Showing papers in "Aiche Journal in 1959"

Viscous flow relative to arrays of cylinders

Abstract: The free-surface model, successfully employed to predict sedimentation, resistance to flow, and viscosity in assemblages of spherical particles, has been extended to the case of flow relative to cylinders. It is shown to be in good agreement with existing data on beds of fibers of various types and flow through bundles of heat-exchanger tubes for cases where it can reasonably be expected to apply. Close agreement in the dilute range with the only theoretical treatment for flow parallel to a square array of cylinders provides interesting validation of the model.

Interfacial turbulence: Hydrodynamic instability and the marangoni effect

Abstract: The origin of interfacial turbulence, spontaneous agitation of the interface between two unequilibrated liquids, has been explained in terms of classical flow, diffusion, and surface processes. The essence of the explanation is the long-known though much neglected Marangoni effect, wherein movement in an interface is caused by longitudinal variations of interfacial tension. It is proposed that interfacial turbulence is a manifestation of hydrodynamic instability, which is touched off by ever present, small, random fluctuations about the interface. A simplified mathematical model has been analyzed in order to detail the mechanism of the “interfacial engine” which supplies the mechanical energy of interfacial turbulence. In its present form the analysis incorporates several drastic simplifications, though ways of removing some of these have been suggested. The groundwork has been laid for the more elaborate analyses that are needed for a decisive test of the theory. The analysis shows how some systems may be stable with solute transfer in one direction yet unstable with transfer in the opposite direction, a striking result. It also suggests that interfacial turbulence is usually promoted by (1) solute transfer out of the phase of higher viscosity, (2) solute transfer out of the phase in which its diffusivity is lower, (3) large differences in kinematic viscosity and solute diffusivity between the two phases, (4) steep concentration gradients near the interface, (5) interfacial tension highly sensitive to solute concentration, (6) low viscosities and diffusivities in both phases, (7) absence of surface-active agents, and (8) interfaces of large extent. That some of these effects have been observed in the laboratory lends credence to the theory.

Turbulent flow of non‐newtonian systems

Abstract: A theoretical analysis for turbulent flow of non-Newtonian fluids through smooth round tubes has been performed for the first time and has yielded a completely new concept of the attending relationship between the pressure loss and mean flow rate. In addition, the analysis has permitted the prediction of non-Newtonian turbulent velocity profiles, a topic on which the published literature is entirely silent. To confirm the theoretical analysis, experimental data were taken on both polymeric gels and solid-liquid suspensions under turbulent-flow conditions. Fluid systems with flow-behavior indexes between 0.3 and 1.0 were studied at Reynolds numbers as high as 36,000. All the fully turbulent experimental data supported the validity of the theoretical analysis. The final resistance-law correlation represents a generalization of von Karman's equation for Newtonian fluids in turbulent flow and is applicable to all non-Newtonians for which the shear rate depends only on shear stress, irrespective of rheological classification. All the turbulent experimental data for the non-Newtonian systems were correlated by this relationship with a mean deviation of 1.9%.

Longitudinal Laminar Flow Between Cylinders Arranged in Regular Array

Abstract: The increasing complexity of heat transfer and process situations which involve fluid flow has demanded the frequent use of flow passages of unusual geometrical configuration. The present investigation is concerned with one such novel configuration, namely the longitudinal flow between solid cylindrical rods which are arranged in regular array. A schematic diagram of the situation under study. The rods may be located either in triangular or square array. The flow will be taken to be laminar and fully developed. The aim of this analysis is to determine the pressure drop, shear stress, and velocity-distribution characteristics of the system. The starting point of this study is the basic law of momentum conservation. The resulting differential equation has been solved in an approximate, but almost exact, manner by the use of truncated trigonometric series. Results are obtained over a wide range of porosity values for both the triangular and square arrays. Heat transfer has not been considered. The configuration under investigation has potential application in compact heat exchangers for nuclear reactors and other situations. Further the results should also be of interest in the theory of flow through unconsolidated porous beds (ia, 9a). The only related analytical work known to the authors is that of Emersleben (S), who considered only the square array. His rather involved solution, based on complex zeta functions, appears to be valid only at high porosities. Experiments covering a porosity range of 0.093 to 0.984 have been made by Sullivan (4) using parallel-oriented fibers, most of the tests being for fibers in random array. These previous investigations will be compared with the present theory in a later section.

Heat and mass transfer from wall to fluid in packed beds

Abstract: Experiments of heat and mass transfer from the tube wall to the fluids flowing through the packed beds were carried out separately. In heat transfer air was used as the fluid, and several kinds of solid particles with low and high thermal conductivities were investigated to determine effective thermal conductivities and wall heat transfer coefficients. In mass transfer the dissolution rate of the coated material on the inner wall of the packed tube to the water stream was measured, and wall mass transfer coefficients were analyzed. It was found that a close similarity exists between the JH and JD factor for the wall coefficients in the turbulent-flow region.

Heat transfer by radiation through porous insulations

Abstract: Radiant transfer through fibrous and foamed insulating materials was investigated theoretically and experimentally. Transmission measurements were made under isothermal conditions with a black-body source varying from 200 to 800 deg F. Bulk density and fiber and pore size were also varied. These data were interpreted successfully in terms of a simple theoretical model. The results provide design information and define the contributions of the several mechanisms of transfer. (auth)

Performance of a reciprocating‐plate extraction column

Abstract: An open type of reciprocating-plate extraction column was developed, and it is proposed that the scaling up of such a column should be straightforward; that is, the height of an equivalent theoretical stage (H.E.T.S.) and the throughput per unit area should be independent of the diameter of the column. Plates having 5/8-in.–diameter holes and 62.8% free space were selected to minimize the resistance to countercurrent flow in the column. With this design low H.E.T.S. values were achieved at throughputs much higher than those reported for other columns. Thus for two systems the present column was shown to require the lowest volume of column to accomplish a given extraction job. Data were obtained in a 3-in.–diameter column on two systems, methyl isobutyl ketone-acetic acid-water and o-xylene-acetic acid-water. Throughputs studied on the first system ranged from 547 to 1,837 gal./hr./sq. ft., and the corresponding minimum H.E.T.S. values achieved were 4.3 and 7.5 in. respectively. For the second system minimum H.E.T.S. values of 7.7 and 9.1 in. were attained at throughputs of 424 and 804 gal./hr./sq. ft. respectively. Extraction column design procedures are discussed. The fabrication of the reciprocating-plate column is relatively simple, and this should encourage its use first in pilot-scale sizes and ultimately in large-scale columns.

Heterogeneous phase equilibria of the hydrogen sulfide–carbon dioxide system

Abstract: An experimental study on the system hydrogen sulfide-carbon dioxide was performed from the critical region to the solid-liquid-vapor region. For seven mixtures individual phase diagrams were determined by the establishment of dew, volume percentage liquid, hubble, critical, and triple points. A splendid study of this system had been reported earlier by Bierlein and Kay (1) for temperatures above 32°F. However from a temperature point of view this earlier work represents about one half of the phase diagram from the critical locus to the locus of triple points. Hence in this study particular attention was devoted to the lower temperature regions. Equilibrium constants were determined from 100 to 1,200 lb./sq. in. abs. Vapor and liquid equilibrium compositions from this investigation were compared with those obtained by Bierlein and Kay (1) at 20, 40, 60, and 80 atm. Solid-liquid-vapor loci were found to meet at a minimum temperature, lower than either of the individual pure component triple points, due to the formation of a eutectic mixture consisting of 12.5 mole % carbon dioxide. Vapor and liquid compositions in equilibrium with solid were established along the vapor-liquid-solid carbon dioxide and vapor-liquid-solid hydrogen sulfide loci.

Axial mixing and extraction efficiency

Abstract: The effect of back mixing of either phase in an extraction column, which decreases the extraction efficiency, is analyzed theoretically by means of an idealized diffusion model that can be characterized by four dimensionless parameters: a Peclet number of each phase, a mass transfer number, and the usual extraction factor. Calculations for a wide range of these parameters were performed on a digital computer. The principal results, presented in a table, will be useful in the design and scale up of extraction columns and in the interpretation of experimental results from extractors and from some reactors in which a first-order reaction occurs.

Turbulent Flow of Pseudoplastic Polymer Solutions in Straight Cylindrical Tubes.

Abstract: Experimental studies are described concerning the fluid dynamics, particularly in the turbulent region, of dilute solutions of free-draining, nonassociating, linear polymers; sodium carboxymethylcellulose, ammonium alginate, polyisobutylene, and carboxypolymethylene, all of which are pseudoplastic. These solutions were run in laminar, transition, and turbulent flow in a pipeline flow apparatus designed to permit measurement of dynamic pressure drop and impact pressure by radial traverse. Photographic studies with dye injection used at the tube wall and at the tube center showed that turbulent flow of these pseudoplastic fluids has the following characteristics compared to Newtonian fluids: poor over-all radial mixing, thicker nonturbulent layer at the wall, and decreased rate of formation of horseshoe vortices at the wall.

Transistion from laminar to turbulent flow in pipes

Abstract: In pipeline design, for which one needs a means of ascertaining whether the flow will be laminar or turbulent, the Reynolds number is the criterion for Newtonian fluids. The principal purpose of this study was to formulate a more general criterion to characterize the flow regime and to test this form in application to non-Newtonian fluids. Intuitive physical arguments suggested the use of a local stability parameter which is a function of the ratio of input energy to energy dissipation for an element of fluid. If the parameter is applied to a Newtonian fluid in laminar pipe flow, one finds that it has a maximum value of 0.385 times the critical Reynolds number, or 808. As the criterion is presumed to be general, it is inferred that the value of 808 defines the boundary between stable laminar and stable turbulent pipe flow for all fluids. The inference has been varified for several pseudoplastic fluids.

The phase behavior and solubility relations of the benzene‐water system

Abstract: In order to contribute to knowledge of the nature of the phase behavior of partially miscible liquid systems, a study of the benzene-water system was undertaken. The pressures at liquid- and vapor-phase boundaries of fifteen mixtures of benzene and water were determined within the temperature range of 200 to 357°C. Along with a complete numerical tabulation, these data are presented graphically as pressure-temperature, pressure-composition, and temperature-composition phase diagrams to show the nature of the boundaries. Up to the three-phase critical end point, the benzene-water system develops in a manner usually ascribed to a partially miscible system in which the vapor compositin at a point of univariance lies intermediate to the two liquid compositions. The three-phase critical end point occurs at 1,364 1b./sq. in. abs. and 268.3°C., and the composition of the critical phase is 25.8 weight % water, with the remaining liquid phase 92.8 weight % water. The pressure, temperature, and composition of the critical solution end point are deduced as 2,300 1b./sq. in. abs., 306.4°C., and 59 weight % water, respectively. At temperatures between these two critical points the phase behavior is likened to that of a dense gas or fluid dissolved in a liquid. Definite limiting values of temperature and pressure are assignable to this behavior by the extension of the three-phase curve up to the critical solution end point. This extended curve is not a phase boundary, but the temperature and pressure at a given point on the curve represents in a mixture of fixed composition the limit of mutual solubility of the benzene-rich fluid phase and the water-rich phase. At a temperature above or a pressure below the given point the liquid phase begins to vaporize. Above the critical solution end point the vapor-liquid phase boundaries are like those of a normal binary mixture.

Flow characteristics in horizontal fluidized solids transport

Abstract: The flow characteristics of dense solid-gas mixtures transported through horizontal pipes were studied with glass beads and coal powders of various sizes (0.0028 to 0.0297 in.) in 1/2-, 3/4- and 1-in. glass pipes and a 1/4-in. steel pipe. Fluidized-bed feeders were utilized, thus permitting solid-gas ratios considerably higher (range 80 to 750) than those possible with conventional pneumatic transport. When such high solid-gas ratios are used, the flow of mixtures in transport lines is characterized by a large amount of slippage between gas and solids. The flow pattern is dicussed on the basis of visual observation through glass pipes. A simple and interesting velocity relationship was noted, namely that the average gas velocity is about twice as large as the average solid-particle velocity. The solid-particle velocities and solid loadings in the pipe line were found to be primary factors affecting pressure drops, and the particle sizes and shapes, on the other hand, exerted a very slight effect on the pressure drops. This is apparently due to the fact that the solids move predominantly in the bottom of the pipes as agglomerated masses rather than as individually suspended particles. A pressure-drop correlation for the dense solid-gas mixtures is proposed, and applications and limitations of the correlation are shown.

Solubility of liquids in compressed hydrogen, nitrogen, and carbon dioxide

Abstract: The vapor-phase solubilities of carbon tetrachloride, iso-octane, toluene, and n-decane were measured in compressed hydrogen, nitrogen, and carbon dioxide at 50° and 75°C. and at various pressures between 20 and 90 atm. The virial equation of state was used to describe the volumetric properties of the vapor mixtures, and the second virial cross coefficients were evaluated from the solubility data. The results indicate that the vapor phase departs from ideality very quickly for these systems as the pressure increases, particularly at pressures greater than 10 atm.

Fluid dynamics and diffusion calculations for laminar liquid jets

Abstract: In connection with a study of the mechanism of gas absorption the problem arose of predicting absorption rates into laminar liquid jets. A solution to the problem is presented in this paper, which provides an example of the application of fluid dynamics to the analysis of mass transfer in a complex flow system. The water jets considered here issued from circular nozzles of about 1.5-mm diameter, flowed intact downward through an atmosphere of solute gas at average velocities of from 75 to 550 cm./sec. over distances of 1 to 15 cm., and were collected in a receiver slightly larger in diameter than the nozzles. Equations describing the liquid flow near the jet surface are deduced from measurements of jet diameter and analogy to related flow situations. When one uses these equations, absorption rates are predicted from unsteady state diffusion theory with the assumption of interfacial equilibrium. The predicted rates for carbon dioxide at 25°C are in close agreement with experimental determinations over the observed range of contact time of the liquid with gas, namely 0.003 to 0.04 sec.

Mass transfer at low flow rates in a packed column

Abstract: Mass transfer in packed columns has been investigated for a variety of column and packing sizes but at flow rates restricted to fully developed turbulent conditions. The present work was undertaken to investigate mass transfer at flow-rate conditions in the transition and laminar regions. A dual treatment of experimental data required a knowledge of the variation of concentration and velocity with radial position. A tracer-injection technique was employed which consisted in the introduction of a tracer gas into the center of a bulk gas stream and the measurement of the tracer-gas concentration at various radial positions downstreanm. The velocity distribution for the packed column was determined by means of a five-loop, circular, hot-wire anemometer. The test column was a vertical 4-in. pipe, packed with 1/4-in. spherical, ceramic catalyst-support pellets. Mass transfer diffusivity and Peclet nunmber were determined from two solutions of the differential-diffusion equation applied in previous investigations. An analytical solution in terms of Bessel functions was used to calculate values of average diffusivity and Peclet number and a seminumerical solution in terms of homogeneous lineardifference equations to calculate values of point diffusivity and Peclet number. Variation of diffusivity and Peclet number with radial position is shown, average diffusivity andmore » Peclet number being correlated with Reynolds number. The interaction of molecular and eddy mass transfer mechanisms with decreasing mass velocity is illustrated by defining a molecular and an eddy Peclet number and correlating with Reynolds number. Eddy diffusivity is correlated as a function of local flow conditions. (auth)« less

Physical and thermodynamic properties of trifluoromethane

Abstract: Trifluoromrtliane is rommonlp called fluoroform after thc corresponding chlorocompound, chloroform. It is also known in the trade as Freon-23 refrigerant, and has various low-temperature applications. For the design of refrigeration units using trifluoromethane it is essential that the physical and thermodynamic properties of the compound be available over the desired ranges. The reported data on trifluoromethane are far from complete and are in some discrepancy among different investigators (1 , 2 ) . The present investigation included determinations of the vapor pressure, saturated liquid density, critical constants, pressure-volume-temperature behavior, and heat capacity a t zero pressure over the desirable ranges. The sample of trifluoromethane, supplied by E. I. du Pont de Nemours and Company, was obtained from middle cuts in repeated fractionation processes and was therefore of very high purity. According to du Pont's analysis (3) the liquid phase had a moisture content of 0.0005 wt. %, and the vapor of the cylinder contained 0.021 vol. ' % noncondensables in liquid nitrogen.

Formation of gas bubbles at submerged orifices

Abstract: The formation of air bubbles at constant pressure at submerged orifices was investigated for several liquids. The frequency of formation of the bubbles was determined by the use of a stroboscope, and the rate of gas flow was measured with conventional rotameters. Several orifices having diameters ranging from 0.0794 to 0.397 cm. were employed, and the gas flow rate was varied from about 0.1 cc. (at standard conditions)/sec. to about 150 cc./sec. It was found that the formation of bubbles could be correlated with the physical variables of the system by the application of Newton's second law of motion to the bubble at the instant just prior to its release from the orifice.

Liquid‐side mass transfer coefficients in packed towers

Abstract: The physical absorption of gas by water in a tower packed with Raschig rings has been investigated. The liquid-side mass transfer coefficient which was separated by dividing the capacity coefficient by the wetted surface area is discussed from the standpoints of the two-film and penetration theories. A new and simpler dimensionless group is presented which correlates about 90% of the data reported, including the author's own, within an accuracy of ±20%.

An improved equation of state for gases

Abstract: Based on properties which are characteristic of all gases, modifications are developed for an equation of state previously proposed in this journal (1). A specific application of the modified equation is made for the PVT data on carbon dioxide, and considerable improvement over the original equation is shown for densities in the neighborhood of 1.4 times the critical density. The new equation differs from the old equation only by the presence of the A5 and C5 terms, these having originally been taken to be zero.

Mechanism of drying thick porous bodies during the falling rate period: I. The pseudo‐wet‐bulb temperature

Abstract: The drying of two highly porous thick textiles is studied and compared. Extremes are chosen in that one package is composed of a Terylene (British form of a polyester fiber) net fabric of open structure and the other of a woolen flannel of close structure. The cloths are wound as bobbins and dried by hot air streaming in a wind tunnel, the air flowing parallel to the axis of the cylinder of material. The weight of water as drying progresses is measured by a balance, and thermocouples within the bobbin provide a temperature record. On investigation of the thermal conductivity of the dry structure, it is found that whereas the coefficient for the wool-air mixture is constant throughout, the coefficient for the Terylene-air mixture applies only in the depths, the apparent thermal conductivity growing larger toward the surface and with increasing air speed, as if the heat transfer through the open structure is assisted by some form of air penetration. As the thick textiles dry, the rate of evaporation falls off, since heat and water vapor have to pass through an increasing layer of dry material. While this is occurring, a constant temperature, the “pseudo-wet-bulb temperature,” is established throughout the wet cloth. This state of equilibrium may be expressed as an equation between the rate of heat conduction inward and that required to produce the vapor diffusion outward. From this equation the pseudo-wet-bulb temperature can be calculated.

Turbulent liquid flow down vertical walls

Abstract: Photoggraphic methods have been used to study the behavior of water flowing freely down vertical surfaces under the influence of gravity at Reynolds numbers between 200 and 30,000. The physical appearances of the liquid layers in transitional and fully turbulent flow have been noted. Layer thicknesses have been obtained from high-speed photographs and correlated with liquid Reynolds numbers, the range of experimental data thus being extended into the fully turbulent region. A simple basis of comparison with flow between parallel plates has been developed.

Particulate fluidization and sedimentation of spheres

Abstract: Particulate fluidization and sedimentation data were taken over the Reynolds number range of 0.005 to 1,800 by means of glass spheres in both water and ethylene glycol. Porosities for each series of measurements varied from about 0.50 to 0.91 and larger. The closely sized samples of spheres used were obtained by grinding between glass plates. The data for Reynolds numbers up to about 0.5 are in excellent agreement with the laminar theory of Ruth and the porosity function from Ruth's theory gave a satisfactory correlation of all the data, both laminar and turbulent.

Solid‐catalyzed reaction in a fluidized bed

Abstract: Results are presented for the solid-catalyzed hydrogenation of ethylene in fixed and fluidized beds. The effect of gas velocity, bed height, catalyst activity, particle size, and internal baffles on fluidized reactor efficiency are given, and Equations derived from a simplified mathematical model correlate the data.

Void fractions in two‐phase flow

Abstract: Void fractions (fraction of the flow cross-sectional area occupied by the gas phase) have been measured for steam-water flows in an adiabatic, horizontal test section of 0.484 in. I.D. at 400, 600, 800, and 1,000 1b./sq. in. gauge. A comprehensive survey of void data for two-phase concurrent flow is included in the paper, and the data, including the Martinelli and homogeneous flow model predictions, are compared. System characteristics, involving one- and two-component flows in horizontal and vertical test sections with and without heat transfer over a range of flow ratios, total flow rates, and pressure, are too complex, and the data available are neither extensive nor precise enough to warrant the generation of over-all correlations. Use of the void data in correlating two-phase frictional pressure drops is discussed. A model has been presented for the prediction of critical flows based upon the void data, and calculations have been made for steam-water critical flows over a range of critical pressures from 15 to 2,000 1b./sq. in. abs.

Interfacial resistance in gas absorption

Abstract: A laminar jet method for contracting a liquid with a gas for contact times down to 1 msec. has been developed. A jet is formed with a very thin square-edged orifice to minimize boundary-layer effects, and the rate of absorption of carbon dioxide into water is found to depend only upon contact time, an indication that the method is self-consistent. The rate of absorption of carbon dioxide into pure water is 1 to 4% lower than the theoretical rate for absorption into a jet in rodlike flow the surface of which is instantaneously saturated. This indicates that, at most, interfacial resistance in this system is small and justifies the common assumption of interfacial equilibrium. Jets with thick boundary layers were formed with other types of orifices, and the absorption rates into these jets were lower than the theoretical value because of the decreased surface velocity. This effect can be easily mistaken for an interfacial resistance. The presence of a commercial surface-active agent causes an apparent interfacial resistance which is due at least partly to a hydrodynamic effect.