonable extrusion die design is still a difficult task, especially for the complex hollow profile. With the development of computational fluid dynamics theory, numerical method becomes an effective way to investigate the complex material forming problems. In the present study, a design strategy for complex hollow profile extrusion die was proposed based on the principles of flow balance. The mathematical model for three-dimensional non-isothermal polymer melt flow within complex extrusion die runner was developed based on the computational fluid dynamics (CFD) theory. The governing equations were deduced based on the finite volume method, and the pressure-velocity coupling problem was solved by using the Semi-Implicit Method for Pressure-Linked Equations (SIMPLE) algorithm. The Arrhenius equation was employed to involve the temperature dependence of material parameters. The flow characteristics of PVC polymer melts in the extrusion process of complex hollow profile were investigated. The distributions of principal field variables including flow velocity, melt temperature, and pressure drop were obtained. The effects of die geometric parameters on the velocity distribution uniformity were further analyzed, and a design strategy was proposed to achieve the flow balance in complex plastic profile extrusion process.

Analysis of steady non-isothermal flow of polymer melts in a single-screw extruder

It is established that in addition to forced flow and counter flow of the melt during reworking of polymer materials, a flow generated by temperature variation of the melt over the height of the screw channel exists in a single-screw extruder.

Injection Molding Simulation of a Compressible Polymer

This study presents the 3-D simulation solutions for mold insert polymer injection molding process. A more complete and robust numerical approach is developed by considering the effects of solidification, compressibility and viscosity changes for high-viscous non-isothermal polymer melt flow conditions. The generated user-defined functions are successfully incorporated into a volume of fluid (VOF) method, which is coupled with a finite volume approach, to represent a more realistic polymer melt flow simulations. A comprehensive high-resolution differencing scheme (CICSAM) is successfully adopted to capture the moving interface. The comparative numerical results demonstrate that the present numerical approach improves the accuracy of simulation predictions of 3-D compressible mold filling process and can be used with a confidence in simulating real molding flow conditions.

Non-isothermal polymer melt flow in sudden expansions

This paper presents numerical results for laminar, incompressible and non-isothermal polymer melt flow in sudden expansions. The mathematical model includes the mass, momentum and energy conservation laws within the framework of a generalized Newtonian formulation. Two constitutive relations are adopted to describe the non-Newtonian behavior of the flow, namely Cross and Modified Arrhenius Power-Law models. The governing equations are discretized using the finite difference method based on central, second-order accurate formulas for both convective and diffusive terms. The pressure–velocity coupling is treated by solving a Poisson equation for pressure. The results are presented for two commercial polymers and demonstrate that important flow parameters, such as pressure drop and viscosity distribution, are strongly affected by heat transfer features.

Measurement of anisotropic energy transport in flowing polymers by using a holographic technique.

Almost no experimental data exist to test theories for the nonisothermal flow of complex fluids. To provide quantitative tests for newly proposed theories, we have developed a holographic grating technique to study energy transport in an amorphous polymer melt subject to flow. Polyisobutylene with weight-averaged molecular mass of 85 kDa is sheared at a rate of 10 s(-1), and all nonzero components of the thermal conductivity tensor are measured as a function of time, after cessation. Our results are consistent with proposed generalizations to the energy balance for microstructural fluids, including a generalized Fourier's law for anisotropic media. The data are also consistent with a proposed stress-thermal rule for amorphous polymer melts. Confirmation of the universality of these results would allow numerical modelers to make quantitative predictions for the nonisothermal flow of polymer melts.

NUMERICAL SIMULATION OF NONISOTHERMAL FLOW OF POLYMER MELT IN A SINGLE-SCREW EXTRUDER: A VALIDATION STUDY

A recently developed approach to simulate the nonisothermal polymer melt flow in a single-screw extruder is validated against experimental data taken from the literature. Comparisons are made with eight sets of experimental results, and for each case several numerical runs are performed to provide some insight into the sensitivity of simulation outcomes to input material parameters (i.e., viscosity, density, thermal conductivity, and specific heat). In general, predictions for the pressure distribution along the extruder and for the mean melt temperature at the exit of the extruder compare favorably with pertinent experimental results. On the other hand, calculated estimates for the power consumption of an extruder are systematically lower than corresponding measured values.

A Numerical Simulation of the Temperature Fields in a Capillary with Consideration of the Viscous Heat Generation and a Study on the Measured Viscosity Data

A numerical simulation of the non-isothermal flow of polymer melts in a capillary was performed with consideration of the effects of viscous heat generation using the finite element method. The constitutive model for polymer melt that we used was the Carreau model with a temperature-dependent viscosity. We studied the effect of viscous heat generation on the viscosity data measured by the capillary viscometer by comparison between the measured viscosity which involved the effect of viscous heat generation and the corrected viscosity from which the effect was removed. The measured viscosity was lower than the corrected viscosity at the wall shear rate γw above 102s-1 and this difference increased with increasing γw. It was predicted that the corrected viscosity was two times as much as the measured viscosity at γw=104s-1 and it was found that the effect of viscous heat generation on viscosity data could not be neglected in the high shear rate region. Also, the temperature rise near the wall reached 50°C when L/R=16 (L: capillary length, R: capillary radius) at γw=104s-1 but near the center of the capillary, the temperature rise was negligible. Therefore a temperature profile developed across the cross-section in the flow direction and the velocity profile changed with temperature profiles.

Nonisothermal flow of polymer melts and solutions in spinneret channels

The effect of dissipation of mechanical energy on the temperature fields of polymer melts and solutions in the channels of spinnerets for fibre spinning has been investigated.

Non-isothermal flow of polymer melts in a curved tube

The results of a numerical study (using finite differences) of heat transfer in polymer melt flow is presented. The rheological behaviour of the melt is described by a temperature-dependent power-law model. The curved tube wall is assumed to be at constant temperature. Convective and viscous dissipation terms are included in the energy equation. Velocity, temperature and viscosity profiles, Nusselt numbers, bulk temperatures, etc. are presented for a variety of flow conditions.