Das Düsenschwellphänomen beim Austritt einer wandhaftenden anorganischen Glasschmelze aus Strangpreßwerkzeugen mit nichtkreisförmigem Öffnungsquerschnitt

Zusammenfassung Eine ausgeprägte Strangaufweitung tritt bei anorganischen Glasschmelzen dann auf, wenn bei schleichender Strömung eine Haftung zwischen der Wand des Matrizenkanals und dem strömenden Medium gegeben ist. Sie rührt dabei von der Umorientierung der Geschwindigkeitsverteilung von einem parabelförmigen zu einem kastenförmigen Profil her.In den experimentellen Untersuchungen konnte festgestellt werden, daß oberhalb einer bestimmten Kanallänge, d. h. bei ausgeprägten Strömungsverhältnissen im Preßwerkzeug die flächenbezogene Strangaufweitung konstant und dabei insbesondere unabhängig von der Profilform etwa 29% beträgt. Daraus wird gefolgert, daß dieser Betrag dem linearen Wert für den zweidimensionalen Fall des unendlich ausgedehnten Spaltes entsprechen muß.In einer theoretischen Analyse wurde die Berechnung dieses Falles ausgehend von der Stokes-Gleichung mit Hilfe der Methode der finiten Elemente durchgeführt. Aus der sich daraus ergebenden Druck- und Geschwindigkeitsverteilung konnte schließlich die Kontur des austretenden Stranges sowie dessen Endhöhe ermittelt werden.Ein Vergleich der experimentell und rechnerisch ermittelten Werte für die Strangaufweitung zeigt dabei eine recht gute Übereinstimmung und bestätigt dadurch auch die weitgehende Unabhängigkeit der flächenbezogenen Aufweitung von der Querschnittsform des Stranges.

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Inorganic glass melts are showing a characteristic die swell, when in the case of slow motion a strong adhesion between the streaming fluid and the wall of the die channel exists. The reason for this phenomenon is the rearrangement of the velocity profile from a parabolic to a box-type design form.The experimental investigations have demonstrated, that above a certain channel length, this means at distinct flow conditions inside the die channel, the value for the extension of the cross-sectional area is constant of about 29%. Particularly it is independent of the shape of the used die profiles. From this result, it is to deduce that this value must correspond to that of the two-dimensional case of the infinite extended slit.In a theoretical analysis the computation of this case was performed, starting from the Stokes-equation by the finite element method. By means of the resulting pressure and velocity distribution, the contour of the emerging rod and its final thickness could be determined.A comparison between experimental and computational results shows good agreement. So the appreciable independence of the magnitude of the die swell from the profile of the extruded rod is confirmed.

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A Fläche - a ^p ,a ^u Knotenpunktsvariablen für Druck bzw. Geschwindigkeit - a, b Seitenlängen des Rechteckprofils - B =L · N ^u Matrix - D Viskositätsmatrix - f Kräftematrix - K Schwerkraftvektor - K ^p ,K ^u Elementdruckmatrix, Elementgeschwindigkeitsmatrix - L Transformationsmatrix für den ebenen Fall - m Kronecker-Symbol für den zweidimensionalen Strömungszustand - N ^p ,N ^u Ansatzfunktionsmatrizen für Druck bzw. Geschwindigkeit - p Preßdruck - R Radius - T Preßtemperatur - t Lastvektor - u = (w, v) Geschwindigkeitsvektor - _A flächenbezogene Strangaufweitung - _R Aufweitung einer linearen QuerschnittsabmessungR - dynamische Viskosität - Dichte - D u/Dt Substantielle Ableitung der Geschwindigkeit nach der Zeit - T Transponierte einer Matrix (oberer Index) Vorgetragen auf der Jahrestagung der Deutschen Rheologischen Gesellschaft in Berlin vom 13.–15. Mai 1985     

Rheological effect on thermocapillary flow of a liquid film jet painted on a moving boundary

In the present paper, a liquid (or melt) film of relatively high temperature ejected from a vessel and painted on the moving solid film is analyzed by using the second-order fluid model of the non-Newtonian fluid. The thermocapillary flow driven by the temperature gradient on the free surface of a Newtonian liquid film was discussed before. The effect of rheological fluid on thermocapillary flow is considered in the present paper. The analysis is based on the approximations of lubrication theory and perturbation theory. The equation of liquid height and the process of thermal hydrodynamics of the non-Newtonian liquid film are obtained, and the case of weak effect of the rheological fluid is solved in detail.     

Integer extended ABS algorithms and possible control of intermediate results for linear Diophantine systems

We present a new class of integer extended ABS algorithms for solving linear Diophantine systems. The proposed class contains the integer ABS (the so-called EMAS and our proposed MEMAS) algorithms and the generalized Rosser’s algorithm as its members. After an application of each member of the class a particular solution of the system and an integer basis for the null space of the coefficient matrix are at hand. We show that effective algorithms exist within this class by appropriately setting the parameters of the members of the new class to control the growth of intermediate results. Finally, we propose two effective heuristic rules for selecting certain parameters in the new class of integer extended ABS algorithms.      

The characteristic‐based split (CBS) meshfree method for free surface flow problems in ALE formulation

A semi‐implicit characteristic‐based split (CBS) meshfree algorithm in the arbitrary Lagrangian Eulerian (ALE) framework is proposed for the numerical solution of incompressible free surface flow problem in the paper. The algorithm is the extension of general CBS method which was initially introduced in finite element framework, this is due to the fact that CBS method not only can enhance the stability, but also avoid LBB condition when equal order basis function is used to approximate velocity and pressure variables. Meanwhile, a simple way for node update and node speed calculation is developed which is used to capture the free surface exactly. The numerical solutions are compared with available analytical and numerical solutions, which shows that the proposed method has better ability to simulate the free surface incompressible flow problem. Copyright © 2009 John Wiley & Sons, Ltd.     

Singular finite elements for the sudden-expansion and the die-swell problems

The singular finite element method is used to solve the sudden-expansion and the die-swell problems in order to improve the accuracy of the solution in the vicinity of the singularity and to speed up the convergence. The method requires minor modifications to standard finite element schemes, and even coarse meshes give more accurate results than refined ordinary finite element meshes. Improved normal stress results for the sudden-expansion problem have been obtained for various Reynolds numbers up to 100 using the singular elements constructed for the creeping flow problem. In addition, the normal stresses at the walls appear to be insensitive to the singularity powers used in the construction of the singular basis functions. The die-swell problem is solved using the singular elements constructed for the stick–slip problem. The singular elements accelerate the convergence of the free surface dramatically.     

Silica surface modification using different aliphatic chain length silane coupling agents and their effects on silica agglomerate size and processability

Silica surface was treated with various aliphatic chain length silane coupling agents and compounded in EPDM using an internal mixer, and their agglomerate sizes, viscosity, and extrudate swell were investigated. The treated silica compounds showed smaller agglomerate size, lower viscosity, and lower swell reduction compared to untreated silica compound after equivalent mixing times. Short chain silane treated silica compound exhibited smallest agglomerate size. Silane acted as dispersing agents and processing aids in silica/EPDM compounds.     

A finite difference technique for solving the Newtonian jet swell problem

A finite difference technique that incorporates a numerical mapping has been successfully applied to analyse both planar and axisymmetric Newtonian jets. A pressure gradient equation and a free-surface slope equation have been derived for free-surface iteration. The computation of pressure inside the jet surface using the pressure gradient equation is stable and accurate at high Reynolds numbers. The free-surface slope equation is needed for updating the free surface and is applicable for jets with strong surface tension effects. The present development can simulate the Newtonian jets for Reynolds numbers as high as 2000 and capillary number as low as 10^?5. Numerical predictions by the present technique are close to the results of previous finite element simulations.     

Water vapor permeability of shape memory polyurethane with amorphous reversible phase

Shape memory thermoplastic polyurethanes (TPUs), based on amorphous soft segment from the reaction of hexamethylene diisocyanate and 1,2‐butane diol, and the crystalline hard segment from 4,4′‐methylenediphenyl diisocyanate and 1,6‐hexanediol, were modified by hydrophilic segments, diol‐terminated poly(ethylene oxide) or dimethylol propionic acid (DMPA). Differential scanning calorimetry, dynamic mechanical testing, tensile testing, and the measurement of shape memory effect, water swell, and water vapor permeability were carried out to examine these TPUs. The hydrophilic segment increased the hysterisis in shape memory effect by reducing the crystallinity of the hard segment. The neutralized DMPA unit enhanced the sensitivity of the thermoresponsive water vapor permeability (WVP) by amplifying the increase of WVP at the temperature range above the glass transition temperature. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 3009–3017, 2000     

基于神经网络的多联变频空调电子膨胀阀控制系统研究

空调制冷系统具有滞后大、非线性等特点,采用普通控制方式时效果不尽人意。采用BP-PID控制器对系统电子膨胀阀开度进行控制,并设计了BP-PID控制器。实践结果表明,该控制方法简单有效,很好地满足了用户的实际需要。     

基于格子Boltzmann方法的挤出胀大的数值模拟

将单相格子Boltzmann方法(lattice Boltzmann method, LBM)引入到粘弹流体的瞬态挤出胀大的数值模拟中,建立了基于双分布函数的自由面粘弹性流动格子Boltzmann模型．分析得到的流道中流动速度分布和构型张量结果与理论解十分吻合．对粘弹流体瞬态挤出胀大过程进行了模拟,并分析了运动粘度比和剪切速率对挤出胀大率的影响,得到的胀大率结果与理论分析和其它模拟结果基本一致．表明给出的LBM可以捕捉挤出胀大的瞬态效应．