Experimental Analysis of Forced Convection Film Boiling from a Flat

EXPERIMENTAL ANALYSIS OF FORCED CONVECTION FILM BOILING FROM A FLAT HORIZONTAL PLATE J R . , I A N D R . Carnegie-Mellon University, Pittsburgh, P a . 40506

J . F. Z E M A I T I S ,

I . KERMODEZ

An experimental study of the effect of velocity on film boiling heat transfer from a flat plate for two liquids, ~ hexane and methanol, has shown that for velocities less than 4 feet per second the NN“ relationship is: N N = 0.1 41 ( N R , ) O . ’ ~ ( N ~ ~ ~ ) O . ~This ~ ( ~study ’ / ~ ) ~verifies . ~ ’ . the N p r ~relationships in the model of Owens. The ~ is much smaller than his model would predict. The large effect of the ratio of the experimental N R effect liquid to vapor viscosity is an effect not accounted for in any existing models for forced convection film boiling. A high speed photographic study indicated that Taylor instability anaksis was appropriate. The experimental “most dangerous wave length” of 0.76 compared favorably with the theoretical value of 0.69 inch.

N THE

boiling process it is possible to increase the temperature

I of the heating surface so that a film of vapor completely covers the heating surface. This insulating vapor layer reduces the heat transferred to a small fraction of that possible with nucleate boiling. This boiling regime, known as film boiling, has been the subject of many experimental and theoretical investigations. Film boiling of pools of liquid has been experimentally studied on heating surfaces such as flat plates, tubes, and wires. Forced convection film boiling has been studied for liquid flow across tubes and wires. Several theoretical models have been proposed for forced convection heat transfer to a saturated liquid in film boiling for the simple geometry of a flat horizontal plate. Unfortunately, no heat transfer data are available to test the proposed models. This study was initiated to provide experimental data for the evaluation of the various models. Previous Theoretical Models

Cess and Sparrow (1961) and Frederking (1963) have published analyses of flow film boiling. Their analysis analytically treated the vapor film as if it behaved as a boundary layer. The treatment of Frederking (1963) may be summarized as follows. Consider a stream of a pure saturated liquid approaching, with a uniform velocity U,, a flat plate which is heated sufficiently to cause film boiling. From the continuity and momentum equations, considering gravity and further inertia effects negligible, the velocity a t any point in the film is given by Equation 1, where 6 is the film thickness. (11

u = U,y/6

where q = -k

(5)

($)f

and for a saturated liquid q f , l = 0. 1 into Equation 3 yields

Substitution of Equation

m = p -

Combining this with Equations 4 and 5 gives

k A T - AHPum 6 2

(g)

(7)

Integration of Equation 7 from x = 0, 6 = 0 to x = x , 6 = 6 gives the film thickness, 6, as a function of the distance, x , from the leading edge of the plate :

The heat flux a t the wall is q = --k(bT/by) and the local heat transfer coefficient becomes :

=![-I

h=?

AT

2

pkU,AH ATx

(9)

If x = L (the whole length of the plate), the heat transfer coefficient can be written as a mean Nusselt number.

At the interface there exists continuity of mass flow density or

mt

=

mil

(2)

where 6

m = p d

dx

udy

(3)

Also at the interface there is a discontinuity in the heat flux which is expressed by: Present address, Esso Research and Engineering, Linden, N. J.

* Present address, University of Kentucky, Lexington, Ky. 354

l&EC PROCESS DESIGN A N D DEVELOPMENT

The heat transfer coefficient given by Equation 10 varies inversely with the square root of the plate length. For anything other than extremely short plates Equation 10 predicts h ‘v 0. T o overcome this difficulty Owens (1965) proposed a model that considers hydrodynamic instability as the controlling factor in flow film boiling. By solving the instability equations for the flow of two fluids, one superimposed above the other, and assuming a linear velocity profile in the vapor, he obtained an expression for the “most dangerous” wave length given by Equation 11.

Figure 1.

G’eometrical model of Owens

For low velocities this reduces to the expression for X for Taylor instability without flow, presented by Hosler and Westwater (1962). Using this hydrodynamic wave length, Owens (1965) postulated that in flow film boiling bubbles were formed in a regular pattern, with an interbubble distance given by Equation 11. The two-dimensional rnodel shown in Figure 1 served as the basis for his analytical treatment. The assumptions used in developing the model are : The vapor generated between two bubbles is carried forward toward the bubble lying in the direction of bulk liquid flow. is flat and the vapor velocity The liquid velocity, profile . profile is iinear. The averace distance between two bubbles is determined bv hydrodynamyc instability considerations. The average film thickness is constant, since the heating surface is isothermal. The vapor flowing between film height a2 and a1 represents newly generated vapor which flows into the forming bubble. All the vapor is generated in the boundary layer between bubbles. The change in film thickness for this area can be found from the boundary layer model by solving Equation 7 for dS/dx. This equation is then integrated for x = cX A, where h is the “most dangerous wave length,” to give:

The Nusselt number can be determined from Equation 13, where c‘ is determined experimentally:

Experimental Equipment and Procedure

The heating surface was made from a 48 X 3 X 3 l / 8 inch bar of electrolytic copper. The surface was originally sanded with various grades of emery cloth and finally was polished with a fine grade of steel wool. The surface in general was repolished after taking a. day’s series of data points. T o check the effect of longer running times, the surface was not polished for a period of 3 days. No change in the heat transfer data was found with time. The plate remained very bright in color for the entire 3 days. When the apparatus was shut down, the power was turned off, but the liquid was still circulated over the plate. I n this way the type of boiling changed from film to nucleate while the copper block was cooling. O n successive days the nucleate boiling changed characteristics, becoming more vigorous. This probably was caused by a slight deposit of carbon on the surface. I t was not an oxide layer, as oxy-

Figure 2. Boiling test section, cartridge heaters, and thermocouple location

gen was excluded from the test section. The film of carbon was extremely thin, as it caused no visual change in the surface. Fifty-two evenly spaced j/*-inch diameter holes were drilled inches from the heating surface. Into each hole a Chromolox 525-watt, 240-volt cartridge heater was inserted. The 52 heaters were divided into four groups of 13 heaters. Each group was wired to independent Powerstat variable transformers with a capacity of 30 amperes a t 240 volts. Thirty thermocouple wells each ‘/8 inch in diameter and 115/16 inches deep were drilled in two rows parallel to the heating surface. The vertical distance between the top row of thermocouples and the heating surface and the distance between the two rows of thermocouples were 7/8 inch. The horizontal spacing of thermocouples was either 2 or 6 inches. The thermocouples were made of A\VG-28 gage Chrome1 and Alumel wire. Good contact between the thermocouples and copper block was obtained by forcing fine copper dust into the hole to fill any void space around the thermocouple. The flow channel, which was 47l/2 inches long and 37/* inches wide, was made by bolting two pieces of 48 X 41/2 X 3/4 inch Transite to the sides of the block. The joints were made liquidtight by inserting an asbestos gasket l / 8 inch thick between the Transite and the copper block. A piece of angle iron was used on the outside of the Transite to spread the force more evenly along the entire length. During film boiling there was no evidence of boiling from the gasket. The top of the channel was covered with a piece of heat-resistant glass which fitted into grooves in the Transite; the glass permitted visual observations as well as photographs t o be made of the boiling. The heating block was covered with 2 inches or more of insulation to reduce heat losses. Figure 2 shoivs the channel, heating cartridges, and thermocouple location. Liquid was introduced into the test section by a rectangular steel duct heated with strip heaters, and sufficient heat was added to the liquid to bring it to saturation. The preheating duct was attached to the boiling channel by a smooth lap joint to avoid entrance effects. A similar joint a t the discharge end of the boiling channel prevented disturbance there also. A schematic of the entire flow boiling equipment is shown in Figure 3. Other parts of the equipment included a liquid reservoir which served as a collection drum for the liquid from the vapor condenser and boiling channel. Next a shell and tube heat exchanger was used to cool the liquid sufficiently to avoid flashing in the pump. The outlet temperature of the heat exchanger actuated a Foxboro proportional controller, which manipulated a pneumatic control valve on the cooling water. A 25-gallon-per-minute Worthington pump pumped the liquid into a shell and tube heat exchanger which reheated the liquid close to saturation. A bypass from the heater back to the reservoir regulated the flow of liquid. Two rotameters just before the saturation preheater were used to measure the liquid flow. The vapor from the channel was condensed in a 2l/4

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rotameter

Figure 3.

Flow boiling test loop

heat exchanger, and returned to the liquid reservoir. The system was kept under a very slight positive pressure to prevent air leakage into the equipment, as the liquids studied were flammable. I n starting up the equipment it was necessary to avoid going through the critical heat flux. The method used, first proposed by Hosler and Westwater (1962), consisted of heating the surface well beyond the critical temperature and then introducing the saturated liquid. Several hours were necessary after startup to reach steady state and to go from one operating condition to another. I t was considered that steady state had been reached when the outputs of three thermocouples a t various lengths along the copper block all indicated no change on a strip chart record for 10 minutes. At this time all the thermocouples were recorded three times at 3-minute intervals. If any of the thermocouples tended to rise or fall, the unit was allowed to run for an additional 15 minutes and the procedure was repeated. Final steady-state temperatures were measured by an L & N potentiometer. The heat transfer test section was operated with a uniform power input over the entire length and film boiling was readily attained. Measurements taken for each experimental run included power inputs, temperatures over the entire test section, and liquid flow rates through the flow channel. The power input to the heaters was maintained at a constant value during each test run. Variations in the temperature of the test section were recorded after the experimental equipment reached steady state. These variations arose in all probability as a result of slight variations in each heater and its location. The large diameter holes required and the machinability of the block material contributed to a detectable variation in heater location. Since steady-state operation was being studied, the temperature in the block could be treated by the Laplace Equation 14.

Two-dimensional heat flow was verified by taking temperature measurements across the width of the test section. With the temperature position variation known for any run Equation 14 could be solved numerically by a relaxation method, presented in detail by Jakob (1949), to obtain the heat flow through the bar. This was compared with the over-all heat flux measurements obtained from the power measurements. Heat losses to the surroundings were determined by heating the bar with no liquid flowing over it, and calculating the heat transferred to the air by natural convection. The heat losses to the surroundings amounted to 4 to 8%;) of the total heat sup356

l&EC

PROCESS DESIGN A N D DEVELOPMENT

Table 1.

Physical Properties

Liquid

P'IP

u'/u

Methanol Hexane

695 to 916 204 to 276

29.1 t o 2 2 . 2 27.8 to21.6

plied, depending upon the temperature difference. Subtracting this from the power input yielded the heat loss of the bar for a given bar temperature. The liquids studied experimentally, methanol and n-hexane, gave the range of physical properties shown in Table I and film boiling could be obtained readily in this equipment. After calculating the heat fluxes and corresponding temperatures, it was found that the heat flux was essentially uniform along the length of the test section, but that for methanol an increase in temperature occurred over the first 2 feet of the test section. For the remaining 2 feet the temperature was uniform for methanol, and for n-hexane the entire bar was isothermal after allowing for the slight variations due to imperfections in heater arrangement. This increase was in the range of 20' to 30' F., and was less than 10% of the total temperature difference. Since this increase was not apparent with the use of n-hexane and occurred only in the first portion of the test block for methanol, it was decided to consider only over-all or mean temperature differences in evaluating the data. Liquid velocities were obtained by metering the total flow of liquid to the test section with a rotameter, and measuring the depth of the fluid as it entered and left the test section. The depth of the fluid at both ends of the test section was about the same. Since most of the vaporized liquid was condensed and recycled through the system, this could be used as additional confirmation of the very small decrease in liquid height at the end of the test section. At the lowest liquid velocity of 1.21 feet per second the liquid was in the test section about 3 seconds. Thus the weight of liquid vaporized was very small compared to the total throughput. Using all of the above checks it was estimated that the liquid level should decrease by less than 0.5%. This was also confirmed by the relative independence of plate temperature and length. No attempt was made to correct the velocity for the exit void fraction. The liquid formed on top of the vapor as a sheet and was rather thin in all cases. Tests were conducted using velocities of 1.21, 1.94, and 3.21 feet per second for methanol and 1.27, 3.05, and 3.82 feet per second for hexane. The pump capacity set the upper limit on the velocities studied.

i

'I0 71-1

I

too

I: i;

I20

0

I

I lot-

3

0

~

O\

\

'\

'0

I-

m

v

\

\ 1

1

50 00

;zoo

I

300

I 400

PT=Tploto-

Toot ( O F ) Figure 4. Heat transfer coefficients for methanol at a liquid velocity o f 'I -21 feet per second

' * O r -

I-

0'

I IO-

100

F

?L

-

,-

'c

590

-

3

k -

Y

t 80

-

.

@\

OO

\* 0

-E

I

L l 1 ' 1

60100

a!oo

300

I 900

I

AT= Tplate- Ttot toF) Figure 5. Heat transfer coefficients for methanol a t a liquid velocity o f 1.94 feet per second

AT= Tplotr-Tsot

(OF)

Figure 6. Heat transfer coefficients for methanol at liquid velocity o f 3.24 feet per second

Results and Discussion

The data recorded during each run permitted calculation of heat flux us. plate temperature for a fixed entrance velocity and of heat transfer coe,?icients. Figures 4 through 9 show plots of the heat transfer coefficients us. the temperature driving force for each liquid at each velocity. The best least squares fit of each gr'oup of data is represented by a solid curve. A second-order equation was used to fit these data. One dashed line on each figure represents the predicted heat transfer coefficient using the model of Owens (1965). The choice of this model \vas supported by examining high speed photographs of the flow film boiling process. A Fastax high speed motion picture camera was used a t 2000 frames per second to establish the effect of liquid velocity on the vapor film and bubble formation. The pictures indicate that bubbles form at regular intervals at the vapor-liquid interface, occur suddenly, and appear to be almost fully grown when they appear. Interbubble distances were measured from the motion pictures (Figure 10). This histogram indicates a distribution which is slightly skewed, and is very similar to the theoretical plot of the growth coefficient us. wave length for methanol. The maximum of the experimentally measured interbubble distance occurs a t a spacing of 0.76 inch, close to the calculated value of 0.69 inch for the "most dangerous" wave length. The bubble diameter a t breakoff was also measured; it showed a mean diameter of 0.41 inch at a A T of 200' F. and a mean diameter of 0.49 inch a t a ATof 295'. At 2000 frames per second the size of the bubble at inception could not be measured, as the bubbles were very close to their final diameter VOL. 7

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01

I

I

I

I

11

I

I

I

I

I

\

Y

-..

'0-

s)

0 0

0

'OI

1 100

300 AT=Tplote- Tat

\

100

(OF)

Figure 7. Heat transfer coefficients for hexane at a liquid velocity of 1.27 feet per second

c

3

400

200

\

-I

%03

tr

roo

i1 300 400 A T = Totate- Tsot ( O F )

200

Figure 8. Heat transfer coefficients for hexane at a liquid velocity of 3.05 feet per second

a t these speeds. These photographic observations support the approach of Owens (1965) toward analyzing flow film boiling. Using properties of the vapor, obtained for a temperature equal to the mean of the heated surface temperature and the liquid temperature, NN", NRe, and N p r g were calculated for the vapor. These dimensionless groups were then substituted into Equation 13 and a value ofc' = 4.14 was obtained 358

I&EC PROCESS DESIGN A N D DEVELOPMENT

o

300 4 T= Tp~ato- Ttot

400 )

(Of

w

Figure 9. Heat transfer coefficients for hexane at a liquid velocity of 3.82 feet per second

n

21

0551

40

200

I

0.693 0.835 0.977 1.1 19 OBSERVED INTERWBBLE DISTANCE (IN1

Figure 10. lnterbubble distance distribution for methanol in flow film boiling

using all the experimental data. I t is evident that this equation does give the trend of h with respect to AT a t any one velocity. A stepwise multiple regression program was used to evaluate the data on a dimensionless group basis after determining the various dimensionless groups possible for a two-phase flow system with heat transfer and change of phase. Using this program the best dimensionless correlation for all the data was found to be

)

1.8810.18

NNu= 0.141 (1VRe)0~14*0~02(iV~~K)0~48*0~02 (1 5) The multiple correlation coefficient for this expression was found to be 0.98. Figure 11 shows Nusselt number calculated from Equation 15 us. the experiment Xusselt number. The standard deviation for this correlation is 4.5%.

Nomenclature

film height, see Figure 1 empirical constants, c, c’, etc. = acceleration due to gravity, ft./hr.2 g AH = enthalpy difference between saturated fluid and vapor at mean film temperature, B.t.u./lb. h = heat transfer coefficient, B.t.u./hr. sq. ft. F. = length of flat heating surface, ft. L rn = mass flow density NNu = Nusselt number, h h / k , dimensionless NprK= Prandel K number, u A H ’ / k A T , dimensionless NRe = Reynolds number, U,ph/p, dimensionless = heat flux, B.t.u./hr. sq. ft. p T = temperature, O F. U, = liquid velocity, ft./hr. U = liquid velocity, ft./hr. u = vapor velocity, ft./hr. x = lateral coordinate, ft. y = vertical coordinate, ft. 6 = film thickness, ft. y = surface tension, Ib./ft. h = “most dangerous” wave length, ft. p = viscosity, lb./ft.-hr. p = density, lb./cu. ft. a

c

100

200

300

400

500

600

Experimental Nusselt Number Figure 1 1.

Flow film boiling parity plot

SUPERSCRIPTS /

Other dimensionless expressions such as Equation 16 were fitted to the data with ,slightly differing correlation coefficients. The differences were not large enough to distinguish truly between the models.

= =

=

liquid phase

Literature Cited

Cess, R. D., Sparrow, E. M., Heat Transfer 83C, 370 (1961). Frederking, T. H. K., “Stability of Film Boiling. Two-Phase Flow f l y u = 32.2(N~,)0~21*0~02(Np,~)0~60*0~21 (16) in Cryogenic Systems,” National Aeronautics and Space Administration, NASA N63-10641 (1963). At present additiona.1 data are necessary a t higher flow rates Hosler, E. R., Westwater, J. W., ARS J . 32 (4), 553 (1962). to confirm the efficacy of Equation 15. I n addition a theoretiJakob, Max, “Heat Transfer,” Vol. 1, Wiley, New York, 1949. cal model similar to that of Owen and Li should be developed Owens, D. C., “Forced Convection Film Boiling on a Horizontal Plate,” M.S. thesis, Carnegie Institute of Technology, 1965. which contains the viscosity of the liquid as a parameter. This would give a theoretical model with a form similar to Equation

RECEIVED for review March 1, 1967 ACCEPTEDApril 8, 1968

15. Acknowledgment

J. F . Zemaitis, Jr., received financial support from the Ford Foundation and the Allied Chemical Co.

Based on material submitted in partial fulfillment of the requirements for the degree of doctor of philosophy, Department of Chemical Engineering, Carnegie Institute of Technology, 1966, “Experimental Analysis of Film Boiling from a Flat Horizontal Plate for Both Pool and Forced Convection Boiling,”

CORREL,ATION OF GRAVITATIONAL FORCE FOR ABSORPTION IN PACKED COLUMNS G. S. JACKSON AND J . M . MARCHELLO Universib of Marq’land, College Park, Md. 20740 Re-examination of gas absorption data in packed columns a t different gravitational force levels resolves existing differences and agrees with the correlation of Onda, Sada, and Murase. An end effect correction is proposed to b e applied for gravitational forces in excess of those a t sea level. A unified correlation is developed cind trends with liquid Reynolds number and body force are presented. HE influence of gravitational force on gas absorption has Tbeen the subject oEsevera1 investigations (Van Kreulen and Hoftijzer, 1947; Vivjan et al., 1965; Vivian and Peaceman, 1956). The purpose of this paper is to resolve existing differences and to present a unified approach. Onda, Sada, and :Murase (1959) developed dimensionless correlation for liquid-phase coefficients in packed columns for Raschig rings. They used the two-film and penetration

theories and separated the interfacial area from the mass transfer coefficient by assuming that the interfacial area is proportional to the total wetted area. For Raschig rings and water a correlation was found between total wetted area and the dry area (Fujita, 1951) : -0.278

a, at

=

1

- 1.02e VOL. 7

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