- Email: [email protected]
H2O solutions
Atmospheric and sub-atmospheric boiling of H,O and LiBr/H,O solutions W . W . S. C h a r t e r s ,
V. R. M e g l e r ,
W . D. C h e n a n d Y. F. W a n g
Key words: refrigerant, lithium bromide, water
Ebullition & la pression atmosph6rique et au-dessous de H20 et de solutions de LiBr-H20
On consid6re diverses 6quations pour corr#/er le transfert de chaleur ~ 6bulfition nuclide et /'on a adopt6 /a m6thode de Rohsenow. Les formes choisies pour I'6quation portent les num6ros (2) et (3) et sont adapt6es ~ un certain nombre de r~sultats de la Iittdrature concernant /'~bu/lition sur des surfaces m#ta//iques /isses outre /es nouve//es va/eurs mesur#es par/es auteurs. Ces #quations uti/isent le nombre de Prandt/ par unit# de puissance, se/on /es recommandations de Rohsenow. On obtient une mei//eure adaptation aux r~su/tats en ~liminant cette restriction.
On a mesur# /es coefficients de transfert de cha/eur oour un tube de cuivre vertica/ de 16 mm de diam#tre ext#rieur et de 250 mm d e / o n g entre de I'eau disti/l#e et des solutions de bromure de fithium et de I'eau ~ des pressions r#duites de 9 ~ 100 kPa. Le chauffage est #/ectrique et /es temperatures sont mesur#es par thermocoup/es. Les r#su/tats du tab/eau I expriment les flux de cha/eur par rapport ~/a force d'entraTnement due aux temperatures.
L'6quation recommand6e qui corr#le 143 points exp6rimentaux pour des surfaces//sses de p/atine, de cuivre et de/alton porte/e num6ro (4); el/e donne un 6cart avec la norme de 0.0030 et uti/ise une seu/e valeur de C~f.
Measurements are presented for the nucleate pool boiling of LiBr-HzO solutions at concentrations typically used in LiBr-HzO air conditioning systems. A commercial grade copper tube was used for all tests as being typical of the testing surface likely to be used in a commercial plant.
The object of this work was to correlate nucleate boiling heat transfer for pure w a te r and aqueous solutions using Re, Pr number expressions and thermophysical properties of the boiling liquid and vapour at a clean surface. Such an equation is proposed and tested.
Nomenclature specific heat of saturated liquid kJ kg -1 K -1 CI C d, C n, Csf
Db f g go Gb hfg
kl n
P Pr
coefficients diameter of bubble as it leaves heating surface, m frequency of bubble formation, I/s acceleration of gravity 9.81 m s -2 conversion factor g o = l , when SI units are used mass velocity of bubbles at their departure from heating surface, kg s -1 m -2 latent heat of evaporation, kJ kg 1 thermal conductivity of saturated liquid,
p~
k W m -1 K -1
Pv
number of nucleation sites
/~
The authors are from University of Melbourne, Mechanical Engineering Department, Parkville, Victoria, Australia, 3052. YFW is currently on leave from China University of Science and Technology, Hefei, Peoples Republic of China. Paper received 5 August 1981
Volume 5 Num6ro 2 Mars 1982
q/A r s Ts Tw T× /~
pressure, kN m -2 C/~ Prandtl n u m b e r = - k heat-transfer rate per unit heating surface area kW m -2 exponent of equation (1) exponent of equation (1) saturation temperature of liquid, °C temperature of heating surface, °C Tw -Ts, K bubble contact angle surface tension of liquid-vapour interface, N m -1 density of saturated liquid, kg m -3 density of saturated vapour, kg m -3 viscosity of saturated liquid, Pa s
In boiling heat transfer it is still difficult to predict the heat transfer coefficient with any degree of accuracy despite many intensive investigations of the boiling process. Nucleate boiling is the most interesting regime for technical applications, and 01 40-7007/82/020107-0853.00 @1982 Butterworth & Co (Publishers) Ltd and IIR
107
considerable work has been done on the mechanism of heat transfer from the heating surface to the liquid.
good agreement with experimentally observed values when the outer contact angle of the bubble/~ at the instant of break away is known.
The formation and consequential growth of bubbles leading to break off and convective rise form some of the essential processes of boiling which govern the heat transfer. Unfortunately, an exact analytical description of those processes is not possible, and approximations may be obtained only by making simplifying assumptions which need to be confirmed by experimental results. It is extremely difficult to predict the number of points of origin in the bubble column per unit area of heated surface and the frequency of bubble formation. These data are very important for overall prediction of boiling heat transfer and are generally obtained from experiment only, by analysis of high speed film taken during the experi ment.
The total heat transfer process is dependent on the frequency of bubble formation, f, and on the number of nucleation sites n. The mean film coefficient, h, and the corresponding Nusselt number, Nu, are therefore functions of unknowns f o n d n, both of which depend upon the heated surface roughness and the properties of the boiling liquid.
Previous work
Jakob 1 suggested, following the work of Fritz, that the Nusselt number for boiling should be simply expressed as a function of the heat flux and an undefined empirical constant. Rohsenow 2 correlated a range of experimental results with a theory based on bubble formation in 1952. The Reynolds number, Re, is defined as /
Re=G °=c0-" b
Past investigations of boiling properties have concentrated primarily on experiments with pure liquids especially distilled water. Some studies have used refrigerant fluids because of their low boiling point and low surface tension. Very few results are readily available for boiling heat transfer and boiling properties of solutions of individual components such as K2CO 3, NaCI or LiBr in water at various concentrations. The early investigations into boiling heat transfer were mostly concerned with the mechanism of bubble formation and the forces acting upon the bubble during its formation and its detachment from the wall. The results from this pioneering work still form the backbone of knowledge today and the formation of the empirical equations used to predict boiling heat transfer despite the considerable amount of additional research still being done in this field. The dynamics of individual bubbles have been well defined and described 12 and the theoretical data are based on the experimental observations for single bubbles. The theoretically calculated results show
2~
\v2
where G b is the mass velocity of the bubbles at their departure from the heating surface. The Reynolds number therefore contains as unknowns, the quantities f, n and/~. The Nusselt number, Nu, is then expressed as ~_
.'~1/2
and therefore the Stanton Number St as, C,Tx Fq/A / ~ ~1/2]'/C,1~s S[ 1_ hfg -CsfLl~lhfgtg(p I -~Pv)) J t ~ l l ]
(1) Where Csf is a correlation coefficient which varies with the nature of the heating surface-fluid combination. Csf therefore, contains the unknown angle ,8 and is influenced by the undefined heating surface roughness. The results are often plotted in the form [ ( q l A ) l # t h j [ ~ / g ( p I -pv)] ~/2 versus St 1pr 17
Circulating pump
~_ with thermostat
L
Cooling water
Dg to voltmeter r ~ I~1 Precision Condenser Manometer
.' I Slide
resistance
Fig. 1
Schematic diagram of the test apparatus
Fig. 1 Sch#rna de I'appareil exp#rimenta/
108
Power supply
Experimental apparatus/present investigation A schematic diagram of the experimental apparatus is given in Fig. 1. The evaporator was submerged in a thermostatically controlled water bath in order to provide and maintain the desired saturation temperature from the test liquid inside the evaporator. Both the evaporator and the water tank were made of glass and permitted direct observation and video taping of the bubble formation over the heated surface.
International Journal of Refrigeration
Table 1. Boiling data Tab/eau 1. R#sultats concernant /'#bul/ition q/A, kw m -2
Tw -T s (average), °C
25% LiBr-water solution at 9.3 kN m -2 4.52 10.2 5.47 10.5 10.74 1 2.8 8.50 10.8 15.71 13.1 12.97 1 3.8 21.36 14.9 6.35 11.3 32.47 1 6.1 21.43 14.3 10.75 13.6 25% LiBr-water solution at 18.7 kN m -2 10.74 11.4 21.26 12.8 32.61 1 5.9 8.28 12.6 1 5.79 13.0 6.35 10.5 26.25 1 3.5 1 2.71 11.7 24.01 1 2.7 33.41 14.5 18.71 10.9 56,5% LiBr-water solution at 9.3 kN m -2 3.24 8.8 10.76 13.0 6.37 10.7 4.22 9.5 8.31 12.2 6.38 9.8 15.55 1 6.0 10.77 1 3.5 21.24 16.4 32.57 18.8 The distilled and degassed liquid evaporated on the outside of an internally heated copper test tube placed vertically in the evaporator. The vapour generated passed to a tube-and-shell condenser and condensed when heat was removed by circulating cooling water. By controlling the cooling water flow rate, a constant pressure was maintained. The condensate was returned to the evaporator at the end of experiments by heating the condenser and cooling the evaporator. The heating unit consisted of a 16 mm od clean, commercial grade copper tube 250 mm long fitted with an internal resistance wire heater heated by a direct current supply. The electrical input was regulated by a slide resistance. The heat flux at the surface of the test tube was calculated from measurement of the current through, and the voltage drop across, the heater using a precision ammeter and a digital voltmeter. The accuracy of the heat flux measurement was estimated to be within 4-1%. The surface temperature of the tube was measured directly by six calibrated thermocouples. The
Volume 5 Number 2 March 1982
q/A, kw m -2
Tw - Ts (average), °C
Distilled water at 101.4 kN m -2 33.57 7.94 10.74 16.04 21.44
7.0 3.8 5.1 5.5 5.9
Distilled water at 47.4 kN m -2 10.76 21.40 42.81 15.66 26.28 44.1 7
4.4 5.5 7.0 4.9 5.7 7.3
Distilled water at 19.9 kN m 2 10.73 21.37 31.78 1 5.69 26.19 44.06
5.2 6.6 7.4 6.6 7.5 8.7
Distilled water at 9.3 kN m -2 2.62 11.74 7.30 40.45 12.93 18.74 25.43 5.32 8.31 33.39 10.75 21.39 10.99 21.28
4.8 6.5 5.4 9.7 7.1 7.5 7.9 5.7 6.3 9.8 7.5 8.1 9.2 12.6
thermocouples were trapped longitudinally between the test tube and an inner copper tube which housed the resistance heater, the rest of the annulus being filled with solder. The bulk fluid temperature was measured with five calibrated thermocouples positioned at various depths below the surface of the test liquid. This method proved quite satisfactory, because at low saturation pressure the temperature difference between the tube wall and the boiling liquid was quite large. The maximum error in measurement of the temperature difference between the tube wall and the boiling liquid was estimated to be +0.25°C. The pressure in the closed system was measured with a closed end mercury filled manometer.
Test runs/experimental results Boiling experiments were conducted with LiBr-H20 solutions and with pure water. LiBr-H20 solutions at two different concentrations were boiled at low pressures using a pressure range between 9.3 and 18.7 kN m-< ie at approximately 0.1 and 0.2 atm
109
Table 2. Physical properties of L i B r - w a t e r solution 3 Tableau 2. Propri~t~s physiques de la solution de LiBr-eau '~ LiBr, wt%
p, t, kN m 2 °C
Ci, #t, kJ kg 1 K 1 Pa s
kl, kWm ~ K -1
o, N m 1
p r, kg m 3
Pv, kg m -3
Pr
25
1 8.67
66.0
2.90
0.000574
0.07!
11 81
0.110
3.42
2583
25
9.33
50.0
2.88
0.000842
0.000562
0.074
1196
0.063
4.32
2596
56.5
9.33
84.2
1.83
0.001 936
0.000470
0.077
1 620
0.061
7.53
2734
0.000678
hfg kJ kg-
Table 3. Physical properties of distilled w a t e r 4 Tableau 3. Propri~t~s physiques d e / ' e a u d/st///~e 4 P~, kg m -3
Pv, kg m 3
Pr
htg
0.0588
961.54
0.598
1.723
2256.9
0.000670
0.0625
971.82
0.29
2.1 0
2308.8
0.000653
0.0660
983.28
0.1 3
2.96
2358.6
0.000643
0.0687
990.10
0.062
3.96
2396.4
p, kN m 2
t, °C
C, I~l, kJkg 1K 1 Pa s
kl, kWm-lK
~, 1 N m 1
101.4
100
4.216
0.000278
0.000681
47.4
80
4.1 97
0.000350
19.9
60
4.1 85
0.000462
44.5
4.1 80
0.000603
9.3
absolute. Experiments using distilled water at pressures of 9.3, 1 9 . 9 , 4 7 . 4 kN m 2and at atmospheric pressure were carried out to give a direct comparison. The phenomenon of bubble formation and heat transfer observed were similar to those described in the literature for liquids at saturation temperature. The temperature of the boiling liquid was uniform throughout. Bubbles of different size were observed at a single fixed value of heat flux, the bubbles being relatively larger at lower pressure than that at higher pressure. The number of nucleation sites increase with increasing heat flux. The experimental results are listed in Table 1. The physical properties used in an analysis of LiBr solutions 3 are shown in Table 2 and those of distilled water 4 in Table 3.
Experimental
analysis
Although the Rohsenow expression (1) has been generally assumed to be of w i d e validity and has been extensively used for the correlation of pool boiling heat transfer, it was derived originally for pure liquids at atmospheric and high pressures and values of C~f quoted in literature is limited to water, organic compounds and K2CQ 3 solutions (Table 4). The parameter Csf varies with concentration and is of great importance for an accurate prediction of boiling heat transfer, since it has an influence of third power on heat transfer rate. In addition, C~f depends on the bubble angle/~, at detachment and the nature of the heating surface. The experimental results were analysed by plotting CiT×/hfg x 1 / P r ~7 against [(q/A)/#lhfg] x [~/g(Pl -Pv)] 1/2
110
kJ kg 1
as shown in Fig. 2. The resulting plot shows t w o curves, one for each concentration tested of the LiBr-H20 solution. The values of Csf are Csf=O.O017 for LiBr concentration of 56.5% by w e i g h t and Csf=O.O052 for 25% by weight. The values could not be correlated to a single curve as predicted by Rohsenow's expression. Rohsenow recommended 5 for water a change of exponent from s = 1 . 7 to s = l . 0 . This led us to an examination of available data in the literature as well as our own experimental data from the present investigation. It has, therefore, been shown that a single curve fit for various LiBr-H20 concentrations may be forced by varying the exponent s.
Table 4. Values of Csf and S w i t h r = 0 . 3 3 , r e c o m m e n d e d by R o h s e n o w 5 Tableau 4. Valeurs de Csf et de S avec r = 0 . 3 3 , recommand#es par Rohsenow 5 Surface combination
Csf
S
Water- nickel 10
0.006
1.0
Water- plati num 6
0.01 3
1.0
Water-copper 6
0.01 3
1.0
Water- brass 7
0.006
1.0
CCI4-copper 8
0.01 3
1.7
Benzene-chromiu m 9
0,O1 0
1.7
n-pentane chromium 9
0.01 5
1.7
Ethyl alcohol-chromium 9
0,0027
1.7
Isopropyl alcohol-copper 8
0,0025
1.7
35% K2CO3-copper 8
0.0054
1.7
50% K2CO3-copper 8
0,0027
1.7
n-butyl alcohol-copper 8
0.0030
1.7
Revue Internationale du Froid
0.1
I00 P, kNm -2
,Or
ot
o
101.4
1.723
z~
2641
0.852
•
5309
0.861
7"
•
8309
0946
x
11047
1.061
o
16996
1.62
¢D +
/ -~N
o
-IN
o,÷
/
0.01
+
gD
o/
+
+
r =0.33 o o
o
• = 0.33 I•
~ 0.(7t31
•/,.
s =1.7
/o
1.0
C,f = 0.0017
/
From Rohsenow2,deto of Addoms 6, pool boiling,plotinum wire - weter
o• Li Br % by wt
P, kNm-z
o
;>5
9.33
+
;>5
18.67
•
56.5
9.33
i
I
O.OOOI
I
=0.0,3 • = 0.33
xl~,I • /
f N
A
•
•x
c,f =0.005;>
P o /oI
T
x A • 10
I
I
I I Ill
I
I
i
i
i
i i i I
i
i
i
i
i
i
I.O
0.1 hfg P f 1.7
I
O.OOI
O.OI
C,rx
Fig. 3a Correlation of Addoms' data, using exponent value s=1.7 Fig. 3a Correlation des rbsu/tats d'Addoms, en uti/isant pour valeur de/'exposant s= 1.7
hfg Pr t7
Fig. 2 Experimental data for LiBr-watersolution vertical copper tube using Rohsenow' correlation
1
001
on smooth I00
Fig. 2 R#su/tats exp#rirnentaux p o u r / a so/ution de LiBr-eau sur un tube de cuivre vertica/ /isse en uti/isant /a corr#/ation de Rohsenow
The data of Addoms 6 for boiling water on a platinum wire, used also by Rohsenhow 2, have been plotted on Fig. 3a, using the exponent s = 1 . 7 giving a standard deviation for Csf of 0.00295. The same data are shown in Fig. 3b, using the exponent s = l . 0 , resulting in an improved standard deviation of 0.00223. The change of the Prandtl number exponent, s, has reduced the standard deviation thereby improving the fit of the line to the data. In spite of the fact that the experiments of Addoms covered a large range of pressures, from 101.4 to 1 6 996 kN m 2, the range of corresponding Prandtl numbers was actually very small, ranging between 0.852 and 1.723 ie very near unity. This will naturally limit the influence of Prandtl number and that of its exponent, s. Due to the change of the exponent, most of the points plotted shifted towards the lower values on the horizontal axis. The largest change occurred for the two values of highest Prandtl numbers, P r = 1 . 7 2 3 and 1.62, due to the change of the exponent s. This illustrated the influence of the Prandtl number exponent s, even in the range of low Prandtl numbers. The influence will be much more pronounced, when operating in the range of high Prandtl numbers naturally encountered during boiling at low pressures.
Volume 5 Num6ro 2 Mars 1982
-..~¢u >
10
•~/o
•
x / - ~ ~
sr
~),,
r
=0.013 =
0.33
s=l.0
o 1.0
/
a
x
°
./o 0, I
I
I I I I
O.OI
I
I
I
I I I I1[ O.I
L
I
L L I
I.O
c~ rx hfg
ii
Pr
Fig. 3b Correlation of Addoms' data, using exponent value s=l .0 Fig. 3b Correlation des r#su/tats d'Addoms, en uti/isant pour va/eur de/'exposant s = 1.0
111
1.0
with the exponent r = 0 . 3 3 , Csf is equal to 0.01 30, or with r = 0 . 3 7 , Csf is 0.0125. Both these values fit the data equally well as shown in Fig. 5. Therefore for boiling water, the relation is either in the conventional form with an exponent of 0.33 from previous investigations, which is based on a least square fit of 106 experimental data points.
/ -~
[- ~/A
C~T×
q/
/
o"
"
\ 1/2q0.33
~
I
hfW=°°13°L fi , tg(p, pv)} J
0.1
pro
(2)
x
x
:> [3
0.53 s =1.7
AZ~
0
x /•
or
C7x=0.0125 hf~
o
A
/
0.01
./ P,kNn~2 154.2 97.5
1.55 1.75
o
60.25
2.03
c, x
29.75 14.17 :3.84
2.58 3,53 5.73
+ z~
[3
o.oa
J~LI
[
i
J
i
n nnll
0.001
)1,21o37
Pr ~.° (3)
(7
g (P. ~Pv)
These relationships are then taken as applicable for all smooth clean metal surface liquid combinations, as on the basis of the above data it can be seen that the change in Csf is negligible.
Pr
I
q/A
In t h e a b o v e analysis we have deliberately omitted the boiling data obtained for a water-nickel surface, 1° originally used by Rohsenow in his analysis. Those data were obtained under forced convection boiling conditions and with significant subcooling. Although Rohsenow considered that the I
I
IO0
0.01
I
C,Tx hi•l Pr o.85
Fig. 4 Correlation of Cryder's data 7 for water-brass pool boiling using exponent value s=1.7
e ~• l ~ . ~
IO
C=f=0.0125 r =0.37 s =1.0
Fig. 4 Correlation des r#su/tats de Cryder 7 p o u r / ' # b u l l i t i o n fibre eau-laiton, en utilisant p o u r valeur d e / ' e x p o s a n t s = 1.7 •l
The value of Csf for a water-brass surface has been quoted in the literature 2 as Csf=O.O06. This value was originally determined with the Prandtl exponent s = 1 . 7 based on results using atmospheric and higher pressures. The value of Csf remained unchanged with the change of Prandtl exponent to s = l . 0 . Using this value of Csf, good correlation was obtained with the experimental results in the region of high pressures (corresponding to low Pr). However, a large discrepancy was shown, when attempting to correlate the results at very low pressures, especially when the Prandtl number had values of P r = 3 . 3 7 and 5.73, as shown in Fig. 4. It is interesting to note that Rohsenow neglected to use data for P r = 5 . 7 3 in his original paper. The boiling data for water on surfaces of platinum, copper and brass, from different sources, 79 also used by Rohsenow, are shown in Fig. 5, which includes also our experimental results at low pressures and therefore at high Prandtl numbers. The range of pressures is 3.84 to 16996 kN m 2 and the corresponding Prandtl numbers P r = 5 . 7 3 down to 0.852. This presentation assumes that a Prandtl exponent of s---1.0 is valid. The analysis shows that it is possible to correlate all the results to a single line with one single value of Csf. On the basis of statistical analysis, assuming s = l . 0 , then
112
• A
LO
e~l/! ./P • ~
~
C,~ =0.013
~ ~ o
s =1.0
0.1
~." x/"/ .~/
0.01
Fluid-heating p kNm-2 surfgce ' Pr • Water-platinums 101.4-16996 0.852-1.723
//
-
/. " x " // // I
0.001
Water-~er"
101.4
Q Water-brass7 x Water-copper
I.~23
&84-154.2 1.545-5.7 9.53-101.4 1.77_3-3.96
(our data)
1
I
I }IIII
I
I
I
0.01
I IlJll
I
I
I
I I I JI
0.1
1.0
c~ Tx
hfg Pr Fig. 5 Correlation of water pool boiling for different surfaces Fig. 5 Correlation d e / ' # b u / / i t i o n / i b r e d e / ' e a u p o u r diff#rentes surfaces
International Journal of Refrigeration
water and aqueous solutions. This results in the following values: C s f = 0 . 0 1 36, r = 0 . 3 4 0 4 , s = 0 . 8 4 5 1 .
I00
Fluid
• Woter z~ 25% LiBr I0 ---A 56.5% LiBr - ÷ 35% KzCO3 - x 50=/=K2C03
?
P, kNn~z
Pr 0.852 - 5.73 3.42- 4.32 7.5:5 :3.81 6.21
~e
~f~
3.84-16996 9.33-18.67 933 IOIA 101.4
Conclusions
•
The following expression in the form [A] = a [ B ] ' [ C ] s based on complete statistical analysis of 143 groupings of A. B, C and valid for pool boiling of pure water or for evaporation of water from aqueous solutions on surfaces of platinum, copper and brass, is proposed.
~.o el
/.
1.0
~ Tx=O.O136rq/A(
~1/21°'34(ClIJ1"~°'85
a
L#~f~\g(P, - p v ) }
c,, = o.o125
I/
(4)
°•~o
This is shown plotted in Fig. 7. The data are predicted well using this expression showing a standard deviation of 0.00298. The equation appears to have a single value of Csf for all smooth surfaces. Further research work is in progress to determine the applicability of the approach for the boiling of other liquids on smooth surfaces.
x ~IP- T M C,f= 0.01:3 xl~ • = 0.33
x ~
s= 1.0
0.OI
.-,,y ,
I
0.0001
l
I
i llAil
\k~-i }
q~Joe
• = 0.37 s = 1.0
0.1
]
le',,
"//,
I00
I
I
I I llll
0.0oi
l
I
I
I IIii
0.01
0.1
,o
c, Tx
h NprO.85
:;
Fig. 6 Correlation for water and aqueous solutions of LiBr and K2CO 3 using exponent value s = 1 . 0
Fig. 6 Correlation p o u r I'eau et des solutions aqueuses de LiBr et K2C03, en utilisant p o u r valeur de I'exposant s = 1.0
effect of subcooling may be neglected, thereby permitting the inclusion of these results in his analysis, we consider that for the present case, these results fall into a special category because of the combined presence of forced convection and significant subcooling. After this the experimental results of boiling LiBr on copper surface were analysed. The basis for analysis is (3) to w h i c h the experimental results have been compared using at the same time some of the data for K 2 C O 3 at two different concentrations. 8 All the data correlate well over the whole range of pressures and concentrations to expressions (2) and (3) as shown in Fig. 6. In all the above relationships the Prandtl number exponent used has been fixed at 1.0 following Rohsenow's recommendation. Vachon et al. 11 determined values for Csf using the method of least squares only after fixing the Prandtl exponent. However, as shown, the value of this Prandtl exponent, s, was changed during the analysis from the value s = 1 . 7 to s = l . 0 . The method of least squares was used to determine simultaneously all the parameters of the equation, ie Csf, r and s for
Volume 5 Number 2 March 1982
"° f
/:
[
~' : t
/.~c,,=oo,36
I'-
eI
"0,[--''~" "
E
/~
r =0.34
:'~/~"
,=0.85
¢%
o.o,k , , L ,/
~
I~" / e ~ L. A 1 :/
O.OOI
w,,,.r "
56.5%LiBr 7.53
~ 25%LiBr
&42-432 + 35%KzCO5 3.81 x 50e~K2C03 6.21
O.01
9.33 9.33- 18.67
101.4 101.4
O.I
1.0
C, rx hfo pr
-0"$5
Fig. 7 Correlation for water and aqueous solutions of L i B r a n d K2CO 3. Csf, r and s were determined using least square method
F i g 7 Correlation p o u r I'eau et des solutions aqueuses de LiBr et de K2C03, Csf ' r et s ont 6t6 d6rermin#s en utilisant la m#thode des plus petits carr#s
113
The authors gratefully acknowledge the facilities provided by the University of Melbourne and the financial backing of the National Energy Research, Developments and Demonstrations Council.
5 6 7
References 1 2 3 4
114
Jakob, M. Heat Transfer, John Wiley & Sons Inc., New York (1949) R o h s e n o w , W. M. A method of correlating heat transfer data for surface boiling of liquids Trans ASME 74 (1952) 969-975 Uemura, T., Hasaba, S. Studies on the lithium bromidewater absorption refrigerating machine Technology Reports of Kansai University 6 (1964) Osaka, Japan H a y w o o d , R. W. Thermodynamic Tables, 2nd Edition, Cambridge University Press (1972)
8 9 10
11
R o h s a n o w , W. M., H a r t n e t t , J. P. Handbook of Heat Transfer, McGraw Hill Inc. (1973) 13 28 A d d o m s , J. N. Heat transfer at high rates to water boiling outside cylinders, Doctoral Dissertation, Massachusetts Institute of Technology (1948) Cryder, D. S., F i n a l b o r g o , A. C. Heat transmission from metal surfaces to boiling liquids: effect of temperature of the liquid on film coefficient Am Inst Chem Eng 33 (1937) 346 Piret, E. L., Isbin, H. S, Two-phase heat transfer in natural circulation evaporators, A/ChE Heat Transfer Syrup St Louis (Dec 1953) Cichalli, M. T., Bonilla, C. F. Heat transfer to liquids boiling under pressure TransAIChE41 (1945) 755 R o h s a n o w , W. M., Clark, J. A. Heat transfer and pressure drop data for high heat flux densities to water at high sub-critical pressures, Heat Transfer Fluid Mech /nst, Stanford, Calif. (1951) Vachon, R. I., Nix, G. H., Tanger, G. E. Evaluation of constants for the Rohsenow pool-boiling correlation, J Heat Transfer, Trans ASME 90 (1968) 239
Revue Internationale du Froid
V. R. M e g l e r ,
W . D. C h e n a n d Y. F. W a n g
Key words: refrigerant, lithium bromide, water
Ebullition & la pression atmosph6rique et au-dessous de H20 et de solutions de LiBr-H20
On consid6re diverses 6quations pour corr#/er le transfert de chaleur ~ 6bulfition nuclide et /'on a adopt6 /a m6thode de Rohsenow. Les formes choisies pour I'6quation portent les num6ros (2) et (3) et sont adapt6es ~ un certain nombre de r~sultats de la Iittdrature concernant /'~bu/lition sur des surfaces m#ta//iques /isses outre /es nouve//es va/eurs mesur#es par/es auteurs. Ces #quations uti/isent le nombre de Prandt/ par unit# de puissance, se/on /es recommandations de Rohsenow. On obtient une mei//eure adaptation aux r~su/tats en ~liminant cette restriction.
On a mesur# /es coefficients de transfert de cha/eur oour un tube de cuivre vertica/ de 16 mm de diam#tre ext#rieur et de 250 mm d e / o n g entre de I'eau disti/l#e et des solutions de bromure de fithium et de I'eau ~ des pressions r#duites de 9 ~ 100 kPa. Le chauffage est #/ectrique et /es temperatures sont mesur#es par thermocoup/es. Les r#su/tats du tab/eau I expriment les flux de cha/eur par rapport ~/a force d'entraTnement due aux temperatures.
L'6quation recommand6e qui corr#le 143 points exp6rimentaux pour des surfaces//sses de p/atine, de cuivre et de/alton porte/e num6ro (4); el/e donne un 6cart avec la norme de 0.0030 et uti/ise une seu/e valeur de C~f.
Measurements are presented for the nucleate pool boiling of LiBr-HzO solutions at concentrations typically used in LiBr-HzO air conditioning systems. A commercial grade copper tube was used for all tests as being typical of the testing surface likely to be used in a commercial plant.
The object of this work was to correlate nucleate boiling heat transfer for pure w a te r and aqueous solutions using Re, Pr number expressions and thermophysical properties of the boiling liquid and vapour at a clean surface. Such an equation is proposed and tested.
Nomenclature specific heat of saturated liquid kJ kg -1 K -1 CI C d, C n, Csf
Db f g go Gb hfg
kl n
P Pr
coefficients diameter of bubble as it leaves heating surface, m frequency of bubble formation, I/s acceleration of gravity 9.81 m s -2 conversion factor g o = l , when SI units are used mass velocity of bubbles at their departure from heating surface, kg s -1 m -2 latent heat of evaporation, kJ kg 1 thermal conductivity of saturated liquid,
p~
k W m -1 K -1
Pv
number of nucleation sites
/~
The authors are from University of Melbourne, Mechanical Engineering Department, Parkville, Victoria, Australia, 3052. YFW is currently on leave from China University of Science and Technology, Hefei, Peoples Republic of China. Paper received 5 August 1981
Volume 5 Num6ro 2 Mars 1982
q/A r s Ts Tw T× /~
pressure, kN m -2 C/~ Prandtl n u m b e r = - k heat-transfer rate per unit heating surface area kW m -2 exponent of equation (1) exponent of equation (1) saturation temperature of liquid, °C temperature of heating surface, °C Tw -Ts, K bubble contact angle surface tension of liquid-vapour interface, N m -1 density of saturated liquid, kg m -3 density of saturated vapour, kg m -3 viscosity of saturated liquid, Pa s
In boiling heat transfer it is still difficult to predict the heat transfer coefficient with any degree of accuracy despite many intensive investigations of the boiling process. Nucleate boiling is the most interesting regime for technical applications, and 01 40-7007/82/020107-0853.00 @1982 Butterworth & Co (Publishers) Ltd and IIR
107
considerable work has been done on the mechanism of heat transfer from the heating surface to the liquid.
good agreement with experimentally observed values when the outer contact angle of the bubble/~ at the instant of break away is known.
The formation and consequential growth of bubbles leading to break off and convective rise form some of the essential processes of boiling which govern the heat transfer. Unfortunately, an exact analytical description of those processes is not possible, and approximations may be obtained only by making simplifying assumptions which need to be confirmed by experimental results. It is extremely difficult to predict the number of points of origin in the bubble column per unit area of heated surface and the frequency of bubble formation. These data are very important for overall prediction of boiling heat transfer and are generally obtained from experiment only, by analysis of high speed film taken during the experi ment.
The total heat transfer process is dependent on the frequency of bubble formation, f, and on the number of nucleation sites n. The mean film coefficient, h, and the corresponding Nusselt number, Nu, are therefore functions of unknowns f o n d n, both of which depend upon the heated surface roughness and the properties of the boiling liquid.
Previous work
Jakob 1 suggested, following the work of Fritz, that the Nusselt number for boiling should be simply expressed as a function of the heat flux and an undefined empirical constant. Rohsenow 2 correlated a range of experimental results with a theory based on bubble formation in 1952. The Reynolds number, Re, is defined as /
Re=G °=c0-" b
Past investigations of boiling properties have concentrated primarily on experiments with pure liquids especially distilled water. Some studies have used refrigerant fluids because of their low boiling point and low surface tension. Very few results are readily available for boiling heat transfer and boiling properties of solutions of individual components such as K2CO 3, NaCI or LiBr in water at various concentrations. The early investigations into boiling heat transfer were mostly concerned with the mechanism of bubble formation and the forces acting upon the bubble during its formation and its detachment from the wall. The results from this pioneering work still form the backbone of knowledge today and the formation of the empirical equations used to predict boiling heat transfer despite the considerable amount of additional research still being done in this field. The dynamics of individual bubbles have been well defined and described 12 and the theoretical data are based on the experimental observations for single bubbles. The theoretically calculated results show
2~
\v2
where G b is the mass velocity of the bubbles at their departure from the heating surface. The Reynolds number therefore contains as unknowns, the quantities f, n and/~. The Nusselt number, Nu, is then expressed as ~_
.'~1/2
and therefore the Stanton Number St as, C,Tx Fq/A / ~ ~1/2]'/C,1~s S[ 1_ hfg -CsfLl~lhfgtg(p I -~Pv)) J t ~ l l ]
(1) Where Csf is a correlation coefficient which varies with the nature of the heating surface-fluid combination. Csf therefore, contains the unknown angle ,8 and is influenced by the undefined heating surface roughness. The results are often plotted in the form [ ( q l A ) l # t h j [ ~ / g ( p I -pv)] ~/2 versus St 1pr 17
Circulating pump
~_ with thermostat
L
Cooling water
Dg to voltmeter r ~ I~1 Precision Condenser Manometer
.' I Slide
resistance
Fig. 1
Schematic diagram of the test apparatus
Fig. 1 Sch#rna de I'appareil exp#rimenta/
108
Power supply
Experimental apparatus/present investigation A schematic diagram of the experimental apparatus is given in Fig. 1. The evaporator was submerged in a thermostatically controlled water bath in order to provide and maintain the desired saturation temperature from the test liquid inside the evaporator. Both the evaporator and the water tank were made of glass and permitted direct observation and video taping of the bubble formation over the heated surface.
International Journal of Refrigeration
Table 1. Boiling data Tab/eau 1. R#sultats concernant /'#bul/ition q/A, kw m -2
Tw -T s (average), °C
25% LiBr-water solution at 9.3 kN m -2 4.52 10.2 5.47 10.5 10.74 1 2.8 8.50 10.8 15.71 13.1 12.97 1 3.8 21.36 14.9 6.35 11.3 32.47 1 6.1 21.43 14.3 10.75 13.6 25% LiBr-water solution at 18.7 kN m -2 10.74 11.4 21.26 12.8 32.61 1 5.9 8.28 12.6 1 5.79 13.0 6.35 10.5 26.25 1 3.5 1 2.71 11.7 24.01 1 2.7 33.41 14.5 18.71 10.9 56,5% LiBr-water solution at 9.3 kN m -2 3.24 8.8 10.76 13.0 6.37 10.7 4.22 9.5 8.31 12.2 6.38 9.8 15.55 1 6.0 10.77 1 3.5 21.24 16.4 32.57 18.8 The distilled and degassed liquid evaporated on the outside of an internally heated copper test tube placed vertically in the evaporator. The vapour generated passed to a tube-and-shell condenser and condensed when heat was removed by circulating cooling water. By controlling the cooling water flow rate, a constant pressure was maintained. The condensate was returned to the evaporator at the end of experiments by heating the condenser and cooling the evaporator. The heating unit consisted of a 16 mm od clean, commercial grade copper tube 250 mm long fitted with an internal resistance wire heater heated by a direct current supply. The electrical input was regulated by a slide resistance. The heat flux at the surface of the test tube was calculated from measurement of the current through, and the voltage drop across, the heater using a precision ammeter and a digital voltmeter. The accuracy of the heat flux measurement was estimated to be within 4-1%. The surface temperature of the tube was measured directly by six calibrated thermocouples. The
Volume 5 Number 2 March 1982
q/A, kw m -2
Tw - Ts (average), °C
Distilled water at 101.4 kN m -2 33.57 7.94 10.74 16.04 21.44
7.0 3.8 5.1 5.5 5.9
Distilled water at 47.4 kN m -2 10.76 21.40 42.81 15.66 26.28 44.1 7
4.4 5.5 7.0 4.9 5.7 7.3
Distilled water at 19.9 kN m 2 10.73 21.37 31.78 1 5.69 26.19 44.06
5.2 6.6 7.4 6.6 7.5 8.7
Distilled water at 9.3 kN m -2 2.62 11.74 7.30 40.45 12.93 18.74 25.43 5.32 8.31 33.39 10.75 21.39 10.99 21.28
4.8 6.5 5.4 9.7 7.1 7.5 7.9 5.7 6.3 9.8 7.5 8.1 9.2 12.6
thermocouples were trapped longitudinally between the test tube and an inner copper tube which housed the resistance heater, the rest of the annulus being filled with solder. The bulk fluid temperature was measured with five calibrated thermocouples positioned at various depths below the surface of the test liquid. This method proved quite satisfactory, because at low saturation pressure the temperature difference between the tube wall and the boiling liquid was quite large. The maximum error in measurement of the temperature difference between the tube wall and the boiling liquid was estimated to be +0.25°C. The pressure in the closed system was measured with a closed end mercury filled manometer.
Test runs/experimental results Boiling experiments were conducted with LiBr-H20 solutions and with pure water. LiBr-H20 solutions at two different concentrations were boiled at low pressures using a pressure range between 9.3 and 18.7 kN m-< ie at approximately 0.1 and 0.2 atm
109
Table 2. Physical properties of L i B r - w a t e r solution 3 Tableau 2. Propri~t~s physiques de la solution de LiBr-eau '~ LiBr, wt%
p, t, kN m 2 °C
Ci, #t, kJ kg 1 K 1 Pa s
kl, kWm ~ K -1
o, N m 1
p r, kg m 3
Pv, kg m -3
Pr
25
1 8.67
66.0
2.90
0.000574
0.07!
11 81
0.110
3.42
2583
25
9.33
50.0
2.88
0.000842
0.000562
0.074
1196
0.063
4.32
2596
56.5
9.33
84.2
1.83
0.001 936
0.000470
0.077
1 620
0.061
7.53
2734
0.000678
hfg kJ kg-
Table 3. Physical properties of distilled w a t e r 4 Tableau 3. Propri~t~s physiques d e / ' e a u d/st///~e 4 P~, kg m -3
Pv, kg m 3
Pr
htg
0.0588
961.54
0.598
1.723
2256.9
0.000670
0.0625
971.82
0.29
2.1 0
2308.8
0.000653
0.0660
983.28
0.1 3
2.96
2358.6
0.000643
0.0687
990.10
0.062
3.96
2396.4
p, kN m 2
t, °C
C, I~l, kJkg 1K 1 Pa s
kl, kWm-lK
~, 1 N m 1
101.4
100
4.216
0.000278
0.000681
47.4
80
4.1 97
0.000350
19.9
60
4.1 85
0.000462
44.5
4.1 80
0.000603
9.3
absolute. Experiments using distilled water at pressures of 9.3, 1 9 . 9 , 4 7 . 4 kN m 2and at atmospheric pressure were carried out to give a direct comparison. The phenomenon of bubble formation and heat transfer observed were similar to those described in the literature for liquids at saturation temperature. The temperature of the boiling liquid was uniform throughout. Bubbles of different size were observed at a single fixed value of heat flux, the bubbles being relatively larger at lower pressure than that at higher pressure. The number of nucleation sites increase with increasing heat flux. The experimental results are listed in Table 1. The physical properties used in an analysis of LiBr solutions 3 are shown in Table 2 and those of distilled water 4 in Table 3.
Experimental
analysis
Although the Rohsenow expression (1) has been generally assumed to be of w i d e validity and has been extensively used for the correlation of pool boiling heat transfer, it was derived originally for pure liquids at atmospheric and high pressures and values of C~f quoted in literature is limited to water, organic compounds and K2CQ 3 solutions (Table 4). The parameter Csf varies with concentration and is of great importance for an accurate prediction of boiling heat transfer, since it has an influence of third power on heat transfer rate. In addition, C~f depends on the bubble angle/~, at detachment and the nature of the heating surface. The experimental results were analysed by plotting CiT×/hfg x 1 / P r ~7 against [(q/A)/#lhfg] x [~/g(Pl -Pv)] 1/2
110
kJ kg 1
as shown in Fig. 2. The resulting plot shows t w o curves, one for each concentration tested of the LiBr-H20 solution. The values of Csf are Csf=O.O017 for LiBr concentration of 56.5% by w e i g h t and Csf=O.O052 for 25% by weight. The values could not be correlated to a single curve as predicted by Rohsenow's expression. Rohsenow recommended 5 for water a change of exponent from s = 1 . 7 to s = l . 0 . This led us to an examination of available data in the literature as well as our own experimental data from the present investigation. It has, therefore, been shown that a single curve fit for various LiBr-H20 concentrations may be forced by varying the exponent s.
Table 4. Values of Csf and S w i t h r = 0 . 3 3 , r e c o m m e n d e d by R o h s e n o w 5 Tableau 4. Valeurs de Csf et de S avec r = 0 . 3 3 , recommand#es par Rohsenow 5 Surface combination
Csf
S
Water- nickel 10
0.006
1.0
Water- plati num 6
0.01 3
1.0
Water-copper 6
0.01 3
1.0
Water- brass 7
0.006
1.0
CCI4-copper 8
0.01 3
1.7
Benzene-chromiu m 9
0,O1 0
1.7
n-pentane chromium 9
0.01 5
1.7
Ethyl alcohol-chromium 9
0,0027
1.7
Isopropyl alcohol-copper 8
0,0025
1.7
35% K2CO3-copper 8
0.0054
1.7
50% K2CO3-copper 8
0,0027
1.7
n-butyl alcohol-copper 8
0.0030
1.7
Revue Internationale du Froid
0.1
I00 P, kNm -2
,Or
ot
o
101.4
1.723
z~
2641
0.852
•
5309
0.861
7"
•
8309
0946
x
11047
1.061
o
16996
1.62
¢D +
/ -~N
o
-IN
o,÷
/
0.01
+
gD
o/
+
+
r =0.33 o o
o
• = 0.33 I•
~ 0.(7t31
•/,.
s =1.7
/o
1.0
C,f = 0.0017
/
From Rohsenow2,deto of Addoms 6, pool boiling,plotinum wire - weter
o• Li Br % by wt
P, kNm-z
o
;>5
9.33
+
;>5
18.67
•
56.5
9.33
i
I
O.OOOI
I
=0.0,3 • = 0.33
xl~,I • /
f N
A
•
•x
c,f =0.005;>
P o /oI
T
x A • 10
I
I
I I Ill
I
I
i
i
i
i i i I
i
i
i
i
i
i
I.O
0.1 hfg P f 1.7
I
O.OOI
O.OI
C,rx
Fig. 3a Correlation of Addoms' data, using exponent value s=1.7 Fig. 3a Correlation des rbsu/tats d'Addoms, en uti/isant pour valeur de/'exposant s= 1.7
hfg Pr t7
Fig. 2 Experimental data for LiBr-watersolution vertical copper tube using Rohsenow' correlation
1
001
on smooth I00
Fig. 2 R#su/tats exp#rirnentaux p o u r / a so/ution de LiBr-eau sur un tube de cuivre vertica/ /isse en uti/isant /a corr#/ation de Rohsenow
The data of Addoms 6 for boiling water on a platinum wire, used also by Rohsenhow 2, have been plotted on Fig. 3a, using the exponent s = 1 . 7 giving a standard deviation for Csf of 0.00295. The same data are shown in Fig. 3b, using the exponent s = l . 0 , resulting in an improved standard deviation of 0.00223. The change of the Prandtl number exponent, s, has reduced the standard deviation thereby improving the fit of the line to the data. In spite of the fact that the experiments of Addoms covered a large range of pressures, from 101.4 to 1 6 996 kN m 2, the range of corresponding Prandtl numbers was actually very small, ranging between 0.852 and 1.723 ie very near unity. This will naturally limit the influence of Prandtl number and that of its exponent, s. Due to the change of the exponent, most of the points plotted shifted towards the lower values on the horizontal axis. The largest change occurred for the two values of highest Prandtl numbers, P r = 1 . 7 2 3 and 1.62, due to the change of the exponent s. This illustrated the influence of the Prandtl number exponent s, even in the range of low Prandtl numbers. The influence will be much more pronounced, when operating in the range of high Prandtl numbers naturally encountered during boiling at low pressures.
Volume 5 Num6ro 2 Mars 1982
-..~¢u >
10
•~/o
•
x / - ~ ~
sr
~),,
r
=0.013 =
0.33
s=l.0
o 1.0
/
a
x
°
./o 0, I
I
I I I I
O.OI
I
I
I
I I I I1[ O.I
L
I
L L I
I.O
c~ rx hfg
ii
Pr
Fig. 3b Correlation of Addoms' data, using exponent value s=l .0 Fig. 3b Correlation des r#su/tats d'Addoms, en uti/isant pour va/eur de/'exposant s = 1.0
111
1.0
with the exponent r = 0 . 3 3 , Csf is equal to 0.01 30, or with r = 0 . 3 7 , Csf is 0.0125. Both these values fit the data equally well as shown in Fig. 5. Therefore for boiling water, the relation is either in the conventional form with an exponent of 0.33 from previous investigations, which is based on a least square fit of 106 experimental data points.
/ -~
[- ~/A
C~T×
q/
/
o"
"
\ 1/2q0.33
~
I
hfW=°°13°L fi , tg(p, pv)} J
0.1
pro
(2)
x
x
:> [3
0.53 s =1.7
AZ~
0
x /•
or
C7x=0.0125 hf~
o
A
/
0.01
./ P,kNn~2 154.2 97.5
1.55 1.75
o
60.25
2.03
c, x
29.75 14.17 :3.84
2.58 3,53 5.73
+ z~
[3
o.oa
J~LI
[
i
J
i
n nnll
0.001
)1,21o37
Pr ~.° (3)
(7
g (P. ~Pv)
These relationships are then taken as applicable for all smooth clean metal surface liquid combinations, as on the basis of the above data it can be seen that the change in Csf is negligible.
Pr
I
q/A
In t h e a b o v e analysis we have deliberately omitted the boiling data obtained for a water-nickel surface, 1° originally used by Rohsenow in his analysis. Those data were obtained under forced convection boiling conditions and with significant subcooling. Although Rohsenow considered that the I
I
IO0
0.01
I
C,Tx hi•l Pr o.85
Fig. 4 Correlation of Cryder's data 7 for water-brass pool boiling using exponent value s=1.7
e ~• l ~ . ~
IO
C=f=0.0125 r =0.37 s =1.0
Fig. 4 Correlation des r#su/tats de Cryder 7 p o u r / ' # b u l l i t i o n fibre eau-laiton, en utilisant p o u r valeur d e / ' e x p o s a n t s = 1.7 •l
The value of Csf for a water-brass surface has been quoted in the literature 2 as Csf=O.O06. This value was originally determined with the Prandtl exponent s = 1 . 7 based on results using atmospheric and higher pressures. The value of Csf remained unchanged with the change of Prandtl exponent to s = l . 0 . Using this value of Csf, good correlation was obtained with the experimental results in the region of high pressures (corresponding to low Pr). However, a large discrepancy was shown, when attempting to correlate the results at very low pressures, especially when the Prandtl number had values of P r = 3 . 3 7 and 5.73, as shown in Fig. 4. It is interesting to note that Rohsenow neglected to use data for P r = 5 . 7 3 in his original paper. The boiling data for water on surfaces of platinum, copper and brass, from different sources, 79 also used by Rohsenow, are shown in Fig. 5, which includes also our experimental results at low pressures and therefore at high Prandtl numbers. The range of pressures is 3.84 to 16996 kN m 2 and the corresponding Prandtl numbers P r = 5 . 7 3 down to 0.852. This presentation assumes that a Prandtl exponent of s---1.0 is valid. The analysis shows that it is possible to correlate all the results to a single line with one single value of Csf. On the basis of statistical analysis, assuming s = l . 0 , then
112
• A
LO
e~l/! ./P • ~
~
C,~ =0.013
~ ~ o
s =1.0
0.1
~." x/"/ .~/
0.01
Fluid-heating p kNm-2 surfgce ' Pr • Water-platinums 101.4-16996 0.852-1.723
//
-
/. " x " // // I
0.001
Water-~er"
101.4
Q Water-brass7 x Water-copper
I.~23
&84-154.2 1.545-5.7 9.53-101.4 1.77_3-3.96
(our data)
1
I
I }IIII
I
I
I
0.01
I IlJll
I
I
I
I I I JI
0.1
1.0
c~ Tx
hfg Pr Fig. 5 Correlation of water pool boiling for different surfaces Fig. 5 Correlation d e / ' # b u / / i t i o n / i b r e d e / ' e a u p o u r diff#rentes surfaces
International Journal of Refrigeration
water and aqueous solutions. This results in the following values: C s f = 0 . 0 1 36, r = 0 . 3 4 0 4 , s = 0 . 8 4 5 1 .
I00
Fluid
• Woter z~ 25% LiBr I0 ---A 56.5% LiBr - ÷ 35% KzCO3 - x 50=/=K2C03
?
P, kNn~z
Pr 0.852 - 5.73 3.42- 4.32 7.5:5 :3.81 6.21
~e
~f~
3.84-16996 9.33-18.67 933 IOIA 101.4
Conclusions
•
The following expression in the form [A] = a [ B ] ' [ C ] s based on complete statistical analysis of 143 groupings of A. B, C and valid for pool boiling of pure water or for evaporation of water from aqueous solutions on surfaces of platinum, copper and brass, is proposed.
~.o el
/.
1.0
~ Tx=O.O136rq/A(
~1/21°'34(ClIJ1"~°'85
a
L#~f~\g(P, - p v ) }
c,, = o.o125
I/
(4)
°•~o
This is shown plotted in Fig. 7. The data are predicted well using this expression showing a standard deviation of 0.00298. The equation appears to have a single value of Csf for all smooth surfaces. Further research work is in progress to determine the applicability of the approach for the boiling of other liquids on smooth surfaces.
x ~IP- T M C,f= 0.01:3 xl~ • = 0.33
x ~
s= 1.0
0.OI
.-,,y ,
I
0.0001
l
I
i llAil
\k~-i }
q~Joe
• = 0.37 s = 1.0
0.1
]
le',,
"//,
I00
I
I
I I llll
0.0oi
l
I
I
I IIii
0.01
0.1
,o
c, Tx
h NprO.85
:;
Fig. 6 Correlation for water and aqueous solutions of LiBr and K2CO 3 using exponent value s = 1 . 0
Fig. 6 Correlation p o u r I'eau et des solutions aqueuses de LiBr et K2C03, en utilisant p o u r valeur de I'exposant s = 1.0
effect of subcooling may be neglected, thereby permitting the inclusion of these results in his analysis, we consider that for the present case, these results fall into a special category because of the combined presence of forced convection and significant subcooling. After this the experimental results of boiling LiBr on copper surface were analysed. The basis for analysis is (3) to w h i c h the experimental results have been compared using at the same time some of the data for K 2 C O 3 at two different concentrations. 8 All the data correlate well over the whole range of pressures and concentrations to expressions (2) and (3) as shown in Fig. 6. In all the above relationships the Prandtl number exponent used has been fixed at 1.0 following Rohsenow's recommendation. Vachon et al. 11 determined values for Csf using the method of least squares only after fixing the Prandtl exponent. However, as shown, the value of this Prandtl exponent, s, was changed during the analysis from the value s = 1 . 7 to s = l . 0 . The method of least squares was used to determine simultaneously all the parameters of the equation, ie Csf, r and s for
Volume 5 Number 2 March 1982
"° f
/:
[
~' : t
/.~c,,=oo,36
I'-
eI
"0,[--''~" "
E
/~
r =0.34
:'~/~"
,=0.85
¢%
o.o,k , , L ,/
~
I~" / e ~ L. A 1 :/
O.OOI
w,,,.r "
56.5%LiBr 7.53
~ 25%LiBr
&42-432 + 35%KzCO5 3.81 x 50e~K2C03 6.21
O.01
9.33 9.33- 18.67
101.4 101.4
O.I
1.0
C, rx hfo pr
-0"$5
Fig. 7 Correlation for water and aqueous solutions of L i B r a n d K2CO 3. Csf, r and s were determined using least square method
F i g 7 Correlation p o u r I'eau et des solutions aqueuses de LiBr et de K2C03, Csf ' r et s ont 6t6 d6rermin#s en utilisant la m#thode des plus petits carr#s
113
The authors gratefully acknowledge the facilities provided by the University of Melbourne and the financial backing of the National Energy Research, Developments and Demonstrations Council.
5 6 7
References 1 2 3 4
114
Jakob, M. Heat Transfer, John Wiley & Sons Inc., New York (1949) R o h s e n o w , W. M. A method of correlating heat transfer data for surface boiling of liquids Trans ASME 74 (1952) 969-975 Uemura, T., Hasaba, S. Studies on the lithium bromidewater absorption refrigerating machine Technology Reports of Kansai University 6 (1964) Osaka, Japan H a y w o o d , R. W. Thermodynamic Tables, 2nd Edition, Cambridge University Press (1972)
8 9 10
11
R o h s a n o w , W. M., H a r t n e t t , J. P. Handbook of Heat Transfer, McGraw Hill Inc. (1973) 13 28 A d d o m s , J. N. Heat transfer at high rates to water boiling outside cylinders, Doctoral Dissertation, Massachusetts Institute of Technology (1948) Cryder, D. S., F i n a l b o r g o , A. C. Heat transmission from metal surfaces to boiling liquids: effect of temperature of the liquid on film coefficient Am Inst Chem Eng 33 (1937) 346 Piret, E. L., Isbin, H. S, Two-phase heat transfer in natural circulation evaporators, A/ChE Heat Transfer Syrup St Louis (Dec 1953) Cichalli, M. T., Bonilla, C. F. Heat transfer to liquids boiling under pressure TransAIChE41 (1945) 755 R o h s a n o w , W. M., Clark, J. A. Heat transfer and pressure drop data for high heat flux densities to water at high sub-critical pressures, Heat Transfer Fluid Mech /nst, Stanford, Calif. (1951) Vachon, R. I., Nix, G. H., Tanger, G. E. Evaluation of constants for the Rohsenow pool-boiling correlation, J Heat Transfer, Trans ASME 90 (1968) 239
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