ENGINEERING, DESIGN, AND EQUIPMENT
Bubble Contact Heaters for Power Plants GEORGE P. KOTELEWSKIJ 801 Court St., Honesdale, Pa.
B
OILER feed water usually is heated by exhaust steam, or steam bled from somewhere in the power plant cycle, except where economizers, which utilize flue gas, are used. Tubular heaters, with water on the tube side, are by far the most common type of heat exchange equipment employed in modern power plants. The use of direct contact heaters, on the other hand, probably has been retarded because of lack of sufficient data needed to make an intelligent engineering and economic comparison. During the early years of power plant development, direct contact heaters were conceded to be relatively inefficient a t low steam pressure, even though they offer several advantages uncommon to tubular heaters. Direct contact exchangers suffer no loss in temperature head, if an initial steam pressure is maintained in the apparatus; water is heated t o the saturation temperature of the steam in the exchanger. In tubular heaters, however, the exit water is generally 2' to 12' F. below the saturation steam temperature in the exchanger. Scale accumulation is always a problem. Direct contact heaters offer another important advantage over tubular heaters-they provide feed water deaeration and a convenient receiver for condensation of steam from various sources. Two different types of direct contact heaters could be employed-the jet exchanger or the bubble exchanger. Jet contact heaters may be ruled out by cursory examination because they require a large steam chamber into which water is sprayed, and high pressure chambers are expensive. Even a t low pressures, difficulties are encountered both in the counterflow of water across the trays or pans and in the exhaust of noncondensed steam. Spray nozzles can be used instead of pans to distribute the water, but this procedure does not circumvent the other difficulties. Bubble contact heaters, where high pressure steam is injected into the water, have none of the disadvantages inherent in the jet exchanger. They do not require special deaeration equipment and condensate coolers, which are also required by high pressure tubular heaters, At high steam pressures (above 120 pounds per square inch absolute), bubble contact heaters are more economical than tubular heaters because of their smaller gize and simpler construction. Cheaper materials of construction may be employed because the bubble contact heater operates a t saturated steam temperature, rather than a t superheated steam temperatures. The high pressure tube heaters in the last stage of the heating system may be replaced by bubble contact heaters. Consequently, the feed pump, which must be provided for necessary submergence, is displaced after the bubble contact heater. This pump usually is placed before the last stage of the tube heaters. The proposed apparatus consists of a vertical closed cylinder, with an upper nozzle for feed water inlet and a bottom nozzle for feed water outlet. The water level in this apparatus is automatically maintained near the upper nozzle by a regulator. Steam enters a t the lower part of the apparatus and flows countercurrently upward through the column of water. Disk-and-ringtoothed baffles, attached to the inside of the cylinder, provide a zigzag path for the steam bubbles. These baffles increase the effective length of the equipment and break up the steam bubbles. 20
Air carried into the system with the entering steam is vented through a nozzle a t the top of the heater. The control of the air outlet allows the pressure in the projected bubble contact heater to be maintained in order to obtain the maximum saturation temperature of the feed water. High pressure exhaust steam usually is superheated. This additional enthalpy may be used for some evaporation in the lower part of the bubble contact heater to provide essentially complete deaeration of the feed water for the boiler. The vapor and steam are absorbed by the feed water in the upper part of the cylinder. The heating system in many power plants inav be simplified considerably by replacing expensive tubular heaters in the last stage with bubble contact heaters, and a t the same time eliminating equipment for deaeration and for cooling the hot water discharged by tubular heaters. Velocity of steam bubbles and heat transfer between steam bubbles and water are basic to contact heater design
To determine under what conditions the bubble contact heater is economically efficient, the two variables must be consideredvelocity of steam bubbles in the feed water and the heat transfer coefficient between steam bubbles and the liquid,
.
E q u i pm e n t T h e s t u d y deSTEAM s c r i b e d in this article was made at atmospheric pressure with a v e r t i c a l , open glass cylinder, 1, of Figure 1, on which a scale (millimeters) for measuring water level was traced. The steam, a t about atmospheric pressure, was driven into the water by means of a tube, 2, on n-hich were set the ring, 3, and the disk, 4, baffle plates R-hich f o r c e d rising steam bubbles t o make zigzag movements. Two sizes of glass c y l i n d e r s were used for the experiments, 35/, and 17/8 inches in Figure 1. Laboratory bubble i n s i d e diameter contact steam condenser and 12 inches in height. The 1n c h aluminum tube, 2, was covered by rubber tubing for insulation and lowered t o 1 inch above the bottom of the c linder. On the tube, over the rubber, were set the ring and J s k baffles made from thin brass sheet.
INDUSTRIAL AND ENGINEERING CHEMISTRY
Vol. 48, No. 1
ENGINEERING, DESIGN, AND EQUIPMENT In the 33/4-in~hcylinder, four ring (3.72 inches in outside and 1.38 inches in inside diameter) and four disk (2.95 inches) baffles were placed. The distance between baffles was 0.617 inch. The lowest disk was fixed a t the end of the tube, and the total baffled height was 4.33 inches. In the 14/s-inch c linder, two ring (1.85 inches in outside and 1.0 inch in inside gameter) and two disk (1.4 inches) baffles were used. The distance between baffles was 1.6 inches and the total baffled height was 4.8 inches. The steam was generated in a closed pot, a p roximately 0.5 gallon capacity, with l/,inch steam outlet a n i l/S-inch relief valve. The steam nozzle was connected with the aluminum tube, 2, by rubber tubing. A mercury thermometer ( O C.) was placed in the lower part of the c linder and extended into the mixture of water and steam bubbLs. Actually, the temperature of the water was measured. The glass cylinder was not insulated. Procedure. Water was boiled in the pot with the relief valve open. When the valve was closed, steam entered the water in the glass cylinder through the aluminum tube. While the steam was rising in the water, all or a part of it was condensing, and, a t the same time, the temperature of the water and the level of the mixture in the cylinder were changing. The following data were recorded:
Bubble Velocity in Water. The volume of the steam bubbles in water a t any moment is (h' - h)a and the time the steam bubbles remain in the heater is h'-h
$ - = -
(2)
V
The average velocity of steam bubbles rising in the water is u' = h' -
(3)
7
Linear steam velocity in the cylinder is (4)
The volume percentage of steam bubbles in the mixture is
b=
100( h' h'
- h)
The coefficient, b, is the bubbling coefficient. From Equations 3, 4, and 5,
Time Temperature of water Height of mixture (water and steam bubbles) Height of water only (for this measurement the steam flow was stopped for a moment by opening the pot relief valve)
T h e v e l o c i t y , u', measured in this integral way is really the average velocity of bubbles rising i n t h e l i q u i d
The following is a sample of recorded data (Test 1 of Table I): Time Min.'
tw 2
0
56 68 75 81 87
1
2 3 4
Calcd. At = 100 tw,
-
h'
h,
c.
Mm. 149
MA.
O
150 152 158 161 155.2
iig 154.3
Mean
c.
(8).
It is known that the velocity of a gas bubble in liquid is inversely p r o p o r t i o n a l to the kinematic viscosity of liquid; bubble velocity increases with the size of the bubble and decreases w i t h s u r f a c e tension. I n the following calculation the effect of t h e v i s c o s i t y of water on steam bubble velocity is considered, with other factors, such
44 32 25 19
155
13
26.6
Growth of water in cylinder Ah = 15'
- 14'
= 2.5 mm./minute
These data are sufficient for the calculation of velocity of steam bubbles and the coefficient of heat exchange. In the experiments on the determination of steam bubble velocity, Ah first was defined by full steam absorption a t a constant steam generation, and the cross-sectional area steam velocity in the cylinder a t 100' C. was calculated by the formula: ua = 2.78Ah cm./second
Table
Test NO.
Changes in Temp. of Water, C. From To
I.
Figure 2. Disk and ring baffle system for bubble contact heater
(1)
Heat Transfer from Steam Bubbles to W a t e r in ~i~~ of Test Min.'
At, O
c.
h', Mm.
(5)
h
MA.
-
h' h, Mm.
1 Atmosphere Absolute Ah
Mm/Min.
Heat Transfer Coeffioient Deviab, % B.t.u:P(ou. tion, Equation f t . ) ( h r . ) ( " F.) % ' (5) (Equation 15)
38/4-Inch Glass Cylinder, e = 2.55
s
9 10 11 12
56 68 95 91.5 90 65 84 92 97 61 80 96
87 94 99 99 100 84 96 98 99 88 94 100
4 4 4 3 2 3 2 1 1 3 3 2
26.6 19.8 3.0 4.0 5.0 24.8 10.0 4.3 2.0 25.5 12.5 2.0
155.2 142.5 163 176.5 179.5 156 164 172 181.5 142.5 128.5 176.5
154.3 141 154.5 167 168.5 155.2 161.5 168 170 141.2 126 156,5
0.9 1.5 8.5 9.5 11.0 0.8 2.5 4.0 11.5 1.3
2.5 20
2.5 3.5 2.5 2.65 3.5 2.5 2.5 2.0 2.0 3.7 2.7 3.5
0.6 1.0 5.5 5.4 6.2 0.5 1.5 2.3 6.3 0.9 2.0 11.4
103 118 98 69 64 128 98 113 88 108 83 88
l'/s-Inch Glass Cylinder, e = 0.25
January 1956
INDUSTRIAL AND ENGINEERING CHEMISTRY
21
ENGINEERING, DESIGN, AND EQUIPMENT
Table
II.
The coefficient of steam absorption per unit of steam bubble surface and degree of temperature difference would be
Steam Bubble Velocity a t 1 Atmosphere Absolute in Water a t 100” C. Bubble Velocity UOI
Test NO.
h’, Mm.
h, hlm.
1 2 3 4 5 6 7 8 9
140 147 152 140 204 230 192 210 188
131.5 132 131 120 165 200 172 175 171
10 11 12 13 14 15
214 207 220 210 230 226 215 225 230
199 173 154 172 170 174 150 154 157
U;,
b % cm./sec. (Eqlation 5) (Equation 6 )
Steam Velocity Wl
uo
cm./Aec. (Equation 1)
ft./sec.
1.94 2.06 1.96 2.11 2.09 2.39 2.33 1.52 2.53
3.6 6.4 8.3 9.2 12.1 11.0 7.4 9.75 6.95
0.118 0.210 0.272 0.302 0.397 0.360 0.242 0.320 0.228
2.35 2.60 2.50 2.53 2.54 2.33 2.71 3.17 3.45
5.0 13 9.1 14.3 20.2 16.3 25 30.6 33.4
0.164 0,426 0.298 0,469 0.662 0.535 0.820 1.00 1.095
ft./aeo.
9
33,’a-Inch Glass Cylinder, e = 2.55 6.1 10.2 13 8 14.3 19.0 l5,O 10.4 16.7 9
59 63 60 64.3 63.7 73 71 58,5 77
l’/a-Inch Glass Cylinder, e
16
17 18
7.0 16.4 11.8 18.5 26 23 30.2 31.6 31.8
3
.4s it is difficult to measure t h e a v e r a g e d i a m e t e r of bubbles in the water (a part of them unite in streams), it is preferable to define the coefficient of absorption as the weight of absorbed steam per unit volume of steam bubbles in water.
0.25
71.5 79.3 76.3 77 77.5 71.0 82.8 96.5
105
(h’ a8 diameter of bubbles and surface tension of water, assumed t o be unchanged. On the basis of the Stokes equation of ball resistance ( 4 ) and t h e data of O’Brien and Gosline for bubble velocity in tubes (S),
U’ = c
(7)
P
In Equation 7, c, which includes all other factors, is assumed as a first approximation to be constant. The average velocity
of bubbles rising in water is dependent on the length of the zigzag movement. The length of the zigzag path (Figure 2) is
L =
N(D2
- 01)+ Ha
e =
N(4
- 01) + iVZ - N Z NZ
(9)
z
Equation 9 may be considered to represent a baffle characteristic. It shows how the bailee (ring and disk) elongate the path of bubbles in water. The path elongation in the 33/r-inch glass cvlinder warn 2.95 - 1.38 = 2.25 e = 0.617 -I
and for the 17/&ch cylinder,
e = 1.4 ~
-
1.0
1.6
= 0.25
aAhp,
If the average diameter of the bubbles is known, the coefficient of abaorption and heat transfer per unit of contact surface may be calculated. Total surface of bubbles in water at any moment is s = nad2
Since the volume of eteam bubbles in water is a(h’
22
540 X 60 X 106p - 32.4 X 10eAhp. 1000 (h’ - h)At
(14)
or, in the English system,
’
=
2.02 X 10*Ahpr (h’ - h)At
The relation between the volume and surface coefficients of heat transfer is qdi
-
71.5
where d i is the average diameter of bubbles in inches. The diameter of the cylinder is not required for calculations and the relation, h/h‘- h, does not depend on the dimensions of the a g paratus. Results of the experiments are presented in Tables I and 11. Volume percentage of steam bubbles i s important coefficient in determining contact heater efficiency
The resultant heat transfer coefficient, q = 203,000 B.t.u. per (cubic foot) (hour) F.) (average of 19 tests), is estimated per cubic foot of steam bubbles a t 1 atmosphere absolute in water. In order to calculate a coefficient based on 1 square foot of bubble contact surface, the average diameter of the steam bubbles, which is difficult to measure, must be known. From observation, bubbles appeared to be approximately 1/2 to 1 inch in diameter, but a part of them had united in streams. By assuming the average diameter of bubbles to be 0.75 inch the heat transfer coefficient per square foot of bubble surface (Equation 16) is ( O
Absorption of Steam Bubbles in Water, For finding the heat transfer coefficient a t the direct contact of steam with water, the followlng formulas were used: The absorption of steam in a cylinder is
s =
k =
q. =
=-Dn - D1
(13)
Accordingly, the heat transfer coefficient of 1 atmosphere steam bubbles in water is
(8)
where the baffled height of the column is Ha = N Z . Bubble path elongation on one unit of baffled height is
- h)At
6a(h’ - h ) d
- h),
qs =
203,000 X 0.75 = 2100 71.5
Compared with the Nusselt film Coefficient, a greater rate of heat transfer by direct contact of steam n-ith water might be expected. However, because the union of bubbles and the average diameter of bubbles cannot be discounted, the coefficient of heat transfer per cubic foot of steam bubbles estimated above is used in the present calculations. It is expected that g would increase with increased steam pressure. It is also expected that the velocity of bubbles in water xould be somewhat greater in the industrial bubble contact heater than
INDUSTRIAL AND ENGINEERING CHEMISTRY
Vol. 48, No. 1
ENGINEERING, DESIGN, AND EQUIPMENT" As the bubbling coefficient increases to over 25%, the bubble velocity evidently increases, because of union of bubbles into the steam streams. Hammering. Fear has been expressed concerning possible hammering produced by driving high pressure steam into water. It may be supposed that steam hammering is the result of kinetic energy strokes of water that rushes into the steam bubbles as a consequence of the steam absorption. This can be calculated. From the general equation of absorption, the volume velocity of absorption for a steam bubble is dub
=
or(t8r
d7
- tw)4ma G0P.r
The volume of a bubble is v b = 4rr8/3. By differentiation,
From equations 19 and 20, the linear velocity of water in a radial direction into the steam bubble is
The energy of hammering when a mms of water rushes into the condensing steam bubble will be proportional to kinetic energy W
4
Figure 3.
8
6
12
16
vo OF
BUBBLING
20
24
Cross-sectional steam velocity
looo c.
28
32
in water at
in the pilot cylinders, (For instance, in the small glass cylinder, l 7 / * inch in diameter, the wall friction might affect the steam bubble velocity.) As the average velocity of bubbles rising in water depends on the baffling, the velocity could be slowed by zigzag path elongation, but the velocity in a vertical direction cannot be increased mechanically. Calculations for an exponential curve (Figure 5) that shows the diameter of bubble contact heater as a function of the steam pressure were based on the steam velocity a t 100' C. and 0.295 cs. kinematic viscosity of water. The influence of water column velocity, in counterflow in a bubble con act heater, is a3sumed to be negligible. The bubbling coefficient is a very important coefficient in calculations of bubble contact apparatus. According to the tests, the average bubbling in a vertical cylinder should not exceed 25 to 27% to prevent the formation of bubbles in great streams and decreasing of contact surface between bubbles and liquid. Table I1 and Figure 3 show that the bubbling is approximately proportional t o the cross-sectional area steam velocity. The steam bubble velocity, however, remains almost constant as the bubbling coefficient increases to approximately 25%, as shown in Figure 4. This result might be expected, according to Equation 6. If b is proportional to u then
b =
C:U
100 u ' = - '=0- 0 ~ 'O0u = - = constant b CIU CI
January 1956
2'25 = 0.57 foot/second 100
- CYLINDER
3-3/4"I D e: 2.55 0 - CYLINDER 1-7/8" 1.0. X
4
8
12
16
20
24
28
32
% OF BUBBLING
Figure
4.
Steam bubble velocity in water at
100" C.
From Equations 21, 22, and 23
(17)
(18)
This result does not agree with the assumption of Geddes ( 1 ) that the bubble velocity is proportional to the height of the mixture. The average,steam bubble velocity in water a t 100' C. was found to be U, = 2.25 feet per second. From the permissible bubbling, b = 25%, maximum linear steam velocity for the bubble contact heater may be determined (Equation 6 ) .
u o = m = - 25
The mass of water is proportional to the volume of steam bubble
Equation 24 shows that energy of hammering de ends on the radius of a steam bubble and on the temperature xfference between steam and water. I n the experiments, the temperature of water was changed at intervals from 20" t o 100" C., but the temperature of steam was constant at 100" C . (1 atmosphere). The hammering took place in water t o 45' to 47' C. and quieted down when the temperature of the water was above 50" C. At high pressure the density of steam will increase in the denominator more than the temperature difference in the numerator of Equation 24. (In the case of superheated steam the coefficient of absorption, 01, will be lower than that of saturated steam.) Therefore, there is no reason to expect trouble in high pressure bubble contact heaters because of hammering.
INDUSTRIAL AND ENGINEERING CHEMISTRY
23
ENGINEERING. DESIGN. AND EQUIPMENT a t 100’ C. and is equal to 0.295 cs. Hence, the diameter of bubble contact heater, in inches, is D = 12 200
2 X 0.785 X 0.295L‘o = 17.65
4‘”~,ovQ’”
(28)
The test data for UOare from Figure 3, according to assumed b. Reaction Space. According to the definition of the heat transfer coefficient (Equation 15),
I80
I60
Minimum vertical height of reaction space is
140
H‘ = _ 1728B _ 2200R 0.78502 = 7
ln w
g
120
z
The dimensions of the bubble contact heater depend on the two principal factors-steam bubble velocity in water and steam absorption (or heat transfer coefficient). These experiments allow the conclusion that, at low steam pressuSe, the size of the bubble contact heater is not limited by steam absorption, but by bubble steam velocity. .4t low steam pressure, tube heaters are more effective than bubble contact heaters. Calculated data for a bubble contact heater may be compared xith the following data for a low pressure tube heater:
IO0 80
60
40
Flow R a t e Pressure ( P ) , Lb./Sq. Temp.F.( T ) , Lb./Hr. (G) Inch Abs. I
20 SuDerheated steam inlet
C
100
200
300
p
400
500
600
Drain inlet (condensate Feed water inlet Feed water outlet Mean temperature difference, A T
650
STEAM PRESSURE, P.S.I.A.
Figure 5. Size of bubble contact heater calculated for inlet steam rate of 36,000 pounds per hour Table 111
Calculations of bubble contact heater show favorable comparison with tubular heaters at high steam pressures
On the basis of the above experiments and considerations, the following formulas for calculations of bubble contact heater apparatus may be developed. From the experiments the vertical average “bubbling” data in the cylinder were found; therefore, for calculations of bubble contact heater diameter, on the basis of these data, the vertical average cross-sectional area steam velocity should be used. If it is assumed that all the steam (except for the air) in bubble contact heater is condensed, for the vertical average steam velocity,
U=- v
+ v,
According to Equation 7,
U’ = c/v/u; = c/vo
hence
From Equations 6, 25, and 26 the crosssectional area of the cylinder is
24
326,760 1 ,500,000
v=
where 12.0 is the specific volume of superheated steam in cubic feet per pound at Tat = 555.7’ F. and P = 53.9. Kinematic viscosity of water at 285.8” F. (assumed to be the temperature of saturated steam) is Y = 0.202. At a bubbling of 20 to 22%, from Figure 3, V O= 0.49 foot per second, and from Equation 28, the diameter is
= 36 000 Ib /hr. Q = 35:000,000 B.t.u./hr. A T = l?a F.
Steam Press. Temp. ( P ), lb./sq. (oTb. inch abs. 10 20 40 60 100 120 140 160
200 250 300 350 400 450 500 600
+ Vdv 2vouo
Design of Bubble Contact Heaters
G
80
YQ
5... 55 7
(285,8 satd.) 293.8 214 3 283 8 16.1
The heat to be exchanged (by condensing plus desuperheating) is equal to Q = 81,300,000 B.t.u. per hour. The tubular heater required would have a shell diameter of 56 inches and U-tubes 232 inches long. For the same conditions of heat exchange, the volume of inlet steam is 74’510 12‘0 = 248 cubic feet/aecond 3600
Table 111.
According t o Equation 6, U = bU’/lOO/ in water at 100’ C., U O = bc70’/100
Where
53 9
(25)
28
A = (V
74.510
Kinematic Viscosity of Water ( u ) , cs. 0.31 0.28 0.226 0.194 0.181 0.178 0.168 0,158 0,155 0.145 0.139 0.134 0.130 0,125 0.123 0.121 0.115
q
b
= =
203,000 B.t.u./(cu. ft.)(hr.)(’ F.) 20 to 2270
UO = 0.49 ft./seo.
Specific V O I . of Steam ( u ) , Cu. Ft./Lb.
VOl. of Inlet Steam (V) Cu. Ft.’/Sec. 384.0 200.0 105.0 71.0 54.8 44.3 37.3 32.2 28.3 22.9 18.4 15.3 13.2 11.6 10.3 9.3 7.7
is the kinematic viscosity of water
INDUSTRIAL AND ENGINEERING CHEMISTRY
Diameter
(D), Inches
(Equation 28)
276.0 190 .0 123.0 93.5 79.5 70.8 63.1 57.0 52.8 40.0 40.4 36.1 33 .O 30.4 28.4 26.8 23.7
Height ( H ’ ) , Inches (Equation
30) 1.47 3 10 7.43 12.7 17.8 22.1 27.8 34.0 39.6 52.3 68.0 85.3 101.5 119.5 137.5 154.0 193
--_-
Vol. 48, No. 1
ENGINEERING, DESIGN, AND EQUIPMENT (In this calculation the volume of air is assumed to be negligible.) The required reaction space (from Equation 29) is
R=
81,300,000 = 124 203,000 X 16.1 X 0.20
and the minimum reaction space height (from Equation 30) is
179 inches and H' = 8.5 inches appears strange and deformed. These calculations demonstrate why bubble contact heaters have appeared to be inefficient at a relatively low steam pressure. They also show that bubble contact heaters may have more advantages as the steam pressure rises above 110 to 120 pounds per square inch absolute. Another example may illustrate this more clearly. A tubular heater with a 36-inch inside diameter shell and 270inch U-tubes is designed for a steam inlet rate G = 36,000 a t P = 317.7 and Tat = 560" F . (422.6' F. saturated), with a heat exchange Q = 35,000,000 at A T = 17' F. These figures are representative of the operation of tubular heaters. Accordingly, u = 18 and Y = 0.131. For a bubble contact heater under these same conditions of operation,
A cylindrical apparatus with D
D
=
17.65
=
t/18'0~4~'131 =
38.7 inches
34J0002000 = 50.7 cubic feet R = 203,000 X 17 X 0.20
These results show that the bubble contact heater in this case is much more profitable than the tube heaters (about 3 to 3.5 times cheaper). As steam pressure rises above 300 pounds per square inch absolute, bubble contact heater would be more and more economical because of their decreased size, very simple construction, and less rigorous temperature conditions. In Table I11 are listed other calculated data for bubble contact heater. Figure 5 shows how the size of the bubble contact heater is affected by an increase in steam pressure a t the same output and heat exchange. In contrast, the size of tube heaters is chiefly determined by the amount of heat exchange and does not depend on the steam pressure, because the steam enthalpy varies little with changes in steam pressure. ASin Table 111,it is assumed that heat exchange is constant (35,000,000 B.t.u. per hour), and the size of the tube heaters (36 to 270 inches) remains almost constant, so the tube heater can be compared with the bubble contact heater for several degrees of steam pressure.
Nomenclature
cross-sectional area of cylinder, s cm. steam bubbles in mixture (bubb%ng coefficient), vol. % C constant d diameter of steam bubble, em. e bubble path elongation E kinetic energy, gram-em. h = height of water column, mm. h' = height of mixture (water bubbles), mm. Ah = growth of water in cylinder, mm./min. k = direct contact heat transfer coeff., kcal./(cu. m,)(hr.)( O C.) m = mam of water, grams n = number of bubbles r = radius of steam bubbles, cm. S = total surface of steam kubbles, sq. cm. t s 1 = temperature of steam, C. = temperature of water, O C. tw At = mean temp. difference between steam and water, O C. U = steam velocity a t cross section of cylinder, cm./sec. = cross section steam velocity in 100" C. water, cm./sec. = steam bubble velocity in water, cm./sec. = steam bubble velocity in water a t 100' C., cm./sec. U,' u w = water velocity, cm./sec. V = volume of inlet steam cc./sec. = volume of a single buLble, cc. vb a = coefficient of steam absorption, grams/(sq. om. of steam bubbles)(min.)(' C.) P = coefficient of steam absorption, grams/(cc. of steam bubbles)(min.)( O C.) Pat = density of steam, grams/cc. P w = density of water, grams/cc. = kinematic viscosity of water, cs. Y 7 = time, see. a
b
E?
A
C
D D, D2 di e
G H H'
Hg
L N
P Q
q
= cross-sectional area of apparatus, sq. ft. = constant = diameter of apparatus, inches
inside diameter of ring baffle, inches diameter of disk baffle, inches = diameter of steam bubbles, inches = bubble path elongation = weight of inlet steam, lb./hr. = height of water column, inches = height of mixture (water bubbles), inches = baffled height, inches = total length of zigzag path, inches = number of bafles = steam pressure, lb./sq. inch abs. = heat exchanged, B.t.u./hr. = direct contact heat transfer coeff., B.t.u./(cu. ft.)(hr.)(" F.) surface coeff. of heat transfer, B.t.u./(sq. ft.)(hr.)( O F.) reaction space, cu. ft. = temperature of steam, a F. = temperature of water, O F. = mean temp. difference between steam and water, O F. = steam velocity a t cross section of apparatus, ft./sec. = cross section steam velocity in 100" C. water, ft./sec. = steam bubble velocity in water, ft./sec. = steam bubble velocity in water in 100' C., ft./sec. = volume of inlet steam, cu. ft./sec. = volume of air, cu. ft./sec. = specific volome of steam, cu. ft./lb. = spacing between baffles, inches = =
+
8Tat AT
The average steam bubble velocity in water a t 100' C. was measured by an integral method and found t o be 2.25 feet per second. This velocity remains almost constant to 25% of bubbling. If the percentage of steam bubbles in the mixture exceeds 25%, the union of bubbles into streams increases. The permissible cross-sectional area steam velocity in the bubble contact heater may be approximately 0.6 foot per second, in water a t 100" C. The heat transfer coefficient between steam bubbles and water per cubic foot of steam bubbles in water was estimated to be 203,000 B.t.u. per (cubic foot) (hour) ( O F.) a t atmospheric conditions. On the basis of the experimental data, it was found by calculation that bubble contact heaters are not practicable a t low steam pressure, but may be efl'ective when the steam pressure is greater than 120 pounds per square inch. Bubble contact heaters are
= = = = = =
+
Tw
Conclusion
January 1956
especially profitable a t high pressures (above 300 pounds per square inch). The heating system in power plants may be considerably simplified by replacing expensive high pressure tube heaters in the last stage on the bubble contact heaters. A t the same time, any special apparatus for deaeration and drain cooling is eliminated.
U
Uo U'
L'i
V V. u
2
literature cited
(1) Geddes, R. L., Trans. Am. Inst. Chem. Engrs. 42, 907 (1946).. (2) Kotelewskij, G. P., J. Chem. Promgshlenosty XIV, 664 (1937);
XVI, 28 (1939).
(3) O'Brien, M. P., and Gosline, J. E., IND.ENQ.CHEM.27, 1436 (1935). (4) Stokes, G. G., Math. and Phys. Papers, 111, 55. RECEIVEDfor review March 9, 1954.
INDUSTRIAL A N D ENGINEERING CHEMISTRY
ACCEPTED July 27, 1955.
a5
