Heat transfer to molten polymers flowing through tubes

A theoretical and experimental study of heat transfer to polymer melts flowing through circular tubes is presented. The mathematical model provides for shear heating and expansion cooling effects, and also heat of reaction during flow for various wall boundary conditions. Experimental results, obtained using low density polyethylene, show reproducible temperature and velocity profiles. The measured inlet melt temperature profile and the axial wall temperature profile provide the boundary conditions for the calculations. The experimental data confirm the predictions of the magnitude of the shear heating and expansion cooling effects during tube flow.     

Effect of process variables on melt velocity profiles in extrusion process using single screw plastics extruder

Abstract

Single screw extruders are used to generate a continuous flow of molten polymer in many industrial polymer processes. The melt velocity profile as extruded is important in determining the properties of the final product and influences process related phenomena such as die swell and the onset of sharkskin. The factors that influence the velocity profile would be expected to be the melt temperature (this affecting the viscosity of the melt), the screw and die geometry, and the output rate from the extruder. In the present work a thermocouple mesh sensor coupled with a cooled stainless tube has been used to determine velocity profiles in melts exiting from the screw of a single screw extruder. The results show that the technique can be used successfully to determine velocity profiles in the extrusion process.

It was found that the main influence on the magnitude of the melt velocity was the extruder screw speed. Melt temperature, and hence melt viscosity, were found to have little effect on the velocity profiles measured. The flow in the centre of the duct was retarded slightly owing to the flow across the screw tip and no rotational component of flow was observed. The velocity profiles measured seemed to be reasonably stable, only small changes being observed in the velocity profiles as the melt flowed along a duct of uniform cross-section, although these changes were limited in nature. Die diameter and length had a limited effect on the velocity profiles generated, although the die entry angle did have a significant effect on the shape of the velocity profile at higher screw speeds.     

Numerical study of nonisothermal polymer extrusion flow with a differential viscoelastic model

A numerical study of nonisothermal viscoelastic flow is conducted to investigate the complex flow characteristics of polymer melts in the extrusion process. A general thermodynamic model for the energy conversion related to viscoelastic fluid flow is introduced. The mathematical model for three‐dimensional nonisothermal viscoelastic flow of the polymer melts obeying a differential constitutive equation (Phan‐Thien and Tanner model) is established. A decoupled algorithm based on the penalty finite element method is performed on the calculation. The discrete elastic‐viscous split stress (DEVSS) algorithm, incorporating the streamline‐upwind Petrov‐Galerkin (SUPG) scheme is employed to improve the computation stability. Essential flow characteristics of polymer melts in the extrusion die for hollow square plastic profile is investigated based on the proposed numerical scheme with ignoring the outer thermal resource. The energy partitioning, which quantified the conversion of mechanical energy into thermal energy, is discussed. The effects of volume flow rate and die contraction angle upon the flow patterns are further investigated. POLYM. ENG. SCI., 2008. © 2007 Society of Plastics Engineers     

Predicting melt flow instability from a criterion based on the behavior of polymer solutions

A criterion, based on the behavior of polymer solutions, is developed and applied for the prediction of the onset of flow anomalies observed at the capillary entrance for polymer melts. It is shown that a direct correspondence exists between the flow anomalies observed for polymer solutions and polymer melts. The onset of these anomalies can be correlated with a critical Weissenberg number which is consistent with the equality of the shear wave velocity and friction velocity. This critical condition can be employed to derive expressions useful for predicting the critical recoverable shear and critical shear stress for melt fracture.     

Heat transfer to polymer solutions and melts flowing between parallel plates

Heat transfer to polymer solutions or melts flowing in parallel plate systems is an important aspect of polymer processing as for example in extrusion through a wide slit. The present work solves the equation of energy for pseudoplastic non-Newtonian fluids flowing between parallel plates. An exact velocity profile rather than an approximation is used. Equations are derived both for temperature profiles and mean temperatures. The results are shown to correctly represent the physical situation.     

Heat transfer to molten polymer flow in tubes

This article presents the results of a numerical study (finite differences) of the heat transfer problem in flowing polymer melts. The tube wall is assumed to be at a constant temperature. The rheological behavior of the melt is described by a power law temperature-dependent model. A convective and a viscous dissipation term are included in the energy equation. Temperature profiles, bulk temperatures, and Nusselt numbers are presented for a variety of flow entry temperatures.     

超声波声速与聚合物熔体密度的单值性

利用一定质量的聚合物熔体在密封容器内其PVT状态变量符合理想气体PVT状态方程的特点,通过自行设计加工的基于PVT原理的实验装置,得到了基于物理定义的聚合物熔体密度和熔体体积弹性模量的数学表达式,验证了聚合物熔体密度和熔体体积弹性模量在理论上存在的一致性变化的特性;在此基础上由聚合物熔体密度、熔体体积弹性模量和超声波传播声速三者之间相互关系,可以推导出超声波声速与聚合物熔体密度存在单值性的数学表达式,并通过实验验证了聚合物熔体密度与超声波声速存在一一对应性。为超声波技术应用于聚合物熔体密度的在线测量提供理论基础和实验数据。     

The experimental measurement and theoretical analysis of flow-system tracer curves by a line-sampling method

An electrical conductivity sampling probe for the accurate measurement of the dispersive effect of velocity gradient on concentration profile has been designed. The probe averages tracer concentration along a single diameter of the tube. The impulse response of this probe system in steady laminar flow in a tube has been derived theoretically and confirmed experimentally. Examples of the determination of unknown velocity profiles by tracer techniques utilizing the probe are presented.     

Temperature measurements of polymer melts in the heating barrel during injection molding. Part I. Temperature distribution along the screw axis in the reservoir

A new procedure has been developed to measure the temperature distribution of the polymer melts along the screw axis during injection by using a small sheath thermocouple. At the same time, the effects of molding conditions on temperature distribution has been studied. The temperature distribution of the polymer melt along the screw axis during injection can be obtained from the difference between the standard temperature profile and the temperature profile of the polymer melt with unknown and non-uniform temperature measured under the same rate of injection. The temperature of a polymer melt within a shot is not uniform. The difference between the maximum and the minimum temperature within a shot may exceed 10°C in some cases. There are two major factors which govern the effects of molding conditions on the temperature distribution of the polymer melts during injection. The first is the amount of shear heating in the metering zone. The second is the amount of heat absorbed into the polymer in the compression and feed zones.     

Prediction of elongation viscosity of polymer melts

Melt extension flow is a common flow pattern during polymer processing, such as entrance converging flow in die extrusion or runner injection of polymer melts from an extruder barrel, blow molding, blowing film and melt spinning. Extensional viscosity is one of the important characterizations of the flow characteristics for polymer fluids. A new extension viscosity equation was established based on White‐Metzner model, Vinogradov‐Malkin viscosity equation and a new relaxation time equation in the present paper. The melt elongation viscosities of metallocene linear low‐density polyethylene (mLLDPE) and polyvinyl butyral (PVB) resins at 130°C were estimated applying this viscosity equation, and the predictions were compared with the measured data of mLLDPE and PVB resins at 130°C reported from reference. The results showed that calculations were close to the experimental data. The parameters in this equation were easy to be determined and the equation was convenient to use for estimating the extension viscosity of polymer melts. POLYM. ENG. SCI., 2010. © 2010 Society of Plastics Engineers     

Effect of die temperature on the flow of polymer melts. Part I: Flow inside the die

The effect of die wall temperature on the flow of polymer melts in circular capillary dies was studied. At constant flow rates, it was found that die wall temperature had a greater effect on the pressure drop than melt temperature. A capillary die with two circular channels with different diameters was designed to simulate the profile extrusion. Changes of wall temperature varied the flow rate ratio between the two channels. An implicit finite difference method was used to simulate the velocity and temperature profiles inside the die. Values predicted by this model matched well with experimental data for both dies.     

ON THE SWELLING OF SUBMERGED JETS OF DILUTE AND SEMI-DILUTE POLYMER SOLUTIONS

Profound jet swelling is shown to exist when a dilute or semi-dilute solution of PEO (POLYOX WSR 301) is ejected from a capillary tube into a stagnant fluid. The jet swells up to ten times the diameter of the capillary tube depending on the shear rate in the tube and on the density difference between the ejected and the stagnant fluid. The diameter ratio (jet/tube) grows as the 1/3 power of the shear rate, regardless of the density difference, tube diameter and polymer concentration and provided the tube is long enough for the development of the flow profile. For SEPARAN AP 45 solutions, displaying a non-Newtonian behaviour in shear, it is shown that the 1/3 power law holds between the diameter ratio and the shear stress, instead of the shear rate. The analogy between the swelling behaviour of these dilute and semi-dilute polymer solutions and the one observed in concentrated solutions and melts is discussed. The possibility of utilizing the submerged jet technique to compute the polymer solution normal stresses is considered.     

ON THE SWELLING OF SUBMERGED JETS OF DILUTE AND SEMI-DILUTE POLYMER SOLUTIONS

Profound jet swelling is shown to exist when a dilute or semi-dilute solution of PEO (POLYOX WSR 301) is ejected from a capillary tube into a stagnant fluid. The jet swells up to ten times the diameter of the capillary tube depending on the shear rate in the tube and on the density difference between the ejected and the stagnant fluid. The diameter ratio (jet/tube) grows as the 1/3 power of the shear rate, regardless of the density difference, tube diameter and polymer concentration and provided the tube is long enough for the development of the flow profile. For SEPARAN AP 45 solutions, displaying a non-Newtonian behaviour in shear, it is shown that the 1/3 power law holds between the diameter ratio and the shear stress, instead of the shear rate. The analogy between the swelling behaviour of these dilute and semi-dilute polymer solutions and the one observed in concentrated solutions and melts is discussed. The possibility of utilizing the submerged jet technique to compute the polymer solution normal stresses is considered.     

微细管内电渗流动的瞬态热效应

建立微细圆管内电渗流动的非稳态数学模型,模型通过温度将电渗流的Poisson-Boltzmann方程、动量守恒和能量守恒方程耦合起来.详细讨论了在电渗流的初始阶段,焦耳效应对温度场和速度场演化的影响.同时讨论了不同冷却条件和外部电势场强度条件下,电渗流速度场及温度场变化的特点以及自热的发生过程.研究发现,由于速度场的发展主要受温度主控的电解液黏度影响,因此速度场和温度场是同步发展起来的.通过所得到的结果可以为微细管内的电渗流确定合适的冷却条件,以便同时达到有效抑制样品温度和获得较高流动速度的目的.     

Effect of temperature on polymer migration II: Concentration equation

Polymer migration is a generally well-known phenomenon in a flow field, and it has been verified that the sources of such phenomena are nonhomogeneity of the flow, concentration effects and hydrodynamic interactions between the polymer molecules. In addition, temperature effects were found to be another source of polymer migration. The Langevin equation for a polymer molecule was first derived from single chain dynamics using a kinetic theory for the bead-spring elastic harmonic dumbbell model, as described in part I (reference [1]). In this paper the diffusion equation and concentration profile of the polymer molecules induced by a temperature gradient are obtained from the Fokker-Planck equation. A new differential operator is also introduced to calculate the concentration profile. From the concentration equation obtained in the general flow geometry, we find that in dilute polymer solution there are significant effects on the polymer migration not only due to the nonhomogeneity of the flow field but also due to temperature gradients.     

Theoretical model for flow of polymer melts in the screw channel

Isothermal and nonisothermal flows of polymer melts in a screw channel are discussed. An exact solution for the isothermal flow of a power law fluid in a rectangular channel including both longitudinal and transverse velocity components is presented. A method to describe the effects of flights and curvature on flow behavior is proposed. The results are extended to deal with various nonisothermal flow conditions. The proposed theory has been numerically verified.     

Investigation of Unsteady Elongational Flow of Polymer Melts

Abstract

A method for estimation of the viscoelastic characteristics of polymer melts in the prestationary elongational flow is given. The experimental data show that at specific strain rates the polymer starts to respond to dynamic deformation as a highly elastic material. The viscoelastic characteristics of the polymer in the prestationary extensional flow can be described by a modified Maxwell equation.     

Computation of forced convection in slow flow through ducts and packed beds—II velocity profile in a simple cubic array of spheres

The velocity profile is calculated for slow three-dimensional flow through a simple cubic array of spheres. The velocity is represented by stream-function expansions which directly satisfy the equation of continuity and the no-slip conditions. The problem is solved by a variational principle which gives a lower bound on the total flow rate. The computed bound is within 0·2 per cent of the experimental results of Martin et al.[6].     

Dispersion of aqueous polymer solutions injected from a point source into turbulent water flows

The dispersion of water and aqueous polymer, when injected from a point source along the flow centre line into two-dimensional, fully developed and uniform turbulent flows with flow Reynolds numbers of the order of 4.6 × 10⁵, have been studied experimentally. Concentration profiles at five locations were obtained for injection concentrations and velocities in the ranges 0 to 1000 w.p.p.m. and equal to or less than the local flow velocity. The concentrations were assessed using a fluorescing dye technique. Empirical equations describing the radial and longitudinal concentration field as a function of the injection and flow parameter are given. A universal concentration profile, independent of the injection flow rate and concentration and length of injection source tube, and valid for water and for polymer solution, under both fully developed and uniform flow, is also presented. The results indicate that the turbulent dispersion of polymer solution is suppressed compared to that of water.     

Modeling contraction flows and swell of polymer melts extruded from dies of various lengths

This article describes isothermal contraction flows and extrudate swell, using our recent model for fast (high Deborah number) contraction flows of polymers melts. The model analyzes the polymer flow in several regions as one continuous process. This approach makes possible to evaluate the extrudate swell as a result of complex contraction polymer flow in dies of various length. Using the asymptotic matching conditions for the change in flow type at the die exit allowed us to calculate the swelling profile for extrudate in the flow direction. The present calculations performed using a multi-mode viscoelastic constitutive equation of differential type, are compared with the experimental/direct numerical data including basic rheological tests. The presented complex model for contraction flow and swelling consists of no fitting parameter and is applicable for calculations using any viscoelastic constitutive equation. POLYM. ENG. SCI., 2008. © 2008 Society of Plastics Engineers