EFFECT OF A DISSOLVED SOLID ON WIPED-FILM EVAPORATION WALTER UNTERBERG'AND DONALD K. ED WARDS Department of Engineering, University of California, Los Angeles, Calif.
Evaporation from saline water films wiped on the outside of a heated vertical copper tube by flexible blades was studied with variable salinity, temperature difference, and wiper speed. An analysis accounting for boiling point elevation due to salinity shows that evaporation rate decreases with increasing salinity and decreasing blade efficiency, a measure of mixing between feed and brine liquids in the blade bow wave. A scraper-wiper combination i s desirable. Free surface evaporation was observed with nonboiling feed. Film continuity was poor for pure water, but high for saline water, because of the effects of temperature and salinity on surface tension gradients. Film thicknesses were measured and used in the analysis. Observed evaporation rates were correlated with the analysis by assignments of blade efficiencies which were unity at low wiper speeds and decreased as wiper speed and evaporation rate increased.
conversion of saline water to fresh water, evaporationcondensation equipment with evaporating and condensing streams on opposite sides of a wall is often used. High evaporation-side heat transfer coefficients are obtained from thin liquid films generated by wipers moving relative to the heated wall. The thinnest films have been obtained with preloaded flexible blades (2, 4, 5 ) . Existing wiped-film evaporators use the inside surface of a cylinder or cone for evaporation, so that no direct observations of film flow phenomena during evaporation or measurements of wiped-film thickness have been made. A lack of such observations has hindered absolute comparisons between evaporation theory and experiments. The objectives of the present investigation are:
I
N THE
I
x !U (axial)
L
:Id
n
T o determine experimentally evaporation rate us. wiper speed, feed salinity, and evaporation temperature difference for thin films wiped on a vertical heating surface with flexible blades. To observe visually the evaporation mechanism, film continuity, and wetting of the heating surface. T o account theoretically for the action of salinity to increase the boiling point and thus decrease evaporation rate. T o compare the present and previous experimental results with the present theory. Wiped-Film Evaporation Theory
Assumptions. Evaporation from a thin wiped film of pure liquid was treated by Lustenader, Richter, and Neugebauer (4) under the assumption of a motionless film with quasisteady heat conduction. The present paper extends the analysis to include boiling point elevation effects. Figure 1 shows the cylindrical evaporator configuration of interest, and Figure 2 the imagined process of film formation by a wiper. For conditions typical of practice, a wiped film can be regarded as motionless on the heating surface, and the heat conduction is quasi-steady, with a linear temperature profile across the film (6). Thus the assumptions made by Lustenader, Richter, and Neugebauer (4) are applicable to the present study. I t is further assumed that evaporation takes place from the free film surface.
Figure 1. rator
Cylindrical wiped-film evapo-
L'L,
t = t,= QIW
Also with Rocketdyne, a Division of North American Aviation, Inc., Canoga Park, Calif. 268
I&EC P R O C E S S DESIGN AND DEVELOPMENT
Figure 2.
Wiped-film profile
Evaporation with Boiling Point Elevation. With these assumptions, the salinity profile across the evaporating film is found in the appendix by solving the requisite salt diffusion equation. For saline water films at moderate temperature differences, a typical value for surface-to-average salinity ratio, &!Sa,., is 1.1. Also, for typical concentration ratios, the density ratio, pav/pi, is 1.1. Thus the free film surface salinity and temperature gradient may be written
The heat transfer across the film by conduction furnishes the latent heat of vaporization needed for evaporation at the free surface : -k
(?$)h
dt
= -Xp dh
Equation 6 after substitution of Equation 11 becomes
T o carry out this integration a relation for A T ( S h ) and Equation l must be substituted into Equation 5 for integration. By combining Equations 5 and 10, He is expressed in terms of Sow with parameter 7, and the result is substituted into Equation 12. Such a solution for S,(x) yields M,,(x) by virtue of Equation 11. Comparison of Solutions. LINEARBOILINGPOINTELEVATION. BPE = p qs.
+
(3) I n this case Equation 5 becomes
Substitution of Equations 1 and 2 into Equation 3 and integration yield the time to reduce the film thickness from h i to h (4) where the properties outside the integral are constant a t a n average value. Since the wiper travels with velocity W, the distance ze between consecutive wipers passing every time t, is Wt, (Figure 2). Equation 4 then becomes
(5) A mass balance on the bow wave yields
- -d M-b w - pW(ht - he) = pWhf(l - He) dx
(6)
where he is the thickness of the wiped film after evaporation during the time between passage of consecutive blades (Figure 2). Conservation of salt in the bow wave ahead of one of the n wiper blades is expressed by
SbmMbm = M d F / n
(7)
The initial film salinity, St, is a function of the degree of mixing between the nonevaporated film residue (at S,) and the bow wave (at S,,), characterized by a “blade efficiency,” 7, defined as
where
(9) Substitution of Equations 1 and 9 with H = He and Sh = Se (approximately) into Equation 8 gives
The evaporation rate, M , , ( x ) , is simply the difference between the feed and bow wave flows, so that from Equation 7
K t In (1
-)
- 1 - He 1
(14)
- Kf
where
An explicit expression for He equivalent to Equation 14 can He) us. b be obtained from curve-fitting a plot such as (1 with lines of constant Ka. The He representation may be entirely numerical or may consist of approximate but integrable analytical expressions. By using such expressions ( = t l O ~ , accurate) in the procedure outlined above, analytical results for Sbm(x) and evaporation rates from wiped saline films are obtained. Table I lists the intermediate and end results for general and special cases. POWER LAW. AT(sh) = f A T o f h - g (over a limited S range). Explicit asymptotic expressions for high and low M e , can be obtained readily from Equation 12 when q = 1 (6). COXSTANT PROPERTY.AT(Sh) = A T = const. This applies to pure water or a fixed S (no BPE) and implies q = 1. Equation 5 is integrated directly to yield
-
which is equivalent to the result of Lustenader, Richter, and Neugebauer (4) and indicates a linear decrease in bow wave flow rate down the evaporator (Equation 6). Utility of the wiped-film analyses above may be exemplified by a design problem in which the vertical evaporator length is to be found. Such lengths are compared in Figure 3. The constant-property solutions underestimate the evaporator length, while the linear BPE and power law solutions yield nearly the same, longer length. Constants f , g, p, and q were based on saline water properties compiled by Unterberg (6).
Experimental Apparatus and Procedures
Evaporator. The outside-wiped-film (OWF) evaporator (Figure 4) consists of a 4-inch o.d., 16-inch high stationary VOL. 6
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JULY 1967
269
Table 1.
Analytical Results of Wiped Saline Water Film Evaporation with linear Boiling Point Elevation (BPE = p (7
Case
- He) asf(b,Ki)
Exact for small horizontal evaporation, b +.0
(1
- Ki)b
Approximate, for any b
(1
- Ki)tanh b
Approximate, for any b
(1
- Ki)tanh b
Exact for BPE-limited evaporation, b -+ w
(1
- K i ) (1 -
t
(7
- H I )asf(Sbwi7)
a(1
Sb,( x )
- H,)* +
Positive root of (1
Any
+ qS)
Numerical integration
- HI)+ ,3 = 0
e-bIRi2)
a = [Sbqq tanh b / ( A T o
- p ) ] - q - tanh b
) (tanh b ) Ki
= 9
I
// //
I
/
I
I
\
I
-p )
k(ATo - p ) .ze/pXWhi2
b
1.0 I
&/(AT0
/
I
10
I
10.6
I
I .
X
Figure 3.
- VERTICAL
LENGTH
-
FT.
Comparison of wiped-film evaporation analytical solutions AT0 = 15’ F. S F = 9%
copper tube heated internally by condensing steam. Pure or saline water feed flows onto the copper surface under gravity through three ducts, one for each blade, attached to a rotating reservoir above the tube. Rotating with the reservoir and feed ducts are three adjustable rubber wiper blades (16 inches long, 1.5 inches wide, and ‘/IO inch thick). A %inch i.d. glass pipe surrounding the copper tube seals the evaporator but allows visual observation. Electrical heating in a Libby-Owens-Ford 81E transparent coating prevents condensation on the glass. Yield vapor is drawn off through a duct at the top of the evaporator into a condenser. Nonevaporated feed flows down the vertical tube ahead of wiper blades and empties through the bottom. Condensed steam inside the tube flows out the bottom center. The blades are made of ethylene propylene rubber (EPR) with a Shore A hardness of 75, which remained constant within 2% through lengthy exposure to 250’ F. steam. I n assembly the blades are stretched so that at the operating temperature they remain flat despite the high coefficient of thermal expansion of rubber. 270
I&EC PROCESS DESIGN A N D DEVELOPMENT
Instrumentation. Temperatures of the various fluid streams were read to 0.1 O F. with calibrated thermocouples. Steam and yield pressures were read on mercury manometers to 1 mm., taking account of the condensed water columns. Feed flow rate was measured to 1% with a calibrated commercial sharp-edged orifice and flow integrator instrument. Brine, steam condensate, and yield condensate flows were obtained by measuring volumes collected during timed periods. Salinity of feed water, brine, and yield was determined by weighing out distilled water and reagent grade NaCl, by a hydrometer, and by temperature-compensated conductivity cells. Salinity readings of feed were considered correct to 0.1% and brine to 0.2 yo. Blade Adjustment and Film Thickness Determination. With the glass pipe removed, distilled water feed and heating steam were introduced, and the blades were rotated slowly so that the copper tube was partially dry between blades. Blade loading was adjusted until the wet-dry boundary line ran vertical, parallel to the blade, with distance between boundary and blade equal for all three blades.
I 0
0
Figure 4.
Cross section of outside wiped-film evaporator
After the apparatus had cooled to room temperature, the wiper was run at desired speed and cold feed flow to obtain a fully wetted, constant film thickness condition. By suddenly disconnecting the wiper drive motor, the wiper was stopped in approximately % / X O revolution, and a n absorbent paper towel of known area and dry weight was applied quickly to the wet surface to blot up the film. The damp towel was then placed in a stoppered vial of known weight, and the vial and contents were weighed on an analytical balance to the nearest milligram. The average of several such weighings was used to compute the film thickness, h,, at room temperature. Evaporation Runs. After blade adjustment, two scale-and oxide-removing feed water additives were used to clean the copper surface, H-400 sulfamic acid scale solvent (Bull and Roberts, Inc., New York, N. Y.) followed hy a saturated solution of ammonium carbonate in ammonium hydroxide. T h e beating steam, feed flow, and heaters were started. Two milliliters of a 10% solution of montan wax in liquid petrolatum (8) were ingested in the steam cavity, and the evaporator was allowed to steam for 30 minutes to obtain good distribution
of the dropwise condensation promoter on all condensing surfaces. After blowing down the entire system to purge it of air, steady-state conditions were set by adjustment of the steam pressure regulator, yield condenser water flow, and feed water trim heater. The feed water entered at approximately 2' F. below saturation, and the heating steam was superheated about 10" F. Data Reduction. Condensation and evaporation temperatures were based on saturation conditions at the measured pressures. The heat for evaporation was taken as the enthalpy difference between incoming superheated steam and leaving steam condensate. T o compute evaporation temperature differences, a constant condensation coefficient of 4550 B.t.u./hr.sq. ft.." F., an average from previous instrumented falling film runs (7) in the same evaporator was adopted, assuming radial heat flow through the copper tube. The entire data reduction (6) was programmed for a digital computer. Ranges of Experiments. Runs were made at 0,7, and 14% NaCl feed salinity (0, 2, and 4 times sea water concentration) and 60, 90, and 120 r.p.m. at atmospheric pressure and a constant feed rate of 86 Ib. per hour, corresponding to a specific feed rate of 62 lb./br.-sq. ft. heating surface. Pressure difference between beating steam and vapor yield was varied from 0.1 to 12 p.s.i., corresponding for pure water t o a range in AT across the wiped film from 0.1' to 16" F. The observed evaporation rates ranged from 0.85 to 29.6 Ib. per hour The accuracy of the evaporation results rests on heat and mass balances for the feed, yield, and brine of the C Y P ~ L P L U L system. I n the mass balance the median error was 2% and t h e largest error was 5.5%. The corresponding errors in the heat balance were 7.1 and 15.5%. Experimental Results
Evaporation Mechanism a n d Film Conk . out the experiments, with liquid, nonboiling feed, only free surface evaporation occurred, as only glassy liquid surfaces were observed. Occasionally, boiling occurred in the lower part of the bow wave at the highest temperature differences. The presence of salt in the wiped film had a pronounced effect on film continuity, as shown by frames from 16-mm. movies taken during evaporation. With pure water at high temperature differences the film broke up, leaving irregular dry patches (Figure 5, left). When salt was present, the film was smooth (Figure 5, right). A second effect observed was liquid streaks on the evaporator tube at high wiper speeds and temperature differences. These streaks were directed slantwise downward from the blade, presumably because bow wave VOL. 6 NO. 3
JULY 1 9 6 7
271
Figure 6.
Effect of wiper s p e e d on evapo,,.,,., AP = 1 to 2 p.9.i. Blades move to right Center. Portly wetted, 25 r.p.m. R;ght. Nearly dry, 10 r.p.m.
MF = 90 Fviiy wetted, 90 r.p.m.
Left.
liquid was leaving the heating surface. Again, a t 7 or 14% salinity no breakup occurred and any ripples were much attenuated. These results may be understood qualitatively jFrom a c(Insideration of the effect of temperature and salinit!i on surf:tce tension which controls film cohesion. When pure wacer is wiped on a cold wall the surface tension is uniform. Under this condition the film, though ripply, would be expected to be continuous, as was observed. When pure water is wiped on a hot wall, a local thin spot (due to ripples) is hotter and not only evaporates faster but has a lower surface tension than the surface of the adjacent thicker film, because of the decrease in surface tension with in creasing temperature. However when salt is present, as the thin spot evaporates, it become: more saline, and the incre ase in salinity raises the surface tension and counteracts the c:ffect of temperature rise. ? . Effect of Wiper Speed ana neea EIOW ... nare. ne c m c t of wiper speed on the evaporation of pure water is shown in Figure 6 . Above a certain speed (value of W i n Equation 16 for which h, = 0), the surface is fully wetted (Figure 6, left). Below this speed, all the liquid a t a point will have evaporated before the next blade arrives, leading to a vertical dry stripe (Figure 6, center) which widens with decreasing speed (Figure 6 , right). T h e effect of reducing the feed flow rate with ~ u r e water was to starve the lower part of 1the blade bow wave of liquid, 1eading to dry areas fni m the b,ottom up. The correspondini% effect with saline wal:er and a high evaporation temI I , x ~ ~ ~ ~ ~ : ~~ : c _ ~ ~ ~ _ , : was a progressive prccipirarion 01 sail Irom perature u~ncrcnct: the bottom up. Evaporation also takes place from the prccipitate, which forms a solid-liquid white slush. Wiped-Film Thickness. T o compare the results with the theory presented, it is necessary to know the film thickness, hi, wiped on the evaporator wall. Figure 7 contains data for pure water a t 77’ F. The slope of the log-log curve of hi us. wiper speed N varied from 0.50 to 0.95 among the three blades. The value of 0.50 would he expected for a rigid blade in laminar creeping flow according to the hydrodynamic theory of lubrication ( I ) . A higher value could indicate the presence of some inertia effects (such as those due to the bow wave), which would depend on the square of the wiper speed. Because of the method of setting the blades, there was a variation in hi
...
~~~~
272
~
~~~~~~
-.
1-1
~
I&EC PROCESS DESIGN AND DEVELOPMENT
among the blades, from 0.3 to 0.6 mil a t 60 r.p.m. (Figure 7 ) . The closeness of the “before” and “after” mints indicates negligible chaniges in h, duri “E ; some 47 hours of evaporator operation. For a compa.rison betweein theory and experiment it was ., ‘ I cola 1 7,. , . - l j j l _,. desired to correcr. rne n, values TO actual not evaporaring conditions. I t was decided to correct for temperature and salinity by the proportionality of film thickness to the square root of the liquid viscosity, according to slider bearing hydrodynamics. This resulted in lower values under “hot” conditions. Evaporation of Pure Water. Figure 8 shows an increase of E with AP and N , in qualitative agreement with theorv (Equation 16, noting that E = p(h, - h,)l N , the increase of E with AP is represented straight-line segments which correspond ohserved evaporation regimes: “fully wettea, ary region ar bottom,” and “complete evaporation.” As AP increased, the tube dried up vertically from the bottom and uniformly around its circumference. Thus no effect due to the different measured film thicknesses at the three blades was found. At low AP the copper tube was fully wetted; the numbers next to all other data points are their associated wetted percentage areas. The “complete evaporation” regime is shown photographically in Figure 6, center and right. The continuing decrease in wetted area with increase in AP no longer corresponds to a n increase in evaporation rate. ~ _ r ~ ~ ~ ~ ~ The observed values of E were below the theoretical ones for all speeds. A major factor responsible for this behavior was the observed drying of the wall from the bottom upward with increasing AP. It was concluded that bow wave liquid was leaving the heating surface p a r t w a y down the wall, becoming unavailable to the wiped film. No liquid was seen being thrown off the wall into the sump or onto the outer glass pipe. Thus it was likely that liquid was thrown against the moving wiper blades by centrifugal force, and ran down the blades into the sump. Computing the evaporation heat transfer coefficient, Us, us. AT, gave results analogous to Figure 8. I n the fully wetted regime ( A T up to about l o F.), U,, averaged 6000 B.t.u./hr.sq. ft.-O F. As the drying u p proceeded, U,, gradually de~
1
* MEASUREMENTS BEFORE AND AFTER WIPED
N
Figure 7.
-
REVOLUTIONS
PER MINUTE
Average initial wiped-film thickness from measurements at
77’ F. M p = 88 Ib./hr.
N
24
m: 60
VISUALLY ESTIMATED WETTED AREAS (%I WITH DATA POINTS STRAIGHT LINE FITS
l
a
I 2 20
SYM:
0
90 0
120 A
-I
I W !-
2 I5
5
>RY REGION 4T BOTTOM
W
2 10 G W
a v) ‘ 5
w
0
, AP
I
I I
2
4
-
OVERALL
Figure 8.
I I
PRESSURE
6 DIFFERENCE
I I
-
8 PSI
Wiped-film evaporation of pure water
s=o
creased down to a value of 1000 a t a maximum AT of 16’ F. The U,, variation was essentially independent of wiper speed. Evaporation of Saline Water. Plots of E us. AP appear in Figure 9 for 7% and in Figure 10 for 14% saline water. Evaporation does not start until a minimum AP has been reached, just sufficient to overcome the boiling point elevation a t the feed salinity. Then E increases with AP a t rates which decrease as AP increases. The increase of E with N is marked for 770, but slight for 14y0 saline water. The copper heating surface was fully wetted a t all times, regardless of salinity, AP, or N . When AP increased beyond a certain point, salt was observed to precipitate uniformly around the tube from the bottom up, while evaporation continued to increase. Data points in this “total, partly precipitated” evaporation regime are shown flagged, together with numbers giving the associated per cent precipitated areas. Discussion
Comparison of Experiment and Theory. Figure 11, a plot of E us. A T , for 7% saline water, contains theoretical evaporation curves computed on the basis of 100% blade efficiency with the linear boiling point elevation (BPE) solution. The particular run conditions were such that BPElimited evaporation occurred a t nearly all data points (see Table I).
The theoretical curves predict finite evaporation rates for the “partial, fully wetted” regime in the A T , interval between the BPE a t the feed salinity (2.1’ F.) and a t saturation (15’ F.). These A T , values are confirmed experimentally for all wiper speeds-i.e., evaporation begins close to 2.1’ F. and salt precipitation begins within a degree of 15’ F. Such confirmation also was found with 14Y0 saline water. I n the “total, partly precipitated” evaporation regime above a A T , of 15’ F., the evaporation mechanism is no longer free surface evaporation from a liquid, but drying of a “slush” mixture of saturated salt solution and solid salt, possibly controlled by heat and mass diffusion through the two-phase mixture. If a 0.050-inch slush thickness (reasonable, based on observation) is assumed, always fully wetted at the free surface, then a slope of 3’ F. per lb./hr.-sq. ft. results. The dashed straight lines in the precipitation regime have been drawn with this slope, and show some agreement with the experiment. The horizontal dashed lines indicate the maximum possible E, obtained when all the saline water wiped on the surface is evaporated to dryness, leaving only the solid salt. A comparison of the experimental and theoretical specific evaporation rates on Figure 11 shows a similarity in shapes. At 60 r.p.m. the curves are practically identical, but a t higher N the experimental curves lie below the corresponding theoretical curves. VOL. 6
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JULY 1 9 6 7
273
-
AP
Figure 9.
I
5 \
20
= 7% I
FLAGGED POINTS : SALT PRECIPITATION FROM BOTTOM NUMERALS: VISUALLY ESTIMATED SALTED AREA (%)
I
w
I
2 PP
Figure
-
PSI
Wiped-film evaporation of saline water
s N
-
OVERALL PRESSURE DIFFERENCE
3 OVERALL
19
I
I
1
I
I
I
I
4
5
6
7
8
9
PRESSURE
DIFFERENCE
-
IO
PSI
10. Wiped-film evaporation of saline water S = 14%
Blade Efficiency. I n an effort to explain the results one may fit the experimental curves of Figure 11 with “apparent” blade efficiencies, using Table I. Figure 12 shows the apparent blade efficiencies for the present 7% data to decrease with The increase in wiper speed and evaporated fraction E/E,,,. first effect would be expected on the basis that the contact time would be reduced a t the higher speed, were the contact distance in the bow wave, A t , to remain unchanged. The second effect would follow from the fact that as the evaporated fraction increased, the average amount of liquid in the bow wave would decrease, and with it the length of A t . I n the outside wiped film evaporator there is a tendency for bow wave liquid to leave the tube wall because of centrifugal force. This fact might be the only reason for the blade efficiences to lie below loo%, if otherwise the contact time is adequate for complete mixing. I n an inside wiped film evaporator the centrifugal force tends to force the liquid to remain on the wall and the blade efficiency would then be primarily dependent on the contact time. Examination of inside wiped-film evaporator data taken over the speed range from GO to 150 r.p.m. by the General Electric Co. (7) with similar geometry leads to the conclusion that the contact time is not yet significant. The dashed curve on Figure 12 shows only a mild decrease in (relative) apparent blade efficiency as wiper speed increases. The magnitude of 274
I&EC PROCESS DESIGN A N D DEVELOPMENT
the decrease is not nearly as much as in the present results for the outside wiped-film evaporator. I n fact, the minimum relative blade efficiency of 83% for the inside wiped-film evaporator corresponds to an evaporation rate which differs from the rate of 100% by an amount possibly of the order of the experimental error. Evaporator Improvements. With saline water there are two salinity effects, both of which can reduce wiped-film evaporator performance : the boiling point elevation which reduces the net temperature difference across the wiped film in the horizontal and vertical directions, and the incomplete mixing between bow wave and highly saline nonevaporated film residue which leads to initial wiped-film salinities above those which would result from complete mixing, and reduces the net temperature difference even more. The second effect seems to apply with particular force to the outside wiped-film evaporator. This situation prompts the search for a wiped-film evaporator configuration in which salinities are kept down to the feed salinity level as much as possible over the entire evaporator surface. An outside wiped-film evaporator arrangement of this type would also be a useful research tool in which bow wave hydrodynamics effects could be studied separate from salinity effects. I n one such arrangement a scraper blade would be added in
&I
I-
LL
AT,
-
EQUIVALENT
Figure 1 1.
PURE
H20
TEMP DIFF.
OF
Wiped-film evaporation of saline water
Comparison with variable property analysis based on measured h , s = 7%
PRESENT DATA
(OWF)
E/EMAX.
WIPER SPEED N, RPM
Figure 12.
Apparent blade efficiencies of wiped-film evaporation s = 770 AP, P.S.1. Tube, In. Surface Blades ~6.0 Outside 3 4 dio. X 16 4.4 Inside 4 6 dia. X 5 0
---
front of the usual wiper blade. The scraper would remove the highly saline wiped-film residue from the tube wall and cause it to flow down the scraper to a sump without coming in contact with the feed. Thus bow wave salinity increases in the vertical direction would be avoided along the whole blade length. T h e blade efficiency in such an arrangement would be close to 100% and evaporator performance would be affected principally by the bow wave hydrodynamics. I t might further be possible to dimension the cross section of the volume contained between scraper, wiper, and tube surface such that this cross section would always be completely filled by the bow wave flow, minimizing adverse hydrodynamic effects. Conclusions Salinity variation across the evaporating film is small, typically 10%. A wiped saline water film evaporation analysis accounting for boiling point elevation (the principal variable property effect) shows that evaporation rates fall with rising feed salinity and with decreasing blade efficiency. I t also predicts the limits of
the “partial, fully wetted” and “total, partly precipitated” evaporation regimes. An improved evaporator would result from the addition of a scraper blade in front of the wiper blade to separate the highly saline nonevaporated film residue from the bow wave flow, thus avoiding vertical salinity increases and maintaining 100% blade efficiency. Wiped-film thicknesses in the 0.3- to 1.0-mil (10-3-inch) range can be set with flexible EPR rubber blades and measured at room temperature. The mechanism of free surface evaporation was observed for all test conditions, with liquid, nonboiling feed. Film continuity was poor for pure water but high for saline water. This fact may be explained by the influence of temperature and salinity on surface tension gradients. For outside-wiped-saline-water-film evaporation at atmospheric pressures with variable feed salinity (7 and 14y0),wiper speed (60 to 120 r.p,m.), and temperature difference (up to 16’ F.), evaporation rates and regimes predicted by theory were verified by assigning a decreasing blade efficiency with increasing wiper speed. Fitting the theory to inside wiped-film evaporation data of others indicated close to 100% blade efficiency. VOL. 6
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275
Salinity Profile in Wiped Film
Appendix.
Transient salinity profiles in the wiped film can be determined a t any x during one-dimensional evaporation from h = ht to h = h, by writing the salt diffusion equation in the film with the proper evaporative boundary condition a t the free surface, as follows:
?!
(h,t) = BS(h’t) Nonvolatile solute at evaporating surface h(t) ~
hY
‘1’
Quasi-steady evaporation film thickness (4, 6) (21)
Lh
Sdy
=
Sihf = S,,h
Over-all salt conservation
(22)
Here the value of St is assumed known at the particular x. A solution of the form S(y,t) = Y ( y )T(t)-Le., by the method of separation of variables-reduces
Equation 17 to
When constants K and y are found from Equations 20 and 22, one obtains the quasi-steady solution
where qj is a function of B given by 9 tanh 6 = B h is a function o f t given by Equation 21
From Equations 24 and 22
Typical values for SS /, , are 1.04, 1.11, and 1.24 a t B = 0.1, 0.3, and 0.6, respectively. For the experimental range of interest, B is less than O.G, so that the salinity profiles are rather flat, the value of being perhaps 1.1 on the average. I n practice, the diffusion may be faster than the molecular rate, so that the profiles will be even flatter. Acknowledgment
J. W. McCutchan and R. L. Perrine acted as program coordinator and project leader, respectively. R. M. Webb collaborated in the experiments and W. Gregson, Jr., in the design of the evaporator.
a quantity defined in Table I and Equation 16 total height of evaporator, ft. mass flow rate (evaporator), lb./hr. wiper rotational speed, r.p.m. number of wiper blades n P‘ = pressure, p.s.i.a. = BPE linear law parameter P R’ = a quantity defined in Table I = BPE linear law parameter Q Q’ = a quantity defined in Table I = salinity, 100 mass of solids/mass of mixture, yo S = temperature, F. or R. T = time, hr. t = time between arrivals of successive wiper blades at te point on evaporator, hr. T,” = evaporation temperature, saturated vapor at P,, and S = Sh(T,,,at S = 0), F. or R. To = temperature of evaporation surface (0.d. of heat transfer tube), O F. or O R. = heat transfer coefficient, B.t.u./hr. sq. ft. F. U V = horizontal radial velocity (y-direction), ft./hr. W = linear wiper speed, ft./hr. = horizontal circumferential velocity (2-direction), ft./hr. W = vertical axial coordinator (x = 0 at top, x = L at X bottom of evaporator), ft. = horizontal radial coordinate ( y = 0 at heating surface, Y y = h at free film surface), ft. = horizontal circumferential coordinate ( 2 = 0 at 2 blade), ft. = circumferential distance between blades, ft.
Ki L M N
= = = = =
GREEKLETTERS AP = over-all pressure difference, P, - P,,,p.s.i. AT = evaporation temperature difference, To - T,,, O F. AT,, = zero salinity temperature difference, To - T,,,, O F. At = circumferential contact length - of bow wave on heating surface, ft. = blade efficiency, 100 (S,- S,)/(S, - Sbw),% 7 h = latent heat of vaporization, B.t.u./lb. = mass density, lb. m/cu, ft. p SUBSCRIPTS av = average 61 = blade bw = bow wave e = end; minimum; at time t , or at distance z, ev = evaporated, evaporation, evaporating F = feed, inlet h = free surface of liquid film (y = h ) i = initial wiped film (thickness) max = maximum o = evaporation surface ( y = 0); zero salinity s = steam x = at x-coordinate literature Cited
(1) Fuller, D. D., “Theory and Practice of Lubrication for Engineers,” Wiley, New York, 1956. (2) General Electric Co., “Evaluation of a Thin-Film Sea Water Distillation Unit for Marine and Shore Base Application,” Office of Saline Water Research and Development, Progr. Rept. No. 54 (OTS PB 181041, Department of Commerce) (October 1961). 131 Goodman. T. R.. Am. Sac. Mech. Enp. Trans. 80. 335 11958).
Nomenclature
b B
BPE D d
E
f,g H h hi
k
276
= = = = = = = =
= = =
a quantity defined in Table I and Equation 14 salinity profile number, kAT/DXp, dimensionless boiling point elevation, F. molecular diffusion coefficient, sq. ft./hr. diameter of evaporation surface (0.d. of heat transfer tube), ft. specific evaporation rate, lb./hr. sq. ft. BPE power law parameters h/hi, dimensionless liquid film thickness (y-direction), ft. initial film thickness (at blade), ft. thermal conductivity, B.t.u./ft.-hr.-O F.
l&EC PROCESS DESIGN A N D DEVELOPMENT
( 6 ) Unterberg, W., “Evaporation from Falling and Wiped of Saline Water,” Ph.D. dissertation, Department of Engineering, University of California, Los Angela; 1964. (7) Unterberg, W., Edwards, D. K., A.I.Ch.E. J . 11, 1073 (1965). (8) . . Watson. R. G. H.. Brunt, J. J.. Birt. D. C. P., “International Developments in “eat Transfer;” Part 11, Paper 35, p. 296. Am. SOC.Mech. Engrs., New York, 1961.
RECEIVED for review July 1, 1966 ACCEPTEDJanuary 13, 1967 55th National Meeting AIChE, Houston, Tex., February, 1965. Work supported by the State of California, through the Statewide Water Resources Center.
