Deep swirling flow down a plughole with air entrainment

Experiments have been carried out to determine the water depth required to entrain a given amount of air with a given circulating water flow discharging through a vertical pipe set in the flat bottom of a vessel. The circulation angle, , between the radial direction and the velocity vector far from discharge pipe was set at 0°, 10°, 30° or 60°.

It is shown that results are not dependent upon the diameter of the offtake pipe, if that is sufficiently small, and results are then expressed either as a dimensionless water depth vs a dimensionless ratio of the flow rates of the two phases or as a dimensionless flow rate of one phase vs the dimensionless flow rate of the other phase. An approximate theory describes trends in the data and is mostly in good quantitative agreement.

The results are used to examine the work of others on the entrainment of air or steam by water flowing along the bottom of a horizontal pipe into a small bottom offtake and the similar entrainment of water by air or steam flowing into a small top offtake. These systems occur in certain PWR loss of coolant accidents.     

Einfluß nichtnewtonscher Stoffeigenschaften auf die Taylor-Wirbelströmung

Zusammenfassung Nach einer kurzen Beschreibung über die Anwendung der Taylor-Wirbelströmung bei der Filtration von nichtnewtonschen Flüssigkeiten werden polymere Modellflüssigkeiten charakterisiert, die als Partikel- und Netzwerklösungen in einer Wirbelströmungsapparatur eingesetzt wurden. Die Fließkurven der Polymerlösungen zeigen aufgrund der extrem hochmolekularen Polymerproben neben strukturviskosen Erscheinungen auch dilatantes Fließverhalten mit besonderer Wirkung auf die Taylor-Wirbelströmung.Die Versuchsflüssigkeiten offenbaren vier verschiedene Typen von Strömungsinstabilitäten: spiralförmige, schwingende und stationäre Instabilitäten sowie gedämpfte Turbulenz. Während die stark strukturviskosen Netzwerklösungen alle genannten Formen aufweisen, fehlt bei den Partikellösungen die spiralförmige Instabilität.Unter Zuhilfenahme des Hantelmolekülmodells zur Beschreibung viskoelastischer Strömungsphänomene gelingt es, durch Einführung einer kritischen Deborahzahl den Einsatzpunkt nichtnewtonscher Taylorströmungseffekte vorauszusagen. Die gefundene Beziehung steht in engem Zusammenhang mit dehnviskositätserhöhenden Polymerwirkungen in Porenströmungen und mit reibungsmindernden Polymereffekten in turbulenten Rohrströmungen.

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Experimental investigations dealing with dilute polymer solutions are described after a short review of the application of Taylor-vortex flow in the filtration processes of non-Newtonian fluids. The test fluids represent both viscoelastic solutions with isolated macromolecules and network solutions with power law fluid behaviour.These solutions show four different types of flow instabilities: spiral-shaped, oscillatory, steady and turbulent phenomena. The Taylor-numbers which depend upon the polymer concentration are determined for the onset of these instability types. For isolated macromolecule solutions, the Deborah-number concept for dilute dumbbell solutions can be applied to describe the first appearance of irregular nonstationary Taylor vortices.The present data are compared to literature values. This fluid behaviour is related to extensional viscosity increases which are also observed in porous media flow and turbulent pipe flow of dilute macromolecular solutions.

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Nomenklatur A, B Konstanten aus Randbedingungen der Ringspaltströmung - C Polymerkonzentration - D Schergeschwindigkeit - De Deborahzahl - l Länge einer Wirbelzelle - L Zylinderlänge - m Gesamtanzahl der Wirbelpaare zur Bestimmung der Wellenzahl - M Molmasse der Polymere - M _w Gewichtsmittel der Molmasse - M _v Viskositätsmittel der Molmasse - n Drehzahl des Rotors - universelle Gaskonstante - r Radius - R _a Radius des Außenzylinders - R _i Radius des Innenzylinders - s Spaltweite - s ^* dimensionslose Spaltweite - T Temperatur - Ta Taylorzahl - v Umfangsgeschwindigkeit - z Anzahl der Wirbelpaare zur Bestimmung der Wellenzahl Griechische Symbole Deformationskoeffizient von Makromolekülen - Wellenzahl - Dehnrate - dynamische Viskosität - [] Grenzviskositätszahl - Relaxationszeit - Dichte - Schubspannung - Winkelgeschwindigkeit - _a Winkelgeschwindigkeit des Außenzylinders - _i Winkelgeschwindigkeit des Innenzylinders Indices c kritisch (erstmaliges Auftreten von Taylorwirbel) - N newtonsch - o onset, Schwellwert - P polymer - r radial - Sch schwingend - Spir spiralförmig - Stat stationär - Turb turbulent - T Taylorströmung - Umfangsrichtung Herrn Prof. Dr. Heinz Harnisch zum 60. Geburtstag gewidmet     

弯曲狭窄管内血液流的分析

与血管狭窄有关的异常血液动力学特征在血管疾病的发生和发展过程中起着重要的作用,由于血管狭窄和弯曲的综合影响,将会出现一系列有趣的流体力学现象,本文研究具有对称狭窄的弯曲小动脉内定常血液流动,在一定的假设条件下,直接从支配血液流动的Navier-Stokes方程求出问题的摄动解,由此求得弯曲狭窄管內血液流动的轴向速度、二次流速度及压力梯度等分析表达式,并进一步求得轴向和周向血管壁切应力。本文的结果是先前有关狭窄直管和弯曲均匀管流动研究的拓广。     

Steady and modulated flow of an Ostwald fluid around a rotating disk

The solutions of the continuity equation and the equations of motion of the flow in the vicinity of a rotating disk have been established for an Ostwald fluid under steady-state conditions and in modulated flow around a mean value. Under steady-state conditions, the kinematics of the flow is scarcely dependent on the rheological parameters close to the disk, however, for n < 1 long-range effects have been put forward. For modulated flow, in the high-frequency range, a behaviour very different from that observed for a Newtonian fluid was found. In the low-frequency range an asymptotic solution has been proposed which is of special interest in mass transfer problems.Presented at the Second Conference of European Rheologists, Prague, June 17–20, 1986     

Lubricated squeezing flow of a Newtonian liquid between elastic and rigid plates

Theoretical force-time relationships were derived for squeezing flow of a Newtonian liquid between lubricated rigid and elastic plates. It is shown how the elastic number, representing the ratio between the elastic plate's rigidity and the specimen's viscosity, affects the force-time curve and under what circumstances the fluid specimen's thickness becomes a significant factor. Potential implications of the analysis in oral sensory evaluations of viscous foods are also considered.     

Pulsierende Druckströmung hochpolymerer Schmelzen im kreisförmigen Kanal

Zusammenfassung Es werden theoretische und experimentelle Untersuchungen pulsierender Strömungen viskoelastischer Flüssigkeiten in einem kreisförmigen Kanal durchgeführt. Unter Voraussetzung einer eindimensionalen, isothermen und vollentwickelten Strömung in Anwesenheit sinusförmiger Druckgradientenschwankungen wird für die rheologische Zustandsgleichung von Bird-Carreau eine asymptotische Lösung erzielt. Die Ergebnisse weisen darauf hin, daß sowohl die relative Amplitude der Ausstoßschwankungen als auch die relative Änderung des mittleren Ausstoßes sich in einer allgemeinen Form darstellen läßt, die bezüglich der Temperatur und der relativen Amplitude der Druckgradientenschwankungen invariant ist. Die theoretischen Ergebnisse werden mit experimentellen Daten für ein Polyethylen niederer Dichte verglichen. Dabei wird eine gute Übereinstimmung der Theorie mit dem Experiment festgestellt.

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Theoretical and experimental studies were carried out on the pulsating flow of viscoelastic liquids through a circular channel. By assuming the flow to be one-dimensional, isothermal, and fully developed and the Bird-Carreau constitutive equation to be applicable, an asymptotic solution was found. The results obtained indicate that both the relative amplitude of pulsation of the output and the relative change in the average output may be presented in a generalized form that is independent of the relative amplitude of the pressure pulsations and temperature. The theoretical results were verified experimentally for a low-density polyethylene. Good agreement was found between the theory and the experimental data.

     

Rheological behaviour of two-phase flow of solid particles in a gas

The present investigation was concerned with the rheological behaviour of dilute suspensions of solid particles in a gas in a vertical cocurrent flow moving upwards. Starting from the experimentally determined dependence of the pressure drop on the concentration of solid particles and the Reynolds number of the carrier medium in the steady flow region, the rheological parameters were estimated using pseudo-shear diagrams. Air was the carrier medium and the dispersed phase was one of six fractions of polypropylene powder and five fractions of glass ballotini. The results show that the investigated two-phase systems have pseudoplastic character which becomes more pronounced with increases in concentration, equivalent diameter and density of solid particles in the flowing suspension. C _d coefficient of particle resistance - d _e equivalent diameter of particles - D column diameter - Fr Froude number - g gravitational acceleration - K rheological parameter - L length - n rheological parameter - p _t pressure drop due to friction - p _m total pressure drop - p _ag pressure drop due to acceleration of the gas phase - p _as pressure drop due to acceleration of the solid phase - p _g hydrostatic pressure of the gas phase - p _s specific effective weight of the dispersed phase - r radius - Re Reynolds number - Re _p Reynolds number of a particle - Re _G generalized Reynolds number - Re _G1 generalized Reynolds number relating to the end of the laminar flow region - Re _G2 generalized Reynolds number relating to the beginning of the turbulent flow region - w _z axial component of velocity - u _t steady free-fall velocity of a single particle - w average velocity - w _g average velocity of the gas phase - w _s average velocity of the dispersed phase of solid particles - relative mass fraction of solid particles - x _s volume fraction of solid particles - _g coefficient of pressure drop due to friction - µ dynamic viscosity - _g density of the gas phase - _m density of the suspension - _s density of solid particles - _ds density of the dispersed phase - _w shear stress at the wall     

Heat transfer in tube assemblies under conditions of laminar axial,transverse and inclined flow

This paper considers laminar flow heat transfer in tube assemblies. The main interest is focused on the virtually unexplored cases of heat transfer under conditions of fully-developed flow inclined to the axes of the tubes and of purely transverse developing flow. The limiting cases of purely axial or purely transverse fully-developed flow are also examined. In all cases, the thermal boundary condition on the tubes is constant heat flux. Governing differential equations are expressed in terms of curvilinear-orthogonal coordinates and solved using finite-differences. Results are compared with available theoretical and experimental data. The effect of the transverse component of the flow on the temperature distribution is found to remain very strong even in nearly-axial flows and therefore considerably higher heat transfer coefficients are exhibited by a nearly-axial flow than a purely axial one.     

Some further observations on the creeping motion of spheres through Ellis model fluids

Using the formulation of Hopke and Slattery, upper and lower bounds on the drag coefficient of a sphere moving slowly in Ellis model fluids have been calculated, over wide range of conditions, and compared with the suitable experimental data available in the literature. C _D drag coefficient - d diameter of sphere - El Ellis number - Re Reynolds number based on zero-shear viscosity - V terminal falling velocity of a sphere - X drag correction factor - Ellis model parameter - ₀ zero-shear viscosity - _1/2 Ellis model parameter     

流动注射化学发光法测定头孢噻肟钠

基于在碱性介质中头孢噻肟钠对鲁米诺-K3Fe(CN)6化学发光体系的增强作用,建立了流动注射化学发光测定头孢噻肟钠的新方法.头孢噻肟钠的质量浓度与化学发光强度的变化在2.4～30 mg/L和60～300 mg/L范围内呈良好的线性关系,检出限为0.63 mg/L,对浓度为30 mg/L的头孢噻肟钠进行9次平行测定,相对标准偏差(RSD)为1.0%.该法简便、快速、可靠,将其用于头孢噻肟钠针剂的测定,结果令人满意.