A low frequency torsional rheometer

Summary An instrument has been developed for measuring the viscoelastic behaviour of polymer melts at low frequencies, in the range 10^–3 to 50 Hz. The sample is contained between a cone and a fixed plate, or between parallel plates. The moving member is driven in torsional oscillation through a torsion wire. The amplitude of the resulting oscillation is compared in amplitude and phase with the driven end of the torsion wire. The amplitudes are measured digitally using optical diffraction gratings, and either an oscilloscope or a high-speed ultra-violet recorder is used to determine the phase angle between the two signals. The moving member is supported on an air bearing, which provides a very low friction support with a high degree of positional control thus giving a well defined sample geometry. The torsion wire is driven using a vibrator with a d.c. drive amplifier fed from a very low frequency oscillator. The sample temperature is controlled to better than 0.01 °C, with temperature gradients across the sample of a similar order of magnitude. The temperature range of the instrument is from –50 °C to +200 °C.The angular resolution of the measuring system is 3 × 10^–5 radius, so that an accuracy of better than ±1% in the amplitude measurements can be obtained with the amplitude of shear in the sample kept sufficiently low that a linear stress-strain relation is maintained.With 3 figures     

A torsional creep instrument and a torsional pendulum,both with accurate temperature control

Summary This paper describes a torsional pendulum and a torsional creep instrument. With the pendulum shear moduli between 10⁶ and 10¹⁰ N/m² can be measured at frequencies from 0.1 to 20 Hz. The creep instrument is suitable for measurement of shear compliances lower than 10^–7 m²/N in the time range from 1 to 10⁵ seconds. In both instruments, specimens are kept at the right temperature by blowing heated nitrogen gas through a surrounding thermostatic chamber. The signal of a platinum resistance thermometer, provided in each chamber, automatically controls the heating of the gas. Temperatures from –180 to +300 °C can be maintained with an absolute accuracy of ±1 °C and a long term stability of ±0.05 °C. It is shown that one cannot directly compare one and the same shear property, calculated from the shear modulus as measured with the pendulum as well as from the shear compliance as measured with the creep instrument. This is due to differences in the temperature of one thermostatic chamber over against the other. Finally, the paper presents a method to reduce these differences to ±0.1 °C, although the absolute accuracy of temperature control remains ±1 °C.

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Zusammenfassung Die Arbeit beschreibt ein Torsionspendel und eine Torsions-Kriechapparatur. Mit dem Pendel können Schermoduli zwischen 10⁶ und 10¹⁰ N/m² bei Frequenzen zwischen 0,1 und 20 °C gemessen werden. Die Kriechapparatur ist geeignet für die Messung von Scherkomplianzen kleiner als 10^–7 m²/N in Zeiten zwischen 1 bis 10⁵ sec. In beiden Geräten werden die Proben durch das Einblasen von erhitztem Stickstoff durch eine umgebende thermostatische Kammer bei der richtigen Temperatur gehalten. Die Anzeige eines Platin-Widerstandsthermometers, das in jeder Kammer angebracht ist, kontrolliert automatisch die Erwärmung des Gases. Es können Temperaturen zwischen –180 und +300 °C mit einer absoluten Genauigkeit von ±1 °C und einer Langzeitstabilität von ±0,05 °C eingestellt werden. Es wird gezeigt, daß ein direkter Vergleich der gleichen Schereigenschaft, die zum einen aus dem mit dem Pendel gemessenen Schermodul und zum anderen aus der mit der Kriechapparatur ermittelten Kriechkomplianz errechnet wird, nicht möglich ist. Das beruht auf Temperaturdifferenzen zwischen den thermostatisierten Kammern.Abschließend stellt die Arbeit eine Methode vor, um diese Differenzen auf ±0,1 °C zu senken. Die absolute Genauigkeit der Temperaturkontrolle bleibt bei ±1 °C.

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Paper presented at the Conference on Experimental Rheology, University of Bradford, April 17–19, 1968.     

Neue Bestimmung des kritischen Punktes von leichtem und schwerem Wasser

Zusammenfassung Im Rahmen der internationalen Wasserdampfforschung [1, 2, 3] wurden in den letzten Jahren genaue Messungen verschiedener Zustandsgrößen von leichtem und teilweise auch von schwerem Wasser vorgenommen. In diesem Zusammenhang war auch die Kenntnis genauerer Werte für die kritischen Zustandsgrößen von großem Interesse.In einer zylindrischen, waagerecht liegenden Druckkammer mit durchsichtigen Beobachtungsfenstern wurden beim langsamen Durchlaufen des kritischen Punktes mit sehr geringfügigen Temperaturänderungen von 0,01 bis 0,03 °C/h fortlaufend Temperaturen und Drücke gemessen. Gleichzeitig wurde die Phasentrennfläche zwischen Flüssigkeit und Dampf beobachtet, die beim Durchlaufen des kritischen Zustandes in einem sehr kleinen Temperatur- und Druckbereich verschwindet bzw. wiedererscheint.Es ergaben sich folgende Werte für die kritischen Temperaturen und Drücke von H₂O und D₂O: H₂O t_krit=(373,91±0,03) °C P_krit=(220,45±0,03) bar D₂O t_krit=(370,66±0,03) °C P_krit=(216,59±0,03) bar.Die Temperaturangaben beziehen sich auf die Internationale Praktische Temperaturskala von 1948.

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New determination of the critical point of water and heavy water

The apparatus used for determining the critical data of water and heavy water consists in principle of a horizontal cylindrical pressure chamber of INCONEL X-750. Observation windows of synthetic saphire (Al₂O₃) are located at the ends.During the experiments the critical point was passed with very small rates of temperature change of about 0.01 to 0.03 °C/h. The disappearance and appearance of the meniscus could be observed continuously with a telescope enlarging 10 times, with simultaneous measurement of pressure and temperature.The following results were obtained for the critical temperature and critical pressure of H₂O and D₂O: H₂O t_crit=(373.91±0.03) °C P_crit=(220.45±0.03) bar D₂O t_crit=(370.66±0.03) °C P_crit=(216.59±0.03) bar.These temperatures are related to the International Practical Temperature Scale of 1948.

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Über diese Arbeit wurde auf dem VDI-Thermodynamik-Kolloquium 1967 in Bad Neuenahr berichtet.     

A technique for measuring the dynamic behavior of materials at high temperatures

A new experimental technique has been developed for the performance of high temperature, high-strain-rate experiments in the compression Kolsky bar (split-Hopkinson pressure bar or SHPB). The new technique (referred to as the High-Temperature Compression Kolsky Bar or HTCKB) uses an infra-red spot-heater to rapidly heat the specimen to the desired temperature, a!nd an electropneumatic actuation system to minimize the development of temperature gradients in the sample. The technique is cheap and relatively easy to implement and yet provides accurate, repeatable results. As an illustration of the application of the technique, we have examined the high-temperature response of the BCC metal vanadium at high-strain rates. Stress–strain curves are obtained for the material at strain rates of 4 × 10³ s⁻¹ and at temperatures ranging from 300 to 1100 K (27–800°C). Quasistatic (10⁻³ s⁻¹) experiments have also been performed on vanadium over a slightly smaller range of temperatures, and the results are compared with the new high-temperature, high-strain-rate data. It is observed that the rate of thermal softening is a function of the strain rate. These results illustrate the importance of including the coupling between temperature and strain r!ate in thermoviscoplastic constitutive models.     

Flow regimes and two-phase pressure gradient in horizontal straight tubes: Experimental results for HFO-1234yf, R-134a and R-410A

Two-phase flow regime visualizations of HFO-1234yf and R-134a in a 6.70 mm inner diameter glass straight tube have been simultaneous investigated by top and side views with a high speed high resolution camera. No major difference was observed between both refrigerants. HFO-1234yf flow regimes were satisfactorily predicted by the Wojtan et al. [1] flow pattern map. In addition, 819 pressure drop data points measured during two-phase flow of refrigerants HFO-1234yf, R-134a and R-410A in horizontal straight tubes are presented. The tube diameter (D) varies from 7.90 to 10.85 mm. The mass velocity ranges from 187 to 1702 kg m⁻² s⁻¹ and the saturation temperatures from 4.8 °C to 20.7 °C. The results are compared against 10 well-known two-phase frictional pressure drop prediction methods. For the entire database, the best accuracy is given by the method of Müller-Steinhagen and Heck [2] with around 90% of the data predicted within a ±30% error band. An analysis was carried out on the maximum pressure gradient and on the corresponding vapor quality. A statistical analysis for each flow regime was also carried out.     

Carbon dioxide flow boiling in a single microchannel - Part I: Pressure drops

Carbon dioxide two-phase flow pressure drops have been investigated in a single horizontal stainless-steel micro-tube having a 0.529 mm inner diameter. Experiments were carried out in adiabatic conditions for four saturation temperatures of −10; −5; 0; 5 °C and mass fluxes ranging from 200 to 1400 kg/m² s, for inlet qualities up to unity. Measurements have been compared to the predictions of well-known methods. The Müller-Steinhagen and Heck correlation and the Friedel correlation gave the best fit as well as the homogeneous model when the liquid viscosity is used to represent the apparent two-phase viscosity. Further, an analysis based on the homogeneous model has not shown any clear appearance of the laminar or the transition regimes in any given range of Reynolds number. The apparent viscosity of the two-phase mixture was found larger than the liquid viscosity at low vapour qualities, namely at the lowest temperatures. Hence, a new expression to determine the equivalent viscosity was suggested as a function of the reduced pressure. Lastly, the Chisholm parameter from the Lockhart-Martinelli correlation was found lower than expected and also mainly dependent on the saturation temperature.     

Experimental investigation in pool boiling heat transfer of ammonia/water mixture and heat transfer correlations

The nucleate pool boiling heat transfer coefficient of ammonia/water mixture was investigated on a cylindrical heated surface at low pressure of 4-8 bar and at low mass fraction of 0 < x_NH3 < 0.3 and at different heat flux. The effect of mass fraction, heat flux and pressure on boiling heat transfer coefficient was studied. The results indicate that the heat transfer coefficient in the mixture decreases with increase in ammonia mass fraction, increases with increase in heat flux and pressure in the investigated range. The measured heat transfer coefficient was compared with existing correlations. The experimental data were predicted with an accuracy of ±20% by the correlation of Calus&Rice, correlation of Stephan-Koorner and Inoue-Monde correlation for ammonia/water mixture in the investigated range of low ammonia mass fraction. The empirical constant of the first two correlations is modified by fitting the correlation to the present experimental data. The modified Calus&Rice correlation predicts the present experimental data with an accuracy of ±18% and the modified Stephan-Koorner correlation with an accuracy of ±16%.     

A note on the coefficient of viscosity of pure molten 2,4,6-trinitrotoluene (TNT)

The viscosity of pure molten TNT has been investigated over the temperature range 82.0°–95.4°C. The temperature dependence of viscosity was found to be best represented by a relation of the type = A e ^B/T whereA = 0.000541,B = 3570, is the viscosity in mPa s andT is the temperature in Kelvin. Earlier work, which suggests an inverse temperature dependence of the flow activation energy, is shown to include an error in the published equation for the temperature dependence of the viscosity of molten TNT.     

Ein vollautomatisch arbeitendes Torsionspendel für den Temperaturbereich von −180°C bis + 250°C

Zusammenfassung Zur Ermittlung des komplexen SchubmodulsG ^* bei Kunststoffen wurde ein Torsionspendel an einen Prozeßrechner angeschlossen. Das Meßsystem gestattet es, Messungen in einem Temperaturbereich von –180°C bis +250°C bei einer konstanten Schwingungsfrequenz von 1 Hz ± 0,09 Hz vollautomatisch durchzuführen. Der Rechner hat die Aufgabe, das Experiment zu steuern, die Versuchsbedingungen zu kontrollieren, die Meßwerte zu erfassen und die Auswertung durchzuführen. Die Ergebnisse können in Form von Tabellen oder graphisch ausgegeben werden. Ferner ist es möglich, die Ergebnisse auf dem Massenspeicher des Rechners in einer Datei abzulegen.

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Summary A torsional pendulum has been connected to a minicomputer in order to measure the complex shear modulus (G ^*). This experimental set-up allows to take computer controlled measurements in the temperaturerange –180°C to +250°C at a constant oscillation frequency of 1 Hz ± 0,09 Hz. The setting and controlling of the experimental parameters, the take-up of the data and the calculations are performed by the computer. The results are obtained in tabulated form or in form of plotted diagrams. In addition it is possible to store the results on the disc of the computer.

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Mit 10 Abbildungen     

Experimental investigation of heat transfer in vertical upward and downward supercritical CO2 flow in a circular tube

An experimental investigation of turbulent heat transfer in vertical upward and downward supercritical CO₂ flow was conducted in a circular tube with an inner diameter of 4.5 mm. The experiments were performed for bulk fluid temperatures from 29 to 115 °C, pressures from 74.6 to 102.6 bar, local wall heat fluxes from 38 to 234 kW/m², and mass fluxes from 208 to 874 kg/m² s. At a moderate wall heat flux and low mass flux, the wall temperature had a noticeable peak value for vertical upward flow, but increased monotonically along the flow direction without a peak value for downward flow. The ratios of the experimental Nusselt number to the value obtained from a reference correlation were compared with Bo^* and q⁺ distributions to observe the buoyancy and flow-acceleration effects on heat transfer. In the experimental range of this study, the flow acceleration predominantly affected the heat-transfer phenomena. Based on an analysis of the shear-stress distribution in the turbulent boundary layer and the significant variation of the specific heat across the turbulent boundary layer, a new heat-transfer correlation for vertical upward and downward flow of supercritical pressurized fluid was developed; this correlation agreed with various experimental datasets within ±30%.     

Experimental measurement of thermophysical properties of oxide-water nano-fluids down to ice-point

This paper presents the measurement of the thermal conductivity and the dynamic viscosity of Al₂O₃-water (1-4% particle volume fraction) and TiO₂-water (1-6% particle volume fraction) nano-fluids carried out at atmospheric pressure in the temperature range from 1 to 40 °C, which is particularly interesting for the application of nano-fluids as thermal medium in refrigeration and air-conditioning.The thermal conductivity measurement was performed by using a Transient Hot Disk TPS 2500S apparatus instrumented with a 7577 probe (2.001 mm in radius) having a maximum uncertainty (k = 2) lower than ±5.0% of the reading. The dynamic viscosity measurement and the rheological analysis were carried out by a rotating disc type rheometer Haake Mars II instrumented with a single cone probe (60 mm in diameter and 1° angle) having a maximum uncertainty (k = 2) lower than ±5.0% of the reading.The thermal conductivity measurements of the tested nano-fluids show a great sensitivity to particle volume fraction and temperature and a weak sensitivity to cluster average size: TiO₂-water and Al₂O₃-water nano-fluids show a thermal conductivity enhancement (with reference to pure water) from −2 to 16% and from −2 to 23% respectively.TiO₂-water and Al₂O₃-water nano-fluids exhibit a Newtonian behaviour in all the investigated ranges of temperature and nano-particle volume fraction. The relative viscosity shows a great sensitivity to particle volume fraction and cluster average size and no sensitivity to temperature: TiO₂-water and Al₂O₃-water nano-fluids show a dynamic viscosity increase with respect to pure water from 17 to 210% and from 15 to 150% respectively.Al₂O₃-water nano-fluid seems to be more promising as thermal medium than TiO₂-water nano-fluid, particularly at low thermal level (between ambient temperature and ice point) where TiO₂-water is not suitable showing worse performance than pure water.Present experimental measurements were compared both with available measurements carried out by different researchers and computational models for thermophysical properties of suspensions.     

Experimental study of in-tube cooling heat transfer and pressure drop characteristics of R134a at supercritical pressures

The in-tube cooling flow and heat transfer characteristics of R134a at supercritical pressures are measured experimentally for various pressures and mass fluxes in a horizontal tube. The tube is made of stainless steel with an inner diameter of 4.01 mm. Experiments are conducted for mass fluxes from 70 kg/m² s to 405 kg/m² s and pressures from 4.5 MPa to 5.5 MPa. The inlet refrigerant temperature is from 80 °C to 140 °C. The results show that the refrigerant temperature, the mass flux and the pressure all significantly affect the flow and heat transfer characteristics of R134a at supercritical pressures. The experimentally measured frictional pressure drop and heat transfer coefficient are compared with predicted results from several existing correlations. The comparisons show that the predicted frictional pressure drop using Petrov and Popov’s correlation accounting for the density and viscosity variations agree well with the measured data. Gnielinski’s correlation for the heat transfer coefficient agrees best with the measured data with deviations not exceeding 25%, while correlations based on supercritical CO₂ heat transfer data overcorrect for the influence of the thermophysical property variations resulting in larger deviations. A new empirical correlation is developed based on the measured results by modifying Gnielinski’s equation with thermophysical property terms including both the property variations from the inlet to the outlet of the entire test section and from the bulk to the wall. Most of the experimental data is predicted by the new correlation within a range of 15%.     

A Kolsky bar: Tension,tension-tension

The present paper introduces a new technique which combines rotation disk and traditional Kolsky bar (often termed as split-Hopkinson bar). This technique can be employed to study the tension stress-strain relations and tension-unloading-tension strain-rate history effects of materials in the strain rate range from 10²–10³s⁻¹. The rise time of the incident wave is as short as 15 μs because of the particular design. An attempt is made to estimate strain error caused by the thread connection between the specimen and the bars, and stress error due to the mismatch of the cross section of the specimen and bars. A short rise-time incident wave appears to be most advantageous in view of maintaining the accuracy of the stress-strain curve obtained near the initiation. Preliminary tests are performed on the instrument. Comments are made for this design configuration. M. Li (Student Member of SEM), presently at the Department of Aerospace Engineering, Mechanics and Engineering Science, University of Florida, Gainesville, FL 32611, was Research Associate; R. Wang (formerly A.J. Wang) is Professor; and M.-B. Han is Associate Professor, Department of Mechanics, Peking University, Beijing 100871, P.R. China.     

Experimental study on oil–water flow in horizontal and slightly inclined pipes

Oil–water two-phase flow experiments were conducted in a 15 m long, 8.28 cm diameter, inclinable steel pipe using mineral oil (density of 830 kg/m³ and viscosity of 7.5 mPa s) and brine (density of 1060 kg/m³ and viscosity of 0.8 mPa s). Steady-state data on flow patterns, two-phase pressure gradient and holdup were obtained over the entire range of flow rates for pipe inclinations of −5°, −2°, −1.5°, 0°, 1°, 2° and 5°. The characterization of flow patterns and identification of their boundaries was achieved via observation of recorded movies and by analysis of the relative deviation from the homogeneous behavior. A stratified wavy flow pattern with no mixing at the interface was identified in downward and upward flow. Two gamma-ray densitometers allowed for accurate measurement of the absolute in situ volumetric fraction (holdup) of each phase for all flow patterns. Extensive results of holdup and two-phase pressure gradient as a function of the superficial velocities, flow pattern and inclinations are reported. The new experimental data are compared with results of a flow pattern dependent prediction model, which uses the area-averaged steady-state two-fluid model for stratified flow and the homogeneous model for dispersed flow. Prediction accuracies for oil/water holdups and pressure gradients are presented as function of pipe inclination for all flow patterns observed. There is scope for improvement for in particular dual-continuous flow patterns.     

Superheating instability in a pulsed xenon discharge

It is shown that previously obtained conditions for superheating instability substantially vary if we take into account secondary xenon ionization. Instability completely vanishes if the density of heavy particles in the discharge is kept constant and whenever a discontinuous time variation of temperature T in a restricted region between 15 · 10³ ° K and 20 · 10³ ° K is possible for a constant effective pressure. The development of instability is studied numerically by a ranging method. Stationary temperature distributions possessing a high contrast as a local temperature passes through a given range of instability with constant pressure are presented.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 1, pp. 27–30, January–February, 1976.     

Progressive fracture of laminated composite stiffened plate

Laminated fiber-reinforced composite stiffened plate with [0/90/±45]_S plies made of S-Glass/epoxy are evaluated via computational simulation to study damage and fracture progression. The loads are pressure and temperature which varies from 21 to 65.5 °C (case I) and from 143.3 to 21 °C (case II). An integrated computer code is used for the simulation of the damage progression. Results show that damage initiation begins at low load level, with matrix cracking at the 0° (bottom and top) plies, fiber fracture at the bottom (0°) ply and interply delamination at the top (0°) ply. Increasing the applied pressure, the damage growth is expended resulting in fracture through the thickness of the structure. At this stage, 90% of the plies damage at applied pressure 15.306 MPa for the case I and 15.036 MPa for the case II. After this stage, the cracks propagate rapidly and the structure collapses.     

Kerr constant of water

Measurements are conducted of the Kerr constant of ultrapure water with resistivity 10⁷ · cm. Values of the Kerr constant of (3.26 ± 0.10) · 10^-7 and (2.29 ± 0.07) · 10^-7 esu were obtained at a temperature of 30 °C for wavelengths of 441.6 nm and 632.8 nm.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 1, pp. 157–160, January–February, 1976.The authors wish to express their appreciation to D. D. Ryutov for useful discussion.     

Linear and branched poly(butyleneisophthalate): Activation energy for melt flow

Several poly(butyleneisophthalate)s of different molecular weight, both linear and randomly branched, were synthetized by bulk polymerization and studied in the molten state with a capillary rheometer in the temperature range 190–220°C. The viscosity shift factors showed to be well correlated to temperature by an Arrhenius-type equation. The melt-flow activation energy at constant shear stressE was found to be 15±1 kcal/mol for both linear and branched samples, whereas for polydisperse poly(butyleneterephthalate) and poly(ethyleneterephthalate) it was found previously that random long-chain branching substantially increases the activation energy.An analysis of our results and of those available in the literature shows that the influence of branches on the temperature coefficient of viscosity of polymers is still a subject open to discussion.     

Can die swell be predicted?

Summary A calculational scheme has been developed to predict die swell values which are defined as the value after completion of the elastic recovery. The constants of the equations have been evaluated at 190 °C from the known results of several polyethylene samples. With the similar type but different sample of polyethylene, it is shown that the prediction is with ±3.4% for the shear rates of 90 to 600 sec^–1, for the dies ofL/D 2–20 and at temperature of 200 °C.With 3 figures and 4 tables     

Viscous properties of polymer melts and elastomers exemplified by ethylene-propylene copolymer

Summary The copolymer of ethylene and propylene possesses a sufficiently high thermo-oxidative resistance, making it possible to study its viscous properties, determine the appearance of elastic turbulence and wall slippage and to measure the rate of the latter over a wide interval of temperatures ranging from room temperature to 260 °C.At low shear stresses and rates the copolymer behaves like aNewtonian liquid with a viscosity of about 10⁸ poise at room temperatures.Elastic turbulence and wall slippage are displayed in sharp form when the viscosity of the copolymer is lowered to its critical value, which depends very little on the temperature and may be accepted as averaging 2.2×10⁴ poise. The corresponding critical shear stress values vary about 10-fold. The criteria of appearance of elastic turbulence suggested in (12, 14) do not agree with experimental data. The entrance losses during the flow of the copolymer through capillaries are low right until elastic turbulence sets in, after which it becomes practically impossible to measure them by the method of capillaries of different length. The average wall slippage rate values of the copolymer at shear stresses above 10⁶ dyne/cm² amount to tens of cm/sec. They increase very abruptly with rising temperature.The temperature dependence of the viscosity and the dynamic characteristics of the copolymer indicate that it has a phase transition at temperatures of about 100–120 °C, which must be related to melting of blocks contained in the copolymer macromolecules, having a structure close to that of high-pressure polyethylene. This shows that the rheological method of studying block-type polymer and grafted polymers is promising.