MASTRR OAK RIDGE NATIONAL LABORATORY-, operated by - » UNION CARBIDE CORPORATION w . NUCLEAR DIVISION | /‘} I( for the 3 U.S. ATOMIC ENERGY COMMISSION ORNL- TM-3718 -z MASS TRANSFER BETWEEN SMALL BUBBLES AND LIQUIDS IN . COCURRENT TURBULENT PIPELINE FLOW . (Thesis) T. S. Kress T CISTIEITTER OF T2 nefrp v i e " Submitted as a dissertation to the Graduate Council of The University of Tennessee in partial fulfiliment of the requirements for the degree Doctor of Philosophy . This report was prepared as an account of work sponsored by the United States Government. Neither the United States nor the United States Atomic Energy Commission, nor any of their employees, nor any of their contractors, subcontractors, or their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, compileteness or usefulness of any information, apparatus, product or process disclosed, or represents that its use would not infringe privately owned rights, Ny ) ORNL~TM-3718 Contract No. W-T7L405-eng-26 MASS TRANSFER BETWEEN SMALL BUBBLES AND LIQUIDS IN COCURRENT TURBULENT PIPELINE FLOW T, 5. Kress Submitted as a dissertation to the Graduate Council of The University of Temnessee in partial fulfillment of the requirements for the degree Doctor of Philosophy. st e N O T | C E — j‘-'i‘.ms port i , t of wor “This t was -prepared as an accoun - s ans;:ép?fby tigli United States Government. I::elther 'til',le"-Uni'téd States nor the United States Atomic nergg; Commission, nogr any of their employ§e§, n?!:'p?;\ge:s ir OF tors, or their e ees, | their contractors, subcontractors, e sonues any 1 mskes any warranty, express or implied, s any -Fability - bility for the accuracy, legal -liability -or_responsi f 2 acy, com ' ness or usefulness of any information, app2 , ‘ g}:?deuzt bf tm disclosed, or represents that its use APRI L 1 972 woutd not infringe privately owned rights. CAK RIDGE NATTONAL LABORATORY Oak Ridge, Tennessee 37830 operated by UNION CARBIDE CORPORATION for the U, 3. ATOMIC ENERGY COMMISSION ACKNOWLEDGMENTS This investigation was performed at the Oak Ridge National Laboratory operated by the Union Carbide Corporation for the U. S. Atomic Energy Commission. The author is particularly grateful for the helpful discussions, guidance, and direction given the research by the major advisor, Dr. J. J. Keyes, and the support of Dr. H., W. Hoffman, Head of the Heat Transfer-Fluid Dynamics Department of the Reactor Division. Dunlap Scott of the Molten-Salt Reactor Program suggested the problem and provided initial funding under the MSR Program. Dr. F. N. Peebles, Dean of Engineering, The University of Tennessee, suggested the use of the oxygen-glycerine-water system and carried out the original analysis of the applicability to xenon-mclten salt systems. The contributions of the following ORNL staff members are also gratefully acknowledged: R. J. Kedl for his bubble generator develop- ment work drawn upon herej; Dr. C. W. Nestor for computer solution of the analytical model; and Frances Burkhalter for preparation of the figures. Special thanks are given to Margie Adair for her skillful and cheerful preparation of the preliminary and final manuscripts, and, of course, to my wife, Dee, for her forbearance. ii ABSTRACT Liquid-phase-controlled mobile-interface mass-transfer coefficients were measured for transfer of dissolved oxygen into small helium bubbles in cocurrent turbulent pipeline flow for five different mixtures of glycerine and water. These coefficients were determined by transient response experiments in which the dissolved oxygen was measured at only one position in a closed recirculating loop and recorded as a function of time, Using an independent photographic determination of the inter- facial areas, the mass-transfer coefficients were extracted from these measured transients and determined as functions of pipe Reynolds number, Schmidt number, bubble Sauter-mean diameter, and gravitational orienta- tion of the flow, Two general types of behavior were observed: (1) Above pipe Reynolds numbers for which turbulent inertia forces dominate over gravitational forces, horizontal and vertical flow mass- transfer coefficients were identical and varied according to the regression equation Sh/Scl’ 2 = 0,34 Re®+9%¢ (dVS/D)l‘O ) The observed Reynolds number exponent agreed genefally'with other liter- ature data for cocurrent pipeline flow but did not agree with expectation based on equivalent power dissipation comparisons with agitated vessel data, (2) Below the Reynolds numbers that marked the equivalence of hor- izontal and vertical flow coefficients, the horizontal-flow coefficients continued to vary according to the above equation until, at low flows, iii iv severe stratification of the bubbles made operation impractical. The vertical-flow coefficients at these lower Reynolds numbers underwent a transition to approach constant asymptotes characteristic of the bubbles rising through the quiescent liquid. For small bubbles in the most viscous mixture tested, both horizontal and vertical-flow coefficients underwént this transition., An expression was developed for the relative importance of turbulent inertial forces compared to gravitational forces, Fi/Fg' This ratio served as a good criterion for establishing the pipe Reynolds numbers above which horizontal and vertical-flow mass-transfer coefficients were identical. In addition, it proved to be a useful linear scaling factor for calculating the vertical-flow coefficients in the above mentioned transition region. A seemingly anomalous behavior was observed in data for water (plus about 200 ppm N-butyl alcchol) which exhibited a significantly smaller Reynolds number exponent than did data for the other fluid mix- tures. To explain this behavior, a two-regime "turbulence interaction" model was formulated by balancing turbulent inertial forces with drag forces. The relationship of the drag forces toc the bubble relative-flow Reynolds number gave rise to the two regimes with the division being at Reb = 2, The resulting bubble mean velocities for each regime were then substituted intb Frossling~type equations to determine the mass-transfer behavior. The resulting Reynolds number exponent for one of the regimes (Reb € 2) agreed well with the observed data but the predicted exponent for the effect of the ratio of bubble mean diameter to conduit diameter, dvs/D’ was less than that observed. The mass-transfer equations v v b particles in agitated vessels and alsc compared favorably with the resulting from the other regime (Re, > 2) agreed well with data for water data mentioned above, For comparison, a second analytical model was developed based on surface renewal concepts and an eddy diffusivity that varied with Reynolds number, Schmidt number, bubble diameter, interfacial condi- tion, and position away from an interface, Using a digital computer, a tentative numerical solution was obtained which treated & dimension- less renewal period, T,, as a parameter. This renewal period was interpreted as being a measure of the rigidity of the interface, I, - 0 corresponding to fully mobile and T, » approximately 2.7 (in this case) to fully rigid interfaces, TABLE OF CONTENTS CHAPTER 1. INTRODUCTION v & o o o o o o o o o o« o » o II. LITERATURE REVIEW . . . . . . . Experimental-Cocurrent Flow . . . . . Experimental-Agitated Vessels .A. . e e Discussion of Available Experimental Data . Theoretical . + ¢ ¢« ¢ ¢ ¢ 4 ¢ ¢ « o o o Surface Renewal Models . ¢« 4 o o & o & Modeling of the Eddy Structure . . Turbulence Interactions . . . . .7. . Dimensional Analysis (Empiricism) . . DisCUuSSion ¢« v v v o o « o o s o & ITT. DESCRIPTION OF EXPERIMENT . . . ¢« « & » & & Transient Response Technique Apparatus . . + + . . o ; e e e e e e Pump . . 0 0 0 0 0 0 e Liquid Flow Measurement . . . . « Temperature Stabilization . . . . . Gas Flow Measurement . . Dissolved Oxygen Measurement . . . . . Bubble Generation . . « ¢« « o « «+ & Bubble Separation . « « ¢ o « o « & Test Section v v ¢« ¢« ¢ ¢« o « o o s & vii "PAGE 11 11 viii CHAPTER PAGE Bubble Surface Area Determination — Photographic SYSTLEM + o o + « o o o « o o o o o s o o s o v o s . 38 ENG BEFECE 4 v o v o v o o o o o o o o o o w0 0w e . W7 Summary of Experimental Procedure . . . « « o o o« o o Lg IV, EXPERIMENTAL RESULTS . & &« « ¢ 4 o o o o o s o s o o s o 55 Unadjusted Results . v ¢ ¢« ¢ o o o ¢ o o o o o o o s o 55 Equivalence of Horizontal and Vertical Flow Mass Transfer . o o o & o o o o s o o o o o o o o o 56 Vertical Orientation Low-Flow Asymptotes . . . . . . . 60 Mass Transfer Coefficients . & o v ¢« ¢ v o o o o o & & 60 Calculating Vertical Flow Mass-Transfer Coefficients forFi/FgLessThanl.5 C e e e e e e e e e e e . BT Comparison with Agitated Vessels . ¢« ¢ « o ¢ o « o o & 69 Recommended Correlations . & ¢« o o+ o o o o o o o o o« o (1 V., THEORETICAL CONSIDERATIONS . . &+ ¢ v o 4 o o ¢ o « « o o« 6 Turbulence Interaction Model .+ v o o v o « o « « = o« &« 76 Surface Renewal Model . & v o« ¢ o 6 o o o o s o o s o 81 VI, SUMMARY AND CONCLUSIONS + & « v o o o o o o « o s o « o o 9h VII. RECOMMENDATIONS FOR FURTHER STUDY . v v o « « & o o o o« o 100 Experimental . . v v & ¢ o ¢ o s s o s o o o o o s s 100 Theoretical v v v v o o « « o o o o+ o o o o o o « o o » 102 ILIST OF REFERENCES .+ 4 & &« o o o o s o s o = » s & o o o o o o o o« 105 APPENDICES s e » e 6 s s s s s s 8 s ® s e s e e e o s e s s « e ¢ 111 A PHYSICAL PROPERTIES OF AQUEOUS-GLYCEROL MIXTURES . . . . . 11l ix CHAPTER PAGE B DERTIVATION OF EQUATIONS FOR CONCENTRATION CHANGES ACROSS A GAS-LIQUID CONTACTOR . v & ¢« o o o o o » & o« o 117 C INSTRUMENT APPLICATION DRAWING . & & o ¢ o o o o « o o & » 121 D INS TRU-MEN-T CALIBRATI ONS L . * . . » . . * - . * - . . . . l 2 3 E EVALUATION OF EFFECT OF OXYGEN SENSOR RESPONSE SPEED ON THE MEASURED TRANSIENT RESPONSE OF THE SYSTEM . . . . . 129 F MASS BALANCES FOR THE SURFACE RENEWAL MODEL ., . . +» « « « 131 G ESTIMATE CF ERROR DUE TO END-EFFECT ADJUSTMENTS . . . . . 13k H MASS TRANSFER DATA . . . & & & ¢ o &« s o s o o o o o« o «» 137 LIST OF SYMBOLS 4 & « 4 o o o o « o o o o o « s o s o « o o o o o« 163 X LIST OF TABLES TABLE PAGE 1. Ranges of Independent Variables Covered . . « « ¢« + + o & 3 IT. Categories of Data Correlation for Mass Transfer from a Turbulent Liquid to Gas Bubbles . . . « +. . + « + « & 12 ITT. Physical Properties of Aqueocus-Glycerol Mixtures (25°C) Data of Jordan, Ackerman, and Berger®® ., . ... ... 20 IV. Experimental Conditions for Runs Used to Validate Surface Area Determination Method for Vertical F:LOWS . . . . . » . - . . . . . . * . . . . » . . - . s L}'L" V. Experimental Conditions for Runs Shown on Horizontal Flow Volume Fraction Correlation . . .« « « o« =« « o .« =« 45 VI. Conditions at Which Horizontal and Vertical Flow Mass-Transfer Coefficients Become Equal (Lamont ! S Data)ll . * . » . . » » - - - * - . . . - . L 5:,:} 10. 11. LIST OF FIGURES PAGE Photograph of the Mass Transfer FPacility « o ¢ & o o o o & 2L Schematic Diagram of the Main Circuit of the Experimental Apparatus . . ¢ &« & & 4 ¢ o o o 0 e o s . 25 Diagram of the Bubble Generator . . .'. s e e e s e e e s 31 Comparison of Measured Bubble Sizes with the Distribution Function « « « « ¢« « « o ¢ o & & o o « « o« 33 Diagram of the Bubble Separator . . « « o o « o « « « » « 30 Comparison of Interfacial Areas Per Unit Volume Measured Directly from Photographs with Those Established Through the Distribution Function. Vertical Flow . . . 43 Correlation of Horizontal Flow Volume Fraction . . . . . . 146 Comparison of Measured and Calculated Interfacial Areas Per Unit Volume, Horizontal Flow . . . . « « « « « « & L8 Typical Experimental Concentration Transient Iliustrating Straight-Line Behavior on Semi-Log Coordinants . . . . 53 Typical Examples of Bubble Photographs: a. Inlet b, Exit Vertical Flow, 37.5% Glycerine-62,5% Water, @, = 20 gpm, Qg/QE = 0.3%, D = 2 inches, and dvs = 0,023 SNCHES &+ v o o b e e e e e e e e e e e e e e e e e 5L Mass Transfer Coefficients Versus Pipe Reynolds Number as a Function of Bubble Sauter-Mean Diameter. Water Plus ~200 ppm N-Butyl Alcohol, Horizontal and Vertical Flow in a 2-inch Diameter Conduit . . . . . . 62 X1 xii FIGURE PAGE 12, Mass Transfer Coefficients Versus Pipe Reynolds Number as a Function of Bubble Sauter-Mean Diameter. 12,5% Glycerine-87.5% Water, Horizontal and Vertical Flow in a 2-inch Diameter Conduit . . v v + &« ¢« « « « . « . 63 13. Mass Transfer Coefficients Versus Pipe Reynolds Number as a Function of Eubble Sauter-Mean Diameter. 25% Glycerine-75% Water. Horizontal and Vertical Flow in a 2-inch Diameter Conduilt . . . . + ¢« ¢« ¢ ¢« & o o 6L 14, Mass Transfer Coefficients Versus Pipe Reynolds Number as a Function of Bubble Sauter-Mean Diameter. 37.5% Glycerine-62,5% Water, Horizontal and Vertical Flow in a 2-inch Diameter Conduit . « & .« ¢ ¢ ¢ ¢ o ¢« « o . 65 15. Mass Transfer Coefficients Versus Pipe Reynolds Number as a Function of Bubble Sauter-Mean Diameter. 50% Glycerine-50% Water. Horizontal and Vertical Flow in a 2-inch Diameter Conduilt . . ¢ ¢ o ¢ « o « o & o & 66 16, Observed Types of Horizontal Flow Behavior, dVS = 0,02 inches and D = 2 inches . ¢ & ¢ o ¢ & & o = 68 17. Equivalent Power Dissipation Comparison of Results with Agitated Vessel Data . & ¢ & ¢« ¢« ¢ ¢ ¢ o & o o o & 70 18, Equivalent Power Dissipation Comparison of Gravity Dominated Results with Agitated Vessel Data . . . . . . 72 19. Correlation of Horizontal Flow Data . . . « . « . + « . . Th 20, Dimensionless Variation of Eddy Diffusivity with Distance from an Interface, Effect of Surface Condition . . . . 88 FIGURE 21, e, 23. 2k, 25, 26, 27 28. 29, 30, 31. 32, 33. 3k, Variation of Eddy Diffusivity with Distance from an Interface, xiii Data of Sleicher . ¢« « . ¢« ¢« ¢« o o o o o o o Numerical Results of the Surface Rénewal Model. of a, b, and ¢ (Exponents on Re, Sc, and d/D, Respectively) as Functions of the Dimensionless Period, T* . » . - - . . . o o . . - ® - . ® Schmidt Numbers of Glycerine-Water Mixtures . . . Henry's Law Constant for Oxygen Solubility in Glycerine-Water Mixtures . « « « ¢ o o ¢ « o & Molecular Diffusion Coefficients for Oxygen in Glycerine-Water Mixtures., and Berger . & o & o o s o o ¢ o o o s s e s Densities of Glycerine-Water Mixtures . . . « « & Viscosities of Glycerine-Water Mixtures . ., . Instrument Application Drawing of the Experiment Facility Bubble Size Calibration Calibration Calibration Calibration Calibration . . » . - L ] ° . . - . - . . . . Range Produced by the Bubble Generator of Rotameter No, 1 (100 gpm) . . . . . of Rotameter No. 2 (40 gpm) . . . . . of Rotameter No. 3 (8 gpm) . . . . . . of Gas-Flow Meter at 50 psig . . . « & of Oxygen Sensors in two Mixtures of Glycerine and Water . . « o« ¢ o o« ¢ ¢ o ¢ o o & Comparison of Calculated Values with Plots Data of Jordan, Ackerman, PAGE 92 112 113 114 115 116 121 123 124 125 126 127 128 FIGURE 35. 36, 37. 38. L5, Xxiv Unadjusted Mass Transfer Data. Water Plus ~200 ppm N-Butyl Alcohol. Vertical Flow . . . « « « « « « & Unadjusted Mass Transfer Data. Water Plus ~200 ppm N-Butyl Alcohol. Horizontal Flow . . « ¢« ¢ ¢ « o« & Unadjusted Mass Transfer Data. 12.5% Glycerine- 87.5% Water, Vertical FIOW « v « o o o o« o « & o & Unadjusted Mass Transfer Data. 12.5% Glycerine- 87.5% Water. Horizontal FIOW . . v « « ¢ « & o o Unadjusted Mass Transfer Data., 25% Glycerine-75% Water., Vertical FIOW . v & o o ¢ o o o o o o o & o Unadjusted Mass Transfer Data. 25% Glycerine-T5% | Water., Horizontal FIlOow ¢ o o v ¢« o o o &+ o o o & & Unadjusted Mass Transfer Data. 37.5% Glycerine- 62.5% Water. Vertical FIOW v v v o o o o o« o o o« & Unadjusted Mass Transfer Data, 37.5% Glycerine- 62,5% Water, Horizontal FIOW « v « v o o o o « o Unadjusted Mass Transfer Data. 50% Glycerine-50% Water., Vertical FIOW . . o & o« ¢« « ¢ o o o & Unadjusted Mass Transfer Data. 50% Glycerine-50% Water., Horizontal FIlOow . « ¢ « v v ¢ o o o o o o & Unadjusted Mass Transfer Coefficients Versus Pipe Reynolds Number as a Function of Bubble Sauter-Mean Diameter. Water Plus ~200 ppm N-Butyl Alcohol. Horizontal and Vertical FIOW .+ & o o o « o s o s » PAGE 138 139 140 141 142 143 1hk 146 1h7 148 FIGURE L6, 47. L. 50. 51, 52. 53. XV Unadjusted Mass Transfer Coefficients Versus Pipe Reynolds Number as a Function of Bubble Sauter-Mean Diameter. 12.5% Glycerine 87,5% Water. Horizontal and Vertical FI1ow . . ¢ o ¢ « « ¢ ¢ o« o o o o o o o Unadjusted Mass Transfer Coefficients Versus Pipe Reynolds Number as a Function of Bubble Sauter-Mean Diameter, ?5% Glycerine-75% Water. Horizontal and Vertical FIOW ., o o & ¢ ¢ ¢ o o o o s o o o Unadjusted Mass Transfer Coefficients Versus Pipe Reynolds Number as a Function of Bubble Sauter-Mean Diameter. 37.5% Glycerine-62,5% Water. Horizontal and Vertical Flow , . + o ¢ ¢« « « « & Unadjusted Mass Transfer Coefficients Versus Pipe Reynolds Number as a Function of Bubble Sauter-Mean Diameter. 50% Glycerine-50% Water. Horizontal and Vertical FI1ow . o ¢ v v ¢« &« o o o o o « & Mass Transfer Data Adjusted for End-Effect. Water Plus ~200 ppm N-Butyl Alcohol., Vertical Flow . . . . . Mass Transfer Data Adjusted for End-Effect. Water Plus ~200 ppm N-Butyl Alicohol, Horizontal Flow . . Mass Transfer Data Adjusted for End-Effect. 12,5% Glycerine-87.5% Water, Vertical Flow . . . . « . . Mass Transfer Data Adjusted for End-Effect, 12,5% Glycerine-87.5% Water. Horizontal Flow . . . . . . PAGE 149 150 151 152 153 154 155 156 FIGURE 5k, 55, 56, 57 58. Xvi Mass Transfer Data Adjusted for End-Effect. Glycerine-75% Water. Vertical Flow . - Mass Transfer Data Adjusted for End-Effect. Glycerine-75% Water. Horizontal Flow . Mass Transfer Data Adjusted for End-Effect. Glycerine-62,5% Water. Horizontal Flow . Mass Transfer Data Adjusted for End-Effect, Glycerine-50% Water, Vertical Flow . Mass Transfer Data Adjusted for End-Effect. Glycerine-50% Water. Horizontal Flow . PAGE 25% s e e e e . . 157 25% e 516 37.5% e o o . 159 50% e e e e . . 160 50% 161 CHAPTER T INTRODUCTICN When gas bubbles are dispersed in a continuous liquid phase, dissolved constituents of sufficient volatility will be exchanged between the liquid and the bubbles, effectively redistributing any concentration imbalances that exist. Common pradtices involve contacting gas bubbles with an agitated liquid in such a manner that a relatively large inter- facial area is available, Techniques such as passing gas bubbles up through a liguid column or mechanically stirring a gas-ligquid mixture in a tank have been studied extensively and the design technology for these is relatively firm., However, one method, cocurrent turbulent flow in a pipeline, has not been given a great deal of attention. A review of the literature has shown that the availlable data are insufficient to‘allow confident determination of the mass-transfer rates in such a system. This research, then, was undertaken to provide additional information that will aid in determining liquid phase controlled mass-transfer rates for cocurrent turbulent flow of small bubbles and liquids in a pipeline. The impetus for this work was provided by the Molten Salt Breeder Reactor (MSBR) Program of the Oak Ridge National Laboratory where recent remarkably successful operation of a molten salt fueled nuclear reactor! has convincingly demonstrated the feasibility of this power system. The economic éompetitiveness of an MSBR, however, depends to a significant extent on the breeding ratio obtainable, The production within the liquid fuel of fission-product poisons, principally xenon-135, exerts 2 a strong influence on the neutron economy of the reactor and consequently on the breeding ratio itself, One method proposed for removing the xenon would require injecting small helium bubbles into the turbulently flowing regions of the fuel- coolant stream and allowing them to circulate with the fuel. Since such bubbles would be deficient in xenon compared to the nearby bulk stream, the dissolved xenon would be transferred by turbulent diffusion across the concentration potential gradient. By continuous injection and removal of the helium bubbles the equilibrium xenon poisoning can be significantly reduced. Since a large amount of gas in the fuel could influence the reactivity of the core, this system would be limited to low volume fractions. Peebles® showed that removal of dissolved oxygen from a given mixture of glycerine and water by small helium bubbles could closely match the hydrodynamic and mass-transfer conditions in an MSBR and suggested using such a system in a similitude experiment from which the actual MSBR behavior might be inferred. Other desirable features of such a system include: (1) convenient variation of the Schmidt number by using differ- ent percentages of glycerine in water, (2) operation at room temperature using glass hardware that allows photographic measurements through an optically clear system, and (3) easy measurement of the dissolved oxygen content by commercially available instruments. Therefore an oxygen- glycerine-water system was chosen for this study. The objective of the program was to measure liquid phase controlled axially averaged mass-transfer coefficients, k, defined by rL k dx X L . k = 3 The local mass-transfer coefficients, kx’ are defined by J=k a [Cavg —-CS] s where J is the mass transferred from the liquid to the bubbles per unit time per unit volume of liquid, a is the interfacial area per unit volume of liquid, Cavg is the bulk average concentration, and CS is the inter- facial concentration, These coefficients need to be established as a function of Schmidt number, Reynolds number, bubble size, conduit diameter, gravitational orientation of the flow (vertical or horizontal), interfacial condition (absence or presence of a surface active agent), and the volume fraction of the bubbles. The scope of this thesis is limited to the ranges of variables listed in Table I, below, which for the most part represent limits of the experimental apparatus. Extensions of this program, how- ever, are projected to include different conduit diametersland different interfacial conditions. Table I. Ranges of Independent Variables Covered Variable Range Schmidt Number (weight percent of glycerine) 370 - 3446 (O, 12-5, 25, 3705) 50) Pipe Reynolds Number 8 x 10® - 1.8 x 10° Bubble Sauter Mean Diameter 0.01 to 0,05 inches Gas to Liquid Volumetric Flow Ratio 0.3 and 0.5 percent Gravitational Orientation of Flow Vertical and Horizontal Conduit Diameter 2 inches The mags~transfer coefficients were extracted from measurements of the coefficient-area products, ka, and independent photographic measure- ments of the interfacial areas per unit volume, a. The products, ka, L were established by means of a unique transient response technique in which the changes in liquid phase concentration were measured as a func- tion of time at only one position in a closed liquid recirculating system while helium bubbles were injected at the test section entrance and removed richer in oxygen at the exit. The apparatus for generating these small bubbles (with an independent control of their mean sizej and effectively separating a high percentage from the flowing mixture had to be developed prior to the start of this research., These are described in Chapter III along with the photographic equipment and technique for estab- lishing the interfacial areas. The fesults of this study are expected to be of immediate benefit to the MSBR Program and should also prove useful to workers in the general chemical industry. Application may extend to such diverse areas as general extraction of radiocactive elements from reactor effluents, bubble lifetimes in the coolant of liquid metal fast breeder reactors, and oxygen treatment of sewage effluents, In addition, benefi%s of a fundamental nature may be derived in that the research concerns transfer of a scalar in a turbulent shear flow field in which the fluid velocity field effectively seen by the bubbles is primarily due to the turbulent fluctuations. The characteristics of mass transfer between dispersed bubbles and a continuous liquid phase in turbulent flow are thus seen to be of immediate scientific and practical importance, CHAPTER IT LITERATURE REVIEW A comprehensive survey was made of literature related to mass transfer between small bubbles and liquids in cocurrent turbulent flow. An exhaustive review of all this literature would be lengthy and some- what pointless. Consequently, only those works that are considered representative of the field (not necessarily of most significance) are included in this chapter and the author intends no derogation or slight- ing by the omission of any work, No significance should be attached to the order in which references appear. For a fairly complete documenta- tion of work related to this subject, the reader is referred to several excellent review articles.2 ® Experimental-Cocurrent Flow There have been very few direct measurements of mass-transfer coefficients for cocurrent turbulent flow of small gas bubbles and liquids, perhaps because substantial special apparatus seems to be required for thesé measurements. Recently Jepsen® measured the liguid phase controlled product of mass-transfer coefficient, k, and inter- facial surface area per unit volume, a, for air/water flow in horizontal pipes with and without spiral turbulence promoters. For straight tubes fiithout turbulence promoters he correlated his data by the equation, kas®l 2 gV 2 (008 po-68 _ 3 47 evo.4 . As shown in Chapter IV, Page 58, the energy dissipation per unit volume, ¢, can be represented as v (o 316) = B paire (1) Therefore, Jepsen's correlation reveals that Sh ~ Re'*l/§ 2a Care must be taken in interpreting the influence of Reynolds number on k when the product, ka, is reported because the interfacial area it- self may depend on the Reynolds number. No attempt was made by Jepsen to separate the area from the product. Scott and Hayduk,'© in admittedly exploratory experiments, dissolved carbon dioxide and helium into water, ethanol, and ethylene glycol in horizontal flow pipelines. Thus they did vary the diffusivity but, like Jepsen, did not separate the ka product. Their results were correlated by the equation ka = 0.0068 v 3074 S°-51 Mo.oia &30 Dl.SB 3 from which may be inferred Sh ~ Re/&*%ta ., Lamont!! and Lamont and Scott® dissolved, in single file fashion, relatively large CO, bubbles into water under vertical and horizontal flow conditions. They did not vary bubble diameter or Schmidt number. At sufficiently large Reynolds_numbers their horizontal and vertical results became identical. The data above these Reynolds numbers were correlated as k ~ Re©+B2 Heuss, King, and Wilke'® studied absorption into water of ammonia and oxygen in horizontal froth flow, The liquid phase coefficients were T controlling only in the oxygen runs and consequently they did not vary the Schmidt number and their results were also obtained as the product of ka. However, using estimates of surface area in froth flow, their data reveal Sh ~ Re®*® ., Hariott'? reported mass-transfer coefficients for particles of boric acid and benzoic acid dissolving in water flowing cocurrently in a two-inch pipeline, A data correlation was not given but a line tan- gent to their data at the high flow end would indicate Sh ~ Re®*93 | Figueiredo and Charles® measured coefficients for dissolution of NaCl particles carried along as a "settling" suspension in water in horizontal flow., They correlated their data with mass-transfer coeffi- cients previously measured for transfer between a liquid and the conduit itself. However, a line tangent to the high flow end of their data indicates Sh ~ Ret*® . Experimental-Agitated Vessels Often the data for transfer to bubbles or particles in agitated vessels are correlated in terms of the power dissipated. Using Equation (1) we might relate these results to what would be expected for flow in conduits, Calderbank and Moo-Young'® correlated data for different particles and small bubbles dispersed in different liquids in agitated vessels, Their equation, determined partly through dimensional analysis, is Using Equation (1) this would give for flow in conduits Sh = 0,082 gel/ 3 Re®+52 (2) They also indicate that in the range of mean bubble diameters, 0.025 < dvs’g 0.1 inches, the mass-transfer coefficients increase linearly, undergoing a transition from "small" bubble behavior where Sh ~ Sc¥ 3 to "large" bubble behavior where S8h ~ Sc¥ 2. They conclude that this tran- sition corresponds to a change in interfacial condition from rigid to mobile, Sherwood and Brian'”’ used dimensional analysis to correlate data for particles in different agitated liquids. Their correlation graphically related Shb/801/3 to (emd4/v3)1/3. Using Equation (1) (with ev/p = em) and drawing a line tangent to the high power dissipation end of their correlating curve gives Sh -~ SC1/3 ReC* 61 (d/D)-o.le . (3) Barker and Treybal'® correlated mass-transfer coefficients for boric acid and benzoic acid particles dissolving in water and 45% sucrose solu- tions with a stirrer Reynolds number, ReT, proportional to the speed of rotation., They reported K ~ ReTC"88 Sct/ 2 g If the power dissipation is assumed proporticnal to the cube of the rotation speed, then k ~ ReC*76 Scl/:a S . The effect of Schmidt number is not as would be inferred from the zbove because § was reported to be essentially proportional to Scfl/z in their experiments. 9 The preceding are representative of data available that may have direct applicability to cocurrent flow in conduits., Some other works that may be of indirect interest include cocurrent turbulent flow of 19-22 mass transfer dispersed liquid drops in a continuous liquid phase, from a turbulent liquid to a free interface,®372® and innumerable studies of the motions of, and mass transfer from, individual bubbles or parti- cles under steady relative flow conditions (e.g., References 26-30). For systems in which bubbles move steadily through a fluid, some relevant findings include the fact that, depending on bubble size and liquid properties, the bubble motion in a gravity field may vary from creeping flow to flow characterized by a turbulent boundary layer. Irrespective of this, the mass-transfer correlations usually take two basic "Frossling" forms (neglecting the constant term) depending on whether there is a rigid interface (no slip condition) or a completely mobile interface with internal circulation of the fluid within the bubble (or drop). In substantial agreement with theoretical treatments, the former data are correlated with Sh’b ~ Rebl/ 2 g01/ 3 and the latter Sh, ~ Re, > ® 8¢/ % =pe V2 | Good accounts of these relative flow equations and their derivations are given by Lochiel and Calderbank®' and by Sideman. =% Discussion of Available Experimental Data It is seen that there have been very few direct measurements of mass transfer to small cocirculating bubbles in a turbulent field and 10 none that are complete in terms of all the independent variables. The product, ka, is often not separated, because of the difficulty in estab- lishing the interfacial area, This makes some of the available data difficult to interpret and of limited value for application at different conditions. Not enough experimental information is available to assess the influence of Schmidt number on Sherwood number although the Schmidt nunber exponent most often appears to vary between 1/3 and 1/2 — apparently determined by the interfacial condition (the Schmidt number exponent may even be greater than 1/2, e.g., Reference 10). The effects of bubble mean diameter and pipe size have received less attention than the Schmidt number and, as yet, no systematic effect can be confidently cited. Calderbank and Moo-Young, however, observed a linear dependence over a limited range of bubble diameters in agitated vessels, The influence of Reynolds number has been the most studied. From References 9-15, it‘yould appear that Sherwood number for gas-liquid flow in conduits may vary with pipe Reynolds number to a power between 0.9 and 1.1 (although Lamont® found it to be 0.52). In contrast, the effect of Reynolds number {turbulence level) in stirred vessels (Refer- ences 16-18) would appear to yield a power between 0.6 and 0.8, This apparent difference between agitated vessels and flow in conduits is surprising because one would think that flowing through a closed con- duit is Jjust another way to stir the liquid. There should be little fundamental difference in the effect of the turbulence produced. 11 Theoretical It is convenient to identify four different analytical approaches designed to provide a description of mass transfer to bubbles from a turbulent liquid that may be applicable to cocurrent flow. The author has chosen to name these (1) Surface Renewal, (2) Turbulence Interac- tions, (3) Modeling of the Eddy Structure, and (4) Dimensional Analysis (Empiricism). These do not necessarily encompass all approaches and there may be considerable overlappifig among areas (for example, a cer- tain degree of empiricism is evident in each). There may be only an indirect equivalence among those within a given category. Some representative works have been categorized according to their approach and listed in Table II. A brief discussion of each category is given below, Surface Renewal Models This category is of considerable historical interest especially the original contributions of Higbie®? and Danckwerts.33 The so-called surface renewal models can be envisioned by imagining the interface as being adjacent to a semi-infinite fluid through which turbulent eddies having uniform concentrations characteristic of the continuous phase, periodically penetrate to "renew" the surface. The mass transfer then depends on the rate and depth of eddy penetration and the eddy residence time near the surface (or the distribution of eddy ages). For a given eddy, the original models are essentially solutions of the diffusion equation 2 L= p2s () Table II., Categories of Data Correlation for Mass Transfer from a Turbulent Liquid to-Gas Bubbles 1., Surface Renewal Brian and Beaverstock (40)2 Danckwerts (33) Davies, Kilner, and Ratcliff (k1) Gal-Or, Hauck, and Hoelscher (L2) Gal-Or and Resnick (L43) Harriot (LL) Higbie (32) King (25) Koppel, Patel, and Holmes (L5) Kovasy (L6) Lamont and Scott (12) Perlmutter (L47) Ruckenstein (48) Sideman (49) Toor and Marchello (34) 3. Modeling of the Eddy ' Structure Banerjie, Scott, and Rhodes (51) Fortescue and Pearson (23) Lamont (11) 2., Turbulence Interactions Boyadzhiev and Elenkov (19) Harriot (50) Kozinski and King (2kL) Levich (36) Peebles (2) Porter, Goren, and Wilke (20) Sideman and Barsky (21) 4, Dimensional Analysis (Empiricism) Barker and Treybal (52) Calderbank and Moo-Young (16) Figueiredo and Charles (15) Galloway and Sage (53) Heuss, King, and Wilke (13) Hughmark (54) Middleman (38) Scott and Hayduk (10) Sherwood and Brian (17) a Reference number. 13 As shown by Toor and Marchello,®* the "film" model first introduced by Whitman®® corresponds to the asymptotic solution of this equation at long times (no surface renewal) where k would be proportional to £ and Sherwood number would be independent of Schmidt number. The "penetra- tion" model first introduced by Higbie®® and later extended by Danckwerts®® corresponds to the asymptotic solution at short times where k would be proportional to &/ 2 or Sh ~ Sc 2. Depending on the distribution of contact times between the eddies and the surface, the transfer may take on characteristics of either or both of the above. King®® generalized this approach to include turbulence effects by replacing Equation (4) with Q/ C [(8+u) &1, o oqu e where o is an eddy diffusivity which he arbitrarily let vary with dis- tance from the surface as This model approaches the same asymptote (Sh ~ Sc*/ ?) at short times but different asymptotes at long times depending on the value of b (with b = 3, Sh~ 8c°"3%; with b = 4, Sn ~ 8c°°%9), To establish an overall mass-transfer rate, it is necessary to assign a frequency with which the surfaces are "renewed" {or the distri- bution of eddy ages). The different extensions and modifications of this model mostly involve the choice of different functions to describe the randomness of the eddy penetrations, None of these models give significant information as to the effect of bubble size, conduit size, or Reynolds number. They are mechanistically unsatisfactory because the 1k hydrodynamic effects are often ignhored or included by relating the eddy age distribution in some way to the flow field. For example, Lamont and Scott’® assumed that the fractional rate of surface renewal, s, (k ~'VQE3 is given by s ~ Re J? . There is really no clear-cut way to establish a relationship between the rate of surface renewal and the hydrodynamics and, consequently, there is a heavy reliance on empiricism. The original intent of these models was to describe transfer to a surface (bubble) that has a distinct steady flow relative to the liquid. Modeling of the Eddy Structure If the fluid velocity field in the vicinity of the interface could be completely described, then the computation of transfer rates, in principal, would be straightforward. However, at the present time, there are no satisfactory descriptions of the details of a turbulent veloclty field and even if such were available, the mathematical account- ing of the differential transfer processes might become intractable. Consequently, there have been idealizations of the eddy structure with, admittedly, unrealistic fields and mass-transfer behavior has been conm- puted based on these idealizations., Lamont's work'® provides an excellent example of this approach. He modeled the eddy structure by considering individual eddy cells that have a sinusoidal form at a sufficient distance away from the interface (corresponding perhaps to an individual component of a Fourier decompo- sition of the turbulent field). As the interface is approached, viscous forces dampen the eddy cell velocities by an amount that depends on the 15 interfacial condition (mobile or rigid). Lamont calculated the mass- transfer coefficient for an individual eddy cell as a function of the daéfiing condition, fluid properties, the wave properties, and the eddy energy. He then used a Kovasznay distribution function for the energy spectrum and summed over a range of wave numbers to obtain the overall coefficient, The results of this procedure were k ~ (SC)—l/ 2 (emv)l/ 4 for a mobile interface and k ~ (Sc)~¥3 ufiflfl4 for a rigid interface, | Using Equation (1), these give gh ~ Scl/ 2 Re-89 and Sh ~ Scl/ 3 Ref- 69 , respectively. The present writer feels that this approach may represent a bridge between surface renewal models and turbulence theory and as such deserves particular mention, Turbulence Interactions Some authors have attempted to analyze the forces and interactions between spheres and fluid elements in a turbulent field to arrive at equations for the fluctuating motion of the spheres. These equations are solved to obtain a "mean" relative velocity between the bubble and the fluid which is then substituted into a steady-flow equation (usually of the Frossling type) to establish the mass-transfer coefficients. The work of Levich®® is of this nature and Peebles® used this approach in 16 his document. For example, Peebles used the result of Hinze®’ for small gas bubbles FrE=3.hF g which essentially comes from an integration of the equation dv dv d 2 g rd? L where W is an added mass coefficient for an accelerating spherical bubble. The relative velocity is then Peebles used the approximations A/'vflz ~ V JF/2 8nd £ ~ Re”l/ B in the above which were then substituted into Frdssling type equations to obtain Sh ~ Re®*%® 8¢/ 2 (4/D)"* 2 for a mobile interface and Sh ~ Re®*%® get @ (a/D)™Y 2 for a rigid interface. In a similar computation which included Stokes law to describe the drag experienced by the bubble, Levich®® obtained for a mobile interface Sh ~ Re¥ % gel/ 2 | Dimensional Analysis (Empiricism) some workers have chosen to postulate the physical variables that may be controlling and have used standard dimensional analysis techniques for ordering the experimental data, The paper by Middleman38 is a splendid example of this approach as applied to agitated vessels. Also for agitated vessels, Calderbank and Moo-Young'® used dimensional anaiysis to obtain Equation (2) and Sherwood and Brian'”’ dimensionally related shb/Sc:l/B to [emd4/v3 1 s, 17 Also included under this category is a most interesting correlation by Figueiredo and Charles!® for a heterogeneous pipeline flow of settling particles. They used an expression for the ratio of pressure gradient for flow of the suspension to the pressure gradient for flow of the liquid alone and assumed that, if altered by the ratio d/D, it could also represent the ratio of mass-transfer coefficients for the particles to those for transfer from the liquid to the pipe wall. They found that they could, indeed, use this ratio to correlate their data for a settling suspension with the data of Harriot and Hamilton.3° Discussion It is seen that the theoretical description of mass transfer to bubbles in cocurrent turbulent flow has by no means been standardized. There seems to be somewhat general agreement as to the effect of Schmidt number, The Sherwood numbers for cases of completely rigid interfaces with zero tangential velocity at the surface (no slip) applicable to solid spheres, very small bubbles, and bubbles with surfactant contami- nation in the interface are generally predicted to vary with Schmidt number to the one-third power. Completely mobile interfaces (negligible tangential stress with non-zero interfacial velocity) are generally pre- dicted to yield a Sc'/ ? variation of Sh. There is only scant and inconsistent information predicting the effects of bubble and conduit diameter. For example, Levich predicts no effect of d/D while Peebles predicts Sh ~ (d/D)"Y =, There is general disagreement as to the effect of Reynolds number as evidenced by the fact that exponents have been predicted that range 18 from 0,45 to > 1, These different exponents may not be mutually exclusive however because an inspection of the experimental data shows disagreement in the measured exponents also, It may be that the proper application of these equations depends on suitable evaluation of the conditions of the experiment. CHAPTER IIT DESCRIPTION OF EXPERIMENT This experiment was designed to measure liquid phase controlled mass-transfer coefficients for cocurrent pipeline flow of turbulent ligquids with up to 1% volume fraction of small helium bubbles having mean diameters from 0.0l to 0,05 inches. The liquids chosen were five mixtures of glycerine and water (0, 12.5, 25, 37.5, and 50% by weight of glycerine) each of which represent a different Schmidt number. The physical properties of these mixtures, obtained from the literature,E’5 are shown graphically in Appendix A and the values used in this study for the given mixtures are listed in Table IIT. Transient Response Technigue A closed recirculating system was used in which helium bubbles were introduced (generated) at the entrance of a well-defined test section and removed richer in oxygen at the exit, allowing only the bubble-free liquid to recirculate, The products of mass-transfer coefficients and interfacial areas were measured by a transient response technique in which the system was initially charged with dissolved oxygen. The oxygen was then progress- ively removed by transfer to the helium bubbles while the oxygen concen- tration was continuously monitored as a function of time at a single position in the system. For a test section of length, L, and cross-sectional area, A, it can be shown (Appendix B) that the ratio of exit concentration to inlet 19 Table III. Physical Properties of Agqueous-Glycerol Mixtures (25°C) Data of Jordan, Ackerman and Berger®® Molecular Glycerol Henry's Law Diffusivity of Schmidt Content Density, p Viscosity, u Constant, H Oxygen, & x 10° Modulus, Sc (wt %) (1b/££>) (1b/ft ohr) (atmeliters/mole) (£t2/hr) (Dimensionless) 0 62, 43 2.15 795, 1 8.215 hi9 12.5 6L, 43 3,07 1127.6 12.865 370 25 66, 49 L, 62 1421,0 9, 261 750 37.5 67.67 6, 3k 1621, 8 L, 650 2015 50 69. 86 10.82 2011.1 4,495 3446 Oc 21 concentration, Ce/ci’ is a constant, K, given by - + e K = Ce/Ci = 3%71;17— ’ (5a) where RTQ 4 and B = kaAL(1l + v) 3, . (5b) In the absence of axial smearing, each time the fluid mekes a com- plete passage around the closed circuit (loop transit time, v, = VS/QE) the concentration at the measuring position would (ideally) decrease instantaneously from its value, C, to a value equal to KC. Therefore, in actuality, the ratio, C/CO, of the concentration at any time to that at an initial reference time {set equal to zero) would be given by c/C_ = Exp IZ ——L—(‘Q’”f t } = Exp ;—— -————(@ns)%t } : L L S . Therefore a plot of @?(C/CO) versus time would be a straight line of slope -(&EK)Qz/VS. Note that the absolute value need not be measured because a signal that is merely proportional to the oxygen concentration would have the same slope. If the system volumé, VS, and the liquid volumetric flow rate, Q,, have been measured, the constant K can be E’ extracted from the slope of the measured transient. Having a measure also of gas volumetric flow, Qg, and the system absolute temperature, T, and knowing R, Hy A, and L, the product, ka, can be obtained from K through Equations (5). If an independent measure is also made of "a," then the mass-~transfer coefficients are fully determinable, 22 This technique was selected as being superior to a once-through test that requires an independent measurement of the oxygen concentra- tion at both ends of the test section for reasons illustrated by the following comparison. Tn a once-through system with a 37.5% mixture and conservative values of Qg/Qz = 1%, bubble mean diameter = 0,01 inches, Reynolds number = 6 x 10%*, and a mass-transfer coefficient of 0.7 ft/hr, a test section length of ~100 feet would be required to obtain a concentration change across the test section of only' ce/ci = 0.9 . At this level a small error in the concentration measurement would be magnified in the determination of ka. In contrast, the same conditions in a transient test with only a 25-~ft-long test section would give a concentration change of C/Cofv O.1 in only about seven minutes — greatly reducing the error magnification in ka. In return for this benefit, the values of total system volume, Vs’ and the time coordinate, t, need also to be measured, These, however, are parameters that can be measured very precisely compared to the concentration measurement. Therefore, the transient tests should result in more reliable data. On the other hand, the concentrations in once-through tests are measured at specific locations that bracket the region of interest and only the transport behavior within that region is important. Whereas in the transient tests all mass transfer occuring outside the test section ig extranecus and represents an "end effect" contribution that must be independently measured and accounted for in determining the "ka'" product. This "end effect," which would include mass transfer occuring in the 23 bubble generating and separating processes, represents the most serious disadvantage and error source in the transient measurementé. The measurement and accounting for the "end effect” are discussed further on page 47, Apparatus In constructing the main circulating systems of the experiment exclusive use was made of stainless steel or glass hardware and all gaskets were Teflon. This was part of careful measures taken to keep the system free of contamination. Figure 1 is a photograph of the facility with the test section mounted in the vertical orientation and Figure 2 is a diagram of the main circuit portion. Figure 28, page 121 (Appendix C) is an instrument application drawing of the system which includes an auxiliary flow circuit used for rotameter calibration and for special tests, The main circuit consisted of a canned rotor centrifugal pump, three parallel rotameters, a heat exchanger, three dissolved oxygen measuring sensors, a helium flow and metering system, a bubble generator, the test section, a bubble separator, a photographic arrangement for determining the bubble interfacial areas and mean diameters, and a drain-and-fill tank equipped with scales for precise determination of the weight percent of glycerine in the mixture., Further descriptions of individual components are given below. Pump The main circulator was a 20 HP Westinghouse "100-A" canned rotor constant speed centrifugal pump capable of delivering about 100 gpm at s Figure 1. Photograph of the Mass Transfer Facility. FILL AND DRAIN TANK _SCALES ORNL-DWG 70-11420 ~=— TEST SECTION ~ 36 ft LONG VERTICAL ORIENTATION ~PHOTO PORTS CAMERA FLASH g;)LOOP PRESSURE BUBBLE GENERATOR INLET (LOOP PRESSURE REGULATION FROM HELIUM BOTTLE) BUBBLE SEPARATOR 2 in. PIPING /- = HEAT EXCHANGER Vol LOOP TEMPERATURE 120 40 gpm gpm gpm CANNED ROTOR PUMP MSBR-Mass Transfer Loop. Figure 2. Schematic Diagram of the Main Circult of the Experimental Apparatus. G2 26 about 180 feet of head, The motor cannings, housing, and impeller were stainless steel and the bearings were graphitar — lubricated solely by the loop fluid. An auxiliary circuit required to cool the pump motor windings circulated transformer oil through the windings and through an external circuit containing an auxiliary oil pump, a filter, and a small water-cooled heat exchanger. The pump was safety instrumented to turn off on loss of pressure in the oil circuit or on high temperature of the motor housing. Liguid Flow Measurement The liquid flow rate was controlled by three parallel stainless steel globe valves downstream of the pump at the entrances to the rota- meters. Three parallel rotameters of different capacities (100, Lo, and 8 gpm) were used for measuring liquid volumetric flow rates. By judicious use of the rotameter scales, parallel rotameters provide greater precision when measurements are required over a wide flow range. In each experiment, however, some flow was allowed to go through each rotameter to prevent having regions that might "lag" the rest of the loop during the transient tests and thereby become concentration "capacitance" volumes. Because of the large differences in viscosities over the range of glycerine-water mixtures used, the rotameters were calibrated, in place, for both water and a 50% mixture. These calibrations were obtained by the use of two identical 6-inch-diameter, 6-feet-long glass tanks in the auxiliary circuit valved together in such a way that, while one was being fillied, the other was being drained. Changing the position of one lever reversed the pfocess before the liquid could spill cver the top. 27 The time required to fill (or empty) a known volume of either of these tanks was measured over the entire range of each rotameter. These cal- ibrations are given in Appendix D. Since there was only a small.difference in the‘calibration between 0 to 50% glycerine, the flow for in-between mixtures was determined by linearly interpolating between the two curves according to the viscosity. Temperature Stabilization The fluid temperature was measured at the inlet and exit of the test section by standard stainless steel sheathed chromel-alumel thermocouples immersed in the fluid., The friction and pump heat were removed and the test section temperature held at 25°C for all tests by a stainless-steel, water-cooled, shell-and-tube heat éxchanger. Gas Flow Measurement Helium for generation of the bubbles was obtained from standard commercial cylinders metered through a pressure regulator, a safety relief valve, and a flow control needle valve. The rate of helium flow was determined by measuring both the exit pressure and the pressure drop across a 6-foot length of tubing of about l/l6-inch internal diameter. These‘measurements were made with a Bourden type pressure gage and a water-filled U-tube manometer, respectively. Calibration at atmospheric conditions was obtained prior to opera- tion by comparing with readings from a wet-test meter timed with a stop watch., The calibration at 50 psig exit pressure (normal operating con- dition) is given in Figure 33, page;lET(Appendix D), The calibration 28 and the leak tightness of this system were checked periodically over the course of the experimental program. Dissolved Oxygen Measurement Two identical commercially available "Polarographic" type instru- ments were used to measure the dissolved oxygen concentration (Magna Oxymeter Model 1070, Magna Corporation-Instrument Division, 11808 South Bloomfield Avenue, Santa Fe Springs, California). Two were used so that an automatic continuocus check was provided by comparing the readings of one with the other. It was felt unlikely that both would use up their electrolyte or fail simultaneously. These Instruments used polar- ographic type sensors inserted into the flowing liquid through penetra- tions in tees provided for that purpose. Electrical signals produced by the sensors were fed through recording adaptors and the resulting millivolt signals recorded on a Brown Multipoint recorder having a measured chart speed of 1.18 inches/sec, Bach sensor assembly consisted of an electrolytic cell made up of a cathode, anode, and an electrolyte mounted in a plastic cylindrical housing., The end of the housing, containing the cell, was encased in a thin oxygen-permeable Teflon membrane which also acted to contain the electrolyte. The dissolved oxygen is electrolytically reduced at the cathode causing a current to flow through the system from cathode to anode., The magnitude of this current is proportional to the oxygen concentration if sufficient liquid velocity exists (~2 ft/sec) to pre- vent concentration polarization at the membrane, 29 The response times for these instruments are greater than 0% in 30 seconds. An analysis showing that this response produces an accept- able error in the transient tests is given in Appendix E. Since the transient response technigque used in these tests requires a signal that is merely proportional to the oxygen concentration, an absolute calibration of these instruments was not necessary. Neverthe- less calibration tests were made for two different mixtures of glycerine and water by bubbling air through the mixtures at different pressures until they became saturated. Knowing the solubility of oxygen in the mixtures, the meter reading could be set on the calculated concentration for an initial "set-point" pressure and subsequent readings at different pressures compared with calculated values (assuming a Henry's Law rela- tionship). Calibrations obtained in this manner are shown on Figure 34, page 128 (Appendix D) which includes readings made with a third instru- ment similar to the Magna instruments but made by a different company. The response speed of this third sensor proved to be slow compared to the Magna sensors and consequently it was used only as an independent monitor on the operability of the Magna sensors throughout these experi- ments, Bubble Generation Special apparatus was required that could generate a dispersion of small bubbles whose mean size could be controlled énd varied over the range 0,01 to 0.05 inches independently of the particular liquid mixture beifig used and of the flow rates of gas and liquid. Two devices con- sidered and discarded as being inadequate were (1) a fine porosity fritted glass disc through which the gas was blown into the liquid, and 30 (2) two parallel stainless steel discs, a rotor and a stator, each equipped with intermingling blades. The gas-liquid mixture flowed between the blades and the gas was broken into fine bubbles by the shearing action. The bubble generator designed and developed for this project 1is shown diagrammatically on Figure 3. The liquid flowed through & con- verging diverging nozzle with a l-inch-diameter throat and a 2-inch- diameter entrance and exit. The section downstream of the throat diverged at an angle of about 12 degrees. A central "plumb-bob" shaped probe of maximum cross-sectional diameter of ~0.812 inches was movable and could be centrally positioned anywhere in the diverging section including the throat and exit. This probe was supported by a tube which carried the gas into the system. The tube, in turn, was supported by a "Swagelok" fitting penetrating a flange on the end of the straight leg of a tee connected to the nozzle entrance, Four small positioning rods near the throat centered the probe within the nozzle and helped support it. They also acted as holders for a section of "honey-comb" straighten- ing vaneg used to minimize the liquid swirl induced by the right angle turn at the tee entrance to the nozzle, Gas entered the liquid through 48 holes (1/64-inch-diameter) around the probe periphery at its maximum thickness and exited as a series of parallel plumes which were broken intc individual bubbles by the turbu- lence in the diverging section of the nozzle. The mean bubble gize for a given flow and mixture was controlled by the position of the probe within the nozzle (the closer the probe was to the throat the smaller the mean bubble size produced). 31 ORNL-DWG 71-8017 2 SITION AND SUPPORT RODS THROAT 4in. LIQUID FLOW STRAIGHTVEAN!NG NE Q.812 in. 48 HOLES, 1/64 in. DIAM GAS FLOW ~— = -we— 41/2———-{ Figure 3. Diagram of the Bubble Generator. 32 Bubbles generated by this device were found to follow closely a size distribution function proposed by Bayens56 and previously used to describe droplet sizes produced in spray nozzles. The function, defined as £(6§)d8 = that fraction of the total number of bubbles that have diameters, &, lying in the range & * 1/2 dé, is given by £(8) = b (/MY 2 82 Exp (-6?) (6) in which | o = [h/w/68]¥ 2 | This function has been normalized so that o [ f(s8)as =1 . o An indication of the suitability of this distribution function is given in Figure U4 where measured cumulative size distributions for bubble populations produced by the bubble generator are compared with the distributions calculated from the function at different liquid flows and different ratios of gas to liquid flows. The measured distri- butions were obtained by painstakingly scaling the sizes of a sufficient number of bubbles directly off photographs taken of the bubble swarms at each condition., These measured areas should be accurate within about 10%. The range of mean bubble sizes capable of being produced by this bubble generator were measured at a constant gas-to-ligquid volumetric flow ratio, Qg/Qz’ of 0.3% at different liquid flow rates, different mixtures of glycerine and water, and different probe positions. The results are shown on Figure 29, page 123 (Appendix D). The mean PERCENT LESS THAN d 33 ORNL-—-DWG 74-7999 99.9 v ( | | | T | { 998 N BUBBLE DIAMETER — 00 5 |l v CUMULATIVE DISTRIBUTIONS ' / A { CALCULATED® MEASURED ] 99 w1 A — v / P p a x10”" SYMBOL Q_ (gpm) Qg/Q_ (%) 98 VH—ar—tF 1 00789 o 20 0.5 — / '. 2 01667 ® 40 0.3 a5 fall | 3 04359 A 80 05 ] o ¥ é A’/& e 4 04981 A 60 03 90 oY 4 / 5 0.8325 7 40 oA — // 7/ ® 6 1.9024 v 60 04 L 80 fi o — n v }{ / /2 CALCULATED FROM ASSUMED DISTRIBUTION FUNCTION -0 / / ‘ ;//’ @ ;1) ; / o / Nt/2 2 L 20 7 /] 1/ o £(d) = 4(%) 4" EXP (-ad?) // /© B 7 ./-"' N 2/3 1 fi/ ./ (/ WHERE o = [——-——4 5 ] 20 T CP | 10 b /Ff N = THE NUMBER OF BUBBLES PER UNIT VOLUME 7 — A —0F @ = THE VOLUME FRACTION OF BUBBLES — 5 E j/f - - g si?zimf_dm L o 2 v f 0.01 002 0.05 o1 0.2 0.5 1 2 d, BUBBLE DIAMETER (in) Figure k4, Comparison of Measured Bubble Sizes with the Distribution Function. 3k diameter used throughout this report is the "Sauter" mean defined by - 83 £(8)ds ., 2o D IOT . Vs @ jo 52 £(8)as which is the volume-to-surface weighted mean commonly used in mass- transfer operations. Bubble Separation Since this project uses the transient mode of testing, bubbles that recirculate and extract dissolved oxygen from the liquid in regions out- side the test section constitute an error source in the measurements. Consequently a high degree of separation is desirable for this method of testing. Some technigues considered were (1) gravitational separa- tion in a tank, (2) centrifugal separation through the use of vanes to induce a strong vortex, and (3) separation by flowing through a porous metal which might act as a physical barrier to the bubbles; Each of these had shortcomings that prevented their use in this project. For example, with gravitational separation the tank size required for the viscous mixtures was pondercusly large. This increases the system volume resulting in a "sluggish'" loop and an accompanying increase in the measurement error. With centrifugal separation there were problems in stabilizing the gaseous core of the vortex over a wide range of operating conditions. In addition, large by-pass of bubbles (inefficient separation) was observed and there was too much liquid carryover through the gas removal duct. 35 The porous physical barriers tested required large frontal areas or had prohibitive pressure drops, and the bubbles were observed to regularly penetrate these barriers, A satisfactory separator was finally developed that combined fea- tures of each of the above. A diagram of this separator is shown on Figure 5. The liquid-bubble mixtures entered the bottom of a 6-inch- diameter pipe. A series of plexiglas vanes Jjust beyond this entrance created a swirl flow within the tank which tended to force the bubbles to the middle. The spinning mixture flowed upward into a converging cone-shaped region with sides of 500-mesh stainiess steel screen, When wetted by the liguid, the screen acted as a physical barrier to the bubbles but allowed the liquid to pass through. The liquid exited from the separator while the bubbles continued to rise through the truncated end of the conical screen to an interface where the gas was vented through a small exit line. The system pressure level was also con- trolled at this interface by providing an auxiliary sweep of helium through the exit line, Good separation was achieved with this apparatus over the test con- ditions of this thesis., No bubbles could be detected in photographs teken downstream of the separator. However, with the use of a light beam, some bubbles that appeared to be smaller than the screen mesh size could be detected visually. After passing through the pump and entering a higher pressure region these bubbles apparently went into solution because they could no longer be visually detected downstream of that region. If indeed they did go into solution along with their small amount of extracted oxygen, they would have hardly constituted 36 ORNL—-DWG 71-8016 SYSTEM PRESSURE CONTROL =~ - = — -== GAS OUT i ~— |~ 2' g—- LIQUID OUT i 500 MESH CONICALLY SHAPED 6 1/2 STAINLESS STEEL SCREEN — e —— SWIRL GENERATOR | IN 2 —__ AND GAS S — Figure 5. Diagram of the Bubble Separator. 37 a gignificant error in the mass-transfer measurements. Nevertheless, several "special" tests were made in which about 10% of the normal gas flow was purposely introduced downstream of the separator and allowed to recirculate. The measured rates of change in loop concentration under these conditions were always less than 3% of the normal rate and the effect of the apparently much smaller amounts of by-pass therefore were felt to be acceptable, This separator was the major factor in limiting the ranges of Reynolds numbers that could be obtained in this system. For a given mixture, as flow was increased a flow rate was eventually reached at which there was an observed '"breskthrough'" of many large bubbles that would continue to recirculate. At this level of flow it was necessary to terminate the tests with the particular mixture, In addition to the flow limiting aspect of the separator, an unexpected large amount of mass transfer occurred there — probably due to the energy dissipation of the swirl and the relatively large amount of contact time between the liquid and gas. Consequently a larger than anticipated "end effect” resulted that had to be accounted for in deter- mining the mass-transfer coefficients applicable to the test section only. This correction resulted in decreased reliability of the results. Test Section The test section was considered as that portion of conduit between the bubble generator exit and the entrance of an elbow ieading into the separator entrance pipe (see Figure 1, page 24). It consisted of five sections of 2-inch-diameter conduit flanged together with Teflon gaskets. As encountered in the direction of flow these were a L4-foot-long section 38 of glass pipe, a 1l0-foot-long section of glass pipe, a 6 l/2-foot-long section of stainless steel "long-radius" U-bend, another 10-foot-long section of glass pipe, and a 5-foot-long section of glass pipe, for a total of 35 1/2 feet of length. The test section and bubble generator were connected to the rest of the loop piping through the bubble gener- ator tee at the entrance and an elbow at the exit which served as pivot points to permit the test section to be mounted in any orientation from horizontal to vertical. Bubble Surface Area Determination — Photographic System The mean sizes and interfacial areas per unit volume of the bubble dispersions were determined photographically using a Polarold camera and two Strobolume flash units. To reduce distortion the photographs were taken through rectangular glass ports fitted around the cylindrical glass conduit and filled with a liquid having the same index of refrac- tion as the glass. The port for "inlet" pictures was located about one foot downstream from the bubble generator exit and the "exit" port was located about two feet upstream from the test section exit. The Polaroid camera was equipped with a specially made telescopic lens that permitted taking photographs in good focus across the entire cross section of the conduit. The camera was semi—permanently mounted onto the facility structure in such a manner that photographs could be taken at the "inlet" port and then the camera pivoted for taking a sub- sequent picture through the "exit" port. For vertical orientation of the test section, photographs were taken directly through the ports, 39 For horizontal tests, the camera remained in its "vertical orientation” position and the photographs were taken through high quality front sur- face mirrors. With the camera focused along the axis of the conduit, bubbles closer to the camera appear larger and those further away appear smaller. To determine the magnitude of this possible error source, small wires of known diameter were mounted inside the conduit across the cross section, Photographs obtained after focusing on the central wire indicated less than one percent maximum error in the apparent diameter reading. The Strobolume flash units (one for each port) produced pictures of best contrast when mounted to provide diffuse back lighting in which the lights were aimed directly into the camera lens from behind the photo ports., Semi-opaque "milky" plexiglas sheets between the lights and the photo ports served as the light diffusers. Bubble diameters could have been scaled directly off the photographs for each run and used to establish the interfacial areas and mean diame- ters Jjust as was done to validate the bubble size distribution function. However, this proved to be such an onerous and time-consuming procedure that it would have been prohibitive due to the large number of experi- mental runs and need for at least two photographs for each run, Conse- quently, the following use was made of the distribution function, The interfacial area per unit volume is defined as ag ” N 82 £(8) as (8) O and the bubble volume fraction is given by 6 = | T8 a6y g =] = - Lo Recalling the definition of the Sauter mean diameter, Equation (7), it is seen from the above that, regardless of the form of the distribution function, the interfacilal area per unit volume can be expressed as . (9) Q—-|O\ o1 a Vs For the distribution function of Equation (6), Equation (8) may be inte- grated to give a8 = ny N\ 2 <€E> 31\11/3 3% 3 = L, po NV 3 ¥ 3 | ' (10) Therefore, by measuring the volume fraction, ¢, it was only necessary to count the number of bubbles per unit volume from the photographs and use Equation (10) to establish the areas. Equation (9) was then used to determine the mean bubble diameters. Counting the number of bubbles in a representative area of the photographs was a considerably easier task than measuring the actual sizes of each bubble, However, it was then necegsary to have an independent determination of the volume fraction occupied by the bubbles, Hughmarks4 presented a volume fraction correlation that graphically related a flow parameter, X, defined from pQ | | ;‘é"=1"9—<-%> (11) g'g e = (Re)V ® (Fr)¥ e /vy * to the parameter 3 il where B vaa,/e,+a) . For p >> D2 Equation (11) reduces to 3 =X Qg/QJz . (12) bl Hughmark's correlation for X at sufficiently large Z is nearly flat with X changing from 0.7 to 0.9 over a 10-fold change in Z. For the conditions of the experiments in this report, X was considered to be constant at an average value of 0,73. When volume fractions were measured in the vertical flow tests, it was found that 3 = 0.73 Qg/% gave a good measure of the mean value for a given test but that the volume fractions were sometimes considerably smaller than this in the riser leg of the test section and, at the same time, comparably larger in the downcomer. It was apparent that this difference was due to buoyancy driven relative flow between the bubbles and the liquid., Separate volume fractions were therefore determined for each leg based on a mass balance, This mass balance between the riser and downcomer sectionsg in a constant area conduit takes the form () = (W), Letting Vr =V + Vb and Vd = V‘—'Vb then vV + Vb @d/@r = Nd/Nr = v——_'_—vb- . (13) The bubble terminal velocity, Vb, depends on the bubble Reynolds number, Re (= Vbdvs/v). Lo If Reb < 2, then Stokes law results in 2 - . a® &lp — o ) b~ 184 * If Re, > 2, then V. is determined from a balance between the drag b b 2 2 3 force [(Cde b/EgC)(nd VS/M)] and buoyancy (pmd vsg/gc6) to be i/ = e [o0e = = A ’ b 3 Cd ] wherelthe drag coefficient, Cd’ is given by _ 0.8 Cd = 18.5/Reb . It was further assumed that the average of the riser and downcomer volume fractions could be calculated by @r + @d ) ~—=0.730a/q, . (1) Then with iterations to establish dvs’ Vb’ and Reb, Equations (13) and (14) were solved to determine the individual leg vertical flow volume fractions, and Equation (10) was used to establish the interfacial areas per unit volume, The averages were used to extract the mass-transfer coefficients from the ka products. As a further indication of the accuracy of the distribution function and the validity of this technique for establishing the vertical flow surface areas, Figure 0 compares some surface areas determined as out- lined above with the areas measured directly from the photographs. The experimental conditions for the run numbers identifying each point are listed in Table IV. In horizontal flows the volume fractions were the same in each leg but stratification of the bubbles near the top of the conduit, especially ORNL—DWG 71-—8000 ac, CALCULATED INTERFACIAL AREA PER UNIT VOLUME (in~h 2.0 VERTICAL FLOW IN 2-in. DIAMETER CONDUIT 19 = 4, = INTERFACIAL AREA MEASURED DIRECTLY FROM PHOTOGRAPHS 18 |- ' a, = 4.22 N3 $2/3 (FROM DISTRIBUTION . FUNCTION) WHERE N = NUMBER OF BUBBLES PER UNIT 16 |- VOLUME TAKEN FROM PHOTOGRAPHS ® = VOLUME FRACTION OCCUPIED BY 5 | THE BUBBLES THE NUMBERS IDENTIFYING THE DATA POINTS ARE 1.4 |— RUNS FOR WHICH CONDITIONS ARE LISTED ELSEWHERE 3 L, +20% . ]_ / / .2 / 1 0217 e 53 J/~20% 0.9 , 08 ’ 0.7 0.6 05 ‘ 0.4 / / o /7 0.3 o1 f 27 (£ 02 |—85 100 01 (= 76 0 0 0.2 0.4 06 0.8 1.0 $.2 1.4 am, MEASURED INTERFACIAL AREA PER UNIT VOLUME (in7h Figure 6, Comparison of Interfacial Areas Per Unit Volume Measured Directly from Photographs with Those Established Through the Distribution Function. Vertical Flow. iy Table IV. Experimental Conditions for Runs Used to Validate Surface Area Determination Method for Vertical Flows Mixture Run No Qfl (gpm) Qg/QE (%) (% glycerine) 71 20 0.5 0 73 20 0.1 0 76 20 0.1 0 83 4o 0.5 0 85 Lo 0.1 0 87 Lo 0.3 0 91 60 0.1 0 92 60 0.5 0 93 60 0.3 0 100 80 C.1 0 10k 80 0.5 0 119 20 0.5 50 130 L0 0.5 50 142 10 0.5 50 155 50 0.3 50 162 20 0.5 37.5 165 30 0.5 37.5 171 Lo 0.5 7.5 198 4o 0.5 37.5 213 20 0.5 37.5 217 4o 0.5 37.5 L5 at low flows, invalidated the use of Equation (14). It was found possible however to correlate the horizontal flow volume fractions at Qg/Qz = 0.3% with the ratio, v/vb, of the axial liquid velocity to the bubble terminal velocity in the liquid. Figure 7 with the identification of the randomly selected runs given in Table V, This correlation is shown in Table V, Experimental Conditions for Runs Shown on Horizontal Flow Volume Fraction Correlation . Mixture Run No. %Y (gpm) % (inches) (% glycerine) 376 35 0.033 50 390 50 0.028 50 382 L0 0.059 50 389 50 0.024 50 391 30 0. 037 50 365 60 0.026 0 355 20 0.049 0 370 30 0,01k 50 368 70 0.01k 0 400 30 0.066 37.5 Lok 35 0.061 37.5 ele 55 0.026 37.5 Lo7 60 0.030 37.5 For V/Vi) less than 30, a least squares line, § = 0.0018 + 0.021/(V/V.) was used while for V/Vb greater than 30 a constant value, ¢ = 0,0025 2 (15) was used. Severe stratification prevented experimentation at values of V/Vb less than about 3. BUBBLE VOLUME FRACTION &, 0.010 0.009 0.008 0.007 0.006 0.005 0.004 ©.003 0.002 0.001 Figure 7. L6 ORNL-DWG 71-8001 VOLUME FRACTION CORRELATION HORIZONTAL FLOW IN A 2-in. DIAMETER CONDUIT Qq/QL = 0.3% - MEASURED FROM PHOTOGRAPHS V/Vp = 0.0188 Q_(u/p)°°1%/a,s"27 WHERE Q_ = gpm @ = Iby/ft-hr 3 p = Ibm/ft3 dys = inches | 355 | @400 ‘ i ® = 0.0018 + 0.021/(V/Vy) LEAST SQUARE LINE FOR DATA WITH V/Vp <30 404 @ 382 376 @427 \OA365 | \42 389 370 — @O e O D) e N O 390 368 391 GLYCERINE (%) 0O 50 375 NUMBERS IDENTIFYING DATA POINTS ® : ARE RUNS LISTED ELSEWHERE A 0 ' i 0 10 20 30 40 50 60 RATIO OF AXIAL TO TERMINAL VELOCITY (V/Vp) Correlation of Horizontal Flow Volume Fraction. 70 b This horizontal flow volume fraction correlation in conJunction with Equation (10) was used to establish the horizontal flow interfacial areas per unit volume. An indication of the adequacy of this procedure is given in Figure 8 in which calculated and measured areas are compared for the runs identified in Table V, End Effect In the transient response mode of operation all mass transfer occuring outside the test section (principally in the bubble separator and generator) must be independently measured and accounted for in establishing the ka products applicable only to the test section. "End-effect" measurements were made after all other scheduled tests were completed by moving the bubble generator to a position at the test section exit which allowed the bubbles to flow directly from the genera- tor into the separator — effectively by-passing the test section. All tests were then repeated duplicating as nearly as possible the original conditions. With the end-effect response‘so measured, the correction was determined as follows, Consider three regions of mass transfer in series representing the bubble generator (Region 1), the test section (Region 2), and the bubble separator (Region 3). The original measurements, indicated here by & subscript "I," determined the ratio, Kps of the outlet to inlet concen- ‘tration across all three regions. Therefore KI=K1 Kg Ks 3 where K,, K5, and K5 are the outlet and iniet concentration ratios across the individual regions. 1.9 1.8 1.7 ‘l-'—: 1.6 £ 15 = _ 1.4 o > - 1.3 = - 942 a 5 1.1 R TR (16) The turbulent inertial force exerted on a bubble essentially traveling at the local fluid velocity in a turbulent liquid is not so easily determined., Consequently, use was made of dimensional arguments. In a turbulent fluid the mean variation in velocity, AV, over a distance, \, (greater than the microscale) is given dimensionally by . /3 ;E:?tg 1 where €, is the power dissipation per unit volume, The 1/3 power on A agrees with the result of Hinze (Reference 37) for the variation in tur- bulent intensity required to result in the Kolmogoroff spectrum law, Similarly, the period, 6, for such velocity variations is given dimen- sionally by 3 e ii”' A.g 1/ e Following Levich,86 it is postulated that the mean acceleration al undergone by a fluid element of size, X, is e g8 \¥3 0 =&V [ Xc z @ A dt 0 : £ 58 A spherical fluid element with this mean acceleration must have experienced a "mean" force given by 3 ¥s sz NFWK ('VC> A It is further postulated that a bubble of diameter, d, in the turbulent ligquid will be subjected to the same mean forces as those exerted on a fluid element of the same size. Therefore the mean turbulent inertial force on the bubble is given by 3 .~-%— Vc. /a3, (17) Dividing by Equation (16) the ratio of inertial forces to gravitational forces is given by ' % 3 F./F [ / &/ 3g (18) e\ ’ For flow in conduits, the power dissipation per unit volume can be expressed as =y 9P e, =V 5 (Reit/Do) £ dx and the pressure gradient can be determined from the Blasius relationship, aP £ oV® 2 3 2 = = D——P—ggc = (f p3/2g_ D® p) Re Using the friction factor for smooth tubes, f = 0.316/(Re)¥ ¢ , the power dissipation per unit volume is e = <——O'316\—-——“8 Rell/ %, (19) v Egc / p2D4 59 Substitution into Equation (18) and replacing the bubble diameter by the Sauter mean gives -~ ! 3 11/ 4 12/:3 F/F NJO.316}.L Re /d1/3 g . (20) i'Tg | Vs L 2% D* Since Equation (20) was established on dimensional grounds, there exists a proportionality constant of unknown magnitude. To establish the value that the ratio should have to serve as a criterion for deter- mining when horizontal and vertical flow mass-transfer coefficients become identical, use was made of the data of Lamont gathered from his report as listed in Table VI below. Table VI. Conditions at Which Horizontal and Vertical Flow Mass Transfer Coefficients Become Equal (Lamont's Data)l? Case I Case IT Conduit Diameter, D (inches) 5/16 5/8 Reynolds Modulus, Re 10% 3 x 10*% Liquid Viscosity, u (centipoise) 0.89 0.89 Liquid Density, o (g/cm®) 1.0 1.0 Bubble Diameter, d (inches) ~5/32 ~5/32 Substitution of the data of Case I into Equation (20) gives Fi/Fg = 1,5 As a check the data of Case II are compared, ; 11/ 6 N 8/ 3 (Fi/Fg)I _ ."I! 104 \ / / 5/16 \\i 0. 82 F/F ) \ 3 ¢ 10, - For the present investigation, the loci of points for Fi/Fg = 1,5 as calculated from Equation (20) are shown on Figures 45-149, pages 148- 152, 60 It is seen that the ratio Fi/Fg seems to be a good predictor for the equivalence of the horizontal and vertical results. Vertical Orientation Low-Flow Asymptotes As liquid flow is reduced, the gravitational forces become more and more dominant over the turbulent inertial forces. Consequently, at low flows, the vertical flow mass-transfer coefficients approach the values that would be expected for the bubbles rising through a quiescent liquid. The conditions of mass transfer for bubbles rising through a column of liquid have been extensively studied (e.g., References 26-30). Resnick and Gal-Or®” have recommended for surfactant-free systems - [Spg (Y2 1-38 k =0,109 | =2 ——— . 7 a ? l_ Moo (1 — g% 3)V/ 2 Vs They caution that this equation may give values slightly higher than the observed data in particular for lower concentrations of glycerol in water-glycerol systems. In the present investigation, the volume fraction is low so that the above equation was approximated as k, = 0.109 [8pg/ul” ? Ja__ (21) Vs and used to determine the "calculated asymptotes” for the vertical flow results as indicated on the various data plots, Mass-Transfer Coefficients With the end-effect accounted for as outlined in Chapter I1III, the mass-transfer coefficients measured in this investigation are given in Figures 50-58, pages 153-161 {Appendix G). The more revealing crossplots 61 of mass-transfer coefficients versus Reynolds number are shown in Figures 11-15 which contain regression lines fitted to the horizontal flow data and calculated lines for the vertical flow cases. Vertical flow data are not shown for the 37.5% mixture because the end effect adjustments were not satisfactory. Excessive vibration of the bubble generation probe that occurred during the 37.5% experiments was elimi- nated by redesign of the probe before the horizontal data were obtained. Time did not permit a reorientation of the system to the vertical posi- tion to repeat the runs, From these figures it is seen that the horizontal flow data for water (plus N-butyl alcohol) apparently have a lesser slope than that for the glycerine-water mixtures. Therefore a regression equation was determined for the water runs alone and a separate regression equation was determined for the combined data for the 12,5, 25, and 37.5% glycerine mixtures., A third behavior was observed for the 50% glycerine mixture (Figure 15). It is seen that all the data for this mixture were obtained at Reynolds numbers less than that required for Fi/Fg = 1.5, However, instead of a steady march of the horizontal flow data down a straight line as observed for the other mixtures, the small bubble horizontal flow mass-transfer coefficients tended to behave like those for vertical flows, This behavior implies that, if the liquid is viscous enough, small bubbles apparently can establish steady relative flow con- ditions in their rise across the conduit cross section, In these runs, the pipe wall apparently did not significantly inhibit the bubble rise rate during transit through the test section and, evidently, the bubbles behaved exactly as if they were rising through a vertical conduit. MASS TRANSFER COEFFICIENT (ft/hr} k, 62 ORNL-DWG 71-7989 /CALCULATED ASYMPTOTES VERTICAL FLOW > (USING Fi/Fg AS SCALE FACTOR) LT WATER + ~200 ppm N-BUTYL ALCOHOL LOCUS OF Fi/Fg=15 ~ SCHMIDT NO. = 449 . 1 1 O 1 HORIZONTAL FLOW REGRESSION BUBBLE EQUATION MEAN DIAMETER HORIZONTAL VERTICAL (Sh = 19436 Re 079 (913)0,85) (in) FLOW FLOW D C.015 ® 0.02 u 0.03 A 004 v 0.2 103 2 n 104 2 5 105 2 5 108 PIPE REYNOLDS NC., Re = VD/v Figure 11. Mass Transfer Coefficients Versus Pipe Reynolds Number as a Function of Bubble Sauter-Mean Diameter. Water Plus ~200 ppm N-Butyl Alcohol., Horizontal and Vertical Flow in a 2-inch Diameter Conduit. MASS TRANSFER COEFFICIENT (ft/hr) k: 63 ORNL-DWG 7%-7990 10 CALCULATED ASYMPTOTES 5 VERTICAL FLOW (USING F,/F, AS SCALE FACTOR) 2 OCUS OF F/Fy = 1.5 1 12.5% GLYCERINE SCHMIDT NG. = 370 FROM HORIZONTAL FLOW REGRESSION EQUATION 05 BUBBLE ' MEAN 22 o071 (dusy! O7 DIAMETER HORIZONTAL VERTICAL (Sh = 000538 Re ™™™ Sc™ (“6“) ) (in.) FLOW FLOW 0015 ® ' 002 » 003 A 02 004 v o1 103 4 2 5 10° 2 5 10% 2 5 10 ‘ PIPE REYNOLDS NO, Re = VD/v Figure 12, Mass Transfer Coefficients Versus Pipe Reynolds Number as a Function of Bubble Sauter-Mean Diameter. 12.5% Glycerine-87.5% Water. Horizontal and Vertical Flow in a 2-inch Diameter Conduit. MASS TRANSFER COEFFICIENT (ft/hr) K, 64 ORNL—DWG 71-7991 10 ALCULATED ASYMPTOTES 5 2 VERTICAL FLOW {USING Fi/fg AS SCALE FACTOR) LOCUS OF 1 FisrFg=15 25% GLYCERINE O SCHMIDT NO. = 750 0.5 BUBBLE FROM HORIZONTAL FLOW MEAN REGRESSION EQUATICON DIAMETER HORIZONTAL VERTICAL o (in) FLOW FLOW Sh = 000538 Re' 22 5cO 7! (fifl 0.015 ® O 002 » 0 0.2 0.03 A A .04 v vV 04 03 2 5 104 2 5 10° 2 PIPE REYNOLDS NO., Re = VD/u Figure 13. Mass Transfer Coefficients Versus Pipe Reynolds Number as a Function of Bubble Sauter-Mean Diameter. 25% Glycerine-75% Water. Horizontal and Vertical Flow in a 2-inch Diameter Conduit. k, MAS5S TRANSFER COEFFICIENT (ft/nr) ORNL—-DWG 71-7992 CALCULATED ASYMPTOTES LOCUS OF Fi/Fq =15 VERTICAL FLOW FROM HORIZONTAL FLOW (USING Fi/Fg AS SCALE FACTOR REGRESSION EQUATION I | . 37.5% GLYCERINE c A g A0 SCHMIDT NO. = 2015 sh : 000538 Re'2? 57" (_y;) RIZONTAL FLOW DATA) 0 BUBBLE MEAN IAMETER {in.} 10 5 2 i 0.5 HO D 0.02 0.0 103 Figure 0.015 0.02 0.03 0.04 2 5 104 2 5 10° 2 PIPE REYNOLDS NO., Re = VD/v 14, Mass Transfer Coefficients Versus Pipe Reynolds Number as a Function of Bubble Sauter-Mean Diameter. 37.5% Glycerine-62.5% Water. Horizontal and Vertical Flow in a 2-inch Diameter Conduit. k, MASS TRANSFER COQEFFICIENT (ft/hr) 66 ORNL-DWG 71-7993 10 50% GLYCERINE SCHMIDT NO = 3446 BUBBLE ' 3 MEAN DIAMETER HORIZONTAL VERTICAL (in) FLOW FLOW — 0.015 ® O D ASYMPTOT . CALCULATED ASYMPTOTES doe in) | 005 . 0 f e ] 0.04 0.03 A A 2 —— —— =4 joos y '1',.. 0.04 v v —— ~_ T ”0915‘] ~ b 1/, 1 ~ ‘Lol' 8 Z - NG \}\‘Q ’ g \0_ FROM REGRESSION EQUATION FITTING ONLY ™ THE 12.5, 25, AND 37.5% GLYCERINE DATA, 107 0.5 d N Sh = 0.00538 Re'?22 5c07! (—5% | T T 0 CALCULATED LINE LOCUS OF Fi/Fg =15 FOR dys = 0.015 | USING Fi/Fg=15 AS SCALE FACTOR [ . ot N N 02 (USING Fi/Fg=1C AS ] SCALE FACTOR) 0.1 10? 2 5 104 2 5 105 2 5 106 PIPE REYNOLDS NO., = VD/v Figure 15. Mass Transfer Coefficients Versus Pipe Reynolds Number as a Function of Bubble Sauter-Mean Diameter. 50% Glycerine-50% Water. Horizontal and Vertical Flow in a 2-inch Diameter Conduit. 67 These three kinds of observed horizontal flow behavior are further illustrated on Figure 16 for 0,02-in. mean diameter bubbles. The regression slope of 0,94 for the glycerine-water mixtures agrees gener- ally with the literature as discussed in Chapter II and the slope of 0.52 for the water plus N-butyl alcchol is, coincidentally, exactly what Lamont found, However, the combined regression slope (0.79) for all the water data which includes the other bfibble mean diameters was greater than the wvalue for the 0.02-in. bubbles by themselves. Calculating Vertical Flow Mass-Transfer Coefficients for Fi/Fg Less Than 1.5 Since the ratio of turbulent inertial forces to gravitational forces is seen to be a good predictor of the Reynolds number at which horizontal and vertical flow mass-transfer coefficients become identical, it is proposed that the varying ratio might alsoc serve as a scaling factor at all Reynolds numbers to determine the relative importance of the purely turbulent coefficients (Fi/Fg > 1,5) and the relative flow coefficients (vertical flow asymptotes). That is, if the values are known for the straight line variation at higher Reynolds numbers where vertical and horizontal coefficients are equal along with the vertical flow asymptotes, it is proposed that the intermediate vertical flow mass-transfer coefficients can be calculated by using Fi/Fg as a linear scaling factor between the two. Since Fi/Fg = 1.5 appears to mark the Reynolds numbers at which turbulent inertial forces dominate over gravi- tational forces, the actual ratio of forces at that condition are assumed to be of the order of 10 to 1 for gravitational forces to begin Sh/sc!/2 68 ORNL-DWG 71-7995 103 GLYCERINE SCHMIDT (%) NO. 50 3446 ¢ 37.5 2015 5 o5 250 SLOPE OF 0.52 12.5 370 (WATER + 200 ppm 0 419 N-BUTYL ALCOHOL = kD/% = ,u./p75 2 Re = VDp/u 8UBBLE DIAMETER, dys = 0.02 in. HORIZONTAL FLOW IN 2-in. CONDUIT 102 CALCULATED 5 e (50% GLYCERINET SLOPE OF 0.94 ° ObOo (375, 25, AND 12.5% . GLYCERINE) ® 2 101 103 2 5 104 2 5 10% 2 5 PIPE REYNOLDS NO, Re = VD/v Figure 16. Observed Types of Horizontal Flow Behavior. dvs = 0,02 inches and D = 2 inches. 69 to be negligible. Consequently 10 (Fi/Fg)/l.5 was chosen as an appro- priate linear scaling factor and the vertical flow mass-transfer coeffi- cients were calculated from 10(F,/F )/1.5 7 kK =k < vk | o | (22) v~ al|l+ 10(F./F )/L.5 1+ 10(F,/F_)/1.5 | ? . i g i g in which ka is the calculated asymptote given by Equation (21) and K, is the value at the given Reynolds number that would be obtained by extend- ing the straight-line variation of the horizontal flow data. Using separate regression lines for kh, the vertical flow mass- transfer coefficients calculated from Equation (22) are compared with the data on Figures 11-15, pages 62-66. Except for the 50% mixture data, Equation (22) provides a relatively good description of the data. Comparison with Agitated Vessels A comparison of the horizontal flow data with that of Sherwood and Brian'’ for particulates in agitated vessels is shown on Figure 17. Sherwood and Brian's coordinates are used by converting e_ (= ev/p) through Equation (19) for flow in conduits. It is seen that, although the relative magnitudes of the coefficients are comparable on an equiva- lent power dissipation basis, there is a Schmidt number separation of this data indicating mobile interfacial behavior. In agreement with the findings of other investigations reported in Chapter II, the variation with Reynolds number for flow in conduits is much steeper than would have been expected from the agitated vessel data. A possible explanation for this difference in slope observed between agitated vessels and flow in conduits may lie in the relative importance of the gravitational forces. For example, the data of this research for 70 100 BUBBLE" 50 Dlnfill\zlléfiER SCHMIDT NUMBER, Sc (in.) 419 370 750 2013 0.015 o 0.02 o 20 0025 o 0.03 @ 10 0.035 ® % GLYCERINE — O 5 ] ~ ‘—U < = SHERWOQOD AINDIBRMN w 2 Sc = 518 1 0.5 HORIZONTAL FLOW IN 2-in. DIAMETER CONDUIT 0.2 o1 /3 4 “mdvs. y3 Figure 17. with Agitated Vessel Data, ORNL-DWG 71-7996 Equivalent Power Dissipation Comparison of Results 71 small bubbles in a 50% mixture of glycerine and water were obviously strongly gravitationally dominated as evidenced by the equality of the horizontal and vertical flow coefficients even at very low Reynolds numbers. A comparison of these "gravity-influenced" data with Sherwood and Brian's correlation shown on Figure 18 indicates a remarkable simi- larity. It may be that gravitational forces are generally less important for flow in conduits than for flow in agitated vessels where there may be a greater degree of anisotropy. Recommended Correlations A regression line through all the horizontal flow data except the water and the 50% mixtures has a Schmidt number exponent of 0.71 using the literature®® values of 8. These valueé of § (Figure 25, page 11k, Appendix A) first increase with addition of glycerol, reach a maximum at ebout 12,5% glycerol, and then decrease. This behavior represents a striking departure from the Stokes-Einstein behavior usually observed for aqueous mixtures. If, instead of using these values for 8, a smooth monotonically decreasing line is drawn through the first, fourth, and fifth data points of Figure 25 and the values of 8§ taken from that line, a regression analysis yilelds a Schmidt number exponent of 0.58 — not much different than the value of 0.5 expected for mobile interfaces. A regression analysis of all the horizontal data for the glycerine- water mixtures (except for the 50% mixture) using the original values of 0 (Table III, page 20) and forcing the Schmidt number to have an exponent of 1/2 results in the eqguation, Sk = 0.3)4 Reo.faéc Scl/z (dVS/D)l.o , (23) 70 ORNL~DWG 71-7997 100 50 20 10 'SHERWOOD AND BRIAN SCHMIDT NO. = 3600 O HORIZONTAL OR VERTICAL FLOW IN 2 2—in. CONDUIT SCHMIDT NO. = 3446 50% GLYCERINE Sh/sc!/3 REYNOLDS NO. 05 12205 15272 18306 20342 22374 01 2 3 1 2 5 10 2 5 10 2 5 10 (€m d?s/vsf/3 Figure 18. Equivalent Power Dissipation Comparison of Gravity Dominated Resultgs with Agitated Vessel Data. 73 with a standard deviation in fr (8h/Sc'/ ?) of 0.19 and an index of determination of 0.86, The comparison of the data with this equation is shown in Figure 10, Since a Schmidt number exponent of 1/2 is expected on theoretical grounds and since there is little loss of precision by using this exponent, it is recommended for design purposes that the horizontal flow mass-transfer coefficients, k , be calculated from Equation {23) as long as V/Vb is greater than about 3. Operation below V/Vb = 3 is not recommended because of severe stratification. Equation (23) can also be used to calculate the vertical flow coefficients, kv, as long as Fi/Fg’ as determined by Equation (20), is greater than 1.5. Other- wise, Equation (22) is recommended for the vertical flow coefficients with the asymptotic values, ka, to be calculated from Equation (21). As evidenced by the observed high Schmidt number exponent, these recommendations are for contamination free systems only., For a con- taminated system with rigid interfacial conditions, the Schmidt number exponent is expected to be 1/3 and the coefficient multiplying the equation should also be different., In the absence of supporting experi- mental data, a tentative correlation for rigid interfacial conditions might be inferred from Equation (23) to be Sh = 0,25 Re®:%% gel/ @ (dVS/D)l'O . The coefficient, 0.25, was obtained by multiplying 0.34 [the coeffi- cient of Equation (23)] by the ratio of rigid-to-mobile coefficients of equations applicable to bubbles moving steadily through a liquid.®! A similar transformation of Equation (21) would be required to obtain the rigid-interface values of the vertical flow asymptotes. The above sn /[s¢"2 (dys/D)] 109 HORIZONTAL FLOW Th ORNL~-DWG 71-79%94 REGRESSICN LiNE FORCED TQ FIT sct@ Yo dVS BUBBLE MEAN SCHMIDT NO., Sc DIAMETER (in.) 370 750 2013 419 C.015 0.02 0.025 0.03 0.035 GLYCERINE — 12.5 Figure 19, o > < O > | d - 0335 Re®%% 5c'? (%) 1 1 1 r | ‘ 10 2 5 10% 2 5 PIPE REYNOL_DS NO.,, Re = VD/v Correlation of Horizontal Flow Data. 75 equation for rigid interfaces should be used with caution as it has not been validated by experimental data, In addition the experimentally observed linear variation with (dVS/D)‘may have been caused by a transi- tion from rigid-to-mobile interfacial condition. For strictly rigid interfaces no such transition would be expected to occur and the exponent on (dvs/D) might then be less than 1.0, CHAPTER V THEORETICAL CONSIDERATIONS Two different viewpoints were considered to describe mass transfer between small bubbles and liquids in cocurrent turbulent flow. In the first, a turbulence interaction approach, the bubbles were considered to be subjected to turbulence forces which impart random motions resulting in "mean" relative velocities between the bubbles and the fluid. These "mean" velocities were then considered as "steady" (albeit multi-direc- tional) and as dictating the mass-transfer behavior. In the second, a surface renewal approach, the bubbles were viewed as being associated with a spherical shell of liquid for an indefinite time during which mass exchange takes place by turbulent diffusion. This indefinite time was assumed to be related to the bubble size and the average relative velocity between the bubble and the liquid, Turbulence Interaction Model A small bubble suspended in a turbulent field will be subjected to random inertial forces created by the turbulent fluctuations. Under the action of & given force, if sufficiently persistent, the bubble may achieve its terminal velocity and move at a steady pace through the liquid before being redirected by another force encounter within the random field, If the "average" value representing the bubble relative velocity in such a turbulent field could be determined, then a convenient formulation would be to use that velocity to determine an average bubble 76 T Reynolds number and stay within the confines of the well-established relative-flow Frossling-type equations to determine the mass-transfer coefficients. The movement of the bubbles through the liquid will be resisted primarily by viscous stresses. The drag force on a sphere moving steadily through a liquid is often expressed in terms of a drag coeffi- cient, Cd’ by the equation, 2 2 paZ _CdApVb_CdTTp Reb F = ’ d EgC —Bgc 0 in which the drag coefficient is itself a function of the bubble Reynolds number, Reb (= vy, dp/u). In relative flows, however, the drag coefficient-Reynolds number correlation depends on the particular Reynolds number range. Frequently, two regimes of flow are identified with the division occurring at Reb ~ 2, Common correlations for the drag coefficients in these two regimes are given below. For Re, 5 2, b — — 2 -, Cy= EM/Reb and F, = 3mu Reb/gco . (2hea) For 2 < Reb < 200, _ Oeb6 _ 2 1.4 - Cq = 18.5/Reb and F, = 18.5mu® Rey /Bgcp . (24-b) In Chapter IV, an expression was developed for the inertial forces experienced by a bubble in a turbulent fluid, ] | L 8/ 3 11/ 6 5 F, 5 (a/D) (Re) ) (25) It might be reasonable to determine "mean" bubble velocities from a balance between the inertial forces and the drag forces for later sub- stitution into the Frossling equations. If it is postulated that the 78 above two relative flow regimes also exist for bubbles in a turbulent field, then two different sets of equations describing the mass transfer will result. Since the inertial forces depend on the bubble size, a dispersion of bubbles with a distribution of sizes may have bubbles in either or both regimes simultanecusly and the mass~transfer behavior may be described by either set of eguations or take on characteristics of a combination of the two. The mass-transfer equations resulting for the two separate regimes are discussed below. Regime-1: Rey < 2 If the bubble motion were predominantly governed by the regime, Re, < 2, the drag forces would be given by Equation (2k-a), A balance between the inertial and drag forces, Fi = Fd’ would then give for the bubble Reynolds number Re, ~ (4/D)8’ @ Retl/ & | (26) By this formulation, the bubble relative flow Reynolds number depends only on the ratio, d/D, and on the pipe Reynolds number which, for a given bubble size, establish the turbulence level, The Sherwood number for mass transfer can therefore be determined as a function of these variables by substitution of Equation (26) into mass-transfer equations that have been established as applicable to a sphere moving through a liquid. These are the Frossling-type equations which, for large Schmidt numbers, usually take the forms ~ 1/ 2 1/ 2 Shb Reb Sc and Sh-b ~ Rebl/ 2 Scl/ 3 79 for mobile and rigid interfaces, respectively. Making the conversion, sh = (D/d) Sh, , and substituting Equation (26) gives for the mobile and rigid interface pipe Sherwood numbers applicable to cocurrent turbulent flow, Sh ~ Sl 2 Re®°22 (d/D)l/S (27) and Sh ~ Sc'/ ® Re®®2 (4/D)V 2 , (28) respectively. Consequently, in this regime, the pipe Reynolds number exponent is 0.92. For comparison, the experimentally determined value for the water-glycerine mixtures in this investigation was 0,94, The theoretical bubble diameter dependence, (d/D)Y 2, however is less than the experi- mentally determined linear variation, Calderbank and Moo-Young* ® point out that the linear variation they observed(for bubbles in this size range probably resulted from a transition from rigid to mobile inter- facial conditions because small bubbles tend to universally behave as rigid spheres while larger bubbles require the presence of sufficient surface active ingredients to immobilize their surface, If such a transition is the reasdn for the linear variation in this instance also, then the effect of conduit diameter will be different from that implied in Equation (23) which did not include actual varia- tions in conduit diameter. Consequently, anticipated future experiments with variations in the conduit diameter should help clarify the influence of bubble mean diameter. In addition, exploratory experiments in this study indicated that the linear variation did not continue up to larger bubble sizes and may, therefore, be limitéd to the relatively narrow mean 80 diameter range of approximately C.01l to 0.05 inches. At larger diameters, the dependence tended to lessen until above mean diameters of about 0.08 inches where the Sherwood number appeared to decrease with increasing bubble diameter., Since the bubble generator was not generally capable of producing larger bubbles, further investigation of the bubble size influence was not possible in this experiment. Regime-2: Reyp > 2 If the bubble motions were predominantly in the regime, Re,_ > 2, the b drag forces would be given by Equation (24-b). The balance, F, = Fg would then give Re, ~ (/D)3 ++2 Re*/ o5 (29) The relative-flow bubble Reynolds number in this regime still depends on the variables that establish the turbulence level but that dependence is different from that of Regime 1. When substituted into the Frossling equations for mobile and rigid interfaces, the results are ah ~ SCL/E ReC* 86 (d/D)—o.a/4.2 and Sh ~ qel/ 3 Rel-86 (d/D)—O.a/é.E , (30) respectively. For this regime the Reynolds number exponent is 0,66. Consequently, if bubbles in cocurrent turbulent flow experience different flow regimes similar to bubbles in relative flow, a transition Qould be expected at higher pipe Reynolds numbers in which the Reynolds number exponent would tend to become smaller, In the present experiments, the data for water (plus ~200 ppm N-butyl alcohol) with no glycerine added was obtained at 81 the highest range of Reynolds numbers covered. The experimentally measured Reynolds number exponent for the water runs was lower than for “the glycerine-water mixtures and compared favorably with the above results. In addition, Equation (30) compares quite well with data for particles in agitated vessels [for example see Equation (3)7. It is felt that the possible existence of different flow regimes even in cocurrent turbulent flows is an important concept that, if further developed, could help explain some of the apparent discrepancies in the literature data. For example, this may explain the different slopes observed in this study and may be the reason for observed differ- ences between mass transfer in agitated vessels and in conduits, It is more likely, however, that the latter difference is due to greater gravitational influence in agitated vessels, Surface Renewal Model In this analysis each bubble is considered to be surrounded by, and exchanging mass with, a spherical shell of turbulent liquid in which the turbulence is isotropic, A mass balance (Appendix F) in a spherical differential element of fluid results in the eguation A _gl3%C, 23 |, 123 a_t—sl:arg+r-a-1_':]+rgar(r UI‘C) . (31) Making Reynolds assumptions, and time averaging gives 82 dC d%C 2 aC 1 3 s A7 .fi=s[;+;—r}+—za(r MC) . (32) H In turbulent scalar transfer, the "Reynolds" term p’'C’, is often assumed to be expressible with an eddy diffusivity, E, defined by However, it is more convenient here to use a recent eddy viscosity defi- nition by Phillips,58 for which an analogous definition for an eddy diffusivity in spherical coordinates would be d 5 dC (r dr) d 2 F = (PP u'c) = = : (33) Using this definition, Equation (32) is expressed more simply as - (8+1) [fi+£§€] . (34) Q| Q/ 2 or? The view is now to be taken that, on the average, a bubble remains associated with a spherical shell of liquid for some indefinite time after which its surface is completely "renewed" — that is, associated with an entirely different spherical shell of liquid that has an initisal uniform concentration characteristic of the bulk fluid., It is felt that the times of asscciation between the bubble and a given region of liquid should be related to the magnitude of the turbulent inertial forces or alternatively to the mean relative velocity between the bubble and the liquid as established by the balance of the inertial and the viscous resisting forces, Therefore a nondimensional time for comparison purposes is proposed to be tv b, = —2 * d * 83 Using this definition along with the following additional definitions of dimensionless quantities C, = E/co r, = r/d Reb = vbdp/p Re = VDp/p Sc =p/pd , Equation (34) can be expressed in nondimensional form as 3, (L +u/8) [ 3%, , 2 Cy ot Re, Sc o1, 2 r, Ory j . Assuming the bubble motion is predominantly in Stokes' regime, Equation (26) can be used to estimate Re, and substituted into the above equation to give 3¢, (1 +u/9) To%c, 5 9, ] 3t, | s (35) * Cy8c(d/D)¥ @ RV ® | 3r,® x OTx where C, 1s a proportionality constant of unknown magnitude but assumed to be of the order ~1072, A similar equation can be developed for Regime-2 of the previous model by using Equation (29) for Re,. Logical boundary conditions for Equation (35) would be l. Cy (o, r,) =1, 2. ¢, (t>o0, 1/2) = 0, and 3C, — = 1/ 3 3. 33 =0at o, 1/2 3 » The third boundary condition above arises from equating the volume fraction with the ratio of bubble volume to equivalent sphere volume. Bl A solution of Equation (35) would give C, as a function of r, and t,. If a radial average, 6;, is defined as r *e 2 — _ Il/g Cyx (r*, t*) Ty~ dry C-X- (t.)(-) = 3 e 2 Il/g Ty~ Ory then the Sherwood number as a function of time can be expressed as ac, .é-;;_- II'_X_ = 1/2 sh (t,) = —-zigifii:———- . If a bubble is assumed to remain associated with a fluid element for some unspecified time, T then the average Sherwood number for that ) period 1s T-)(— ", sho(t,) dt, Sh = T . (36) The above analysis is similar to normal surface renewal models in that the dimensionless time period T, is analogous to a surface age. There is no real basis for being able to relate T, to the flow hydrody- namics or the surface conditions; however, it could be treated as a parameter and the mass-transfer coefficients determined as a function of this parameter. "Surface age" distributions could then be established from the experimental data or specified arbitrarily just as they have been in other surface renewal models. For example, one common assump- tion has been that the surface is "renewed" each time the bubble travels (relative to the fluid) a distance egual to its diameter. With the formulation used here, this assumption would be particularly convenient because then T* =1, 85 Equation (35) along with its boundary conditions is considered as a8 surface renewal model. For a solution, a function, He/"g (Re, sc, d/D: r*) » - must first be established to describe the variation in eddy diffusivity. In arriving at his eddy viscosity definition, Phillips®® used a Fourier decomposition of the turbulent field and, by an elegant analysis, determined the contributions to the local eddy viscosity due to each component "wave" making up the field. Through a paraliel analysis for mass transfer, it is inferred here that the individual component contributions to the eddy diffusivity are proportional to the energy of the transverse velocity fluctuations and inversely proportional to their wave number, Me,n ™ u?/n - (37) Defining f(n)dn as the fraction of eddies that have wave numbers in the range n * 1/2 dn, and summing the contributions over all wave numbers gives po ~ [, o= f(man . (38) & If XKolmolgoroff's energy spectrum is used, the distribution function defined above can be assumed to be inversely proportional to the wave number, £(n) ~ l/n ’ and Equation (38) becomes My N'fn (Ei/ne) dn . (39) To assess the effect of the interface, use was made of Lamont's'? analysis in which he idealized each component as & sinusoidal viscous 86 "eddy cell" in which the velocities are damped by viscous stresses as an interface is approached. His analysis gave for a spacial average (parallel to the interface), -1/ 3 s u ~ E (¥) 1 where y is a coordinate defined as y = r —-d/2 and E(y) is a damping factor depending on the interfacial condition. Lamont's solution of the viscous "eddy-cell" equation gave for a rigid interface, §r = [0.294 ny sinh ny + 0.388 sinh ny —0.388 ny cosh ny] , and for a mobile interface, §m = [0.366 sinh ny —0.089 ny cosh ny] In addition, it is assumed here that only the range of eddy sizes smaller than, or equal to, the bubble diameter interact with a bubble to produce eddy transfer to the bubble itself and that each of these eddies is effectively damped only if it is within a distance from the interface equal to the wave gize. The eddy sizes assumed present range from a minimum given by the Kolmolgoroff microscale for pipe flow, N = D/Rell/ 16 min to an arbitrary maximum of one-half the pipe diameter, Mooy = D/2 Consequently, using Equation (39), the ratio of eddy diffusivity effec- tive to the bubble at a position y to the eddy diffusivity existing away from the interface, pe/po, is calculated from the following relations: 1. For fl/y > fl/d, 87 fl/y fl/d . In/k n~® 3 gn + J‘fl/ n~® 3 g2 gn _ min Y )-F = =7 . (L4oa) max o-s/s g ffl/k D = min 2. For m/y < n/d (no damping), fl/d I n—8/ 3 dn He fl/Kmin == =7 . (Lob) ”O j‘ max n_s/ a an /. min A numerical integration of Equation (40) with Mgy = & 1s shown on Figure 20 for both mobile and rigid damping. The actual relative eddy diffusivity variation calculated from Equation (40) will not approach unity in midstream as in Figure 20 because the integration of the numerator is to include only eddies up to the size of the bubble diameter whereas the denominator is to be integrated over all wave sizes in the field. Comparing the mobile and rigid interface curves on Figure 20 indi- cates that the two conditions would result in very little difference in mass~-transfer behavior for an essentially passive bubble being acted upon simultaneously by many eddies — a result not too displeasing intuitively., A significant difference in behavior then, by this formulation, must come about by assigning a longer renewal period, T, to rigid interfaces than to mobile interfaces. The variation of pe/fi required for a solution to Equation (35) can be obtained from the product IJ‘e “O o) () “*” if the values for eddy diffusivity in midstream, Hos are known. e Mo o o ® © 06 0.5 0.4 0.3 0.2 0.1 88 ORNL-DWG 74-8013 I I l | o | I PLOT OF /N /Yy T/ Amax [ N—8/3 + N—8/3 62 dN T dN fwy Ho 7/ X max - l; N—8/3 dN ~ FOR A RIGID INTERFACE L AND & = [0.366 sinh NY — 0.089 NY cosh NY:I FOR A MOBILE INTERFACE | ! WHERE £R = [0.294 NY sinh NY + 0.388 sinh NY — 0.388 NY cosh NY:, — y — MOBILE /4? / // RIGID 4 / Figure 20, A O 01 02 03 04 05 06 07 08 09 Y/ Xmax Condition. Dimensionless Variation of Eddy Diffusivity with Distance from an Interface, Effect of Surface 89 For the standard definition of eddy diffusivity, Groenhof®® gives a correlation applicable to the midsection of a pipe, E = 0,04 J%Wgc7p D . (42) Letting 7= f p V2/8gC and f = 0,316/Re? * for smooth tubing, then E from Equation (42) is given by E/v = 0,04 J/F/8 Re = 0.04 ,/0.316/8 Re™/ & . (L43) Phillip's definition of eddy viscosity reduces to the standard definition in the midsection of a pipe. Consequently, it is acceptable to convert Equation (43) to po/ag = 0.04 ,/0.316/8 Sc Re /8 (L) which along with Equation (41) and Equations (40) fully determine a function uo/,@ (Re, Sc, d/D, r,) for use in solving Equation (35). Tt is realized that Phillip's analysis for eddy viscosity is not strictly applicable near an interface nor is the "eddy-cell" idealization a realistic picture of the turbulence. WNevertheless, the variation in eddy diffusivity based on these concepts was determined through Equations (43) and (40)., It is felt that the behavior of a pseudo-turbulence such as this may be similar to a real turbulent field in that the essential features are retained and the trends predicted in this manner may be useful. For example, for the condition of turbulent transfer to a con- duit wall itself there have been measurements of the standard eddy diffusivity distributions. Therefore, a comparison was made in Figure 21 of eddy diffusivities calculated in the above manner with Sleicher's ORNL—-DWG 71-8014 2 320 XCALCULATED FROM CURVE OF 300 MHe/Ho VERSUS y/Amax (RIGID INTERFACE) WITH: 280 p, = 0.028 f/2 Re 260 AND A\mgx ASSUMED = 0.5, r, = PIPE RADIUS 240 ' : DATA OF SLEICHER 220 |[O@ CALCULATED| o o__¢o ® VALUES™ 200 Re = 80,300 180 ~ 160 @O 1 / 140 120 // o 100 o |/ o L/ ——Re = 14 20 o M O 0 0.2 0.4 0.6 0.8 1.0 y/rg Figure 21, Variation of Eddy Diffusivity with Distance from an Interface. Comparison of Calculated Values with Data of Sleicher, 91 data,®° For this application of transfer to a conduit, the value of a in Equation (40a) (the maximum eddy size in this case) was arbitrarily set equal to 1/2 of the pipe radius, s and the coefficient in Equation (43) was adjusted slightly to require ue/v to coincide exactly with Sleicher's value in the pipe midsection at Re = lh,SOO. Cofisidering the difference in the eddy diffusivity definitions, the comparison is favor- able and it appears that use of a pseudo-turbulence idealization such as this may provide a unique @eans of predicting eddy viscosity and eddy diffusivity variations. Since the determination of eddy diffusivities and their variation was not the primary concern of this thesis, further development of these concepts was not considered. Equations (35), (36), (40), and (uh),-which represent the present surface renewal model were programmed on a digital computer and numeri- cal solutions obtained using T, as a parameter. Time did not permit a complete evaluation of this computer program and the results can only be presented here as tentative. Figure 22 illustrates the values of the exponents obtained for an equation of the form Sh, ~ Re® scP (a/D)° as a function of T,. The value of T, for which the Schmidt number exponent was 1/3 (corresponding to rigid interfaces) was approximately 2.7. At this value of T,, the solution for the time-averaged pipe Sherwood number was essentially independent of the bubble diameter and varied according to Sh ~ Re®*%% get/ 2 (45) The computer results as T, approached zero appeared to approach the classical penetration solution of Equation (35) obtained for pe/ 8 =0, 10 a, b, ¢ 0.5 02 0.1 Figure 22. 92 ORNL-DWG 71-10753 SURFACE RENEWAL MODEL PLOT OF a, b AND ¢ VERSUS Ty FOR A SOLUTION OF THE FORM Sh, ~ Re® sc” (d/D)° VARIABLE VALUE HELD CONSTANT S¢ = 3000 Re d/D = 0.01 Re 5 x 103 { { ASYMPTOTIC SOLUTION AT T, = OTIC SOLUTION « =0 e = 5 x 107 Sc 3000 2 5 10 20 50 100 Ty Numerical Results of the Surface Renewal Model., Plots of a, b, and ¢ (Exponents on Re, Sc, and d/D, Respectively) as Functions of the Dimensionless Period, T,. 93 Sh ~ ./8c (a/D)¥ 2 Re*'Y © / (a/D) or Sh ~ qpl/ 2 Reg.ez (d/D)l/B which is identical to Equation (27). Consequently, if the surface renewal period, T, , is interpreted as being a measure of the rigidity of the interface, T, + O being characteristic of mobile interfaces and T, + ~2,7 (in this case) being characteristic of rigid interfaces, then this surface renewal model may be useful, Neither this model nor the preceding turbulence interaction model satisfactorily predict the observed variation of pipe Sherwood number with bubble diameter for this range of bubble sizes. Indirect support is therefore provided for the supposition that the observed linear variation may be the result of a transition from rigid to mobile behavior. CHAPTER VI SUMMARY AND CONCLUSIONS Transient response experiments were performed using five different mixtures of glycerine and water. Liquid-phase-controlled mass-transfer coefficients were determined for transfer of dissolved oxygen into small helium bubbles in cocurrent turbulent gas-liquid flow. These coeffi- cients were established as functions of Reynolds number, Schmidt number, bubble mean diameter, and gravitational orientation of the flow. An analytical expression was obtained for the relative importance of turbulent inertial forces compared with gravitational forces, Fi/Fg' For conditions in which this ratio was greater than ~1.,5, the variation in the observed mass-transfer coefficients with Reynolds numbers was linear on log-log coordinates with identical behavior for horizontal and vertical flows. Below Fi/Fg = 1.5, the horizontal coefficient vari- ation continued to be "linear" until the ratio of liquid axial velocity to bubble terminal wvelocity, V/Vb, decreased to about 3, where severe stratification made operation impractical., The vertical flow coeffi- cients underwent a transition from the "linear" variation and approached constant asymptotes characteristic of bubbles rising through a quiescent liguid. The variable ratio of Fi/Fg proved to be a useful linear scaling factor for describing the vertical flow coefficients in this transition region for which Equation (22) is the recommended correlation. The Schmidt number exponent for the straight-line portions of the data was observed to be greater than 1/2 based on physical property data for & which may be suspect. Fitting the data with a Schmidt number oL B exponent of 1/2 resulted in only slightly less precision than for the case in which the actual regression exponent was used, and a definitive choice could not be made between the two. Based on theo- retical expectations, a Schmidt number exponent of 1/2 would seem to be appropriate, and consequently, the recommended correlation is Equation (23). The variation in mass-transfer coefficient with bubble mean diameter over the range covered was observed to be linear in agreement with the findings of Calderbank and Moo-Young'® for agitated vessels. Some pre- liminary runs made with bubble mean diameters outside the range of this report indicated that the linear variation does not continue but that the coefficients level off at both smaller and larger diameters. Furthermore the coefficients tentatively appear to decrease slowly with increasing mean diameters above about 0.08 inches. Consistent with findings of other investigations, the Reynolds number exponent was significantly greater than expected based on agitated vessel data compared on an equivalent power dissipation basis, One explanation is that there may exist greater gravitational influence in agitated vessels. Another is the postulated existence of different bubble relative flow regimes. A seemingly anomalous behavior was observed for the Reynolds number variation in that the data for water (plus about 200 ppm N-butyl alcohol) exhibited significantly smaller Reynolds number exponents and a corres- pondingly smaller exponent for the ratio, (d/D), than that for the glycerine-water mixtures., There may have been a difference in the interfacial conditions (the addition of the surfactant creates a "rigid" 96 interface while the glycerine-water mixtures apparently generally had "mobile" interfacial behavior). However, under steady relative flow conditions this would result in no difference in the Reynolds number exponent, Consequently, it was postulated that this difference resulted from the possible existence of different bubble relative flow regimes. In support of the above contention, a two-regime "turbulence interaction" model was formulated by balancing turbulent inertial forces with drag forces that depend on the bubble relative flow Reynolds num- ber. The resulting mean bubble velocities were substituted into "Frossling”" equations to determine the mass-transfer behavior. The resulting Reynolds number exponent for one regime (Reb < 2) agreed very well with the experimental value for the glycerine-water mixtures and that for the other regime (Reb > 2) compared favorably with the water data and with agitated vessel data on an equivalent power dissipation basis. The dependence of Sherwood number on the bubble-to-conduit diameter ratio, d/D, predicted by the interaction model did not agree with the observed linear variation. Calderbank and Moo-Young'® pointed out that the linear variation they observed in agitated vessels for bubbles of this size range probably resulted from a transition from "small" bubble to "large" bubble behavior. Such a transition could also explain the present observations, however, there was no satisfactory means for vali- dating this. For comparison, a second analytical model was developed based on surface renewal concepts which could also include different flow regimes. This model incorporated an eddy diffusivity that varied with Reynolds o7 number, Schmidt nunber, bubble diameter, interfacial condition, and position away from the interface. The variation of eddy diffusivity was established by using a pseudo-turbulent model in which the turbulence was simulated by superposed viscous eddy-cells damped by the bubble interface in a menner determined by Lamont,!!? The surface renewal model assumed that the "renewal" period for the bubbles was related to the bubble "mean" velocity resulting from a balance between turbulent inertial forces and viscous resisting forces, thus allowing the casting of the equations into nondimensional form with the pipe Reynolds number, the Schmidt number, and d/D as parameters. A closed solution of the equations was not obtained but a tentative numer- ical solution employing a digital computer indicated that, in the limit of small dimensionless renewal period, T, — interpreted as representing mobile interfacial behavior, the classical penetration solution of this particular form of the diffusion equation resulted. As T, approached a value of approximately 2,7 (in this case), the computer solution was independent of‘(d/D) and resulted in a Schmidt number exponent of.ul/3. Therefore, this value of T, was interpreted as representing rigid interfacial behavior. Explicit results based 'on the models described above along with a listing of the more significant observations of this study are given below: 1. Bubbles generated in a turbulent field are well characterized by the distribution function £(8) = 4 (o®/mMV 2 82 Exp (—a8®) , where Q I = [b /7 N/687% 2 98 2, The average volume fractions occupied by gas in bubbly flow are approximated by Hughmark's correlation®% only at higher flows. In horizontal flow, when the ratio of axial velocity of the liquid to the bubble terminal velocity is below ~25, Hughmark's correlation predicts volume fractions lower than those observed, In vertical flow, while the volume fractions are higher in downcomer legs than in riser legs, they can be established by using Hughmark's correlation for the mean and accounting for the buoyant relative velocity of the bubbles in each leg. 3. At low turbulent flows stratification of the bubbles in hori- zontal conduits prevented operation for ratios of axial velocity to bubble terminal velocity below ~3. 4, Even at Reynolds numbers well into the turbulent regime, hori- zontal and vertical flow mass-transfer coefficients differ. The Reynolds numbers above which they become equivalent are marked by the dominance of turbulent inertial forces over gravitational forces. 5. As Reynolds numbers are reduced, vertical flow mass-transfer coefficients approach asymptotes characteristic of bubbles rising through a quiescent liquid, The ratio of turbulent inertial forces to gravita- tional forces serves as a useful linear scaling factor for estimating the mass-transfer coefficients at these lower Reynolds numbers. 6. The effect of Reynolds number on Sherwood number for flow in conduits is not as would be expected based on comparison with agitated vessel dafia on an equivalent power dissipation basis, For example, the observed turbulence-dominated data are correlated by Sh/scl/ 2 = 0,34 Re®*®% (g/D)1*° (23) 29 whereas one obtains from the agitated vessel data of Calderbank and Moo-Young' ® for small bubbles Sh/Sct/ ® = 0,082 Re®-%° (2) and of Sherwood and Brian'” for particulates Sh/Schs ~ ReC* 61 (d/D)—o.lz . (3) In thisrthesis the two-regime turbulence interaction model and the surface renewal model exhibit identical results for mobile interfaces in the "Stokes" regime (Re, < 2), b Sh ~ ScV/ 2 Re®?2 (4/D)Y 2 which compares well with the observations represented by Equation (23). In the second regime (Re. > 2), the turbulence interaction model b for rigid interfaces results in Sh ~ Scl/ 8 Re0-86 (d/D)‘o'a’4'2 and the rigid interface interpretation of the surface renewal model gives Sh ~ Scl/ 3 Re©-85 as compared, for example, with Equations (2) and (3). 7. The observed linear wvariation of Sherwood number with bubble diameter was not predicted theoretically. Consequently, following Calderbank and Moo-Young,'® it is conjectured that this variation re- sults from a transition from rigid (small bubbles) to mobile (large bubbles) interfacial behavior for this size range. 8. Data of this study that were obviously gravitationally influ- eficed compare favorably with data for particulates in agitated vessels, giving rise to the speculation that gravitational forcegs may be more influential in agitated vessels where there may exist a greater degree of anisotropy compared with flow in conduits. CHAPTER VII RECOMMENDATIONS FOR FURTHER STUDY Experimental Time did not permit a complete investigation of the effects of all the independent variables, Consequently, projections of this study into the future include experiments involving variations of the conduit diam- eter and the interfacial condition. It is anticipated that these studies will help clarify the role of d/D, in particular with regard to the observed linear variation of mass-transfer coefficient with bubble diam- eter. These projected studies will also attempt to extend the ranges of variables covered through improvements in the bubble generating and separating equipment., It is hoped that these improvements will reduce the magnitude of the "end-effect" and thereby provide greater precision to the data. Parenthetically, the high rates of mass transfer observed in the bubble separator may qualify it for further investigation as a possible efficient in-line gas-liquid contactor. For practical purposes it is recommended that mass-transfer rates also be measured in regions of flow discontinuities such as elbows, tees, valves, venturis, and abrupt pipe size changes. An objective of these "discontinuity" studies would be to test Calderbank and Moo-Young's hypothesis that mass-transfer rates can be universally correlated with the power dissipation rates. As a direct extension of the work of this thesis, others might con- sider use of different fluids to provide a more definitive variation of the Schmidt number and of the interfacial condition. The studies could 100 101 have the additional objective of demonstrating that surface tension is not an influential variable other than for its effect on the mobility of the interface., Experiments designed to look at the actual small- scale movements of bubbles in cocurrent turbulent flow and the eddy structure very close to the interface would help guide further theoret- ical descriptions and may help validate the dimensionally determined expression for the average turbulent inertial forces, One contention of the present work, the possible existence of different flow regimes yielding different Reynolds number exponents, should be further tested. A substantially widened range of Reyneclds number for a given bubble size in a viscous fluid might uncover a tran- sition from one regime to another. In practical applications, the interfacial area available for mass transfer is equally as important as the mass-transfer coefficient. Therefore, for systems in which relatively long term recirculation of the bubbles is anticipated, the bubble dynamic behavior becomes of interest. For example, more information is needed on bubble breakup and coalescence which tend to establish an equilibrium bubble size in a turbulent field. More important perhaps, is the effect of bubbles passing through regions with large changes in pressure (e.g., across a pump) where they may go into solution and, as the pressure is again reduced, renucleate and grow in size. The effects on mean bubble sizes and the interfacial areas available under such conditions are not well known and this particular aspect of bubble behavior could provide a fruitful field for further research, 102 Theoretical Two extreme viewpoints were taken in this report in which bubbles were considered as being either essentially passive in a turbulent field with the mass-transfer behavior being governed by the "sweeping" of the surface with random eddies or, alternatively, as moving through the tur- bulent liquid and establishing a boundary-layer type of behavior. The "surface renewal" model developed in this report was only ten- tatively evaluated. TFurther development of the model is anticipated and additional solutions should demonstrate the technique by which surface renewal concepts can be applied to cocurrent turbulent flow., A complete mechanistic description of mass transfer between bubbles and liquids in cocurrent turbulent flow would presumably include the transient effects of a developing boundary layer as a bubble is acceler- ated in first one direction and then the other by random inertial forces, Superimposed on this would be the effects of the surrounding eddy struc- ture and the characteristics of the eddy penetrations through the developing boundary layer. Further efforts to theoretically describe these simultaneous effects should be considered with possible solutions on a digital computer. The use of pseudo-turbulent fields (e.g., an eddy-cell structure) to determine the transport rates and to establish such properties as an eddy diffusivity should provide useful insights into the actual behavior in real fluids and should help predict data trends. For example, the miltiple boundary layer structure established by Busse®! for the vector field that maximizes momentum transport in a shear flow strongly resembles 103 an artificial eddy-cell structure. Starting with such a structure, one could work "backwards" to calculate eddy viscosities (for example) as a function of position away from a solid boundary. LIST OF REFERENCES 1. Oak Ridge National Laboratory, Molten Salt Reactor Program Semi- annual Progress Report for Period Ending February 29, 1968, USAEC Report ORNL-425L4, August (1968). 2, Peebles, F. N., "Removal of Xenon-135 from Circulating Fuel Salt of the MSBR by Mass Transfer to Helium Bubbles," USAEC Report ORNL-TM-2245, Oak Ridge National Laboratory, July (1968). 3. Harriott, P., "A Review of Mass Transfer to Interfaces,” The Can. Journal of Chem. Eng., April (1962). L, Calderbank, P. H., "Gas Absorption from Bubbles-Review Series No. 3., The Chemical Engineer, 209-233, October (1967). 5. Gal-Or, B., G. E. Klinzing, and L. L. Tavlarides, "Bubble and Drop Phenomena,” Ind. and Eng, Chem., 61(2): 21, February (1969). 6. Tavlarides, L. L., et al., "Bubble and Drop Phenomena,"” Ind. and Eng. Chem., 62(11): 6, November (1970). 7. Regan, T. M. and A. Gomezplata, "Mass Transfer,” Ind. and Eng. Chem,, 69(2): 41, February (1970). 8. Regan, T. M. and A, Gomezplata, "Mass Transfer,” Ind. and Eng. Chem., 62(12): 140, December (1970). 9. Jepsen, J. C., "Mass Transfer in Two-Phase Flow in Horizontal Pipelines," AIChE Journal, 16(5): 705, September (1970). 10. Scott, D. S. and W. Hayduk, "Gas Absorption in Horizontal Cocurrent Bubble Flow," Can, J. Chem. Eng., Lh: 130 (1966). 11. Lamont, J. C., "Gas Absorption in Cocurrent Turbulent Bubble Flow," PhD Thesis, The University of British Columbia, August (1966). 12, Lamont, J. C. and D. S. Scott, "Mass Transfer from Bubbles in Cocurrent Flow," Can. J. Chem. Eng., 201-208, August (1966). 13. Heuss, J. M., C. J. King, and C. R, Wilke, "Gas-Liquid Mass Transfer in Cocurrent Froth Flow," AIChE Journal, 11(5): 866, September (1965). 14, Harriott, P., "Mass Transfer to Particles: Part II, Suspensed in a Pipeline," AIChE Journal, 8(1): 101, March (1962). 15« Figueiredo, O. and M. E, Charles, "Pipeline Processing: Mass Transfer in the Horizontal Pipeline Flow of Solid-Liquid Mixtures," The Can. J. of Chem, Eng., 45: 12, February (1967). 105 106 16. Calderbank, P. H. and M. B, Moo-Young, "The Continuous Phase Heat and Mass-Transfer Properties of Dispersions," Chem, Eng. Sci., 16: 37 (1961). 17. Sherwood, T. K. and P. L. T. Brian, "Heat and Mass Transfer to Particles Suspended in Agitated Liquids,” U. S. Dept. of Interior Research and Development Progress Report No. 334, April (1968). 18, Barker, J. J. and R, E. Treybal, "Mass Transfer Coefficients for Solids Suspended in Agltated Liquids," AIChE Journal, 6(2): 289-.295, June (1960). 19. Boyadzhiev, L. and D. Elenkov, "On the Mechanism of Liquid-Liquid Mags Transfer in a Turbulent Flow Field," Chem. Eng. Sci., 21: 955 (1966). 20. Porter, J. W., S. L. Goren, and C. R, Wilke, "Direct Contact Heat Transfer Between Immiscible Liquids in Turbulent Pipe Flow," AIChE Journal, 14(1): 151, January (1968). 21, Sideman, S. and Z. Barsky, "Turbulence Effect on Direct-Contact Heat Transfer with Change of Phase,” AIChE Journal, 11(3): 539, May (1965). 22, Sideman, S., "Direct Contact Heat Transfer Between Immiscible Liquids," Advances in Chemical Engineering, Vol. 6, pp. 207-286, Academic Press, New York (1966), 23, Fortescue, G. E, and J. R. A. Pearson, "On Gas Absorption into a Turbulent Liquid," Chem. Eng. Seci., 22: 1163-1176 (1967). 24, Kozinski, A. A, and C. J. King, "The Influence of Diffusivity on Liquid Phase Mass Transfer to the Free Interface in a Stirred Vessel, AIChE Journal, 12(1): 109-110, January (1966), 25. King, C. J., "Turbulent Liquid Phase Mass Transfer at a Free Gas- Liquid Interface," Ind, Eng. Chem. Fund., 5(1): 1-8, February (1966). 26, Peebles, F. N. and H. J, Garber, "Studies on the Motion of Gas Bubbles in Liquids, Chem. Eng. Progr., 49(2): 88-97, February (1953). 27. Ruckenstein, E., "On Mass Transfer in the Continuous Phase from Spherical Bubbles or Drops," Chem. Eng. Sci., 19: 131-146 (1964), 28. Griffith, R. M., "Mass Transfer from Drops and Bubbles," Chem. Eng. Sci., 12: 198-213 (1960). 29, Redfield, J. A, and G. Houghton, "Mass Transfer and Drag Coefficients for Single Bubbles at Reynolds Numbers of 0.02-5000," Chem. Eng. Sci., 20: 131-139 (1965). 30. 31, 32. 33. 3k, 35. 36. 37. 38, 39. Lo, L1, Lo, b3, L, 107 Chao, B, T., "Motion of Shperical Gas Bubbles in a Viscous Liquid at Large Reynolds Numbers," Phys. Fluids, 5(1): 69-79, January (1962). Lochiel, A, C. and P. H. Calderbank, "Mass Transfer in the Contin- uous Phase Around Axisymmetric Bodies of Revolution,'" Chem. Engr. Sci., 19: 475-4BL, Pergamon Press (1964). Higbie, R., "The Rate of Absorption of a Pure Gas Into a Still Liquid During Short Periods of Exposure,’ Presented at American Institute of Chemical Engineers Meeting, Wilmington, Delaware, May 13-15 (1935). Danckwerts, P. V., "Significance of Liquid-Film Coefficients in Gas Absorption,” Ind. Eng. Chem., Engineering and Process Develop- ment, 43(6): 1460-1467, June (1951). Toor, H. L. and J. M, Marchello, "Film-Penetration Model for Mass and Heat Transfer," AIChE Journal, 4{(1): 97-101, March (1958). Whitman, W. G., Chem. and Met. Eng,, 29: 147 (1923). Levich, V. G., Physicochemical Hydrodynamics, Prentice-Hall, Inc., Englewoods Cliffs, N. J. (1962). Hinze, J, O., Turbulence, McGraw-Hill Book Co., Inc,, New York (1959). Middleman, S., "Mass Transfer from Particles in Agitated Systems: Application of the Kolmogoroff Theory," AIChE Journal, 11(4): 750-761, July (1965). Harriott, P. and R. M, Hamilton, "Solid-Liquid Mass Transfer in Turbulent Pipe Flow," Chem, Eng. Sci., 20: 1073-1078 (1965). Brian, P. L. T. and M. C. Beaverstock, "Gas Absorption by a Two- Step Chemical Reaction," Chem, Eng. Sci., 20: 47-56 (1965). Davies, J. T., A. A. Kilner, and G. A. Ratcliff, "The Effect of Diffusivities and Surface Films on Rates of Gas Absorption," Chem, Eng. Sci., 19: 583-590 (1964). Gal-Or, B., J. P. Hauck, and H., E. Hoelscher, "A Transient Response Method for a Simple Evaluation of Mass Transfer in Liquids and Dis- persions,”" Intern. J. Heat and Mass Transfer, 10: 1559-1570 (1967). Gal-Or, B. and W. Resnick, "Mass Transfer from Gas Bubbles in an Agitated Vessel with and without Simultaneous Chemical Reaction,” Chem, Eng. Sci., 19: 653-663 (1964), Harriott, P., "A Random Eddy Modification of the Penetration Theory," Chem. Eng. Sci., 17: 1h49-15L (1962), L5, Le, e ho. 50, 51. 52, 5Lk, 5. 56. 57. 58. 59, 108 Koppel, L. B., R. D. Patel, and J. T. Holmes, "Statistical Models for Surface Renewal in Heat and Mass Transfer,” AIChE Journal, 12(5): 9k1-955, September (1966), Kovdsy, K., "Different Types of Distribution Functions to Describe a Random Eddy Surface Renewal Model," Chem. Eng. Sci., 23: 90-91 (1968). Perlmutter, D. D., "Surface-Renewal Models in Mass Transfer," Chem, Eng. Sci., 16: 287-296 (1961). Ruckenstein, E., "A Generalized Penetration Theory for Unsteady Convective Mass Transfer," Chem, Eng. Sci., 23: 363-371 (1968). Sideman, S., "The Equivalence of the Penetration and Potential Flow Theories,”" Ind. Eng. Chem., 58(2): 54-58, February (1966). Harriott, P., '"Mass Transfer to Particles: Part I. Suspended in Agitated Tanks," AIChE Journal, 8(1): 93-101, March (1962). Banerjee, S., D. S. Scott, and E. Rhodes, "Mass Transfer to Falling Wavy Liquid Films in Turbulent Fiow," Ind. Eng. Chem, Fund., 7(1): P2-26, February (1968), Barker, J. J. and R. E. Treybal, "Mass Transfer Coefficients for Solids Suspended in Agitated Liquids," AIChE Journal, 6(2): 289-295, June (1960), Galloway, T. R. and B. H. Sage, "Thermal and Material Transport from Spheres,'" Intern. J. Heat Mass Transfer, 10: 1195-1210 (1967). Hughmark, G, A,, "Holdup and Mass Transfer in Bubble Columns," Ind. Eng. Chem., Process Design and Development, 6(2): 218-220, April (1967). Jordan, J., E. Ackerman, and R. L. Berger, "Polarographic Diffusion Coefficients of Oxygen Defined by Activity Gradients in Viscous Media," J. Am. Chem. Soc., 78: 2979, July (1956). Bayens, C., PhD Thesis, The Johns Hopkins University, Baltimore, Maryland (1967). Resnick, W. and B. Gal-Or, "Gas-Liquid Dispersions,' Advances in Chemical Engineering, Academic Press, New York, Vol. 7, pp. 295-395 (1963). Phillips, O. M., "The Maintenance of Reynolds Stress in Turbulent Shear Flow," J. Fluid Mech., 27(1): 131-144 (1967). Groenhof, H, C., "Eddy Diffusion in the Central Region of Turbulent Flows in Pipes and Between Parallel Plates," Chem, Eng. Sci., 25: 1005-1014 (1970). 60. 61. 109 Sleicher, Jr., C. A., "Experimental Velocity and Temperature Pro- files for Air in Turbulent Pipe Flow," Transactions of the ASME, 80: 693-704, April (1958). Busse, F. H., "Bounds for Turbulent Shear Flow,” J. Fluid Mech., h1s 219-240 (1970). APPENDIX A PHYSICAL PROPERTIES OF AQUEOUS-CLYCEROL MIXTURES 111 112 ORNL-DWG 71-8003 106 SCHMIDT NUMBERS CALCULATED FROM DATA OF JORDAN, ACKERMAN AND BERGER - 25°C 5 2 109 N MTX GLYCERINE AND WATER 5 P S N Il 2 o o) o = 4 . 10 o = T & 5 2 103 5 2 0 20 40 60 80 100 GLYCERINE (%) Figure 23, Schmidt Numbers of Glycerine-Water Mixtures. P/C (atm~liters/mole x 1072) HENRY'S LAW CONSTANT, H 113 ORNL—-DWG 71—8004 4 l | [ [ SOLUBILITY OF OXYGEN IN MIXTURES OF GLYCERINE AND WATER - 25°C 3 2 ,'---_’/ 1 e C DATA OF JORDAN, ACKERMAN AND BERGER 0 0 10 20 30 40 50 60 70 80 GLYCERINE (%) Figure 2L, Henry's Law Constant for Oxygen Solubility in Glycerine- Water Mixtures. 90 11k ORNL-DWG 71-8005 DIFFUSION OF OXYGEN THROUGH DIFFERENT MIXTURES OF GLYCERINE AND WATER AT 25°C /C\ %, MOLECULAR DIFFUSION COEFFICIENT (cm@/sec x 10°) 90 S O\ \O\ \\ N O-O“O DATA OF JORDAN, ACKERMAN AND BERGER 10 20 30 40 50 60 70 80 GLYCERINE (%) Figure 25. Molecular Diffusion Coefficients for Oxygen in Glycerine- Water Mixtures, Data of Jordan, Ackerman, and Berger. p, DENSITY (g/cc) 115 ORNL-DWG 71-8006 DENSITIES OF GLYCERINE AND WATER MIXTURES - 25°C ‘o/fig v 1.200 1.100 y ¥ /O ’b\ > @ O O > JORDAN, ACKERMAN AND BERGER HANDBOOK OF CHEMISTRY AND PHYSICS CHEMICAL ENGINEERING HANDBOOK BEILSTEIN'S HANDBOOK OF ORGANIC CHEMISTRY | | 1.000 E?// 20 40 60 80 100 120 GLYCERINE (%) Figure 26, Densities of Gly cerine-Water Mixtures. 140 p, VISCOSITY (CP) 109 116 ORNL-DWG 71-8007 VISCOSITY OF GLYCERINE-WATER MIXTURES AT 25°C DATA OF JORDAN, ACKERMAN AND BERGER 10 20 30 40 50 60 ' ' GLYCERINE (%) Figure 27, Viscosities of Glycerine-Water Mixtures. 70 APPENDIX B DERIVATION OF EQUATIONS FOR CONCENTRATION CHANGES ACROSS A GAS-LIQUID CONTACTOR Consider the cocurrent flow of a gas and a liquid in a constant area pipeline of cross section AC and length L., In a differential element of length df, a dissolved constituent of concentration C in the ligquid is transferred into the gas as shown below. e ' ; _— -_— Q,C - I[_ . ] +Q, (C + 4ac) - v ; — - , d et L 0% (€« Cg) < eee df e A mass balance for the dissolved constituent gives Q,dC = —ka A dd (C — CS) (B-1) il c C - -2 dicg +ka A a4 (C cs) , (B-2) where C is the liquid phase average concentration,'fig is the gas phase concentration, and CS is the concentration existing at the gas-liguid interface, Dividing Equetion (B-2) by Equation (B-1) gives ac Q dC g Integrating Equation (B-3) and letting Eé - O when C = Cy gives G, = (a /e )(c; = C) . (B-4) If the interfacial concentration is assumed to be at "equilibrium" and the solubility of the dissolved constituent is expressible by Henry's 117 118 Law, then HC = ¢ RT . (B-5) Q cs=§i (?”i)(ci—fi) . (B-6) Equation (B-6) can be substituted into Equation (B-1) to obtain Q, &€ = —xa A, 4 [T = (RI/H)(Q,/Q)(c; —T)] i ~ka A_ 44 C (1 + RTQE/HQg) — (RTQz/HQg) c.l . (-7 Expanding and dividing by dez gives = — kaAc'YCi By mPC T T G - where B’ = ka A, (1 + Y)/Qfl and y = (RT/H)(Qfl/Qg). / Use of the integration factor eB 4 permits the following solution = Y \ B4 0 = ~ l | ) SEDESSR NI | : ettt ‘ _ )RR ANEMOMETER ' ; S S LS B s j mmm e . g ' \ | ¢ gvn¥oen oy ' w ' RNy ey oo : ™ STROBELUME 3 : N & KRRRRARIRE HOT Frm u SELLIME. i : N _ : 9 | PROBE 25 LA e | i ] 0.k = e T e 9 g9 12 § ¥R ¥ 9 5 = SAFETY SHIELDING i 3 & E ; Q - TN . \\ - 2 S | e 1 : TR-1, ; 3 T AR i < T XX N L | R o 38 L Pl & : 32 ] ; @ v gt ¥ Q vl B i forerermterdy o770 & | v | : BRI T TN ¥ B 8 . T ARG SR Q 83 ; ; 0-/100F51 f‘?-' ?_-g—i-i-‘ TN S ) - 5 _ - ¢ ' Ifx | : R S S I ¢ § N g 3 0 by boodge E o 11 OXYCEN Wl o, . CALIBRATION ; I bedo—m -4 FY¥QY W TANKS b r-=-—2 Y SATURATION, ST N I ! I " . 4 TANK NN s b N el o (0 pgAN¥ Mo TTTme-- : ! : , | | AANK N o N POLAROI O ' 5 Y oM\ Aogh | gl kT acrivarep CAMERA @ @ @— & Nady BY CAMERA 3k LENS OPENING. ! ! ! ! ! 4 T =X F oy ey . e P e b - i ( ! U Aad ! l < ‘3 : S o~ FLASH CONTROLS! : i ! | 28/ w Qg o TURN ON & THME ! ! ! ! | | v R 2O ¢ bLenTH OF FLASHL _ A AN A A TILY _ B COOLING - oY o @ ? i Tuohk swe| |} N 00 6.8 M. DRAIN He0 b o - 8 p t:';‘ y 8 ‘;’]" - } 5 EXPANSION e . —_ e —— - — — - UNLESS STHLRwisx UNION CARBIDE CORP. I | | 1 E | I EE%E?:. E:';i ,j 5. K’//uM—-A—,/ A Hitrc s, IW%, She o No. i“:'-‘::o’":':_"l ario I DatE i oRAWN I ArFD. l Arrml arrD. Ann,—l REVISIONS . 'C‘L-'NONE I_IO497—QF_OO |_D_O Figure 28. Instrument Application Drawing of the Experiment Facility. dys, BUBBLE MEAN DIAMETER (in) 123 APPENDIX D INSTRUMENT CALIBRATIONS ORNL-DWG 71-7998 1 T L r 1 r BUBBLE GENERATOR CHARACTERISTICS LIQUID FLOW, Q_ (gpm)—~20 30 35 40 45 50 55 60 65 70 75 80 85 90 SYMBOL—~©C ® A &4 V ¥ 0 © & & 4 & V¥V V 010 || Lt ! || sese GENERATOR (SCHEMATIC) "~ | 6As To LIQUID VOLUMETRIC FLOW . ! PROBE SHOWN AT 4 1/2-in. RATIO, Qg/QL = 0.3% POSITION (FULLY WITHDRAWN) 0.09 FLIQUID = INDICATED MIXTURE OF <=FLOW DIRECTION (LIQUID} GLYCERINE AND WATER Y a-—(GAS) oop LOAS = HELIUM . . A <7 { % Yo 37.5% 50% 0% GLYCERINE 12.5% 25% QL (gFIH'n) 0.07 | 30y QL (gpm) ' a_ (gpm) \, 30 35 Q_ (gpm) \ a5 0.06 — N 20 \ N\ N \ N\, 5 X LN A 005 === 5 % 40 \ \ \ 50 \ N AN \ a5 A\ A 0.04 _50\\\ h 50 VN ~ 45 A N 559, \ 50 50N \ A P> v\ ~N \ v A\ NGO 55 N\ 4\ A 60 003 : 653\ e, \ —656 Ny \ o5 \\fi\, NN 554 0, v \\ ; \ 75-?"&- \ ?o'°x\\ ,& ?O-a..._\ L. i ; " 0.02 |80=ggi ™o A)‘, —( Sa ¥, A= ~ QA | OBV | [T ~ o RNy d .l 0.01 0 3 5 7 9 3 5 7 9 3 5 7 o 3 5 7 9 3 5 7 9 PROBE POSITION (in) Figure 29. Bubble Size Range Produced by the Bubble Generator. ROTAMETER SCALE 12k ORNL-DWG T1-8008 100 WATER (0% GLYCERINE) S0 80 " < 60 50% GLYCERINE | 1 UPSCALE DOWNSCALE 50 o \ | - .18/ CALIBRATION OF ROTAMETER 1 FOR TWO MIXTURES OF GLYCERINE AND WATER 0 | | 0 20 40 60 80 - 100 FLOW (gpm) Figure 30. Calibration of Rotameter No. 1 (100 gpm). 125 ORNL—DWG 74—8009 100 / o0 // ® 80 / 50% GLYCERINE / 70 UPSCALE / DOWNSCALE& / WATER {0% GLYCERINE) 60 / S @ 2 / 50 b / bl -] [ QO 7 o\ 40 30 ./ 20 [l 10 CALIBRATION OF ROTAMETER 2 FOR TWO MIXTURES OF GLYCERINE AND WATER o | | | 0 10 20 30 40 50 FLOW (gpm) Figure 31. Calibration of Rotameter No. 2 (40 gpm). SCALE READING (%) 126 ORNL-DWG 71—-80!0 100 .:O 20 / @ 80 50% GLYCERINE UPSCALE V DOWNSCALE& 70 / 60 @ WATER (0% GLYCERINE) 50 2 / / @ 30 // 20 &4 {0 CALIBRATION OF ROTAMETER 3 FOR TWO MIXTURES OF GLYCERINE AND WATER i | | 0 2 4 6 8 10 FLOW (gpm) Figure 32. Calibration of Rotameter No. 3 (8 gpm). AP, PRESSURE DROP ACROSS CAPILLARY TUBE (inches of water) 127 ORNL-DWG 71-8011 CALIBRATION OF CAPILLARY-TUBE FLOWMETER AT A PRESSURE OF 50 psig ATMOSPHERIC PRESSURE, Pg = 29.41 in. HG ATMOSPHERIC TEMPERATURE, To = 27.6°C HELIUM FLOW MEASURED WITH A WET-TEST METER ~ ‘./ 0 0.02 C.04 0.06 0.08 0.10 HELIUM FLOW (SCfM) Figure 33. Calibration of Gas-Flow Meter at 50 psig. 0.12 DISSOLVED OXYGEN READING (ppm) 40 38 36 34 32 30 28 26 24 22 20 128 ORNL-DWG 71-8018 ® A POLAROGRAPHIC MEASUREMENT OF DISSOLVED OXYGEN CONCENTRATION IN TWO MIXTURES OF GLYCERINE AND WATER O MAGNA CORPORATION PROBE f MAGNA CORPORATICON PROBE 2 BECKMAN CORPORATION PROBE / oL WATER (0% GLYCERINE) CURVE CALCULATED FOR HENRY'S LAW CONSTANT (H = P/C) EQUAL TO 1.74 psi AIR/ppm DISSOLVED OXYGEN TAKEN FROM PERRY, "CHEMICAL ENGINEERS HANDBOOK" /| 3/ / A/}?.S% GLYCERINE CURVE CALCULATED /7~ FOR H = 355 psi AIR/ppm DISSOLVED W ACKERMAN, AND BERGER © OXYGEN TAKEN FROM DATA OF JORDAN, W / l////// N\ e W Figure 3k, 20 30 AlR 40 50 60 70 80 PRESSURE (psiq) Calibration of Oxygen Sensors in two Mixtures of Glycerine and Water. S0 APPENDIX E EVALUATION OF EFFECT OF OXYGEN SENSOR RESPONSE SPEED ON THE MEASURED TRANSIENT RESPONSE OF THE SYSTEM Instrument responses are typically exponential in nature. Thus, if the sensor reading is defined as Cr’ and the actual loop concentra- tion as 6'(both functions of time) it is safe to assume an instrument response equation of the form dC T =k, (C-c) , (E-1) where Kr is an instrument response coefficient. The transient response of the loop itself is given by an equation of the form Therefore, Equation (E-1) can be expressed as -z-z-ll +kK.C, =K, Coe-KLt . (E-2) Integration of Equation (E-2) with the initial condition Cr = Co at t = 0 gives cr/co = [1 - Kr/(Kr - %)) ey [Kr/(Kr — k)] e Xpt - A (E-3) The manufacturers stated response time for the Magha oxygen sensors is 90% in 30 seconds., This response results in a value of K =4.61 . r The maximum observed rate of change of oxygen concentration in the transient experiments corresponded to 129 130 KL = 0.75 (On the average, the experiment transients resulted in KL < 0.3.) There~ fore, for this case, A = =0.19, B = 1.19 and cr/co = 1,19e7°*78% — g 19e %81t | (E-k) An examination of Equation (E-U4) shows that as time progresses the second term becomes negligible compared to the first, and the measured slope approaches the actual transient slope of 0,75, For example, the measured slope for this "worse" case is 0.7k after only one minute of transient compared to the real value of 0.75. Therefore, to further minimize this possible error, the slopes of the measured transients were taken only from the final six minutes of the curve permitting an initial n "response adjustment" time of several minutes. The error due to the instrument response, then, is assumed to be negligible, APPENDIX F MASS BALANCES FOR THE SURFACE RENEWAL MODEL Consider a differential region in a spherical shell of fluid surrounding a bubble as shown below, Mass balances for the concentration, C, of a dissolved constituent within the liquid are obtained as follows: Convection in: U C bmr® T 3(U c) out: Um (r + dr)® EU C +-—7§——— dr 3(U c) net convection = (out-in) = [4mr? “5“_ dr + 8mrdr (U C)! (F-1) Diffusion ins O Lmr® oC ar out: 8 bw (r + dr)® [ BC + é——-d ] o r 3p? r X A A 5 8 C ac net diffusion = (out-in) = |8 bmr dr + 8 8mrdr 3> (F-2) ar® | 131 132 Storage -LI-TT a a3 oC net loss = —- [(r + dr) r3] % N2 o = |=brr® dr 5t | (F-3) Summing the contributions (F-1) through (F-3) gives ot a(Urc) 5 +hrr? dr | ——+=(UC)} =0 r T Dividing by Umr® dr gives 2 3(r°U_C) 53_(1:39 é_.g.+§..a_q +.1'......_.....__r...... . (F_)_@) ot arg r or rg 2 orr? dr £ 4§ bmr® dr [_a_ng%g_g] Meking the Reynolds assumptions substituting into Equation (F-4), expanding and collecting terms gives ~ ’ 2~ 2n ! ~ ’ _a_c_+ac=&[ac+ac+_2_ac+§§_c_] r or r 3r ot ot 372 3r2 T d0(u’C) |, d3(u’c’) . 2, = P oyt $ommml S 2 (u'C) + = (u'c?) . (F-5) The time average of a quantity, C, is defined as jtta ¢ dt 1 in which the time interval, (t; — t,), is long enough for the time average of the fluctuating quantities in Reynolds assumption to be zero but short compared to the transient changes in C. Therefore, = time average of Equation (F-5) gives (F-6) APPENDIX G ESTIMATE OF ERROR DUE TO END-EFFECT ADJUSTMENTS The measured ratios of exit-to-inlet concentration, K, across a gas-liquid contacter were extracted from the measured slope, S, of the log-concentration versus time data by the relation -8V /Q K = e s" Al The error involved in measuring the various quantities used to establish K are estimated to be AS 'S_" -~ O. Ol s oy £~ 0.03 S and N L. 0.03 . 9 Consequently, the error in K can be estimated from K - K LK max min K K ’ where (8 —AS)(VS -—AVS) Kpax = Bxp | — (Qz + AQE) and (8 + M8)(V_ + AVS) Kpin = B¥P |~ g —Acs,zj : PRy ] 135 The minimum ratio measured for K was ~0.9, therefore the maximum estimate of the error is .99) .01) (1.03) K O.gclaz%%ggg%fi _.0,9(L—g%54§7%§ K 0.9 ~ 0,02 In Chapter III, the ratio, Ky, applicable to the test section above was calculated from Ko = KI/KII , where KI was the measured ratio across the bubble generator, the test section, and the bubble separator together, and KII was that across just the bubble generator and bubble separator. Therefore, the maximum instrument-precision induced error in Kg is estimated to be K3 Kz,max u'Ka,min Kz ~ Kz 1l + 0,02 1 -0,02 KI/KII<1—O.OE> KI/KII<1 +o.02> . ~ K /K < lOO . T 11 In establishing KIland KII in separate tests, the inability to exactly duplicate conditions results in an error greater than the above. An estimate of the maximum magnitude of this error can be had by examin- ing the data for the 75% water-25% glycerine mixture (Figure 13, page 63). Before the end-effect adjustment, the calculated vertical and horizontal flow mass-trénsfer coefficients for the 0.02-inch mean diameter bubbles were essentially identical. However, after the adjustment they differed by ~25%, It is felt that this difference mostly arises from the inabil- ity to exactly recreate the vertical flow conditions as a result of alterations made in the bubble generator between the original test and 136 the end-effect test, Consequently the horizontal flow data are consid- ered the more "exact" although they should still reflect the ~10% error estimated due to measurement precision, APPENDIX H MASS TRANSFER DATA 137 k, UNADJUSTED MASS TRANSFER COEFFICIENT (ft/hr) 38 WATER + ~200 ppm N-BUTYL ALCOHOL VERTICAL FLOW IN 2-in. CONDUIT 3 b ® [scHmioT No. u 419 Q/QL (%) Qi {gpm) Re 34 0.3 0.5 O ® 20 35,583 32 O N 35 62,269 A A 40 71,165 30 ¢ ¢ 50 88,955 >8 Vv v 60 106,748 A ¢ 65 115,642 26 v v 80 142,381 A A 100 177,913 24 22 100 20 18 l‘ ‘,/15’65 ,80 16 }VZ pad 14 ’,/' ',r35 ' VW & de0 49 50,!]//,20 VeV Q‘A// Q00 10 AN AT L= e s // 8 A a’ / 0O 6 SR ~ | 4 2 0 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 dys, BUBBLE MEAN DIAMETER (in.) Figure 35. Unadjusted Mass Transfer Data., Water Plus 200 ppm 138 ORNL-DWG 71-7965 N-Butyl Alcohol. Vertical Flow. 26 249 20 18 k, UNADJUSTED MASS TRANSFER COEFFICIENT (ft/hr) 139 ORNL—-DWG 71-7966 WATER + ~200 ppm N-BUTYL ALCOHOL [HORIZONTAL FLOW IN 2-in. CONDUIT Q, (gpm) re Qg/QL = 0.3% _ — 5o [ SCHMIDT NO. = 419 O 50 88,955 _ ® 60 106,748 A 70 124,537 | A 80 142,331 v 90 160,119 _ 50 . P 80 14 // 1 70 A / 12 P4 60 A / /AS o ' 48’0'—__0_0‘0"‘---50 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 d,,, BUBBLE MEAN DIAMETER (in.) Figure 36. Unadjusted Mass Transfer Data. Water Plus ~200 Ppm N-Butyl Alcohol. Horizontal Flow. k, UNADJUSTED MASS TRANSFER COEFFICIENT (ft/hr) 18 16 14 12 10 140 ORNL-DWG 71-7967 12.5% GLYCERINE Qqg/QL = 0.3% VERTICAL FLOW IN 2-in. CONDUIT FSCHMIDT NO. = 370 W1 THOUT™ WITH® Q. (gpm) Re — O ® 15 19,288 0 B 20 25,718 A A 35 45,006 O ¢ 50 64,294 v v 65 83,583 *ADDITION OF ~200 ppm N-BUTYL ALCOHOL - 65 / | 50 v// /35 \ O/ ¢ b H,20 O \ N5 P -~ B 0 0.0 0.02 0.03 0.04 0.05 0.06 0.07 0.08 dys, BUBBLE MEAN DIAMETER (in.) Figure 37. Unadjusted Mass Transfer Data. 12.5% Glycerine-87.5% Water. Vertical Flow. 14 12 k, UNADJUSTED MASS TRANSFER COEFFICIENT (ft/hr) 141 ORNL—-DWG 71—7968 HORIZONTAL FLOW IN 2—in. CONDUIT 12.5% GLYCERINE Q_ (gpm) Re SCHMIDT NO. = 370 O 35 45,006 - o Qg/QL = 0.3% o 50 64.294 A 65 83,583 A 75 96,442 v 85 109,302 85 75 A 10 / / 65 8 ’ A" A’ ._,-1-50 ‘ 6 % o 0— i — | ® a , / 35 0 0.0 0.02. 0.03 0.04 0.05 0.06 0.07 0.08 dys, BUBBLE MEAN DIAMETER (in) Figure 38. Unadjusted Mass Transfer Data. 12.5% Glycerine-87.5% Water. Horizontal Flow. UNADJUSTED MASS TRANSFER COEFFICIENT (ft/hr) k, 1k2 ORNL-DWG 74-7969 10 25% GLYCERINE Qg/QL = 0.3% VERTICAL FLOW IN 2—in. CONDUIT , 9 | SCHMIDT NO. = 750 ) / 8 V. 2 6 5 4 3 2 /o QL (gpm) Re 20 O ® 20 17,636 O n 30 26,454 1 A A 40 35,272 O ¢ 50 44,090 Vv v 60 52,908 o TADDITION( OF ~ 200 ppm N-BUTYL ALCOHOL 0 0.01 0.02 003 0.04 0.05 dys, BUBBLE MEAN DIAMETER {in.) .06 0.07 0.08 Figure 39. Unadjusted Mass Transfer Data. 25% Glycerine-75% Water. Vertical Flow. k, UNADJUSTED MASS TRANSFER COEFFICIENT (ft/hr) 143 ORNL-DWG 71-7970 8 7 6 5 4 3 > O 40 35,272 ® 45 39,681 A 50 44,090 9 56: 48,498 25%, GLYCERINE 57,317 { - ’ 1 Qq/QL = 0.32 — v 76 66,135 97/t SCHMIDT NO. = 750 HORIZONTAL FLOW IN 2-in CONDUIT 0 _ { | { 0 0.01 002 0.03 0.04 0.05 0.06 0.07 dys, BUBBLE MEAN DIAMETER (in.) Figure L40. Unadjusted Mass Transfer Data., 25% Glycerine-75% Water. Horizontal Flow. k, UNADJUSTED MASS TRANSFER COEFFICIENT (ft/hr) 14k ORNL-DWG 71-—79714 WITHOUT™® WITH* QL (gpm) Re o O o 20 13,079 o » 30 19,619 A A 40 26,159 v v 45 29,429 —*ADDITION OF ~200 ppm N-BUTYL ALCOHOL /45 / /A Y prd // /’/Qr 40 30 é | 20 s Or A 7 / ~ | 0 I/. - e - 37.5% GLYCERINE SCHMIDT NO. = 2015 Og/QL = 0.3% VERTICAL FLOW IN 2-in. CONDUIT 0 0.04 0.02 0.03 0.04 0.05 0.06 0.07 dys, BUBBLE MEAN DIAMETER (in.) Figure L1, Unadjusted Mass Transfer Data. 37.5% Glycerine-62,5% Water. Vertical Flow. 0.08 UNADJUSTED MASS TRANSFER COEFFICIENT (ft/hr) K, 10 145 CRNL—DWG 71-7972 0.08 l I QL (gpm) Re O 30 19,619 @ 35 22,889 — A 40 26,159 A 45 29,429 v 50 32,699 v 55 35,968 —— a 60 39,238 N 7C 45,777 60 /55 Y _, 50 45 35 P e— i-.___ i _‘0'30 37.5% GLYCERINE SCHMIDT NO. = 2015 —— Qg/QL = 0.3% HORIZONTAL FLOW IN 2-in. CONDUIT O 0.01 0.02 0.04 0.05 C.06 0.07 dvs, BUBBLE MEAN DIAMETER (in.) Figure 42, Unadjusted Mass Transfer Data. 37.5% Glycerine-62.5% Water. Horizontal Flow. k, UNADJUSTED MASS TRANSFER COEFFICIENT (ft/hr) 146 ORNL-DWG 71-7973 ] WITHOUT® WITH*® oL (gpm) Qg/QL (%) Re — O o 10 0.5 4,068 0 n 20 0.5 8,137 A A 30 0.5 12,205 O ¢ 40 0.5 16,274 v v 50 0.3* 20,342 *ADDITION OF ~200 ppm N-BUTYL ALCOHOL tEXCEPT WHERE NOTED '/50 ro.5°/o | | o 30 ] /v,ro.s /o /A//.zo 4 Z A /g/fi 8 / a A %& 10 _] T o7 @ - rfff” L~ ~ S -~ / u 5 + 50% GLYCERINE SCHMIDT NO. = 3446 VERTICAL FLOW IN 2-in. CONDUIT | l | 0.04 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 dyvs, BUBBLE MEAN DIAMETER (in.) Figure 43. Unadjusted Mass Transfer Data. 50% Glycerine-50% Water. Vertical Flow. k, UNADJUSTED MASS TRANSFER COEFFICIENT (ft/hr) 147 ORNL—DWG 71{-7974 Q. (gpm) Re O 30 12,205 ° 35 14,238 A 40 16,274 A 45 18,306 Vv 50 20,342 v 55 22,374 @ —— 35 —\m 30 | 50% GLYCERINE SCHMIDT NO. = 3446 Qg/QL = 0.3% HORIZONTAL FLOW IN 2-in. CONDUIT i { | ] O 0.014 0.02 0.03 0.04 0.05 0.06 0.07 dvs, BUBBLE MEAN DIAMETER (in.) Figure 44, Unadjusted Mass Transfer Data. 50% Glycerine-50% Water, Horizontal Flow, UNADJUSTED MASS TRANSFER COEFFICIENT (ft/hr) K, 148 ORNL-DWG 71-7984 LOCUS OF FI/FQ = 1 71 / HORIZONTAL VERTICAL FLOW FLCW 5 104 2 5 105 2 3 PIPE REYNOLDS NO., Re = VD/» 100 WATER + ~200 ppm N~BUTYL ALCOHOL SCHMIDT NO. = 419 BUBBLE 50 MEAN DIAMETER HORIZONTAL VERTICAL " (in) FLOW FLOW 0.015 0.02 0.03 20 0.04 10 CALCULATED ASYMPTOTES 5 > 1 103 2 Figure b5, Unadjusted Mass Transfer Coefficients Versus Pipe Reynolds Number as a Function of Bubble Sauter-Mean Diameter. Water Plus ~200 ppm N-Butyl Alcochol., Horizontal and Vertical Flow. UNADJUSTED MASS TRANSFER COEFFICIENT (ft/hr) K, 100 50 20 149 — n—— — VERTICAL/ FLOW 2 PIPE REYNOLDS NO., Re = VD/v 12 5% GLYCERINE SCHMIDT NO. = 370 BUBBLE ME AN DIAMETER HORIZONTAL VERTICAL (in) FLOW FLOW 0.015 ° O 0.02 N a 0.03 A A 0.04 v v CALCULATED ASYMPTOTES 103 2 5 104 Figure 46, ORNL-DWG 71-7985 OCUS OF Y "/ \—HORIZONTAL FLOW 105 Unadjusted Mass Transfer Coefficients Versus Pipe Reynolds Number as a Function of Bubble Sauter-Mean Diameter. 12.5% Glycerine-87.5% Water. and Vertical Flow. Horizontal k, UNADJUSTED MASS TRANSFER COEFFICIENT (ft/hr) 50 20 150 ORNL-DWG 74-7986 25% GLYCERINE SCHMIDT NO. = 750 BUBBLE MEAN DIAMETER {in)) ! | HORIZONTAL VERTICAL FLOW FLOW ©.015 0.02 0.03 0.04 LOCUS OF Fi/Fg = 1.5 ALCULATED ASYM PTOTES t HORIZONTAL FLOW VERTICAL FLOW 103 2 5 104 2 5 105 PIPE REYNOLDS NO., Re = VD/v Unadjusted Mass Transfer Coefficients Versus Pipe Reynolds Number as a Function of Bubble Sauter-Mean Diameter. 25% Glycerine-75% Water. Horizontal and Vertical Flow. UNADJUSTED MASS TRANSFER COQEFFICIENT {ft/hr) k, 151 ORNL—DWG 71-7987 100 37.5% GLYCERINE SCHMIDT NO. = 2015 o o BUBBLE ME AN DIAMETER HORIZONTAL VERTICAL (in.) FLOW FLOW 0.015 0.02 0.03 0.04 ™ o LOCUS OF Fi/Fg = 15 o |82 / ' o1 C T f!f —— __CALCULATED — /ASYMPTOTES - l’..’ | HORIZONTAL A FLOW | VERTICAL FLOW 103 2 5 104 2 5 10° ' PIPE REYNOLDS NO., Re = vD/» Figure 48. Unadjusted Mass Transfer Coefficients Versus Pipe Reynolds Number as a Function of Bubble Sauter-Mean Diameter. 37.5% Glycerine-62,5% Water. Horizontal and Vertical Flow. k, UNADJUSTED MASS TRANSFER COEFFICIENT (ft/nr) 50 no O o w N 152 50% GLYCERINE SCHMIDT NO. = 3446 | ORNL-DWG 71—7988 5 103 BUBBLE MEAN DIAMETER HORIZONTAL VERTICAL (in.) FLOW FLOW 0.015 O 0.02 0 0.03 A 0.04 v LOCUS OF Fi/Fq = 1.5 A4S A CALCULATED V/fi—-fi' ASYMPTOTES 1% Ua® -0 - o 103 2 5 104 2 PIPE REYNOLDS NO., Re = VD/v Figure 49, Unadjusted Mass Transfer Coefficients Versus Pipe Reynolds Number as a Function of Bubble Sauter-Mean Diameter., 50% Glycerine-50% Water. Vertical Flow. Horizontal and k, MASS TRANSFER COEFFICIENT (ft/hr) 153 ORNL—DWG 71-—7975 QL (gpm) Re O 20 35 583 P 35 62,269 o A 50 88,955 A 70 124,537 v 80 142 328 v 100 177,913 5 /20, 35 6 ° / 4 e A =7 50, 70 3 J 100/ 2 / A , _ WATER + ~200 ppm N-BUTYL ALCOHOL 8O// SCHMIDT NO. = 419 A Qg/OL = 0.3% 70/{ VERTICAL FLOW IN 2—in. CONDUIT 1 504 20, 35 0 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 dys, BUBBLE MEAN DIAMETER (in.) Figure 50. Mass Transfer Data Adjusted for End-Effect. Water Plus ~200 ppm N-Butyl Alcohol, Vertical Flow. ' 154 ORNL-DWG 7T1-7976 7 o QL (gpm) Re S o 50 88,955 _ ® 60 106,746 5 A 70 124,537 5 La 80 142,328 E v 90 160,119 5‘5 e = == | EAST SQUARES LINES PASSING THROUGH = ORIGIN FOR DIAMETERS UP TO 0.035 w 4 o 70,80 o ? / 60 1t p / i 90 2 / & 50 3 A\ A7 s’ - g 5 < p= ‘f/// xfl / / / WATER + ~200 ppm N-BUTYL 1 ALCOHOL | /’ SCHMIDT NO. = 419 Qg/QL = 0.3% HORIZONTAL FLOW IN 2-in. CONDUIT 0 i | l 0 0 .01 0.02 0.03 0.04 0.05 0.06 dys, BUBBLE MEAN DIAMETER (in.) Figure 51, Mass Transfer Data Adjustéd for End-Effect. Water Plus ~200 ppm N-Butyl Alcohol. Horizontal Flow. k, MASS TRANSFER COEFFICIENT (ft/hr) 155 ORNL—DWG 71-7977 dvs, BUBBLE MEAN DIAMETER (in.) Figure 52. Mass Transfer Data Adjusted for End-Effect. 12.5% Glycerine-87.5% Water. Vertical Flow, 9 QL (gpm) Re O 20 25,718 8 L © 35 45,006 A 50 64,294 A 65 83,583 . 20 6 5 / 35,50 o /‘65 A o A 7 A”A A 12.5% GLYCERINE SCHMIDT NO. = 370 Qq/QL = 03% VERTICAL FLOW IN 2-in. CONDUIT | | | I 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 K, MASS TRANSFER COEFFICIENT (ft/hr) 156 ORNL—-DWG 71-7978 8 12.5% GLYCERINE SCHMIDT NO. = 370 Qg/QL = 0.3% 2 HORIZONTAL FLOWAIN 2—in. CONDUIT QL.(gpm) BQ O 35 45,006 6 —e 50 64,294 — A 65 83,583 A 75 96,442 v 85 {09,302 5 — —_— ] —-— | FAST SQUARES LINES PASSING THROUGH ORIGIN FOR DIAMETERS UP TO 0.035 in. 1 //85 4 3 ’.—- 2 35 o~ / i O O 0.01 0.02 0.03 0.04 0.05 0.06 dys, BUBBLE MEAN DIAMETER (in.) Figure 53. Mass Transfer Data Adjusted for End-Effect. 12.5% Glycerine-87.5% Water. Horizontal Flow. k, MASS TRANSFER COEFFICIENT (ft/hr) 157 ORNL—DWG 71-7979 dvs, BUBBLE MEAN DIAMETER (in.) 7 ; | 25% GLYCERINE SCHMIDT NO. = 750 s | Qa/Q = 03% VERTICAL FLOW IN 2-in. CONDUIT OL (gpm) Re O 20 17,636 5 ® 30 26,454 A 40 35 272 A 50 44,090 | v 60 52,908 4 | 207 O 0 30 / 3 ® 60 y N 2 / // Y/ j/d o’ Az ” 1 | / x M_. | 0 i 0 0.01 002 0.03 0.04 0.05 0.06 Figure 54. Mass Transfer Data Adjusted for End-Effect. 25% Glycerine-75% Water. Vertical Flow. 158 ORNL—-DWG 71{—7980 k, MASS TRANSFER COEFFICIENT (ft/hr) 7 25% GLYCERINE SCHMIDT NO. = 750 Qg/Q-{_ = 0.3% 6 HORIZONTAL FLOW IN 2—in. CONDUIT | | | Q_ (gpm) Re o 40 35272 5 o 45 39,681 A 50 44,090 A 55 48,498 v 65 57,317 v 75 66,135 4 }— ' ] LEAST SQUARES LINES PASSING THROUGH ORIGIN FOR DIAMETERS UP TO 0035 in. 3 2 1 O O Q.01 0.02 003 0.04 0.05 0.06 dvs, BUBBLE MEAN DIAMETER (in.) Figure 55. Mass Transfer Data Adjusted for End-Effect. 259 Glycerine-75% Water. Horizontal Flow. 159 ORNL—DWG 71—7981 S [37.5% GLYCERINE SCHMIDT NO. = 2015 Qg/QL = 0.3% HORIZONTAL FLOW IN 2-in. CONDUIT - 5 = | | < QL {gpm) Re }_ O 35 22.889 zZ ., |e 40 - 26,159 o A 45 29,429 i A 50 32,699 il S v 55 35,968 x ° [V 60 39,238 § D 70 45,777 2 55 b> F. C. Zapp Central Research Library Y-12 Document Reference Section Laboratory Records Department Laboratory Records Department (RC) EXTERNAL DISTRIBUTTION Norton Haberman, AEC-Washington Milton Shaw, AEC-Washington Division of Technical Information Extension (DTIE) Laboratory and University Division, ORO Director, Division of Reactor Licensing Director, Division of Reactor Standards Executive Secretary, Advisory Committee on Reactor Safeguards