Effects of variable viscosity on the steady melting of thermoplastics during spin welding

The steady melting of several amorphous and semicrystalline polymers during spin welding is analyzed by solving a simplified set of momentum and energy balance equations, assuming a shear-rate and temperature-dependent viscosity. A numerical model is developed for predicting the flow field and the temperature distribution in the molten film. It is shown that the steady melting rate of the thermoplastic solid is affected by the variable viscosity, by the pressure applied on the parts to be joined, and by a balance between the viscous heat generation in the melt and the convection of colder material into the molten film. The convection of heat in the outflow direction is shown to have a much smaller effect on the melting process.     

Estimation of melt film variables during the steady‐state penetration phase of thermoplastic vibration welding using a generalized newtonian fluid model

The thickness of the melt film and the temperature profiles within the melt film in the weld zone are key process variables governing the development of weld‐zone microstructures and the resulting development of weld strengths, during vibration welding of thermoplastics. The mathematical model described in this report is aimed at investigating the role of the rheology of the melt—specifically the magnitude and shear‐rate as well as temperature dependence of the melt viscosity—in governing the process variables such as the molten film thickness and the viscosities, stresses, and the temperatures within the melt film during vibration welding. The analysis is focused on the steady‐state penetration phase (phase III) of vibration welding. The coupled steady‐state momentum balance and heat transfer within the melt film, formulated using the Cross‐WLF (Williams‐Landel‐Ferry) relationship for viscosity, are solved in an iterative finite element framework. The model has been implemented for two different polymers displaying significant differences in viscosities and shear thinning behaviors. An attempt has been made to correlate the trends in the estimated melt film variables with the experimentally measured weld quality. POLYM. ENG. SCI., 2012. © 2011 Society of Plastics Engineers     

Heat transfer in the melting of solids to non-newtonian liquids

Relationships relevant to the design of industrial melters are developed for the case in which the molten material is a time-independent non-Newtonian fluid of the Power Law type. Expressions are derived for the local and mean values of the heat transfer coefficient in the melting of a solid slab on a hot, inclined, plane surface at constant temperature. The equations developed are restricted to laminar flow of the melt, and a criterion is therefore presented for checking that the molten film between the hot surface and the slab is actually in laminar flow throughout its entire length.     

A dynamic melting model for a single-screw extruder

A new theoretical concept is given which provides an efficient and consistent method for predicting flow and heat transfer characteristics of the melting zone for a large single-screw extruder. In contradistinction to previous, theories, significant melt accumulation in the molten films as observed experimentally is considered, instead of postulating the melt accumulation in the “melt pool”. The mathematical model has been obtained by the simultaneous solution of the momentum and energy equation of the melt flow and. solid bed, allowing for the existence of the pressure gradient: The theory is supplemented by a numerical example which shows good agreement with experimental data obtained on a 90 mm extruder with polypropylene, where the down-channel pressure profile and me profile of the solid bed Were taken as yardsticks for the melting process. For exact determination of the area for applicability of this theory, more experimental information is required.     

Heat transfer to molten polymers

The processing of polymers and other solids, such as waxes and acids, often requires the melting of a bulk or granular charge before its introduction into a process stream. Two approximate techniques for relating heat transfer and melting rates are presented here and the shielding effect of the melt formation is considered. The heat available for melting is sometimes remarkably decreased by the heat carried away by the flowing melt. Means are presented for quantitatively determining the shielding or sensible heat effect of the film. The thermal efficiency of the phase transformation process is discussed, and the effects of heat loss to both increased bulk temperature of the flowing melt and conduction in the solid are demonstrated. A comparison with experiment is made using temperature and melt flow data for polyethylene and polyoxymethylene. Heat transfer coefficients and melting correlations useful in practice are presented.     

对应熔窑构型及玻璃品种规模的玻璃液流熔制特征

对应熔窑构型及玻璃品种规模的玻璃液流熔制特征杨志强，胡桅林，过增元（清华大学，工程力学系，北京１０００８４）Ｇ１ａｓｓＭｅｌｔＦｌｏｗＰａｔｔｅｒｎＲｅｌａｔｅｄｗｉｔｈＦｕｒｎａｃｅＳｔｒｕｃｔｕｒｅｆｏｒＤｉｆｆｅｒｅｎｔＳｃａｌｅｓａｎｄＰｒｏ...     

Melting of thermoplastics in single screw extruders

Some experiments on the melting of thermoplastic polymeric materials in single screw extruders are described. Although these were of the now familiar screw extraction type, special care was taken to distinguish between material melted by screw rotation and that melted during the subsequent cooling operation. A barrel which could be split longitudinally was also used, thus avoiding some of the disadvantages of axial extraction. A theoretical model is proposed which, unlike previous models, allows the solid bed of material in the screw channel to accelerate naturally, and also allows for the presence of a film of molten material between the bed and the screw. This model gives satisfactory predictions of melting performance. Comparison with experimental results shows that break-up of the solid bed occurs when the model predicts rapid acceleration of the bed. Bed break-up and the resulting surging may be reduced or prevented by the use of screw cooling which has the effect of inhibiting the formation of a melt film at the screw surface.     

HEAT TRANSFER STUDIES OF HIGHLY VISCOUS NON-NEWTONIAN FLUIDS IN VERTICAL TUBES BY FINITE ELEMENT METHOD

A numerical method capable is developed for handling steady laminar flow and heat trans-fer of a highly viscous power-law fluid whose density,viscosity,specific heat and thermalconductivity,vary with temperature.The governing equations are found to be continuity,monmentumand energy expressions.Important effects such as varying viscosity,natural convection and viscousdissipation are incorporated in the theoretical model.These equations are being attracted by employing a decoupled finite element method.Galerkin'sprinciple is used to handle the momentum and continuity equations.Consistent(SU/PG)andnon-consistent(SU)streamline upwind methods are employed for the energy equation.Comparisonof calculated results and experimental data shows good agreement.Similar results are obtained withSU and SU/PG methods.Velocity and temperature profiles which provide insights into the processare also given.     

A simple analytical model for estimation of melt film variables in thermoplastic vibration welding

The strength of vibration welds of thermoplastics is governed by the weld zone microstructure, which in turn, is closely tied to the welding process variables, such as the thickness of the weld melt film and the temperature profiles therein. The mathematical model described in this report is aimed at describing the role of the rheology of the melt—specifically the magnitude and shear rate dependence of the melt viscosity—in governing the melt film variables during the steady state penetration phase (Phase III) of vibration welding. The steady state momentum balance and heat transfer within the melt film are solved by using the power law model for viscosity. Closed‐form analytical expressions are obtained for estimating the melt film thickness, the shear rates, and the temperature field within the film. This model has been used to estimate weld zone variables for four different polymers displaying a wide range of viscosities and shear thinning behaviors. POLYM. ENG. SCI., 54:499–511, 2014. © 2013 Society of Plastics Engineers     

Viscosity of glass-forming melt at the bottom of high-level waste melter-feed cold caps: Effects of temperature and incorporation of solid components

During the final stages of conversion of melter feed (glass batch) to molten glass, the glass-forming melt becomes a continuous liquid phase that encapsulates dissolving solid particles and gas bubbles that produce primary foam at the bottom of the cold cap (the reacting melter feed in an electric glass-melting furnace). The glass-forming melt viscosity plays a dominant role in primary foam formation, stability, and eventual collapse, thus affecting the rate of melting (the glass production rate per cold-cap area). We have traced the glass-forming melt viscosity during the final stages of feed-to-glass conversion as it changes in response to changing temperature and composition (resulting from dissolving solid particles). For this study, we used high-level waste melter feeds—taking advantage of the large amount of data available to us—and a variety of experimental techniques (feed expansion test, evolved gas analysis, thermogravimetric analyzer-differential scanning calorimetry, X-ray diffraction, and viscometer). Starting with a relatively low value at the moment when the melt connects, melt viscosity reached maximum within the primary foam layer and then decreased to its final melter operating temperature value. At the cold-cap bottom—the boundary between the primary foam layer and the thermal boundary layer—where physicochemical reactions of a melter feed influence the driving force of the heat transfer from the melt to the cold cap, the melt viscosity affects the rate of melting predominantly through its effect on the temperature at which primary foam is collapsing.     

Conditions for Transformation and Equilibrium of Iron Oxides in Glass Melting

It is demonstrated that transformations of iron oxides in glass melting occur mainly in the solid phase. The ratio between the two forms of iron oxides in a glass melt is determined by the melt temperature. Achieving an equilibrium with the gaseous medium requires a long time due to high melt viscosity and low diffusion coefficients. To ensure high service parameters in products, one needs stability of raw material compositions and melting process parameters, including diathermancy of the melt.     

Nonconventional Production of Glass Nanofibers by Laser Spinning

The production of very long glass nanofibers with lengths up to several centimeters was demonstrated using the Laser Spinning technique. It employs a laser to melt a small volume of a solid precursor material while a high‐pressure gas jet drags the molten material away. Thus, the molten material forms glass fibers as result of its viscous elongation by the drag force and rapid cooling promoted by the gas jet. High quantities of nanofibers can be quickly produced with tailored chemical compositions. Previously reported analyses of the process revealed that the dimensions and temperature of the molten volume together with its viscosity to surface tension ratio are the main factors governing the formation of the nanofibers. Therefore, the influence of the working conditions on these parameters must be understood to control the efficiency of the process. In this work, we demonstrate that the surface tension of the melt can be controlled independently of its temperature, and consequently of its viscosity, by adjusting the relative humidity of the gas jet. This outcome increases the productivity of the process and expands its capability for the synthesis of glass nanofibers from fragile melts.     

Mathematical Modeling of Drying of Liquid/Solid Slurries in Steady State One-Dimensional Flow

A mathematical model of simultaneous mass, heat and momentum transfer for two-phase flow of a gas and a solid/liquid slurry was developed. The model was applied to calculation of the drying process of coal-water slurry droplets in a gas medium in a steady one-dimensional flow. The model was based on the well-known two-stage drying process for slurry droplets. After the first period of drying, in which the evaporation rate is controlled by the gas phase resistance, the evaporating liquid diffuses through the porous shell (crust) and then, by convection, into the gas medium. Inside the dry external crust of the drop, a wet central core forms, which shrinks as evaporation proceeds. The temperature of the slurry droplet rises. The process ends when the temperature of the dry outer crust reaches the coal ignition temperature in the case of combustion or when the moisture of the particle reaches the final required moisture. The developed model was based on one-dimensional balance equations of mass, energy and momentum for the liquid/solid and gas phases. The system of governing equations was represented by first-order differential equations and solved simultaneously. The numerical solution of the governing equations was obtained using Gear's method. The model permitted calculation     

Haake密炼机三维流场的非等温数值模拟研究

本文利用流体力学计算软件FLUENT对69cm3哈克密炼机内的聚合物熔体进行了三维非等温非稳态数值模拟,得到了三维流场的瞬时温度分布,并对熔体与密炼室之间的热量传递过程进行了分析。当粘性耗散生热量等于向外传热量时,达到热平衡状态,熔体平均温度不再变化。由于聚合物熔体具有较高的粘性生热,仅靠自然对流不足以使密炼室壁保持初始的设定温度,壁温会有所增加。流场的混合指数分布说明混合流场中剪切流动占主导地位,还包括一小部分拉伸流动和收敛流动。     

Mathematical Modeling of Drying of Liquid/Solid Slurries in Steady State One-Dimensional Flow

ABSTRACT

A mathematical model of simultaneous mass, heat and momentum transfer for two-phase flow of a gas and a solid/liquid slurry was developed. The model was applied to calculation of the drying process of coal-water slurry droplets in a gas medium in a steady one-dimensional flow. The model was based on the well-known two-stage drying process for slurry droplets. After the first period of drying, in which the evaporation rate is controlled by the gas phase resistance, the evaporating liquid diffuses through the porous shell (crust) and then, by convection, into the gas medium. Inside the dry external crust of the drop, a wet central core forms, which shrinks as evaporation proceeds. The temperature of the slurry droplet rises. The process ends when the temperature of the dry outer crust reaches the coal ignition temperature in the case of combustion or when the moisture of the particle reaches the final required moisture. The developed model was based on one-dimensional balance equations of mass, energy and momentum for the liquid/solid and gas phases. The system of governing equations was represented by first-order differential equations and solved simultaneously. The numerical solution of the governing equations was obtained using Gear's method. The model permitted calculation     

Adhesive Dispensing Process Analysis: Steady-State Dispensing of One-Component Adhesives

The process of dispensing one-component heat-cure adhesives was investigated in order to understand current application processes and to guide new process development. Typical one-component adhesives exhibit non-Newtonian rheological behavior, and hence Newtonian fluid mechanics does not adequately describe the dispensing process. In the present study, the adhesives were modeled as Bingham fluids possessing a yield stress and a steady state viscosity. The model of the dispensing apparatus includes four major flow sections connected in a serial configuration. The fluid mechanics equations derived for Bingham fluids in the individual flow sections were solved by numerical methods in order to understand the interrelationships between the material variables (e.g. yield stress, viscosity, temperature dependencies) and process variables (e.g. pressure, flow geometry, temperature, output). The concept of the model is generic and the details of the model can be modified for any forced-flow adhesive application process.

The adhesive flow properties significantly influence the process output. Dispensing temperature, among the process variables, has the strongest effect on process output. A ± 1.0·C perturbation in the dispensing temperature can cause as much as a 14% variation in the bead size for the range of adhesives studied. Differences in flow characteristics result in differences in processability and non-linear temperature/pressure sensitivity. The non-linear sensitivity can be eliminated by operating the dispensing process isothermally. Finally, the process limits for one-component adhesives, which are susceptible to chemical instability induced by viscous heating during processing, are defined and discussed in terms of a modified Brinkman number that takes into account viscous dissipation, heat conduction and convection, and chemical stability of the material during processing.     

泡沫金属在熔盐相变蓄热中的强化传热特性

搭建了熔盐蓄热特性实验平台,开展相变蓄热过程传热特性实验研究。建立了蓄热容器二维轴对称、瞬态固液相变数学模型,相变过程模拟采用Solidfication & melting模型,相变区域采用Boussinesq近似,对比了纯硝酸盐蓄热工况和填加泡沫金属后蓄热工况数值模拟结果。采用实验与数值模拟相结合的方法,重点分析了泡沫金属对熔盐蓄热过程的强化传热作用。结果表明,填加泡沫金属能够有效提高熔盐换热速率,泡沫金属孔隙率越小强化蓄热效果越显著。泡沫铜的热导率较高,相对于泡沫镍和泡沫铝有更好的强化传热效果,蓄热速率是纯硝酸盐蓄热的1.6倍。在相变蓄热后期自然对流换热占主导地位,此时泡沫金属会抑制自然对流。同时,填加的泡沫金属越靠近容器中心位置,对自然对流抑制作用越强,蓄热性能越差。     

聚合物固体粒子在熔体中的流动和传热数值分析

对螺杆挤出机螺槽建立了准三维的流动和传热模型,模拟了聚合物固体粒子在熔体中的流动、受热、温升和熔融行为;采用横纵向截面研究了聚合物固体粒子的速度和温度随时间的变化情况;通过计算得出了固体粒子熔融所需要的时间以及流场总能量增量中外部传热和内部黏性耗散生热所占的百分比。结果表明,机筒传热和黏性耗散对系统能量增加的贡献为3.68∶1。     

Evaluation of bubble suspension behavior in electrolyte melts

The viscosity of a molten electrolyte mixture commonly used in direct coal fuel cells (DCFCs) was evaluated. The measurements were obtained from near the melting temperature to a high temperature at which a considerably bubbly flow was induced by decomposition. A gravity-driven capillary viscometer was employed to obtain the viscosity data under low Reynolds flow conditions, using a modified Poiseuille flow relationship. The importance of carbon dioxide addition in measuring the intrinsic viscosity was clearly observed. In addition, the effect of the bubble suspension on the viscosity was quantified in terms of the volume fraction and capillary number. The results showed that the increase in viscosity was best explained only by the difference in the volume fraction of spherical bubbles in the electrolyte melt.