I
GEORGE F. HADLEY1 and ARTHUR L. THOMAS Photo Products Department,
E. I. du
Pont de Nemours & Co., Inc., Parlin, N. Y.
A Mathematical and Experimental Study of a Climbing Film Evaporator This preliminary study of a climbing film evaporator gives derived quantitative expressions, supported by experimental measurements, which predict evaporator performance. These expressions can be used as the starting point in the design of a climbing film evaporator
Analysis of a climbing film type of evaporator has given expressions for volume holdup, holdup time, and power requirements in terms of dmmensions of the evaporator, the rotor speed, and the properties of the fluid entering and leaving the evaporator. Experiment has agreed with theory. Heat transfer coefficients were also measured. The water evaporation film coefficient for a test system was found to be 542 B.t.u./hr. sq. ft./" F. Over-all coefficients were also determined as a function of rotor speed in revolutions per minute.
A technology
in evaporator is the impeller-type falling film evaporator developed by the Luwa Co. (2, 4). Another impeller-type evaporator is the climbing film evaporator. The climbing film evaporator of Haley (7) operates under vacuum. An R E C E N T DEVELOPMENT
impeller extending the length of a vertical tube maintains a thin film of feed on the inside tube wall. The controlled centrifugal field, forced convection, thin-film principle of the rising film evaporator provides advantages n terms of uniform product rate, product uniformity a t low throughput rates, low holdup time, minimum encrustation o the heated surfaces, compactness, ease of cleanability, and uniform throughput temperature. Feed is introduced at the bottom of the evaporator body and, in rising to the top of the evaporator, is maintahed as a thin film by the centrifugal action of a high speed rotor (see page 72). The rotor, a shaft with three planar vanes, spaced 120' apart, passing through the axis of rotation, extends the full length of the evaporator and is powered
by a 1.5-hp. Varidrive. The clearance between rotor and wall is inch. Heat of vaporization is provided by jacketed steam surrounding the evaporator body. Product leaving the evaporator flows by gravity to a receiver and the vapors generated by evaporation rise through the evaporator between the rotor lades into a water-cooled tubular conde ser. The evaporator system, including evaporator, product receiver, condenser, and condensate receiver is maintained under vacuum. The vacuum source is located a t the base of the condenser. Condensed vapor discharges by gravity into ,the condensate receiver and noncondensables enter the vacuum line. The pressure level of the apparatus is regulated by a pneumatic controller. The feed rate is measured by a
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VOL. 52, NO. 1
JANUARY 1960
71
TO VACUUM su PPLY
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Block diagram of climbing film evaporator system A.
Rotameter F. Motor B. Evaporator P. Vacuum g a g e C. Tubular condenser T. Thermometer well D. Product receiver - - - - Vacuum line E. Condensate receiver Evaporator dimensions. Feed inlet to feed outlet, 20 inches Inside diameier, 2.8 inches Clearance between rotor and wall, 1/17 inch
rotameter and is controlled by a valve between rotameter and evaporator.
Theory
To determine the shape of the liquid film within the evaporator two regions are considered : the annular space between the rotor blade tips and the wall, and the space inside the cylinder formed by the tips of the rotor blades. With high feed rate, the space berll-een
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rotor blades and wall is filled with fluid. This, in general, is a necessary condition for satisfactory operation. 141th low feed rate, sufficient material may be evaporated so that the annular space between blade tips and wall is not filled in the upper portion of the tube. I n this work, however. this space is assumed filled. The problem is then reduced to finding the shape of the film formed by the tips of the rotor blades inside the cylinder. T o compute film thickness,
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it is assumed that the force balances for laminar flow, the Navier-Stokes equations, apply. A solution is obtained which neglects any change in film thickness in the vicinity of the rotor blades-i.e., it is assumed that the film is uniform in thickness in a radial direction although the thickness can vary with position along the length of the tube. I n the chosen coordinate system, the y axis is coincident with the rotor shaft center line, and the origin is the point of intersection of the axis and a line formed by the intersection of the plane of the p axis and the horizontal plane containing the evaporator fluid outlet. The position direction of the p axis is downward. Cylindrical coordinates are used, with distances perpendicular to the rotor shaft measured in terms of a radius vector r and an angle 0. A point is then represented by the coordinates (11, r , 0 ) . I n cylindrical coordinates, the Navier-Stokes equat'ons describing thr motion of the fluid are (3):
CLIMBING F I L M E V A P O R A T O R
m
I
LT
IC
50
I Volume holdup when (R.P.M.)> (R.P.MJo
j.
where u and u are the radial and tangential components of the velocity in a plane perpendicular to the rotor, and p , 7, g are the density and viscosity of the fluid and the acceleration of gravity, respective]y. Solution of these equations for the climbing film evaporator gives several useful expressions. The critical angular velocity of the rotor below which the evaporator fills u p is given by
where ro = radius of rotor shaft, rl = radius of rotor blades, h = height of evaporator, g = acceleration of gravity and w o = critical angular velocity. For rotor speeds less than w o the tube is partially filled with liquid. The volume holdup ( V I ) within the cylinder formed by the rotor blade tips, neglecting the rotor blade thickness, for w > w o and equal inlet and outlet densities, is : Vl = irgh2/w2
v2
40
0
180
begins to fill up=(R.I?M.),
m
Power L l i v r r e d t o material flowing through evaporator
where V is the total volume of the rotor from feed inlet to product outlet. Equation 3 shows that the volume holdup (VI) within the cylinder formed by the rotor blade tips is independent of the radius of the rotor blades and depends only on the height. As the radius increases the centrifugal force increases making the film thinner, thus compensating for the increased circumference. Also, V I varies inversely as the square of the rotor r.p.m. Thus Vi decreases sharply as the rotor speed increases. The asymptotic value for the total volume holdup is V 2 . If i t is assumed that there is no channeling, then an average holdup time is :
I70 160
150 35
7
30
-k 25
6
lr
z
= 20
N
.V= V,
+ lT t2(2r,+
130
t,)h
Y
i;!
110
; ;
V
5 4
8 o mcz ( +N
5 A
5
15
100
70
91%
c
-
120
Y
L-.
\
n
-
I ; 90 u
h
u
140
Note: The total volume holdup i s :
3
2
60 50
10
2
40
5
I
30 20
IO
(4)
where V Z is the volume of the annular space between rotor blade tips and wall. The total volume holdup when the evaporator is partially filled up corresponds to improper operation-Le. , the rotor revolutions per minute (r.p.m.) is too low. However, it is of interest to see if theory and experiment agree in this region. Volume holdup is found for ~ e ) < w o for the case of equal inlet and outlet density. If the tube is filled to the point yo the volume is :
m
9
(3)
T h e total volume holdup ( V ) is:
v = v,+
190
II R.I?M. at which evaporator
45
200
1
0
O 200
600
1000
1400
1800
2200 2600 3000
R. P.M.
Figure 1. These design curves for climbing film evaporator are valid for the case of equal inlet and outlet densities
s
(6)
= v/qo
8 = average holdup time V = volume holdup 40 = volumetric feed rate In finding an expression for the power requirements, it is assumed that there is no slip between liquid holdup and wall and between holdup and rotor blades and that all’the liquid within the cylinder formed by the rotor blade tips is moving at the same angular velocity as the rotor. The power requirements are in units of horsepower : P = 0.263 X 10-8
( h r 1 3 / t 2 ) N2
qcp
(7)
where t 2 = clearance between rotor blade tips and wall, N = rotor r.p.m., and rl,, = average holdup viscosity.
Experiment I n the case of cold water, volume
holdup data were obtained by fil :ng the evaporator with water, and allowing the rotor to turn a t the desired r.p m. for 6 minutes. Evaporator contents were then weighed immediately Holdup data for boiling water were obtained as follows. After 10 minutes a t steady state conditions, feed line to the evaporator, outlet valve a t the base of the condenser, outlet product valve and vacuum line valve, jacket steam valve, and rotor were shut; shut-down operations required less than 30 seconds. T h e evaporator was emptied and the weight of liquid holdup was obtained. T o find a measure of holdup time for boiling water, Du Pont Halopont Blue dye was injected by a hypodermic needle into the Tygon feed line to the evaporator at a point 10 to 20 cm. from the base cf the evaporator. Dye entered the line for a period of about 2 seconds. Elapsed time between injection of the dye and its visual appearance in the product outlet of the evaporator is a measure of the VOL. 52, NO. 1
JANUARY 1960
73
holdup time. The elapsed time between injection of the dye and visual appearance of the first and last traces of bluetinted water to appear in the product outlet was measured with a stop watch. Ha!opont Blue was used as the dye because of its solubility and good visibility in water. Power requirements of water holdup were measured with a M‘estinghouse Type TL4industrial analyzer and manufacturer’s efficiency curves for the motor. The power requirements were found by measuring the no load electrical input to the motor while evaporating water. The product of the motor efficiency and the difference between load and no load input to the motor is the power required by water. The over-all heat transfer coefficient for water was measured by weighing the amount of wate- evaporated per unit time. The average steam film coefficient was determined by use of a Wilson plot.
Comparison of Theory and Experiment Data and theory are in agreement for holdup in the climbing film evaporator with cold water and water evaporation. The holdup volume decreases sharply benveen 0 to 1600 r.p.m. and is essentially constant above 1600 r.p.m. for the test evaporator. Holdup time given by the expression = V / q , falls within the curves outlined by the data for visual appearance and The initial disappearance o’ dye. holdup time data are independent of rotor r.p.m. because they are a measure of the feed rate which is held constant. T h e final holdup time data are a measure of the holdup volume as. well as of feed
e
74
rate, so that with increasing r.p.m. the time required for disappearance of the dye diminishes. Over-all heat transfer data for water evaporation show that the effect of rotor r.p.m. on the evaporation rate is considerable. For the test system, the evaporation rate increases 40 to 70y0 from 1000 to 2000 r.p.m. The rotor power consumption data and predicted curve show that the power increases greatly with increased r.p,m.viz., as the square of the r.p.m. Figure 1 shows a set of curves Ivhich can be used for design purposes. The curves are valid for the case of equal inlet and outlet densities. Any design must be a compromise between high volume holdup and holdup time, and high power requirements, because with increasing rotor speed the po\z’er increases sharply. I t is not satisfactory to operate at low speed because of low heat transfer. Also, as the volume holdup is essentially independent of the radius, while the poxver depends on the radius cubed and directly on the height, a minimum radius and maximum height are desirable.
t2
= clearance between rotor blade tip
and wall radial component of velocity tangential component of velocity V = total volume holdup VI = volume holdup w-ithin cylinder formed by the rotor blade tips Vz = volume holdup in annular space between blades and wall V = rotor volume w = rotor angular velocity w o = angular velocity at which the tube begins to fill y = coordinate measured along rotor shaft j = velocity in J direction j = acceleration in y direction 7 = point viscosity of liquid holdup $cp = = average viscosity of liquid holdup = coordinate angle 9 = average holdup time p = liquid density vzj = Laplacian of) u u
= =
e
Acknowledgment Advice and encouragement from C ‘I. Cargill during the course of this work is gratefull\ acknoitledged
Nomenclature g h
= acceleration of gravity = height of evaporation area
p
= =
P
=
qo
=
r
=
A\-
INDUSTRIAL AND ENGINEERING CHEMISTRY
YO
rl t
= = =
r.p.m. ofrotor static pressure rotor power requirements to maintain liquid holdup volumetric feed rate into evaporator magnitude of the radius vector in cylindrical coordinates radius of rotor shaft radius of rotor blades time
Literature Cited (1) Haley, F. C. (to E. I. du Pont de Nemours & Co.; Inc.), E. S. Patent 2,866,499 (1958,. (2) Hauschild, W.. Cheni. Ingr. Tech. 2 5 ,
573 (1953).
(3) Lamb, Sir Horace, “Hydrodynamics,” 6th ed.. u. 579. Dover. Yew York. 1945. (4) Schneider, S . , Chen;. Ingr. Tech. 27,
237 (1955). RECEIVED for review March 27, 1959 ACCEPTEDAugust 28,1959
