Shear creep and recovery of a technical polystyrene

The torsional creep and recoverable bahaviour of a technical polystyrene is reported over seven orders of magnitude of the value of the compliance from 10^–8 to 10^–1 Pa^–1 and over more than seven decades in time. The results for the recoverable compliance J_R (t) reveal a dispersion region seen between the glass transition and the steady-state recoverable compliance J_e. The limiting value of the final dispersion J_e = 4.7 · 10^–4 Pa^–1 indicates a broad molecular-weight distribution. The steady-state recoverable compliance J_e is independent of the temperature. The temperature dependence of the final dispersion was found to be indistinguishable from that of viscous flow. However, this temperature dependence differs significantly from that of the glass-rubber transition. A proposal has been made for the construction of creep compliance and recoverable compliance over an extended time scale.     

The anisotropy of simple shearing flow

Summary The optical analogue of the second normal stress difference, namely,n ₂₂ –n ₃₃ has been measured for several polymer systems. The experimental method is direct and makes use of capillary and slit dies. For the polymer melts examined — ranging from a polystyrene with a viscosity of 10⁴ Ns/m² to a PIB of viscosity 50 Ns/m² — a non-zero (n ₂₂ –n ₃₃) was found which could not be accounted for by any systematic errors. Except for one case, where (n ₁₁ –n ₂₂) could not be evaluated, the ratio (n ₂₂ –n ₃₃)/(n ₁₁ –n ₂₂) was found to be negative with an absolute value of 0.05 to about 0.1. For solutions the results are not clear-cut: in several casesn ₂₂ –n ₃₃ was immeasurably small but in one case (23% PIB in oil) the above ratio was the same as for the melts. A modification of the (dilute solution) molecular theories is suggested which is qualitatively able to describe most of the experimental results here outlined.

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Zusammenfassung Die optische Analogie der zweiten Normalspannungs-Differenz, nämlichn ₂₂ –n ₃₃ wurde für verschiedene Polymersysteme gemessen. Dabei wurden Kapillaren und Schlitzdüsen benutzt. Bei allen untersuchten polymeren Schmelzen, die sich von einem Polystyrol mit einer Viskosität von 10⁴ Ns/m² bis zu einem Polyisobuten mit einer Viskosität von 50 Ns/m² erstreckten, wurde n₂₂ –n ₃₃ signifikant ungleich Null gefunden. Mit Ausnahme eines Falles, in dem (n ₁₁ –n ₂₂) nicht bestimmt werden konnte, ergab sich die Größe (n ₂₂ –n ₃₃)/(n ₁₁ –n ₂₂) negativ mit einem Absolutwert zwischen 0,05 und 0,1.Für Lösungen waren die Ergebnisse nicht so eindeutig: In mehreren Fällen warn ₂₂ –n ₃₃ unmeßbar klein, in einem Fall aber (23% PIB in Öl) war diese Größe von der gleichen Ordnung wie für die Schmelzen.Es wurde eine Modifikation der molekularen Theorie verdünnter Lösungen vorgeschlagen, die die meisten der hier dargestellten experimentellen Ergebnisse zu beschreiben gestattet.

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With 12 figures     

Longitudinal volume viscosity of poly (vinyl chloride)

The volume flow of poly (vinyl chloride) ( = 45,000,T _g = 350 K) has been measured in an Instron Capillary Rheometer.The elastic modulus in longitudinal compression, the longitudinal volume viscosity and initial longitudinal volume viscosity, and retardation times were determined at temperatures both below (324 – 343 K) and above (403 – 453 K) the glass transition temperatureT _g , and at compression rates between approximately 10^–5 and 200 · 10^–5 s^–1.An increase in the longitudinal volume viscosity was observed for decreases in the volume deformation, increases in the compression rate and increases in temperature.T _g decreased at 0.16 K/MPa. The volume flow activation energy was found to be equal to that for shear flow with a constant value of 91.37 kJ/mol.     

Influence of mean stress on the fatigue crack growth characreristics of CrlMo steel tube at elevated temperature

The fatigue crack growth characteristics of CrlMo steel have been investigated at 861 K over the R-ratio range 0.1–0.7 utilising a dwell time of 10 min. at maximum load. All tests were conducted under load control in a laboratory air environment. It was established that the R-ratio significantly affected the fatigue crack extension behaviour inasmuch that with increasing R-ratio, the critical ΔK level for the onset of creep fatigue interactive growth, ΔK^IG, decreased from 20 to 7 MPa√m and the threshold stress intensity, ΔK_th, decreased from 9 to about 3 MPa√m. At intermediate ΔK levels, i.e. between ΔK_th and ΔK^IG, the fatigue crack extension rates, for all R-ratio values, resided on or slightly below the CTOD line, which represents the upper bound for contrnuum controlled fatigue crack growth. Creep fatigue interactive growth was typified by crack extension rates that reside above the CTOD line with a ΔK^IG dependence; the attainment of some critical creep condition or crack linkage condition which causes the abrupt change in crack extension behaviour at ΔK^IG; and crack extension occurs almost exclusively in an intergranular manner. The R-ratio and ΔK^IG followed a linear relation. A literature review concerning the effect of temperature on the threshold fatigue crack growth characteristics of low alloy ferritic steels demonstrated powerful effects of temperature; the magnitude of these effects, however, were dependent upon the testing temperature regime and R-ratio level. The effect of R-ratio on ΔK_th was greatest at temperatures >400°C, significant at ambient temperatures and least in the temperature range 90°C to <300°C. The relationship between temperature and ΔK_th, at a given R-ratio, exhibited a through and a minimum ΔK_th value was observed in the temperature range 200–250°C. The magnitude of the temperature effects on ΔK_th decreased with increasing R-ratio. Such effects of temperature and R-ratio on ΔK_th was reasonably explained in terms of crack closure effects. Finally, the present elevated temperature fatigue crack growth data exhibited massive crack extension enhancement values when compared to ambient near-threshold fatigue crack growth data for CrlMo steel. Such large enhancement values were the combined effects of temperature (environment) and frequency.     

A new method for measuring the complex shear modulus of a viscoelastic material coupled with an elastic material

Summary In the mechanical-dynamic characterization of viscoelastic materials as a function of temperature, considerable difficulties are encountered, due to the change of joint, to the strong variation of the modulus of elasticity and the increase ofQ ^–1.This paper deals with a theoretical and experimental method for the determination of the shear modulusG₂ and of the internal lossQ ₂ ^–1 of a viscoelastic material by measurements at torsional vibration of a composite test-piece. Experimental measurements were carried out on composite test-pieces by gluing of polystyrene and of pinchbeck. The results obtained are in good agreement with the values found by other methods.     

Messung der Wärmeleitfähigkeit von Stickstoff und Kohlenmonoxid bei hohen Temperaturen im Stoßwellenrohr

Zusammenfassung Die Meßergebnisse für die Wärmeleitfähigkeit von Stickstoff bei Temperaturen zwischen 1230 und 6000 K und Drückenzwischen 1 und 10 bar und von Kohlenmonoxid zwischen 1150 und 5000 K bei 1 bar werden mitgeteilt. Diese mit dem Stoßwellenrohr gemessenen Werte werden mit jenen verglichen, die sich aus der strengen kinetischen Gastheorie ergeben. Auch verfügbare Daten anderer Autoren werden zum Vergleich herangezogen.

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Measurement of thermal conductivity of nitrogen and carbon monoxide at high temperatures in a shock tube

The paper presents results of shock-tube measurements of thermal conductivity of nitrogen at temperatures between 1230 and 6000 K and at pressures between 1 and 10 bar and of carbon monoxide at temperatures between 1150 and 5000 K at 1 bar. Experimental results are compared with several variants of theoretical values, computed from rigorous kinetic theory, and with available data of other authors.

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Bezeichnungen (Einheiten in Klammern) a [m² s^–1] Temperaturleitzahl - C _p[J mol^–1 K^–1] molare Wärmekapazität - k [J K^–1] Boltzmann-Konstante - M [kg mol^–1] molare Masse - p bar Gesamtdruck - R [J mol^–1 K^–1] Gaskonstante - T [K] thermodynamische Temperatur - t [s] Zeit - U [J mol^–1] innere Energie - w [m s^–1] Geschwindigkeit - x [m] Ortskoordinate - x _i [1] Molanteil der Komponentei im Gasgemisch - [Wm^–1 K^–1] Wärmeleitfähigkeit - [mol m^–3] molare Konzentration Indizes i die Komponentei im Gasgemisch - g bezieht sich auf das (kalte) Gas bei der Wandtemperatur - w bezieht sich auf die feste Wand - p bei konstantem Druck Dieser Beitrag wurde auf dem Thermodynamik-Kolloquium des VDI im Oktober 1969 in Zürich vorgetragen.     

On the laminar forced convection with axial conduction in a circular tube with exponential wall heat flux

The values of the fully developed Nusselt number for laminar forced convection in a circular tube with axial conduction in the fluid and exponential wall heat flux are determined analytically. Moreover, the distinction between the concepts of bulk temperature and mixing-cup temperature, at low values of the Peclet number, is pointed out. Finally it is shown that, if the Nusselt number is defined with respect to the mixing-cup temperature, then the boundary condition of exponentially varying wall heat flux includes as particular cases the boundary conditions of uniform wall temperature and of convection with an external fluid.

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Über laminare Zwangskonvektion mit Längswärmeleitung in einem Kreisrohr mit exponentiell veränderlichem Wandwärmefluß

Zusammenfassung Es werden die Endwerte der Nusselt-Zahlen für vollausgebildete laminare Zwangskonvektion in einem Kreisrohr mit Längswärmeleitung und exponentiell veränderlichem Wandwärmefluß analytisch ermittelt. Besondere Betonung liegt auf dem Unterschied zwischen den Konzepten für die Mittel- und die Mischtemperatur bei niedrigen Peclet-Zahlen. Schließlich wird gezeigt, daß bei Definition der Nusselt-Zahl bezüglich der Mischtemperatur die Randbedingung exponentiell veränderlichen Randwärmeflusses die Spezialfälle konstanter Wandtemperatur und konvektiven Wärmeaustausches mit einem umgebenden Fluid einschließt.

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Nomenclature A _n dimensionless coefficients employed in the Appendix - Bi Biot numberBi=h _e r ₀/ - c _n dimensionless coefficients defined in Eq. (17) - c _p specific heat at constant pressure of the fluid within the tube, [J kg^–1 K^–1] - f solution of Eq. (15) - h ₁,h ₂ specific enthalpies employed in Eqs. (2) and (4), [J kg^–1] - h _e convection coefficient with a fluid outside the tube, [W m^–2 K^–1] - rate of mass flow, [kg s^–1] - Nu bulk Nusselt number,2r ₀ q _w /[(T _w –T _b )] - Nu _H fully developed value of the bulk Nusselt number for the boundary condition of uniform wall heat flux - Nu _T fully developed value of the bulk Nusselt number for the boundary condition of uniform wall temperature - Nu ^* mixing Nusselt number,2r ₀ q _w /[(T _w –T _m )] - Nu _C ^* fully developed value of the mixing Nusselt number for the boundary condition of convection with an external fluid - Nu _H ^* fully developed value of the mixing Nusselt number for the boundary condition of uniform wall heat flux - Nu _T ^* fully developed value of the mixing Nusselt number for the boundary condition of uniform wall temperature - Pe Peclet number, 2r ₀/ - q ₀ wall heat flux atx=0, [W m^–2] - q _w wall heat flux, [W m^–2] - r radial coordinate, [m] - r ₀ radius of the tube, [m] - s dimensionless radius,s=r/r ₀ - T temperature, [K] - T ₀ temperature constant employed in Eq. (14), [K] - T reference temperature of the fluid external to the tube, [K] - T _b bulk temperature, [K] - T _m mixing or mixing-cup temperature, [K] - T _w wall temperature, [K] - u velocity component in the axial direction, [m s^–1] - mean value ofu, [m s^–1] - x axial coordinate, [m] Greek symbols thermal diffusivity of the fluid within the tube, [m² s^–1] - exponent in wall heat flux variation, [m^–1] - dimensionless parameter - dimensionless temperature =(T _w –T)/(T _w –T _b ) - ^* dimensionless temperature ^*=(T _w –T)/(T _w –T _m ) - thermal conductivity of the fluid within the tube, [W m^–1 K^–1] - density of the fluid within the tube, [kg m^–3]     

Diffusion of14C in dense saturated bentonite under steady-state conditions

Diffusion coefficients are critical parameters for predicting migration rates and fluxes of contaminants through clay-based barrier materials used in many waste containment strategies. Cabon-14 is present in high-level nuclear fuel waste and also in many low-level wastes such as those generated from some medical research activities. Diffusion coefficients were measured for¹⁴C (in the form of carbonate) in bentonite compacted to a series of dry bulk densities, _b, ranging from about 0.9 to 1.6 Mg/m³. The clay was saturated with a Na-Ca-Cl-dominated groundwater solution typical of those found deep in plutonic rock on the Canadian Shield. Both effective,D _e, and apparent,D _a, diffusion coefficients were determined.D _e is defined asD _{0 a} n _e, where D₀ is the diffusion coefficient in pure bulk water, _a the apparent tortuosity factor, andn _e the effective porosity available for diffusion; andD _a is defined asD _{0 a} n _e/(n _e + _b K _d ), where K_d is the solid/liquid distribution coefficient. BothD _e andD _a decrease with increasing _b:D _e values range from about 10×10^–12 m²/s at _b0.9 Mg/m³ to 0.6×10^–12 m²/s at 1.6 Mg/m³, andD _a values vary from approximately 40×10^–12 to 4×10^–12 m²/s over the same density range. The decrease inD _e andD _a is attributed to a decrease in both _a andn _e as _b increases. The data indicate thatn _e is <10% of the total solution-filled porosity of the clay at all densities.K _d values for¹⁴C with the clay range from about 0.3 to <0.1 m³/Mg; this indicates there is a small amount of¹⁴C sorbed on the clay and/or some¹⁴C is isotopically exchanged with¹²C in carbonate phases present in the clay. Finally, theD _e values for¹⁴C are lower than those of other diffusants — I^–, Cl^–, TcO₄ ^–, and Cs⁺ — that have been measured in this clay and pore-water solution. This is attributed to lower values for bothn _e andD ₀ for¹⁴C species relative to those of the other diffusants.     

Optimum rib size to enhance forced convection in a horizontal triangular duct with ribbed internal surfaces

The optimum rib size to enhance heat transfer had been proposed through an experimental investigation on the forced convection of a fully developed turbulent flow in an air-cooled horizontal equilateral triangular duct fabricated on its internal surfaces with uniformly spaced square ribs. Five different rib sizes (B) of 5 mm, 6 mm, 7 mm, 7.9 mm and 9 mm, respectively, were used in the present investigation, while the separation (S) between the center lines of two adjacent ribs was kept at a constant of 57 mm. The experimental triangular ducts were of the same axial length (L) of 1050 mm and the same hydraulic diameter (D) of 44 mm. Both the ducts and the ribs were fabricated with duralumin. For every experimental set-up, the entire inner wall of the duct was heated uniformly while the outer wall was thermally insulated. From the experimental results, a maximum average Nusselt number of the triangular duct was observed at the rib size of 7.9 mm (i.e. relative rib size ). Considering the pressure drop along the triangular duct, it was found to increase almost linearly with the rib size. Non-dimensional expressions had been developed for the determination of the average Nusselt number and the average friction factor of the equilateral triangular ducts with ribbed internal surfaces. The developed equations were valid for a wide range of Reynolds numbers of 4,000 < Re _D < 23,000 and relative rib sizes of under steady-state condition. A Inner surface area of the triangular duct [m²] - A _C Cross-sectional area of the triangular duct [m²] - B Side length of the square rib [mm] - C _P Specific heat at constant pressure [kJ·kg^–1·K^–1] - C ₁, C ₂, C ₃ Constant coefficients in Equations (10), (12) and (13), respectively - D Hydraulic diameter of the triangular duct [mm] - Electric power supplied to heat the triangular duct [W] - f Average friction factor - F View factor for thermal radiation from the duct ends to its surroundings - h Average convection heat transfer coefficient at the air/duct interface [W·m^–2 ·K^–1] - k Thermal conductivity of the air [W·m^–1 ·K^–1] - L Axial length of the triangular duct [mm] - Mass flow rate [kg·s^–1] - n ₁, n ₂, n ₃ Power indices in Equations (10), (12) and (13), respectively - Nu _D Average Nusselt number based on hydraulic diameter - P Fluid pressure [Pa] - Pr Prandtl number of the airflow - _c Steady-state forced convection from the triangular duct to the airflow [W] - _l Heat loss from external surfaces of the triangular duct assembly to the surroundings [W] - _r Radiation heat loss from both ends of the triangular duct to the surroundings [W] - Re _D Reynolds number of the airflow based on hydraulic diameter - S Uniform separation between the centre lines of two consecutive ribs [mm] - T Fluid temperature [K] - T _a Mean temperature of the airflow [K] - T _ai Inlet mean temperature of the airflow [K] - T _ao Outlet mean temperature of the airflow [K] - T _s Mean surface temperature of the triangular duct [K] - T Ambient temperature [K] - U Mean air velocity in the triangular duct [m·s^–1] - _r Mean surface-emissivity with respect to thermal radiation - Dynamic viscosity of the fluid [kg·m^–1·s^–1] - Kinematic viscosity of the airflow [m²·s^–1] - Density of the airflow [kg·m^–3] - Stefan-Boltzmann constant [W·m^–2·K^–4]     

Measurement of the probability of the transition P20 (00 °1–10 °0) in CO2 and impact broadening in collisions with CO2, N2, and He

We measured the dependence of the absorption, coefficient on the pressure for the vibrational-rotational transition P20 (00 °1–10 °0) in CO₂ using a CO₂ laser as a light source. We consider the question of the systematic error due to the contribution of impact broadening, when finding the probability from the experimental absorption. The refined value of the transition probability A _{10 °0.20} ^{00 °1.19} =0.169 sec^–1. We obtain the values of the impact half-widths for collisions of the type CO₂-CO₂, CO₂-N₂, CO₂-He, the values of which at J=300 °K are respectively 3.28, 2.74, and 2.27 MHz/torr.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 6, pp. 24–28, November–December, 1972.The authors thank A. K. Konyukhov for interest in the work and for valuable discussions.     

Measurement of the Coefficient of Transverse Dispersion in Flow Through Packed Beds for a Wide Range of Values of the Schmidt Number

Experimental values of the coefficient of transverse dispersion (D _T) were measured with the system 2-naphthol/water, over a range of temperatures between 293K and 373K, which corresponds to a range of values of viscosity () between 2.83×10^–4 Ns/m² and 1.01×10^–3 Ns/m² and of molecular diffusion coefficient (D _m) between 1.03×10^–9 m²/s and 5.49×10^–9 m²/s. Since the density () of water is close to 10³ kg/m³, the corresponding variation of the Schmidt number (Sc=/D _m) was in the range 1000 – 50. More than 200 experimental values of the transverse dispersion coefficient were obtained using beds of silica sand with average particle sizes (d) of 0.297 and 0.496mm, operated over a range of interstitial liquid velocities (u) between 0.1mm/s and 14mm/s and this gave a variation of the Reynolds number (Re=du/) between 0.01 and 3.5.Plots of the dimensionless coefficient of transverse dispersion (D _T/D _m) vs. the Peclet number (Pe_m=ud/D _m) based on molecular diffusion bring into evidence the influence of Sc on transverse dispersion. As the temperature is increased, the value of Sc decreases and the values of D _T/D _m gradually approach the line corresponding to gas behaviour (i.e. Sc 1), which is known to be well approximated by the equation D _T/D _m=1/+ud/12D _m, where is the tortuosity with regard to diffusion.     

Experimental study of heat and mass transfer from a horizontal cylinder in downward air-water mist flow with blockage effect

An experimental study was made on convective heat and mass transfer from a horizontal heated cylinder in a downward flow of air-water mist at a blockage ratio of 0.4. The measured local heat transfer coefficients agree fairly well with the authors' numerical solutions obtained previously for the front surface of a cylinder over the ranges mass flow ratio 0–4.5×10⁻², a temperature difference between the cylinder and air 10–43 K, gas Reynolds number (7.9–23)×10³, Rosin-Rammler size parameter 105–168 μm, and dispersion parameter 3.4–3.7. Heat transfer augmentation, two-pahse to single-phase of greater than 19 was attained at the forward stagnation point. For heat transfer in the rear part of the cylinder, an empirical formula is derived by taking into account the dimensionless governing variables, that is, coolant-feed and evaporation parameters.     

A Numerical Study of Micro-Heterogeneity Effects on Upscaled Properties of Two-Phase Flow in Porous Media

Commonly, capillary pressure–saturation–relative permeability (P ^c–S–K _r) relationships are obtained by means of laboratory experiments carried out on soil samples that are up to 10–12 cm long. In obtaining these relationships, it is implicitly assumed that the soil sample is homogeneous. However, it is well known that even at such scales, some micro-heterogeneities may exist. These heterogeneous regions will have distinct multiphase flow properties and will affect saturation and distribution of wetting and non-wetting phases within the soil sample. This, in turn, may affect the measured two-phase flow relationships. In the present work, numerical simulations have been carried out to investigate how the variations in nature, amount, and distribution of sub-sample scale heterogeneities affect P ^c–S–K _r relationships for dense non-aqueous phase liquid (DNAPL) and water flow. Fourteen combinations of sand types and heterogeneous patterns have been defined. These include binary combinations of coarse sand imbedded in fine sand and vice versa. The domains size is chosen so that it represents typical laboratory samples used in the measurements of P ^c–S–K _r curves. Upscaled drainage and imbibition P ^c–S–K _r relationships for various heterogeneity patterns have been obtained and compared in order to determine the relative significance of the heterogeneity patterns. Our results show that for micro-heterogeneities of the type shown here, the upscaled P ^c–S curve mainly follows the corresponding curve for the background sand. Only irreducible water saturation (in drainage) and residual DNAPL saturation (in imbibition) are affected by the presence and intensity of heterogeneities.     

The viscous air flow pattern in the Stefan diffusion tube

In this paper, we consider the problem of the binary viscous diffusion of vapour through a Stefan tube, which is the model of an elementary capillary. While some preceding results in particular cases supposed parabolic velocity profiles and showed air recirculation, we treat here the general problem of a tube of finite length, submitted to a double viscous diffusion of vapour and air from a liquid surface. The movement of gas is expressed with conservation equations and ideal gas equations. The following added restrictions: constant temperature, no buyoancy effect, no inertial forces, are compatible with a capillary. A numerical solution based on the control volume method is obtained at every point in the tube. The results give the vapour and air flux, describe the circulation pattern and show that the vapour profile of concentration is level. In the lower part of the cylindrical tube space, over a distance of the length of a radius an important radial movement occurs, due to the recirculation of air which changes direction once it reaches the liquid surface. The velocity profile of the gas flow then becomes parabolic in the upper part of the tube.In order to easily obtain a numerical solution, the system of dimensionless equations is expanded to a series and transformed into a set of sub-systems. The little parameter used for this expansion is tied to the vapour concentration on the liquid surface. The solution of the sub-system of order zero, which is easier to compute, represents a good approximation of the complete solution. These solutions are situated in comparison with the Stefan diffusion and show that the influence of the viscous effect on the vapour flux is limited to a few percents.In order to apply the results to porous media where the pores are not so regular, we consider at last the diffusion in a tube including a contracted section in the middle of the tube. Since the diffusion paths are longer, the vapour flux is reduced, while the viscosity effect becomes more considerable. The reduction of the air flux is more significant than that of the vapour. This part of the study provides a better understanding of the diffusion through the pits at the wall fiber, and gives data for the air flux which permeates into the oak wood and produces tannin oxidation and thus discolouration.Nomenclature m _v/ vapour concentration - m _l vapour concentration in equilibrium with its liquid phase - D coefficient of molecular diffusion of a vapour in air (m²/s) - J _a vector density of mass flux of dry air (kg/m²s) - J _v vector density of mass flux of vapour (kg/m²s) - L Capillary length (m) - M _a dry air molar mass (kg/mole) - M _v Vapour molar mass (kg/mole) - P _atm atmospheric pressure - P gas mixture total pressure (Pascal) - R Ideal gas constant (J/mole K) - r _a= R/M _a,r _v=R/M _v - r ₀ tube or capillary radius (m) - T Temperature (K) - u axial component ofV - V gas mixture velocity vector (m/s) - v radial component ofV Greek Letters density of gas (kg/m³) - gas mixture dynamic viscosity (kg/ms) Numerical Values of Parameters D 3×10^–5m²/s (water vapour in air) - 2×10^–5kg/ms - M _a 29×10^–3kg/mole - M _v 18×10^–3kg/mole - T 323K - R 8.31 J/moleK - P _atm 10⁵Pa     

Effect of inertia on thermoelastic flow instability

Thermal effects induced by viscous heating cause thermoelastic flow instabilities in curvilinear shear flows of viscoelastic polymer solutions. These instabilities could be tracked experimentally by changing the fluid temperature T₀ to span the parameter space. In this work, the influence of T₀ on the stability boundary of the Taylor–Couette flow of an Oldroyd-B fluid is studied. The upper bound of the stability boundary in the Weissenberg number (We)–Nahme number (Na) space is given by the critical conditions corresponding to the extension of the time-dependent isothermal eigensolution. Initially, as T₀ is increased, the critical Weissenberg number, We_c, associated with this upper branch increases. Increasing T₀ beyond a certain value T^* causes the thermoelastic mode of instability to manifest. This occurs in the limit as We/Pe → 0, where Pe denotes the Péclet number. In this limit, the fluid relaxation time is much smaller than the time scale of thermal diffusion. T₀ = T^* represents a turning point in the We_c–Na_c curve. Consequently, the stability boundary is multi-valued for a wide range of Na values. Since the relaxation time and viscosity of the fluid decrease with increasing T₀, the elasticity number, defined as the ratio of the fluid relaxation time to the time scale of viscous diffusion, also decreases. Hence, O(10) values of the Reynolds number could be realized at the onset of instability if T₀ is sufficiently large. This sets limits for the temperature range that can be used in experiments if inertial effects are to be minimized.     

Application of Hildebrand's fluidity model to non-Newtonian solutions

Summary The fluidity model ofHildebrand has been applied to dilute aqueous polymer solutions exhibiting non-Newtonian behaviour. As for Newtonian fluids, it is found that the temperature dependence of apparent viscosity of non-Newtonian fluids is determined entirely by the temperature dependence of fluid density. However, whereas the parameters ofHildebrand's equation are constants, independent of the conditions of shear for Newtonian fluids, these parameters become shear-rate dependent for non-Newtonian fluids. The magnitude of the parameters and their variation with shear rate can be explained qualitatively in terms of interactions of polymer molecules and their behaviour in a shear field.

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Zusammenfassung Das Fließmodell vonHildebrand wird auf verdünnte wäßrige Polymerlösungen mit nicht-newtonschem Verhalten angewandt. Wie bei newtonschen Flüssigkeiten findet man hierfür, daß die Temperaturabhängigkeit der schergeschwindigkeitsabhängigen Viskosität ausschließlich durch die Temperaturabhängigkeit der Flüssigkeitsdichte bestimmt ist. Während jedoch die Parameter derHildebrandschen Gleichung für newtonsche Flüssigkeiten von den Scherbedingungen unabhängige Konstanten darstellen, werden diese bei nichtnewtonschen Flüssigkeiten schergeschwindigkeitsabhängig. Die Größe dieser Parameter und ihrer Variation mit der Schergeschwindigkeit kann qualitativ als eine Folge der Wechselwirkung der Polymermoleküle und ihres Verhaltens im Scherfeld gedeutet werden.

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Notation B Parameter inHildebrand's fluidity equation, eq. [1] (N^–1 m² s^–1) - K Consistency parameter in the power-law (Nm^–2 s ⁿ ) - n Flow behaviour index in the power-law (–) - T Temperature (K) - V Molar volume (m³ mol^–1) - V ₀ Intrinsic molar volume; parameter inHildebrand's fluidity equation, eq. [1] (m³ mol^–1) - Shear rate (s^–1) - Viscosity or apparent viscosity (Nm^–2 s) - Density (kg m^–3) - ₀ Intrinsic density; modified parameter inHildebrand's fluidity equation; eq. [5] (kg m^–3) - Shear stress (Nm^–2) With 4 figures and 1 table     

Supersonic molecular beams production and temperature distribution in free expanding jets

Summary A supersonic molecular beam production system is described in which a continuous flux of Argon molecules can be produced as high as4 · 10 ¹⁸ molecules sterad^–1 sec^–1 in a vessel where the background pressure can be kept below10 ^–6 mmHg using relatively little cryo and diffusion pumping facilities. The beam intensity is measured at different stagnation pressures as a function of nozzle-skimmer separation and skimmer diameter. The results are compared with the existing theories, and information is obtained on the radial temperature distribution in the free expanding jet.

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Sommario Si descrive un apparecchio per la produzione di fasci molecolari supersonici nel quale, facendo uso di stazioni di pompaggio, a diffusione e criogenico, relativamente modeste, si può produrre un flusso continuo di molecole di Argon di4 · 10 ¹⁸ molecole sterad^–1 sec^–1 in un ambiente in cui la pressione di fondo è mantenuta inferiore a10 ^–6 mmHg. Vengono riportate misure di intensità del fascio, a diversi valori della pressione nell'ugello, in funzione della distanza ugello-primo collimatore e del diametro del primo collimatore. I risultati vengono confrontati con le teorie esistenti e dal confronto si ottiene informazioni sulla distribuzione della temperatura radiale nei getti in espansione libera.

     

Simulation of turbulent flows around a circular cylinder using nonlinear eddy-viscosity modelling: steady and oscillatory ambient flows

Steady incident flow past a circular cylinder for sub- to supercritical Reynolds number has been simulated as an unsteady Reynolds-averaged Navier–Stokes (RANS) equation problem using nonlinear eddy-viscosity modelling assuming two-dimensional flow. The model of Craft et al. (Int. J. Heat Fluid Flow 17 (1996) 108), with adjustment of the coefficients of the ‘cubic’ terms, predicts the drag crisis at a Reynolds number of about 2×10⁵ due to the onset of turbulence upstream of separation and associated changes in Strouhal number and separation positions. Slightly above this value, at critical Reynolds numbers, drag is overestimated because attached separation bubbles are not simulated. These do not occur at supercritical Reynolds numbers and drag coefficient, Strouhal number and separation positions are in approximate agreement with experimental measurements (which show considerable scatter). Fluctuating lift predictions are similar to sectional values measured experimentally for subcritical Reynolds numbers but corresponding measurements have not been made at supercritical Reynolds numbers. For oscillatory ambient flow, in-line forces, as defined by drag and inertia coefficients, have been compared with the experimental values of Sarpkaya (J. Fluid Mech. 165 (1986) 61) for values of the frequency parameter, β=D²/νT, equal to 1035 and 11240 and Keulegan–Carpenter numbers, KC=U₀T/D, between 0.2 and 15 (D is cylinder diameter, ν is kinematic viscosity, T is oscillation period, and U₀ is the amplitude of oscillating velocity). Variations with KC are qualitatively reproduced and magnitudes show best agreement when there is separation with a large-scale wake, for which the turbulence model is intended. Lift coefficients, frequency and transverse vortex shedding patterns for β=1035 are consistent with available experimental information for β≈250−500. For β=11240, it is predicted that separation is delayed due to more prominent turbulence effects, reducing drag and lift coefficients and causing the wake to be more in line with the flow direction than transverse to it. While these oscillatory flows are highly complex, attached separation bubbles are unlikely and the flows probably two dimensional.     

Understanding the Piche evaporimeter as a simple integrating mass transfer meter

Results are presented of a comparison of measured and calculated evaporation rates of the Piche evaporimeter under indoor and outdoor (within a meteorological screen) conditions. In both cases, application of mass transfer formulae in use for horizontal (turbulent) flow to the evaporating blotting paper of the instrument yield very good results under pure forced convection conditions. For mixed convection regimes, comparisons using either pure free (combined heat and mass transfer) or pure forced convection equations give as expected too low calculated values. Reasons for such differences with measured values are reviewed. Our forced convection results confirm that main stream turbulence is only of influence on mass transfer to a zero incidence flow in combination with pressure gradient (bluff body) effects, which under our conditions appear to be absent around the Piche surfaces. The same results prove absence of any influence of the particular temperature distribution over the blotting paper on the mass transfer. The understanding and importance of these conclusions in relation to the use of the Piche evaporimeter as a simple integrating mass transfer meter under actual farming conditions are discussed. The importance to obtain such mass transfer data is explained in the introduction.Nomenclature A Numerical constant in free convection Sherwood number - Coefficient of thermal expansion (K^–1) - C _{(s, b)} Water vapour concentration average at the evaporating surface (s) and in the bulk air (b) (g m^–3) - D Coefficient of molecular diffusion of water vapour in air (m² s^–1) - d Characteristic dimension of the paper disc in the direction of flow (m) - E _{(c, m)} Evaporation rates of the Piche evaporimeter, calculated (c) and measured (m) (units in text) - e _{(s, b)} Partial water vapour pressure average at the evaporating surface (s) and in the bulk air (b) (mbar) - Gr Grashof number - g Acceleration of gravity (m s^–2) - m Number of measuring periods - n Numerical constant in free convection Sherwood number - Coefficient of kinematic viscosity of air (m² s^–1) - P Atmospheric pressure (mbar) - Re Reynolds number - _{(s, b)} Air density average at the evaporating surface (s) and of the bulk air (b) (g m^–3) - Sh Sherwood number - T _{(s, b)} Temperature average of the evaporating surface (s) and in the bulk air (b) (K) - T _{(vs, vb)} Virtual temperature average at the evaporating surface (s) and in the bulk air (b) (K) - U Wind speed (air movement) average of the bulk air (m s^–1)     

Mixing of Stably Stratified Gases in Subsurface Reservoirs: A Comparison of Diffusion Models

Numerical simulations of the mixing of carbon dioxide (CO₂) and methane (CH₄) in a gravitationally stable configuration have been carried out using the multicomponent flow and transport simulator TOUGH2/EOS7C. The purpose of the simulations is to compare and test the appropriateness of the advective–diffusive model (ADM) relative to the more accurate dusty-gas model (DGM). The configuration is relevant to carbon sequestration in depleted natural gas reservoirs, where injected CO₂ will migrate to low levels of the reservoir by buoyancy flow. Once a gravitationally stable configuration is attained, mixing will continue on a longer time scale by molecular diffusion. However, diffusive mixing of real gas components CO₂ and CH₄ can give rise to pressure gradients that can induce pressurization and flow that may affect the mixing process. Understanding this coupled response of diffusion and flow to concentration gradients is important for predicting mixing times in stratified gas reservoirs used for carbon sequestration. Motivated by prior studies that have shown that the ADM and DGM deviate from one another in low permeability systems, we have compared the ADM and DGM for the case of permeability equal to 10^–15 m² and 10^–18 m². At representative reservoir conditions of 40 bar and 40°C, gas transport by advection and diffusion using the ADM is slightly overpredicted for permeability equal to 10^–15 m², and substantially overpredicted for permeability equal to 10^–18 m² compared to DGM predictions. This result suggests that gas reservoirs with permeabilities larger than approximately 10^–15 m² can be adequately simulated using the ADM. For simulations of gas transport in the cap rock, or other very low permeability layers, the DGM is recommended.