Showing papers in "Aiche Journal in 1961"

Boundary‐layer behavior on continuous solid surfaces: I. Boundary‐layer equations for two‐dimensional and axisymmetric flow

Abstract: This study deals with boundary-layer flow on continuous solid surfaces. Flow of this type represents a new class of boundary-layer problems, with solutions substantially different from those for boundary-layer flow on surfaces of finite length. In this paper the boundary-layer behavior on continuous surfaces is examined, and the basic differential and integral momentum equations of boundary-layer theory are derived for such surfaces. In subsequent papers these equations will be solved for the boundary layer on a moving continuous flat surface and a moving continuous cylindrical surface, for both laminar and turbulent flow in the boundary layer.

Boundary‐layer behavior on continuous solid surfaces: III. The boundary layer on a continuous cylindrical surface

Abstract: The behavior of laminar and turbulent boundary layers on a moving continuous cylindrical surface is investigated by the integral method, based on assumed velocity profiles that satisfy the appropriate boundary conditions. Equations for the characteristic boundary-layer parameters are presented for both the laminar and turbulent boundary layers, and comparison is made with the boundary-layer behavior over a cylindrical surface of finite length. The analysis for the laminar boundary layer with a logarithmic velocity profile leads to satisfactory results. The turbulent boundary-layer behavior on continuous cylindrical surfaces, and cylindrical surfaces of finite length, can best be investigated experimentally.

The measurement of rapid surface temperature fluctuations during nucleate boiling of water

Abstract: The surface temperature during nucleate boiling was measured with a special thermocouple so designed as to measure the temperature of a small area and to have an extremely rapid response time. The surface temperature was found to drop occasionally 20 to 30 deg F in about 2 msec during the boiling of water. This indicates a rapid extraction of heat during a short time interval. The significance of this observation is that it provides an important new clue to an understanding of nucleate boiling. A hypothesis is advanced to explain these observations. (auth)

Flow of non‐Newtonian fluids in a magnetic field

Abstract: The analytical solution to the equation of motion is given for the steady laminar flow of a uniformly conducting incompressible non-Newtonian fluid between two parallel planes. The fluid is under the influence of a constant pressure gradient and is subjected to a steady magnetic field perpendicular to the direction of motion. Two non-Newtonian models are considered: the Bingham plastic model and the power-law model. Flow rates and the velocity profiles for various values of the Hartmann number and the generalized Hartmann number are presented and compared with those corresponding to Newtonian fluids.

A finite‐difference method of high‐order accuracy for the solution of three‐dimensional transient heat conduction problems

Abstract: A finite-difference method is presented for solving three-dimensional transient heat conduction problems. The method is a modification of the method of Douglas and Rachford which achieves the higher-order accuracy of a Crank-Nicholson formulation while preserving the advantages of the Douglas-Rachford method: unconditional stability and simplicity of solving the equations at each time level. Although the method has not yet been applied, the analysis in this paper suggests that it will prove to be the most efficient method yet proposed for the numerical integration of three-dimensional transient heat conduction problems.

A thermodynamic correlation of gas solubilities

Abstract: Low-pressure solubility data have been correlated for eleven gases in nine solvents over a wide temperature range by considering the dissolution process in two steps. First the gas is condensed isothermally to a hypothetical liquid at 1 atm. pressure, and then this hypothetical liquid is dissolved in the solvent. The free energy of the first step depends only on the properties of the solute, which in the case of nonpolar gases can be adequately described by the theorem of corresponding states. The second step depends on the properties of both solute and solvent and, in the case of nonpolar systems, can be described by the theory of regular solutions. The correlation depends on three solute parameters: the solubility parameter, the molar volume, and the fugacity of the hypothetical liquid; the last of these has been plotted as a generalized function for the reduced temperature range of 0.7 to 3.2. A separate plot is given for hydrogen. These parameters may be used to make good estimates of low-pressure gas solubilities (or K values) in nonpolar solvents over a wide range of temperature. A semiempirical method for correlating the solubilities of gases in polar solvents is also described and illustrated for several cases. Since the correlation presented in this paper covers a wide temperature range, it is possible to make estimates of the heats of solution of gases in liquids. These may be useful in enthalpyblance calculations as required in certain phase-separation operations.

A general correlation of vapor-liquid equilibria in hydrocarbon mixtures

Abstract: A general correlation of vapor-liquid equilibria in hydrocarbon mixtures is developed. The vaporization equilibrium ratio (K-value) is calculated through a combination of three factors The quantity ν0 is a pure liquid component property and is correlated within the framework of Pitzer's modified form of the principle of corresponding states. The quantity γ is calculated from Hildebrand's equation, with regular liquid solutions assumed. The necessary parameters in this equation are specially determined for the very light components. The vapor state quantity ϕ is calculated from Redlich and Kwong's equation of state. The correlation is in the form of a compact set of equations which are especially suitable for application with an electronic digital computer. The correlation applies to hydrocarbons of various molecular types, including paraffins, olefins, aromatics, and naphthenes. Hydrogen in hydrocarbon mixtures is likewise correlated. The correlation has been tested with a systematic compilation of literature data on mixtures of these components. The over-all average deviation from 2,696 data points is 8.7%.

Two‐phase concurrent flow in packed beds

Abstract: Pressure drop and liquid saturation accompanying two-phase concurrent flow have been studied in a variety of packings and with gas-liquid systems having a wide range of fluid properties. Two basic flow patterns were observed with nonfoaming systems. Correlations of pressuredrop and liquid-saturation data were obtained in terms of the single-phase friction losses for the liquid and the gas when each flows alone in the bed. Deviations from the correlation with foaming systems are discussed and illustrated with sample data.

Agitation of viscous Newtonian and non-Newtonian fluids

Abstract: Viscous fluids are frequently agitated by multiple impellers and in vessels only slightly larger than the impeller. This paper presents data for both Newtonian and non-Newtonian fluids agitated under such conditions. The large decreases in power requirements (at a given level of mixing rate in the non-Newtonian system) which are possible by use of low tank diameter, impeller diameter ratios and/or two impellers, have been quantitatively studied. The types of impellers used in the non-Newtonian work and the ranges of conditions over which power requirement correlations were developed are summarized as follows: Text Table Text. D T/D n NRe Marine propeller 0.42-1.0 1.4 -4.8 0.16-1.0 0.67-1320 Fan turbine 0.33-0.67 1.3 -3.0 0.21-1.4 6.6 -160 Flat-Bladed turbine: one impeller 0.17-0.67 1.3 -5.5 0.20-1.5 2.0 -1800 two impellers per shaft 0.33-1.00 1.023-3.5 0.14-1.00 0.15-620 The results generally confirm an approach developed earlier, for the broader ranges of variables listed above. For the non-Newtonian fluids of primary interest in this study, that is purely viscous materials having flow behavior indexes of less than unity (pseudoplastics, Bingham plastics), the prediction of power requirements has been developed to nearly the same level of perfection as for Newtonian fluids.

Initiation of roll waves

Abstract: The theory proposed by Jeffreys to explain roll-wave transition on a liquid surface is applied to the concurrent flow of a gas and liquid. Data are presented for the concurrent flow of air with water-glycerine solutions, water-butanol solutions, and water-sodium lauryl sulfate solutions. Agreement is obtained between theory and experiment.

Heats of mixing: Alcohol- aromatic binary systems at 25°, 35°, and 45°c.

Abstract: A new isothermal calorimeter with no vapor space is described. It allows the accurate and rapid determination of heats of mixing of endothermic liquid systems. Data are presented for eighteen binary systems composed of a lower alcohol and a simple benzene derivative at 25°, 35°, and 45°C. Precise equations for representing these data are also presented.

Effects of superheated vapor and noncondensable gases on laminar film condensation

Abstract: A boundary-layer analysis of laminar film condensation on a vertical plate has been carried out to study the effects of superheated vapor and noncondensable gases. For a pure, superheated vapor the effects of superheating on the surface heat transfer are accounted for by a simple modification of previously available results for saturated vapors. For a given temperature difference between the plate surface and the liquid-vapor interface, superheating increases the heat transfer to the surface, but only to a modest extent for most practical situations. Although free convection was not included in the analysis, its role has been estimated to be small. For noncondensable gases the analysis shows that the presence of a few per cent of noncondensable in the bulk of the vapor causes a great reduction in the surface heat transfer. The fact that the predicted reduction is substantially larger than that found experimentally indicates that free convection, which is not included in the analysis, plays an important role when noncondensables are present.

Isothermal growth of hydrogen bubbles during electrolysis

Abstract: The investigation was concerned with measuring growth rates of bubbles in an isothermal medium where growth is controlled by mass diffusion. The conditions were met by generating hydrogen bubbles at a platinum cathode during the electrolysis of water. Growth data were obtained by motion picture photography at 800 to 2,400 frames/sec. taken through a microscope to produce an enlargement of 30X on the film. Growth took place in 0.1 normal and 1.0 normal sulfuric acid in water at 77°F. Current densities between 0.1 and 0.2 amp./sq. cm. were used. The observed diameters were all less than 0.006 in., and the growth times were less than 2 sec. Beside growth phenomena interesting features recorded included the coalescence of bubbles, the jumping of bubbles off the solid and then back again, and the slip of the bubble contact at the solid surface. Some bubbles grew with their radii proportional to the square root of time as predicted theoretically by Scriven. For these bubbles the calculated supersaturation of hydrogen in the solution was found to be from eight to twenty-four times the concentration at saturation.

Heat transfer characteristics of porous rocks: II. Thermal conductivities of unconsolidated particles with flowing fluids

Abstract: Experimental heat transfer studies were carried out in beds of unconsolidated glass beads and sand through which fluids were flowing. The scope of the measurements included four fluids, helium, air, carbon dioxide, and water liquid at atmospheric pressure in beds packed with four sizes of glass beads, 110, 370, 570, and 1,020 μ and with two sizes of sand, 110 and 240 μ. Flow rates ranged form 1 to 26 lb./(hr. sq.ft.) in a direction parallel and countercurrent to energy flow. The data were interpreted in terms of apparent, effective thermal conductivities of the bed. The values of ke increase significantly with mass velocity of fluid. By considering the mechanism of heat transfer in porous media a relationship was developed between ke and the heat transfer coefficient between fluid and particle. Treatment of the experimental data in this fashion, combined with available information for larger particles, results in a correlation of Nusselt and Reynolds numbers for air that covers the range N = 10−1 to 104.

Holdup and pressure drop with gas-liquid flow in a vertical pipe

Abstract: Vertical upward concurrent air-liquid flow was investigated under isothermal conditions in a test section of 1-in. schedule 40 pipe. Pressure drop was measured with a mercury manometer connected to two pressure taps 20 ft. apart in the section. Liquid was trapped between two quick shutoff valves activated by two solenoid valves. The liquid was druined from the section to provide the holdup data. Six liquids were used to determine the effect of density, viscosity, and surface tension. The experimental holdup, and two-phase pressure drop data were not in agreement with Lockhart-Martinelli type of correlation for horizontal flow. A statistical correlation for holdup was developed to include fluid physical properties, total mass velocity, and the air-liquid ratio entering the pipe. Similarly a pressure drop correlation was developed which expressed the two-phase pressure drop as a function of the slip velocity, liquid physical properties, and total mass velocity. This correlation showed an average percentage error of less than 15% between the observed and the calculated total pressure drop.

Some observations on the mechanics of drops in liquid-liquid systems

Abstract: Data on the rate of rise and distortion of drops in several liquid-liquid systems have been collected. These are compared with correlations developed by other investigators, and in some cases discrepancies between observed and predicted values are noted which do not seem to be related to any easily measured physical property. However evidence is given showing that they are most likely due to the presence of surface-active materials. Photographs and shadowgraphs showing the nature of the flow around and behind moving drops are also included. The point of boundary-layer separation on the drop surface as indicated by these photographs has been related to the internal drop circulation. It is the shift in this point of separation which is the primary cause for the reduction in drag of liquid drops as compared with solid spheres. A previous theory for the breakup of rain drops explains the existing data for drop breakup in liquid-liquid systems.

Swirling flow in cylinders

Abstract: The presence of vortex motion in a vertical cylinder in which water is passed upward can result in three types of velocity profiles: net upward motion at all points in the tube, an ascending outer annulus and a descending central core, and outer annulus and central core ascending and an intermediate annulus descending. All three types of velocity profiles are functions of three factors: the tangential velocity, the manner of decay of the tangential velocity, and the wall pressure drop. A fourth factor, boundarylayer growth, is proposed to explain the third type of profile. Experimental work was carried out to prove the mechanisms proposed for the first two types of profiles. Photographic observations were taken showing the existence of the third type.

The drag coefficients of single spheres moving in steady and accelerated motion in a turbulent fluid

Abstract: Drag coefficients of aerodynamically smooth spheres having a density variation of from 0.252 to 1.91 g./cc. and a diameter variation from 1.56 to 3.21 mm. were obtained for acceleration rates varying from 103.5 ft./sec.2 to -30 ft./sec.2 and for relative intensities of up to 45%. The particle-to-Eulerian macroscale ratios varied from 0.50 to 0.16, and the diameter-to-Eulerian microscale ratios varied from 10 to 2. The drag coefficients were found to be a function of the particle Reynolds number and of the relative intensity but not of the acceleration and relative macro-and-microscale variations. A transition theory for the system investigated is presented, which predicts that the product of the critical Reynolds number and the square of the relative intensity should be a constant; it is supported by the experimental results obtained.

The viscosity of polar gases at normal pressures

Abstract: Experimental viscosity data available in the literature for fifty-two nonpolar gases have been utilized in conjunction with a dimensional analysis approach to relate the viscosity at atmospheric pressure to temperature. The substances investigated are both simple and complex and include the inert and diatomic gases, carbon dioxide, carbon disulfide, carbon tetrachloride, and the hydrocarbons up to n-nonane, including normal and isoparaffins, olefins, acetylenes, naphthenes, and aromatics. The dependence of the product μ*ξ on reduced temperature was found to be the same for all of these substances, except helium and hydrogen. Both theoretical considerations and dimensional analysis indicate that the viscosity product of a gas might depend on the compressibility factor at the critical point. However the results of this study show that for these nonpolar substances this viscosity product at normal pressure is independent of zc and depends only on temperature. The only information required for the calculation of viscosity with the relationships developed in this study is the molecular weight, critical temperature, and critical pressure of the substance. Values calculated with these relationships have been compared with 785 experimental points from all reliable sources of experimental data and produced an average deviation of 1.77%. Comparisons have also been made with the values calculated with the Licht-Stechert and Bromley-Wilke equations.

Phase relations of miscible displacement in oil recovery

Abstract: Miscible displacement as an oil recovery process has received wide interest in the literature recently. Essentially three basic processes have been proposed for attaining miscible displacement in our oil reservoirs: high pressure gas, enriched gas, and miscible slug processes. The present paper relates and compares the phase relations and mass transfer mechanisms of these various basic miscible displacement processes. It also discusses the effects of the various operating variables, such as pressure, temperature, injected gas composition, etc., on the applicability of the process and considers the pertinent conditions that restrict the application of each process. It is to be recognized that at times a miscible displacement may be attempted but not attained, or unforeseen conditions may destroy miscibility once it has been attained. The authors discuss the results of such conditions. The mechanisms of the miscible displacement processes are explained in a conceptual analysis based on the triangular phase diagram. Although the multicomponent reservoir fluid system cannot be represented rigorously from a thermodynamics standpoint by these diagrams, they are useful for cenceptual analysis. Their limitations are presented by the authors along with data supporting the concepts developed.

On the steady flow of a non-Newtonian fluid in cylinder ducts

Abstract: The flow of a power law fluid in cylindrical ducts is considered, with a variational principle evolved from minimum entropy considerations used. This principle is applied to flow in rectangular ducts and between two flat plates with the method of Ritz and Galerkin to determine the velocity profiles used. These velocity profiles are used to determine the relationship between the friction factor and the Reynolds number.

Energy balances in solar distillers

Abstract: There has been considerable doubt as to the manner in which the productivity of solar stills is affected by many of the designs and operating variables. To assist in designing solar stills of improved performance, theoretical equations are derived to describe the complete energy and mass transfer relationships involved in the operation of the basin type of solar still. These are supplemented with data from field operation of a 2,500-sq. ft. still. With these relationships and the aid of a digital computer, the effects of variations of design parameters on the performance of solar stills is predicted. Distiller productivity is correlated with atmospheric temperature, wind velocity, solar radiation, absorptivity and slope of transparent cover, and other variables. Curves showing the magnitude of the effects of design changes on cover temperature, brine temperature, and productivity are presented.

Transport characteristics of suspensions: ii. minimum transport velocity for flocculated suspensions in horizontal pipes

Abstract: The minimum transport velocity was determined for flocculated thorium oxide and kaolin suspensions flowing in glass pipes. The pipes ranged from 1 to 4 in. in diameter, and the concentration was varied from 0.01 to 0.17 volume fraction solids. Two flow regimes were observed depending on the concentration of the suspension. In the first the suspension was sufficiently concentrated to be in the compaction zone and hence had an extremely low settling rate. The second regime was observed with more dilute suspensions which were in the hindered-settling zone and settled ten to one-hundred times faster than slurries which were in compaction. The concentration for transition from one regime to the other was dependent on both the tube diameter and the degree of flocculation. The suspension particles were smaller than the thickness of the laminar sublayer, and they settled according to Stokes' law for the particular conditions of this study. Under these circumstances the relation developed for dilute suspensions is consistent with particle transfer in the radial direction owing to Bernoulli forces on the particle and the action of turbulent fluctuations which penetrate the laminar sublayer. For concentrated suspension in compaction the minimum transport velocity was given by a characteristic criticalmore » Reynolds number. (auth)« less

Thermodynamics of solvent selectivity in extractive distillation of hydrocarbons

Abstract: The selectivity of a polar solvent is expressed in terms of an approximate theory of solutions. The theoretical results are insufficiently precise for the accurate prediction of activity coefficients, but the analysis shows that in the absence of chemical effects selectivity depends primarily on the difference in molar volumes of the hydrocarbons to be separated and on the polar energy density of the solvent. The effectiveness of a solvent is related to its polarity (which should be large) and to its molecular size (which should be small). In cases where chemical effects are important or where the molar volumes of the hydrocarbons to be separated are only slightly different, selectivity also depends on the relative ability of the hydrocarbons in acting as electron donors and on the ability of the solvent to act as an electron acceptor in forming acid-base complexes. The theoretical conclusions, which are based on modern thermodynamics and on the theory of intermolecular forces, are in agreement with experimental observations. The results obtained in this work provide theoretical criteria for the selection of an optimum solvent for a given separation and give semiquantitative explanations of solution phenomena related to extractive distillation.

Kinetic data from nonisothermal experiments: Thermal decomposition of ethane, ethylene, and acetylene

Abstract: A rigorous method was developed to account for nonuniform temperature distributions in the analysis of kinetic data. The rate constants cannot be determined directly since they are functions of temperature, so equations were derived and solutions developed for the substantially temperature independent kinetic parameters, activation energy, and pre-exponential factor. A digital computer was used to evaluate numerically various integrals involved in the solution of the equations. The method developed here will be useful in all laboratory kinetic studies where limitations of heat transfer do not permit an isothermal experiment and in the analysis of kinetic data obtained from commerical or pilot plant units where the temperature distribution is nearly always nonuniform. Kinetic studies were made of the thermal decompositions of ethane, ethylene, and acetylene, all of which are high temperature fast reactions. The experimental conditions covered highly nonuniform temperature distributions with peaks from 730° to 1,330°C., a total pressure of 1 atm., varying amounts of nitrogen dilution, and residence times in the millisecond range.

The effect of organic substances on the transfer of oxygen from air bubbles in water

Abstract: The liquid film coefficient is related to bubble diameter and velocity in pure water and to the physical properties of the liquid. The addition to water of organic substances which influence the surface tension and viscosity will decrease the size of the air bubble released from a diffuser and reduce the transfer of oxygen into the solution. The maximum reduction in oxygen transfer occurs in the region of maximum surface tension change. The effect of the addition of several organic substances on the oxygen transfer characteristics are shown.