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Effect of orientation on heat and mass transfer in stacked beds of spheres Galloway, Leslie Robert 1955

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EFFECT OF ORIENTATION ON HEAT AND MASS TRANSFER IN STACKED BEDS OF SPHERES by LESLIE ROBERT GALLOWAY A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE in the Department of CHEMICAL ENGINEERING We accept this thesis as conforming to the standard required from candidates for the degree of MASTER OF APPLIED SCIENCE Members of the Department of Chemical Engineering THE UNIVERSITY OF BRITISH COLUMBIA September, 1955 ABSTRACT Heat, mass and momentum transfer rates have been measured in two stacked beds of porous spheres having equal fractional void volume but dif-ferent orientation with respect to the direction of fluid flew* An air-water system was studied under essentially adiabatic conditions over a Reynolds number range 100-1200* Orientation had negligible effect on heat and mass transfer rates though considerable effect on friction factor* An explanation for this behaviour is presented in terms of a dif-ference in the degree of turbulent wake formation for the two assemblages, similar to that observed in comparable banks of closely packed staggered and in-line heat exchanger tubes* The experimental results contradict simple analogies between momen-tum, heat and mass transfer which show a direct proportionality between total friction factor and heat and mass transfer factor* Measured friction factors were about 50% in excess of those obtained by Martin for similar assemblages of smooth metal spheres. This is explained by the higher surface roughness of the refractory-like spheres used in the present investigation* A0KNOWLM)GMSNT3 I wish to acknowledge the assistance and encouragement received from Dr. Norman Epstein, under whose guidance this investigation was made and the helpful suggestions and assistance i n constructing the apparatus of Mr. Frank Sawford, Workshop Technician* I am also indebted to the National Research Council for providing financial assistance. TABLE OF CONTENTS Page ACKNOWLEDGMENTS ABSTRACT NOMENCLATURE INTRODUCTION 1 LITERATURE REVIEW 3 1. METHODS OF CORRELATING DATA 3 a* Pressure Drop b- Mass Transfer and Heat Transfer 4 2. THE EFFECTS OF ORIENTATION , 7 3. THE EFFECTS OF SURFACE ROUGHNESS 6 4. THE EFFECTS OF VOIDS 8 5. THE ANALOGY BETWEEN HEAT AND MASS TRANSFER AND MOMENTUM TRANSFER 9 APPARATUS 12 1* AIR SUPPLY 12 2* ENTRAINMENT SEPARATOR 15 3. ORIFICE 15 4. HUMIDITY DETERMINATION 16 5. THERMOMETERS 17 6. PACKING 17 EXPERIMENTAL PROCEDURE AND RESULTS 25 1. OPERATING PROCEDURE 25 2. CALCULATING PROCEDURE 25 3* RESULTS 28 Page DISCUSSION 1. ASSUMPTION OF WET BULB TEMPERATURE AT THE SURFACE OF THE PACKING 34 2. EFFECTS OF ORIENTATION 37 3. ANALOGIES BETWEEN HEAT, MASS AND. MOMENTUM TRANSFER IN PACKED BEDS 40 4. SURFACE ROUGHNESS 41 5. RELIABILITY OF THE DATA 41 6* COMPARISON WITH PUBLISHED RANDOM PACKING DATA 42 IROPOSALS FOR FURTHER STUDY 44 SUMMARY 46 BIBLIOGRAPHY 48 APPENDIX 51 Appendix 1* Flow Coefficient, K, for Flange Taps in 2" Pipe 52 Appendix 2* Calibration of Thermometers 53 Appendix 3. Humidity as a Function of Dew Point 55 Appendix 4* Saturation Pressure of Water Vapor as a Function of Dew Point 56 Appendix 5* Schmidt Number and (Schmidt Numberf^ as a Function of Temperature 57 Appendix 6* Viscosity of Air as a Function of Humidity and Temperature 58 Appendix 7. Pressure Drop through the Packing as a Function of the Fluid Velocity with Number of Layers of lacking as Parameter 59 Appendix 8* Calibration of Thermocouples 61 Appendix 9* Psychrometric Chart Based on Wet Bulb Temperature 6g Appendix 19. Original Data and Calculated Data 66 LIST OF T.A'RT.Tgj Table Page I Characteristics of the Packings 21 II Experimental Values of J H, j d and f 33 LIST OF FIGURES Figure Page 1. Schematic Diagram of Apparatus 13 2* Schematic Diagram of Air Sampling Lines 14 3* Isometric Views of the two Orientations of Packings Used 18 4* Photograph of the Orthorhombic No* 2 Assemblage 23 5* Photograph of the Orthorhombic No. 4 Assemblage 24 6* A.Plot of Heat Transfer Factor versus Reynolds Number 29 7* A Plot of Mass Transfer Factor versus Reynolds Number 30 8. A Comparison of Friction Factors obtained in this Investigation with those of Martin for Smooth Spheres 31 NOMMCLATOHE a = Surface area of the solids per unit volume of bed, sq.ft./cu.ft* A§ = Area available to heat or mass transfer, sq.ft. A » Constant dlmensionless B a Constant, dlmensionless b a Constant, dlmensionless o * Constant, dlmensionless C^  a Concentration of diffusing component in inlet stream, lb* moles/cu.ft. Cg a Concentration of diffusing component in exit stream, lb* moles/cu.ft. C* a Equilibrium concentration of diffusing component in stream, lb* moles/cu.ft. 0^ a Specific heat at constant pressure, B.t.u./(lb.)(°F.) D a Inside pipe diameter, ft. Dp a Effective particle diameter, ft. D T a Diffusion coefficient of gas in the film, sq.ft./hr. f a Friction factor • g^AlDp { in packed bed, dlmensionless 2G2 L fjj. a Modified friction factor a %f • £ 3 , dlmensionless SO 1 - *3 G a Mass velocity based on empty column, lb*/(hr.)tsq.ft.) o go a Gravitational constant, (lb.-foree)(ft.)/(lb.-mass)(sec. ) h » Heat transfer coefficient for gas, B.t*u»/(hr.)(sq.ft.)(°F.) a Mass transfer factor a kgPgfM^ ( ^(A \ 2^ 3, dlmensionless JH a Heat transfer factor a h / Op/* | *, dlmensionless k' a Mess transfer coefficient, lb./(hr.)(ft2)(humidity difference) k a Thermal conductivity of f luid, B.t.u./(hr. Hsq.ft. ) l ° F . / f t . ) k = Mass transfer coefficient of gas film, (lb. moles)/(nr.)(sq.ft.)(atm.) K « Orifice flow coefficient, dimensionless 1 s Height of column, ft . M^ = Average molecular weight of fluid, lb . / lb . mole Nu s Nussult number for heat transfer = hDp/k, dimensionless Nu1 s Mass transfer number analogous to Nu for heat transfer 8 3 KgPgf^ mDp/^  ° v f o r packed beds, dimensionless q B Rate of heat transfer, B.t.u./hr. Pgf B Arithmetic mean partial pressure of the non-transferred gases in the gas film, l n . H g » - P l ) + (p g - pgj/2 P«l « Partial pressure of water vapor at temperature t W l , in. Hg P« = Partial pressure of water vapor at temperature t , in. Hg B Partial pressure of water vapor in entrance air, in. Hg Pg » Partial pressure of water vapor in exit air , in. Hg A Pl.m. s Log mean partial pressure of the transferring gas in the gas film - (P» i - PI) - C P » 8 " PS) f a t m . In *1 " p l F s Total pressure, atm. A P = Pressure drop, lb * * foree / sq . f t « -dP B Decrease in pressure, lb.-force/sq.ft. Pl B Absolute pressure at inlet of bed, in. Hg Pg s Absolute pressure at outlet of bed, in. Hg Fr B Prandtl number = G^ji/k, dimensionless Re B Reynolds number » DpVo^//^ l n packed bed, dimensionless Sc B Schmidt number = jxJ £ D V , dimensionless • Temperatare of Inlet air , °F* tg = Temperature of outlet air , °F* tn^ * Wet bulb temperature of inlet air , °F* t_ « Wet bulb temperature of exit air, °F* w2 A t i . m # = Log mean temperature difference = (*•! " *1> - ( t , 2 - t 8 ) ^ 0 y < in *»1 • *1 tw2 - t2 -CAt) = Decrease in temperature of the transfer medium, ° f« V 0 B Superficial velocity based on empty column, f t . / sec V s Volume of packing, cu.ft. w • Rate of mass transfer, lb* moles diffusing component/hr. Greek Symbols 6 = Fractional void volume in packed bed, dimensionless 0 - Function in momentum transfer equations, dimensionless 0' = Function in mass transfer equations, dimensionless 0" a Function in heat transfer equations, dimensionless a Density of f luid, lb./cu.ft. s Viscosity of f luid, lb . / ( f t . ) (sec) 1 INTRODUCTION In the past decade the field of heat, mass and momentum trans-fer in systems where assemblages of particles are contacted by a fluid stream has received considerable attention* New industrial applications, the demand for reliable design equations and the desire to understand more fully the basic mechanisms of these transfer processes have been reasons for this increased activity* Fixed beds, that is beds in which the fluid moves past a station-ary assemblage of particles, were probably the f irst venture into this very broad f ield. For example, blast furnace operation and filtration have been used for centuries. Moving beds, fluidized beds and a late in-novation - spouted beds - are developments of more recent years. The subject of heat, mass and momentum transfer in fixed beds has been investigated extensively (27). Many empirical correlations relating various modified Reynolds numbers with friction factor, mass transfer factor and heat transfer factor have been presented. The bulk of this work, however, has been made with random packed beds. The fact that published data on pressure drop through packed beds have not correlated too well led Martin et al (43) to investigate the effects of orientation of packing on pressure drop. They found that con-siderable effect due to orientation did exist. Lit t le or no attention, however, has been paid to heat and mass transfer rates in orientated beds. The object, then, of this investigation has been to measure heat and mass transfer rates in two specific packings used by Martin. These 2 packings, although having the same voidage and even the same basic arrange-ment when viewed in isolation, differed in orientation with respect to the direction of flow and yielded considerably different friction factors, a l l other variables being equal. LITERATURE REVIEW The transfer processes that occur when a f l u i d flows through a fixed assemblage of solid particles have received the attention of a mul-titude of investigators in the past. Their objectives were to obtain equations that could be used for design purposes and to increase the know-ledge of the basic mechanisms involved in these transfer processes. It was apparent that the complexity of these mechanisms did not lend them-selves to immediate theoretical treatment. Hence, the treatment of this subject by most workers has been on an empirical basis. 1. METHODS OF CORRELATING DATA a. Pressure Drop f r i c t i o n is found, by application of dimensional analysis, to be expressed by the following equation This expression csn be integrated across the length of the duct i f the velocity, density, and diameter of the duct are assumed to remain constant to give When f l u i d flows in a circular duct the pressure drop due to I D (2) This can be written as 4 where Equation 3 is the so-called Fanning equation* By rearrangement of equation 3 i t is found that f « APB eD (5) By experimentation i t is possible to establish the relation that exists between friction factor and Reynolds number* A modified version of equation 5 has been used to calculate friction factor in packed beds: f « APgeDp (5a) 2 £ V § L This value of friction factor is obtained as a function of a modified Reynolds number. Dp7 0?^i • Several authors have proposed other modifications of the Fanning equation to take account of variables in the packing such as voids, roughness and shape of particles* These shall be considered under separate headings* b. Mass Transfer and Heat Transfer When a concentration gradient of a component exists within a phase, there is a potential available tending to transfer the component In the direction of decreasing concentration. The rate at which this component is transferred is directly proportional to the concentration gradient and the area available for transfer. Thus, w X V - A C ) (6) or w » k A g ( - A C) (7) 5 Under steady state conditions, for mass transfer in the gas phase, equation 7 becomes (24) w = kg-BAPi.m. 18) An analogous situation exists for heat transfer in as much as the rate of heat transfer is also direct ly proportional to the driving force, in this case temperature gradient, and the area available for heat transfer. That i s , q <x AgC-At) (9) or q = hAg(-At) (10) Under steady state conditions, equation 10 becomes (24) q = hAgAt!.^ (11) Three methods are available for expressing transfer rates. These are the transfer coefficients, k g for mass transfer and h for heat transfer; the transfer factors for mass transfer and jjj for heat transfer; and the height of a transfer unit , (H.T.U.) H for heat transfer and (H.T.U.)^ for mass transfer. The transfer coefficients have the advantage of sim-p l i c i t y but have the disadvantage of not being dimensionless and not re-lating the properties of the system. Chilton and Colburn overcame this problem by developing the transfer factors (10) and the height of the transfer unit (11). The development of the transfer factors came about in the follow-ing manner. If dimensional analysis i s applied to the correlation of mass transfer coefficients in wetted-wall columns and to the correlation of heat transfer coefficients in circular ducts for turbulent flow, the following equations are obtained: for mass transfer, fcgPgfMmD and for heat transfer, 0 75> (12) h D (13) k l \ / c / A k For empirical correlation purposes i t is usually assumed that equations 12 and 13 may be simplified respectively to e»v (14) and h D B c^-y (- (15) By rearranging the terms in equations 14 and 15, they become respectively / \ b - l , \ c-1 G ( M \ ^\ (16) and B CpG (17) Chilton and Colburn (10) have defined the transfer factors as 2/3 Jd _kgP, G (18) and C pG 2/3 (19) If z = C = 1/3, as has been demonstrated experimentally (55), then equations 16 and 18, and equations 17 and 19 can be combined respectively to give 7 J d » AtRe) (20) and J H » B(Re) y" 1 (21) These correlations have been extended to heat and mass transfer in packed beds by making the necessary modifications to the dimensionless groups. These modifications are attempts to adequately describe the flow of fluid past the solid particles and include substitution of D p for D and, in some cases, the introduction of a voidage term and a particle shape factor* A more general expression for equations 20 and 21 applied to packed beds would be, respectively, Jd - 07 (Re) (22) and J H - P l (Re) (23) since i t is found that the constants A, B, b and z when the fluid is tur-bulent are different in value from those when the fluid is laminar* 2* THE EFFECTS OF ORIENTATION Of the multitude of works published in heat transfer (8, 21, 24, 42, 49, 52, 60), mass transfer (12, 13, 17, 22, 24, 26, 27, 29, 46, 51, 52, 56, 57, 61) and momentum transfer (4, 7, 8, 14, 16, 24, 35, 38, 39, 47) in packed beds, comparatively no attention has been paid to possible effects of orientation. Martin, McCabe and Monrad (43) made perhaps the only formal in-vestigation on the effects of orientation of packing on transfer rates. Their work was confined only to friction factor measurements. They found that packings of equal voidage but different orientation produced, at 8 equal Reynolds numbers, widely differing f r i c t i o n factors* Orientation effects i n heat and mass transfer have received even less attention* Taecker and Hougen (57) mention, in passing, that no significant differences in j H were obtained in comparing random with staggered arrangements of pack-ings (saddles and rings)* 3. THE EFFECTS OF SURFACE ROUGHNESS Surface roughness effects on pressure drop through packed beds have been studied by Leva et a l (40). They report an increase in f r i c t i o n factor as surface roughness i s increased when testing aloxite granules, clay Raschig rings, alundum cylinders and clay balls in tubes in turbulent flow* Campbell and Huntington (7a) report similar results. Brownell and Katz (5) found that comparison of data on lead spheres and on celite spheres indicated that the c e l i t e spheres exhibited a greater resistance to flow than did the lead spheres under similar conditions. This difference they attribute to roughness. No studies on the effects of particle surface roughness on heat and mass transfer between fluids and packed beds have been found reported. 4. THE EFFECTS OF VOIDS The effects of void volume on pressure drop have been investigated by many workers (3, 6, 7, 14, 16, 19, 20, 25, 33, 34, 40, 41, 44, 58). The Importance of including a void volume term in correlating f r i c t i o n factor measurements i s well known, but how this should be done has become a point of controversy (14). The effects of voids on heat and mass transfer have not received the same amount of consideration. Several authors (15, 17, 22, 23, 29, 31) use the void fraction term in their correlations of mass transfer with Reynolds number. In some cases, i t is used in an attempt to define a 9 Reynolds number of the fluid moving past the solid particles (15, 22). Others introduce the term in order to correlate fixed beds with fluidized beds (17, 31), while s t i l l others have used i t to relate published data (23,29) for different packings* Gamson (23), when he plotted reported mass transfer data for spherical particles (24, 27, 46) as J d versus a modified Reynolds number, 6G/a/i, found that a series of curves resulted with the void volume of the system as parameter* He was able to consolidate a l l these reported data for spherical particles into a.single generalized correlation 0 2 by plotting J d/(l-fc) * versus 6G/a/t.'C» D pG^ (1-6) ). Data reported by Hobson and Thodus (27) and McCune and Wilhelm (46) were not ln as good agreement in the transition region (10 < BG/syU, < 100). This lack of agreement was attributed by Gemson to the indefinite flow pattern of this region* Gamson et al (24) in their investigation found that while pressure drop was a function of the voidage, mass and heat transfer factors were not affected at a l l . 5. THE ANALOGY BETWEEN HEAT AND MASS TRANSFER AND MOMENTUM TRANSFER - Considerable theoretical and empirical work has been done to establish an analogy between heat, mass and momentum transfer in circular conduits (32). Several authors (15, 31, 50) have attempted to extend this analogy to packed beds* Ranz (50) considers that transfer rates in packed beds of spheres occur as a summation of the transfer rates about the consituent spheres in isolation, the effective velocity past the spheres being taken as the super-f i c i a l velocity divided by the minimum fractional free area of the packing. He is thus able to correlate turbulent heat, mass and momentum transfer data in randomly packed beds with those for an isolated sphere. His derivation 10 leads to the result that two packed beds of spheres with the same voids, but so alighed as to offer quite different minimum fractional free area to fluid flow, would not only show markedly different fluid friction characteristics, but also correspondingly different heat and mass transfer rates. Ergun (15) has proposed for packed beds an equation which he found correlated fluid friction data quite well. The equation presented is f k » 150^ (1-6 ) + 1.75 (24) D p G The analogy for mass transfer claimed here is that F K = J ! P _ E ^ °2 " C l t 2 5> L 1-6 <Z Dv C + - C 2 for complete longitudinal mixing of the fluid in the bed and f k - _Dp_ e M l a o * - Qi f26) L 1 - <£ D,. c * - c 2 for the case of no longitudinal mixing. Some degree of correlation was ob-tained between mass transfer and fluid friction for liquid systems on assum-ing no fluid mixing. However, l i t t l e success was obtained with gaseous systems for which perfect mixing was assumed. Ergun claims that this was due to the deficiency and uncertainty of published gas stream data but he offers no direct experimental evidence for his mixing assumptions. No attempt was made to correlate heat transfer data. Ju Chin Chu et al (31) have investigated mass and momentum transfer in fixed and fluidized beds and have proposed a modification to the Chilton and Colbura analogy (10) which may be written (f/2) ( 6 5 / l - £) - 5(Sc) 2 / 3 (27) V g f v<> or j d - (f/10) (£ 3 / l - 6) (28) 11 Fair agreement with experimental data for randomly, packed and fluidized beds is obtained over a Reynolds number range of 1 - 10*000. Here again the results indicate, as in equation 28, a direct dependence of j d on f, regard-less of what factors (e.g. orientation) bring about the variation of f at a given Reynolds number and packing voids. APPARATUS 12 The rates of heat, mass and momentum transfer vere made using an air-water system. Air was passed through a bed of porous spheres (to be described later) which had been previously soaked, in water. This method corresponds to that used by (Samson et al (24), Taecker and Hougen (57), Wilke and Hougen (61) and Hobson and Thodos (27). The apparatus is illustrated schematically in Figure 1. Air, which was obtained from the building supply, was conveyed to the packed bed through 2-inch commercial steel pipe. Air flow rates were measured with a standard orifice using flange pressure taps. The pressure drop through the orifice was measured with a 60-inch vertical water manometer. Calibrated thermometers reading to the nearest 0.1°F were positioned at the inlet and outlet of the column housing the packing. A series of sampling lines shown schematically in Figure 2 were used to enable humidity determinations to be taken of both inlet and outlet air streams throughout the run. Humidity was measured with a Foxboro *Dewcelrt Dew Point Recorder. Pressure drop measurements through the packing were made with a Hays Corporation Draft Gauge reading to the nearest 0*005 inches of water* A more detailed description of the apparatus wil l now follow* 1. AIR SUPPLY The air, which was used at room temperature for a l l runs, was ob-tained from the building supply. It has a maximum rate of 127 lb./hr. which corresponds to a Reynolds number of approximately 1200 through the packing. A centrifugal air blower driven by a 2 H.P* motor and delivering air at a maximum flow rate of 50,000 cu* ft./hr* at a pressure of 12 inches of water was also installed in the system in order to obtain higher Reynolds numbers; however, it was not used. Draft Gauge measuring Pressure Drop through Packing Upstream Pressure Air from Blower 1 M Orifice Pressure Drop Orif ice Pressure at Bottom of Packing From " Dewcel " Sample to "Dewcel" Entrainment Separator Air from Building Supply Thermometer Assemblage of Spheres Thermometer Sample to " Dewcel' To I Atmosphere) ? t Figure 1. Schematic Diagram of Apparatus To Atmosphere Inclined Manometer ca l ibrated as Velocity u of Air through Dewcel Chamber Exit Air Sample Check Valve -o<-X Chamber housing "Dewce l ' 3 i Constr ict ion in Line Vert ica l M a n o m e t e r measuring P r e s s u r e in Chamber To Atmosphere To ^ Atmosphere -oo-X T h r e e - way Cocks — Air from Building ^_ Supply •HX3-To Packed Column Air f rom Blower 4X] 1 Figure 2. Schematic Diagram of Air Sampling Lines 15 2. ENTRAINMENT SEPARATOR An entrainment separator was installed in the lines coming from the building air supply to remove entrained water* It consisted of a closed cylinder 2 3/4 inches in diameter and 9§ inches long, fitted with standard 3/4-inch pipe couplings at both end3. Two baffles were placed perpendicular to the air flow and 4 inches from either end of the cylinder* These baffles were circular and of the same diameter as the inside of the cylinder* Holes, 3/8-inch in diameter, were drilled in the baffles in such an arrangement that the air which passed through the holes of the fi r s t baffle would im-pinge upon the second baffle. 1-^-inch lengths of 3/8-inch brass tubing were pressed into the holes in order to prevent the separated water from being picked up again by the air stream* Drains were installed slightly upstream from each baffle* 3* ORIFICE Air was metered through standard orifices constructed according to the specifications given in the A.S.M.E. Report on fluid meters (2)* Pressure drops were measured with flange taps made according to the re-commendations in the report* Three orifice plates were machined having openings of and 3/4-inches, thereby allowing flow rates to be measured over a wide range* Values of flow coefficient K were taken from this report and plotted as a function of the Reynolds number through the orifice with the ratio of the diameter of the orifice to the diameter of the pipe as par-ameter* This plot may be found in the appendix. The £-ineh orifice was calibrated using a 900 cu. f t . per hr* capacity diaphragm-type gas meter calibrated to an accuracy of Z% The calibration of the orifice showed an average deviation in K from those given in the report of. only VjU It was therefore considered unnecessary to calibrate the other two orifices* 16 4, HUMIDITY DETERMINATION The determination of moisture content by measuring the dew point is considered by Ewell (18) as the most accurate absolute method. Wet bulb measurements require elaborate set-ups (54) while gravimetric methods have been found inaccurate for highly humid air (45). Consequently, a Foxboro "Dewcel", which measures dew point automatically to the nearest 0.5°F, was considered best for this investigation. Moisture determination by the •Dewcel" is based on the fact that for every water vapor pressure in contact with a saturated salt solution, there is an equilibrium temperature at which this solution neither absorbs nor gives up moisture to the surrounding atmosphere. The "Dewcel" is a thin-walled metal socket covered with a woven glass tape Impregnated with lithium chloride, and wound with a pair of silver wires connected to a 25-volt alternating current power supply. The lithium chloride, being hygroscopic, absorbs moisture and becomes a solution. The conductiv-ity of the salt is increased, allowing a larger current to flow through the silver wires with the result that the temperature of the "Dewcel" rises, the solution dries up and the amount of current passing through the wires is re-duced. The "Dewcel" then cools, absorbs more moisture and the cycle is re-peated until equilibrium is attained. A liquid expansion thermometer in-dicates the temperature of the "Dewcel" and is recorded on a chart calibrated in dew point temperature. An attempt to calibrate the instrument with a gravimetric deter-mination resulted in the "Dewcel" reading consistently higher humidities than the gravimetric method. This result would be expected i f the absorbing material (in this case magnesium perchlorate) did not remove a l l the moisture. A further check was made using wet and dry bulb thermometers. In this case the "Dewcel" indicated a lower humidity. Since it is probable that the 17 wet bulb thermometer was reading too high and therefore indicating too high a moisture content, and since the gravimetric and wet and dry bulb deter-minations bracketed the "Dewcel" determination, i t was believed that the "Dewcel" was reading accurately. A further calibration was made by checking the temperature indicating element of the "Dewcel" against a calibrated ther-mometer. This resulted in an average deviation of 0.38$ in the humidity corresponding to the temperature of the "Dewcel" element from the humidity corresponding to the temperature indicated by the calibrated thermometer. 5. THERMOMETERS The thermometers were calibrated against a Leeds & Northrup Co. platinum resistance thermometer bearing a National Bureau of Standards certificate dated August 14, 19S9. Calibration curvea are included in the appendix. 6. PACKING Perhaps the major portion of this investigation was spent in formulating a suitable packing material, finding a method of molding the packing and performing the manufacturing operation. The objective of this investigation was to compare two packings used by Martin et al (43) having the same voidage but showing widely different friction factors. Such packings are those designated by Martin as Orthorhombic No. 2 Clear Passage and Orthorhombic No. 4. Figure 3 shows these packings in isometric view. It will be noted that the basic arrange-ment of the spheres is the same in both packings when the packings are viewed in isolation; however, when viewed along the major axis of flow the orienta-tions are quite different. This investigation was, therefore, a study of Direction of ORTHORHOMBIC NO. 2 ORTHORHOMBIC NO.4 Figure 3. Isometric Views of the two Orientations of Packing Used 20 were required for the two packings. Each sphere was measured to the nearest •001-inch across three diameters with a micrometer and an average diameter determined. The average diameter was 0.673-inch with a standard deviation of 0.004-inch. In order to pin the spheres together, i t was necessary to d r i l l six holes in each sphere in appropriate locations. The spheres were pinned together with 0.022-inch diameter stainless steel fishing wire, the wire being secured in each hole with Araldite AN-104 cement. The characteristics of each of the two packings are given in Table I. In determining surface area, the correction for the transfer area lost by d r i l l i n g six holes in each of the spheres was calculated to be only 1.08$ and was considered negligible. Wall porosity was eliminated by using fractional spheres at the walls as was done by Martin et a l (43). It was therefore necessary to construct two columns in which to housethe packings: a square column for Orthorhombic No. 2 and a hexagonal column for Orthorhombic No. 4. The bundles of spheres were enclosed on a l l sides except the top and bottom by l/16-inch brass plate glued to the faces of the fractional spheres with Araldite AN-104. This was done mainly to afford protection to the somewhat delicate packing and had the additional advantage of avoiding the use of a supporting grid, thereby eliminating a source of entrance effects. In order to measure entrance and exit effects i n the packing as well as the total pressure drop through the packing, pressure taps were located in one of the brass sides at five different locations: at the bottom of the packing, between the 2nd and 3rd layers of spheres, between the 4th and 5th layers, between the 6th and 7th layers, and at the top of the 8-layer packing. This allowed pressure differentials between the bottom and any of TABLE I CHARACTERISTICS OF PACKINGS Orientation Shape of Container Cross-Sectional Dimensions Inches Cross-Sectional Area ft2 No* of Spheres Height of Bed Inches Smallest Fraction Free Area Surface Area Void Volume Orthorhombic No. 2 Square i i i x 4 ± i 16 16 0.1526 392 4.660 0.219 3.8690 0.3954 Orthorhombic Regular No.4 Hexagon 2 i i on 16 a l l sides 0.1303 384 5.381 0.093 3.7900 0.3954 to 22 the other four positions to be measured. The two columns used to house the assemblages of spheres were made from and 1/8-inch aluminum plate. The inside cross-sectional dimensions of these columns were slightly larger than the outside dimensions of the corresponding packing. This afforded a snug f i t when the assemblage of spheres with brass side plates was placed in the column. In order to maintain a constant cross-sectional area throughout the entire length of the column, the column was lined with brass plate above and below the packing. The columns were made in two longitudinal sections, bolted together with a flange. The bottom section housed the packing assembly, the top of which was flush with the top of this section. Pressure lines from the taps in the side of the assemblage were brought through the column at the flange. This was done by running the lines from the taps to a brass plate at the top of the packing assembly. This plate, which was placed perpendicular to the direction of flow and parallel to the flange, was attached to the top of the wall containing the pressure taps. It contained five 1/8-inch diameter channels, one for each of the pressure lines. The plate was of sufficient length to project through the aluminum column past the periphery of the flanges. Compression f i t t i n g s were screwed into the projecting end of the plate, to allow connection of pressure leads to the draft gauge. The columns were insulated with approximately 2 inches thick glass wool. Figure 5. Photograph of the Orthorhombic No. 4 Assemblage 25 EXPERIMENTAL PROCEDURE AND RESULTS 1. OPERATING- PROCEDURE Each, packing was soaked in tap water for a period of not less than three hours. The temperature of the water was controlled by placing the container holding the packing and water in a constant temperature bath. The temperature was held as close as possible (+ 3.0°?.) to the wet bulb temperature of the ai r entering the packing during the experimental run* The packing, when removed from the water, was shaken vigor-ously to remove excess water, and then immediately placed in the bottom section of the column* In order to prevent a i r by-passing the packing by flowing in the small space between the outside wall of the packing and the inside wall of the column, this space was sealed off at the top of the column with scotch tape* A gasket of latex dental dam was used around the brass plate housing the pres-sure lines to prevent air leaking to the atmosphere. The entire operation of preparing the column for a run required about 15 minutes* Once the column was secured in place, pressure lines attached, thermometers installed and insulation applied, the run was begun. The air rate was adjusted to the desired setting and the time clock started. Readings of inlet a i r temperature and humidity, o r i f i c e pressure drop, upstream pressure, pressure at the bottom of the packing, pressure drop through the packing, and pressure in the "Dewcel" sampling chamber were taken either every 15 minutes or every 30 minutes depending upon the rate of flow of air. 2. CALCULATING PROCEDURE Orifice pressure drop, or i f i c e upstream pressure, pressure at the bottom of the packing, and pressure drops through the packing were av-26 eraged from the data taken over the entire length of the run, thus eliminating the effect of small c y c l i c a l flow fluctuations caused by the on-off building compression. Inlet and exit temperatures and humidities used in the c a l -culations were taken at the point when the column was believed to have reached steady state* Some d i f f i c u l t y was experienced i n deciding when this situation occurred for the lower flow rates. For runs of high flow rate the column reached steady state, as indicated both by a constant exit temperature and constant exit humidity, in approximately 15 minutes. However, at low flow rates, the time required to bring the temperature of the column and i t s large volume of insulation to a steady state condition was much longer, resulting i n a slowly but detectably f a l l i n g outlet a i r and packing temperature. The cor-responding effect on outlet a i r humidity was even smaller* The procedure follow-ed in this case was to use the data taken when the exit humidity had reached a constant value even though the exit temperature may not have become perfectly constant. Waiting for the exit temperature to become absolutely constant was not feasible i n runs using low flow rates because there existed the danger of reaching the f a l l i n g rate period of drying before complete steady state was attained. Flow rates were calculated according to the method and equations set forth i n the A.S.M.E. Report on flow meters (2). Appropriate temperature and pressure corrections were applied to convert from o r i f i c e to column conditions. Moisture content of the air was determined from the dew point reading according to the method described by the "Deweel* operating manual supplied by the Foxboro Company. This included a correction for de-viation of the "Dewcel* chamber pressure from 760mm. of mercury. 27 The rates of liquid evaporation were calculated from the change in humidity of the air stream and the flow rate of air. The mass transfer coefficient, k g, was calculated according to equation 8 and the mass transfer factor, J d , according to equation 18. The Schmidt number, which is temperature dependent but practically pressure independent, was plotted as a function of temperature (see appendix) and the value used in equation 18 was that corresponding to the average temperature in the column. In calculating k g from equation 8, the log mean partial pres-sure difference of the transferring gas, A P i . m . , w a s evaluated by assuming that the surface temperature of the packing was equal to the wet bulb tem-perature of the a i r . Partial pressure of water vapor at the surface temperaturea and at the dew point temperatures of the air were taken from the Foxboro oper-ating manual for the "Dewcel". These values were identical with the values list e d i n Table I, page 762 of Perry (48). The evaluation of the heat transfer coefficient was made according to equation 11. The log mean temperature difference was calculated from the assumed surface temperature and the measured air temperatures* The heat transfer factor, j H , was evaluated according to equation 19. The Prandtl number was assumed to be constant over the small range of temperatures used in this investigation. It was given a value of 0.8280 at 70°F, which was calculated from a value of C p = 0.2401 B. t.u./(lb. )(°F) as listed on page 79 of the International C r i t i c a l Tables (30); k =0201284 B.t.u./(sq. f t . )(hr.) (°F/ft.) as lis t e d on page 213 of the International C r i t i c a l Tables (30); and Jl* 1.23 x 10 (It* )/(ft.)(sec.) taken from Figure 2 of Gamson et a l (24). The last mentioned plot is reproduced i n the appendix and was used for deter-mining a l l values of viscosity. 28 Friction factor was calculated according to equation 5a. Pressure drops between the top of the second layer and the top of the sixth layer were used for the calculations. Pressure drop data were plotted against the superficial velocity on a log-log plot, with the number of layers of spheres encompassed as a parameter. This resulted i n four straight, parallel lines (see appendix). Calculation of the average incremental pressure drop per layer of packing from these lines showed that entrance and exit effects, i f present at a l l , were very small. However, to ensure that such effects were not included in the calculated f r i c t i o n factors, the pressure drop across the four middle layers were used i n calculating them. This i s essentially the method employed by Martin et a l (43). The mass transfer factor, J D , the heat transfer factor, J H , and the f r i c t i o n factor, f, were plotted on log-log paper against the Reynolds number based on particle diameter, defined by Re - D pV n f 129) M Empirical equations giving J H and j d as exponential functions of Reynolds number were determined by the method of least squares. 3. RESULTS Figures 6, 7 and 8 represent graphically a l l the results obtained from the main experimental portion of this work. The two assemblages showed entirely different f l u i d f r i c t i o n characteristics, but similar rates of mass and heat transfer. The data for the mass transfer factor of both assemblages were correlated by the empirical equation ev||«o I Q. O J o Q-O II X " 3 0.3 0.2 0 . I 0.08 0.0 6 0.0 5 0.04 0.03 Fi@ ire 6. A P: .ot of Heat Trail 3fer Fac tor ve rsus Re: no'. .ds Ni ml ier o • OR' 0R1 rHC "HC )Rh RH 0 ME ME *!C #2 3IC *4 u 7 ii ^ u 1 u 30 40 60 100 200 300 400 600 1000 2000 CMJK> „_ Q. > Q j CD 0.3 0.2 0. I 0.08 0.06 0.05 0.04 Figure 7. A lie t of Mass Traisfer Fastor \ e r s u 3 Reynold 3 Nun ber o O R T H O R H O M B I C 2 • O R T H O R H O M B I C #4 0.03 30 40 60 100 200 300 400 600 1000 Re= D p V o e JU 2000 ° Q. a II 50.0 40.0 30.0 20.0 10.0 8.0 6.0 5.0 4.0 3.0 N A R T I N - O R T H O R H O M B I C 4* M A R T I N - O R T H O R H O M B I C =1^ 2 o O R T H O R H O M B I C # 2 • O R T H O R H O M B I C # 4 F i * ;ure A Cbmbarison of F r i c t i o n Ftctors v i t i ihose of Mart: n f o r snooth obtd inept i p tjhip (investigation 3phej 'es 30 40 60 100 200 Re = 300 400 e 600 1000 2000 03 DpVo X L 32 J d = 0.1261 ( R e ) " 0 ' 1 1 0 7 (30) with an average deviation of + 6.05$, while the combined data for heat transfer were correlated by J H = 0.1669 ( R e ) " 0 * 1 1 2 3 (31) with an average deviation of + 4.78$. Table II l i s t s the observed values of jg, J d and f and the corresponding Reynolds numbers. The average ratio of heat transfer factor to mass transfer factor, JH/J u» was 1.310. The original and calculated data are included in the appendix. f f t f f f f f f f r W W ^ t O t O l O N W l O t O t O t O N rr & I" & (3-I to tO Ol M tO tO tO jjp CJ1 CP CP P rfk SI to U Ol • • • • • tO tO H 1 tO t> CP tO tO O Ol Ol 03 O • » • to oo to -a o u rf>- if> O tf) O Ol - . M (B H SI ^ H H M d> .. _ *> to -o H o u> <o n * • if- oi cn 00 to a> to o to o o i if* * * s i . • > • • • • • H O O C J l O U M O W O o o o o o o o • • • • • • • 0 o o o o o o 01 Ol 0> Q> O* O* OI M 0) O i f W H CD * » S J o * » w <o to rfk OD to M O 00 CP o o o • • « o o o cr> o> g? *• to o g a s o o o o o o o o o o o o p » • • • • • • • • • • • • o o o o o o o o o o o o o o » - o s j o o c p o > o > o i < i o » a > o > a ) 0 > 0 1 » 0 < D O H O » H £ ^ S s j M O l D H ' O H ' O ' P O i t 8 -a U) w U l I— » - — m o H W O i i o s i i i D O i ^ a i o o o o o o o o o o o • • • • • • • • • • o o o o o o o o o o --3SJ03CDOD-<3000D^3-<1 Ol03-SJCT><l<SOOlrf^CD i&oito-<jtf*.i©o>cnc*>io if>s3towtotoc>io">-<jro o o o o o o o o o o o o p » • • • • • • • • • • • • O O t - ' M h - ' t - ' p O p O O O O • O f f i O O O O f f i C D t D l O - O t D C D oosjoioooiotoooo-a-vi-o at « ID 0> Ol < Ol -3 OJ Ol OJ CO CP CP ep [O tO ip» tO -0 tO H • • • • • • • M O ) O i H ^ O O l M O) M W H W to SI CP ca to OJ o o • • tO SJ 03 M OD o to oo • • • • cn -o -a Ol - f r i f a i U> Ol 3 CP CP 34 DISCUSSION 1. ASSUMPTION OF WET BULB TEMPERATURE AT THE SURFACE OF THE PACKING The assumption that the surface of the packing is at the wet bulb temperature has become a very controversial issue. This assumption was f i r s t employed by Gamson et a l (24), and later by Wilke and Hougen t61) and Taecker and Hougen (57). In their f i r s t paper Gamson et a l (24) made no checks on the actual surface temperature,.but i n view of their_exaellent correlation (+ 3§#) they f e l t that this assumption was valid. Moreover, i t was stated by T.H. Chilton during the discussion of this paper (24) that D.M. Hurt had made an attempt to determine ** ... the temperature of the wetted solids during evaporation and as close as the experimental data could be obtained the check with the temperature of adiabatic saturation, or the wet bulb temper-ature, was as good as the agreement is between these two temperatures.* Wilke and Hougen (61) found that after many t r i a l s ..surface temperatures could not be measured with any degree of accuracy by attaching thermocouples to the surface. Taecker and Hougen (57) report no attempts to measure surface temperature. Hobson and Thodus (27) doubted the accuracy of this assumption at low Reynolds numbers. In order to overcome this assumption they embedded thermocouples i n the surface of the packing and have reported differences between wet bulb temperatures and measured surface temperatures as high as 5.5°F. In two out of the five runs made they report measured surface tem-peratures to be less than wet bulb temperatures. No attempt was made to make their process adiabatic, however, and exit wet bulb temperatures calculated from their data are consistently higher than the measured inlet wet bulb tem-peratures, the difference ranging from 1.7°F to 6.1°F. No mention is made of the temperature at which their packings were soaked. 35 An attempt was made in the present Investigation to measure surface temperatures and to compare the measured surface temperature with the adiabatic saturation temperature of the air* Measurements were made in a random packed glass column, 3 inches in diameter, containing approximately 100 porous spheres similar to the spheres used i n the or instated packing* Height of the bed was approximately 5§- inches* Surface temperatures were measured with thermocouples calibrated with a Leeds and Northrup platinum resistance thermometer ce r t i f i e d by the National Bureau of Standards* Each thermocouple was placed in a groove inscribed in the surface of the sphere* Four such spheres were f i t t e d with thermocouples and distributed at random throughout the bed in positions approxi-mately 1, 2,3, and 4 inches above the inlet of the bed* Reynolds numbers for each of these suns were in excess of 1200* The f i r s t few runs showed a decrease in measured surface temperature from inlet to exit* Adiabatic saturation temperature of the a i r was found to be less than the measured surface tempera-tures, although near the exit of the packing the difference was only 1.5°F. It was thought that contacting the thermocouples may have been causing some error i n the measurement* Therefore, the thermocouples were shielded from direct contact with the air by placing a small Strip of plastic adhesive tape over them* Runs with these shielded thermocouples showed marked reductions i n the measured surface temperatures* Those measured 1 inch from the inlet differed from the adiabatic saturation temperature by as much as 4*5°F*, while the sur-face temperatures measured 1 inch from the exit were only 0*4°F. above the adiabatic saturation temperature* In a l l runs the adiabatic saturation tem-perature of the inlet and exit air differed by only 0*3°F. In no case was the measured surface temperature less than the adiabatic saturation temperature* It was believed that the a i r , which was higher in temperature than the surface of the spheres, was s t i l l affecting the temperature indicated by the thermocouples, causing them to read higher than the actual surface tempera-36 ture. The plastic strip did prevent the thermocouples from being in direct contact with the a i r ; however, quite conceivably, the plastic strip could be heated by the a i r to some degree, and since i t was indirect contact with the thermocouple a higher temperature would be indicated* As the a i r proceeds through the packing, i t is cooled. Hence the tendency of the a i r to cause the thermocouples to read higher than the actual surface temperature i s re-duced. This i s indicated by the reduction in measured surface temperature proceeding from the inlet to the outlet of the packing. The conclusions deduced from this preliminary investigation were that reliable surface temperature measurements could not be obtained by attaching thermocouples to the surface, and that the assumption of either wet bulb or adiabatic saturation temperature at the surface of the sphere was more accurate than direct measurement. This argument would hold for the turbulent region of flow but ex-tending i t to the laminar and-transition region without further investigation may be open to criticism. The data of Hobson and Thodus (27) would indicate that i t could not be extended to the laminar region. However, the r e l i a b i l i t y of their measurements is open to question, especially in two cases where they report surface temperatures lower than the wet bulb temperature, despite the fact that the surroundings were at a higher temperature than the packing. It is hard to conceive that such a situation would occur at steady state, even in the unpredictable laminar and transitional zones. In making runs with the orientated packings i t was at f i r s t planned to run adiabatically. This was achieved with runs of high Reynolds number; however, with the lower flow rates the danger of entering the f a l l i n g rate period of drying before adiabatic conditions were established became apparent Consequently, the wet bulb temperature, although only slightly different in 37 value from the adiabatic saturation temperature, was considered to be a more reliable assumption of the surface temperature. A psychrometric chart was constructed using equation 47, page 812 of Perry (48) with a value of h^k' * 0.26 as reported in Table VII, page 100 of Sherwood and Pigford (55). This value does not include radiation effects, which were absent i n the pres-ent set-up. Wet bulb temperatures were read from the chart, which is included in the appendix, to the nearest 0.1°F. using the measured values of dry bulb temperature and humidity. A similar chart was made for adiabatic saturation curves using equation 46, page 811 of Perry (48). Increases in wet bulb temperature from inlet to exit air streams were found to be never greater than 3.0°F and i n most cases less than 0.5°F* Increases in adiabatic satura-tion temperatures were generally higher, though these never deviated by more than 1.5°F from the corresponding wet bulb temperatures. Calculations of for a l l runs were made using both wet bulb temperature and adiabatic saturation temperature as the assumed surfaoe temperature. No noticeable change occurred i n the spread of results; however, the assumption of wet bulb temperature at the surface yielded approximately 3$ lower values of Jd« No noticeable difference in the values of j g occurred. 2. EFFECTS OF ORIENTATION Figures 6, 7 and 8 illustrate rather clearly that i n the Reynolds number range covered, orientation has negligible effect on heat and mass transfer, whereas i t has considerable effect on f r i c t i o n factor. An explanation for the above results may be presented in view of work done with the flow of fluids past immersed bodies and past banks of heat exchanger tubes (32). The resistance to the movement of a solid in a f l u i d (or conversely, a f l u i d moving past a stationary solid) is known as drag. 38 This drag may be brought about by the shear stresses exerted i n the boundary layer of the f l u i d next to the solid surface, i n which case i t i s referred to as surface drag or skin f r i c t i o n . In the case of f l u i d flow across circular cylinders, the pressure gradient in the fl u i d varies from negative to positive. This variation in pressure gradient causes the phenomenon of flow known as "separation" of the boundary layer. Separation of the boundary layer occurs at the point on the cylinder surface where the pressure gradient i s zero. This can be visualized i f a circular cylinder, placed at right angles to the f l u i d flow, i s considered. As the f l u i d in the main stream flows past the cylinder, i t i s accelerated as a result of moving around the cylinder. This acceleration, which i s an in-crease in kinetic energy, i s accompanied by a decrease in pressure making the pressure gradient negative. However, as the f l u i d in the main stream goes past the cylinder, the expanding cross section of flow requires a deceleration of the flu i d and a corresponding increase i n pressure, making the pressure gradient positive. The boundary layer i s thus flowing against an adverse pressure gradient as i t moves around the cylinder. This results in a marked change in the velocity profile in the boundary layer. In order to maintain flow in the direction of this adverse pressure gradient, the boundary layer separates from the solid surface and continues in space. Beyond the point of separation of the boundary layer from the surface of the cylinder the f l u i d i s flowing i n a d i r -ection opposite to that in the main stream. Thus, the area behind the cylinder is an area of disturbed flow characterized by eddies. This area of disturbance beyond the cylinder i s known as the turbulent wake. If separation of the boundary layer accurs, causing a turbulent wake behind the solid body, a loss of energy in addition to that lost owing to surface drag also occurs. This lose of energy due to the turbulent wake 39 is known as form drag and i s a function both of the form or shape of the body past which the f l u i d i s flowing, and of the Reynolds number. An increase in turbulence which does not affect the laminar sub-layer results only in an increase in energy loss and does hot appreciably increase the heat transfer (32). A turbulent wake behind an immersed body aids only slightly in transferring heat to the body but contributes to a considerable extent to the drag of the body (32). Wallis (59), as reported by Knudsen and Katz (32), has studied visually the flow of fluid s perpendicular to tube banks. The tube banks in-vestigated were four different in-line or rectangular arrangements and four different staggered or triangular arrangements. The in-line arrangements com-pare, to some extent, with a cross-sectional view, taken parallel to the f l u i d flow direction, of the Orthorhombic No. 4 orientation used in this investigation while the staggered arrangement is similar to Orthorhombic No. 2 packing, taken in the same cross-section. Photographs of the pattern of f l u i d flow are shown. For the tubes in the in-line arrangement, i t appears that the turbulent wake continues to the next tube i n line and only a very thin boundary layer forms on that tube. For the closely packed staggered arrangement, the turbulent wake behind each tube is considerably reduced. The tubes are so placed that they are not in the turbulent wake of the tubes immediately upstream. This results in a considerable reduction of the size of the turbulent wake, and' thus there should be a considerable reduction in energy dissipation (32). It would seem, then, that here i s a plausible explanation for the results obtained in this investigation. If the fluid, flows i n the packed beds according to the patterns witnessed by Wallis, then the spheres in the Ortho-rhombic No, 4 packing would have a greater turbulent wake on their downstream side than the spheres in the Orthorhombic No. 2. This would explain the fact that the Orthorhombic No 4 arrangement displays a considerably greater pressure 40 drop than Orthorhombic No. 2. The reason that heat and mass transfer factors are not affected could be explained by the statement of Knudsen and Katz that this turbulent wake behind en immersed body aids only slightly in transferring heat from the body. 3. ANALOGIES BETWEEN HEAT, MASS AND MOMENTUM TRANSFER IN PACKED BEDS The results of this investigation would appear to contradict any notion that a simple universal analogy exists between heat and mass transfer and mo-mentum transfer. Because orientation does affect f r i c t i o n factor but not heat and mass transfer, in the turbulent region at least, some method must be introduced to take account of orientation. Two s t a t i s t i c a l l y random packed beds would show no difference i n orientation. It is doubtful, however, whether beds as they are packed in practice achieve such s t a t i s t i c a l randomness. This probably explains the fact that even the best correlations for f l u i d f r i c t i o n in "randomly" packed beds, though they employ elaborate functions to account for voids, s t i l l ybld some spread in the data points (40). Attempts to express heat and mass trans-fer as a simple function of f r i c t i o n factor, without reference to orientation, are therefore, at best, approximate only. Furthermore, such attempts are s t r i c t l y empirical and limited to particular cases, unless based on skin f r i c t i o n alone rather than on total drag. By subtracting form drag from t o t a l drag in the case of flow around a cylinder, Sherwood (53) estimated f/2 based on skin f r i c t i o n alone for flow normal to an isolated cylinder, and showed that i t was very close to both J H and j d for this case. Unfortunately, the proportions of skin f r i c t i o n and form drag for other cases such as packed beds are not known at present. 41 4* SURFACE ROUGHNESS In figure 8 the data for f r i c t i o n factor obtained in this investiga-tion are compared with the f r i c t i o n factor curves for the same orientations obtained by Martin et a l (43). In.both cases the results are higher than those reported by Martin. This may be expected when i t is considered that the spheres used by Martin were smooth steel b a l l bearings, while the packing material used here was an assemblage of rough refractory spheres. That i s , the difference, i t i s believed, can be attributed to surface roughness, an effect recorded by other investigators (5, 7a, 40). Leva (40), for instance reports that, i n turbulent flow, clay and alundum particles packed to the same voids as glass spheres, show a 50% increase in pressure drop, while rougher particles show an even greater increase. As clay and alundum are large constituents of the spheres used here, the results obtained are in accord with Leva's findings. 5. RELIABILITY OF THE DATA • It is d i f f i c u l t to make an overall quantitative estimate of the re-l i a b i l i t y of the data due to uncertainties arising out of the assumption of the surface temperature. However, i t is possible to investigate the probable errors in isolated data. The values of the heat transfer factor are believed to be more ac-curate than the mass transfer factor. If equation 8 is considered, the mass transfer coefficient is seen to be a function of the log mean partial pressure difference, A p ^ ^ , which i s defined by aPl.au " (P*! " Pl) " fPw2 " P s ) l 3 2 ) in P"l " Pl Pw2 " P2 42 The driving force at the top of the column ( p ^ - p 2 ) , i s generally quite small so that small errors in the values of p ^ and p 2 result i n large errors in the value of . This is also true for the log mean temperature d i f -ference, A t , _ , which i s used in the calculation of heat transfer coefficient. However, the errors in the measurement of individual temperatures are approx-imately 0.3$ compared to approximately 1.6$ for partial pressure terms. Cal-culations have shown that an approximate error of 0.3$ in measuring temperatures could result in an approximate error of 3.5$ in the log mean temperature d i f -ference, while 1.6$ error in partial pressure terms could result in a 7.0$ error in the log mean partial pressure difference. Pressure drop data at Reynolds numbers below 150 for the Orthorhombic No. 4 arrangement and below 250 for the Orthorhombic No. 2 arrangement are not reliable due to the very small pressure drop. In this region the pressure drops were of the order of 0.010 to 0.020-inch of water, while readings could be estimated only to the nearest 0.005-inch of water. However, in the higher Reynolds number range, the results should be quite reliable. 6. COMPARISON WITH PUBLISHED RANDOM PACKING- DATA The values of J H and j d obtained in this investigation agree quite well with the results on random packing obtained by other workers (23, 24, 26, 27, 52) at a Reynolds number of 1000. However, the slope of the straight line through the points is found to be less than that reported by several in-vestigators (23, 24, 27, 52, 57, 61). This discrepancy i s , however, no great-er than the discrepancies existing within the previously reported data (15). No reason can be put forth as to why this slope should be less than the slope reported by Gamson et a l (24), who used the same system and who made the same assumption regarding surface temperature. 43 That a discrepancy exists in absolute values of J H and J d between those reported and those obtained here i s , however, not important for the present purpose, which was not to measure absolute values of J H and j d , but rather to compare the results obtained from two different orientations, both measured on the same basis* The ratio of j H r to j d 0 D t a i n e a n e r e l s slightly higher than that reported by Gamson et a l ('24) but agrees quite well with the value of 1*37 obtained by Scatterfield and Resnick (52). 44 PROPOSALS FOR FURTHER STUDY 1* Heat and mass transfer measurements on the two orthothombic assemblages should be extended into the laminar region in order to establish the effect of orientation where molecular transfer of heat and mass dominates completely over eddy transfer. In order to reduce the time required for the column to reach e q u i l i -brium at these low flow rates, the inlet a i r should be heated to a point where its adiabatic saturation temperature is close to the room temperature. To eliminate the possibility of entering the f a l l i n g rate period of drying during the experimental run, studies should be made on each packing to determine the length of the constant drying rate period as a function of the Reynolds number through the packing. The length of time for each experi-mental run could then be safely determined in advance. It would be necessary to know how the surface temperature of a material during the constant rate period of drying behaves- at low flow rates of a i r . A number of ways of arranging thermocouples on or under the surface should be tried in order to determine some method of obtaining reliable sur-face temperature measurements. 2. A formal investigation of the effect of fractional void volume on heat and mass transfer rates can be made using the present apparatus. It would, however, require the construction of two or three additional packing assemblages of different voidage—for instance, a simple cubic which represents the loosest arrangement of spheres and a face-centred cubic which represents the tightest arrangement of spheres* Only one orientation per arrangement would have to be constructed, as the present investigation has already shown 45 that no appreciable orientation effect on heat and mass transfer exists in turbulent flow, while Martin's (43) f l u i d f r i c t i o n data points to no orien-tation effects for a given arrangement in laminar flow except for the two assemblages studied here* Orderly arrangements of uniform spheres display a voidage range of 26% to 47*6$, while the spread between random dense and random loose beds of spheres is less than half this range (43). The advantage of studying fraction-a l void volume in orderly arrangements is thus apparent. 46 SUMMARY 1. Experimental measurements have been made of the rates of heat, mass and momentum transfer in two packed beds having the same voidage, and the same arrangement when viewed in isolation, but different orientation with respect to the direction of f l u i d flow. The results indicate that over the range of Reynolds numbers covered orientation, while having considerable effect on pressure drop, has l i t t l e or notmeasurable effect on the rates of heat and mass transfer* 2. The packing arrangements have been compared with in-line and staggered arrangements of heat exchanger tube banks* The observations made on these tubes have been used i n an attempt to explain the results obtained in this investigation* 3* It is suggested that no simple analogy between momentum transfer and mass and heat transfer exists in packed beds* Neglecting the effects of orientation in deriving these analogies is believed to be erroneous in principle and, therefore, they can be regarded only as empirical approximations. 4. The empirical equations -0.1107 J. » 0.1261(Re) a -0.1123 and J_ = 0.1669 (Re) have been used to relate the experimentally obtained values of J"H and J d with Reynolds number over a Re-range of 100 to 1200. Average deviation in the mass transfer factor was + 6.05$ while that of heat transfer factor was + 4. 78$. 47 5. Friction factors were found to be higher than those reported for smooth spheres. This was attributed to surface roughness. 6. A number of attempts have been made to measure surface tempera-tures of the packing during the constant rate period of drying. The con-clusions reached were that surface temperatures were d i f f i c u l t to measure reliably by attaching thermocouples to the surface, and that the assumption of wet bulb temperature was more accurate than direct measurement, at least in turbulent flow. 7. Proposals for further study have been presented and include the extension of the measurements of heat and mass transfer rates into the laminar region, an investigation to determine more reliable methods of measuring surface temperature and the i n i t i a t i o n of 8 project to determine the effects of voids on heat and mass transfer rates* 48 BIBLIOGRAPHY 1. Andrews, A.I., Ceranic Tests and Calculations, John Wiley & Sons Inc., New York, 1950. 2. A. S. M. E., Fluid Meters, Their Theory and Application, Part 1, Report of A.S.M.E. Special Research Committee on Fluid Meters, 4th ed., 1937. 3. Blake,.F.E., Trans. Am. Inst. Chem. Eng., 14, 415 (1922). 4. Brotz, W., Chem.-Ing.-Tech., 23 , 408 (1951). 5. Brownell, L.E., and Katz, D.L., Chem. Eng. Prog., 43, 537 (1947). 6. Burke, S.P., and Plummer, W.B., Ind. Eng. Chem., 20, 1196 (1928). 7. Carman, P.O., Trans. Inst. Chem. Eng., (London), 15, 150 (1937). 7a. Campbell, J . M . and Huntington, R.L., Petroleum Refiner, 30, 127 (1951). 8. Chilton, T.H., and Colburn, A.P., Ind. Eng. Chem., 23, 913 (1931). 9. Chilton, T.H., and Colburn, A.P., Trans. Am. Inst. Chem. Eng., 26, 178 (1931). 10. Chilton, T.H., and Colburn, A.P., Ind. Eng. Chem., 26, 1183 (1934). 11. Chilton, T.H., and Colburn, A.P., Ind. Eng. Cham., 27, 255 (1935). 12. Chilton, T.H., and Duffey, H.R., and Vernon, H.C., Ind. Eng. Chem., 29, 298 (1937). 13. Dryden, C.E., Strang, D.A., and Withrow, A.E., Chem, Eng, Prog., 49, 191 (1953). 14. Ergun, S., Chem, Eng. Prog., 48, 89 (1952). 15. Ergun, S., Cham, Eng. Prog., 48, 227 (1952). 16. Ergun, S., and Orning, A.A., Ind. Eng, Chem., 41, 1179 (1949). 17. Evans, G.C., and Gerald, CF., Chem, Eng. Prog., 49, 135 (1953). 18. Swell> A.W., "Thermometry in Hygrometric Measurements", Temperature- Its Measurement and Control in Science and Industry, Am. Inst. Phys., Reinhold Publishing Co., New York, 1941, p. 649. 19. Fair, G.M., and Hatch, L.P., J. Am. Water Works Assoc., 25, 1551 (1933). 20. Fowler, J.L., and Hertel, K.L., J. Applied Phys., 11, 496 (1940). 49 21. Furnas, C C , Ind. Eng. Cham., 22, 26 (1930). 22. Gaffney, B. J., and Drew, T.B*, Ind. Eng. Chem., 42, 1120 (1950). 23. Gamson, B.W., Chem. Eng. Prog., 47, 19 (1951). 24* Gamson, B.W., Thodus, G», and Hougen, O.A», Trans. Am. Inst. Chem. Eng., 39, 1 (1943). 25. Hatch, L.P., J. Applied Mechanics, £, 109 (1940). 26. Hobson, M., and Thodus, G., Chem. Eng. Prog., 45, 517 (1949). 27. Hobson, M., and Thodus, G., Chem. Eng. Prog., 47, 370 (1951). 28. Hurt, D.M., Ind. Eng. Cham., 35, 522 (1943). 29. Ishino, Toshio, Tsutaootake, and Okada, Tadayoski, Chem. Eng. (Japan), 15, 255 (1951). 30. International C r i t i c a l Tables, vol. 5, McGraw-Hill Book Company, Inc., New York. 31. Ju Chin Chu, K a l i l , J., and Wetteroth, W.A., Chem. Eng. Prog., 49, 141 (1953). 32. Knudsen, J. C , and Katz, D.L*, Fluid Dynamics and Heat Transfer, Engineering Research Institute, Bulletin No. 37, University of Michigan Press, 1954. 33. Kozeny, J., Sitzber. Akad. Wiss. Wien, Math.-naturw. KLasse, 156, (Abt. I l a ) , 271 (1927). 34. Lea, F.M., and Nurse, R.W., Trans. Inst. Chem. Eng. (London), 25, Supplement, 47 (1947). 35. Leva, Max, Chem. Eng. Prog., 43 , 549.(1947). 36. Leva, Max, Ind. Eng. Chem., 39, 857 (1947). 37. Leva, Max, Ind. Eng. Chem., 42, 2498 (1950). 38. Leva, Max, and Grummer, M., Chem. Eng. Prog*, 43, 713 (1947). 39. Leva, Max, and Grummer, M., Ind. Eng. Chem., 40, 415 (1948). 40. Leva, Max, Weintraub, M., Grummer, M., Pollchik, M., and Storch, H.H., Fluid Flow Through Packed and Fluidized Systems, Bulletin 504, U.S. Bureau of Mines, U.S. Government Printing Office, Washington, D.C., 1951. 41. Lewis, W.E., Gil l i l a n d , E.R., and Bauer, W.C, Ind. Eng. Cham., 41, 1104 (1949). 42. ' Lof, G.O.G., and Hawley, R.W., Ind. Eng. Chem., 40, 1061 (1948). 50 43. Martin, J. J., McCabe, W.L., and Monrad, C C , Chem. Eng. Prog., 47, 91 (1951). 44. Morse, R.D., Ind. Eng. Chem., 41, 1117 (1949). 45. Mc Adams, W.H., Pohlenz, J.B., and St. John, R.C, Chem. Eng. Prog., 45, 241 (1949). 46. McCune, L.K., and Wilhelm, R.H., Ind. Eng. Chem., 41, 1124 (1949). 47. Oman, O.A*, and Watson, K.M., Nat. Pet. News., 36, R 795, (1944). 48. Perry, J.H., ed., Chemical Engineers' Handbook, 3rd ed., McGraw-Hill Book Company, New Tork, 1950. 49. Flautz, D.A«, and Johnstone, H.7., University of I l l i n o i s , Personal communication. 50. Ranz, W.E., Chem. Eng. Prog., 48 , 247, (1952). 51. Resnick, W., and White, R.R., Chem. Eng. Frog., 45, 377 (1949). 52. Scatterfield, C.N., and Resnick, H., Chem. Eng. Prog., 50, 504 (1954). 53. Sherwood, T.K*, Ind. Eng. Chem., 42, 2077, (1950). 54. Sherwood, T.K., and Comings, E*W., Trans. Am. Inst. Chem. Eng., 28, 88 (1932). 55. Sherwood, T.K., and Pigford, R.L., Absorption and Extraction, 2nd ed., McGraw-Hill Book Company, Inc., New York, 1952. 56. Shulman, H.L*, and De Gouff, J.J., Ind. Eng. Chem., 44, 1915 (1952). 57. Taecker, R. G«, and Hougen, O.A., Chem. Eng. Prog., 45, 188 (1949). 58. Traxler, R.N., and Baun, L.A.H., Physics, 7_, 9 (1936). 59. Wallis, R.F., Engrg., 148, 423 (1934). 60. Weisman, J., and Bonilla, CF,, Ind. Eng. Chem., 42, 1099 (1950). 61. Wilke, CR., and Hougen, O.A*, Trans. Am. Inst. Chem. Eng., 41, 445 (1945). 62. Winding, C C , Ind. Eng. Chem., 30, 942 (1938). 51 APPENDIX REYNOLDS NUMBER THROUGH ORIFICE If* T H E R M O M E T E R R E A D I N G ° F o o UJ a O l HUMIDITY, G R A I N S / L B S . DRY A IR H Z 9 a. MX O 240 .260 .280 300 320 .340.360 380 400 420 .440 .460 .480 .500 -520 .540.560 .580 .600 .620 ,640 1 S A T U R A T I O N P R E S S U R E OF W A T E R V A P O U R , I N S . OF Hg. 1 . r mm • -\i,'.L APPENDIX 5 m Schmidt Number and (Schmidt Number) 2/3 as Function of Temperature •tn; :-ir — — I -:!.... 60 62 64 66 68 JOB 7g 74 76 79 8Q 83 84 96 99 9Q 92 94 . : : :: T E M P E R A T U R E _ F — mm gg o UJ CO Ll_ in o >• I-co o o to - - H P ; 1 56 58 Hi 6 2 — — A P P E N D i x 6 cosi ty of Air at a Funct ion of Humidity and Temperature (Taken from Gamson, Thodos and Hougen (24)) m 64 66 68 70 7 2 74 76 78 80 82 84 86 88 90 92 94 96 98 T E M P E R A T U R E FLUID V E L O C I T Y , FT. / SEC. 65 09 M I L L I V O L T S M I L L I V O L T S s M I L L I V O L T S M I LLI V OLTS APPENDIX 9 Psychrometric Chart Based on Wet Bulb Temperature DC < >-cc o CO z < a: o >-H O X 50 • • i - .. ; — i r . . ™ t ' ! : ' ' ' .11 * ' ' 1' • 1 "ill 1— ' ' I " " "?-->. --v-.-v w^. -v v. -v. x ^ N . x, -. -s S , \ A . \ \ . \ \ , N -k^ >> /VX.J^J H 3 7>V P* i |> T^Ti 1 • 52 54 56 58 60 62 64 616 68 70 72 74 76 7B 80 82 84 B€ 88 90 92 DRY BULB TEMPERATURE, °F. APPENDIX 10. ORIGINAL DATA AND CALCULATED DATA Run Orientation P across No. o r i f i c e in. H20 2-1 Orthorhombic #2 24.04 2-2 5.78 2-3 45.78 2-4 5.89 2-5 15.90 2-6 30.61 2-7 11.74 2-8 44.42 2-9 -• 24.42 2-10 12.27 2-11 9,57. 2-12 17.52 2-13 14.67 . 4-1 Orthorhombic #4 27.30 4-2 43.68 4-3 6.03 4-4 12.26 4-5 47.64 4-6 32.12 4-7 40.57 4-8 7.44 - 4--92 15.43 4-10 14.66 Absolute Temperature Density of upstream of inlet air dry a i r at pressure o r i f i c e in. Hg °F. lb./cu.Ft. 31.50 72.2 0.07854 30.23 84.0 0.07373 33.04 84.9 0.08047 30.50 83.7 0.07444 31.14 88.3 0.07537 32.16 80.2 9.07901 30.95 85.3 0.07532 33.04 79.9 0.08121 31. 66 84.1 0.; 07722 30.72 78.5 0.07572 30.53 83.6 0.07453 31.25 88.3 0.07564 30.77 85.7 0.07483 32.01 88.6 0.07744 33.27 81.7 0.08151 30.37 78.4 0.08203 30.95 85.8 0.07525 33-30 91.3 0;08016 32.39 82.8 0.07919 32.86 78.5 0.08098 30.51 81.6 0.07476 31.17 85.2 0.07587 30.8 6 C 83.3 0.07538 Dew Point Correction Density of of inlet to density moist air air for moist- at o r i f i c e ure °F. lb./cu. f t . 39.0 °0.9971 0.07831 39.4 0.9970 0.07351 42.4 0.9969 0.08022 38.1 0.9970 0.07422 41.9 0.9968 0.07513 41.7 0.9969 0.07877 40.8 0.9968 0.07508 41.2 0.9970 0.08097 39.5 0.9972 0.07700 38.4 0.9971 0.07549 38.5 0.9971 0.07431 44.0 0.9964 0.07537 46.3 0.9961 0.07454 43.3 0.9966 0.07718 42.8 0.9970 0*08127 38.6 0.9970 0.08178 41.7 0.0068 0.07501 42.6 0.9970 0.07992 40.5 0.9969 0.07894 40.7 0.9970 0.08074 39.6 0.9971 0.07454 43.4 0.9965 0.07560 47.1 0.9961 0.(57509 APPENDIX 10. ORIGINAL DATA Orifice Expansion Viscosity of Discharge Flow Rati diameter factor air through coeff. orifice x 10 5 inch l b . / t f t . K'sec) lb./sec. 0.500 0.9835 ' 1.232 .6002 .02017 0.500 0.9959 1.250 .6030 .00990 0.500 0.9701 1.252 .5995 .02777 0*500 0.9959 1.250 .6030 .00990 0.500 0.9890 1.256 .6010 .01619 0.500 0.9794 1.243 . 5999 S.02274 0.500 0.9918 1.253 .6015 .01396 0.250 0.9710 1.247 .6047 .006942 0.250 0.9834 1. 250 .6058 .005094 0.250 8.9914 1.241 .6075 .003620 0.250 0.9932 1.250 .6084 .003178 0.500 0.9979 1.257 .6008 .01717 0.750 0.9896 1. 253 .6078 .03534 0.500 0.9816 1.257 .6002 .02132 0.500 0.9717 1.246 .5995 .02735 0.500 0.9957 1.241 .6027 .01051 0.500 0.9922 1.253 .6014 .01426 0.250 0.9691 1.261 .6046 .007128 0.250 0.9786 1.248 .6052 .005881 0.250 0.9734 1.241 .6048 .006647 0.250 0.9947 1.246 .6092 .002815 0.500 0.9893 1. 253 .6010 .01600 0.750 0.0896 1.248 .6078 .03540 AND CALCULATED DATA (CON'T) i Reynolds Temperature Average Average number of exit air temperature Absolute through - of a i r in pressure i n orifice column column x 10~ 4 °F. °f in. Eg 5. 00 56.2 64.2 29.85 2.42 63.3 73.6 29.81 6.78 63.0 73.9 28.88 2.42 61.7 72.7 30.08 3.94 64.4 76.4 30.05 5.59 60.5 70.4 30.05 3.40 62.7 74.0 30.14 3.40 59.9 69.9 29.83 2.49 64.3 74.2 29.90 1.78 62.5 70.5 29.82 1.55 65.2 74.4 29.84 4.17 64.3 76.3 30.04 5.75 65.4 75.6 29.81 5.18 63.9 76.2 30.05 6.71 60.3 71.0 30.21 2.59 58.5 68.5 29.93 3.48 62.4 74.1 30.09 3.45 64.9 78.1 29.91 2*88 62.6 72.7 30.04 3.27 59.3 68.9 29.92 1.38 64.5 73.1 29.96 3.90 63.5 74.4 30.09 5. 78 63.1 73.2 29.88 APPENDIX 10. ORIGINAL DATA AND CALCULATED DATA (CON'T) Density of Air in Column Superficial a i r velocity (based on empty column) lb./cu.ft. ft./sec. Viscosity of air in column x 10 5 lb./ft.(sec.) Modified Reynolds number Corrected Humidity inlet air gr./lbtdry ai r Dew Point exit air °F. Corrected Humidity exit air gr./l&.dry air Relative Humidity exit air Adiabatic Sat'n Temp, inlet air ?F. 0.07556 1. 749 1.219 607.6 33.2 53.0 60.4 88.8 54.0 0.07414 0.8750 1.236 294.2 35.0 58.7 74.5 84.7 59.1 0.07426 2.4506 1.237 824.6 35.8 57.9 72.5 83.5 59.6 0.07493 0.8658 1.232 295.2 33.0 58.0 72.1 87.6 58.5 0.07434 1.4272 1.238 430.3 37.3 59.5 76.7 85.1 61.2 0.07519 1.9819 1.230 679.0 35.7 56.3 68.2 85.9 57.8 .0.07490 1.2214 1.237 414.5 35.2 58.8 74.6 86.8 59.6 0.07468 0.6091 1.228 207. 6 34.9 57.2 70.6 91.0 57.6 0.07428 0.4494 1.234 • 151.6 33.4 60.6 80.3 87.8 58.8 0.07460 0.3176 1.228 108.1 32.7 58.3 73.5 85.5 56.5 0.07410 0.2811 1.235 94.56 33.4 60.8 80.5 85.8 58.6 0.07434 1. 5135 1.238 509.4 40.4 60.6 79.6 87.8 61.9 0.07386 3.1355 1.237 1049.4 44.6 60.6 80.0 84.6 61.9 0.07437 2.1999 1.238 741.0 38.3 60.2 78.6 87.7 61.5 0.07550 2.7799 1.230 956.2 36.2 56.9 69.6 88.4 58.6 0.07515 1.0732 1.225 368.8 33.7 55.9 67.2 91.1 56.7 0.07477 1.4636 1.237 495.9 37.6 59.1 75.J5 88.6 60.4 0.07377 0.7415 1.241 247.1 35.8 60.7 80.1 86.5 61.9 0.07484 0.6030 1.233 205.1 34.1 59.0 75.2 87.6 58.5 0.07507 0.6795 1.226 233.2 33.7 56.3 68.3 90.0 56.7 0.07457 0.3897 1.233 132.1 34.9 60.1 78.2 85.6 58.2 0.07453 1. 6474 1. 235 557.2 39.5 59.8 77.3 87.5 60.6 0.07437 3.6528 1.233 1234.9 45.7 59.7 77.6 88.4 61.3 s APPENDIX 10. ORIGINAL DATA AND CALCULATED DATA (CON'T) Adiabatic Wet Bulb Wet Bulb Average Partial Sat'n Temp. Temp, of Temp, of Wet Bulb Press, of exit a i r inlet a i r exit air Temp. Water Vap. °F. °F. eF. °F. in. Hg 54-4 54.6 54.5 54.6 0.430 60.4 59.7 60.6 60.2 0.516 60.0 60,2 60.0 60.1 0.526 59.4 59.2 59.4 59.3 0.506 61.5 61.8 61.5 61.7 0.557 '58.0 58.4 58.1 58J.3 0.492 60.4 60.2 60.4 60.3 0.526 58.4 58.1 58.4 58.3 0.487 62.2 59.4 62. r 60.7 0. 510 60.0 57.0 60.0 58.5 0.469 62.6 59.2 62.6 60.9 0.506 62.0 62.5 62.0 62.3 0.572 62.6 62.4 62.5 62.5 0.570 61.7 62.1 61.7 62.4 9.566 58.3 59.1 58.3 58.7 0.585 57.0 57.2 57.0 57.1 0.473 60.5 61.0 60.5 61.3 0. 542 62.4 62.6 62.3 62.5 0.574 60.5 59.1 60.5 59.8 0.505 57.6 57.3 57.7 57.5 0.474 61.8 58.8 61.8 60.3 3.498 61.3 61.2 61.3 61.3 0.546 61.2 61.8 61.2 61.5 0.557 Partial P a r t i a l ' Partial Log Mean Press, of Pressure of Press, of Partial Water Vap. Water Vap. Water Vap. Pressure in inlet at t w„ i n exit Difference air * air in. Hg in. Hg in. Hg in. Hg 0.239 0.428 0.404 0.08060 0.243 0. 534 0.498 0.1171 0.272 0.522 0.485 0.1128 0.231 0. 510 0.486 0.1030 0.267 0. 553 0. 512 0.1274 0.265 0.487 0.457 0.09745 0.256 0.530 0.500 0.1094 0.260 0.492 0.473 0.08394 0.244 , 0.564 0. 534 0.1083 0.233 0. 522 0.489 0.1033 0.234 0. 574 0. 538 0.1168 0. 289 0.561 0.534 0.1091 0.315 0. 572 0.534 0.1141 0.282 0.555 0.526 0.1119 0.276 0.490 0.467 0.08974 0.236 0.469 0.450 0.08648 0.265 0.532 0. 505 0.1075 0.274 0.568 0.537 0.1187 0.254 0.534 0.503 0.1053 0.255 0.482 0.457 0.08949 0.245 0.557 0. 524 0.1081 0. 283 0. 548 0. 518 0.1074 0.325 0.546 0.516 0.09886 APPENDIX 10. ORIGINAL DATA AND CALCULATED DATA (C0N*T) Change i n Rate of Mass Pressure Press. Drop Mean Part. Mass (Schmidt Jd Log met Humidity Liquid Transfer at Bottom through Press, of Velocity 2/3 Temp. Transfer Coeff. of Column Packing non-trans. No.) Diff . lb.water/ component lb.mole/ lb.dry air lb.mole/ (hr.)(atm) lb. mass/ nr. (sq. f t . ) in. Hg in. Hg atm. (hr)(ft2) °F. 0.00388 0.01557 1.4939 0.19 0.02 0.9866 475.83 0.7182 0.06440 *6V8104 0.00564 0. OHIO 0.7330 0.15 0.04 0.9840 233.55 0.7167 0.06408 9.8416 0.00524 0.02893 1.9834 0.27 0.05 0.9860 655.12 0.7167 0.06194 10.3048 0.00559 0.01100 0.8259 0.31 0.03 0.9933 233.55 0. 7169 0.07290 9.3944 0.005628 0.01811 1.0993 0.4412 0.0061 0.9913 381.94 0.7165 0.05918 10.6788 0.004642 0.02099 1. 6657 0.4493 0.0121 0.9923 536. 46 0.7172 0.06397 8.8023 0.0Q5628 0.01562 1.1041 0.4941 0.0050 0.9947 329.33 0.7167 0.06919 9.5506 0.005100 0.007039 0.6485 0.2610 0.0013 0.9843 163.77 0.7173 0.08093 7.5932 0.006700 0,006787 0.4846 0.2478 0.0008 0.9863 120.17 0.7168 0.08253 9.4466 0.005828 0.004190 0.3137 0.2390 0.0005 0.9846 85. 28 0.7173 0.07521 8.8398 0.006728 0.004252 0.2815 0.1625 0.0004 0.9846 74.97 0.7167 0.07670 9.7470 0.005600 0.01910 1.3539 0.3257 0.0077 0.9903 405.06 0.7165 " 0.06865 9.7319 0.005057 0.03549 2.4054 0.2103 0.0308 0.9820 833.71 0.7166 0.05877 9.8010 0.005757 0.02439 1.7210 0.4926 0.0568 0.9916 589.04 0.7166 0.06010 9.7749 0.004771 0.02594 2.2819 0.6566 0.1066 0.9973 755.64 0.7172 0.06253 8.5050 0.004786 0.01000 0.9129 0.3221 0.0130 0.9890 290.38 0.7175 0.06458 7.4465 0.005414 0.01534 1.1265 ©.4875 0.0254 0,9933 393.98 0.7167 0.05893 8.9239 0.006329 0.008968 0.5967 0.2507 0.0069 0.9863 196.94 0.7164 0.06198 10.8807 0.005871 0.006866 0.5147 0.3963 0.0040 0.9916 162.48 0.7170 0.06520 8.9225 0.004942 0.006532 0.5762 0.3162 0.0059 0.9883 183.65 0.7175 0.06441 7.5936 0.006185 0.003461 0.2528 0.1934 0.0012 0.9886 77.77 0.7169 0.06669 9.4316 0.005400 0.01717 1.2621 0.3897 0.0309 0.9923 442.06 0.7167 0.05878 9.1332 0.004557 0.03203 2.5578 0.4044 0.1544 0.9846 978.05 0.7169 0.05344 8.0875 1 APPENDIX 10. ORIGINAL DATA AND CALCULATED DATA (CON'T) Heat of Heat Heat Press. Press. Press. Press. Press. f Evap'n at Trans- Transfer Drop Drop Drop Drop Drop Average ferred Coeff. across 2 across 4 across 6 across 8 between Surface B. t.u./ Layers Layers Layers Layers 2 and 6 Temp. Layers B.t.u./lb. ( h r ) t f t 2 ) B.t.u./hr (°F.) in. H20 in. H20 in. H20 in. H20 in. H2O 1062.2 297.95 11.3074 0.08727 1058.8 211.76 5.5612 0.08745 1059.9 552.42 13.8555 0.07767 1059.5 209.99 5.7773 0.09085 1058.2 345.29 8.3571 0.08036 0. 010 0.044 0.054 0.080 0.054 8.555 1060.1 400.93 11.7724 0.08059 0.0150 0.074 0.120 0.165 0.120 9.749 1058.9 297.97 8.0637 0.08993 0.0150 0.035 0.050 0.070 0.050 10.735 1060.1 134.42 4.5754 0.1026 0.0025 0.0075 0.010 0.020 0.010 8., 658 1058.7 129.48 3.5426 0.1083 0 0 0 0.010 1060.0 80.02 2.3396 0.1008 0 0 0 0.005 1058.6 81.09 2.1503 0.1053 0 0 0 0.005 1057.8 363.99 9.6660 0.08765 0.029 0.047 0.076 0.105 0.076 10.707 1057.7 676.29 17.8343 0.07856 0.110 0.210 0.311 0.419 0.311 10.278 1057.7 464.75 12.5448 0.03822 0.232 0.378 0.610 0.784 0. 610 33.93 1059.8 495.24 15.3638 0.07467 0.950 1.45 1060.7 191.14 6. 7726 0. 08566 0.050 0.085 0.135 0.175 0.135 31.23 1058.4 292.54 8.6494 0. 08063 0.093 0.167 0.260 0.345 0.260 32.51 1057.7 170.92 4.1447 0.07729 0.030 0.045 0.075 0.094 0.075 37.03 1057.2 130.78 3.8673 0.08742 0.015 0.025 0.040 0.055 0.040 39.43 1060.5 134.82 4.3370 0.08673 0. 025 0.035 0.060 0.080 0.060 34. 66 1058.9 66.02 1.8469 0.08722 0 0 0 0. 015 1058.4 327.36 9.4571 0.07857 0.127 0.203 0.330 0.420 0.330 32.67 1058.3 615.82 20.0908 0.07544 0.570 1.03 1. 60 2.10 1.60 32.29 

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