bluuebunny/crossref_metadata_2025 huggingface dataset:
Mass transfer in liquid metals
Authors: Dunn W. E. , Bonilla C. F. , Ferstenberg C. , Gross B.
Published: June 2004

The rate of mass transfer was measured for solid metal shapes dissolving into mercury at room temperature. Sherwood numbers for horizontal tin, cadmium, zinc, and lead cylinders dissolving by natural convection agreed with Nusselt numbers for heat transfer in nonmetallic liquids at the same Rayleigh (Grashof × Prandtl) numbers. Dissolving of zinc tubes by mercury flowing turbulently within them agreed with heat transfer to nonmetals in tubes. Dissolving of random beds of lead spheres by mercury flowing through the bed agreed with similar nonmetal systems. It is concluded that mass transfer processes in liquid metals follow substantially the correlations for other fluids in heat or mass transfer, which with moderate safey factors may thus be used for at least preliminary design purposes.
Rate of flow and mechanics of bubble formation from single submerged orifices. I. Rate of flow studies
Authors: Leibson Irving , Holcomb Eugene G. , Cacoso Anthony G. , Jacmic John J.
Published: June 2004

A study has been made of the rate of flow and mechanics of bubble formation from single submerged orifices 1/64, 1/32, 1/16, and 1/8 in. in diameter installed in an 8‐in. I.D. column operating in the air‐water system. The coefficients of discharge obtained for sharpedged orifices operating with this system indicate that the effective orifice discharge area for this type of operation is greater than that for an orifice of the same size and type operating at the same pressure ratio in the air‐air system. The effective orifice discharge areas for a round‐edged orifice operating in either the air‐water or air‐air systems appear to be identical at the same pressure ratio. The thick‐plate orifice operating in the air‐water system exhibits a constancy of discharge coefficient at ratios of the downstream to upstream pressures less than 0.33. Inasmuch as bubble formation occurring close to the downstream face of a sharp‐edged orifice operating in the air‐water system influences the effective orifice discharge area, liquid physical properties may be expected to be important in determining the rate of flow from this type of orifice for other gas‐liquid systems.

In Part II photographic studies of bubble formation reveal that nonuniformity of bubble size is initiated by the onset of turbulence in the air stream flowing through the orifice. In the section of the laminar‐flow range studied in this investigation (200 <NRe< 2,100) the frequency of bubble formation is nearly constant with respect to Reynolds number. The bubble size is relatively uniform at a given Reynolds number and depends markedly upon orifice diameter. Stroboscopic examination reveals that as turbulence is fully developed for the air flow through the orifice, a counterclockwise spiraling, swirling motion of the air jet is initiated. In the turbulent‐flow range the bubblesize–distribution data are fitted reasonably well by a logarithmic‐normal‐probability distribution. More data for bubble formation in other liquids (particularly liquids of low surface tension) are necessary before a general correlation for bubble size in gasliquid systems can be developed.
Ferric ion removal from dilute acidic solutions by fixed‐bed cation exchange
Authors: Mar Brian W. , David M. M.
Published: June 2004

The removal of a trivalent ion (Fe+++) from acidic nitrate solutions by a fixed bed of Dowex‐50 cation‐exchange resin was studied at entering iron concentrations from 14 to 4 meq./liter, flow rates of 0.073 to 1.20 liters/(hr.)(sq. cm.), and bed sizes from 3.7 to 5.4 g. of dry resin/sq. cm. Acid strengths were below 0.45 N. The results were correlated is a relatively simple break‐through equation based on the assumptions of an equilibrium extremely favorable to iron adsorption and liquid‐film diffusion being the rate‐controlling factor. The capacity of the resin for iron was dependent upon the acid concentration of the sulation.

The results provide a design equation requiring a minimum of experimental work.
Interpretation and correlation of ion exchange column performance under nonlinear equilibria
Authors: Hiester Nevin K. , Radding Shirley B. , Nelson Richard L. , Vermeulen Theodore
Published: June 2004

Various methods are known for interpreting experimental data for linear‐equilibrium cases or constant‐pattern break‐through curves where either external or internal diffusion alone controls the rate in the ion exchange column. The present paper provides interpretive techniques for nonlinear equilibrium cases where the rate is controlled by a combined diffusion mechanism. The techniques can be applied whether or not the value of the equilibrium constant is known.

A completely general correlational method is derived for adding the mass transfer resistances under conditions of nonlinear equilibrium. Published break‐through results from numerous sources and from new measurements, evaluated by the techniques described, are used to determine the numerical constants for the general correlation.
Mass transfer in a horizontal liquid‐liquid extraction tube
Authors: Murphy Nelson F. , Lastovica John E. , Skrzec Adam E.
Published: June 2004

A study was made of the effect of physical properties and of geometrical and dynamical characteristics of several liquid‐liquid extraction systems on the mass transfer coefficients. The two‐component systems studied consisted of the following solvents with water: cyclohexanol, methyl ethyl ketone, furfural, normal butanol, and nitromethane. The transfer studies were made in a horizontal glass pipe with the phases flowing counter‐currently at velocities from 1,000 to 15,000 lb./(hr.)(sq. ft.). The transfer of solvents into the water phase and of the water into the solvent phase was measured. The film coefficients of mass transfer for a solvent through the water film and for water through the solvent film were correlated by new dimensionless equations which include interfacial tension and diffusivity.
Mass transfer rates in ion exchange
Authors: Selke W. A. , Bard Y. , Pasternak A. D. , Aditya S. K.
Published: June 2004

The rates of both the liquid‐phase mass transfer and the internal‐diffusion steps in ion exchange were studied by means of shallow‐bed experiments. The mass transfer coeffcients obtained fitted the general correlations for other packed‐bed operations when the Schmidt group was evaluated with experimentally determined ionic counterdiffusivities. An incremental calculation of the diffusion rates within the particles yielded a value of the counterdiffusivity in the resin phase. A general design procedure based on these findings is proposed.
Measurements of bubbles formed in boiling Methanol
Authors: Perkins A. S. , Westwater J. W.
Published: June 2004

The photographic method was used to measure bubble sizes and frequencies for methanol boiling at atmospheric pressure outside a 3/8‐in. O.D., steam‐heated, horizontal copper tube. The average temperature of the tube was measured by use of the tube as a resistance thermometer. For nucleate boiling at heat fluxes up to 80% of the maximum, the product of bubble diameter and frequency was constant at 4 in./sec. In this region both the Rohsenow equation and the Forster‐Zuber equation gave good predictions of the heat transfer. At higher fluxes the productf×Dincreased and the equations were much less suitable. The critical temperature difference for copper to methanol was not a single value but was a region extending from 52° to 62°F. The heat flux was nearly constant throughout this range at a maximum of 115,000 B.t.u./(hr.)(sq. ft.). For film boiling,f×Dwas nearly constant at 11 sec.−1Bromley's equation was unsuitable for ΔTvalues less than 180°F., but it became applicable at this ΔT. The use of Nusselt's equation for steam condensing inside the tube was found to be satisfactory, proof that the slight slope of the tube was sufficient to permit adequate condensate drainage.
Composition change in binary‐component spray vaporization at atmospheric pressure
Authors: Culverwell J. F. , Grounds P. W. , Lamb G. G. , Stevens W. F.
Published: June 2004

This paper describes an investigation of the factors affecting the change in composition with vaporization of a binary‐component spray in heated air at atmospheric pressure. The behavior of the system orthodichlorobenzene‐tetrachloroethylene was studied in air ranging from 400° to 1,000°F. Initial drop diameters in the sprays were in the 20‐ to 400‐µ range. The experimental data obtained indicated that the rate of change of spray composition during vaporization was affected only by the chamber‐air temperature, the initial feed composition, and the nozzle characteristics.

Equations are presented which mathematically describe the vaporization process, liquid diffusion being assumed within the drop controls. These equations have been solved by a stepwise procedure for three initial drop sizes. Results of these calculations have been added statistically according to the initial‐drop‐size distribution in order to predict the vaporization behavior of the spray. Details of this process of statistical combination have been summarized by Culverwell (1).

The calculations agreed with the experimental data previously obtained during the first 5 in. of nozzle‐to‐tray travel. After 5 in. the deviation was great. Future experimental work to determine more precise values of drop‐size distribution, initial drop velocity, and liquid diffusion coefficient may result in more complete agreement.
Ignition of solid propellants by forced convection
Authors: Churchill S. W. , Kruggel R. W. , Brier J. C.
Published: June 2004

Experimental data are reported for the ignition of single grains of solid propellant in a stream of gas at high temperature. The investigation encompassed gas temperatures from 578° to 1,070°K., gas velocities corresponding to free‐stream Reynolds numbers from 156 to 624, a complete range of oxygen‐nitrogen mixtures, and a few oxygen‐carbon dioxide mixtures. Pyrocellulose and double‐base propellants were tested. The grains were approximately 1/8 in. in diameter and extended through the gas stream, so that ignition was forced to take place on the cylindrical surface rather than on the end of the grain. The exposure before ignition was measured for a large number of grains. The data can be represented by an equation that is consistent with the known effect of flow rate on convective heat transfer and the known effect of temperature on chemical reaction rates, an indication that both processes are important in ignition.
Vapor‐liquid equilibria for hydrogen–light‐hydrocarbon systems at low temperatures
Authors: Benham Alvin L. , Katz Donald L.
Published: June 2004

Experimental equilibrium vapor and liquid compositions are reported for the hydrogen‐methane system at −150°, −200°, and −250°F. and at pressures of 500 to 4,000 lb./sq. in. The ternary system hydrogen‐methane‐propane was studied at 0°, −100°, and −200°F. at 500 and 1,000 lb./sq. in. Phase compositions were determined for a limited number of similar conditions for the hydrogen‐methane‐propylene and hydrogen‐methane‐ethylene‐ethane‐propylene‐propane systems.
Void fractions in two‐phase steam‐water flow
Authors: Isbin H. S. , Sher Neil C. , Eddy K. C.
Published: June 2004

The pressure‐drop characteristics associated with one liquid and one gaseous phase flowing concurrently in a pipe or tube have yet to be understood. The operation of evaporators, boilers, and condensers has long stimulated interest in the pressure drop of steamwater mixtures, and more recently this specialized case of one‐component, two‐phase flow has received even greater attention from the applications in cooling nuclear reactors. The two‐phase–flow problems have not been amenable to through theoretical analyses, and therefore empirical and semiempirical correlations have attained unusual prominence in practical applications. The present investigation employs a new research tool for the study of two‐phase–flow structure.

A variety of geometric flow patterns is possible. Bergelin, Alves, and others have classified these patterns according to visual appearance; whereas the Martinelli classifications were based upon whether the flow in each phase was termedviscousorturbulent. The distinction between viscous and turbulent flow in either phase is rather arbitrary, and if the Reynolds number for one phase, calculated on the basis of the total tube diameter, is greater than 2,000, the flow in the phase is calledturbulent. This investigation is confined to the study of annular flow, in which most of the liquid is found in an annular ring surrounding the central vapor core and the flow in each phase is turbulent.

Boiling or flashing occurs when superheated water rises in an insulated vertical tube at atmospheric pressure. For a separated two‐phase flow geometry, the mean linear steam velocity may exceed that of the water. The fraction of the tube occupied by the steam (void fraction) at a given cross section cannot be obtained directly from a determination of the thermodynamic quality. Void fractions, however, must be known for the estimation of the pressure drops due to head and momentum changes.

Void fractions and pressure drops for steam‐water flows were measured in an 0.872‐in. I.D. vertical tube at atmospheric pressure over a quality range of 0 to 4%. The test section was the hot leg of a natural‐circulation loop, and the inlet liquid flow rate ranged from 1 to 3 ft./sec. A new technique for measuring void fractions was used, and the method utilizes the difference between the gamma‐ray absorption coefficients of water and steam.
Absorption and stripping‐factor functions for distillation calculation by manual‐ and digital‐computer methods
Authors: Edmister Wayne C.
Published: June 2004

New absorption‐ and stripping‐factor functions have been developed for use in computing multicomponent separations in fractionators, reboiled absorbers, refluxed strippers, and columns with side‐stream strippers. Charts of fraction not absorbed vs. A factor and fraction not stripped vs. S factor are included with the equations for these operations.

These functions and procedures are of particular advantage in computing complex columns, i.e., two or more feeds and three or more products, where the proposed A and S factor equations provide a method for converging on a solution.
Phase behavior of hydrogen–light‐hydrocarbon systems
Authors: Benham A. L. , Katz D. L. , Williams R. B.
Published: June 2004

The decreasing solubility of hydrogen in hydrocarbons with decreasing temperature continues down to the freezing point of the hydrocarbons, around −300°F. This behavior is shown to be an enlargement of phenomena exhibited by normal hydrocarbon mixtures. Methods of predicting equilibrium‐phase compositions are presented for hydrogen in ligh‐hydrocarbon systems. The correlations are satisfactory for binary and certain ternary systems, but are not reliable for complex mixtures.
Discharge coefficients through perforated plates
Authors: Kolodzie P. A. , Van Winkle Matthew
Published: June 2004

The design variables that affect the pressure drop across dry perforated plates were determined and correlated. Average orifice coefficients were calculated for the perforated plates by using a modified form of the single‐orifice flow equation.

The variables which affected the orifice coefficients were found to be the hole diameter, hole pitch, plate thickness, fraction of the plate covered by the perforated area, and a Reynolds number based on the hole diameter. The orifice coefficients have been correlated with these variables in dimensionless groupings.

The correlation presented covers a practicable range of variables for which the pressure drop may be predicted in design.
Equilibrium rations of hydrogen and the critical loci of hydrogen‐paraffin mixtures
Authors: Lenoir J. M. , Hipkin H. G.
Published: June 2004

This paper presentes a correlation to predict the equilibrium ratios of hydrogen in hydrocarbon mixtures by use of the parameters of pressure and convergence pressure. Also a procedure to predict convergence pressures of hydrogen‐containing mixtures was developed from a correlation of critical loci. With the predicted convergence pressure the measured values of hydrogen equilibrium ratios in binary hydrogen‐paraffin mixtures were predicted with a statistical deviation of 8.1% for 237 measurements. Including hydrogen‐olefin and multicomponent mixtures of hydrogen, paraffins, and olefins, the statistical deviation was found to be 11.3% for a total of 375 comparisons with measured values of hydrogen equilibrium ratios.
Simple theory of an idealized turbulent mixer
Authors: Corrsin Stanley
Published: June 2004

With stationary isotropic turbulence postulated, the rate of decrease in concentration fluctuations of a scalar contaminant is estimated in terms of the turbulence scale and the power input to the system.
Graphical solution of turbulent‐flow diffusion equations
Authors: Longwell P. A.
Published: June 2004

Linear partial‐differential eqations are often encountered when thermal or material diffusion in flowing systems is considered. Analytic solutions of such equations are known for only the simplest situations. In two examples a graphical method of solution is presented and demonstrated which makes feasible, without excessive labor or special computing facilities, the use of available knowledge concerning turbulent flow in the prediction of thermal or material transfers in complex situations involving linear steady flow.
Studies on effective thermal conductivities in packed beds
Authors: Yagi Sakae , Kunii Daizo
Published: June 2004

Applying both their own assumptions and the mechanism of lateral mixing proposed by Ranz (20), the authors obtained theoretical formulas for effective thermal conductivities ke in packed beds. Previously reported experimental data were analyzed with these equations, and the usable data for predicition of ke were shown.

In order to see the influence of both packing characteristics and temperature on the effective thermal conductivities, experimental data were obtained with air for beds with various kinds of packing, i.e., iron spheres, porcelain packings, cement clinker, insulating fire brick, and Raschig rings. Correlation of these data with Equation (15) showed that this equation adequately expressed the heat transfer mechanisms in packed beds with motionless gases, especially at hight temperatures.
Thermal and material transfer in turbulent gas streams: Local transport from spheres
Authors: Hsu N. T. , Sage B. H.
Published: June 2004

Local convective thermal transfer is difficult to predict for nonuniform three‐dimensional boundary flows. Direct measurements of local transfer from objects of practical interest are therefore useful in the prediction of thermal transfer and in an understanding of multidimensional boundary flows.

Measurements of the gross and local transfer were made upon a silver sphere 0.5 in. in diameter and a ceramic porous sphere of the same size from whichn‐heptane was permitted to evaporate. The air stream had a level of turbulence of approximately 5.4% and only small variation in velocity with position. Temperature distributions in the boundary flows around these spheres were determined, and from these distributions local transfer coefficients were established for the forward hemisphere. The gross transfers were established from the electrical energy added to the silver sphere and from the quantity ofn‐heptane evaporated from the porous sphere.

The local thermal transfers were in reasonable agreement with some of the theoretical analyses based upon a three‐dimensional laminar‐boundary layer. Satisfactory agreement was obtained between spatial integration of the local transfer and the simultaneously measured over‐all values. These, in turn, were in fair agreement with correlated values of the gross thermal and material transfer from spheres.
Unsteady state heat transfer in stationary packed beds
Authors: Reilly Park M.
Published: June 2004

A new solution is presented of the differential equations describing unsteady state heat transfer in stationary beds of small granular solid particles through which a fluid is flowing. Arbitrary initial solid temperature distribution and arbitrary variation of inlet gas temperature are allowed. The solution presented appears easier to apply in practice than those previously published and affords an example of the versatility of Fourier integrals and series. An application of the solution to the regeneration of Dow type‐B butylene dehydrogenation catalyst is described.
Thermal resistance of an eddy
Authors: Clark L. G. , Hagerty W. W.
Published: June 2004

By experimental means a relation is obtained between the thermal resistance of an eddy and its angular momentum. The eddy is stationary, and no extraneous motion is present. The secondary motion which may develop in the annulus between concentric rotating cylinders is used to obtain the eddies. The fluid motion is well defined at all times and at all points of space. Heat is passed through the eddies, and the Nusselt number is obtained, which varies linearly with the angular momentum. Both Nusselt number and angular momentum vary linearly with the peripheral velocity of the inner rotating cylinder, which can be interpreted in terms of a Reynolds number associated with fluid flow perpendicular to a cylinder.
Heat transfer from superheated vapors to a horizontal tube
Authors: Balekjian Garen , Katz Donald L.
Published: June 2004

Experimental data are reported for condensing Freon‐114 (tetrafluorodichloroethane) and steam at several pressures. The condition of the vapors ranged from saturation to 180°F. of superheat. The condensing tube containing embedded thermocouples was 3/4 in. in diameter and 3 ft. long. Visual observation showed that steam condensed by dropwise condensation in part. Increase of superheat in the vapor at constant pressure caused a lowering of the tube‐wall temperature, which was indicative of a lowering of the surface temperature of the condensate. The lowering of the condensate‐surface temperature below the saturation temperature was computed from the experimental tube‐wall temperatures, the heat flux, and Nusselt's equation for the condensate‐film resistance. The lowering of the condensate‐surface temperature is correlated with degree of superheat. An interfacial coefficient of heat transfer between the superheated vapor and the condensate surface is reported based on the computed surface temperatures. Schrage's analysis and equations for relating mass and heat transfer with conditions at an interface were simplified and used to correlated the experimental condensing load with the degree of superheat.
A new electric analogue model for nonsteady state flow problems
Authors: Fatt Irving
Published: June 2004

A new, simple electric analogue model is demonstrated which gives solutions, accurate within ten %, to problems in nonsteady state flow of heat, diffusion, and flow of liquids in porous media. The analogue consists essentially of a sandwich of electrical conducting paper, polyethylene or polyester sheeting, and metal foil. One‐ or two‐dimensional problems can be treated. This analogue provides a medium with distributed resistance and capacitance rather than the finite steps of conventional analogues; therefore two‐dimensional problems of complex shape can easily be modeled. The analogue is pulsed by a square wave generator and the transient potential response is displayed on a cathode‐ray oscilloscope.
Effect of superatmospheric pressures on nucleate boiling of organic liquids
Authors: Mesler Russell B. , Banchero J. T.
Published: June 2004

Superatmospheric pressures greatly reduce the temperature differences in nucleate boiling of or ganic liquids. Since nucleate boiling is characterized by bubble formation at the heating surface, it seems logical to investigate the pressure difference that causes bubble formation. It has been found that for organic liquids the difference in vapor pressure corresponding to the temperature difference behaves in a regular manner with pressure but does not vary greatly. This regular behavior permits prediction of temperature differences at higher pressures with a knowledge of only vapor‐pressure and boiling data at one pressure. New boiling data have been obtained in the investigation.
Heat transfer to water in turbulent flow in internally heated annuli
Authors: Stein Ralph P. , Begell William
Published: June 2004

Nearly 900 values of local heat transfer coefficients were correlated for water flowing through long annuli 1/8, 1/4, and 3/8 in. wide, electrically heated at their inner surfaces and containing three spacer ribs. Both cosine and uniform lengthwise heat‐flux distributions were employed. All heat transfer coefficients were computed for positions corresponding to (L/De) ratios larger than 150. Several methods of correlation were attempted and compared, especially with respect to the method of evaluating physical properties. The proportionality of the Colburnjfactor to the Prandtl and Reynolds numbers with their usual exponents was verified, and the dependence ofjuponD2/D1was analyzed. There was no significant effect of cosine heat‐flux distribution on the heat transfer coefficients. Evaluating physical properties at the usual film temperature gave the best correlation. A simplified dimensional equation for water at moderate temperatures and pressures was also developed.
Estimation of the stage efficiency of simple, agitated vessels used in mixer‐settler extractors
Authors: Treybal Robert E.
Published: June 2004

A method of calcuation is presented by which estmates may be made of the stage efficiency of continuously operated, agitated, baffled vessels used in mixer‐settler extractors. The calculations are limited to cases where the agitatiing impeller is a flat‐blade turbine, and do not include estimates of the entrance and exit effects. The method has been tested with all the available experimental data, which include three different sizes of vessels, systems, and impeller sizes, and a variety of operating conditions including speeds of agitation, rates of flow, and ratios of contacted liquids. Because of limitations of the author's knowledge, the calculations are necessarily approximate, but they nevertheless correctly indicate the nature of the variations in stage efficiency to be expected with all of the design and operating variables for which tests could be applied.
Flow of two‐phase carbon dioxide through orifices
Authors: Hesson James C. , Peck Ralph E.
Published: June 2004

Experimental flow rate data are presented for saturated liquid, saturated vapor, and two‐phase liquid‐vapor carbon dioxide through a convergent nozzle and a square‐edged orifice. The data cover the range from the triple‐point pressure to the critical pressure. Charts have been prepared for this complete range at critical flow. Results are also presented for subcritical flow.

The tests at various back pressures indicate that the saturated liquid behaved as a cold liquid without evaporation ahead of the throat.

Saturated vapor became supersaturated in the nozzle, and the vapor behaved as if no condensation occurred.

Equations are presented for the flow rates of saturated vapor, and two‐phase mixtures in the critical flow region.

A Mollier (pressure‐enthalpy) diagram is used to determine the flow rates of saturated vapor and two‐phase mixtures where supersaturtation takes place. In these cases, the lines of constant specific volume or density are extrapolated from the superheated region into the normal two‐phase region to obtain values corrected for supersaturation.
Freezing points of binary mixtures of methane
Authors: Brewer Jerome , Kurata Fred
Published: June 2004

The experimental freezing‐point data of the methane‐n‐hexane and the methane‐n‐octane binaries are presented and compared with the methane–carbon dioxide system investigated by Donnelly and Katz. A step‐by‐step variation of the freezing point in the paraffin homologous series is exploited to provide reasonably accurate extrapolation of the experimental data on the two binaries and scattered freezing‐point data on the methane‐n‐butane mixture to other paraffin hydrocarbon mixtures of methane in which the heavier constituent ranges from ethane to n‐nonane, inclusive.

A composite graph of the freezing points of the various binaries with methane, from ethane to n‐nonane, is presented.
Characteristics of gas pockets in fluidized beds
Authors: Yasui George , Johanson L. N.
Published: June 2004

Some characteristics of gas pockets rising through beds of fluidized solids have been measured directly with a light probe technique. The vertical thickness, numerical frequency, and rate of rise of the bubbles were obtained from oscillographs of dual probe signals. Room‐temperature air at 1‐atm. pressure was used in 4‐ and 6‐in. columns. Glass beads, a crushed rock, commerical cracking catalysts, coal, and hollow resin spheres were studied in particle sizes from 12‐µ fluid cracking catalyst to 450‐µ coal.

Vertical bubble thickness was found to increase with particle size, distance above the bed support, and gas velocity. Size growth upon rising was mainly the result of coalescence of bubbles. The rise velocity ranged from 1 to 2 ft./sec., relatively unaffected by operating conditions. Bubble frequency decreased with height above the bed support owing to coalescence. Total bed‐depth variation from 1.0 to 2.5 ft. did not significantly influence the results, which should be of interest in studying gas by‐passing in fluidized beds and predicting the slugging behavior and fluidization uniformity.
Fugacities in high‐pressure equilibria and in rate processes
Authors: Prausnitz J. M.
Published: June 2004

This work considers the importance of vapor‐phase nonideal mixing in high‐pressure equilibrium and rate‐process calculations. New techniques are presented for calculating vapor‐phase fugacity coefficients in nonideal mixtures.

The equilibrium properties of gaseous mixtures are represented by a virial equation of state which is adequate for the vast majority of chemical engineering problems. Techniques based on an extension of the corresponding‐states theory are given for estimating the various coefficients appearing in the equation of state; these estimates appear to be reliable for a large variety of nonpolar or weakly polar systems. Techniques based on the theory of intermolecular forces are also presented for polar systems and for a limited class of mixtures containing hydrogen‐bonding components. The proposed methods of calculation are illustrated by a large variety of problems occurring in common chemical engineering calculations, and it is shown that failure to correct for vapor‐phase nonideal mixing can, in some cases, lead to very large errors.
Thermodynamic properties of acetylene
Authors: Weber James H.
Published: June 2004

The derived thermodynamic properties of acetylene have been determined over a temperature range of 32 to 500°F. and up to pressures of 2,000 lb./sq. in. abs. The data were calculated from vapor pressure, volumetric, and heat‐capacity data by the use of rigorous thermodynamic relationships. The calculated data were found to be internally consistent. The enthalpy values are believed to be accurate within ±1.0 B.t.u./lb. and the entropy values to ±0.001 B.t.u./(lb.)(°R.).
The study of flow and reaction rates in turbulent flames
Authors: Barbor R. P. , Larkin J. D. , Von Rosenberg H. E. , Shipman C. W.
Published: June 2004

It is proposed that measurements of reaction rate as a function of position within turbulent flames be the basis of an approach to the problem of turbulent‐flame propagation. As a test of the method, measurements of static pressure, impact pressure, and chemical composition were made at several positions within the burning zones of two simulated ramjet combustion chambers. From these measurements a complete mapping of compositions, velocity components, densities, and static pressures could be carried out. By calculation of the appropriate derivatives of the latter quantities, the differential form of the equation of continuity for the species desired could be solved for net reaction rate as a function of position, turbulent diffusion being neglected. By a similar technique the equation of momentum was used to obtain eddy viscosities. The latter results were used to estimate the effect of turbulent diffusion by assuming a turbulent Schmidt number of unity.

It is concluded that the method of attack used is a reasonable approach to the problem of turbulent flame propagation, having a special advantage in that it can be used to discover relationships between the rate of reaction and the patterns of the mean flow.
Some effects of baffles on a fluidized system
Authors: Overcashier R. H. , Todd D. B. , Olney R. B.
Published: June 2004

Some characteristics are reported for the fluidization of an air‐microspheroidal catalyst system in a 16‐in.‐diameter bed equipped with baffles. The back‐mixing characteristics and retention‐time distributions of gas and solids, allowable gas and solids velocities, entrainment rate, and bed density are studied as functions of baffle design.

It is shown that the use of baffles narrows the retention‐time spectrum and permits either concurrent or countercurrent flow while not seriously reducing gas or solids throughput or solids holdup.
Engineering applications of relaxation procedures by digital computation
Authors: Radd M. E. , Tek M. R.
Published: June 2004

A generalized computing method is developed to perform mathematical “relaxation” on a Datatron digital computer. The application of the developed relaxation or iteration procedures results in obtaining numerical solutions to several engineering boundary‐value problems expressed by elliptic differential equations. The developed digital relaxation routine is found to be effective, fast, and practical in solving numerous steady‐state heat and mass transfer problems with arbitrary and quite often complex boundary conditions. While the specific speed and accuracy of the developed digital method is found to depend upon the type of differential equation, the grid size, and computational tolerance requirements, a typical problem indicates that 250 iterations/min. speed and 1% accuracy may be achieved in an average case.

The examples presented in this paper are chosen from the more classical heat transfer and temperature and pressure distribution problems in order to indicate some other areas where similar engineering problems can be solved however complex the boundary conditions may be.
Reduced density correlation for hydrogen: Liquid and gaseous states
Authors: Schaefer Charles A. , Thodos George
Published: June 2004

The available experimental density data for hydrogen have been complied to produce a reduced density correlation for the liquid and gaseous states. This investigation has utilized fifty‐seven sources of data, extending from the early studies of Amagat (1880) to the recent contributions of Johnston, Keller, and Friedman (1954).

Based on the concept of a reduced density, a correlation for hydrogen has been developed ranging in temperature from the melting point (14°K.) to 3,300°K. and in pressure as high as 2,550 atm. This correlation provides continuity between the liquid and gaseous phases; whereas existing equations of state fail to describe the experimental behavior in the transitional region, particularly near the critical point.

Four hundred and eighty‐five experimental points covering the entire region were checked to establish the reliability of this correlation, which reproduced the experimental data to within 0.49%.
Characteristics of transition flow between parallel plates
Authors: Whan G. A. , Rothfus R. R.
Published: June 2004

Measurements of pressure drop and mean local fluid velocities have been made in a smooth rectangular duct of large aspect ratio. Data have been taken on the steady, isothermal flow of water at room temperature in the viscous, transition, and lower turbulent ranges of flow. Impact probes were installed in the center of the stream, where flow between infinitely broad parallel plates was closely approximated. The limits of the transition range are discussed, and mean local fluid velocities are correlated. Comparison is made with transitional behavior in smooth tubes.
Treatment of thermodynamic data for homogeneous binary systems
Authors: Ness H. C. Van , Mrazek R. V.
Published: June 2004

This paper describes general methods for the treatment of binary data which are both precise and convenient. In particular a new and accurate graphical method of determining partial molal quantities is presented.
Flow characteristics in horizontal fluidized solids transport
Authors: Wen Chin‐Yung , Simons H. P.
Published: June 2004

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.
Effective collision diameters and correlation of some thermodynamic properties of solutions
Authors: Prausnitz J. M. , Benson P. R.
Published: June 2004

Volumetric data on gas mixtures and vapor‐phase data for gas‐liquid equilibria have been correlated within the framework of the theory of corresponding states. An expression based on the London potential for dispersion forces was used to compute characteristic temperatures for various binary systems, and a correlation was developed relating these temperatures to the polarizabilities, ionization potentials, and critical volumes of the pure components. The correlation shows how the molecular shape of a liquid affects its vapor‐phase solubility. With the help of this correlation it is possible to make very good predictions of such gas‐liquid equilibria as are required in high‐pressure distillation, absorption, and petroleum hydrofining operations.
Particulate fluidization and sedimentation of spheres
Authors: Loeffler A. L. , Ruth B. F.
Published: June 2004

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.
Longitudinal laminar flow between cylinders arranged in regular array
Authors: Sparrow E. M. , Loeffler A. L.
Published: June 2004

An analytical solution has been obtained for the longitudinal fully developed laminar flow between cylinders arranged in triangular or square array. Numerical results for the pressure drop and the friction factor are given over a wide range of spacing‐to‐diameter ratios. For large spacings the results can be represented by a single expression independent of the type of array. Plots are also given of velocity distributions and of the variation of the local shear stress around the periphery of a cylinder.
Some aspects of fluid mechanics in chemical engineering
Authors: Sage B. H.
Published: June 2004

The prediction of the transfers of momentum, energy, and material is of ever‐pressing concern to the engineer interested in process design. Recently developed facts concerning the transport of momentum which are of particular use in predicting transfers of energy and material are reviewed, as well as the background of thermodynamics associated with transport processes. The more elemental relationships pertaining to thermal and material transfer in flowing streams are considered, and some of the interrelations of the transport processes are presented.
Experimental foundations of chemical engineering
Authors: White R. R. , Churchill S. W.
Published: June 2004

Fundamental knowledge consists of understanding not only the models which correlate and rationalized observations but also the quantity and quality of the observations. The degree of correlation attempted should be consistent with this quantity and quality.

The scientist correlates and rationalizes observations primarily to broaden his general understanding of the physical universe, and his efforst at correlation are more often than not a way of speculating on the future experiments which should be undertaken to test his concepts. For this purpose he is often satisfied with accuracy to one order of magnitude. The engineer, faced with the design and operation of expensive equipment, is almost always interested in a much higher accuracy in his correlations.

Virtually all existing data in the rate processes are forced into rationalizations based upon either potential‐difference or potential‐gradient models. The application of these models to systems of even relatively simple geometry gives rise to mathematical complexity beyond present analtic ability. Even so, our ability to measure and observe seems to be far below our ability to analyze. These two models have been used effectively in chemical engineering in the past and have served to organize a great deal of information in the rate processes. Present research efforts appear to be directed primarily toward filling in gaps in available data and in refining the application of the models. We seem to suffer from a lack of models to test and a lack of data designed to test critically the existing models. There is relatively little exploratory research in chemical engineering as compared, for example, to physics.

When one views chemical engineering as a chain extending from economics, markets, mechanical design, process design, and process development to process research, the uncertainties inherent in some of the links easily involve variances of 50 to 80%. Under these circumstances it would appear that the present orientation of research is distributed much too heavily toward refinement of existing ideas and not nearly enough toward exploration.
Continuous stirred tank reactors: Designs for maximum conversions of raw material to desired product. Homogeneous reactions
Authors: Trambouze P. J. , Piret Edgar L.
Published: June 2004

It is shown in a series of illustrative examples how the conversion efficiency of many reactions can be markedly affected by the type of reactor used, even though the temperatures, catalyst, and basic kinetics are already fixed by the chemistry of the process.

For such purpose graphical and analytic criteria are developed which permit the selection of a continuous stirred tank or tubular reactor system to obtain the most advantageous conversion of raw material to desired product. When a continuous stirred tank reactor process is preferable, the optimum number of reactor stages for maximum conversion is one. An example is given of a case where a combination of a continuous stirred tank and a tubular reactor is advantageous.

A new graphical method of reactor design for simple or complex reactions is also introduced. This method utilizes continuous stirred tank reactor data directly rather than batch data or kinetics analyses.

Reactions are classified according to the kinetic and stoichiometric characteristics which determine the allowable design procedures and the differences in the compostions paths occurring in batch, tubular, or continuous stirred tank reactors.

The mathematical analysis of continuous stirred tank reactor systems for complex reactions leads to a set of difference equations. For cases of zero‐ or first‐order reactions these are readily solved as illustrated in examples, even when several independent components influence the reaction kinetics.
Transistion from laminar to turbulent flow in pipes
Authors: Ryan N. W. , Johnson M. M.
Published: June 2004

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.
Heat transfer by radiation through porous insulations
Authors: Larkin Bert K. , Churchill Stuart W.
Published: June 2004

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°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.
Interfacial resistance due to thin films of alcohols and its effect on the rate of evaporation of water
Authors: Udani Lalit H. , Gordon Kenneth F.
Published: June 2004

Measurements were obtained of the interfacial resistance due to thin films of straight‐chain higher alcohols and their effect on the evaporation of water. This was done by passing preheated dry air at a constant rate over water in a beaker. Unlike previous studies both phases were stitted. Four alcohols, dodecyl, myristyl, cetyl, and stearyl, were studied. A large reduction in evaporation was observed when 0.00025 gm. of cetyl alcohol was added to 1 liter of water with gas‐liquid interfacial area of 0.2015 sq. ft. A much higher amount of stearyl alcohol, 0.0006 g., was needed for commensurate effect. Resistance due to films of dodecyl and myristyl alcohols was neglibible. For the most part cetyl alcohol is the most effective of those tested. Plots are given of the pseudo mass transfer coefficients and interfacial resistances as a function of the amount of the various alcohols.
Automatic control of fluid flow
Authors: Ceaglske N. H.
Published: June 2004

This paper illustrates the use of analytical methods for the design of a flow‐control system. Linearized equations are derived and a complete analysis is made of the control of the system. The effect of controller modes and process time constants is investigated. The calculations show that there is an optimum value of the process time constant for optimum response.