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Evaporation of water sprays withsuper-heated steam or hot air
Item Type text; Thesis-Reproduction (electronic)
Authors Erickson, Kenneth Lynn, 1946-
Publisher The University of Arizona.
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Link to Item http://hdl.handle.net/10150/554552
. EVAPORATION OF WATER SPRAYS WITH
SUPERHEATED STEAM OR HOT AIR
A Thesis Submitted to the Faculty of the
DEPARTMENT OF CHEMICAL ENGINEERING
In Partial Fulfillment of the Requirements For the Degree of
MASTER OF SCIENCE
In the Graduate College
THE UNIVERSITY OF ARIZONA
by/
Kennetl Erickson!
1 9 7 3
STATEMENT BY AUTHOR
This th es is has been submitted in partial fulfillment of requirements for an advanced degree at The University of Arizona and is •deposited in the University Library to be made availab le to borrowers under ruleS\of the Library.
perm ission, provided that accurate acknowledgment of source is m ade. Requests for perm ission for extended quotation from or reproduction of this manuscript in whole or in part may be granted by the head of the major department or the Dean of the Graduate College when in his judgment the proposed use of the material is in the in te res ts of scho larsh ip . . In all other in s ta n c e s , however, permission must be obtained from the author.
Brief quotations from this th es is are allowable without spec ia l
SIGNED:
APPROVAL BY THESIS DIRECTOR
This thes is has been approved on the date shown below:
J.N t i l l U . V_/UX
Professor of Chemical Engineering
. Z 5 . / 9 7 3Date.
ACKNOWLEDGMENTS
The author gratefully acknowledges the support and
encouragement afforded him by the Department of Chemical Engineering,
University of Arizona and the Tau Beta Pi A ssocia tion . Special thanks
are extended to Dr. Neil D. Cox, director of resea rch , whose a s s i s
tance was invaluable during the laboratory investigation and subsequent
writing of this th e s is . Further thanks go to the author 's fellow graduate
students for their help and timely sugg es tion s , and to Thomas Breen,
machinist for the College of M ines, in appreciation of his advice and
aid in constructing the experimental ap p a ra tu s .
TABLE OF CONTENTS
Page
LIST OF TABLES . . . . . . . . . . . . o « vi
LIST OF ILLUSTRATIONS . . . . . . . . . . . . . . . . . . . . . ix
ABSTRACT . . . . . . . . . . . . . . . . . . . . . . . . . . . . xi
2. REVIEW OF LITERATURE . . . . . . . . . . . . . . . . . . . . . 4
3. THEORETICAL CONSIDERATIONS . . . . . . . . . . . . . . . . . 7
Factors Influencing Evaporation Temperature . . . . . . . 7O ver-a ll Heat Transfer C oeffic ien t . . . . . . . . . . . . 13Reasons for Comparing Heat Transfer Rates . . . . . . . . 17
4. APPARATUS . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
Gas Regulation and Heating . . . . . . . . . . . . . . . . 20Evaporating Column . . . . . . . . . . . . . . . . . . . . 26Spraying System . . . . . . . . . . . . . . . . . . . . . . 30
5.-o E DU E . . . . . . . . . . 0 0 . . . . . 0 . . . . 0 . 0 0 . 3 2
Rotameter Calibration . . . . . . . . . . . . . . . . . . . 32Operating Problems . . . . . . . . . . . . . . . . . . . . 33Spraying Solution ................... 35Operating Procedures for Superheated Steam . . . . . . . 35Variations in Procedures for Hot Air . . . . . . . . . . . . 38
6. DISCUSSION OF RESULTS . . . . . . . . . . . . . . . . . . . . 40
Experimental Results . . . . . . . . . . . . . . . . . . . 40Considerations Concerning h*a* . . . . . . . . . . . . . 47Considerations Concerning Spraying Rate . . . . . . . . . 47Comparison with Previous Research . . . . . . . . . . . . 49
iv
V
TABLE OF CONTENTS—Continued
Page
7. RECOMMENDATIONS FOR FURTHER RESEARCH . 53
Specific Recommendations . . . . . . . . . . . . . . . . . 53Recommendations for Apparatus . . . . . . . . . . . . . . 54
' APPENDIX A: EXPERIMENTAL DATA . . . . . . . . . . . . . . . " 56
APPENDIX B: STEAM CALCULATIONS . . . . . . . . . . . . . . . 68
APPENDIX C: AIR CALCULATIONS . . . . . . . . . . . . . . . . 96
APPENDIX D: ERROR ANALYSIS . . . . . . . . . . . . . . . . . 119
APPENDIX E: VARIANCE OF B . . . . . . . . . . . . . . . . . . 141
APPENDIX F: VARIANCE OF F . . . . . . . . . . . . . . . . . . 151
APPENDIX G: VARIANCE OF Wg . . . . . . . . . . . . . . . . . 153
APPENDIX H: VARIANCE OF TA . . . . . . I . . . . . . . . . . 1552
APPENDIX I: HEATER CONSTRUCTION':. . . . . . . . . . . . . . . . 157
NOMENCLATURE . . . . . . . . . . . . . . . . . . . . . . . . . 160
REFERENCES CITED . . . . . . . . . . . . . . . . . . . . . . . 166
42
45
57
58
59
60
61
62
63
64
65
66
67
74
LIST OF TABLES
Values of ha Versus Re
Values of h*a* Versus R e ..............................................................
Number of Separate Sets of Data Corresponding toEach Experiment with Superheated S t e a m .......................
Titration of Feed (Spray) and Bottoms (Brine) So lu tions , Superheated Steam .................................................................
Experimental D a ta , Superheated Steam: Values of Feed, Heating Medium, and Condensate Flow R a t e s ................
Experimental D ata, Superheated Steam: Values ofBottoms, C ondensate , and Feed Flow Rates and of P .
Experimental D ata , Superheated Steam: Values ofT p # T] , ' a n d T^ ........................................................................................
Number of Separate Sets of Data Corresponding to Each Experiment with Hot A i r ..........................................................
Titration of Feed (Spray) and Bottoms (Brine) Solutions, Hot A i r ............................................................................................
Dry and Wet Bulb T e m p e ra tu re s ..................................................
H u m id it ie s ............................................................................................
Experimental D a ta , Hot Air: Values of Bottoms, F eed , and Heating Medium Flow R a t e s ..........................................
Experimental D a ta , Hot Air: Values of P, Tp, T ^ , and T^.
Values of T^ and i^ . Superheated S te am ...................................
vi
vii
ige
78
.82
87
88
89
90
91
'92
93
95
106
108
109
110
111
112
113
114
115
LIST OF TABLES—Continued
Feed Rotameter Calibration Data ...................................
Heating Medium Rotameter Calibration D a t a ................
Correction Factors for W g ..................................................
Superheated Steam: Values of (F-B), (C+B-F) # BZ, and Ve A T m g .........................................................................
Superheated Steam: Values of B, C, F / and Wg . . .
Superheated Steam: Values of Tp, T^, Tg, and Z . .
Superheated Steam: Values of Tg, a, ( i i ' i g ) , and aTmg
Superheated Steam: Values of (F-B)cp CTg'Tg),(F-B) A, ^p p (T g -T p ) , and . . . / ...........................
Superheated Steam: Values of Re, ha, and h*a* . . .
Values of Re/Wg Versus T ^ ..................................................
Correction Factors for ..................................................
Values of Re/W ^ Versus T^, A i r .......................................
Hot Air: Values of B, F, , and Z ...............................
Hot Air: Values of Tp, T^, T^, H^ , and H ^ ................
Calculation of Ta ..................................................................A1
C alcula tion of Ta .....................................................................R2
Hot Air: Values of F(TA -Tp), 0 .46 (Tg-T^ ),(F-B), and a' . ? .................................? ......................
Hot Air: Values of Q, aTm ^, and V ^ a T m ^ ....................
Hot Air: Values of T ^ , T ^ , T22 , and ................
viii
LIST OF TABLES—Continued
Table Page
C -1 0 . Hot Air: Terms Involving T p T ^ , T^3, T ^ , Tg^,and T23 ....................................................................................................116
C - l 1. Hot Air: Values of H^Cp (T^-T^), (iD - i D )
+ H1c p^(T1-T 2) / and Q * ................................................................. 117
C - l 2. Hot Air: Values of ha, h*a* , Re, and B Z ......................................118
D - l . Orders of M agnitude , Superheated S t e a m ....................................... 122
D -2 . C alculation of V(ha), Superheated Steam ....................................... 123
D -3 . Orders of M agnitude, Hot A i r ............................................................ 126
D -4 . Calculation of V(ha), Hot Air ............................................................ 128
D -5 . Data for Tests of S ignificance, Superheated S te a m .......................129
D -6 . Results of Error Analysis , Superheated S t e a m ............................. 135
D -7 . Experimental R esults , Superheated S t e a m ..................................... 136
D -8 . Data for Tests of S ignificance, Hot A i r .........................................137
D-9 . Experimental Results , Hot A i r ............................................................140
E - l . Terms Involved in Calcula tion of V(B), SuperheatedS t e a m ....................................................................................................... 145
E -2 . Calculation of V(B), Superheated S t e a m .........................................146
E-3. Terms Involved in C alculation of V(B), Hot A i r .............................149
E -4 . Calculation of V(B), Hot A i r ................................................................150
F - l . Calculation of V (F ) ...................................................................................152
G - l . C alculation of V (W g)...............................................................................154
LIST OF ILLUSTRATIONS
Figure Page
1. Schematic Diagram of the Evaporator 2
2 . Spray Evaporation (Air), Adiabatic 11
3 = Spray Evaporation (Air), Not Adiabatic 12
4 o Schematic Flow Diagram of Experimental Equipment(Gas Heating and Flow Rate Measuring) . . . . . . . . -21
5. Schematic Flow Diagram of Experimental Equipment(Spraying and Evaporating) . . . . . . . . . . . . . . . 22
6. Schematic Diagram of Connections Used forM easuring W et and Dry Bulb Temperatures . . . . . . . 23
7. Schematic Diagram Showing Construction of theThermometer W ells . . . . . . . . . . . . . . . . . . . 25
8. Removable Stand for the Evaporating Column . . . . . . . . . 27
9. Schematic Diagram of the Lid and Nozzle Assembly . . . . . 29
10. Experimental Results: ha as a Function of Reynoldsu m 3 3 r . . . . . . . . . . . . . . . . . . . . a . . . . 4 3
11. Experimental Results Corrected for Heat L osses:h*a* as a Function of Reynolds Number . . . . . . . . 46
B -l . M aterial and Energy Balance Diagram, Superheated Steam . . 69
B-2. Feed Rotameter Calibration Chart . . . . . . . . . . . . . . . 79
B-3. Heating Medium Rotameter Calibration Chart . . . . . . . . . 84
C '-l . M aterial and Energy Balance Diagram, Hot Air . . . . . . . . ? 9.7
ix
X
LIST OF ILLUSTRATIONS—Continued
Figure Page
1-1, Schematic Diagram of the Hehters . . . . . . . . . . . . . . 158
1-2. Asbestos Cement Sections . . . . . . . . . . . . . . . . . . 159
ABSTRACT
Research was conducted to evaluate the heat transfer rates
developed in an evaporating column when sa lt water sp rays , maintained
at constan t spraying r a t e s , evaporated into heating mediums of either
superheated steam or hot a ir , a lso maintained at constan t flow r a t e s .
Success ive experiments provided data for different combinations of
spraying rate and gas flow r a t e . Empirical heat transfer coefficients
were ca lcu la ted from
ha = Q/Ve aThi
where a = heat transfer area per unit volum e, f t^ /f t^
h = heat transfer coeffic ien t, Btu/hrft^op
Q = heat transfer ra te , Btu/hr
Ve = evaporator volume, ft'*
aTiti = arithm etic mean temperature d ifferen ce , °F
S ta tis t ica l analyses indicated a significant variation of ha with
gas flow rate but indicated no significant variation with spraying r a t e .
For each gas flow ra te , the Reynolds number (Re) and mean (ha) of all
corresponding ha were computed. For each heating medium, ha varied
linearly with Re. Values of ha obtained using superheated steam showed
a greater variation with Re and, except for lower Re, were larger than
values of ha obtained using hot a ir . At lower Re, va lues of ha obtained
xi
using hot air were equal to or greater than values obtained using
superheated steam .
CHAPTER 1
INTRODUCTION
For small evaporative desa lting ope ra tion s , it has been
suggested that p rocesses could be approached by using superheated
steam to evaporate sa l t water sprays (Cox 1967). Heat transfer data for
the evaporation of water sprays in contact with superheated steam were
prerequisite to an examination of the feasib ili ty of such o p e ra tio ns . A
search of the literature revealed no usable information. That lack of
data became the motivation for the study described here inafter.
The research under d iscu ss io n had two o b je c t iv e s . One was to
obtain data describ ing the s te a d y -s ta te heat transfer ra tes achieved in
an evaporator (similar to that shown in Figure 1) during simultaneous
heat and mass transfer between a sa line w ater, hollow cone spray and
each Of two heating m edia , superheated steam or hot a ir . The second
objective was to correlate the experimental data such that a comparison
could be made between the heat transfer ra tes obtainable with each
medium.
A rigorous approach to the evaporative process would have re
quired analysis of the sp ray 's drop s ize d istribution . H ence, an ap
proach of that nature was considered beyond the scope of this t h e s i s .
1
2
S p ray in g S o lu t io n
Thermometer in W ell
> n
Thermometer i n W ell
> ----------S u p erh ea ted Steam or Hot A ir
n
Thermometer in W ell
<Steam or Humid A ir
£ P r e ssu r e GaugeRem ovable L id and N o z z le
. A ssem bly , S e a le d w ith V G ask et and H eld by Clamps rS _________
6"T N o z z le
E v a p o r a tin gColumn
iji.22%
6 9 ^
DrainB r in e
Rem ovable S tan d
F lo o r
/ / ~ y / / / / / /Figure 1. Schematic Diagram of the Evaporator
3
Instead , the heat transfer process was approached empirically using an
over-a ll heat transfer coeffic ien t.
CHAPTER 2
REVIEW OF LITERATURE
A review of the literature showed that those previous research
efforts most nearly rela ted to this thes is can be generally categorized as
follows: (1) the evaporation of single drops and a lso of sprays into a ir ,
(2) the use of superheated steam to dry granular solids in a tray d r y e r , .
(3) the evaporation of pure liquids into their superheated vapors , and
(4) condensation of steam using water sprays „ Specific publications cor
responding to each respec tive category are cited in the paragraphs below .
Ranz and M arshall (1952) investigated the factors influencing
the rate of evaporation of pure liquids into air. Charlesworth and
M arshall (1960) studied the evaporation, into a hot air stream , of single
liquids drops containing d isso lved s o l id s . Dickinson and M arshall
(1968) studied the ra tes of evaporation of sprays of pure liquids into air;
drops having negligible velocity with respec t to the air and those having
ve loc ities great enough to affect the rate of evaporation were studied .
Dlouhy and Gauvin (1960) reported the resu lts of s tud ies of heat and
mass transfer in spray drying. Manning and Gauvin (1960) studied thea
process of heat and mass transfer occurring in the evaporation of
dece le ra ting , finely atomized sp rays .
5
Chu, F in let, Hoerrner, and Lin (1959) investiga ted both the
use of superheated steam and the use of mixtures of superheated steam
and air for drying granular solids in a tray dryer. W enzel and White
(1951) studied the drying rates achieved when superheated steam was
used to dry sand in a tray dryer; the resulting data provided a quantita
tive b a s is for comparing steam and air as heating media for drying
granular s o l id s .
Chu, Lane,and Conklin (1953) studied the evaporation of
liquids into their superheated vapors . In that investiga tion a stream of
e ither superheated vapor or hot air passed over the liquid exposed as a
plane surface in an open container. For each liquid s tud ied , the ra tes
of evaporation obtained by using the corresponding superheated vapor
were compared with similar rates of evaporation obtained by using a ir.
It was found that for fixed mass ve loc ities and temperatures of 300°F or
above, the superheated vapor produced significantly greater ra tes of
evaporation than did a ir . Water was one of the liquids inves tiga ted .
Weinberg (1952) studied the condensation of steam by direct
contact with water from what were termed "coarse industria l" spray
n o zz les . The flow of water from the nozzles was considered as in itia lly
being in the form of a conical film, which at some fixed d is tance from
the nozzle , was assumed to d isin tegrate into large drops. Two se ts of
heat transfer coefficien ts were reported. One set pertained to the film
portion of the nozzle stream , and the other to the large drop portion.
The work of Chu, Lane, and Conklin (1953) and that of
Weinberg (1952) appeared to be the previous research efforts most
nearly rela ted to the work reported in th is th e s is . However, the l i te ra
ture search provided no information concerning the use of superheated
steam as a heating medium for the evaporation of water s p ra y s .
CHAPTER 3
THEORETICAL CONSIDERATIONS
For this resea rch , the pertinent theore tical considera tions can
be grouped as follows: (I) those factors that determine the temperature
at which evaporation occurs and, there fo re , determine the mean temper
ature driving fo rce , (2) the definition of the em pirical, over-a ll heat
transfer coefficient and of the terms a sso c ia ted therew ith , and (3)
those reasons for attempting to compare the heat transfer ra tes obtained
by using each heating medium.
Factors Influencing Evaporation Temperature
During the s te a d y -s ta te evaporation of a sa line water spray
into a heating medium of e ither superheated steam or hot a ir , the surface
area of the spray is very large; and rela tive to la ten t heat requirem ents,
the sensib le heat necessa ry to ra ise the spray d ro p le ts1 temperature to
that of evaporation is sm all. Therefore, it may be assum ed that the
spray comes almost instan taneously to the temperature at which evapor
ation occurs and that any in itia l varia tion in droplet temperature need
not be included in a consideration of temperature driving force (Ranz
and M arshall 1952; Foust et a l . 1966, pp. 340-349;.McCabe and Smith
1956, pp. 881-903).
8
Charlesworth and M arshall (1960) showed that when the d is
solution of so lids does not greatly change the vapor pressure exerted by
the corresponding so lvent, the evaporation of droplets of the resulting
solution is bes t treated by assuming that the temperature at which
evaporation occurs is not dependent on the so lids in so lu tion . Con
sequently , in this s tu d y , the temperature of evaporation is considered
to be that for pure water.
If superheated steam were used as the heating medium to
evaporate a spray of droplets inside of a v e s s e l , the steam would enter
the top of the column at a high temperature; would flow concurrently
downward with the spray; would leave the evaporator at a much lower
tem perature , and would contain the water evaporated from the spray.
The temperature at which the spray droplets evaporate would be indepen
dent of whether or not evaporation occurs ad iabatica lly and would be
equal to the saturation temperature-T0 of pure.water, for the pressureo
inside of the v e s s e l .
If, instead of superheated steam , hot air were used as the
heating medium, hot air would enter the column at a high temperature
and low humidity; would flow concurrently downward with the spray,
and would leave the evaporator at a much lower temperature and higher
humidity. The temperature at which spray droplets evaporate would be
dependent on whether or not evaporation occurs ad iaba tica lly and
would be equal to an appropriate adiabatic sa turation temperature or
would vary over an appropriate range of ad iabatic sa turation tempera
tu res .
H ere , it should be noted that for given conditions of air
temperature and humidity # the wet bulb tem perature , although a ssoc ia ted
with a different physical p ro c e s s , is approximately equal to the cor
responding adiabatic saturation tem perature , and for most com putations ,
any differences between the two temperatures can be ignored (McCabe
and Smith 1956, p. 845; Perry 19 63, p. 15-2). It should a lso be noted
th a t , rather than interpolating between lines on a humidity chart, it is
often more sa tis fac to ry to ca lcu la te ad iabatic sa turation temperatures
using the equation (McCabe and Smith 1956, p. 841):
H-HS _ 0 .24 + 0.46HT 5 T “
where H = humidity of the a ir , lb HgO/lb BD air
Hg = humidity at sa tu ra tion , lb HgO/lb BD air
T = temperature of the a ir , °F
= adiabatic sa turation tem perature , °F
= la ten t heat of vaporization at T^, Btu/lb
If the evaporative process assoc ia ted with the use of hot air
as a heating medium occurs ad iabatica lly (represented on a humidity
chart as shown in Figure 2), there are no heat lo sse s from the column,
and the adiabatic saturation temperature and saturation humidity Hg
of the air remain con s tan t . The temperature of the air entering the
10
column can be ob se rv ed # and the corresponding ad iabatic saturation
temperature T^, humidity , and saturation humidity Hg can be de te r
mined by measuring the appropriate wet and dry bulb temperatures and
referring to the humidity chart. The humidity of the air leaving the
evaporator can be determined by observing the temperature Tg and then
referring to the appropriate adiabatic sa turation line of the humidity
chart. Graphically (as shown in Figure 2), the condition of the air as it
proceeds through the column corresponds to the path , from and
to Tg and H g, followed by the ad iabatic sa turation line terminating at
and Hg. The spray droplets evaporate at a constant temperature equal
to Ta .
If (as in the research being reported) the evaporative process
a ssoc ia ted with the use of hot air does not occur ad iabatica lly (repre
sented on a humidity chart as shown in Figure 3), heat lo sse s from the
column cause both the ad iabatic sa turation temperature and saturation
humidity of the air to change from initia l values of TA > and Hc to final1 b l
values of TA and Hg , respec tive ly . The temperature T^ of the air
entering the column can be observed, and the corresponding adiabatic
saturation temperature T. , humidity H, , and saturation humidity HQ1 1
can all be determined by measuring the appropriate wet and dry bulb
temperatures and then referring to the humidity c h a r t . Similarly, the
temperature of the air leaving the evaporator can be obse rved , and
Hum
idit
y,
lb H
gO/lb
BD
Air
11
100%R e la t iv eH um idity
HSh 2
A d ia b a t icS a tu r a t io nL in e
T a T T
Dry Bulb T em p eratu re, °F
Figure 2. Spray Evaporation (Air) # Adiabatic
Hum
idit
y,
lb H
.O/lb
BD
Air12
100$R e la t iv eH um idity
S1S22
Adi a b a t i cS a t u r a t i o nL in e
1
T T TA.A T
Dry Bulb T em p eratu re, °P
Figure 3. Spray Evaporation (Air) # Not Adiabatic
13
the corresponding adiabatic sa turation temperature , humidity Hg,
and saturation humidity H n can all be determined by measuring the2
appropriate wet and dry bulb temperatures and again referring to the
humidity chart. The condition of the air as it flows through the column
correponds to some path (such as that shown by the dotted line in
Figure 3) which proceeds from and to T2 and H2 and is bounded by
the adiabatic sa turation line terminating at T. and Hc and by another1 b l
line terminating at T. and H . The temperature at which spray drop-2 2
le ts evaporate varies from T, to T, .1 2
O ver-all Heat Transfer Coefficient
The over-a ll heat transfer coefficient representing transport
from hot gas to spray was defined by
Q = haVe ATm (2)
where a = heat transfer area per unit volum e, ft^ /f t^
h = heat transfer coeffic ien t, Btu/hrft^°F
Q = heat transfer r a t e , Btu/hr
Ve = evaporator volum e, ft^
ATm = arithmetic mean temperature d ifference , °F
The product ha was used for correlating d a ta , because it would , in
g en e ra l , for a particular ap p a ra tu s , be quite difficult to separa tely
evaluate the terms h and a; w he reas , the values of , Q, and ATm can
be readily obtained.
14
The volume Ve of the evaporator is constant and eas ily c a l
culated from linear m easurem ents . The heat transfer rate Q can be
evaluated by measuring the amount of water evaporated over a given time
interval and then determining the total amount of sensib le and latent
heat required under experimental conditions. With superheated steam as
the heating medium # the arithmetic mean temperature difference is
given by
ATms = (T1-Ts ) + (T2-Ts ) (3)2
With a ir , ATmD = C l^-T ^) + (T2-TA ) (4)
2
The incoming gas temperature T^ and outgoing temperature T2 can be
measured d irec tly . The saturation temperature of water T can be found
in the steam ta b le s , and adiabatic sa turation tem pera tu res , T and T ,1 A 2
for incoming and outgoing a ir , re spec tive ly , can be determined as
d iscu ssed in the preceding section .
In the error ana lysis d iscu ssed in Appendix D, it was not
possib le to rigorously consider the errors introduced into the experimen
ta l resu lts because of random heat lo sse s to the surroundings. In order
to augment the error ana ly s is and a s s e s s the experimental resu lts in
terms of poss ib le errors introduced by random heat lo s s e s , it was con
sidered worthwhile to examine the general nature of the experimental
resu lts appropriately adjusted to account for random heat lo sse s to the
surroundings.
For all experiments involving superheated s team , Tg was always
within 1 or 2°F of , and for all experiments involving hot air, Tg was
within 10oF (usually 5 or 6°F) of T, . It w as, therefo re , assumed that2
if av a ilab le , further heat could have been absorbed by the spray until the
fraction of the spray evaporated became so large as to reduce the area
available for, hence the rate of, heat transfer and thus cause T2 to be
come greatly different from Tg. During the experiments under d iscussion ,
heat lo sse s to the surroundings were not large; and if there were no
lo s s e s , it appears reasonable to assume that a ll of the energy available
in the hot gas entering the column would have been transferred to the
spray at the rate Q * .
If, for all experiments involving a given se t of experimental
conditions, heat lo sse s to the surroundings were equal and constan t,
such lo sse s would have no impact on the error ana lysis given in Appen
dix D. A heat transfer coefficient h* and heat transfer area per unit
volume a * , both based on constan t and equal heat lo s s e s , could be
ca lcu la ted from
Q* = h*a*Ve ATm (5)
Values of h*a* would e ssen tia lly be the values of ha which would have
been obtained if heat lo sse s were constant and , in this c a s e , all equal
16
to zero . Although adiabatic conditions are implied h e re , the implica
tion is only co incidental and resu lts from Q* being the only term which
involved equal and constant heat lo s se s and could be evaluated . By
comparing the general trends exhibited by values of h*a* with those
trends exhibited by corresponding values of ha , it was felt that the
in f luence , if any, of random heat lo sse s on the va lid ity of experimental
resu lts could be judged.
In Equations 2 and 5 abo ve , it would, at first* appear that
instead of using the arithmetic mean, the logarithmic mean temperature
difference should be u sed , since in heat transfer p ro cesses similar to
those being inves tiga ted , the logarithmic mean temperature difference,
is more correct than the arithmetic mean or i s , in f a c t , the true av erag e .
For example, the logarithmic mean represen ts the true mean temperature
difference when the temperature of one of the two fluids involved re
mains constant and there are no heat lo sse s (McCabe and Smith 1956,
p. 432; McAdams 1954, p. 191). However, if the denominator of the
logarithmic mean were zero or a finite number divided by zero , the ex
pression for the logarithmic mean would be undefined, and it would be
necessa ry to use the arithmetic mean. In the research under d isc u ss io n ,
the logarithmic mean was often a finite number divided by zero . H ence,
it was n ecessa ry to base all ca lcu lations on the arithmetic mean
temperature d ifference . The undefined logarithmic mean resu lted from .
steam temperatures (leaving the column) equal to the sa turation
17
temperature for water at the pressure inside of the column. Apparently,
the gas phase res idence time was long enough for near thermal equ ilib
rium conditions to be obtained between the cooled steam and evaporating
spray.
Reasons for Comparing Heat Transfer Rates *
It was suspec ted that the heat transfer ra tes obtained using
superheated steam as the heating medium would be different and probably
greater than those ra tes obtained using hot a ir . The reasons for an tic ipa
ting such resu lts were based on a qualita tive analysis of the physical
p rocesses involved.
It was noted that in some gas film which surrounds an evapora
ting droplet and which extends from the droplet 's surface to the bulk g a s , •
evaporation of the droplet into superheated steam involves different
phenomena than evaporation into hot a ir . In the case of superheated
steam , heat transfer is res tr ic ted to a single component, and vapor
motion in the film is due to density differences resu lting from a tem pera
ture gradient. The newly formed vapor will move away from the liquid
surface slow ly, and sensib le heat will be transferred to that vapor by
molecular conduction. The presence of newly formed vapor will influence
the temperature gradient near the liquid surface , but should have little
influence on the temperature gradient throughout the remainder of the
film. In the case of hot a ir , heat transfer involves two components, and
18
fluid motion in the film is due to molecular diffusion and density dif
ferences resu lting from both temperature and concentration gradients „ In
diffusing from the liquid surface to the bulk g a s , the temperature of the
newly formed vapor will increase from that at the surface of the drop to
that of the bulk g a s . The temperature gradient throughout the entire gas
film will be influenced by the sensib le heat transfer to the diffusing
vapor.
At the drop le t 's su r fa ce , the heat flux due to molecular
conduction will depend on the physical properties of the heating medium
and the temperature gradient in the film. Considerations given by Bird,
Stewart, and Lightfoot (i960, pp. 328-330, 574, 65 8-668) concerning
transpira tion cooling and sim ultaneous heat and m ass transfer indicate
that for a given bulk temperature driving force, heat transfer accompa
nied by oppositely directed mass transfer will produce temperature
gradients which are reduced rela tive to the corresponding heat transfer
without m ass transfer . For the system s under considera tion , it would
appear that under given conditions, the heat transfer ra te s o b ta inab le '
with each heating medium should differ because of d ifferences in physi
cal properties and because of differences in temperature gradients in the
film. It further appears that when the heating medium is hot a ir , the
temperature gradient and heat flux by molecular conduction at the drop
surface will be lower rela tive to the gradient and flux which would be
obtained when the medium is superheated steam . Therefore, heat
19
transfer ra tes should not only differ, but should be higher when super
heated steam is u sed . The work of Chu, Lane and Conklin tends to
support this conclusion .
J
CHAPTER 4
APPARATUS
Schematic diagrams of the experimental apparatus are shown in
Figures 4 and 5. The following sections d iscu ss the construction and
employment of the various items of equipment shown there in .
Gas Regulation and Heating
In the laboratory, steam was available from a regulator at
50 psig and was supplied to the apparatus using a ga lvanized iron p ipe
line (one-inch, schedule 40) isu la ted with 1 i - inch th ick , prefabricated
fiberg lass se c t io n s . The bypass line taking steam direc tly to the
evaporator was used to prevent flooding of the heaters and rotameter
when blowing condensate from the steam p ipes .
Air was available from a compressor at 100 psig and was sup
plied to the apparatus using a galvanized iron pipeline ( i - in c h ,
schedule 40). The rate of air flow through the line was controlled by the
two pressure regulators connected in p a ra lle l . To aid in accurately
measuring wet and dry bulb tem peratures, the pipe connections shown in
Figure 6 were extended from a tee immediately following the reg u la to rs .
The gas p hase , e ither steam or a ir , first p a ssed through the
se ries of h ea te rs , constructed as shown in Appendix I , and then through
20 ■
21
Steam
P r e ssu r e R e g u la to r A ir
---------- X H <rC o n n e c tio n s - f o r M easu rin g Wet Bulb Temp P r e ssu r e R e g u la to r
Nichrome W ire H ea te rsR otam eter
70 C o i l s H4.O C o i l s 140 C o ils
70 C o i l s 140 C o i ls 140 C o i lsV ent
Nichrome Wire H ea ters
v ivV a r ia c
Steam Trap
Figure 4. Schematic Flow Diagram of Experimental Equipment(Gas Heating and Flow Rate Measuring)
22
<\ /
C ondenserSteam or Humid A ir
C o o lin g W ater
w • >Ni chrome W ire H eater 70 C o i l s
V a r ia cV
\J/ V ent f o r Humid A ir
R otam eterC on densate
^ S t i r r i n g M otor and S t i r r e r
S p ra y in g S o lu t io n X —
Therm ometer in W ellP r e ssu r e Gauge
Thermometer W ell
\ z
zEtxj
B rin e
A
< <Super he a ted Steam or Hot Air
E v a p o ra to r
Thermometer i n W ell
/ \
>C o n n e c tio n s f o r M easuring Wet Bulb T em p eratu res
D rain
F eed Tank GearPump
Tr ap
B a ro m etr ic Leg
Figure 5. Schematic Flow Diagram of Experimental Equipment(Spraying and Evaporating)
23
Thermometer
/ \
l /8 - in c h pipe nipple threaded such that the end of the nipple extended well into the cross
— DXh >
■vlj;Mit
.<u
Rubber stopper could be tightly p laced in the cross so that the bulb was directly in front of the end of the nipple and only ,about 1/8 inch d is tan t
/ \
Valve used to increase air velocity sufficiently to allow accurate measurement of wet and dry bulb temperatures Cross p laced so that
thermometer is inserted vertically
Air line
Figure 6. Schematic Diagram of Connections Used forMeasuring Wet and Dry Bulb Temperatures
24
the rotameter (provided with a bypass to avoid unnecessa ry fouling) „
The hot gas then entered the evaporator near its top and flowed concur-
1 rently downward with the spray . Nearly saturated steam or highly
humidified air left the bottom of the column.
The gas lines entering and leaving the evaporator were equipped
with thermometer w e l ls , constructed as shown in Figure 7. The '
thermometer used in the well near the top of the evaporator was graduated
in 1 C° increm ents, from -10 to 400°C; that used in the well near the
bottom was similarly graduated from -10 to 360°C .
All pipe (one-inch, schedule 40, galvanized iron) carrying hot
gas to the evaporator was insulated by covering with two layers of one-
inch th ick , prefabricated sections of magnesite pipe insula tion or by
wrapping, to an appropriate th ickn ess , with pyrex wool. All pipe (one-
inch, schedule 40, galvanized iron) carrying gas to the condenser was
insulated with 1? -inch th ick , prefabricated fiberg lass se c t io n s .
The drain pipe descending vertica lly from the pipe line con
necting the evaporator with the condenser was in s ta lled such that any-
steam condensing enroute to the condenser would co llec t in the drain
p ipe, below the level of the evaporator, and could be periodically
removed and m easured , Also, to again aid in measuring wet bulb
tem peratures, the pipe connections shown in Figure 6 were extended
25
8-inch length of i - inch copper tubing
Copper tube
Copper tube
Nipple Two-inch galvanized pipe nipple
___________I___ IEnd of copper tube crimped and then sea led by brazing
brazed to nipple
Figure 7. Schematic Diagram Showing Construction of the Thermometer W ells
The copper tube was packed with silicone b a sed , high temperature grease (manufactured by Dow Corning), into which the thermometer was in se rted .
26
from a tee immediately following the thermometer well in the line
leaving the evaporator.
When superheated steam was the heating medium, the con
d en se r and accompanying barometric leg provided an accurate means of
measuring the flow rate of vapor leaving the evaporator. The s teady -
s ta te flow of condensate from the barometric leg was co llec ted over a
given time in terval and then m easured. During that in te rval, it was
found that the amount of vapor condensing in the pipe leading to the
condenser was neg lig ib le . When air was the heating medium, the
humidified air was vented to the atmosphere as shown in Figure 5.
Evaporating Column
The evaporating column was made by welding together, end to
end, two 55-gallon drums, each with its bottom cut away and removable
lid de tached . To one end of the resulting cylinder, a conical sec tion
was welded. Into the apex of that sec tion , a one-inch pipe nipple was
then welded. To support the resulting column vertica lly and to ra ise its
base above the floor, the removable stand (constructed as shown in
Figure 8) was required.
Of the two drains connected to the one-inch nipple at the base
of the column, one was simply a short length of one-quarte r- inch pipe
having a valve at the lower end; the other drain consis ted of a valve fol
lowed by a trap made from one-quarter- inch pipe and appropriate fittings.
27
Circular iron band welded to legs
Bolt which allowed adjustment of the band
M etal plate welded to le g s— hole in center supported conical base of column <ty>
&>
Legs made from angle iron
&
Circular d isc s welded to legs to provide additional support
Figure 8. Removable Stand for the Evaporating Column
28
The height of water held in the trap was fifteen inches and was suf
ficient to sea l steam or air in the evaporator while allowing concen
trated brine to continuously drain. The water which accumulated in the
trap amounted to approximately one hundred m il l i l i te rs .
Because of the requirement to frequently c lean or change the
spray n o z z le s , it was necessa ry to assem ble both the uppermost portion
of the feed line and the removable lid of the upper drum as shown in
Figure 9. In th is configuration, the pressure gauge was required to
help regulate the spraying rate; the thermometer well was constructed
much like those already d iscu ssed (except that a one-inch coupling was
u se d ) , and the nichrome heater , used to bring the feed solution to near
the evaporation tem perature , was constructed similarly to those men
tioned previously and was connected to a va riac .
The cylindrical sec tion of the evaporator was insulated with
five layers of one-inch thick fiberg lass insulation; the conical bottom by
covering with a one-inch layer of asbes to s cement, and the removable
top by covering with a tw o-inch th ickness of pyrex wool. The fiberg lass
insulation and pyrex wool were then covered with c a n v a s . The asbes to s
cement was secured to the conical bottom using duct sea ling tape and
wooden sh im s.
Although found to be water tigh t, a ll welded seam s w ere , as an
added precaution, sea led with silicone rubber sea lan t (which was ap
plied on the inside of the column). At the top of the column, seventeen
29
Thermometer Variacin Well
Pressure Gauge'r~i
Nichrome Heater
Feed Line
UnionC" ClampRemovable Top_______ Nipple brazed over hole through the
~ > V center of the removabletopLip around
top of columnG asket
-X- i Nozzle r j ' adapter
Nozzle' Column
Figure 9. Schematic Diagram of the Lid and Nozzle Assembly
The portion of the feed line below the union, to include the nozzle and adapter, passed through the center of the pipe cap and was sea led to the cap by brazing; the pipe cap could be turned down over the nipple and would place the nozzle consis ten tly in the same position— about six inches below the incoming gas stream and centered in the column ax ia lly .
30
small "C" clamps and a gasket fashioned from an automobile inner tube
were used to se a l the removable lid of the upper drum aga inst the rim of
the column. No apparent leaks from the column were de tec ted during
any of the experim ents.
Spraying System
The supply tank for the sa l t water feed was fashioned from a
55-gallon drum. In itia l ly , several coats of paint were applied to the
inside of the tank, and subsequent repainting was periodically required
to prevent rusting . The sm all, variable speed s tirrer was clamped to the
supply tank and used to provide constant stirring during experim ents.
The small gear pump provided feed solution under p ressures
sufficient to obtain the desired spraying ra te s . Although made of
bronze and having s ta in le s s s te e l sh a f ts , the pump was severely
damaged at the conclusion of experimentation; however, much of the
damage was believed due to cavita tion rather than corrosion. The small
rotameter employed to measure spraying ra tes was provided with a by
p a s s , which was used to prevent fouling of or damage to the rotameter
when contaminants were being flushed from the spraying system .
Of the pipe fittings used in constructing the spraying system ,
most were made from copper or galvanized iron, and a few from s ta in le s s
s te e l . Fittings made from copper or s ta in le s s s tee l suffered little from
corrosion; w h e rea s , those made from galvanized iron were badly damaged.
31
The spray nozzles were manufactured by W m„ Steinen Mfg.
Co. , Newark, New Jersey . The nozzle having cata log number A150
was used to provide spraying ra tes which varied from four to ten pounds
per hour. The respec tive pressures which were required varied from
twenty to forty p s ig . The nozzle having catalog number A200 was used
to produce spraying ra tes of approximately seventeen pounds per hour.
The corresponding pressure required was about 40 p s ig . The nozzles
produced a hollow cone spray , which, at a d is tance of about s ix to nine
inches from the nozz le , appeared to be completely d ispe rsed into a
fine m ist.
CHAPTER 5
PROCEDURE
This chapter provides a de ta iled d iscu ss io n of the procedures
used to operate the experimental apparatus and to co llec t d a ta . Actions
taken prior to , during, and after experiments and explanations concern
ing specific operating problems are incorporated into the d isc u ss io n .
Rotameter Calibration
Prior to conducting any experim ents , each of the two
rotameters was ca lib ra ted . The procedures for calibrating the rotameter
measuring spraying ra tes were as follows: The valves on the gas lines
were c lo sed , and for at le a s t one hour, the spraying rate was constan tly
maintained at a given meter reading; after which, severa l consecutive
measurements of the rate of drainage from the column were m ade, and if
the resu lts were co n s is ten t , it was assum ed that s te a d y -s ta te operation
had been achieved and that the average flow rate ass igned to the given
meter reading was sufficiently a c c u ra te . „
Calibration of the rotameter measuring hot gas flow rates was
accomplished as follows: In the absence of a sa lt water spray, steam
having a temperature of approximately 460°F was c ircu la ted through the
apparatus; the flow rate of the steam was constantly maintained at a
„ .
33
given meter reading until the temperature of the gas entering and of the
gas leaving the evaporator and the rate of flow of condensate from the
barometric leg all remained constant and s te a d y -s ta te could be assum ed
to ex ist; severa l consecutive measurements of the rate of flow of
condensate were then made; the average of those measurements was
taken as the steam flow rate corresponding to the given meter read in g .
The valid ity of the calibration data thus obtained was la te r confirmed by
a comparison with similar data derived from the resu lts of those experi
ments in which superheated steam flowed with ra tes a t , or near, those
corresponding to the appropriate meter read ings. When correlating
experimental d a ta , the flow rates determined from the rotameter were
ad jus ted , by means of the appropriate ca lcu la tion s , to compensate for
the d ifference, at specif ic tem peratures, between the density of steam
and the density of a ir , and to compensate for the varia tion , over the
appropriate temperature range , of the density of each of the two heating
m edia.
Operating Problems
The most serious problem encountered during the research was
fouling of the spray n o z z le s . The fouling substance was apparently a
combination of d irt, ru s t , g r e a s e , and possib ly organic matter of ex
tremely small d im ensions. •
34
Each nozzle came equipped with a fine mesh, s ta in le s s s tee l
sc reen , which served as a f ilter. The screen would become so fouled
as to completely stop flow through the nozzle . If the sc reen were absen t
during spraying, the channels and orifice of the nozzle would become
fouled.
It was found that filter paper could only remove a very small
fraction of the fouling substance from a sample of sa l t so lu tion , and all.
attempts at constructing a filter for the feed line were u n su ccess fu l.
Fortunately, spraying could be conducted continuously for about twelve
to fifteen hours before a nozzle became badly fouled.
Additional experimental problems included both frequent, un
pred ic tab le , severe reductions in laboratory steam quality and failures
of one or more of the h e a te r s . The former problem is se lf-exp lana to ry .
The la tter was e ither caused by breaking of the copper leads connected
to the nichrome c o ils , because of extreme oxidation, or caused by
fouling of the packed sec tions of s ta in le s s s tee l pipe to the extent that
the necessa ry steam flow rate could not be m aintained. Breaking of the
copper leads occurred frequently but usually only upse t an experiment
rather than terminate i t . Fouling of the packed sec tio ns occurred only
once but was so severe that all of the heaters had to be rebuilt around
new pipe.
Finally , minor variations in the quality of the laboratory 's
steam frequently occurred during most of the experiments with
35
superheated s te am . As a r e s u l t , the variac connected to the las t
heating coil had to be periodically ad justed in order to help maintain
s te a d y -s ta te operation.
Spraying Solution
The spraying (feed) solution was always approximately 1.6
percent by weight sodium chloride and was made using deionized water
and non-iodized table s a l t . If a given feed supply was not exhausted
within forty-eight hours, the solution was d iscarded , and a fresh supply
was prepared. The frequent changing of spraying solution was done to
limit the growth of any organic matter that could contribute to fouling of
the spray n o z z le s .
Operating Procedures for Superheated Steam
In general, the operating procedures employed in experiments
involving the use of superheated steam were much the same as those
employed in experiments involving the use of hot a ir . The procedural
de ta ils applicable to the use of superheated steam are considered f i r s t .
In itia lly , condensate was flushed from the laboratory 's steam
lin e s . In order to prevent flooding of the hea te rs , the bypass leading
directly to the evaporator was used while flushing. When it appeared
that the steam lines were c lear of condensa te , the bypass was c losed ,
and steam was sent through the h ea te rs , to the evaporator and condenser.
A quick inspection was made to insure proper functioning of the system .
and then power was applied to the h e a te r s . U sually , about three hours
were required for the heaters to become warm enough to heat the steam
to the desired tem perature . When the temperature of the steam had
reached the appropriate va lue , spraying and heating of the spraying
solution were in it ia ted . The temperature of the spraying solution was
maintained near the temperature of evaporation, in order to minimize
sensib le heat requirements during evaporation. After spraying was b e - •
gun, steady s ta te operation was normally achieved within five to seven
hours and was assum ed to e x is t .a t the following condition: The
temperature and flow rate of the steam entering and of the steam leaving
the column, the spray temperature and flow r a te , the flow rate of brine
from the evaporator, and the concentration of NaCl in that brine Were a ll
remaining cons tan t .
In a l l , twenty-two experiments were performed (twelve with
superheated steam , and ten with hot air). W hen, during each experiment,
s te a d y -s ta te was assumed to e x is t , an attempt was made to obtain, ,in ;
quick su c ce ss io n , three se ts of da ta . However, in some in s ta n c e s ,
fouling of the n o z z le s , severe reductions in steam qua lity , or failure of
the heaters terminated the experiment before three se ts had been col
lec ted .
Each se t of data was co llected by identical m eans. W herein,
the brine leaving the evaporator was co llec ted over a ten minute in ter
va l, and condensate from the barometric leg was co llec ted for eight of
37
those ten minutes (from the end of the first through and including the
end of the ninth minute); throughout the in terval, thermometer and
rotameter readings were monitored to insure that s te a d y -s ta te was main
ta ined , and all thermometer and rotameter readings were noted at the
beginning and at the end of the ten minute interval and were recorded.
While co llec ting a se t of da ta , the spraying ra te , as indicated
by the rotam eter, w as , by manipulating the valve regulating the pump
recycle , held as constant as p o ss ib le . Such control was complicated by
frequent, severe fluctuations of the rotameter float and by minor de
c reases in flow ra te , caused by fouling of the n o zz les . Thus, the
rotameter reading recorded e sse n tia l ly represented an "eyeball" average
for the given time period.
The value of atmospheric p ressu re , as read from the laboratory 's
barometer, was recorded immediately prior to collecting the first se t of
data and again recorded.immediately after co llec ting the third (or last)
s e t . If, after co llec ting the third se t of d a ta , the nozzles were not too
badly fouled., a new gas flow rate was imposed, and four to five hours
allowed for the system to again come to s te ad y -s ta te operation.
During each experiment, the chloride ion served as a tie e le
ments The presence of the ion provided a convenient means of helping
to determine if s te a d y -s ta te operation had been achieved and a lso pro
vided an approximate means of checking the value of the spraying ra te ,
as determined from the rotam eter. By titrating spraying and brine
38
solutions with the same standard so lu tion , an accurate ratio of con
centrations could be obtained without calculating individual numerical
v a lu e s . The ratio of concentrations multiplied by the flow rate of the
brine was used as a check of the spraying rate read from the rotameter.
Analyses for the chloride ion were made using the Mohr method
(Skoog and W est 1965, pp. 209-220). It was found that a 1 .6 percent
by weight sa l t solution and a 0 .2 N silver nitrate solution were ideal
for analy tica l purposes. It was a lso found that tw enty-five m illiliter
samples of e ither brine or feed, with the addition of a pinch of sodium
bicarbonate and two m illiliters of five percent by weight potassium
chromate so lu tion , could be titrated quickly and with exce llen t precision.
Here, it should be noted that before a n a ly s is , brine sam ples had to be
allowed to cool to room tem perature .
Variations in Procedures for Hot Air
W ith the exception of flushing steam lines and collecting
condensate from the barometric leg , the only significant procedural
differences encountered when using hot air were the manner in which gas
flow was regulated and the requirement, during every experiment, to
periodically measure the wet and dry bulb temperatures of the hot air
entering and of the cooler air leaving the evaporator. The wet bulb
temperatures determined for the air leaving the column were somewhat in
error, because the ve locity of.the air flowing by the bulb was only about
39
seven feet per se co n d , and fifteen feet per second is usually necessary
for accurate measurements (McCabe and Smith 1956, p . 848).
Wet bulb temperatures were determined by wrapping the bulb
of a thermometer with gauze soaked with water and then , using the
appropriate connections described in the preceding chap ter, placing the
bulb in the air stream . After obtaining a value for the wet bulb tempera
ture , the bulb was examined to make certa in that it had remained wet.
CHAPTER 6
DISCUSSION OF RESULTS
The data obtained during experimentation is given in
Appendix A. Appropriate calcu lations are given in Appendices B through
Ho This chapter summarizes the resu lts of those ca lcu lations and
compares the resu lts with data from previous resea rch e ffo r ts ..
Experimental Results
For the appropriate combinations of spraying rate and he'a ting
medium flow r a t e , the mean, denoted by ha , of all corresponding values
of ha was computed. From a s ta t i s t ic a l analysis of the computed va lues
of h a , there could be de tected no significant varia tion which could be
attributed to different spraying ra tes being used with the same heating
medium flow r a t e . Therefore, any effects resulting from variations
among the values of spraying rate were considered neg lig ib le .
The Reynolds number corresponding to each heating medium
flow rate was ca lcu la ted , as appropriate, from either
: ■ ■ / , ' ■
40
41
Re = 4Wg/jtdM (6)
or
Re = 4WD/jtdM (7)
where d = diameter of the cylindricial portion of the evaporating column, ft
= hot air flow r a t e , lb /h r
Wg = superheated steam flow ra te , lb /h r
= v iscos ity of the hot gas entering the column, Ib /f t-h r
For each Reynolds number, the mean, again denoted by "Ha", of all cor
responding values of ha was computed. When all Reynolds numbers
were considered , it was found that (as shown in Table 1 and Figure 10):
The values of ha resulting from the use of each medium increased
linearly with Reynolds number; the slopes a ssoc ia ted with those linear
increases differed for each heating medium. In considering specific
Reynolds numbers within the range of values stud ied , it was found that
at the larger Reynolds numbers, values of ha resulting from the use of
superheated steam were larger than the values of ha resu lting from the
use of hot a ir . At the lower Reynolds num bers, it was found that no
s ignificant difference could be found between the va lues of ha obtained
using superheated steam and those values obtained using hot a ir . How
ever, the general trend (with Re) of the values of ha for each heating
medium indicated that at lower Reynolds num bers, va lues of ha obtained
42
Table 1. Values of ha Versus Re
Reha . Superheated Steam
■ (Btu/hrft3oF)h a , Hot Air
(Btu/hrft3oF)
638 ± 11 2 .0 8 + 0 .0 9
625 + 11 2.05 + 1.04. .
561 + 23 1 .39 + 0.19
551 + 9 1.27 + 0 .04
541 + 23 1.34 + 1.46
441 + 20 1 . 2 0 + 0 .2 9
424 + 19 0 . 9 9 + 0 . 8 0
407 + 19 1 . 0 5 + 0 . 2 2
320 + 19 . 0 .74 + 0 .1 0
312 + 23 0 . 6 0 + 0 . 8 0
280 + 23 0.57 + 0 .75
252 + 23 0 .68 + 0 .31
ha,
(Btu
/hrf
t30F
)4 .00
3.00
2 . 0 0
1 . 0 0
0 . 0 0100 200 300 400 500 600
Re
Figure 10. Experimental Results: ha as a Function of Reynolds Number
44
using hot air could be greater than or equal to those obtained using
superheated s te am .
Using a confidence coefficient of 95 percent, confidence limits
were determined for both ha and Re. In Table 1, the confidence limits
are indicated by the numbers to the right of the + signs in each column.
In Figure 10, the confidence limits are shown by the rec tang les about
each point. The rec tang les represent two dimensional domains; in
which, the probability of finding the true values of Re and corresponding
ha is approximately 9025 chances out of 10 ,000.
Additionally, for each Reynolds number, the m ean , denoted by
h*a*, of all corresponding values of h*a* was computed. The obtained
values of h*a* are given in Table 2 and shown as a function of Reynolds
number in Figure 11.
Since values of h*a* were independent of heat lo sse s to the
surroundings, it appeared that if the trend shown by values of h*a* as a
function of Re were sim ilar to the trend shown by values of ha , then the
error analysis given in Appendix D was not seriously degraded by neg
lecting heat lo sse s to the surroundings. The trend shown by h*a* in
Figure 11 and by ha in Figure 10 appear to be e sse n tia l ly the sam e , and
the confidence limits calculated for Ha" should be reasonably valid .
45
Table 2. Values of h*a* Versus Re
h* a* , Superheated Steam h*a*. Hot AirRe ____________ (Btu/hrft^°F)___________ (Btu/hrft^°F)
638 + 11 2.19
625 + 11 2.18
561 + 23 1.88
5 5 1 + 9 1.45
541 + 23 1.76
441 + 20 1.50
424 + 19 1.14
407 + 19 1.04
320 + 19 0 .88
312 + 23 1.02
280 + 23 0 .95
252 + 2 3 0 .68
h*a*
, (B
tu/h
rft3
oF)
4 .00
3.00
2 . 0 0
1 . 00
0 . 0 00 200100 300 400 500 600
Re
Figure 11. Experimental Results Corrected for Heat Losses: h*a* as a Function of Reynolds Number
47
Considerations Concerning h*a*
The heat l o s s e s , responsib le for the difference between a
value of h*a* and the corresponding value of ha, appeared to vary in a
random manner, and for these random varia tions , no explanation was
found which could be substan tia ted from the experimental d a ta . Gen
era lly , during experiments with hot a ir , heat lo sse s were less than
those occurring during experiments with superheated s team , and it was -
believed that the lower heat lo sse s a sso c ia ted with air were entirely
due to a lower average temperature driving force between the heating
medium flowing through the column and the ambient a ir .
Considerations Concerning Spraying Rate
In values of ha corresponding to a given heating medium flow
r a t e , the inability to de tec t significant varia tions with spraying rate was
of considerable concern . In fac t , it was considered n ecessa ry to
present a reasonable explanation for such re su l ts .
. Theoretically , if the same nozzle and same heating medium flow
rate were u sed , an increase in spraying rate would create a greater area
(per pound of feed) for heat transfer, and would, there fo re , create
greater heat transfer r a t e s . The increase in area would be due to the
sm aller, more numerous droplets produced by the greater pressure
necessa ry to increase the spraying ra te . In the research being con
sidered , the same nozzle and same heating medium flow rate were used
with spraying ra tes of approximately eight and ten pounds per hour.
The s ta t i s t ic a l analyses of Appendix D showed that for each heating
medium, there was no significant difference between the values of ha
obtained at each of the two spraying ra te s . For such r e s u l ts , one ex
planation would be that any effects due to variation of the spraying
rate were smaller than those effects which could accura te ly be examined.
That is , changes in ha may have occurred when the spraying rate was
changed, but such changes were so small that they could not be d e te c t
ed from the experimental da ta , because the measuring techniques and
general experimental procedures were not sufficiently sen s it iv e or
p rec ise .
Cox (1962) reported information which tends to support the
above explanation . In studying how pressure affected the rate of area
production, Cox found that at p ressures below 200 p s ig , the rate of area
production, for those nozzles examined, was e s se n t ia l ly independent of
changes from one nozzle to another. Cox a lso found that for small
changes in p ressu re , occurring below pressures of 200 p s ig , changes in
the rate of area production were sm all.
During the research which has been the sub jec t of this th e s is ,
the maximum pressure used to operate any nozzle was about 70 psig , and _
the minimum used about 20. Therefore, based on the re su l ts reported by
Cox, it appears entirely possib le that ha could have increased with
49
increases in spraying r a t e , but such resu l ts could not be detected from
the experimental da ta .
Comparison with Previous Research
The experimental resu l ts presented in this thes is appeared to be
cons is ten t with the data obtained by previous research efforts . Appro
priate comparisons are made in the following paragraphs.
The work of Chu, Lane, and Conklin (1953) indicated that for a
given value of Reynolds number, the use of superheated steam should •
produce greater evaporation rates and should thus yield greater heat
transfer coeff ic ien ts . The experimental resul ts presented in Table 1 and
Figpre 10 appear to be partial ly cons is ten t with the resu l ts obtained by
Chu, Lane, and Conklin in that , for a given Reynolds number, values of
ha obtained from the use of superheated steam were larger than those
coefficients obtained from the use of hot air except in the range of lower
Reynolds numbers.
For the research under d iscu ss ion , Ranz and Marshall (1952),
Manning and Gauvin (1960), and Dickinson and Marsha l l (1968) all
indicate that a heat transfer coefficient of approximately 36 to 90
Btu/hrft2°F could be expected from the use of hot air . Weinberg (1952)
obtained heat transfer coefficients of 1000 to 3000 Btu/hrft^°F for the
condensat ion of steam by water sp rays . However, Weinberg did not
50
present sufficient information to allow a comparison of his resul ts with
those of the research under d iscu ss ion .
In order that values of ha could be compared with the coeffi
cients indicated above , the value of the term a was es t imated . For the
purpose of making that e s t im a te , the following assumptions were made:
1. The spray leaving the nozzle was init ial ly in the form of a
cone; at some d is tance from the n o z z le , this cone was com
pletely d ispersed into a fine mis t, and heat transfer occurred
almost entirely between the heat ing medium and the mist.
2. Since ha was not affected by varying the spraying rate F , only
one value of F (equal to 10 lb/hr) needed to be considered.
3. Based on the type of nozzle used in the exper im ents , a rea son
able average diameter for the individual spray droplets should
have been on the order of 300 microns or approximately 10""^ft
(Foust et a l . 1966, p. 347) , and it was assumed that it was
sufficiently accurate to consider the spray 's drop size d i s
tribution to be represented by one average diameter, denoted
by ,2r, equal to 10"" ft .
4. From the correlations given by Foust et a l . (1966, pp. 451-
452) and by considering the droplets to be spheres falling un
hindered, the terminal ve locity of the droplets was estimated
to be 3.3 f t / s e c ; since the spray fell approximately 5 feet and
some mixing and droplet coll is ions had to be allowed for, it
51
was assumed that the maximum time required for spray
droplets to fall through the column should not have exceeded
three s e c o n d s .
Based on the above a ssum pt ions , the heat transfer area per
pound of sp ra y , denoted by a , was est imated by
a = (4jrr2) 3 1 f t2 = 96 f t 2 , xQ \°)
4Jtr 62. 4 lb lb
At any given time # the weight of spray descending through the column
was est imated to be equal to 3 F / (3600 sec /hr) ; therefore , an est imate of
the value of the term a was taken as
a = (9 6 ft2/ lb ) (301b/3600)/l7 f t3 = 0.047 f t2/ f t 3 (9)
Assuming that a s in g le , representat ive value for all ha in
Table 1 could be taken equal to 1.5 Btu/hrft3oF # an average heat transfer
coefficient h was then est imated by
h = 1.5 x 102/ 4 . 7 = 32 Btu/hrft2oF (10)
The value est imated for h would appear somewhat small when compared
with the coefficients indicated by previous research; however, h does ,
at l e a s t , appear reasonable in view of the following: The calculation of
the terms a" and a represented only reasonable guesse s and did not even
consider the effect evaporat ion would have on heat transfer area; there
was no consideration of the rela tionship between spraying rate and area
production; s ince each heating medium leaving the evaporator was at
e ssen t ia l ly saturated condit ions, it is entirely poss ible that if higher gas
52
flow rates could have been used , much larger values of both ha and h
could have been obtained. -
CHAPTER 7
RECOMMENDATIONS FOR FURTHER RESEARCH
The work reported in this thes is is an in i t ia l , empirical study of
the heat transfer ra tes developed during the evaporat ion of sa l t water
sprays which were in contact with heat ing mediums of e ither super
heated steam or hot air; in analyzing the r e su l ts , a very simplified com
parison was made between the heat transfer ra tes obtained by using each
heating medium. Further experimentation could be done to expand the
information so far obtained and to more-rigorously examine the appropri--
ate heat and mass t ransfer p ro ce sse s .
. Specific Recommendations
First , it is recommended that the heat and mass transfer pro
c e s s e s developed when using superheated steam to evaporate water
sprays should be investigated throughout a much larger range of values
of spraying fa tes and heat ing medium flow rates than the range a s s o c i a
ted with the work being reported. In addition to comparing the use of
superheated steam with the use of hot air, it may be worthwhile to com
pare the use of superheated steam with a variety of other heat ing media.
Second, the influence of changing the mean temperature differ
ence could be studied by varying the inlet temperature of the gas through
53
54
a range of values which is sufficiently large to insure that significant
resul ts might be obtained. An investigation of this nature would require
a procedure for determining (at lea s t approximately) the temperature
dist r ibut ion of the gas inside of the evaporating column (the temperature
dist r ibut ion being necessa ry in order to accura tely est imate a mean
temperature difference) „
Finally, ana lyses of the drop s ize distr ibution in the spray,
when correlated with appropriate other d a t a , would provide a means for
obtaining separate va lues of h and a . Invest igations could be made of
the mixing and flow conditions inside of the column and of the influence
of the dimensions and design of the evaporator on the heat transfer
p r o c e s s , and s tudies could be made to determine the evaporator r e s i
dence times a ssoc ia ted with various operating cond i t ions .
Recommendations for Apparatus
In conclusion, the following comments are offered for consider
ation when designing future apparatus:
1. As mentioned in Chapter 5, fouling of the spray nozzles was a
major problem occurring in this research . In future s tud ies ,
as much effort as possible should be directed toward finding
the nozzle or nozzles whose design will make them the leas t
suscept ib le to fouling.
The amount of nozzle-fouling material in the system can be
reduced by using corrosion res is tan t materials when con
structing any apparatus in contact with sa l t water.
Depending on the specif ic s i tuat ion , it may be advantageous
to construct a spraying system which could use a single
nozzle to produce all of the desired spraying r a t e s . This
would be a definite advantage when fouling of the nozzle
could be prevented .
Finally, the heaters used in this research were fairly easy to
construct and served their intended purpose , but the heaters
were fragile and required frequent repair . Another problem was
that the a sbes tos cloth was extremely de l ica te and deterior
ated at e levated tem pera tures . Thus, use of such heaters
would be very difficult in s i tuat ions requiring frequent repos i
tioning. Therefore, it is strongly suggested that some type of
commercial steam generat ing equipment be used which can
furnish superheated steam at the desired temperatures and flow
r a t e s .
APPENDIX A
EXPERIMENTAL DATA
The experimental data obtained during research is presented
in Tables A-l through A-11.
5.6
57Table A - l . Number of Separate Sets of Data Corresponding to Each
Experiment with Superheated Steam
Number of Separate Sets Experiment Number_________________________ of Data Collected
1 • 1
2 2
3 3
4 3
5 3
6 3
7 3
8 2
9 2
10 1
11 3
12 1
58
Table A-2. Titration of Feed (Spray) and Bottoms (Brine) So lu t ions , Superheated Steam
Milli l iters of Standard AgNOo Solution Experiment Set Required to Titrate 25-mil l il i ter Sample
Number Number Feed Solution ______ Bottoms Solution
1 1 16.3 ,15.9
16 .0 , 16.1 2 2 .0 , 22 .4 , 22.0 21.7
2 1 20 .0 , 20 .05 , 19.9 24 .55 , 24 .5 , 24.42 Same 25 .25 , 2 5 .2 , 24.9
24.83 1 20.25 , 2 0 .3 , 20.25 2 7 .2 , 2 7 .0 , 27.1
2 Same 2 7 .6 , 27.53 Same 27 .55 , 27.5
4 ' 1 20.45 , 2 0 .3 , 20.45 3 1 .7 , 31.752 Same 31 .9 5 , 32.03 Same 31 .75 , 31.7
5 1 20 .9 , 20.9 3 5 .7 , 35.652 Same 3 5 .6 , 35.653 Same 3 5 .7 , 35.6
6 1 20.15 , 20.25 2 7 .3 , 27.32 Same 27 .35 , 27.43 Same 27 .25 , 27.3
7 1 20.25 , 20.15 2 2 .8 , 22.82 Same 2 3 .2 , 23.23 Same 2 3 .0 , 23.05
8 1 20.25 , 20.25 23 .45 , 24 .45 , 24.52 Same 2 4 .5 , 24 .5 , 24.15
9 ' 1 19.9519.95
, 19.95 , 19.10
22 .75 , 22.65
2 Same 22 .65 , 22.710 1 19 .0 , 19 .15 , 19.05 2 6 .3 , 26.3511 1 19.05 , 19 .0 , 19.15 2 8 .2 , 28.3c 2 Same 27 .8 5 , 27.85
3 Same 28 .05 , 28.0512 1 19 .1 , 19.1 3 4 .1 , 34.1
59
Table A -3 . Experimental Data, Superheated Steam: Values of Feed,Heating Medium, and Condensate Flow Rates
CondensateHeating Collected
Feed Medium During 8Flow Rate Flow Rate Minute
Experiment Set (Rotameter (Rotameter IntervalNumber Number. Reading) Reading) (cc)
1 1 78 47 26022 1 125 47 2608
2 125 47 .25993 1 125 47 2721
2 123 47 26883 ' 125 47 2689
4 1 75 47 26012 75 47 26723 75 47 2673
5 1 60 47 27992 60 47 2704 .3 60 47 2752
6 1 60 35 18722 60 35 18243 60 35 1825
7 1 60 22 9992 CD O 22 10643 60 22 1065
• 8, 1 6.3 24 11442 63 24 1160
9 1 65 25 12162 64 25 1201
10 1 37 42 227911 1 60 43 2376
2 60 43 23533 60 43 2377
12; 1 31 43 2328
60
Table A-4 . Experimental D a ta , Superheated Steam: Values of Bottoms,Condensa te , and Feed Flow Rates and of P
Bottoms Condensate FeedExperiment Set Flow Rate Flow Rate Flow Rate P
Number Number (cc/min) (cc/min) (cc/min) (in./Hg)
1 1 52.4 325 76.9 27.872 1 . 9 8.4 326 124.1 28.03
2 97.8 325 124.1 . 28.03 .3 1 89.4 340 124.1 28.04
2 89.5 336 124.1 28.043 89.3 336 124.1. 28.04
4 1 39.4 325 74.3 28.042 40.0 334 74.3 28.04 .3 39.4 334 74.3 28.04
5 1 23.9 350 58.5 27.672 24.0 338 58.5 27.673 25.0 . 344 58.5 27.67
6 1 38.5 234 58.5 27.482 38.5 228 58.5 27.48.3 38.0 228 58.5 27.48
7 1 47. 6 125 58.5 27.472 47.3 133 58.5 27.473 47.4 133 58,5 27.47
8 1 52.5 143 61 .5 27.512 52.5 145 61.5 27.51
9 1 55.3 152 63.5 27.51i 2 54.4 " 150 62.5 27.51
10 1 13.0 285 36.1 27.7011 1 32.7 297 58.5 27.70
2 33.2 294 58.5 27.703 32.7 297 .5 8 .5 27,70
12 1 9.9 291 30.1 27.73
Table A-5. Experimental D a ta , and Tg
Superheated Steam:
61
Values of T-p, ,
Experiment Set h T2Number Number (°C) (°C) (°C)
1 1 65 230 992 1 65 245 99
2 65 244 993 1 98 244 99
2 96 253 993 99 249 . 99
4 1 96 243 992 . 97 244 993 95 244 99
5 1 97 244 992 97 243 993 97 242 99
6 1 97 247 992 97 244 993 97 243 99
7 1 98 237 992 98 237 993 98 236 99
8 1 97 244 992 97 244 99
9 1 97 231 992 98 230 99
10 1 97 240 10411 1 97 247 99
2 97 245 993 97 248 99
. 12 1 99 245 104
62
Table A -6 . Number of Separate Sets of Data Corresponding to Each ............. Experiment with Hot Air
Experiment NumberNumber of Separate Sets
of Data Collected
i s : - 3
14 3
15 3
16 3 ;
17 3
18 3
19 3
20 2
21 3
22 3
63
Table A-7. Titration, of Feed (Spray) and Bottoms (Brine) Solut ions, Hot Air
Mil li l iters of Standard AgNOo Solution Experiment Set Required to Titrate 25-mil l il i ter Sample
Number Number Feed Solution________ Bottoms Solution
13 1 19.15, 19.1 2 7 .1 , 27.12 Same 2 6 .3 , 26.353 Same 26 .2 , 26.2
14 1 19.15 , 19.1 30 .7 5 , 30.852 Same 3 1 .3 , 31.253 Same 3 1 .4 5 , 31.5
15 1 19.25 , 19.1 26 .6 , 26.62 Same 26 .15 , 26.13 Same 26 .55 , 26.55
16 1 19.25 , 19.1 3 1 .3 , 31.3. 2 Same 31 .25 , 31.3
3 Same 3 1 .2 , 31.217 1 19.25 , 19.1 29 .75 , 29.7
2 Same 3 0 .5 , 30.63 Same 3 0 .6 , 30.6
18 1 19.25, 19.1 24 .15 , 24.052 Same 23 .95 , 24.03 Same 24 .2 , 24.2
19 1 17 .8 , 17.75 2 7 .2 , 27.12 Same 2 7 .7 , 27.653 Same 27 .55 , 27.55
20 1 17 .8 , 17.75 25 .1 , 25.152 Same 25 .4 , 25.35
21 1 17 .8 , 17.75 21 .95 , 21.952 Same 2 2 .4 , 22.453 Same 22 .45 , 22.5
22 1 17.8 , 17.75 2 2 .5 , 22.452 Same 21 .85 , 22.153 Same 21 .95 , 21.9
64
Table A-8. Dry and Wet Bulb Temperatures
Air Entering Heaters Air Leaving ColumnDry Bulb Wet Bulb Dry Bulb Wet Bulb
Experiment Set Temperature Temperature Temperature TemperatureNumber Number (°F) (°F)__________(°F) (°F)
13 1 72 48 120 1122 72 48 120 1123 72 48 120 . 112
14 1 69 48 118 1112 69 48 118 1113 69 48 118 111
15 1 69 51 120 1122 69 51 ' 120 1123 69 51 120 . 112
16 1 69 51 117 1122 . 69 51 117 1123 69 51 117 112
17 1 69 51 129 1002 69 51 127 1003 69 51 126 100
18 1 68 51 117 1042 68 - 51 118 1043 68 51 118 104
19 1 68 51 122 1002 68 51 120 1003 68 51 122 100
2,0' 1 68 51 118 1002 68 51 118 100
21 1 68 51 113 1002 68 51 113 1003 68 51 113 100
22 1 68 51 111 1002 68 51 111 1003 68 51 111 100
65
Table A -9 . Humidities
ExperimentNumber
SetNumber
Air EnteringColumnHumidity
(lb H20 / l b BD air)
Air LeavingColumn*Humidity
(lb H2C / lb BD air)
13 1 0.0031 0.0712 0.0031 .0 .0 6 83 0.0031 0.069
14 1 0.0031 0.0752 0.0031 0.0753 0.0031 0.071
15 1 0.0048 0.061 '2 0.0048 0.0733 0.0048 0.068
16 1 0.0048 0.0702 0i0048 0.0713 0.0048 0.073
17 1 0.0048 0.0742 0.0048 0.0783 0.0048 0.084
18 1 0.0048 0.0712 0.0048 0.0763 0.0048 0.079
19 1 0.0048 0.0682 0.0048 0.0683 0.0048 0.066
20 1 0.0048 0.0742 0.0048 0.077
21 1 0.0048 0.056. 2 0.0048 0.067
3 0.0048 0.06722 1 0.0048 0.065
2 0.0048 0.0653 0.0048 0.065
*Calculated from H 2 = + (F - B)/Wg
66
Table A-10. Experimental D a ta , Hot Air: Values of Bottoms, Feed, andHeating Medium^Flow Rates
HeatingFeed Medium
Bottoms Flow Rate Flow RateExperiment ' Set Flow Rate (Rotameter (Rotameter
Number Number (cc/min) Reading) (cc/min) Reading)
13 1 99.3 125 124.1 . 472 . 106.0 130 .1 2 9 .1 473 105.0 130 129.1 47
14 1 48.4 76 75.3 472 48.1 76 75.3 473 48.7 76 75.3 47
15 1 105:2 126 125.1 472 106.8 132 131.1 473 109.1 132 131.1 47; ,
16 1 55.2 80 79.3 . 472 54.2 80 79.3 473 53.2 80 79.3 47
17 1 39.5 60 58.5 472 38.5 60 58.5 473 36.6 60 58.5 47
18 1 33.6 60 58.5 472 31,7 60 58.5 473 30.7 60 58.5 47
19 1 36.0 60 58.5 472 36.0 60 58.5 473 36 i 6 60 58.5 47
20 1 39.5 60 58.5 382 38.6 . 60 58.5 38
21 1 46.8 • 59 57.5 302 44.4 59 57.5 303 43.4 59 57.5 30
. 22 1 • 43.9 .59 57.5 302 44.4 59 57.5 303 43.4 59 57.5 30
67
Table A-l 1. Experimental D a ta , Hot Air: Values of P, T p, T and
ExperimentNumber
SetNumber
P(in. Hg)
TP•(°G)
T1(°C)
T2(°c)
13 1 27.73 37 236 492 27.73 37 238 493 27.73 37 238 49
14 1 27.71 37 239 . 482 27.71 37 239 483 27.71 37 239 48
15 1 27.69 36 233 .492 27.69 36 234 493 27.69 36 234 49
16 1 27.69 36 235 47 .2 27.69 36 235 47 '3 27.69 36 235 47
17 1 27.70 38 239 ' 542 27.70 38 239 533 27.70 38 239 52
18 1 27.69 36 239 472 27.69 36 238 483 27.69 36 238 48
19 1 27.65 35 234 502 27.65 35 234 493 27.65 36 234 50
20 1 27.65 36 241 482 27.65 36 240 48
21 1 27.65 36 223 452 27.65 36 224 453 27.65 36 225 59
22 1 27.65 36 224 442 27.65 36 224 443 27.65 36 227 44
APPENDIX B
STEAM CALCULATIONS
Referring to Figure B - l , the over-a l l material balance for the
evaporat ive process is
Wg + F = C + B (11)
where B = flow rate of bottoms (brine) leaving the bottom of the evaporator, lb /h r
C = condensate flow rate leaving the barometric leg, lb /hr
F = feed (spray) flow r a t e , lb /hr
Wg = superheated steam flow ra te , lb /hr
The energy balance is
+ FiF = C i 2 + BiB + L (12)
where ig = enthalpy of brine leaving the evaporator, Btu/lb
ip = enthalpy of the feed, Btu/lb
i^ = enthalpy of the hot gas entering the evaporator, Btu/lb
ig = enthalpy of gas leaving the evaporator, Btu/lb
L = heat lo sses to the surroundings, Btu/hr
As brine init ial ly left the evaporator and entered the drain, the
temperature Tg of the brine was e ssen t ia l ly the temperature Tg at which
evaporat ion occurred . Since the height of water held in the trap was only
about fifteen inches and represented the maximum difference between
68
69
W g , lb /hr ofsuperheated steam
T i , °FBtu/lb
< 6lb /h r of saturated or nearly saturated steam °FBtu/lb
F, lb /hr feed (spraying solution) X, weight % NaCl TF . ° f
iP , Btu/lb
V
L# heat loss to the surroundings, Btu/hr
B, lb /hr of bottoms (brine) Y, weight % NaCl
B#lB#
°FBtu/lb
Figure B-l. Material and Energy Balance Diagram, SuperheatedSteam
70
atmospheric pressure and the gauge pressure inside of the column, the
gauge pressure was considered to be negligibly different from atmos
pheric . Assuming that dissolved solids had no effect on the tempera
ture of evaporation (Charlesworth and Marshall I960), the value and
of Tg were then both taken equal to the saturat ion temperature for pure
water at atmospheric p re s su re .
Furthermore,
*2 = + A + c p (13)
where c = heat capaci ty at constant pressure of water vapor,Pv Btu/lb°F
a = the latent heat of vaporizat ion of water at atmospheric p re s su re , Btu/lb
*6 = ^ + c pv ( W (14)
where Cp = heat capacity at constant pressure of the spraying F solution, Btu/lb°F
Tp = temperature of the feed entering the evaporator , °F
Substituting Equations 11 , 13 , and 14 into Equation 12
yields
Ws (i1- i 2) = (F-B) * + CPv (T2 TS> + Fcpf (t s ' t f ) + l (15)
In the equat ion,
h*a * = 0*/KATmg (16)
where a* = corrected heat transfer area per unit volume, f t^/f t^
71
h* = corrected heat transfer coeff ic ien t# Btu/hrft^°F
Q* = total energy avai lable for transfer from superheated steam to spray, Btu/hr
Ve = evaporator volume, ft^
ATmg = arithmetic mean temperature difference (steam), °F
the term Q* is given by
Q * = W s (i1- i 2) (17)
In the equation,
ha = Q/VgATmg (18)
where a = heat transfer area per unit volume, ft^/ft^
h = heat transfer coeff icient , Btu/hrft^0F
Q = heat transfer ra te , Btu/hr
the term Q is given by
Q = (F-B) K+ c pv (T2 TS> + F C p p C V V (19)
In Equations 16 and 18 , the terms V and ATmc are given, respec t ive -6 O
ly, by
Vg = 3,1416(1. 88ft)2 x 6.15 ft = 17.04 ft3 (20)4
and
A lm s = (T-^-Tg) + (Tg-Tg) (21)
The flow rate could be expressed as
W g = Up(3.1416)d2/ 4 (22)
where d = diameter of the cylindrical portion of the evaporat ing column, ft
U = average velocity of the hot gas flowing through the column, f t /hr
p = density of hot gas at atmospheric pressure and temperature T v l b / f t 3
Substitution of Equation 22 into the express ion for the Reynolds
number corresponding to gas conditions at the entrance to the column
Re = dllp/p
where w = v iscos i ty of the hot gas at atmospheric pressure and temperature , Ib/fthr
yielded a convenient express ion for using experimental data to ca lcula te
Reynolds numbers
Re = 4Wg/jrdM (23)
The following paragraphs d iscuss the evaluation of the
various terms in Equations 17 , 19 , 21 , and 23 . The computa
tions a ssoc ia ted with the calculat ion of values of ha, h * a* , and Re are
given in tabular form at the end of this appendix.
The thermometers used for determining values of Tp, T^ , and Tg
only permitted measurement to the neares t 1°C. Hence, those values
were only converted and rounded off to the nearest 1°F .
Atmospheric pressure was determined fairly accurately; the
pressure inside of the column was not. However, it was known that the
lat ter pressure could not exceed the former by more than the equivalent
of fifteen inches of water, and it was assumed that this small of a
73
difference between pressures could be considered negligible . The
poss ibi l i ty that this assumption would introduce very small errors
limited the determination of both Tg and aTm to the neares t 1°F. The
minimum value recorded for atmospheric pressure was 27.47 in. Hg, and
the maximum 28.04 . For the former v a lu e , Tg = 208°F and for the lat ter
Tg = 209°F; the corresponding values of a are 972. 8 and 972. 2 B tu / lb#
respect ively (Himmelblau 1962, p. 402).
By assuming that throughout the temperature range involved in
the experiments , the effect of the small concentration of NaCl in
solution had negligible effect on heat c a p a c i ty , c was taken as con-PF
slant and equal to 1.00 Btu/lb (Perry 1063, p. 3-123). Since the
properties of liquids are little affected by p re s su re , in determining the
value of c , minor deviations of atmospheric pressure away from PF
standard were ignored.
For values of temperature T^ , the corresponding values of i^
were interpolated from the steam tables (Perry 1963, p. 3-193) and
are given in Table B - l . For values of temperature T ^ / the corresponding
values of ^2 were calcula ted from
i2 = is + 0 .46 _Btu_(T2-Tg) (24)lb°F
where ig = enthalpy of saturated steam at Tg, Btu/lb
At Ts = 208°F, ig = 1148.8 Btu/lb, and at Tg = 209°F, ig = 1149 .2°F.
74
Table B-l„ Values of T^ and i Superheated Steam
Steam Enthalpy (Btu/lb) for Pressures of:Temperature
00CO 1—
1 1LOCOi—1 14.7 10
(°F) (psia) (psia) (psia)
500 1285.5 1285.4 1285.8490 1280.8489 1280.3482 1277.1480 1276.2477 1274.8474 1273.4473 1272.9472 1272.4471 1272.0470 1271.5469 1271.0467 1270.1464 1268.8460 1266.9457 1265.4455 1264.5450 1262.2 1262.1 1262.5447 1260.8446 1260.3440 1257.5430 1252.9420 1248.2410 1243.6400 1238.9 1238.9 1238.9
75
In order to measure the flow rate B, effluent brine was co l
lected , in a large graduated cylinder, during a ten minute in te rval .
When the temperature of the brine cooled to 70°F, the volume was
determined, and the volumetric flow rate B' was recorded to the neares t
0 .1 cc .
For a given brine sample,
let E = the volume of a given sample of the solution, cc
w^ = the weight of H^O in the same sample of the solution, gm
W2 = the weight of NaCl in the same sample of the solution, gm
X = concentration of NaCl in spray solution, percent by weight
Y = concentration of NaCl in bottoms (brine) solut ion, percent by weight
Z = Y/X
pg = densi ty of bottoms (brine) solution, gm/cc
p = density of pure water , gm/ccP
Then, assuming that the concentration of NaCl in a sample of solution
is so small that any difference between the volume of the original so l
vent and the volume of resul ting solution can be ignored,
p B = (w ]. + W2 ^ E
where
W -L = PpE
w = Y(w + w )
76
Furthermore, in all experiments (as confirmed by periodic analysis of
the spraying so lu t ion) , X = 1.6%, and Y = 0 . 016Z(100%).
Then,
Wg = Y(w^ + Wg) = 0 . 016Z(w^ + Wg)
and
Wg = 0 . 0 1 6 Z w j
1-0.016Z
S ince ,
p E + p E0.016Z P _P________
1-0.016Z
(25)
then
P B Pp 1 + 0.016Z1-0.016Z
(26)
At 70°?, Pp = 0 .978 gm/cc (Perry 1963, p. 3-70), and values of B were
given by
B = 0.0978 gm cc
'l + 0.016Z B' lb 60min1 - 0 . 016Z J _ 454gm hr
or
B = 0.129 lb min cc hr
1 + 0.016Z B' 1-0.016Z
(27)
During all of the experiments, the maximum value of Z was 1 .74 , and the
minimum value 1 .13 . By substi tuting the maximum, minimum, and in ter
mediate values of Z into Equation 27 , values of B were obtained as
fo l lows:
When Z is equal to or less than 1 .19 ,
B = 0.131 lb min B* (28)cc hr
when Z is equal to or greater than 1.20 and less than 1 .60 ,
B = 0.132 lb min B' (29)cc hr
and when Z is equal to or greater than 1 .60 ,
B = 0.133 lb min B' (30)cc hr
The rotameter measuring the spraying rate F was cal ibrated
with a sa l t solution of the same composition as that used in all of the
experiments. Calibrat ion data are shown in Table B-2 and Figure B-2
and are d i scussed further in Appendix F. During calibrat ion and all
subsequent experiments, the temperature of the feed entering the
rotameter never varied from 20°C by more than 2°C, and corresponding
to each given meter reading, any variation (in spraying rate) a ssoc ia ted
with densi ty changes due to variations in composition or temperature
were considered negligible .
Proceeding as be fore ,
F = PpF' (31)
where F' = the flow rate read from the rotameter, cc /m in .
Pp = the density of the feed (spraying solution), gm/cc
The term is given by
78
Table B-2 . Feed Rotameter Calibration Data
Flow Measured OverRotameter Average Flow Rate One Minute Interval
Reading (cc/min) (cc)
40.0 39.1 40.038.538.540.538.0
60.0 58.5 60.059.558.557.557.0
79.0 77.9 78.077.079.078.577.0
100.0 99.3 100.599.597.5
100.5 9815:
129.0 128.1 129.5129.5127.5 127.0127.5
Stea
m Flo
w R
ate
79
130
120
110
100
90
_ 80
| 70u
^ 60
50
40
30
20
10
00 10 20 30 40 50 60 70 80 90 100 110 120 130
Rotameter Reading
Figure B-2. Feed Rotameter Calibrat ion Chart
80u
and
w2 = 0 .1 6 w 1 (3 2 )
Then,
0.984
Pp = PpE + p^E (0 .016/0 .984) (33)
or
p_ = P (1 + 0 .016 /0 .984) (34)F P
At 20°C, p = 0 .998 gm/cc (Perry 1963, p. 3-70), By substi tuting
Equation 34 into Equation 31, F was then given by
F = 1.014 gm F' lb 60 min454 gm hr
or
F = 0.132 lb min F' (35)cc hr
For the evaporator, the material balance on NaCl is
FX = BY
or
F = BZ
The values of BZ tabulated at the end of this appendix were found to be
in fairly good agreement with values of F calculated using Equation 35.
Values of BZ were generally smaller than the corresponding values of F ,
and were great ly smaller when BZ was derived from data obtained at low
spraying r a t e s . It is thought that this discrepancy was due to sa l t
81
caking on the walls and bottom of the column, which then caused a low
NaCl concentration in the brine leaving the evaporator.
Calibrat ion data for the rotameter measuring the flow rate Wg
are shown in Table B-3 and Figure B-3 and are d iscu ssed further in
Appendix G. The steam used during calibration was at a temperature of
460°F. The condensate leaving the barometric leg was c o l le c te d , over
an eight minute in te rva l , in large graduated cylinders . The temperature
of the condensate was always within three degrees of 70°F. S ince ,
during cal ibrat ion, there was no spraying, values of Wg were given by
the corresponding values determined for C.
The densi ty of water at 70°F is e ssen t ia l ly 1.00 gm/cc
(Perry 1963, p. 3-70). Therefore, the flow rate C is given by
C = C 1. OOqm lb 60 min (3 6)cc 454gm hr
or
C = 0.132 lb min C cc hr
where C = condensate flow rate from the barometric leg, cc/min
Since values of T^ varied considerably from 4 60°F, it was
necessary to derive, for the rotameter cal ibration d a t a , a series of
correction factors by which the hot gas flow rate corresponding to a
given rotameter reading and gas temperature of 460°F could be miltiplied
to give the hot gas flow rate corresponding to the same meter reading
Table B-3 „ Heating Medium Rotameter Calibrat ion Data
Flow Collected Average Steam FlowDuring 8-minute Rate During the
Rotameter Interval 8-minute; IntervalReading (cc) (cc/min) (lb/hr)
47.0 2321 290 38.22362 295 38.92375 297 . 39.22382 298 39.4 .2383 298 39.42386 298 39.42400 300 39 . 62408 301 39 o 7 .2417 302 39.9 .2421 303 40.02440 305 40.32495 312 41.32497 312 41.32513 314 41.52535 317 41 .82542 318 41.92665 333 43.9
(Mean) 305 (Mean) 40.3
43.0 2065 258 34.12137 267 35.22228 276 36.5 .2234 277 36.6
(Mean) 270 (Mean) 35.6
35.0 1605 201 26.51649 206 27.21665 208 27.51753 219 28.91768 . 221 29.2
(Mean) 211 (Mean) 27.9
25.0 1072 134 17.71089 136 18.01174 147 19.41201 . 150 19.8
(Mean) 142 (Mean) 18.7
83
Table B -3 , Continued
Flow Collected Average Steam FlowDuring 8-minute Rate During the
Rotameter Interval 8-Minute IntervalReading (cc) (cc/min) (lb/hr)
22.0 859 107 14.1881 110 14.6953 119 . 15.7 .
1022 128 16.9(Mean) 116 (Mean) 15.3
84
40
30
co
0 10 20 30 40
Rotameter Reading
Figure B-3 . Heating Medium Rotameter Calibration Chart
85
and any gas temperature other than 460° F. Referring to Perry
(1963, p. 5-13),
Wa/ Wb = MaV ( p r Pa) /P a / MbV ( p f-Pb)Pb (37)
where = constant for a given float (gas temperature T^) , ft5"/hr
= constant for a given float (gas temperature of 460°F), ftT/ h r
WQ = flow rate of the hot gas corresponding to a given rotameter reading and a hot gas temperature T other than 460°F, lb /hr
= flow rate of the hot gas corresponding to the same given rotameter reading and a hot gas temperature of 460°F, lb /hr
p = density of the hot gas at temperature T, , lb /f t^
p = density of the hot gas at 460°F, lb/f t^b
= densi ty of float material, lb/f t^
Since the same rotameter was always used , and since densi ty variations
assoc ia ted with changes in were not too g rea t , it was assumed that
M_ = M, . Furthermore, since p , is much greater than e ither p or p , ita D i a b
was a lso assumed that ( p - p ) / ( p - p ) is e ssen t ia l ly 1 .00 .t a t b
Then,
W /W = ( p / p )? = (v / v )2 (38)a D a t ) d a
where vg = specif ic volume of steam at temperature T^, f t^ / lb
v = specif ic volume of steam at 460°F, f t^ / lb b
For a given rotameter read ing , values of can be found from
the calibration chart of Figure B-3. Then, depending on the temperature
86
T^, the flow rate of hot gas entering the evaporator can be found from
Wa = w b (vb/ v a ^ (39)
Using an average atmospheric pressure of 13.6 psia and
assuming minor deviations from that average could be ignorpd, the
specif ic volumes of steam at 400 and 500°F were taken equal to 38.15
and 42.15 f t 'Vlb, respect ive ly (Perry 1963, p. 3-193). At temperatures
between 400 and 500oF , specific volumes of steam were determined
by l inear interpolation between 38.15 and 42.15 f t^ / lb . Then, for the
appropriate values of T^, the corresponding values (given in Table B-4)
of (v^/vg)! were ca lcu la ted .
From Equation 11 ,
Wg = C + B - F (40)
As shown in Table B-5 , values of W determined from the rotameter
were found to be in fairly good agreement with values of W found from
Equation '‘40 .
Referring to Equation 23 ,
Re = 4W /jtdM
To conveniently work with the experimental d a t a , it was advantageous
to calcula te values of Re/Wg , which were given by
Re/W = 4/jrdM (41)
and which were then multiplied by experimentally determined values of
Wg in order to compute the corresponding Reynolds numbers .
87
Table B-4 . Correction Factors for Wg
Temperature(°F)...........
v, Steam (ft3/lb)
(va/ v b)1/2
400 38.15 »
430 39.50 1.017
440 39.95 1.011
450 40.40 1.006
460 40.85 1.000
470 41.30 0.995 '
480 41.75 0.989 .
490 42.20 0.984
500 42.65
88
Table B-5. Superheated Steam: Values of (F-B), (C+B-F), BZ, andV ATmq e o
ExperimentNumber
SetNumber
(F-B)(lb/hr)
(C+B-F)(lb/hr)
BZ(lb/hr)
V TmS(£t3oFV
1 1 3.38 39.5 ' 9 .55 20282 1 3.64 39.4 15.98 2249
2 3.72 39.2 15.75 ■ 22323 1 4.83 40.1 15.70 2249
- 2 4.82 39 . 6 15.94 23863 4.84 39.6 15.92 .2334
4 1 4.76 38.1 8 .06 22152 4.68 39.4 8.30 2232.3 4.76 39.3 8.06 . 2249
5 1 4.69 41.5 5.39 22492 4.67 40.0 5.39 . 22323 4.54 40.9 7.00 2232
6 1 2.76 28.2 6 .86 ■ 23172 2.76 . 27.3 6.91 22663 2.82 27.3 6 .78 2232
7 1 1.56 15.0 7.10 21472 1.60 16.0 7 .18 21473 1.58 16.1 7 .14 2130
8 1 1.31 17.6 8.39 22662 1.31 17.8 8.39 2266
9 1 1.27 18.8 8.25 2067' 2 1.25 18.5 8.13 2145
10 1 3.12 34.7 2.37 226611 1 3.52 35.6 6.39 2300
2 3.46 35.4 6.39 22663 3.52 35.6 6.35 2334
12 1 2.71 35.6 2.30 2351
/
89
Table B-6. Superheated Steam: Values of B, C, F, and Wg
Experiment Set B C F WgNumber Number (lb/hr) (lb/hr) (lb/hr) (lb/hr)
1 1 . 6.92 42.9 10.30 40.72 1 12.99 43.0 16.63 40.0
: 2 . 12.91 42.9 16.63 40.13 i 11.80 44.9 16.63 40.0
2 11.81 44.-4 16.63 39.73 11.79 44.4 16.63 39.8
4 1 5.20 42.9 9 .96 40.1 .2 5. 28 44.1 9 .96 . 40 .13 . 5.20 44.1 9 .96 40.1
5 1 3.15 46.1 7.84 40 .1 .2 3.17 44.6 7.84 • 40 .13 .3 .30 45.4 7.84 40.2
6 1 5.08 30.9 7.84 . 27.62 5.08 30.0 7 .84 27.73 5.02 30.0 7.84 27.8
7 1 6.28 16.5 7.84 15.4 •2 6.24 17.6 7.84 15.43 6.26 17.6 7.84 15.3
8 1 6.93 18.9 8.24 17.62 6.93 19.1 8.24 17.6
9 1 . 7.24 20.1 8.51 18.82 7.13 19.8 8.38 18.8
10 1 1.72 37.8 4.84 34.711 1 .4 .32 39.1 7.84 35.3
' 2 4 .38 38.8 7.84 35.43 4.32 39.1 7.84 35.2
12 . 1 1.32 38.3 4.03 35.4
90
Table B-7. Superheated Steam: Values of Tp, T^, Tg, and Z
ExperimentNumber
SetNumber
tt(°F)
1—> Pm
T2
(°F) Z
1 1 150 446 210 1.382 1 150 474 210 1.23
2 150 471 210 1.223 1 208 474 210 1.33
2 205 489 210 1.353 210 482 210 1.35 .
4 1 205 469 210 : . 1.552 207 471 210 1.573 203 471 210 1.57
. 5 1 207 471 210 1.712 207 469 210 1.70 .3 207 467 210 1.70
6 1 207 477 210 1.352 207 471 210 1.363 207 467 210
LOCO1—1
7 1 208 457 210 1.132 208 457 210 1.153 208 455 210 . 1.14
8 1 207 471 210 1.212 207 471 210 1.21
9 1 207 447 210 1.142 208 446 210 1.14
10 ' 1 207 464 220 1.3811 1 207 477 210 1.48
2 207 474 - 210 1.463 207 480 210 1.47
12 1 210 474 220 1.74
91
Table B -8 . Superheated Steam: Values of Tg , k , ' A-1-mg
Experiment SetNumber Number
1 12 1
23 1
2 3
4 1 2 3
5 1 2 3
6 1 2 3
7 1 . 2
38 1
29 1
210 . 111 1
2 3
12 1
Tqm
"k- (Btu/lb)
( i i _ i2) (Btu/lb),
ATmq: <°f >
209 972.2 111.1 119209 972.2 124.2 132209 972.2 122.8 131209 972.2 123.2 132209 972.2 130.6 140209 972.2 127.4 137209 972.2 121.3 130209 972.2 122.3 131209 972.2 122.3 132209 972.2 122.3 132209 972.2 : 121.3 131208 972.8 120.4 131208 972.8 125.1 136208 972.8 122.3 133208 972.8 120.4 131208 972.8 115.7 126208 972.8 115.7 126208 972.8 114.8 125 .208 . 972.8 122.7 133208 972.8 122.7 133208 972.8 111.1 121208 972.8 110.6 120209 ; 972.2 : 114.9 133209 972.2 125.1 135209 972.2 123.2 . 133209 972.2 126.5 137209 972.2 118.5 138
92
Table B-9 . Superheated Steam: Values of-(F-B)c (Tg-Tg), (F-B)a ,% F(TS - TF>' a n d W S(ll - 12> '
ExperimentNumber/
SetNumber
(F-B)Cp^ T 2- Ts )
(Btu/hr)
( F - %
(Btu/hr)
FV Ts - v
(Btu/hr)WsVi2>(Btu/hr)
1/1 0 3287 603 45222/1 0 3539 981 4968/ 2 0 3617 981 4924
3/1 0 4696 17 4928/ 2 0 4686 66 5185/ 3 0 4905 0 5071
4/1 0 4628 40 4864 ./ 2 0 4550 20 4904 •/ 3 0 4629 55 4904
5/1 0 4561 20 .4904/2 0 4542 .VI2 4864/ 3 4417 8 4828
6/1 2685 8 3453/ 2 1 2685 8 3388/ 3 1 2744 8 3347 .
7/1 1 1518 0 1782/ 2 1 1557 0 1782/ 3 1537 0 1756
8/1 1274 8 2150/ 2 1 1274 8 2150
9/1 1 1236 9 2089/ 2 0 1216 0 2079
10/1 0 3035 7 39 8711/1 0 3424 12 4416
/ 2 0 3365 12 4361« / 3 0 3424 12 4453
12/1 ; ■ 5 2636 0 4195
9.3
Table B-10. Superheated Steam: Values of Re, ha, and h*a*
Experiment Set Re ha h*a*Number Number (Btu/hrft^°F) (Btu/hrft3°F)
1 1 675 1.92 2.232 1 634 2.00 2.20
2 638 2.06 2.213 1 634 2.10 2.19
2 618 1.99 2.173 625 2.11 2 .18
4 1 640 2.11 2.202 638 2.05 2.203 638 • 2 .08 2 .18
5 1 638 2.04 2.182 640 2.04 2.183 642 1.99 2.17
6 1 436 1.17 1.502 441 1.19 1.503 445 1.24 1.50
7 1 252 0.71 0.832 252 0.73 0.833 251 0.60 0.83
8 1 280 0.57 0.95 •2 280 0.57 0.95 '
9 1 312 ’ 0.61 1.022 312 0.59 1.02
10 1 557 1.34 1.7611 1 558 1.49 1.92
2 561 1.49 1.933 554 1.48 1.92
12 . 1 561 1.12 1.79
- 94
At low p r e s s u r e s , v iscosi ty is essen t ia l ly independent of
pressure (Bird, S tewart , and Lightfoot 1960, p. 21). Therefore, the
e f f e c t , on v i s c o s i ty , of atmospheric pressures being slightly different
from standard was ignored.
However, v iscos i ty did change signif icantly over the range of
values of T^. The v isco s i t ie s of steam at 490 and 430°F are 0.0180
and 0.0168 cp, respec t ive ly (Perry 1963, p. 3-197). Therefore, at
490°F,
Re/Wg = ________4____________ 1__________cp = 15.55 hr / lb3.1416 (1.88 ft) 0 .0 1 80cp 2.42 Ib/f thr
and at 430°F
Re/W = 16.70 hr / lb
For temperatures T between 490 and 430°F, values of Re/W (given1 b
in Table B - l l ) were determined by l inear interpolation between 15.55 and
16.70 h r / lb .
i
Table B - l l . Values of Re/Wg Versus
19§
T1 Re/Wg(°F) (hr/lb)
490 15.55489 15.57482 15.71480 15.74477. 15.80474 15.85473 15.87 .472 15.89471 15.91470 15.94469 15.96467 16.00464 16.05460 16.12457 16.17455 16.21450 16.30447 16.37446 16.39440 16.50430 16.70
APPENDIX C
AIR CALCULATIONS
Referring to Figure C - l , the over-a l l material balance for the
evaporative process is
WD + Wd H1 + F = WD + Wd H2 + B (42)
where = humidity of the air entering the evaporator, lb HgO/lb BD air
H.2 = humidity of the air leaving the evaporator , lb H^O/lb BD air
Wq = flow rate of bone dry air flowing through the evaporator, lb BD a ir /h r
The energy balance is
Wd V WDHl i H1 + FiF - WDiD2 + + BiB + L (43)
where i = enthalpy of bone dry air in the humid air entering the ■ ^ 1 evaporator, Btu/lb BD air
ij-) = enthalpy of bone dry air in the humid air leaving the 2 evaporator, Btu/lb BD air
ijr = enthalpy of water in the humid air entering the evaporator,1 Btu/lb H O
i = enthalpy of water in the humid air leaving the evaporator,H2 Btu/lb H20
In developing Equation 43 , it was assumed that any heat of mixing
a ssoc ia ted with the humid air was negligible and that the enthalpy of the
humid air was given by
96
w D , lb /h r BD air - humiditylb HoO/lb BD air
°FBtu/lb BD air
WDHi lb HzO/hrBtu/lb H20
Wq # lb /h r BD air - humidityH9 lb H O / lb BD air
t 2 , 0f 2 2ig / Btu/lb BD air Wd H2 , lb HgO/hrig, Btu/lb HgO
F , lb /hr feed (spraying solution)
X, weight % NaCl TF , °F i p , Btu/lb
L, heat loss to thesurroundings, Btu/hr
B, lb /hr bottoms (brine) Y, weight % NaCll BB'
°FBtu/lb
v
Figure C - l . Material and Energy Balance Diagram, Hot Air
where H = humidity of the air, lb H^O/lb BD air
i = enthalpy of the humid air, Btu/lb
ip = enthalpy of bone dry air in the humid air, Btu/lb BD air
i = enthalpy of water vapor in the humid air, Btu/lb H^O
Solving Equation 42 for B and then substi tut ing the result into
Equation 43 yields
WD ^ D 1~1D2 + FiF = WD^H21H2” H11H1 + WD^H1"H2^1B + FiB + L
Furthermore,r 1 l
99
where cPD Btu/lb°F
= heat capaci ty at constant pressure of bone dry air.
cPP
= heat capaci ty at constant pressure of water, Btu/lb°F
cP.= heat capaci ty at constant pressure of water vapor, Btu/lb°F
va ' = latent heat of vaporization of water at T , Btu/lb
2For an ideal g a s , heat capaci ty at constant pressure is inde
pendent of pressure (Smith and Van Ness 1959 , p. 120). Since air at
atmospheric pressure is e ssen t ia l ly an ideal g as , it was assumed the
c was not influenced by minor changes in atmospheric p res su re .PD
Furthermore, because the quantity of water vapor in the humid air and
the deviations of atmospheric pressure from standard were both small , it
was assumed that c was constant and equal to 0 .46 Btu/lb°F. It waspv
found that this assumption caused negligible errors in computat ions ,
were both taken as constant and equal to 1.00 Btu/lb°F. Whereby,
was assumed that c was also not influenced by minor variations in* " \ 7V
atmospheric p re s su re .
For each range of values a ssoc ia ted with T
since values of W ^H were very small . Hence, the term (i
was given by
(52)
By arguments similar to those given in Appendix B, c and cpf 1PP
In units of Btu/lb mole°F, c is given by Himmelblau (19 62,PD
p. 147) as
c n = 6.900 + 2 .8 8 4 x 1 0 ” + 2 .4 2 9 x 1 0 “ 7T2 + 8 .0 5 2 x 10“ 11T3 (55)D
where T = temperature of the air, ° F . Taking the molecular weight of air
equal to 29 .00 lb / lb mole and integrating both s ides of Equation 55 with
respect to T (between upper and lower limits of and T , respectively)
gave (i^ - i 0 ) in units of Btu/lb as U1 2
r Tic dT = 0 .252(T j-T 2) + 4.97 x 10 6 ( t2 - t2 ) + (56)
T2
2.93 x 10_9(Tj-T3) + 6 .93 x 10" 14(Tj*-T^)
Substituting Equations 51 , 52 , 53 , and 54 into
Equation 45 and noting that
101
then gave
+ W D Hl c pv (Tr T2) = F c pF(TA2- TF) + (5 7)
(F-B) A' + CPv *T2"TA2^ + L
In Equation 57 , (i^ -i^. ) is determined using Equation 56 . The1 2
calculat ions a ssoc ia ted therewith are tabulated at the end of this
Appendix.
In the equation.
h*a* = Q*/VeATmD (5 8)
the term Q* was then given by
Q* = WD *1D 1 lD + H 1CPV*T1 T2* (59)
and in the equation
ha = Q/V^ ATmD (60)
the term Q was given by
Q = (F-B) V + CPv (T2 FA 2) + Fcp f <t a 2 - t f ) (61)
In Equations 58 and 59 , ATm^ was given by
XmD = (Tr TAi) + (T2-TA2) (62)
Values of Reynolds number were given by
Re = 4W^/jrdM (63)
102
Because of the extremely small values of , the humidity of the air
entering the evaporator was considered to be of negligible concern when
the express ion for Re was developed.
The following paragraphs consider evaluation of the various
terms in Equations 57 , 59 , 61 , 62 , and 63 . Appropriate c a l
culations are tabulated at the end of this Appendix.
Evaluation of the terms c , c , c , and (in - i n ) havePP v F ^1 2
already been mentioned, and evaluation of the terms B, F , Tp, , and
Tg was e ssen t ia l ly the same as in Appendix B. Values of a ' were found
by interpolation from the steam tables (Himmelblau 1962, p. 402), with
the assumption that minor deviations of atmospheric pressure from
standard could be ignored.
The value of was determined by measuring the wet and dry
bulb temperatures of the air prior to entering the heaters and then
referring to the humidity chart (Zimmerman 1964, p. 144). Based on wet
and dry bulb temperature measurements , the va lue of , as found from
the humidity c h a r t s , only indicated the evaporation of approximately
one-half of the amount of spray that actually had evapora ted . It was
thought that this discrepancy occurred because the velocity of the air
pass ing the bulb was only about one-ha lf of the fifteen feet per second
normally required. It w a s , therefore , decided to ca lcula te values of
from
103
H2 = H1 + (F-B)AVd (64)
For a given rotameter read ing , values of corresponding to
equal to 460°F were obtained by conversion of the calibration data
for steam at the same temperature. Using arguments similar to those in
Appendix B.
WD “ MdV (Pf" PD) Pr / \ / ( Pf"PS)PS (65)
WS MS
and
WD/W S = (PD/p S^
where = constant for a given float (air at 460°F), f t? /h r
Mg = constant for the same float (steam at 460°F)/ f t? /hr
= flow rate of air at 460°F, lb /h r
Wg = flow rate of steam at 460°F, lb /hr
= densi ty of air at 460°F/ lb/f t^
p = densi ty of steam at 460°F/ lb/f t^
At 13.6 psia and 460°F,
pg = 1/v = (1/40. 85) l b / f t3
where v g = specif ic volume of steam, ft3/ l b
At 14.7 psia and 32°F (Perry 1963, p. 3-71),
PD = 0.0808 l b / f t 3
104
Assuming that the ideal gas law was sufficiently a c c u ra te , at
13.6 psia and 4 60°F was then given by
PD = 0.0808(492/920) (13. 6 /14 .7) = 0.0400 l b / f t 3
H ence ,
WD//WS = (O-0400/ 0 - 0245)* = 1. 28 (66)
During experiments with hot a ir , values of again varied
significantly from 460°F, and it was necessa ry to develop, for given
meter readings and flow rates corresponding to 460°F, correction factors
which could be used to obtain the appropriate flow rates at temperature
T^. Again assuming that the ideal gas law was sufficiently a cc u ra te ,
p /p , was given by a b
pa = na/// a = P/RTa
pg nb/Vb P/R 9 20°R
where na = moles of hot gas at temperature
nb = moles of hot gas at 460°F
R = gas constant
Ta = temperature other than 920°R3
V = volume of hot gas at temperature T. , ft
Vb = volume of hot gas at 920°R, ft^
or
Pa/ p b = 920°R/Ta (67)
105
and
W / W u = (920OR/T ) t (68)a d a
where = flow rate of the hot gas corresponding to a given rotameter reading and a hot gas temperature other than 460°F, lb /hr
= flow rate of the hot gas corresponding to a given rotameter reading and a hot gas temperature of 460°F, lb /hr
Values of (920°R/Ta) are given in Table C - l . Values of correspond
ing to a given rotameter reading and temperature of 460°F were multi
plied by the appropriate value of (920°R/T )7 in order to obtain the hota
gas flow rate corresponding to the same meter reading and tempera
ture T-l . Because was always extremely small , the value calcula ted
for was considered to represent the flow rate of bone dry air.
Because of diff iculties a ssoc ia ted with interpolating between
lines on the humidity c h a r t , values of adiabatic saturat ion temperature
Ta corresponding to given conditions of H. and T were calculated fromi f
H i - H s = - 0 . 2 4 + 0 . 4 6 Hi (5 9 )
T i - tAi ^
where Hg = humidity at sa turat ion, lb H^O/lb BD air
a " = latent heat of vaporizat ion of water at TA , Btu/lb
Since was never greater than 0 .005 , 0 .46 was negligible com
pared to 0 .2 4 , and since a" was found to be either 1026 or 1027 Btu/lb,
Equation 69 was written as
Ta = T1 - 4 .16(Hg - H 1)103 (70)
•10.6
Table C - l . Correction Factors for Wq
Temperature(°F)
920°R/Ta (pa/ pb H
476 ■ 920/930 0.995
460
ooI—1 1.000
450 920/910 liOOS
440 920/900 1.011
430 920/890 1.016 ,
Values of T were obtained by a trial and error solution of Equation 70 A1
A value of T, was found, as accurately as p o s s ib l e , from the humidity 1 .
c h a r t , and the corresponding values of Hg and a " were found from the
humidity chart and steam t a b l e s , respect ively; the va lues of Hg and
were then inserted into Equation 70 , and a new value for T, was
calculated; using the new value of T. to determine H and a " , a newer1
value of T was similarly c a lc u la t e d , and so forth; newer values of 1
T. were success iv e ly calculated until there was found the value of A1
T w hich , when the corresponding value of H was inserted into A S
Equation 70 , was in the c loset agreement with the value of next1
c a lc u la te d . Sample calculat ions are tabulated at the end of this
Appendix.
Values of were all between 0.056 and 0.084 lb H^O/lb BD
air; values of a ' varied between 1027 and 1030 B tu / lb# and Equation 69
was wri t ten , with no loss of acc u ra c y , in terms of and Hg as
TA = T2- 3 ' 7(HS ' H2) (71)
Values of T. were found in the same manner as values of T. , and 2 1
sample calculat ions are tabulated at the end of this Appendix.
The v iscos i ty of air at 1 atm and 470°F is 0 .0263 cp, and at
430°F, 0 .0266 cp. Values of Re/W ^ were calculated in a similar man
ner as for s te a m , and are given in Table C - 2 , as a function of T^.
io a
Table C-2 . Values of Re/W^Versus T , Air
T1(°F)
Re/WD(hr/lb)
470-456 10.67
455-446 10.62
445-436 10.58
436-430 10.51
109
Table 0 3 . Hot Air: Values of B, F , WD , and Z
ExperimentNumber
SetNumber
B(lb/hr)
F(lb/hr) Z
13 1 13.11 16.63 51.6 1.412 13.99 17.30 51.5 1.373 13.86 17.30 51.5 1.36
14 1 6.44 10.09 51.5 1.602 6.40 10.09 51.5 1.633 6.48 10.09 51.5 1.64
15 1 13.89 16.76 51 .7 1.392 14.10 17.57 51 .7 ' 1.363 14.40 17.57 51.7 1.39
16 1 7.34 10.63 51 .6 1.632 7.21 10.63 51 .6 1.633 7.08 10.63 51 .6 1.63
17 1 5.21 7.84 38.2 1.262 5.08 7.84 38.2 1.253 4.83 7.84 38.2 1.26
18 1 4.44 7.84 51.5 1.552 4.18 7.84 51.5 1.593 4.05 7.84 51.5 1.59
19 1 4.75 7.84 51.6 1.532 4.75 7.84 51.6 1.563 4.83 7.84 51.6 1.55
20 1 5.21 7.84 39 .8 1.412 5.10 7.84 39 .8 1.43
21 1 6.18 7.71 30.4 1.242 5.86 7.71 30 .4 1.263 5.73 7.71 30.3 1.26
22 1 5.79 7.71 30.4 1.262 5.86 7.71 30.4 1.243 5.73 7.71 30.3 1.23
Table C -4 . Hot Air: Values of Tp, T1# T 2, H 1, and H g
1 1 0
ExperimentNumber
SetNumber
(°F). V
(°F)T2
(°F)Hi
lb H20 ]H2
' lb H2 ° )lb BD air, lib BD air/
13 1 98 457 120 0.003 0.0712 98 460 120 0.003 0.068 .3 98 460 120 0.003 0.069
14 1 98 462 118 0.003 0.0752 98 462 118 0.003 0.0753 98 462 118 0.003: 0 .071
15 1 .97 . 451 120 0.005 0.0612 97 453 120 0.005 0.0733 97 453 120 . 0.005 0.068 .
16 1 97 455 117 0.005 0.0702 97 455 117 0.005. 0.0713 97 455 117 0.005 0.073
17 1 100 462 129 0.005 0.0742 100 . 462 127 0.005 0.078:3 100 462 126 0.005 0.084
18 1 97 460 117 0.005 0.0712 97 460 118 0.005 0.0763 97 460 118 0.005 0.079
19 1 95 453 122 0.005 0.0682 95 453 120 0.005 0.0683 97 453 122 0.005 0.066
20 1 97 466 118 0.005 0 .074 .2 97 464 118 0.005 0.077
21 1 97 433 113 0.005 0.0562 97 435 113 0.005 0.0673 97 437 113 0.005 0.067
22 1 . 97 435 112 0.005 0.0652 97 . 435 112 0.005 0.0653 97 441 112 0.005 0.065
I l l
Table C-5 „ Calculat ion of T
\ Hs A’ i—1
>Experiment . Set
(°F)lb H20 1 Btu lb H2C | Calculated
(°F)Number Number ■ lb..ED ..aid IbJ lb BD a i r
13 1 118 0.083 1026 0.080 1162 118 0.083 1026 0.080 1193 118 0.083 1026 0.080 119
14 1 118 0.083 1026 0.080 1212 118 0.083 1026 0.080 1213 118 0.083 1026 0.080 121
15 1 118 0.083 1026 0.078 1182 118 0.083 1026 0.078 1203 . 118 0.083 1026 0.078 120
16 1 118 0.083 1026 0.078 1222 118 0.083 1026 0.078 1223 118 0.083 1026 0.078 122
17 1 119 0.086 1026 0.081 1172 119 0.086 1026 0.081 1173 119 0.086 1026 0.081 117
18 1 118 0.083 1026 0.078 1172 118 0.083 1026 0.078 1173 118 0.083 1026 0.078 117
19 1 118 0.083 1026 0.078 120) 2 118 0.083 1026 0.078 120
3 118 0.083 1026 0.078 12020 1 119 0.086 1026 0.081 121
2 119 0.086 1026 0.081 11921 . 1 117 0.080 1027 0.075 113
2 117 0.080 1027 0.075 1153 117 0.080 1027 _0.075 117
22 1 117 0.080 1027 0.075 1152 117 , 0.080 1027 0.075 1153 117 0.086 1027 0.075 121
Table C - 6 . Calcula tion of TA2
112
ExperimentNumber
A2Set (°F)
Number
H, HS H1
1 lb h 2 ° 1 I Btu' lb H2Clb BD air J I lb j ; lb BD air,
Calculated(°F)
13
14 ,
15
16
17
18
19
20
21
22
1 114 0.073 1029 0.002 1132 113 0.070 1029 0.002 . 1133 113 0.070 1029 0.001 1161 115 0.076 1028 0.001 1142 115 0.076 1028 0.001; 1143 114 0.073 1029 0.002 1131 110 0.063 1031 0.002 1132 114 0.073 1029 0.000 1203 113 0.070 1029 0.002 1121 113 0.070 1029 0.000 1172 114 0.073 1029 0.002 1103 . 114 0.073 1029 0.000 1171 116 0.078 1028 0.004 1142 117 0.080 1027 0.002 1203 119 0.085 1026 0.001 1221 114 0.073 1029 0.001 1092 115 0.076 1028 0.000 1153 116 0.080 1028 0.001 .1141 113 0.070 1029 0.002 1152 113 0.070 1029 0.002 1133 112 0.068 1030 0.002 1151 115 0.076 1028 0.002 1112 116 0.078 1028 0.001 1141 107 0.057 1033 0.001 1092 112 0.068 1030 0.001 1093 112 0.068 1030 0.001 1091 111 . 0.065 1030 0.000 1122 I l l 0.065 1030 0.000 1123 111 . 0.065 1030 0.000 112
113
Table C -7 . Hot Air: Values of F(TA -Tp) , 0.46(T2~TA ), (F-B), and A’
ExperimentNumber
SetNumber
F(Ta -Tf ) 2 r
(Btu/hr)
0 - « < T 2 - TA2>
(Btu/hr)
(F-B)
(lb/hr)
A1Btulb
13 1 266 3 3.52 10292 ■ 260 3 3.31 10293 260 3 3.44 1029 .
14 1 172 1 3.65 10282 172 1 3.69 10283 161 2 3.61 .1029
15 1 218 5 2.87 10312 299 3 3.47 10293 281 3 3 .17 1029
16 1 170 2 . 3 .29 10292 181 1 ' 3.42 10293 181 1 3.55 1029
17 1 125 6 2.63 10282 133 5 2.76 1027 .3 149 3 3.01 1026
18 1 133 1 3.40 10292 141 1 3.66 10283 149 1 3.79 1028
19 1 141 4 3.09 10292 141 3 3.09 10293 118 5 3.01 1030
20 1 141 1 2.63 10282 149 1 2.74 1028
21 1 77 3 1.53 10332 116 0 1.85 10303 116 0 1.98 . 1030
22 1 108 0 1.92 10302 108 • 0 1.85 1030
. 3 108 0 1.98 1030
114
Table C -8 . Hot Air: Values of Q , ATm-Q, and VgATmg
Experiment Set Q ATmD Ve ATmDNumber Number (Btu/hr) (°F) (ft3oF)
13 1 3891 172 29312 3669 175 29823 .3803 175 2982
14 1 3925 173 29482 3966 173 29483 3878 174 296.5
15 1 3182 171 29142 3873 170 28973 3546 171 2914
16 1 3557 170 28972 3701 170 28973 3835 170 2897
17 1 2835 178 30332 2973 176 29993 3240 175 2982
18 1 3633 172 29312 3904 172 29313 4046 172 2931
19 1 3325 172 29312 3324 171 29143 3223 172 2931
20 r 2846 175 29822 2967 173 2948
h 1 1660 161 27432 2022 159 27093 2155 160 2726
22 1 2086 159 27092 ' 2014 159 27093 2147 162 2760
115
Table C-9 . Hot Air: Values of , T13 , T2 2, and Tg3
T12 x 10"5 T13 x 10-9 T22 x 10“ 3 T 3 x 10"9Experiment Set
Number Number (°F2) (°F3) (°F2) (°F3)
13 1 . 2.09 9.64 0.14 0.172 2.12 9.75 0.14 0.173 2.12 9.75 0.14 0.17
14 1 2.13 9.84 0.14 0.162 2.13 9.84 0.14 0.163 2.13 9.84 0.14 : 0 .16
15 1 2.03 9 .16 0.14 0.172 2.05 : 9.29 0.14 0.173 2.05 9.29 0.14 0 .17
16 1 2.07 9.42 0.14 0 .162 2.07 9.42 0.14 0.163 2.07 9 .42 0 .14 0 ,16
17 1 2.13 9.84 0 .17 0.212 2.13 9.84 0 .16 0.203 2.13 9.84 0 .16 0.20
18 1 2.12 9.75 0.14 0 .162 2.12 9.75 0.14 0.163 2.12 9.75 0.14 0.16
19 1 2.05 9. 29 0.15 0.182 2.05 9.29 0 .14 0.173 2.05 9.29 0 .15 0.18
20* 1 2.17 10.11 0.14 0 .162 2.15 9 .98 0 ,14 0.16
21 1 1.87 8.10 0.13 0.152 1.89 8.22 0 .13 0.153 1.91 8.35 0.13 0.15
22 1 1.89 8.22 ■ 0 .12 0 .142 1.89 . 8.22 0 .12 0.143 1.94 8.56 0 .12 0.14
1,16
Table C - 1 0 . Hot Air: Terms Involving , T^%, T ^^( T ^ , T ^ and T ^
ExperimentNumber/
SetNumber
0.2517(T1-T2)
(Btu/lb)
4 .97(T12-T22)10-6
(Btu/lb)
2.93 (T j3_T23) i o - 9
___ (Btu/lb)
13/1 84 o 8 0.97 0 .28/ 2 85.6 0.98 0.28/ 3 85.6 0.98 0.28
14/1 86.6 0.99 0.28/ 2 86.6 0.99 .0 .2 8 ./ 3 86.6 0.99 0.28
15/1 83.3 0.94 0.26/ 2 83.8 0.95 0.27/ 3 83.8 0.95 0.27
16/1 85.1 0.96 0.27/ 2 85.1 0.96 0.27/ 3 85.1 0 .96 0.27
17/1 83.8 0.97 0.28/ 2 84.3 0.98 0.28/ 3 84.6 0.98 0.28
18/1 86.3 0 .98 0.28/ 2 86.1 0 .98 0.28
. / 3 86.1 0 .98 0.2819/1 83.3 0.94 0.27
/ 2 83.8 0.95 0.27/,3 83.3 0.94 0.27
20/1 87.6 1.01 0.29/ 2 87.1 1.00 0.29
21/1 80.5 0 .86 0.23/ 2 81.1 0 .87 0.24/ 3 81.6 0 .88 0.24
22/1 81.3 0.87 0.24/ 2
CO1—1
00 0.87 0.24/ 3 82.8 0.90 0.25
117
Table C - l l Hot Air: Values of H^Cp (T^-Tg),
(lDl " iD2) + H-LC p ^ ( T 1 - T 2 ) , a n d Q v
ExperimentNumber/
SetNumber
H1cPv (T1 -T2)
(Btu/lb)
( i D " b . ) + H l c p ( t l " T 2 ) . Q *1 2 v _______ (Btu/lb) (Btu/hr)
13/1 • / 2
/ 3 14/1
/ 2 / 3
15/1 / 2
. / 3 16/1
/ 2 / 3
17/1 / 2 / 3
18/1 / 2 / 3
19/1 / 2 / 3
2 0 /1 / 2
2 1 /1 / 2 / 3
2 2 /1 / 2 / 3
0.470.480 .480 .480.480.480.760.770.770.780 .780 .780.770.770.770.790.790.790 .760.770.760.800.800.740.740.750.740.740 .76
86.587.387.388.488.488.485.385.885.887.187.187.185.886.38 6 . 688.38 8 . 1 88 . 185,85,85,89,89,82,83.0 83.583.183.1 84.7
44634494449445514551455144104436443644934493449332773299
.330744994535453543954422439535643548249725222531252525252565
118
Table C -12 . Hot Air: Values of ha , h* a* , Re, and BZ
Experiment Set ha h*a* Re BZNumber Number (Btu/hrft^QF) (Btu/hrft ^°F)___________ (lb/hr)
13 1 1.33 1.53 551 18.492 1.23 1.51 550 19.173 1.28 1.51 550 18.85
14 1 1.33 1.53 550 . 10.302 1.35 1.53 550 10.433 1.31 1.53 550 10.63
15 1 1.09 1.51 552 19.312 1.34 1.53 552 19.183 1.22 1.53 552 20.02
16 1 1.23 1.55 551 11.962 1.28 1.55 551 11.753 1.33 1.56 551 11.54
17 1 1.07 1,.'08 407 6.562 0.99 1.10 407 6.353 1.09 1.11 407 6.08
18 1 1.24 1.55 550 6.882 1.33 1.55 550 6.653 ’ 1.38 1.55 550 6.44
19 1 1.14 1.50 551 7.272 1.14 1.52 551 7.413 1.10 1.50 551 7.49
20 1 0 .96 1.20 424 7.352 1.01 1.20 424 7.29
21 1 0.61 0.91 . 320 7.66■' 2 0.75 0.93 320 . 7 .38
3 0.79 0.93 319 7.2222 1 0.77 1.07 320 7.30
2 0.74 1.07 320 . 7 .273 0.78 0.93 319 7.05
APPENDIX D
ERROR ANALYSIS
If ha is given by
ha = Q/VgATm
and V( ) denotes the variance of the term in paren thes is , then the
variance of ha is approximately given by (Davies 1961, pp. 41, 49)
V(ha) = I 3ha 3Q
or
2 V (Q) + 3ha | 2 V(aTm)3aTm
V(ha) = I 1Aim
/ e ,
1 VtaTm)Aim
For steam,
Q = (F-B) '1 + c pv (T2_TS)
Tm0 = (T,-T0) + (T0-Tc)1 S 2 "S'
(72)
(73)
Vand it was assumed that c and c were e ssen t ia l ly constant for the
PF P,temperature range involved. Then,
V(Q) = 3 0 2V(F) + 1 a o | 2V(B) 3 03F *bI adg-Tp)
'V(Tg-Tp) (74)
_ a a |2v(\) + 3 0I 3" 1 a T2“TS
•v (t 2- ts )
119
120
Furthermore ,
iQ. = ‘ + c p (Ts - V + c p (T2 -T 3 ) 9F I V
k - c (T -T )9 B Pv Z J
ajQ = Fca(Ts - T p ) F
9Q = (F-B)c p(T2- Ts) V
Since c n (T0 -Tc) was either zero or tr ivial compared to c (T - T j + A ,Pp u r
the terms d_Q and were assumed to be given, respec t ive ly , by 3 F 0 B
X + cPf (TS' TF)
and
3-.Q38
= -A
H en ce ,
V(ha) = 1 / 1 V / [a2 + c (To-Tp ) 2
f c U P r+ 2op Tf) V(F) (75)
+ a 2 V(B) + F 2 c pF 2 V(Tg-TF) + (F-B) 2 V(a) + (F-B) 2 cp 2 V(T^-Tg)j
VfTj-Tg) + V (T2 -TS)+ Q 2 1 14 V(T
ATms
As shown in Appendix F , V(F) = 0 .0241, and as shown in
Appendix E, V(B) = 0 .0501 . Based on the variation, with p re s su re , of
enthalpy and saturation temperature , it was assumed that the grea tes t
errors (equal to three standard deviations) that could occur in x and Tg
could not have exceeded 2 Btu/lb and 2°F, respec t ive ly . Hence ,
V(x) = (2/3)2 = 0.44 Stu2/ l b 2
and
V(Tg) = (2/3)2 = 0 .44 F2
It was further assumed that the maximum error (equal to three standard
deviations) that could have occurred in each of the terms T^, , and
was 1°C ( 1 . 8°F). H ence , the corresponding variances were all equal to
0 . 36°F2 .
The orders of magnitude for the various terms of Equation 75
are given in Table D - l . From w hich , it can be seen that with negligible
loss of accu racy # Equation 75 can be reduced to
V(ha) = (xATmQ) 2 V(F) + V(B) (76)
or
V(ha) = 2.56 x 10-4 A2/aTms 2 (77)
The c a lcu la t io n , using Equation 11, of values of V(ha) is tabularly
shown in Table D - 2 .
Table D - l . Orders of Magni tude , Superheated Steam
122
Term Order of Magnitude
( l / V e 2) ( l A T m g ) 2 1CT7
A2 1 0 6
CpF (Ts -TF) 2 IQ2
2c X(T -T ) 105PF S F
V(F)
CM1Or—1
V(B) icr1
FS 2 102
VfTg-Tp) = V(Tg ) + V(Tp) 10” 1
(F-B)2 10
V(x) 10"1
Q 2/ 4V 2 e 104
( lA T m s ) 4 10-8
V (T x —Tg) i
V(T2 -T s ) i
(F-B)2c 2 10V
Table D - 2 . Calculat ion of V(ha), Superheated Steam
123
ExperimentNumber/
SetNumber
A2 x 10-4 2 .5 6 a2 x 10-4 (Btu2/ l b 2) (Btu 2/ h r %t
Aim2 (°F 2)
V(ha)(Btu 2/ h r 2ft ®°F 2)
1/1 94.6 220 14200 . 0.01622/1 94.5 239 17600 0.0142/ 2 94.5 236 17200 0.0143
3/1 94.5 247 17400 0.0142/ 2 94.5 257 19600 0.0132/ 3 94.5 253 18600 . 0.0136
4/1 94.5 244 17000 0.0145/ 2 94.5 . 245 17200 0.0143/ 3 94 .6 245 17400 0.0141
5/1 94.6 245 17400 0.0141/ 2 94.6 244 17200 0.0142/ 3 94.7 243 17000 0.0143
6/1 94.7 . 250 18600 0.0134/ 2 94.7 249 17600 0.0142/ 3 94.7 243 ' 17000 0.0143
7/1 94.7 237 15800 0.0150/ 2 94.7 237 15800 0.0150/ 3 94.7 235 15500 0.0151
8/1 94.6 246 17700 0.0139/ 2 94.6 246. 17700 0.0139
9/1 94.6 230 14500 . 0.0159/ 2 94.6 229 14400 0.0159
10/1 94.6 236 17700 0.013311/1 94.6 249 18200 0.0137
/ 2 94.6 247 17700 0.0140/ 3 94.6 252 18600 0.0135
12/1 94.6 240 19000 0.0126
124
and
aTmD = > + (79)
Then,
V (Q) = [?F
9ZV(F) + 1 dQ 2V(B) +
\ / »(T2-TA2>j'V(T2 -TA2) (80)
+ | 3 0 | V(A') + I Q .a(TA2- TF)
■V(TA2-TF)
Furthermore,
dF*' + CPv (T2 -TA2) + cPf (TA2 tf )
b Q _ A* + Cp (T2 -Ta )>B v 2
>0 = (F-B) 3V
?Q = (F-B)Cj
«t r 2 -TA2)V
V(F) = 0.0241
V(B) = 0.0430 (as shown in Appendix E)
v (t 2- ta ) = v (t 2) + v (ta )
V(T2-Tp) = V(T2) + V(Tp)
125
VC^) = V(T ) = 0 . 36°F^ (as shown for steam)
V(T, ) = 24°F^ (as shown in Appendix H)*2
Furthermore, since V(T^ ) = 240f 2 / the maximum error (equal to three
standard deviations) in is approximately 15°F# and from the steam
t a b le s , the corresponding maximum error in a1 should not have e x c e e d e d
2
and V(ATm^) is given by
V(ATmn ) = 1 V(TJ +V(T» ) + V(Tj + V(T. )4L 1 Z 2 J
Examination of the experimental data and of the humidity chart showed
that the maximum error in T* should not have exceeded 3°F; therefore ,A1
The orders of magnitude for the various terms of Equations 72
and 80 are given in Table D - 3 . From which, it can be seen that with
negligible loss of a ccu racy , Equation 80 can be written as
9 Btu/lb; hence, V (a') = 9 Btu^/ lb^ .
The term ATm^ is given by
flTmD = + (T2 -TA2>
V(Ta ) = 1°F2 , and V(aTmD) = 4 .2 9 °F 2 .
(81)
and that Equation 72 again reduces to
(82)
or
V(ha) = 2.29 x 10 4 a ' 2A i m 2 (83)
126
Table D-3 . Orders of M agnitude , Hot Air
Term Order of Magnitude
x1 103
cPv 2(T 2"TA2) 10
c p f <t a 2 "t f > 10
10dh'
------ a 2 _»(T2 -T a 2)
»Q 13(Ta -Tp)
2 r
v (Ta 2 - t f ) 10
V(T2 -T a ) 102
V(V) 10
(l/Ve1mD)2 IQ"?
k'2 106
Q2/Ve 2 104
( lATm D)4 10-9
V(4TmD) 1
127
The c a lcu la t ion , using Equation 83, of values of V(ha) is tabularly
shown in Table D - 4 .
Several te s ts of significance were required in order to examine
the variation which resul ted in values of ha when different spraying
rates were used in combination with one given heating medium flow
r a t e . First , consider the data shown in Table D - 5 , derived from the use
of superheated steam.
In experiments 2, 3, 4, and 5, the value of Wg is e ssen t ia l ly
the sa m e , while values of F differ considerably . Since V(Wg) was
equal to 1 .71 , with corresponding standard deviation equal to 1 .31 , it
was assumed that minor differences between values of Wg could safely
be neglected and that the data for experiments 2 and 3 could be
averaged.
For two mean values of ha, denoted by ha^ and h a ^ , the
standard error of (ha^-hag), denoted by S .E . ( h a ^ - h ^ ) , is given approx
imately by
S.E . (ha^-ha^) = V(ha^) + V(ha2) (84)
and the number of degrees of freedom <p is given approximately by
21 = 1 V(Ha ) 2
+ 1 V(Ea2)<t> <t> V t h a ^ W ^ ) <t>2 V(ha1)W(ha2)
(85)
where = number of degrees of freedom assoc ia ted with ha^
* 2 - number of degrees of freedom assoc ia ted with h a 2
Table D-4 „ Calculat ion of V(ha), Hot Air
128
ExperimentNumber/
SetNumber
a ' 2 x 1 0 - 4
(Btu2/ l b ^
2.29 k' x 10"4
(Btu2/ h r ^ t 6)
UTmD)2
(°F2)
V(ha)
( B t u ^ / h r ^ f t G o p Z )
13/1. 106 242 29600 0.00818/ 2 106 242 30600 0.00791/ 3 106 242 30600 0.00791
14/1 106 242 29900 0.00807/ 2 106 242 29900 0.00807/ 3 106 242 30300 0.00780
15/1 106 243 29200 0.00832/ 2 106 ■ 242 28900 0.00837/ 3 106 242 29200 0.00827
16/1 106 242 28900 0.00838/ 2 106 242 28900 0.00838/ 3 106 242 28900 0.00837
17/1 106 242 31700 0.00763/ 2 105 241 31000 0.00778 ■/ 3 105 241 30600 0.00787
18/1 106 242 29600 0.00818/ 2 106 242 29600 0.00817/ 3 105 242 29600 0.00817
19/1 106 242 29600 0.00819/ 2 106 v 242 29200 0.00827/ 3 106 243 29600 0.00820
2 0 / 1 106 242 30600 0.007892 105 242 29900 0.00808
21/1 106 244 25900 0.00940/ 2 106 243 25300 0.00959/ 3 106 243 25600 0.00947
22/1 106 243 25300 0.00960/ 2 106 . 243 25300 0.00960/ 3 106 243 26200 0.00925
129
Table D-5 . Data for Tests of Significance , Superheated Steam
ExperimentNumber/
SetNumber
lbhr
W,
“ Ihri
ha h*a* V(ha)
Btu ]/ )
Btu ' 1 Btu^hrftSoFi hrft^opj hr2ft6op2(
1/1 10.30 40.7 1.92 2.23 0.01622/1 16.63 40.1 2.00 2.20 0.0142/ 2 16.63 40.0 2.06 2.21 0.0143
3/1 16.63 40.0 2.10 2.19 0.0142/ 2 16.63 39.7 1.99 2.17 0.0132/ 3 16.63 39.8 2.11 2.18 . 0.0136
4/1 9.96 40.1 2.11 2.20 0.0145/ 2 ' 9 .96 40.1 2.05 2.20 0.0143/ 3 9.96 40.1 2.08 2.18 0.0141
5/1 7.84 40.1 2.04 2.18 0.0141/ 2 7.84 40.1 2.04 2.18 0.0142/ 3 7.84 40.1 1.99 2.17 0.0143
6/1 7.84 27.6 1.17 1.50 0.0134/ 2 7.84 27.7 1.19 1.50 0.0142/ 3 7.84 27.8 1.24 1.50 0.0143
7/1 7 .84 15.4 0.71 0.83 0.0150/ 2 7.84 15.4 0.73 0.83 0.0150/ 3 7.84 15.3 0.60 0.83 0.0151
8/1 8.24 17.6 0.57 0 .95 0.0139/ 2 8.24 17.6 0.57 0.95 0.0139
9/1 8.51 18.8 0.61 1.02 0.0159/ 2 8.38 18.8 0.59 1.02 0.0159
10/1 4.84 34.7 1.34 1.76 0.013311/1 7.84 35.3 1.49 1.92 0.0137. / 2 7.84 35.4 1.49 1.93 0.0139
/ 3 7.84 35 .3 1.48 1.92 0.013512/1 4.03 35.4 1.12 1.79 0.0128
130
If the confidence interval for (ha^-hag) includes z e r o , then there is no
significant difference between ha^ and ha 2 (Davies 1961, p. 54).
From experiment 4 , let ha = 2 . 08 and V(ha ) = 0 .00477.
From experiments 2 and 3, let ha 2 = 2.05 and V^ag) = 0 .00278. Then,
V(ha^) + V(ha2) = 0.00755
S.E . (ha^-hag) = 0.0869
1 = 1 <p 4
0.00278 \ 2 + 1 0 . 00477 | 2 = 0 . 2 3 0.00755,0 .0 0 7 5 5 1 2
<t> = 4
t = 2.13 (at 90% confidence level)
(ha1- h a 2) = 2 .0 8 -2 ,0 5 ± 2. 13(0.0 869) = 0.03 ± 0 .18
The confidence interval includes z e r o , and there is no significant d if
ference between ha^ and ha 2 .
Again, from experiment 4, let ha^ = 2.08 and V(ha^) = 0.0477
From experiment 5, let hd 2 = 2.02 and V(ha 2 ) = 0 .0466 . Then,
V(hax) + V(ha2) = 0.00943
1 = 1 0.00466] 2 + i<p 2 0.00943 2
0 .00477 \ 2,0 .00943 /
<P = 4
t = 2.13 (at 90% confidence level)
(ha^-ha2) = 2 .0 8 -2 .0 2 + 2. 13(0.097) = 0 .06 +0 . 21
The confidence interval includes z e ro , and there is no significant dif
ference between ha^ and h a 2 .
131
In experiments 10, 11, and 12, values of F also differ, while
the value of Wg is e ssen t ia l ly the sa m e . It was again assumed that
minor differences between values of Wg could be neglected . Then, from
experiment 11, let ha^ = 1.49 and V(ha^) = 0.0057. From experiment 12,
let ha = 1.12 and V(ha) = 0 .0128. The standard error of ha^-ha is
given by
S.E . (ha^-ha) = [v th a ^ V(ha)]T
and it was assumed that <p could be calculated from
1 = 1 V(ha i ) 2 + 1 V(ha)4> <P V(ha j J+V (ha) *2 V(ha^)W(ha)
where <t> = 2 and <p = I . Then,
V(ha^) + V(ha2) = 0.0185
0 ,0057' 2 + 0 0128' 2 = 0.530 0 h—• 00 Cn 0 ,0185]
<p = 2
t = 2.9 2 (at 90% confidence level)
(ha1- h a 2) = 1 .4 9 -1 .1 2 + 2 .92(0 . 136) = 0.37 + 40.
The confidence interval includes zero, and there is no significant
difference between ha^ and ha.
Finally, from experiment 11, let ha^ = 1.49 and V(ha^) = 0 .00 5 7 .
From experiment 10, let ha = 1.34 and V(ha) = 0 .0133 . Then,
132
V(hai) + V (ha) = 0.0190
1 = 1 0 . 005 7 r +0.0190/
I2 0.01330 .0 1 9 0 j
2 = 0.54<t> 2
<P = 2
t = 2.9 2 (at 90% confidence level)
(har ha) = 1 .49-1 .37 + 2 .92(0. 138) = 0. 12 + 0 .4 0 .
The confidence interval includes zero, and there is no significant dif
ference between ha^ and ha.
The preceding tes ts of s ignificance showed that for a constant
value of Wg, no significant difference could be detected between the
values of ha corresponding to each of the different spraying ra tes .
Therefore, differences in values of F were neglected when correlating
the data from experiments involving superheated s t e a m .
Corresponding to each value of W , the Reynolds number was
calculated from
Re = (Re/Wg)Wg
Values of Re/Wg depended on the temperature T^ and varied from 15.57
to 16 .59 . The variance of Re was given by
V(Re) = / 3(Re/Ws )Wg \ 2V(Re/Ws ) +
>3 (Re/Wg)
a(Re/Wg)Wg \ 2V(Wg)
8 W S
or
V(Re) = Wg 2V (Re/Wg) + (Re/Wg) 2V (Wg)
133
The maximum possible error in R e/W g (due to an error in of 1 . 8°F)
was on the order of 0.03 h r / lb . Therefore, V (Re/W g) was approximately
0.0001 h r ^ / I b a n d the term Wg^vfRe/W^) was negligible compared to
(Re/W g) 2V(Wg). Hence,
V(Re) = (Re/Wg) 2v ( W)
and
S .E . (Re) = 1. 31 (Re/Wg)
For Re/Wg = 15 .57 , S.E.(Re) = 20.4; for Re/Wg = 16.59 , S.E.(Re) = 21.7.
For experiments involving values of W^ which differed by not
more than 0 .1 lb /h r , it was considered appropriate, because of the
large variance of W g , to compute a Reynolds number based on the mean
value of Wg and to compute ha from all corresponding values of ha. In
so doing, it was a lso considered appropriate to take S.E.(Re) equal to
the maximum possible value of 21 .7 .
Since the values of Wg used to derive the rotameter calibration
chart shown in Figure 14 were average values for N measurements of W g ,
the confidence limits for each Reynolds number were given by t21. 7/(Np" .
Referring to Table B-3 and Table B-10, for Re greater than 600, N = 17;
for Re between 400 and 500, N = 5, and for all other Re, N = 4. The
value of <P was 29, and at the 95 percent confidence leve l , t = 2 .05 .
Therefore , since values of Re could only be determined accurately to the
neares t whole number, the appropriate confidence limits for Re greater
134
than 600, between 400 and 500, and for all other values were 11, 20,
and 23, respec t ive ly .
The resul ts of the error analys is for superheated steam are
shown in Table D - 6 . The confidence intervals for Re equal to 638 and
634 and for Re equal to 625 and 618 great ly overlapped, and the data for
the corresponding experiments was averaged. The experimental resu l ts ,
presented in "Discuss ion of R esu l ts , " are given in Table D - 7 .
Now, consider the data shown in Table D - 8 , derived for the
use of hot air. Examination of that data indicates that if there is no
significant difference between mean values of ha corresponding to values
of F equal to 17 .30 , 10 .09 , and 7.84 (with equal to 5 1 .5 , 51.6 and
51 .7 ) , then there is no detectable variation of ha with spraying r a t e .
Proceeding as with superheated steam and neglecting small
di fferences in values of , from experiment 14, let
ha^ = 1.34 and V(ha^) = 0 .00266.
From experiment 13, let
ha^ = 1.28 and V(ha^) = 0.00267.
Then,
V(ha^) + V(ha2) = 0.00533
S.E . (ha^-hag) = 0.0730
1 = 1 0.00266 2 + 0.00267 2 = 0.284<*> 2 _0 . 0 0 612_ 0.00612
135
Table D - 6 . Results of Error Analysis , Superheated Steam
w s V(ha) . V(ha)2 t— 1 Re Btu2 ' 1 B t u ) 95%
, hr I hr2f t6oF2j hrftBoF 1 <t> Confidence
*40.7 675 + 11 0.0162 0.127 - 12.7 1.9240.1 638 + 11 0.00183 0.0428 6 2.45 2.0 840.0 634 + 11 0.00713 0.0844 1 12.7 2.08
*39.8 625 + 11 0.0136 0.117 - 12.7 2.11*39.7 618 + 11 0.0132 0.115 . - 12. 7 1.99
35.4 561 + 23 0.00338 0.0582 3 3.18 1.3934.7 541 + 23 0.0133 0.115 1 12.7 1.3427.7 441 + 20 0.00465 0.0683 2 4.30 1.2018.8 312 + 23 0.00398 0.0631 1 12.7 0.6017.6 280 + 23 0.00348 0.0590 1 12.7 0 .5715.4 252 + 23 0.00501 0.071 2 4.30 0 .68
*Only one se t of data was obtained for the given experimental conditions „
136
Table D - 7 . Experimental R e s u l t s , Superheated Steam
Wclbhr
ReV(ha)Btu^
h r2f t 6oF2j
V(ha)2 .Btu I
hr f t3oF/ *
t95%
Confidence
haBtu
hrft3oFi
40.1 638 + 11 0.00158 0.0398 7 2.36 2.08 + 0.0939.8 625 + 11 0.00670 0.0819 1 12.7 2.05 + 1.0435.4 561 + 23 0.00338 0.0582 3 3.18 1.39 + 0 . 1 934.7 541 + 23 0.0133 0.115 1 12.7 1 . 3 4 + 1 . 4 627.7 441 + 20 0.00465 0.0683 2 4.30 1.20 + 0.2918.8 312 + 2 3 0.00398 0.0631 1 12.7 0. 60. + 0 .8017.6 280 + 2 3 0.00348 0.0590 1 12.7 0.57 + 0.7515.4 252 + 23 0.00501 . 0.071 2 4.30 0.68 + 0 .31
.1.37
Table D - 8 . Data for Tests of Significance, Hot Air
Experiment F w D ha h*a* V(ha)Number/ / \ / - \
, ■ Set fib] fib.] Btu I Btu ' Btu^Number 1 hr) (hr) hrft3oF/ i hrft3oF J hr2f t6oF^j
13/1 16.63 51.6 1.33 1.45 0.00818/ 2 17.30 51.5 1.25 1.44 0.00791/ 3 17.30 51.5 1.30 1.44 0.00791
14/1 10.09 51.5 1.35 1.45 0.00807/ 2 10.09 51.5 1.36 1.45 0.00807/ 3 10.09 51.5 1.31 1.44 . 0.00780
15/1 16.76 51.7 1.10 1.44 0.00832/ 2 17.57 51.7 1.35 1.45 0.00837/ 3 17.57 51.7 1.23 1.44 0.00827
16/1 10.63 51.6 1.23 1.47 0.00838/ 2 10,63 51.6 1.28 1.47 0.00838/ 3 10.63 51.6 1.34 1.48 0.00837
17/1 7 . 84 38.2 0.99 1.03 . 0.00763/ 2 7.84 38.2 1.00 1.05 0.00778/ 3 7.84 38.2 1.10 1.06 0.00787
.18/1 7.84 51.5 1.24 1.47 0.00818/ 2 7.84 51.5 1.34 1.47 0.00817/ 3 7.84 51.5 1.39 1.48 0.00817
19/1 7.84 . 51.6 1.14 1.42 0.00819. / 2 7.84 51.6 1.15 1.44 0.00827
/ 3 7.84 51.6 1.10 1.42 0.0082020/1 7.84 39.8 0.96 1.14 0.00789
/ 2 7,84 39.8 1.02 1.15 0.0080821/1 7.71 30.4 0.61 0.87 0.00940
/ 2 7.71 30.4 0.75 0 .88 0.00959/ 3 7.71 30.3 0.79 0 .88 0.00947
22/1 7.71 30.4 0.77 0 .88 0.009 60/ 2 7.71 30.4 0.75 0 .88 0.00960/ 3 7.71 . 30.3 0.78 0 .88 0.00925
.138
<t> = 3
T = 2.35 (at the 90% confidence level)
(hai-hag) = 1 .3 4 -1 .2 8 + 2.35(0.0730) = 0 .06 + 0. 172
The confidence interval includes z e ro , and there is no signif icant dif
ference between ha^ and hag.
Again, from experiment 14, let ha^ = 1.34 and V(ha^) =0 .00266 .
From experiments 18 and 19, let hag = 1.23 and Vfhag) = 0.00137.
Then,
V(ha^ + V(ha ) = 0.00403
S .E .(ha^-ha^) = 0.0635
1 = 1 <P 2
0 .0 0 2 6 6 ]2 + 1 0 . 0 0 1 3 7 )2 = 0 . 2 4 ^ 0 . 0 0 4 0 3 j,0 .00403/ 5
<9=4
t = 2.13 (at the 90% confidence level)
(ha^-ha^) = 1 .3 4 -1 .2 3 + 2.13(0.0061) = 0.11 + 0. 13
The confidence interval includes zero, and there is no signif icant
difference between ha^ and hag.
Again, the t e s t s of s ignif icance indicated that ha did not vary
significantly with F when remained constant . Therefore, differences
in values of F were a lso disregarded for purposes of correlating data
derived from the use of hot air.
For air , V(Wg) was equal to (1.28)2(1.71) or 2 .7 9 , with
standard deviation equal to 1 .67 . For D = 51 .7 , 5 1 .6 , and 51.5 and for
139
Wq = 30.3 and 3 0 .4 , it was again considered appropriate to compute a
Reynolds number based on the mean value of and to compute ha
from all corresponding values of ha. The standard error of Re was then
given by
S.E.(Re) = 1 . 6 7 (Re/W^)
For air, Re/W ^ varied from 10.51 to 10.67. Taking Re/VV^ equal to
10.6 made S .E . (Re) equal to 17.7 and introduced negligible error.
For Reynolds numbers greater than 500, N = 17; for all other
values , N = 4, and the confidence limits for Re are 9 and 19, respec t ive
ly. The resul ts of the error analysis on data obtained using hot air are
given in Table D - 9 , which are the same resul ts as given in “Discuss ion
of R esu l ts . "
140
Table D-9 . Experimental Results , Hot Air
WD V(Ea) V ( E # t ha
f lb! Re I Btu2 ) Btu j 95% I Btu '1 hr I hr2f t6oF2/ hrft2oF/ <$> confidence lh r f t2oFj
51. 6 551 + 9 0.000482 0.0220 17 2.11 1 . 2 7 + 0 . 04
CDCO 8 424 + 19 0.00399 0.0631 1 12.7 0 . 9 9 + 0 . 80
COCO 2 407 + 19 0.00259 0.0508 2 4.30 1 . 0 5 + 0 . 22
GO o 4 320 + 19 0.00158 0.0398 5 • 2.57 0.74 + 0. 10
;
APPENDIX E
VARIANCE OF B
For superheated s te am , it was assumed that c (T9-Tq) couldv
again be considered neg lig ib le , and Equation 15 was rearranged to give
B = F"Ws (i1- i 2) + Fcp^(Ts -TF) + L (86)
For hot air , c ) was likewise considered negligible , andv 2
Equation 57 was rearranged to give
6 = F + FcPf (TA2-Tf ) -WD(iD - i D ) -WDH1c Pv(T1-T2) + L (87)
X1 X' X'
Between the individual se t s of data obtained during a given experiment,
values of (or W^) and varied slightly and thus influenced the ex
perimentally determined values of B corresponding to some constant
value of F. Therefore, referring to Davies (1961, p. 54), for data ob
tained by using superheated s te am , V(B) was given by
(88 )V(B) = 1 9812V(F)V 98 1 2V(WC) + 3B
iaWs 1 s a(ir
+ #B 2V(TQ-Tp) +Lai]3(Ig-TF) o r [jxj
141
and for data obtained by using hot air , V(B) was given by
l2v u ; f ia w
V(B) = a B ^ V ( F ) + /_aL B . \2V(Wn ) + dFl I aWd
dBa(TA -T p )
2 1
2v <ta 2- t f ) +
dB
a B (89)
+ dB 2V ( V ) + 4B \
ld v l l * H l l
'V(H^) +
JV(Tr T2)
In Equations 15 and 57, the term L was not independently
measured or ca lcu la ted . However, as found from the experimental d a t a ,
the terms L/a and L / a ' were at least one order of magnitude smaller than
the term B. Furthermore, ambient conditions in the laboratory varied only
sl ightly during an experiment, or from one experiment to another. There
fore, it was decided that for purposes of s implif ication, the terms L / a
and L / a' could be ignored when developing express ions for V(B) .
Then, considering Equation 86,
i Ba(Tg-TF)
A 2
3Qdh
- Wg (l1- i 2) -F c p (Tg-Tp)~ n — t
143
(94)
(95)
The term Fc (T -T ) is very small compared to Pp b r
Wg ( i j - ig ) , anda 2
aBj was considered to be given by f,A
aBd A
Since the maximum value of c 2 (T - ! „ ) 2/ a was aboutPp b r
3 .6 x 10~3, aB \ was given approximately by 5F
M l 2 = l - 2 c (Tg-Tp) ?F---------- ----- -
(9 6)
(97)
Furthermore,
V(F) = 0.0241 lb^/hr^ (as shown in Appendix F)
V(WS) = 1 . 7 1 lb^/hr^ (as shown in Appendix G)
V(Tg) = 0. 44° f 2 (as shown in Appendix D)
V(Tp) = 0 . 36°F^ (as shown in Appendix D)
V(a) = 0 . 4 4 Btu^/lb^ (as shown in Appendix D)
With the maximum error in either or equal to 1. 8 °F , the corre
sponding maximum error in i^ and , equal to three standard d ev ia t io n s ,
was about 0 .9 Btu/lb; V(i^) = V^^) = 0.09 Btu^/ lb^ , and =
144
V(i^) + Vtig) = 0 . 1 8 Btu^/lb^. H ence , with very little loss of accuracy,
V(B) can be calcula ted from
V(B) = 1- 2oPF(Ts - Tr) V(F) + (i1- i 2)2V(Wg) (98)
Appropriate calcula t ions are given in Tables E - l and E-2
Next, considering Equation 87,
f.5B3F
- 1_CPF (TA2"TF) (99)
d B ' 2 = 1 - 2 cdJ T Ao-T f ) + c pF2 (TA2-TF) 2BF _PF a 2
K' A 1
( 1 0 0 )
dB
l * WD
_iDo _Hl Cp (Tr T2)1 2 V
dB
*(TA - v
2 ^ I F C p p 12
A1
_aB_ = ^ D . ( i r, - i ^ ) - H lCr, (Tt-To) 5A' A' 2 lDl D2 1 pv 1 2
A'2
dB | 2 = "aHn
dB
wi 2 P p v f r i - T 2)
a ( T l - T 2 )
2 = W p H ^ C px' v
( 1 0 1 )
A'
dB
A'
2 =w d | 2 (102)
A'
(103)
(104)
(105)
(106)
145
Table E - l . Terms Involved in C alculation of V(B), Superheated Steam
ExperimentNumber
SetNumber
A(Btu/lb)
(Tg-Tp)(°F)
( i l - 1 2 )(Btu/lb)
1 1 972. 2 s. 59 111.12 1 972.2 59 124.2
2 972.2 59 122.83 1 972.2 1 123.2
2 972.2 4 130.63 972.2 0 127.4
4 1 972.2 4 121,32 972.2 2 122.33 . 972.5 6 122.3
5 1 972.5 3 122.32 972.5 2 121.33 .973 .0 1 120.4
6 1 973.0 I 125.12 973.0 1 122.33 973.0 1 120.4
7 1 973.0 0 115.72 973.0 0 115.73 973.0 0 114.8 ,
8 1 972.9 1 122.72 972.9 1 122.7
9 1 972.9 1 111.12 972.9 0 . 110.6
10 1 972.9 2 114.911 1 972.6 2 125.1
2 972.6 j 2 123.23 972.6 2 126.5
12 1 972.6 0 118.5
146
Table E-2 „ Calculation of V(B), Superheated Steam
ExperimentNumber
SetNumber
1-2(Ts -Tf )v (f) X1 x2 v(ws)
(Ib^/hr^) (Ib^/hr^)
V(B)
(Ib^/hr^)
12
9)1011
12
112123123123123123121211231
0 . 0 2 1 20 . 0 2 1 20 . 0 2 1 20.02410.02390.02410.02390.02400.02380.02400.0240.0.02410.02410.02410.02410.02410.02410.02410.02410.02410.0241.0.02410.02400.02400.02400.02400.0240
0.02240.02800.02730.02750.03090.02940.02670.02710.02710.02710.02670.02630.02830.02710.02620.02420.02420.02380.02720.02720.02230 . 0 2 2 10.02400.02830.02750.02900.0254
0.04360.04920.04850.05160.05480.05350.05060.05110.05090.05110.05070.05030.05240.05120.05030.04830.04830.04790.05130.05130.04640.04620.04800.05230.05150.05300.0494
Since c ^(T, -Tr )^ /a 1 was very small compared with P r r
1 2cpf (ta2 t f ) '
A'
a3 2 was cons idered to be given by
3B 2 = 1 " 2cpf (TA2"Tf )A 1
and since H ,c (T-,-T7) was very small compared with1 Pv
147
(107)
(in - i n ) / x ' , I u l 2 ?W
was considered to be given by
D/
/ a 6 | 2 = 2 (108)
1and finally , H e (T -T ) was very small compared with (i^ - i ^ ),
1 pv 1 2 a'2 U l 2
and— V ?
2 was considered to be given by
dB 2 = W D 2(iD 1' i D 2)23 A 1
(109)
Furthermore,
V(F) = 0.241 lb2/ h r 2
V(WD) = 2 . 7 9 lb^/hr^ (as shown in Appendix D)
V(T. - T J = 24 .3 6 °F 2 2 ^
V(T1-T 2) = 0 . 72°F2
V(a') = 9 Btu2/ l b 2
Using arguments similar to those used for V ^ - i g ) , the value of
V(i^^- i^^) was determined to be approximately equal to 0.05 Btu2/ lb2 .
148
H ence , with very litt le loss of accu racy , V(B) was calcula ted from
V(B) = 1 - 2cpv (ta 2- t f > V(F) 2v (w d ) (110)
A ' 1 1Appropriate calculat ions are shown in Tables E-3 and E - 4 .
Because of the difference between the physical properties of
air, and because of the difference between the evaporat ive processes
a ssoc ia ted with each heating medium, it was decided to calculate a
pooled variance for all data derived from the use of superheated steam
and to calculate another pooled variance for all data derived from the
use of hot air . For superheated s te a m , V(B) = 0.0501 lb^/hr for hot
air, V(B) = 0.0430 lb2/ h r 2 .
Table E-3 „ Terms Involved in C alculation of V(B), Hot Air
149
' - TF> b i - lg )Experiment Set ^
Number Number (Btu/lb) (°F) (Btu/lb)
13 1 1029 17 86.62 1029 16 87.33 1029 16 87.3
14 1 1028 19 87.32 1028 19 87.33 1029 17 87.3
15 1 1031 14 : 85 .32 1029 19 85.83 1029 17 85.8
16 1 1029 17 87.12 1029 18 87.13 1029 19 87.1
17 1 1028 17 85.92 1027 18 86.53 1026 21 86.6
18 1 1029 18 88.42 1028 20 88.13 1028 21 88.1
19 1 1029 19 85.32 1029 19 85.83 1030 16 85.3
20 1 . 1028 19 89.6i 2 1028 21 89.221 1 1033 12 82.3
2 1030 16 82.93 1030 16 83.5
22 1 1030 15 83.12 1030 15 83.13 1030 15 84.8
150
Table E -4 . Calculation of V(B), Hot Air
' 1-2 (Tg-Tp)" ( i l ' i 2)2
V(F)- a '
v (w D) V(B)
Experiment SetNumber Number__________(lb^/hr^)_________ (lb^/hr^) (lb^/hr^)
13 1 0 . 0234 0 . 0199 0 . 04 332 0. 0234 0 .0200 0 . 0434
' 3 0 . 0234 0 . 0200 0 . 043414 1 0 . 0233 0 . 0202 0 . 0435
2 0 . 0233 0 .0202 0 . 04353 0 . 0234 0 .0205 ' 0 . 0439
15 1 0. 0235 0 . 0191 0 ,04262 0 . 0233 0 .019 4 0 . 04273 0 . 0233 0 .0194 0 . 0427
16 1 0 . 0233 0 . 0200 0 . 04332 0 . 0233 0 .0200 0 . 04333 0 . 0233 0 . 0200 0 . 0433
17 1 0 . 0233 0 . 019 6 0 . 04292 0 . 0233 0 . 0199 0 . 04323 0 . 0232 0 . 0199 0 . 0431
18 1 0 . 0233 0 .0 207 0 . 04402 0. 0233 0 .0205 0 . 04 383 0 . 0232 0 . 0205 0 . 0437
19 1 0 . 0233 0 . 0192 0 . 04252 0 . 0233 0 . 0194 0 . 04 273 0 . 0234 • 0 .0192 0 . 04 26
20 1 0 . 0233 0 .0212 0 . 04452 0 . 0232 0 . 0210 0 . 0442
21 1 0 . 0236 0 . 01 78 0 . 04142 0 . 0234 0 . 0181 0 . 04153 0 . 0234 0 .0184 0 . 04 18
22 1 0 . 0234 0 . 0183 0 . 04172 0. 0234 0 . 0183 0 . 04173 0 . 0234 0 .0189 0 . 0423
APPENDIX F
VARIANCE OF F
Feed rotameter calibrat ion data and the variance of F a ssoc ia ted
with each rotameter reading are shown in Table F - l . Based on the data
tabulated, it was considered appropriate to pool the va r iances , since
there was no reason to suspec t there would be any signif icant difference
between individual v a r i a n c e s . Therefore,
V(F) = V = 0.0210 + 0.0290 + 0.0139 + 0.0304 + 0.02615
or V(F) = 0 .0241.
151
152
Table F - l . Calculation of V(F)
F
Rotameter z cc i
F . (F-F)
[ O C X ' I cc |
(F-F)
c c ^
2 V(F)
[ l b 2 l
Readinq I min Iminj I mini i m i n ^ hr 2,
40.0 40.0 39.1 0.9 0.81 . 0 .021038.5 0 .6 0 .3638.5 0 .6 0 .3640.5 1.4 1.9638.0 1.1 1.21
60.0 60.0 58.5 1.5 2.25 0 .029059.5 1.0 1.057.5 1.0 1.058.5 0 057.0 1.5 2.25
79.0 78.0 77.9 . 0 .1 0.01 0 .013977.0 0.9 0 .8179.0 1.1 1.2178.5 0 .6 0 .3677.0 0.9 0.81
100.0 100.5 99.3 1.2 1.44 0 .30499.5 0 .2 0.0497.5 1.8 3 .24
100.5 1.2 1.4498.5 0 .8 0 .64
129.0 129.5 128.1 1.4 1.96 0 .261129.5 1.4 1.96127.5 0 .6 0 .36127.0 1.1 1.21127.5 0 .6 0 .36
APPENDIX G
VARIANCE OF Wg
The rotameter calibrat ion data and the variance of WS
corresponding to each rotameter reading are shown in Table G - l .
There was no apparent reason why the variances should no t be pooled.
Therefore,
V(WS) = Vp = 16(2.02) + 3(1.41) + 4(1. 26) + 3(1. 11) + 3(1.55). 29
or V(WS) = 1 .71 .
..15.3
Table G - l , Calcula tion of V(W0)U
154
RotameterReading
WS
(lb/hr) (lb/hr)
(Ws -w s )
(lb/hr)
(Ws - Ws ) 2
(Ib^/hr^)
V(Wg)
(Ib^/hr^)
47.0 38.2 . 40.3 2.1 4 .41 • 2.0238.9 1.9639.2 1.2139.4 0 .8139.4 0 .8139.4 0.81 :39.6 0.4939.7 0 .3639.9 0 .1640.0 0.0940.3 041.3 1.041.3 1 .041.5 1.4441.8 2.2541.9 2 .5643.9 12.96
OCO*xr 34.1 35.6 1.5 2:25 1.4135.2 0 .4 0 .1636.5 0.9 0 .8136.6 1.0 1.00 .29.2 1.3 1.69
.35.0 28.9 27.9 1.0 1.00 1.2627.5 0.4 0 .1627.2 0.7 0.4926.5 1.4 1 .9619.8 1.1 1.21
25.0 19.4 18.7 0 .7 0.49 1.1118.0 0 .7 0.4917.7 1.0 1.0014.1 1.2 . 1.44
22.0 14.6 15.3 0 .7 0.49 1.55. 15.7 0 .4 0 .16
16.9 1 .6 2 .56
APPENDIX H
VARIANCE OF T2
In calculat ing a variance for T, , it was first necessary to2
determine the maximum error which could have occurred in values of .
From Appendix C ,
H2 = HjtF-Bj/Wjj
Then, the variance of H, was given by
V(H,) = V(H.) + V/F-B\UD/
or
V(H2) = VtH^VfF-Bj/Wp2 + (F-B)2V(Wd ) /W d 4 (111)
The term V(F-B) is given by
V(F-B) = V(F) + V(B) = 0.0671
and
V(WD) = 2 . 7 9
To calculate the maximum value of V(H^); the maximum value of (F-B),
equal to 3 .7 , and the minimum value of equal to 3 0 .3 , were used
in Equation 111. From the humidity chart , it appeared that the maximum
error in (taken as equal to three standard deviations) was approx
imately equal to 0 .006 lb H^O/lb BD air , and V(H^) was taken equal to
155
156
4 x 10"6 (lb H20 ) 2/ ( l b BD air)2 . Then, V(H ) was given by
V(H ) = 4 x ICT6 + 0.0671 + 13.7 (lb H2Q)2(30.3)2 (30.3)4 (ib BD air)2
or
V(H2) = 10~^(lb H20 )^ / ( lb BD air)^ (approximately)
and the maximum error in (taken as equal to three standard deviations)
was taken equal to 0.03 lb H20 / l b BD air.
The air leaving the evaporator was e ssen t ia l ly sa tu ra ted , as
determined from the values of B, , F, , and T2 . The humidity chart
was examined in the region corresponding to nearly sa turated condit ions,
and it was determined that in T , 12°F was the maximum error (equal2
to three standard deviations) which would have occurred if was in
error by as much as 0 .03 lb H20 / l b BD air. Hence, the variance of
Ta was taken equal to 160F2 .M2
APPENDIX I
HEATER CONSTRUCTION
A schematic diagram of the heaters is shown in Figure T-fl,.
To make those h ea te rs , appropriate sect ions of s ta in le s s s tee l pipe
were first insulated with asbes tos c lo th, and then around the cloth, the
appropriate number of coils of 20 gauge nichrome wire were wrapped
(cloth and wire being held in place by hose clamps).
Galvanized iron pipe fittings were used to connect the lengths
of s ta in le s s s tee l pipe. All hea ters , to include pipe and f i t t ings, were
packed with aluminum sh a v in g s , which were held in place by small
sc reens inserted in appropriate f i t t ings.
Pipe fi ttings e ither were insulated with two layers of one-inch
thick sect ions of magnesi te pipe insulat ion, or were insulated by wrap
ping to a similar th ickness with pyrex wool. The a sb es to s cement
sect ions shown in Figure 1-2 were made in an improvised mold. Two
such sect ions were used to insulate the lengths of s t a in le s s s teel pipe
wrapped with nichrome wire.
157
Two-
foot
le
ngth
of
stai
nles
s st
eel-
pipe
158
Variac
Union
Nichrome Heater - coil of 140 turns
Nichrome Heater - coil of 140 turns
N ichrome Heater - coil of 70 turns
Cord toe lec tr ica loutlet
Five-foot length of s ta in less s tee l pipe
Nichrome Heater - coil of 140 turns Nichrome NichromeHeater - coil of 140 turns
Union
Heater - coil of 140 turns
Cord toelectr ica loutlet
Nichrome Heater - coil of 70 turns
Five-foot length of type 304 s ta in le s s s tee l pipe (one- inch , schedule 40) wrapped with a sbes tos cloth and 20-gauge nichrome wire
Figure 1-1. Schematic Diagram of the Heaters
159
xl/ / h\ l / „ 6"2" 4 xlz
/|X /(X
xl' xlz
\ 3 y
V—/K 3
Figure 1-2. Asbestos Cement Sections
NOMENCLATURE
heat t ransfer area per unit volume, f t^ /f t^
heat transfer area per unit volume based on calculat ions for no heat lo s se s to the surroundings, f t^ /f t^
heat t ransfer area per pound of spray, ft 2 / lb
flow rate of bottoms (brine) leaving the bottom of the evaporator, lb /h r
volumetric flow rate of bottoms (brine) from the bottom of the column, c c /m in
condensate flow rate leaving the barometric leg, lb /hr
condensate flow rate from barometric leg , cc /min
heat capaci ty at constant pressure of bone dry air, Btu/lb°F
heat capaci ty at constant pressure of the feed (spraying) so lution, Btu/lb°F
heat capaci ty at constant pressure of pure water , Btu/lb°F
heat capaci ty at constant pressure of water vapor, Btu/lb°F
diameter of the evaporating column, ft
the volume of a given sample of a solu t ion , cc
feed (spray) flow ra te , lb /h r
feed (spray) flow ra te , cc /min
humidity of the air, lb HgO/lb BD air
humidity at sa turat ion, lb HgO/lb BD air
’ humidity at saturat ion for the air entering the evaporator, lb H^O/lb BD air
humidity at saturat ion for the air leaving the evaporator, lb H O / lb BD airLhumidity of the air entering the evaporator, lb H^O/lb BD air
humidity of the air leaving the evapora t ior , lb HgO/lb BD air
heat t ransfer coeff icient , Btu/hrft^op
heat t ransfer coefficient based on calculat ions for no heat lo sses to the surroundings, B t u / h r f t ^ b p
mean heat t ransfer coeff icient , Btu/hrft^op
specif ic values of the product of h and a , Btu/hrft^°F
mean of severa l values of ha, Btu/hrft^°F
mean of several values of h*a* , Btu/hrft^°F
different values of ha: corresponding to given experiments and se ts of d a t a , Btu/hrft^0F
the enthalpy of the humid air, Btu/lb
enthalpy of brine leaving the evaporator, Btu/lb
enthalpy of bone dry air in the humid a ir , Btu/lb BD air
enthalpy of bone dry air in the humid air entering the evaporator, Btu/lb BD air
enthalpy of bone dry air in the humid air leaving the evaporator, Btu/lb BD air
enthalpy of feed (spray) entering column, Btu/lb
enthalpy of water vapor in the humid air , Btu/lb H^O
enthalpy of water in the humid air entering the evaporator, Btu/lb H^O
enthalpy of water in the humid air leaving the evaporator, Btu/lb H20
enthalpy of saturated steam at Tg, Btu/lb
enthalpy of the hot gas entering the evaporator, Btu/lb
enthalpy of gas leaving the evaporator, Btu/lb
heat lo sses to the surroundings, Btu/hr
constant for a given rotameter float (gas temperature ofT ^ , f F / h r
constant for a given rotameter float (gas temperature of 460°F), ffz /hr
constant for a given rotameter float (air at 460°F),ftV hr
constant for a given rotameter float (steam at 460°F), ft i / h r
number of tr ials
moles of hot gas at temperature
moles of hot gas at 920°R
atmospheric pressure , in .Hg
heat t ransfer r a t e , Btu/hr
heat transfer rate which was assumed should resul t if there were no heat lo s se s to the surroundings, Btu/hr
gas cons tan t , in .H gf t^ / lb moles°R
Reynolds number
standard error of the term in parenthesis
temperature of the air, °F
adiabatic saturation temperature , °F
adiabatic saturat ion temperature of the air entering the column, °F
adiabat ic saturat ion temperature of the air leaving the evaporator , °F
temperature , °R
temperature of feed (spraying solution) entering.the column, °F
temperature of feed (spraying solution) entering the column, °C
saturation temperature of pure water for the pressure inside of the column (taken equal to that for atmospheric p ressure) , °F
temperature of the hot gas entering the evaporator, °F
temperature of the hot gas entering the evaporator, °C
temperature of the gas leaving the evaporator, °F
temperature of the gas leaving the evaporator, 0C
average bulk velocity of hot gas flowing through the column, f t /h r
the variance of the term in parenthesis
volume of nQ moles of the hot gas at temperature T^., ft^
volume of n^ moles of the hot gas at temperature 1^ , ft^
evaporator volume, ft^
specif ic volume of steam at temperature T , f t^ / lb1
specif ic volume of steam at 460°F, f t^ / lb
specif ic volume of s te a m , f t^ / lb
flow rate of the hot gas corresponding to a given rotameter reading and a hot gas temperature other than 460°F, lb /hr
flow rate of the hot gas corresponding to a given rotameter reading and a hot gas temperature of 460°F, lb /hr
flow rate of bone dry air flowing through the evaporator, • lb /hr
flow rate of air at 460°F, lb /h r *•
superheated steam flow r a t e , lb /h r
flow rate of steam at 460°F, lb /hr
the weight of H^O in volume E , gm
the weight of NaCl in volume E , gm
concentration of NaCl in spraying solut ion, percent by weight
concentration of NaCl in bottoms (brine) solution, percent by weight
ratio of concentration of NaCl in bottoms (brine) solution to that in feed (spray) solution -
arithmetic mean temperature d i f ference , °F
arithmetic mean temperature difference (air) , °F
arithmetic mean temperature difference (s team), °F
the latent heat of vaporizat ion of water at atmospheric p re s su re , Btu/lb
the latent heat of vaporizat ion of water at temperature T, , Btu/lb %
the latent heat of vaporizat ion of water at temperature TA , -Btu/lb
the latent heat of vaporizat ion at T^, Btu/lb
v iscos i ty of hot gas at atmospheric pressure and tempera ture , Ib/fthr
densi ty of the hot gas at atmospheric pressure and - temperature , lb /f t^
densi ty of the hot gas at temperature other than 460°F, l b / f t 3
densi ty of bottoms (brine) solution, gm /cc
densi ty of the hot gas at 460°F, l b / f t 3
densi ty of the air at 460°F, l b / f t 3
densi ty of feed (spraying) solution, gm/cc
densi ty of float material, l b / f t 3
densi ty of pure water, gm /cc
densi ty of steam at 460°F, l b / f t3
number of degrees of freedom
number of degrees of freedom assoc ia ted with ha^ and ha respect ive ly
REFERENCES CITED
Bird, Byron R. , Warren E. Stewart, and Edwin N. Lightfoot. Transport Phenomena. New York: John Wiley and Sons , I n c . , 1960/
Charles worth, D . H. and W . R. M a rsh a l l , Jr. "Evaporation from Drops Containing Dissolved Sol ids ," A. I. Ch. E. Journal , Vol. 6,No. 1 (March 1960).
C h u , Ju Chin, Stanley Finlet , William Hoerrner, and Min Shuey Lin. "Drying with Superheated Steam-Air M ix tures ," Industrial and Engineering C hemis try , Vol. 5, No. 3 (March 1959).
Chu, Ju Chin, A . M . Lane, and D. Conklin. "Evaporation of Liquids into Their Superheated Vapors," Industrial and Engineering Chemistry , Vol. 45, No. 7 (July 1953).
Cox, N. D. Ph.D. D isser ta t ion . University of W iscons in , Madison (1962).
Cox, N. D. Personal Communication. University of Arizona,. Tucson (1967).
D avies , Owen L. Sta t is t ica l Methods in Research and Production. New York: Hafner Publishing Company, 1961.
Dickinson, Dean R. and W. R. Marsha l l , Jr. "The Rates of Evaporation of Sprays ," A. I . Ch. E. Journal , Vol. 14, No. 4 (July 1968).
Dlouhy, Jan and W. H. Gauvin. "Heat and Mass Transfer in Spray Drying," A. I. Ch. E. Journal , Vol. 6, No. 1 (March 1960).
Foust, A. S . , L. A. W enzel , C. W. Clump, L. M aus , and L. B.Anderson. Principles of Unit O pera t ions . New York: John Wiley and Sons, I n c . , 1966.
Himmelblau, David M . Basic Principles and Calculat ions in Chemical Engineering. Englewood Cliffs: Prentice Hall, I n c . , 1962.
166
167
Manning, W. P. and W. H. Gauvin. " Heat and M ass Transfer..to Decelerating Finely Atomized Sprays ," A. I . Ch. E. Journal ,Vol. 6, No. 2 (June, 1960) „
■ McAdams , William H. Heat T ransmiss ion New York: McGraw-Hill Book Company, I n c . , 1954.
McCabe, Warren L. and Julian C. Smith. Unit Operations of ChemicalEngineering. New York: McGraw-Hill Book Company, I n c . , 1956.
Perry, John H. Chemical Engineers' Handbook. 4th ed . New York: McGraw-Hill Book Company, Inc. , 1963/
Ranz, W. E. and W. R. Marshall J r . , "Evaporation from Drops ,"Chemical Engineering Progress , Vol. 48, No. 3 (March 1952).
Skoog, Douglas M. and Donald M. W est . Analytical Chemistry . New York: Holt, Rinehart, and Winston, 1965.
Smith, J. M. and H. C. Van N e ss . Introduction to Chemical Engineering Thermodynamics . New York: McGraw-Hill Book Company, I n c . , 1959.
Weinberg, Sidney. "Heat Transfer to Low Pressure Sprays of Water ina Steam Atmosphere, " Proceedings of the Inst i tu t ion of Mechanical Engineers . Vol. .162 (1952) .
W enzel , Leonard and Robert R. White. "Drying Granular Solids inSuperheated Steam," Industrial and Engineering Chem is t ry , Vol. 43, No. 8 (August 1951).
Zimmerman, Oswald Theodore. Psychometric Tables and C h a r ts . Dover: Industrial Research Service, 1964.
