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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 d i f ferent orientation with respect to the direction of fluid flew*  An a i r -  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 f r i c t i o n factor* An explanation for this behaviour is presented in terms of a d i f 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 momentum, heat and mass transfer which show a direct proportionality between total friction factor and heat and mass transfer factor* Measured f r i c t i o n 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 t h i s i n v e s t i g a t i o n was made and the h e l p f u l suggestions and assistance i n constructing the apparatus of Mr. Frank Sawford, Workshop Technician* I am also indebted to the National Research Council f o r providing f i n a n c i a l assistance.  TABLE OF CONTENTS Page ACKNOWLEDGMENTS ABSTRACT NOMENCLATURE INTRODUCTION  1  LITERATURE REVIEW  3  1. METHODS OF CORRELATING DATA a* Pressure Drop b- Mass Transfer and Heat Transfer 2. THE EFFECTS OF ORIENTATION  3 4 ,7  3. THE EFFECTS OF SURFACE ROUGHNESS  6  4. THE EFFECTS OF VOIDS 5. THE ANALOGY BETWEEN HEAT AND MASS TRANSFER AND MOMENTUM TRANSFER  8  APPARATUS  9 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 2. EFFECTS OF ORIENTATION  34 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* Appendix 6* Appendix 7. Appendix 8* Appendix 9*  Schmidt Number and (Schmidt Numberf^as a Function of Temperature Viscosity of Air as a Function of Humidity and Temperature Pressure Drop through the Packing as a Function of the Fluid Velocity with Number of Layers of lacking as Parameter Calibration of Thermocouples Psychrometric Chart Based on Wet Bulb Temperature  Appendix 19. Original Data and Calculated Data  57 58 59 61 6g 66  LIST OF T.A'RT.Tgj Table I II  Page Characteristics of the Packings  21  Experimental Values of J , j and f  33  H  d  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, f t .  Dp  a Effective particle diameter, f t .  D  a Diffusion coefficient of gas in the film, sq.ft./hr.  T  f  a Friction factor •  g^AlDp { in packed bed, dlmensionless 2G 2 L  fjj. G  a Modified friction factor a  %f SO  •  £  , dlmensionless  3  1 - *3  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 \ ^ , dlmensionless 2  3  JH  a Heat transfer factor a  k'  a Mess transfer coefficient, lb./(hr.)(ft )(humidity difference)  h  / Op/* |  2  *, dlmensionless  k  a  Thermal conductivity of f l u i d , 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 Height of column, f t .  1  s  M^  =  Average molecular weight of fluid, l b . / l b . mole  Nu  s  Nussult number for heat transfer  s  Mass transfer number analogous to Nu for heat transfer KgPgf^mDp/^ ° v f o r packed beds, dimensionless  Nu1  83  =  hDp/k, 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 , i n . Hg  P«  =  Partial pressure of water vapor at temperature t  B  Partial pressure of water vapor in entrance a i r , i n . Hg  »  Partial pressure of water vapor in exit a i r , in. Hg  Pg A Pl.m.  , i n . Hg  Log mean partial pressure of the transferring gas i n the gas film - ( P » i - PI) - C P » 8 " PS) f a t m .  s  In * 1 " l p  F  s  Total pressure, atm.  AP  =  Pressure drop, l b * * f o r e e / s q . f t «  -dP  B  Decrease in pressure,  Pl  B  Absolute pressure at inlet of bed, i n . Hg  Pg  s  Absolute pressure at outlet of bed, in. Hg  Fr  B  Prandtl number =  Re  B  Reynolds number »  Sc  B  Schmidt number = jxJ £ D V , dimensionless  lb.-force/sq.ft.  G^ji/k,  dimensionless  DpVo^//^  l  n  packed bed, dimensionless  •  Temperatare of Inlet a i r , ° F *  tg  =  Temperature of outlet a i r , ° F *  tn^  *  Wet bulb temperature of inlet a i r , ° F *  t_  «  Wet bulb temperature of exit a i r , ° F *  =  Log mean temperature difference  w  2  A ti.  m #  (*•! " *1> - ( t , in  2  - t8) ^  =  0 y <  *»1 • *1  tw 2 - t2 -CAt)  =  Decrease in temperature of the transfer medium, ° f «  V0  B  Superficial velocity based on empty column, f t . / s e c  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  -  0'  =  Function in mass transfer equations, dimensionless  0"  a  Function in heat transfer equations, dimensionless  a  Density of f l u i d , l b . / c u . f t .  s  Viscosity of f l u i d ,  Function in momentum transfer equations, dimensionless  lb./(ft.)(sec)  1  INTRODUCTION  In the past decade the field of heat, mass and momentum transfer i n 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 stationary assemblage of particles, were probably the f i r s t venture into this very broad f i e l d .  For example, blast furnace operation and f i l t r a t i o n have  been used for centuries.  Moving beds, fluidized beds and a late i n -  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 a l (43) to investigate the effects of orientation of packing on pressure drop. siderable effect due to orientation did exist.  They found that con-  L i t t l e or no attention,  however, has been paid to heat and mass transfer rates i n 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 arrangement when viewed in isolation, differed i n 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 s o l i d p a r t i c l e s have received the attention of a mult i t u d e of investigators i n the past.  Their objectives were to obtain  equations that could be used f o r design purposes and to increase the knowledge of the basic mechanisms involved i n these transfer processes.  It  was apparent that the complexity of these mechanisms d i d not lend themselves to immediate t h e o r e t i c a l treatment.  Hence, the treatment of t h i s  subject by most workers has been on an empirical basis.  1. METHODS OF CORRELATING DATA a. Pressure Drop When f l u i d flows i n a c i r c u l a r duct the pressure drop due t o f r i c t i o n i s found, by application of dimensional analysis, to be expressed by the following equation ID  This expression csn be integrated across the length of the duct i f the v e l o c i t y , density, and diameter of the duct are assumed to remain constant to give  (2)  This can be w r i t t e n as  4  where  Equation 3 is the so-called Fanning equation*  By rearrangement of equation  3 i t is found that f  «  APB e D  (5)  By experimentation i t is possible to establish the relation that exists between f r i c t i o n 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 f r i c t i o n factor is obtained as a function of a modified Reynolds number. D p 7 ? ^ i • 0  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.  V-AC)  w X  Thus,  (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 i n as much as the rate of heat transfer is also d i r e c t l y 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)  q  =  hAg(-At)  (10)  or  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 relating 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 i n the following manner.  If dimensional analysis i s applied to the correlation of mass  transfer coefficients i n wetted-wall columns and to the correlation of heat transfer coefficients i n circular ducts for turbulent flow, the following equations are obtained:  for mass transfer,  fcgPgfMmD  0  (12)  75>  and f o r heat transfer, h D  (13)  l \  k  /c  k  /A  For empirical c o r r e l a t i o n purposes i t i s usually assumed that equations 12 and  13 may  be s i m p l i f i e d respectively to (14)  e»v  c^-y (-  and h D  B  By rearranging the terms i n equations 14 and / G  (15)  15, they become respectively  \b-l ,  ( \  \  M ^\  c-1  (16)  and B  (17)  CpG Chilton and Colburn (10) have defined Jd  the transfer factors as 2/3  _kgP,  (18)  G and 2/3  (19)  CG p  I f z = C = 1/3, equations 16 and to give  as has been demonstrated experimentally (55), then 18, and equations 17 and  19 can be combined respectively  7  J  d  »  AtRe)  (20)  J  H  »  B(Re) "  and y  1  (21)  These correlations have been extended to heat and mass transfer in packed beds by making the necessary modifications groups.  to the dimensionless  These modifications are attempts to adequately describe the flow  of f l u i d past the solid particles and include substitution of D for D and, p  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  -  0 7 (Re)  (22)  J  -  P  (23)  and H  l  (Re)  since i t i s found that the constants A, B, b and z when the f l u i d is turbulent are different in value from those when the f l u i d i s 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) i n packed beds, comparatively no attention has been paid to possible effects of orientation. Martin, McCabe and Monrad (43) made perhaps the only formal investigation 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 d i f f e r i n g f r i c t i o n factors*  Orientation  e f f e c t s i n heat and mass transfer have received even l e s s attention* Taecker and Hougen (57) mention, i n passing, that no s i g n i f i c a n t differences in j  H  were obtained  i n comparing random with staggered arrangements of pack-  ings (saddles and r i n g s ) *  3. THE EFFECTS OF SURFACE ROUGHNESS Surface roughness e f f e c t s on pressure drop through packed beds have been studied by Leva et a l (40).  They report an increase i n f r i c t i o n factor  as surface roughness i s increased when t e s t i n g a l o x i t e granules, clay Raschig r i n g s , alundum cylinders and clay b a l l s i n tubes i n turbulent flow* and Huntington (7a) report s i m i l a r r e s u l t s .  Campbell  Brownell and Katz (5) found that  comparison of data on lead spheres and on c e l i t e spheres indicated that the c e l i t e spheres exhibited a greater resistance to flow than did the lead spheres under s i m i l a r conditions.  This d i f f e r e n c e they a t t r i b u t e to roughness.  No studies on the e f f e c t s of p a r t i c l e surface roughness on heat and mass transfer between f l u i d s and packed beds have been found reported.  4. THE EFFECTS OF VOIDS The e f f e c t s 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 i n c o r r e l a t i n g f r i c t i o n f a c t o r measurements i s w e l l known, but how of controversy  t h i s should be done has become a point  (14).  The e f f e c t s of voids on heat and mass transfer have not received the same amount of consideration.  Several authors (15, 17, 22, 23, 29,  use the void f r a c t i o n term i n t h e i r correlations of mass transfer with Reynolds number.  In some cases, i t i s used i n an attempt to define a  31)  9  Reynolds number of the fluid moving past the solid particles (15, 22). Others introduce the term i n 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 versus a modified d  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 /(l-fc) d  * versus 6G/a/t.'C» D G ^ (1-6) ). Data reported p  by Hobson and Thodus (27) and McCune and Wilhelm (46) were not l n 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 a l (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 i n 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 i n isolation, the effective velocity past the spheres being taken as the superf i c i a l velocity divided by the minimum fractional free area of the packing. He i s 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 f l u i d 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 f r i c t i o n data quite well. f  »  k  The equation presented i s  150^ (1-6 ) D G  + 1.75  (24)  p  The analogy for mass transfer claimed here i s that F K  J!P_  =  L  ^  E  C  <Z  1-6  °2 " l D C - C  t25  +  v  >  2  for complete longitudinal mixing of the fluid i n the bed and f  -  k  L  M  e  _Dp_  1 - <£  for the case of no longitudinal mixing.  l  a  D,.  o * - Qi c  f26)  *- 2 c  Some degree of correlation was ob-  tained between mass transfer and f l u i d f r i c t i o n for liquid systems on assuming 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 a l (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 / l- £) 5  Vgf  v<>  j  -  -  5(Sc)  2 / 3  (27)  or d  (f/10) (£ / l - 6) 3  (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.  12 APPARATUS 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, i n water.  This method  corresponds to that used by (Samson et a l (24), Taecker and Hougen (57), Wilke and Hougen (61) and Hobson and Thodos (27). The apparatus i s 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. was measured with a Foxboro *Dewcel Dew Point Recorder. rt  Humidity  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 w i l l now follow*  1. AIR SUPPLY The air, which was used at room temperature for a l l runs, was obtained 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 a i r blower driven by a 2 H.P* motor and delivering a i r 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, i t was not used.  Draft Gauge measuring Pressure Drop through Packing  1  Upstream Pressure  Thermometer  M  Orifice Pressure Drop  To  Pressure at Bottom of Packing  I Atmosphere)  ? Assemblage of Spheres  Orifice  Air from Blower From  Thermometer  " Dewcel "  Sample to " D e w c e l "  Entrainment Separator  Figure 1.  Air from Building Supply  Schematic Diagram of Apparatus  Sample to " Dewcel'  t  To  Packed Column  Check Valve To  X  -o<-  Atmosphere  3 i  Inclined Manometer c a l i b r a t e d as Velocity of Air through Dewcel Chamber  u  Constriction  in Line  Chamber housing "Dewcel'  Vertical M a n o m e t e r measuring P r e s s u r e in C h a m b e r  To Atmosphere  To ^ Atmosphere Air  Exit Air Sample  X T h r e e - way Air f r o m Building Supply  Figure 2.  from Blower  -oo-  Cocks —  ^_  Schematic Diagram of A i r Sampling Lines  •HX3-  4X]  1  15 2. ENTRAINMENT SEPARATOR An entrainment separator was installed in the lines coming from the building a i r 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 a i r 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 a i r which passed through the holes of the f i r s t baffle would impinge 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 recommendations in the report* openings of  Three orifice plates were machined having  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 parameter*  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 i n contact with a saturated salt solution, there i s an equilibrium temperature at which this solution neither absorbs nor gives up moisture to the surrounding atmosphere. The "Dewcel" i s 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 i s 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 i s reduced.  The "Dewcel" then cools, absorbs more moisture and the cycle i s re-  peated until equilibrium i s attained.  A liquid expansion thermometer in-  dicates the temperature of the "Dewcel" and i s recorded on a chart calibrated in dew point temperature. An attempt to calibrate the instrument with a gravimetric determination resulted i n the "Dewcel" reading consistently higher humidities than the gravimetric method.  This result would be expected i f the absorbing  material ( i n this case magnesium perchlorate) did not remove a l l the moisture. A further check was made using  wet and dry bulb thermometers.  case the "Dewcel" indicated a lower humidity.  In this  Since i t 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 determinations 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 thermometer. 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 a l (43) having the same voidage but showing widely different f r i c t i o n factors.  Such packings are those designated by Martin  as Orthorhombic No. 2 Clear Passage and Orthorhombic No. 4. these packings in isometric view.  Figure 3 shows  It w i l l be noted that the basic arrange-  ment of the spheres i s the same i n both packings when the packings are viewed in isolation; however, when viewed along the major axis of flow the orientations are quite different.  This investigation was, therefore, a study of  Direction of  O R T H O R H O M B I C NO. 2 Figure 3.  ORTHORHOMBIC NO.4  Isometric Views of the two Orientations of Packing Used  20  were required f o r 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 s i x holes i n each sphere i n appropriate locations.  The spheres were  pinned together with 0.022-inch diameter stainless s t e e l f i s h i n g wire, the wire being secured i n each hole with A r a l d i t e AN-104 cement. The c h a r a c t e r i s t i c s of each of the two packings are given in Table I.  In determining surface area, the c o r r e c t i o n f o r the transfer  area l o s t by d r i l l i n g six holes i n each of the spheres was calculated to be only 1.08$ and was considered n e g l i g i b l e . Wall porosity was eliminated by using f r a c t i o n a l spheres at the walls as was done by Martin et a l (43).  I t was therefore necessary to  construct two columns i n which to housethe packings: a square column f o r Orthorhombic No. 2 and a hexagonal column f o r 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 f r a c t i o n a l spheres with A r a l d i t e AN-104.  This was done mainly to afford protection to  the somewhat delicate packing and had the a d d i t i o n a l advantage of avoiding the use of a supporting g r i d , thereby eliminating a source of entrance effects. In order to measure entrance and e x i t e f f e c t s i n the packing as well as the t o t a l pressure drop through the packing, pressure taps were located i n one of the brass sides at f i v e d i f f e r e n t 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 d i f f e r e n t i a l s 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  iii x 4±i 16 16  0.1526  392  4.660  0.219  3.8690  0.3954  Orthorhombic No.4  Regular 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 s l i g h t l y 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 i n the column.  In order t o maintain  a constant cross-sectional area throughout the entire length of the column, the column was l i n e d with brass plate above and below the packing.  The columns  were made i n two longitudinal sections, bolted together with a flange.  The bottom  section housed the packing assembly, the top of which was f l u s h with the top of t h i s section.  Pressure l i n e s from the taps i n the side of the assemblage  were brought through the column at the flange.  This was done by running the  l i n e s from the taps to a brass plate at the top of the packing assembly.  This  plate, which was placed perpendicular to the d i r e c t i o n of flow and p a r a l l e l to the flange, was attached to the top of the w a l l containing the pressure taps. I t contained f i v e 1/8-inch diameter channels, one f o r each of the pressure lines.  The plate was of s u f f i c i e n t 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 i n tap water f o r a period of not l e s s than three hours.  The temperature of the water was controlled by placing the  container holding the packing and water i n a constant temperature bath. temperature was held as close as possible (+ 3.0°?.) t o the wet bulb  The  temperature  of the a i r entering the packing during the experimental run* The packing, when removed from the water, was shaken vigorously to remove excess water, and then immediately placed i n the bottom section of the column*  In order to prevent a i r by-passing the packing by flowing i n the  small space between the outside w a l l of the packing and the inside w a l l of the column, t h i s space was sealed o f f at the top of the column with scotch tape* A gasket of latex dental dam was used around the brass plate housing the pressure l i n e s to prevent a i r leaking to the atmosphere.  The entire operation of  preparing the column f o r a r u n required about 15 minutes* Once the column was secured i n place, pressure l i n e s attached, thermometers i n s t a l l e d and i n s u l a t i o n applied, the run was begun. was adjusted to the desired s e t t i n g and the time clock started.  The a i r rate  Readings of  i n l e t a i r temperature and humidity, o r i f i c e pressure drop, upstream pressure, pressure a t the bottom of the packing, pressure drop through the packing, and pressure i n the "Dewcel" sampling chamber were taken either every 15 minutes or every 30 minutes depending upon the rate of flow o f a i r .  2. CALCULATING PROCEDURE O r i f i c e pressure drop, o r 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 e f f e c t of small c y c l i c a l flow fluctuations caused by the on-off b u i l d i n g compression. Inlet and exit temperatures and humidities used i n 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 t h i s s i t u a t i o n  occurred f o r the lower flow rates.  For runs of high flow r a t e the column  reached steady state, as indicated both by a constant exit temperature and constant e x i t humidity, i n 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, r e s u l t i n g i n a slowly but detectably f a l l i n g outlet a i r and packing temperature. responding effect on outlet a i r humidity was even smaller*  The cor-  The procedure f o l l o w -  ed i n t h i s case was to use the data taken when the exit humidity had reached a constant value even though the e x i t temperature may not have become p e r f e c t l y constant.  Waiting f o r the e x i t temperature to become absolutely constant was  not f e a s i b l e i n runs using low flow rates because there existed the danger of reaching the f a l l i n g r a t e period of drying before complete steady state was attained. Flow rates were calculated according to the method and equations set f o r t h 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 t o column conditions. Moisture content of the a i r 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 f o r de-  v i a t i o n of the "Dewcel* chamber pressure from 760mm. of mercury.  27  The rates of l i q u i d evaporation were calculated from the change i n humidity of the a i r stream and the flow rate of a i r . The mass transfer c o e f f i c i e n t , k , was g  calculated according  to equation 8 and the mass transfer f a c t o r , J , according to equation 18. d  The Schmidt number, which i s temperature dependent but p r a c t i c a l l y pressure independent, was plotted as a function of temperature (see appendix) and the value used i n equation 18 was i n the column.  that corresponding to the average temperature  In c a l c u l a t i n g k  g  from equation 8, the l o g mean p a r t i a l pres-  sure difference of the t r a n s f e r r i n g gas, A P i . m . ,  w  a  s  evaluated by assuming  that the surface temperature of the packing was equal to the wet bulb temperature of the a i r . P a r t i a l pressure of water vapor at the surface and at the dew  point temperatures  a t i n g manual f o r the "Dewcel".  temperaturea  of the a i r were taken from the Foxboro oper-  These values were i d e n t i c a l with the values  l i s t e d i n Table I, page 762 of Perry (48). The evaluation of the heat t r a n s f e r c o e f f i c i e n t was made according to equation 11.  The l o g mean temperature difference was  calculated  from the assumed surface temperature and the measured a i r temperatures* heat transfer factor, j , was H  evaluated according to equation 19.  The Prandtl  number was assumed to be constant over the small range of temperatures i n t h i s investigation.  I t was  calculated from a value of C  p  The  used  given a value of 0.8280 at 70°F, which was = 0.2401 B. t.u./(lb. )(°F) as l i s t e d 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 l i s 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* ) / ( f t . ) ( s e c . ) taken from Figure 2 of Gamson et a l (24).  The l a s t mentioned plot i s reproduced mining a l l values of v i s c o s i t y .  i n the appendix and was used f o r deter-  28 F r i c t i o n factor was calculated according to equation 5a. Pressure drops between the top of the second layer and the top of the s i x t h layer were used f o r the calculations.  Pressure drop data were plotted  against the s u p e r f i c i a l v e l o c i t y on a log-log p l o t , with the number of layers of spheres encompassed as a parameter. p a r a l l e l l i n e s (see appendix).  This resulted i n four straight,  Calculation of the average incremental  pressure drop per layer of packing from these l i n e s showed that entrance and exit e f f e c t s , i f present at a l l , were very small. that such e f f e c t s were not included  However, to ensure  i n the calculated f r i c t i o n f a c t o r s ,  the pressure drop across the four middle layers were used i n c a l c u l a t i n g them.  This i s e s s e n t i a l l y the method employed by Martin et a l (43). The mass transfer factor, J , the heat transfer factor, J , D  and  H  the f r i c t i o n factor, f , were plotted on log-log paper against the  Reynolds number based on p a r t i c l e diameter, defined by  Re  Empirical  -  D V f p  M  129)  n  equations g i v i n g J H and j  d  as exponential  functions of Reynolds number were determined by the method of l e a s t squares.  3. RESULTS Figures 6, 7 and 8 represent graphically a l l the r e s u l t s obtained from the main experimental portion of t h i s work.  The two assemblages  showed e n t i r e l y d i f f e r e n t f l u i d f r i c t i o n c h a r a c t e r i s t i c s , but s i m i l a r rates of mass and heat transfer. The data f o r the mass transfer factor of both assemblages were correlated by the empirical equation  Fi@ ire  6.  A P: .ot of Heat Trail 3fer Fac tor ve rsus Re: no'. .ds Ni ml ier  o •  0.3  OR'rHC)Rh 0 ME*!C #2 0R1"HC RH ME3IC *4  ev||«o I  0.2  Q. O  J  o  QO  II  0 . I u  0.08  7 ii  u  ^  1  u  X " 3  0.0 6 0.0 5  0.04 0.03 30  40  60  100  200  300 400  600  1000  2000  Figure 7.  A l i e t of Mass T r a i s f e r Fastor  0.3  \ersu3  Reynold  3  Nun ber  o  ORTHORHOMBIC  2  •  ORTHORHOMBIC  #4  CMJK> „_ >  Q  0.2  j  Q.  CD  0. I 0.08 0.06 0.05 0.04 0.03  30 4 0  60  100  200 Re=  300 400 600 D Voe p  JU  1000  2000  °  50.0 40.0 30.0 NARTIN-  O R T H O R H O M B I C 4*  MARTIN-  ORTHORHOMBIC  20.0 Q.  =1^2  a  10.0 II  8.0 6.0 5.0 4.0 3.0  o  O R T H O R HOMBIC  # 2  •  ORTHORHOMBIC  #4  F i * ;ure  30  40  60  A Cbmbarison o f F r i c t i o n Ftctors obtd inept i p tjhip ( i n v e s t i g a t i o n v i t i ihose o f Mart: n f o r snooth 3phej 'es  100  200 Re =  300 400 DpVo e XL  600  1000  2000  03  32  J  d  =  0.1261 ( R e ) " ' 0  (30)  1 1 0 7  with an average deviation of + 6.05$, while the combined data f o r heat transfer were correlated by J  H  =  0.1669 ( R e ) " * 0  (31)  1 1 2 3  with an average deviation of + 4.78$. Table I I l i s t s the observed values of j g , J corresponding Reynolds numbers.  d  and f and the  The average r a t i o of heat transfer factor to  mass transfer factor, JH/J » was 1.310. u  The o r i g i n a l and calculated data are included i n the appendix.  f f t f f f f f f f r  WW^tOtOlONWlOtOtOtON  rr  (3-  &  I  I"  &  to  tO Ol M tO tO tOt> CP tO -a jjp CJ1 CP CP P rfktO O Ol rf>Ol O M SI to U Ol • 03 »• • • • • • tO tO H 1 tO to oo to  ou H HM if> O tf) O Ol - ... (B H SI ^ . o H * • if- oi H O O C J cn  o ooooooo oo  oooooooooooop » • • • •••••• •• • 8o o o o o o o o o o o o o  • •« • ••••••o oo cr> o> g? 0 o o o o o o *• to o 01 Ol 0> Q> O* O* OI M 0) O i f W H CD g a s  * » S J o * » w <o to rfk OD to M O 00 CP  d> _ *> to to o o i •o >u>• <o • l O U M  00 to a> - to o if* * * s i •n • • O W O  U)» - o swj oUol c p oI— > o > o» i < i-o — »a>o> -a o a ) 0 > 0 1 » 0 < D O H O » H £ ^ S soj H MW OO l Di iHo ' sOi iHi D ' OO' iP^Oa ii o t m  oooooooooo  oooooooooooop  • •••••••••  O O t - ' M h - ' t - ' p O p O O O O •OffiOOOOffiCDtDlO-OtDCD  oooooooooo  --3SJ03CDOD-<3000D^3-<1 Ol03-SJCT><l<SOOlrf^CD  i&oito-<jtf*.i©o>cnc*>io  if>s3towtotoc>io">-<jro OJ Ol OJ CO CP CP ep CP [O tO • • MO) to SI  ip» tO -0 tO H • • • • • OiH^OOlM O) M W H W  ca  to OJ  » • • •  • • • • • • • • •  oosjoioooiotoooo-a-vi-o at  « ID 0> Ol < Ol -3  o o  OD  03 M  cn Ol 3- f-or i -a fai U> Ol  •• tO SJ  o  to  oo  • • • •  CP CP  34  DISCUSSION  1. ASSUMPTION OF WET BULB TEMPERATURE AT THE SURFACE OF THE PACKING The assumption that the surface of the packing i s at the wet bulb temperature has become a very c o n t r o v e r s i a l issue.  This assumption was  first  employed by Gamson et a l (24), and l a t e r by Wilke and Hougen t61) and Taecker and Hougen (57). the  In t h e i r f i r s t paper Gamson et a l (24) made no checks on  a c t u a l surface temperature,.but i n view of their_exaellent c o r r e l a t i o n  (+ 3§#) they f e l t that t h i s assumption was v a l i d .  Moreover, i t was stated by  T.H. Chilton during the discussion of t h i s paper (24) that D.M.  Hurt had made  an attempt to determine ** ... the temperature of the wetted s o l i d s during evaporation and as close as the experimental data could be obtained the check with the temperature of adiabatic saturation, or the wet bulb temperature, was as good as the agreement i s between these two temperatures.* Wilke and Hougen (61) found that a f t e r many t r i a l s ..surface temperatures could not be measured with any degree of accuracy by attaching thermocouples to the surface. temperature.  Taecker and Hougen (57) report no attempts to measure surface  Hobson and Thodus (27) doubted the accuracy of t h i s assumption  at low Reynolds numbers.  In order to overcome t h i s 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 f i v e 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 t h e i r data are consistently higher than the measured i n l e t wet bulb temperatures, the difference ranging from 1.7°F to 6.1°F. of the temperature at which t h e i r packings were soaked.  No mention i s made  35 An attempt was made i n the present Investigation t o measure surface temperatures and to compare the measured surface temperature with the adiabatic saturation temperature of the a i r *  Measurements were made i n a random packed  glass column, 3 inches i n diameter, containing approximately 100 porous spheres s i m i l a r to the spheres used i n the or instated packing* approximately 5§- inches*  Height of the bed was  Surface temperatures were measured with thermocouples  calibrated with a Leeds and Northrup platinum resistance thermometer c e r t i f i e d by the National Bureau of Standards*  Each thermocouple was placed i n a groove  inscribed i n the surface of the sphere*  Four such spheres were f i t t e d with  thermocouples and d i s t r i b u t e d at random throughout the bed i n positions approximately 1, 2 , 3 , and 4 inches above the i n l e t of the bed* each of these suns were i n excess of 1200*  Reynolds numbers f o r  The f i r s t few runs showed a decrease  i n measured surface temperature from i n l e t t o exit*  Adiabatic saturation  temperature of the a i r was found to be less than the measured surface temperatures, 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  d i r e c t contact with the a i r by placing a small Strip of p l a s t i c adhesive tape over them*  Runs with these shielded thermocouples showed marked reductions i n  the measured surface temperatures*  Those measured 1 inch from the i n l e t d i f f e r e d  from the adiabatic saturation temperature by as much as 4*5°F*, while the surface 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 i n l e t and exit a i r d i f f e r e d by only 0*3°F.  In no case was  the measured surface temperature less than the adiabatic saturation temperature* I t was believed that the a i r , which was higher i n temperature than the  surface of the spheres, was s t i l l a f f e c t i n g the temperature indicated by  the  thermocouples, causing them to read higher than the actual surface tempera-  36 ture.  The p l a s t i c s t r i p did prevent the thermocouples from being i n d i r e c t  contact with the a i r ; however, quite conceivably, the p l a s t i c s t r i p could be heated by the a i r to some degree, and since i t was  i n d i r e c t contact with the  thermocouple a higher temperature would be indicated* through the packing, i t i s cooled.  As the a i r proceeds  Hence the tendency of the a i r to cause  the thermocouples to read higher than the actual surface temperature duced.  i s re-  This i s indicated by the reduction i n measured surface temperature  proceeding from the i n l e t to the outlet of the packing. The conclusions deduced from t h i s preliminary investigation were that r e l i a b l e 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 d i r e c t measurement. This argument would hold f o r the turbulent region of flow but extending i t to the laminar and-transition region without further investigation may be open to c r i t i c i s m .  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 t h e i r measurements i s open to question, e s p e c i a l l y i n two cases where they report surface temperatures  lower than the wet bulb temperature, despite the  f a c t that the surroundings were at a higher temperature  than the packing.  It  i s hard to conceive that such a s i t u a t i o n would occur at steady state, even i n the unpredictable laminar and t r a n s i t i o n a l zones. In making runs with the orientated packings i t was at f i r s t to run a d i a b a t i c a l l y .  planned  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 s l i g h t l y d i f f e r e n t i n  37  value from the adiabatic saturation temperature, was considered to be a more r e l i a b l e 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 i n Table VII, page 100 of Sherwood and Pigford (55). This value does not include r a d i a t i o n e f f e c t s , which were absent i n the present set-up.  Wet bulb temperatures were read from the chart, which i s included  i n the appendix, to the nearest 0.1°F. using the measured values of dry bulb temperature  and humidity.  A similar chart was made f o r adiabatic saturation  curves using equation 46, page 811 of Perry (48).  Increases i n wet bulb  temperature from i n l e t to exit a i r streams were found to be never greater than 3.0°F and i n most cases less than 0.5°F*  Increases i n adiabatic satura-  t i o n temperatures were generally higher, though these never deviated by more than 1.5°F from the corresponding wet bulb Calculations of  temperatures.  f o r a l l runs were made using both wet bulb  temperature and adiabatic saturation temperature temperature. the assumption  No noticeable change occurred i n the spread of r e s u l t s ; however, of wet bulb temperature at the surface yielded  3$ lower values of J « d  2.  as the assumed surfaoe  approximately  No noticeable difference i n the values of j g occurred.  EFFECTS OF ORIENTATION Figures 6, 7 and 8 i l l u s t r a t e rather c l e a r l y that i n the Reynolds  number range covered, orientation has n e g l i g i b l e effect on heat and mass transfer, whereas i t has considerable effect on f r i c t i o n f a c t o r . An explanation f o r the above r e s u l t s may be presented i n view of work done with the flow of f l u i d s past immersed bodies and past banks of heat exchanger tubes (32).  The resistance to the movement of a s o l i d i n a f l u i d  (or conversely, a f l u i d moving past a stationary s o l i d ) i s 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 s o l i d 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 c i r c u l a r cylinders, the pressure gradient i n the f l u i d v a r i e s from negative to p o s i t i v e .  This v a r i a t i o n i n  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 v i s u a l i z e d  i f a c i r c u l a r cylinder, placed at r i g h t angles to the f l u i d flow, i s considered. As the f l u i d i n the main stream flows past the cylinder, i t i s accelerated as a r e s u l t of moving around the cylinder.  This acceleration, which i s an i n -  crease i n k i n e t i c energy, i s accompanied by a decrease i n pressure making the pressure gradient negative.  However, as the f l u i d i n the main stream goes past  the cylinder, the expanding cross section of flow requires a deceleration of the f l u 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 r e s u l t s i n a marked change i n  the v e l o c i t y p r o f i l e i n the boundary layer.  In order to maintain flow i n the  d i r e c t i o n of t h i s adverse pressure gradient, the boundary layer separates from the s o l i d surface and continues i n 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 i n the main stream.  Thus, the area behind the cylinder  i s an area of disturbed flow characterized by eddies.  This area of disturbance  beyond the cylinder i s known as the turbulent wake. I f separation of the boundary layer accurs, causing a turbulent wake behind the s o l i d body, a loss of energy i n addition to that l o s t owing to surface drag also occurs.  This lose of energy due to the turbulent wake  39  i s 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 i n turbulence which does not a f f e c t the laminar sublayer r e s u l t s only i n an increase i n energy loss and does hot appreciably increase the heat transfer (32).  A turbulent wake behind an immersed body aids only  s l i g h t l y i n t r a n s f e r r i n g heat t o 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 v i s u a l l y the flow of f l u i d s perpendicular to tube banks.  The tube banks i n -  vestigated were four d i f f e r e n t i n - l i n e or rectangular arrangements and four d i f f e r e n t staggered or t r i a n g u l a r arrangements.  The i n - l i n e arrangements com-  pare, to some extent, with a cross-sectional view, taken p a r a l l e l to the f l u i d flow d i r e c t i o n , of the Orthorhombic No. 4 o r i e n t a t i o n used i n t h i s i n v e s t i g a t i o n while the staggered arrangement i s s i m i l a r t o Orthorhombic No. 2 packing, taken i n the same cross-section.  Photographs of the pattern of f l u i d flow are shown.  For the tubes i n the i n - l i n e arrangement, i t appears that the turbulent wake continues to the next tube i n l i n e and only a very t h i n boundary layer forms on that tube.  For the c l o s e l y packed staggered arrangement, the turbulent  wake behind each tube i s considerably reduced.  The tubes are so placed that  they are not i n the turbulent wake of the tubes immediately upstream.  This  r e s u l t s i n a considerable reduction of the size of the turbulent wake, and' thus there should be a considerable reduction i n energy d i s s i p a t i o n (32). It would seem, then, that here i s a plausible explanation f o r the r e s u l t s obtained i n t h i s investigation. I f the f l u i d , flows i n the packed beds according to the patterns witnessed  by W a l l i s , then the spheres i n the Ortho-  rhombic No, 4 packing would have a greater turbulent wake on t h e i r downstream side than the spheres i n the Orthorhombic No. 2.  This would explain the f a c t  that the Orthorhombic No 4 arrangement displays a considerably greater pressure  40 drop than Orthorhombic No. 2.  The reason that heat and mass transfer f a c t o r s  are not affected could be explained by the statement of Knudsen and Katz that t h i s turbulent wake behind en immersed body aids only s l i g h t l y i n t r a n s f e r r i n g heat from the body.  3. ANALOGIES BETWEEN HEAT, MASS AND MOMENTUM TRANSFER IN PACKED BEDS The r e s u l t s of this investigation would appear t o contradict any notion that a simple universal analogy exists between heat and mass transfer and momentum transfer.  Because orientation does a f f e c t f r i c t i o n factor but not  heat and mass transfer, i n the turbulent region at l e a s t , 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.  I t i s doubtful, however, whether beds as they are packed i n  practice achieve such s t a t i s t i c a l randomness.  This probably explains the  f a c t that even the best correlations f o r f l u i d f r i c t i o n i n "randomly" packed beds, though they employ elaborate functions to account f o r voids, s t i l l ybld some spread i n the data points (40).  Attempts t o express heat and mass trans-  f e r 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 p a r t i c u l a r cases, unless based on skin f r i c t i o n alone rather than on t o t a l drag.  By subtracting form drag from t o t a l  drag i n the case of flow around a cylinder, Sherwood (53) estimated f/2 based on skin f r i c t i o n alone f o r flow normal to an isolated cylinder, and showed that i t was very close to both J  H  and j  d  f o r t h i s case.  Unfortunately, the  proportions of skin f r i c t i o n and form drag f o r other cases such as packed beds are not known at present.  41 4* SURFACE ROUGHNESS In figure 8 the data f o r f r i c t i o n factor obtained i n t h i s investigat i o n are compared with the f r i c t i o n factor curves f o r the same orientations obtained by Martin et a l (43). those reported by Martin.  In.both cases the r e s u l t s are higher than  This may be expected when i t i s considered that  the spheres used by Martin were smooth s t e e l 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 e f f e c t recorded by other investigators (5, 7a, 40).  Leva (40), f o r instance  reports that, i n turbulent flow, clay and alundum p a r t i c l e s packed to the same voids as glass spheres, show a 50% increase i n pressure drop, while rougher p a r t i c l e s show an even greater increase.  As clay and alundum are  large constituents of the spheres used here, the r e s u l t s obtained are i n accord with Leva's findings.  5. RELIABILITY OF THE DATA •  I t i s d i f f i c u l t to make an o v e r a l l quantitative estimate of the r e l i a b i l i t y of the data due to uncertainties a r i s i n g out of the assumption of the surface temperature.  However, i t i s possible to investigate the probable  errors i n isolated data. The values of the heat transfer factor are believed to be more accurate than the mass transfer factor.  I f equation 8 i s considered, the mass  transfer c o e f f i c i e n t i s seen to be a function of the log mean p a r t i a l pressure difference, A p ^ ^ ,  which i s defined by aPl.au  "  (P*! " Pl) " fPw " 2  in  P"l " P l Pw  2  " P2  P s )  l 3 2 )  42  The d r i v i n g force at the top of the column ( p ^ - p ) , i s generally quite 2  small so that small errors i n the values of p ^ i n the value of  .  and p  2  r e s u l t i n large errors  This i s a l s o true f o r the l o g mean temperature d i f -  ference, A t , _ , which i s used i n the c a l c u l a t i o n of heat transfer c o e f f i c i e n t . However, the errors i n the measurement of i n d i v i d u a l temperatures are approximately 0.3$  compared to approximately  1.6$  f o r p a r t i a l pressure terms.  culations have shown that an approximate error of 0.3$ could r e s u l t i n an approximate error of 3.5$ ference, while 1.6$  Cal-  i n measuring temperatures  i n the log mean temperature d i f -  error i n p a r t i a l pressure terms could r e s u l t i n a  7.0$  error i n the l o g mean p a r t i a l pressure d i f f e r e n c e . Pressure drop data at Reynolds numbers below 150 f o r the Orthorhombic No. 4 arrangement and below 250 f o r the Orthorhombic No. 2 arrangement are not r e l i a b l e due to the very small pressure drop. drops were of the order of 0.010  In t h i s region the  pressure  to 0.020-inch of water, while readings could  be estimated only to the nearest 0.005-inch of water.  However, i n the higher  Reynolds number range, the r e s u l t s should be quite r e l i a b l e .  6. COMPARISON WITH PUBLISHED RANDOM PACKING- DATA The values of J  H  and j  d  obtained i n t h i s i n v e s t i g a t i o n agree quite  w e l l with the r e s u l t s on random packing obtained by other workers (23, 26, 27, 52) at a Reynolds number of 1000.  24,  However, the slope of the straight  l i n e through the points i s found to be less than that reported by several i n vestigators (23, 24, 27, 52, 57, 61).  This discrepancy  i s , however, no great-  er than the discrepancies e x i s t i n g within the previously reported data (15). No reason can be put f o r t h as to why reported by Gamson et a l (24), who  t h i s slope should be l e s s than the slope  used the same system and who made the same  assumption regarding surface temperature.  43 That a discrepancy e x i s t s i n absolute values of J  H  and J  d  between  those reported and those obtained here i s , however, not important f o r the present purpose, which was not to measure absolute values of J  H  and j , but d  rather to compare the r e s u l t s obtained from two d i f f e r e n t orientations, both measured on the same basis* The r a t i o of j  H r  to j  d0  D  t  a  i  n  e  a  n  e  r  e  l  s  s l i g h t l y higher than that  reported by Gamson et a l ('24) but agrees quite w e l l with the value of 1*37 obtained by S c a t t e r f i e l d 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 i n order to e s t a b l i s h the e f f e c t of o r i e n t a t i o n where molecular completely  transfer of heat and mass dominates  over eddy t r a n s f e r . In order to reduce the time required f o r the column to reach e q u i l i -  brium at these low flow rates, the i n l e t a i r should be heated to a point where i t s adiabatic saturation temperature i s close to the room temperature. To eliminate the p o s s i b i l i t y 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 f o r each experi-  mental run could then be s a f e l y determined i n 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 t r i e d i n order to determine some method of obtaining r e l i a b l e surface temperature measurements. 2.  A formal investigation of the e f f e c t of f r a c t i o n a l 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 a d d i t i o n a l packing assemblages of d i f f e r e n t v o i d a g e — f o r  instance, a simple cubic which represents  the loosest arrangement of spheres and a face-centred cubic which represents the t i g h t e s t arrangement of spheres*  Only one o r i e n t a t i o n per arrangement  would have to be constructed, as the present  investigation has already shown  45  that no appreciable orientation e f f e c t on heat and mass t r a n s f e r exists i n turbulent flow, while Martin's (43) f l u i d f r i c t i o n data points to no orient a t i o n e f f e c t s f o r a given arrangement i n laminar flow except f o r the two assemblages studied here* Orderly arrangements of uniform spheres display a voidage range of 26% to 47*6$, while the spread between random dense and random loose beds of spheres i s less than h a l f t h i s range (43).  The advantage of studying f r a c t i o n -  a l void volume i n orderly arrangements i s thus apparent.  46  SUMMARY  1.  Experimental measurements have been made of the rates of  heat, mass and momentum transfer i n two packed beds having the same voidage, and the same arrangement when viewed i n i s o l a t i o n , but d i f f e r e n t orientation with respect to the d i r e c t i o n of f l u i d flow.  The r e s u l t s indicate that over  the range of Reynolds numbers covered orientation, while having considerable e f f e c t on pressure drop, has l i t t l e or notmeasurable e f f e c t on the rates of heat and mass transfer*  2.  The packing arrangements have been compared with i n - l i n e and  staggered arrangements of heat exchanger tube banks*  The observations made  on these tubes have been used i n an attempt to explain the r e s u l t s obtained i n t h i s investigation*  3*  It i s suggested that no simple analogy between momentum t r a n s f e r  and mass and heat transfer exists i n packed beds*  Neglecting the e f f e c t s of  orientation i n deriving these analogies i s believed to be erroneous i n p r i n c i p l e and, therefore, they can be regarded only as empirical approximations. 4.  The empirical equations -0.1107 J. » 0.1261(Re) a -0.1123  and  J_  = 0.1669 (Re)  have been used to r e l a t e the experimentally obtained values of J"H and with Reynolds number over a Re-range of 100 to 1200.  Jd  Average deviation i n  the mass t r a n s f e r factor was + 6.05$ while that of heat transfer factor was + 4. 78$.  47 5.  F r i c t i o n factors were found to be higher than those reported  f o r smooth spheres. 6.  This was attributed to surface roughness.  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 r e l i a b l y by attaching thermocouples to the surface, and that the assumption of wet bulb temperature was more accurate than d i r e c t measurement, at least i n turbulent flow. 7.  Proposals f o r 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 r e l i a b l e methods of measuring surface temperature and the i n i t i a t i o n of 8 project to determine the e f f e c t s of voids on heat and mass transfer rates*  48 BIBLIOGRAPHY  1.  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Traxler, R.N., and Baun, L.A.H., Physics, 7_, 9 (1936).  59.  Wallis, R.F., Engrg., 148, 423 (1934).  60.  Weisman, J . , and B o n i l l a , C F , , 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*  THERMOMETER  READING  °F  o  o UJ  a  Ol  HUMIDITY,  GRAINS/LBS.  DRY  AIR  H Z  9  a.  MX  O  240 .260 .280 300 320 .340.360 380 4 0 0 420 .440 .460 .480 .500 -520 .540.560 .580 .600 .620 ,640 SATURATION  PRESSURE  OF  WATER  VAPOUR,  I N S . OF  Hg.  1  .  1  r  mm  •  APPENDIX  -\i,'.L  m  5  Schmidt Number and (Schmidt Number) Function of Temperature as  •tn;  2/3 :-ir  — —  I -:!....  .:: ::  60  62  64  66  68 JOB  7g  74  76  79  8Q  83  TEMPERATURE  _ F  84  96  99  9Q  92  94  — —  —  mm  gg  --HP;  Hi  APPEND i x  6 c o s i t y of Air at a F u n c t i o n of Humidity and Temperature (Taken from Gamson, Thodos and Hougen (24))  m  o UJ  CO Ll_  in  o  >• Ico o o to  1  56  58  62  64  66  68  70  72  74  76  78  T E M P E R A T U R E  80  82  84  86  88  90  92  94  96  98  FLUID  65  VELOCITY,  FT. / SEC.  09  MILLIVOLTS  MILLIVOLTS  s MILLIVOLTS  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  52  -  .. ;  54  —i  56  r  . .™t  58  '!:'''  .11  * ' ' 1' •  1  "ill  1—  ' '  I " "  "?-->.  --v-.-v ^w. -v  v.  -v. x ^ N .  60 62 64 616 68 70 72 74 DRY BULB TEMPERATURE, °F.  76  x,  -.  7B  -s  S , \ A . \ \ . \ \ , N  80  82  -k^>>  84  /VX.J^J  B€  H 3  88  7>V  90  P * i |> T^Ti 1 •  92  APPENDIX 10. Run No.  Orientation  P across orifice in.  2-1 2-2 2-3 2-4 2-5 2-6 2-7 2-8 2-9 2-10 2-11 2-12 2-13  Orthorhombic #2  4-1 4-2 4-3 4-4 4-5 4-6 4-7 4-8  Orthorhombic #4  - 4--92 4-10  -•  ORIGINAL DATA AND CALCULATED DATA  Absolute upstream pressure  Temperature of i n l e t a i r  Density of dry a i r at orifice  Dew Point of i n l e t air  Correction to density for moisture  Density of moist a i r at o r i f i c e  H0  i n . Hg  °F.  lb./cu.Ft.  °F.  24.04 5.78 45.78 5.89 15.90 30.61 11.74 44.42 24.42 12.27 9,57. 17.52 14.67 .  31.50 30.23 33.04 30.50 31.14 32.16 30.95 33.04 31. 66 30.72 30.53 31.25 30.77  72.2 84.0 84.9 83.7 88.3 80.2 85.3 79.9 84.1 78.5 83.6 88.3 85.7  0.07854 0.07373 0.08047 0.07444 0.07537 9.07901 0.07532 0.08121 0.; 07722 0.07572 0.07453 0.07564 0.07483  39.0 39.4 42.4 38.1 41.9 41.7 40.8 41.2 39.5 38.4 38.5 44.0 46.3  °0.9971 0.9970 0.9969 0.9970 0.9968 0.9969 0.9968 0.9970 0.9972 0.9971 0.9971 0.9964 0.9961  0.07831 0.07351 0.08022 0.07422 0.07513 0.07877 0.07508 0.08097 0.07700 0.07549 0.07431 0.07537 0.07454  27.30 43.68 6.03 12.26 47.64 32.12 40.57 7.44 15.43 14.66  32.01 33.27 30.37 30.95 33-30 32.39 32.86 30.51 31.17 30.8 6 C  88.6 81.7 78.4 85.8 91.3 82.8 78.5 81.6 85.2 83.3  0.07744 0.08151 0.08203 0.07525 0;08016 0.07919 0.08098 0.07476 0.07587 0.07538  43.3 42.8 38.6 41.7 42.6 40.5 40.7 39.6 43.4 47.1  0.9966 0.9970 0.9970 0.0068 0.9970 0.9969 0.9970 0.9971 0.9965 0.9961  0.07718 0*08127 0.08178 0.07501 0.07992 0.07894 0.08074 0.07454 0.07560 0.(57509  2  lb./cu. f t .  APPENDIX 10. Orifice diameter  Expansion factor  Viscosity of a i r through orifice x 10  ORIGINAL DATA AND CALCULATED DATA (CON'T)  Discharge coeff.  Flow Rati i  5  inch  l b . / t f t . K'sec)  lb./sec.  Reynolds number through orifice  Temperature of e x i t a i r -  x 10~  °F.  4  Average temperature of a i r i n column  Average Absolute pressure i n column  °f  i n . Eg  0.500 0.500 0.500 0*500 0.500 0.500 0.500 0.250 0.250 0.250 0.250 0.500 0.750  0.9835 0.9959 0.9701 0.9959 0.9890 0.9794 0.9918 0.9710 0.9834 8.9914 0.9932 0.9979 0.9896  ' 1.232 1.250 1.252 1.250 1.256 1.243 1.253 1.247 1. 250 1.241 1.250 1.257 1. 253  .6002 .6030 .5995 .6030 .6010 . 5999 .6015 .6047 .6058 .6075 .6084 .6008 .6078  .02017 .00990 .02777 .00990 .01619 S.02274 .01396 .006942 .005094 .003620 .003178 .01717 .03534  5. 00 2.42 6.78 2.42 3.94 5.59 3.40 3.40 2.49 1.78 1.55 4.17 5.75  56.2 63.3 63.0 61.7 64.4 60.5 62.7 59.9 64.3 62.5 65.2 64.3 65.4  64.2 73.6 73.9 72.7 76.4 70.4 74.0 69.9 74.2 70.5 74.4 76.3 75.6  29.85 29.81 28.88 30.08 30.05 30.05 30.14 29.83 29.90 29.82 29.84 30.04 29.81  0.500 0.500 0.500 0.500 0.250 0.250 0.250 0.250 0.500 0.750  0.9816 0.9717 0.9957 0.9922 0.9691 0.9786 0.9734 0.9947 0.9893 0.0896  1.257 1.246 1.241 1.253 1.261 1.248 1.241 1.246 1. 253 1.248  .6002 .5995 .6027 .6014 .6046 .6052 .6048 .6092 .6010 .6078  .02132 .02735 .01051 .01426 .007128 .005881 .006647 .002815 .01600 .03540  5.18 6.71 2.59 3.48 3.45 2*88 3.27 1.38 3.90 5. 78  63.9 60.3 58.5 62.4 64.9 62.6 59.3 64.5 63.5 63.1  76.2 71.0 68.5 74.1 78.1 72.7 68.9 73.1 74.4 73.2  30.05 30.21 29.93 30.09 29.91 30.04 29.92 29.96 30.09 29.88  APPENDIX 10. Density of Air i n Column  Superficial air velocity (based on empty column)  V i s c o s i t y of a i r i n column x 10  lb./cu.ft.  ft./sec.  lb./ft.(sec.)  0.07556 0.07414 0.07426 0.07493 0.07434 0.07519 .0.07490 0.07468 0.07428 0.07460 0.07410 0.07434 0.07386  1. 749 0.8750 2.4506 0.8658 1.4272 1.9819 1.2214 0.6091 0.4494 0.3176 0.2811 1. 5135 3.1355  1.219 1.236 1.237 1.232 1.238 1.230 1.237 1.228 1.234 1.228 1.235 1.238 1.237  0.07437 0.07550 0.07515 0.07477 0.07377 0.07484 0.07507 0.07457 0.07453 0.07437  2.1999 2.7799 1.0732 1.4636 0.7415 0.6030 0.6795 0.3897 1. 6474 3.6528  1.238 1.230 1.225 1.237 1.241 1.233 1.226 1.233 1. 235 1.233  5  ORIGINAL DATA AND CALCULATED DATA (CON'T) Modified Reynolds number  Corrected Humidity inlet a i r  gr./lbtdry air 607.6 294.2 824.6 295.2 430.3 679.0 414.5 207. 6 • 151.6 108.1 94.56 509.4 1049.4 741.0 956.2 368.8 495.9 247.1 205.1 233.2 132.1 557.2 1234.9  Dew Point exit a i r  °F.  Corrected Humidity exit a i r  Relative Humidity exit a i r  Adiabatic Sat'n Temp, inlet a i r  ?F.  gr./l&.dry air  33.2 35.0 35.8 33.0 37.3 35.7 35.2 34.9 33.4 32.7 33.4 40.4 44.6  53.0 58.7 57.9 58.0 59.5 56.3 58.8 57.2 60.6 58.3 60.8 60.6 60.6  60.4 74.5 72.5 72.1 76.7 68.2 74.6 70.6 80.3 73.5 80.5 79.6 80.0  88.8 84.7 83.5 87.6 85.1 85.9 86.8 91.0 87.8 85.5 85.8 87.8 84.6  54.0 59.1 59.6 58.5 61.2 57.8 59.6 57.6 58.8 56.5 58.6 61.9 61.9  38.3 36.2 33.7 37.6 35.8 34.1 33.7 34.9 39.5 45.7  60.2 56.9 55.9 59.1 60.7 59.0 56.3 60.1 59.8 59.7  78.6 69.6 67.2 75.J5 80.1 75.2 68.3 78.2 77.3 77.6  87.7 88.4 91.1 88.6 86.5 87.6 90.0 85.6 87.5 88.4  61.5 58.6 56.7 60.4 61.9 58.5 56.7 58.2 60.6 61.3  s  APPENDIX 10. Adiabatic Sat'n Temp. exit a i r  Wet Bulb Temp, of inlet a i r  °F.  °F.  54-4 60.4 60.0 59.4 61.5 '58.0 60.4 58.4 62.2 60.0 62.6 62.0 62.6  54.6 59.7 60,2 59.2 61.8 58.4 60.2 58.1 59.4 57.0 59.2 62.5 62.4  61.7 58.3 57.0 60.5 62.4 60.5 57.6 61.8 61.3 61.2  62.1 59.1 57.2 61.0 62.6 59.1 57.3 58.8 61.2 61.8  Wet Bulb Temp, of exit a i r  F.  Average Wet Bulb Temp.  ORIGINAL DATA AND CALCULATED DATA (CON'T) Partial Press, of Water Vap.  Partial Press, of Water Vap. in inlet air  Partial' Pressure of Water Vap. at t „ * w  Partial Press, of Water Vap. i n exit air  Log Mean Partial Pressure Difference  i n . Hg  i n . Hg  °F.  i n . Hg  i n . Hg  54.5 60.6 60.0 59.4 61.5 58.1 60.4 58.4 62. r 60.0 62.6 62.0 62.5  54.6 60.2 60.1 59.3 61.7 58J.3 60.3 58.3 60.7 58.5 60.9 62.3 62.5  0.430 0.516 0.526 0.506 0.557 0.492 0.526 0.487 0. 510 0.469 0.506 0.572 0.570  0.239 0.243 0.272 0.231 0.267 0.265 0.256 0.260 0.244 0.233 0.234 0. 289 0.315  0.428 0. 534 0.522 0. 510 0. 553 0.487 0.530 0.492 , 0.564 0. 522 0. 574 0.561 0. 572  0.404 0.498 0.485 0.486 0. 512 0.457 0.500 0.473 0. 534 0.489 0. 538 0.534 0.534  0.08060 0.1171 0.1128 0.1030 0.1274 0.09745 0.1094 0.08394 0.1083 0.1033 0.1168 0.1091 0.1141  61.7 58.3 57.0 60.5 62.3 60.5 57.7 61.8 61.3 61.2  62.4 58.7 57.1 61.3 62.5 59.8 57.5 60.3 61.3 61.5  9.566 0.585 0.473 0. 542 0.574 0.505 0.474 3.498 0.546 0.557  0.282 0.276 0.236 0.265 0.274 0.254 0.255 0.245 0. 283 0.325  0.555 0.490 0.469 0.532 0.568 0.534 0.482 0.557 0. 548 0.546  0.526 0.467 0.450 0. 505 0.537 0.503 0.457 0. 524 0. 518 0.516  0.1119 0.08974 0.08648 0.1075 0.1187 0.1053 0.08949 0.1081 0.1074 0.09886  e  i n . Hg  APPENDIX 10. Change i n Humidity  Rate of Liquid Transfer  lb.water/ lb.dry a i r lb.mole/ nr.  Mass Transfer Coeff. lb.mole/ (hr.)(atm) (sq. f t . )  Pressure at Bottom of Column  in. Hg  ORIGINAL DATA AND CALCULATED DATA (C0N*T) Press. Drop through Packing  i n . Hg  Mean Part. Press, of non-trans. component atm.  Mass Velocity  (Schmidt 2/3 No.)  Log met Temp. Diff.  Jd  l b . mass/ (hr)(ft2)  °F.  0.00388 0.00564 0.00524 0.00559 0.005628 0.004642 0.0Q5628 0.005100 0.006700 0.005828 0.006728 0.005600 0.005057  0.01557 0. OHIO 0.02893 0.01100 0.01811 0.02099 0.01562 0.007039 0,006787 0.004190 0.004252 0.01910 0.03549  1.4939 0.7330 1.9834 0.8259 1.0993 1. 6657 1.1041 0.6485 0.4846 0.3137 0.2815 1.3539 2.4054  0.19 0.15 0.27 0.31 0.4412 0.4493 0.4941 0.2610 0.2478 0.2390 0.1625 0.3257 0.2103  0.02 0.04 0.05 0.03 0.0061 0.0121 0.0050 0.0013 0.0008 0.0005 0.0004 0.0077 0.0308  0.9866 0.9840 0.9860 0.9933 0.9913 0.9923 0.9947 0.9843 0.9863 0.9846 0.9846 0.9903 0.9820  475.83 233.55 655.12 233.55 381.94 536. 46 329.33 163.77 120.17 85. 28 74.97 405.06 833.71  0.7182 0.7167 0.7167 0. 7169 0.7165 0.7172 0.7167 0.7173 0.7168 0.7173 0.7167 0.7165 0.7166  0.06440 0.06408 0.06194 0.07290 0.05918 0.06397 0.06919 0.08093 0.08253 0.07521 0.07670 " 0.06865 0.05877  *6V8104 9.8416 10.3048 9.3944 10.6788 8.8023 9.5506 7.5932 9.4466 8.8398 9.7470 9.7319 9.8010  0.005757 0.004771 0.004786 0.005414 0.006329 0.005871 0.004942 0.006185 0.005400 0.004557  0.02439 0.02594 0.01000 0.01534 0.008968 0.006866 0.006532 0.003461 0.01717 0.03203  1.7210 2.2819 0.9129 1.1265 0.5967 0.5147 0.5762 0.2528 1.2621 2.5578  0.4926 0.6566 0.3221 ©.4875 0.2507 0.3963 0.3162 0.1934 0.3897 0.4044  0.0568 0.1066 0.0130 0.0254 0.0069 0.0040 0.0059 0.0012 0.0309 0.1544  0.9916 0.9973 0.9890 0,9933 0.9863 0.9916 0.9883 0.9886 0.9923 0.9846  589.04 755.64 290.38 393.98 196.94 162.48 183.65 77.77 442.06 978.05  0.7166 0.7172 0.7175 0.7167 0.7164 0.7170 0.7175 0.7169 0.7167 0.7169  0.06010 0.06253 0.06458 0.05893 0.06198 0.06520 0.06441 0.06669 0.05878 0.05344  9.7749 8.5050 7.4465 8.9239 10.8807 8.9225 7.5936 9.4316 9.1332 8.0875 1  APPENDIX 10. Heat of Evap'n at Average Surface Temp.  Heat Transferred  Heat Transfer Coeff.  ORIGINAL DATA AND CALCULATED DATA (CON'T) Press. Drop across 2 Layers  Press. Drop across 4 Layers  Press. Drop across 6 Layers  Press. Drop across 8 Layers  Press. Drop between 2 and 6 Layers  in.  in. H 0  in.  in. H2O  0.080 0.165 0.070 0.020 0.010 0.005 0.005 0.105 0.419 0.784 1.45 0.175 0.345 0.094 0.055 0.080 0. 015 0.420 2.10  B.t.u./lb.  B. t.u./ (hr)tft ) B.t.u./hr (°F.)  1062.2 1058.8 1059.9 1059.5 1058.2 1060.1 1058.9 1060.1 1058.7 1060.0 1058.6 1057.8 1057.7  297.95 211.76 552.42 209.99 345.29 400.93 297.97 134.42 129.48 80.02 81.09 363.99 676.29  11.3074 5.5612 13.8555 5.7773 8.3571 11.7724 8.0637 4.5754 3.5426 2.3396 2.1503 9.6660 17.8343  0.08727 0.08745 0.07767 0.09085 0.08036 0.08059 0.08993 0.1026 0.1083 0.1008 0.1053 0.08765 0.07856  0. 010 0.0150 0.0150 0.0025 0 0 0 0.029 0.110  0.044 0.074 0.035 0.0075 0 0 0.047 0.210  0.054 0.120 0.050 0.010 0 0 0 0.076 0.311  1057.7 1059.8 1060.7 1058.4 1057.7 1057.2 1060.5 1058.9 1058.4 1058.3  464.75 495.24 191.14 292.54 170.92 130.78 134.82 66.02 327.36 615.82  12.5448 15.3638 6. 7726 8.6494 4.1447 3.8673 4.3370 1.8469 9.4571 20.0908  0.03822 0.07467 0. 08566 0. 08063 0.07729 0.08742 0.08673 0.08722 0.07857 0.07544  0.232 0.950 0.050 0.093 0.030 0.015 0. 025 0 0.127 0.570  0.378  0.610  0.085 0.167 0.045 0.025 0.035 0 0.203 1.03  0.135 0.260 0.075 0.040 0.060 0 0.330 1. 60  f  2  in.  H20  H0  0  2  2  H0 2  0.054 0.120 0.050 0.010  8.555 9.749 10.735 8., 658  0.076 0.311  10.707 10.278  0. 610  33.93  0.135 0.260 0.075 0.040 0.060  31.23 32.51 37.03 39.43 34. 66  0.330  32.67 32.29  1.60  

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