Reprinted from May 1983, Vol. 105, Journal of Solar Energy Engineering

C. K. B. Lee Senior Research Specialist.

S. L. Ridgway Program Manager of

Mist Flow Heat Engine.

R&D Associates Marina del Rey, Calif. 90291

Vapor/Droplet Coupling and the Mist Flow (OTEC) Cycle The present experiments have demonstrated that water droplets ( -200-pm dia) can be lifted to substantial heights ( -50 m ) by their own vapor produced in flashing over temperature differences typical of the tropical seas. The coupling between the vapor and droplets is found to be excellent. The efficiency for momentum coupling is over 90percent, and that for energy coupling is shown to vary inversely with the slip ratio. For the conditions in the present experiments, it varies from 50 to 80 percent. The momentum transfer is correlated with an interaction parameter which is the product of the liquid fraction, the slip, and the amount of flashing. For the high vapor flow cases, the pressure difference across the lift column is found to be proportional to the interaction parameter. The relevance of the two-phase flow to a class of open-cycle ocean thermal energy conversion (OTEC) schemes is con- sidered, and the implications of the observed strong vaporldroplet coupling to the feasibility of the mist-flow OTEC cycle are discussed.

Introduction The temperature difference between the surface and the

depths of the tropical seas is a potential source of low cost energy. D'Arsonval [ 11 suggested exploiting this temperature difference with a Rankine cycle that used a working fluid such as sulphur dioxide. This is known today as a closed-cycle system, the cost of which depends mainly on the cost of the large heat exchangers. Claude [2] was first to design and build an open-cycle system. In the Claude cycle, the warm surface water evaporates in an evacuated chamber, the vapor passes through a turbine to do work, and is condensed in a second chamber by cold water from the depths. The extremely low density of the vapor requires a very large turbine.

In 1975, Beck [3] proposed an open cycle that avoids the use of a vapor turbine. He proposed a vapor lift pump where the warm surface water is allowed to flash in a vacuum chamber into a bubbly mixture which naturally underwent transition to slug flow and then to dispersed flow. The water collected at the top of the vapor lift pump is allowed to fall over the lifted height to do work in a water turbine. Another cycle, proposed the same year by Zener and Fetkovich [4], is known as the foam lift cycle. It uses a detergent to create and stabilize a bubbly foam while the water is flashing. The expansion of the foam is utilized to lift the water, which, after foam-breaking, falls to drive a water turbine.

In 1977, Ridgway [5] proposed the mist flow cycle. In this cycle, the warm water at the surface of the ocean is first allowed to fall for a depth of -100 m, and the potential energy released is extracted by a hydraulic turbine. Then the warm water is lifted back to the ocean surface by its thermal energy. The lifting is achieved by spraying the warm water as a uniform mist of fine droplets (-200-pm dia) up an ~

Contributed by the Solar Energy Division and presented at the ASME/JSME Thermal Engineering Joint Conference, Honolulu, Hawaii, March 20-24, 1983. Manuscript recieved by the Solar Energy Division July 19, 1982.

Journal of Solar Energy Engineering

evacuated lift column. The vapor produced in the flashing of the water drags the droplets back to the ocean surface. Cold water from the depths of the ocean (e.g., 700-m deep) is pumped to the ocean surface and sprayed into the condenser at the top of the evacuated lift column to condense the flashed

I

225 -

200-

175 - - E

I-

_I

I

:: 150-

c w

1 0 5 10 15 20

TEMPERATURE DIFFERENCE ( O C )

Fig. 1 Theoretical lift and specific volume versus temperature dit. ference Ti - T,, for Ti = 25°C

MAY 1983, Vol. 1051181

MIST SEPARATOR UPPER DRAIN SUMP /

Fig. 2 The bench-scale mist lift experiment apparatus

vapor to maintain the upward vapor flow. The mixture of lifted droplets, condensate, and cold water is then returned to the ocean at a convenient depth.

The common feature among these three lift cycles is the use of two-phase flow to achieve the desired lift. In fact, the success and failure of each of these cycles depend largely on the choice of the two-phase flow regime. The amount of theoretical work available (in terms of distance lifted against gravity) from the isentropic expansion of water from the saturation line to the two-phase region as a function of the temperature difference and specific volume is plotted in Fig. 1. Most of the work is done at specific volumes (of the two- phase mixture) > 500 cm3 /g. The small liquid fraction of the final mixture determines the appropriate two-phase flow regime to be the mist flow regime. Furthermore, due to the large interface area provided by the droplets, the coupling between the phases is excellent.

This paper presents the experimental results of a small-scale experiment where the coupling process is studied in a (0.24-m x 0.375-m) rectangular column 4-m tall. It is shown that the energy imparted to the droplets in this short column is suf- ficient to carry them to substantial heights (many tens of meters).

Experimental Apparatus and Procedure The apparatus (Fig. 2) comprises six major components: a

source tank, a fallback tank, an output tank, a condenser, a vacuum pump, and the plexiglass lift column. Warm water from the source tank is led to the mist generator assembly and forced through the nozzle plate, which produces numerous tiny jets of water that break up into droplets just above the mist generator. Simultaneously, vapor flashed from the jets accelerates the droplets up the lift column. As mentioned in the introduction, since most of the work is done at large mixture specific volumes, the ratio of nozzle area to total area of the mist-generator is chosen such that initial mixture specific volumes of - 1000 cm3/g are achieved.

Droplets that strike the wall will coalesce in a water film that drains past the mist generator into the fallback tank. Most of the droplets, however, continue up the lift column. At the top, the droplets are separated from the vapor and allowed to drain into the upper drain sump and then the output tank. The vapor is ducted into the ice-filled tank where it condenses. In the present experiments, the ice charge suffices for 20 min of operation. The experiment is started by opening valve V4, allowing the warm water to flow into the mist-generator assembly. The water injection pressure is controlled by adjusting valve V4. The pressure difference across the lift column is measured by a manometer using ethylene glycol. The pressure difference across the upper half of the lift column is measured by a differential pressure gauge (manufactured by Setra Systems), which is sensitive to pressure changes of 1 Pa and has a range of 0 to 138 Pa. The

Nomenclature'

c CP c,

F

F W d

F W R

G g h

proportionality constant specific heat velocity coefficient momentum flux of water jets, see equation 1 drag force per unit volume between the vapor and the droplets droplet momentum losses per unit volume due to wall ef- fects Momentum losses for the vapor due to wall effects mass flux acceleration due to gravity column height latent heat of vaporization effective lift height

' Bar over a variable denotes arithmetic average.

m p e p, S

mass flow rate exit pressure injection pressure slip ratio

flashdown temperature exit temperature injection temperature transport velocity (average droplet velocity) droplet velocity at exit injection droplet velocity vapor velocity exit vapor velocity

CS=Cvge + vgi)/(ve + vt))

V, = slipvelocity

x = z = a = P = P = B = E =

t =

quality vertical distance void fraction liquid fraction density interaction parameter energy coupling efficiency fraction of momentum shared by the vapor flashing in a one-dimensional flow (see reference [6], equation (3.49))

Subscript d = water droplets g = vapor

1821Vol. 105, MAY 1983 Transactions of the ASME

temperature of the mist at the top of the column is measured with a YSI precision thermistor encased in a thin-walled glass tube and inserted into the flow.

The velocity coefficient of a mist-generator plate sample was determined by measuring the momentum flux, F, and the mass flux, m, out of the sample at a known nozzle plate pressure differential, AP. The velocity coefficient is given by

C, = F/ m(2AP/p) E (1)

A typical nozzle plate, made of a 0.25-mm-thick stainless steel perforated plate with electron-beam-punched holes distributed on a square matrix with a 1.8-mm pitch, was tested. The flow entered the side with the large diameter (0.175 mm) and exited at the side with the smaller diameter (0.1 mm) just like the flow through a nozzle.

The equipment to measure the quantities in equation (1) consisted of a water supply line, a Bourdon pressure gauge (0-400 kPa gauge), a 90-deg turning plate, and a spring scale (0-500 g range). The water jets quickly break up into a mist of tiny droplets due to Rayleigh instability. The diameter of the drops is twice that of the jets. The jets are directed downward toward a 90-deg turning plate placed on the spring scale. The momentum flux is measured as the difference between the scale reading with and without the jets. The mass flow rate is measured by collecting the water over a minute.

The results are given in Table 1. The clogged mist generator had been submerged in a tank of Santa Monica City water for a month. Some clogging of the nozzles was visually observed; however, the effect on the velocity coefficient was small. The clogging in sea water has not yet been investigated. The results

indicate that (0 the flow is proportional to the square root of the pressure difference, and (ii) the velocity coefficient is 0.95 for a clean nozzle plate. The expected hydraulic efficiency of the mist generator is therefore approximately 0.9.

Data Reduction Procedure and Error Bounds

The one-dimensional momentum equation for the vapor appropriate for the present experimental condition in the lift column consists of the vapor acceleration term, the pressure force term, the gravity term, the vapor/droplet interface drag term, Fdg, the wall friction term, F,, and a term representing the momentum change due to flashing, and is

1 100 .O1 ? <<Fdg 1 Pa/m

(2)

Table 1 Measured velocity coefficient

Momentum Mass Gage Velocity flux F, flux i , pressure coefficient

kg-m/s2 kg/s AP, Pa CIJ

Clogged 8.52 0.0948 4.15 x 10' 0.94 injector plate 4.61 0.0667 2.52 x I O 5 0.93

Clean 13.63 0.15 4.15 x io5 0.95 injector plate 8.23 0.113 2.72 x 10' 0.95

Table 2 Mist-lift experiment results (velocity coefficient = 0.9)

@2 Average Average Pa sbpvel. qudity

Pj (ABS) M1 Run T, Pa Te Pa No. "C x 1 0 - ~ "C XIO-' x ~ o - ~ I/,,m/s X

20 35.8 1.01 13.0 21 35.8 1.70 13.1 23 24 25 26 27 28 51 52 53 54 55 56 57 61 62 71

100 101 102 103 104 105 106 107 108 109 110 111 115 117 119 120 121 122 123 124 125 126

35.8 0.67 12.3 38.9 1.01 10.7 35.6 0.51 i3 . i 39.2 0.68 13.0 39.2 0.51 13.1 38.9 0.41 13.4 37.2 1.3 11.7 37.2 0.47 12.5

27.8 0.5 7.8 25.0 2.36 14.9 25.0 2.02 10.3 ~...

46.1 0.3- 12.3 40.0 0.46 13.1 30.5 1.01 8.6 30.0 1.01 9.4 30.0 1.01 9.9 30.0 1.35 10.8

~ ~. ....

30.0 1.35 11.3 30.0 1.35 11.6 30.0 1.70 12.0 29.5 1.70 12.1 -~

29.5 2.05 12.8 37.2 2.3 11.6 24.4 1.01 8.2 24.4 1.35 11.4 24.4 1.70 12.1 25.0 2.2 11.4 24.4 2.2 i0.2 24.4 2.2 9.5 24.4 2.2 8.2 24.4 3.4 10.2 24.4 3.4 10.2 23.9 3.7 10.6 23.9 3.1 11.1

1.8 2.7 1.6 1.5 1.3 1.5 1.1 0.86 4.0 0.7 1.7 1.7 1.9 2.0 1.8 1.21 1.21 0.88 1.3 2.2 2.0 2.0 2.2 2.2 2.2 2.7 2.7 2.8 5.5 1.7 1.5 1.3 2.2 2.6 3.0 2.8 3.9 3.4 3.9 2.8

0.78 1.30 0.63 0.70 0.53 0.65 0.47 0.28 2.0 0.2 0.9 0.6 0.4 0.3 0.2 0.3 0.6 0.2 0.54 0.71 0.68 0.6.5 0.74 0.74 0.74 0.89 0.88 1.05 1.94 0.50 0.50 0.51 0.77 0.83 1.08 1 .oo 1.3 1.3 1.5 1 .o

13.9 17.0 11.7 30.5

14.6 13.6 11.9 26.9 15.0 16.2 15.3 10.8

7.80

9.10 7.10

-0.0 16.7 11.3 18.9 24.23 21.04 18.89 18.58 16.37 15.16 14.38 12.6 11.56 26.45 16.24 7.64 7.74

10.49 12.19 14.25 22.59 12.02 14.73 9.49 9.09

0.0372 0.0365 0.0385 0.0463 0.0370 0.0431 0.0433 0.0536 0.0397 0.0412 0.0267 0.0285 0.0301 0.0309 0.0315 0.0164 0.0238 0.0567 0.023 0.018 0.017 0.017 0.016 0.016 0.016 0.015 0.015 0.014 0.022 0.014 0.01 1 0.01 1 0.012 0.013 0.013 0.014 0.013 0.013 0.01 1 0.01 1

Average Mass liquid flux

fraction G a x io4 kg/rn2 - s

5.5 5.8 4.8 5.9 2.2 3.6 5.1 4.2 5.4 5.9 6.9 6.0 4.7 4.1 3.6 8.1 3.5 4.3 6.18 5.76 6.04 6.03 6.42 6.42 6.42 6.47 6.47 6.76 5.42 6.50 7.24 7.91 7.39 7.03 6.79 6.95 7.04 7.34 7.21 7.49

10.9 14.2 8.9

10.9 7.7 8.9 7.7 6.8

17.4 1.4

15.4 12.7 9.8 8.9 7.7

16.9 15.6 6.1 8.9

12.0 12.0 12.0 13.9 13.9 13.9 15.6 15.6 17.1 18.2 12.0 13.9 15.6 17.9 17.9 17.9 17.9 22.1 22.1 23.2 21.0

Coupling eff.

0.59 0.59 0.61 0.38 0.67 0.55 0.52 0.51 0.54 0.44 0.59 0.58 0.66 0.70 0.74 1 .o 0.55 0.56 0.43 0.46 0.49 0.51 0.54 0.57 0.59 0.63 0.66 0.68 0.56 0.53 0.72 0.72 0.70 0.68 0.65 0.53 0.72 0.67 0.77 0.75

E L e rn 34.3 48.7 34.0 26.0 27.7 30.6 20.9 16.3 81.0 12.5 27.7 30.9 44.6 53.1 52.9 14.2 14.5 24.9 21.4 38.2 32.8 32.9 34.3 34.3 34.3 40.8 40.8 40.6

101.5 25.5 21.4 16.7 29.8 37.6 43.8 39.5 54.7 44.9 53.3 36.7

Journal of Solar Energy Engineering MAY 1983,Vol. 1051183

r T Table 3 Relative errors calculated based on Run 20

Quality Error in measurement Percent

where a! is the void fraction, x is the quality, and < is the fraction of the momentum change due to flashing that is expended in the vapor stream. Listed below each term is the estimated order of magnitude of that term either from direct measurements or from calculations. The vapor velocity and the quality in the lift column can be calculated using a heat balance and the steam table. The wall friction term is expected to be much smaller than the interface drag term since the surface area of the wall, even with a wavy liquid film on it, is substantially less than that of the droplets. The pressure drop is a measured quantity, and the gravity term is negligible. Thus equation (2 ) can be approximated by

dP dz - G -Fdg (3)

recognizing that a! - 1 in the present experiments. This means that over 90 percent of the force exerted by the vapor is spent in dragging the droplets.

Next, consider the momentum equation for the droplets:

?

.01 1 100 1 1 Pa/m

Again, the orders of magnitude of the terms are given below each term. All the terms, except the interface drag and the wall friction, are calculated by the same method. The in- terface drag term is taken to be dP/dz from the analysis of the vapor momentum equation. The wall friction term requires some physical interpretation. In the lift column, the wall acts as a sink for the droplets. The momentum of the droplets that hit the wall is lost. The quantity of droplets collected at the wall is observed to be about 3 percent of the total flow per meter of height. Therefore, the momentum loss is

where Gd is the droplet mass flux, and Vd is the droplet velocity averaged over the column. The actual momentum loss is less than this since most droplets strike the walls in the lower half column. These droplets have not been worked on by the vapor to the extent that they have acquired a velocity of V d . The loss of liquid due to the wall effect actually reduces the liquid fraction in the main-stream such that for the same pressure difference a larger velocity is imparted to the droplets in the mainstream. From this analysis it is clear that over 90 percent of the interface drag goes to accelerate the droplets and a few percent to overcome gravity. Equation (4) can therefore be approximated by

F , E 0.03Gd Vd ( 5 )

Integrating over the column, equation (6) becomes

(7)

where VI and V, are the velocities of the droplets at the inlet and at the exit respectively; AP, is the pressure difference across the column, and jl denotes the integral from the bottom to the top. Thus, a simple estimate of the average transport velocity will determine the amount of momentum coupled to the droplets in the column. The recorded measurements were the injection pressure, P I , and tem- perature, T I , the pressure difference across the entire column, PI, the upper half column, AP2, and the top temperature, Te .

The data reduction procedure begins by calculating the saturation pressure at the top of the column based on T,. Then the pressure at the bottom of the column, P,, is determined using AP,. The pressure difference PI - PB is used to calculate the mass flow rate, riZ, and the injection velocity, V I . Finally, the effective lift height is given by

Ve2 - V,'+2gh Le =

2g where h is the column height. The measured and the calculated data are tabulated in Table 2 along with the corresponding two-phase flow parameters.

An analysis was performed, based on the errors in the measured quantities, to determine the errors involved in the calculated quantities. Table 3 presents the results. The magnitudes of these errors are larger than those incurred by the neglect of the minor terms in the momentum balance equations; therefore, the use of the simplified data reduction procedure is justified.

Discussion of Results The results of the present experiments clearly demonstrate

that a mist of droplets produced by the present mist generator can be lifted to substantial heights by its own flashing- generated vapor.

From the analysis of the momentum equations in the previous section, it is observed that almost the entire pressure drop in the vapor is invested in the acceleration of the droplets. An energy coupling efficiency can be defined by the ratio of energy gain in the droplets to the corresponding loss in the vapor, i.e.,

G c - c + 2 g h (8) E = -

AP 2Vg and, using equation (7)

€ = U S = Vd/V8 (9) Equation (9) indicates that the energy coupling efficiency is inversely proportional to the average slip ratio, s. From Table 2, the data also reveal that an energy coupling efficiency of - 70 percent was achieved although no attempt was made to maximize it. It is expected that efficiencies of 80 percent will be easily achieved when the experimental conditions are optimized.

Since the pressure difference is a direct measure of the momentum transfer (or coupling) between the vapor and the mist, it would be advantageous to correlate it with other two- phase flow parameters. Physically, it is expected that the pressure difference would depend on the liquid fraction, 0, the slip velocity, V,, the vapor flow, the droplet size spec- trum, the corresponding velocity spectrum (both dependent on the amount of coalescence and breakup), as well as the amount of flashing during the transport. For a given size spectrum the liquid fraction can be used as a measure of the relative distance between droplets and therefore as a measure of the probability of coalescence. It is also a measure of the amount of liquid available for the vapor to lift.

1841Vol. 105, MAY 1983 Transactions of the ASME

m P

P' a

400

300

e .

0 .. ..

the droplets are much higher, the breakup of coalesced droplets becomes more probable upon colliding with another droplet. Hence, the droplet spectrum is more likely to stay approximately the same throughout the transport. For a slip of 20 m/s (Re -5 in the experiments) deviation from Stokes drag is small, and therefore the drag is approximately proportional to the slip velocity. Since vapor flow is a measure of the amount of energy available, it is expected that the momentum transfer is proportional to the vapor flow. These arguments suggest the use of a simple parameter to correlate the interaction between the vapor and the droplets

"/ .. where

The exit vapor velocity is used rather than the average because it is proportional to the temperature difference, AT, in the

0 0.2 0.4 0.6 0 .a 1 .o flashing, which represents the total available energy. Here, c, 0 V V I

* * q. mLlr'

Fig. 3 Measured pressure difference versus interaction parameter

- DISCHARGE

Fig. 4 The mist flow power plant

Coalescence and breakup are governed by the collision cross sections, which depend mainly on the radii of the in- teracting droplets and their velocities of approach. Higher approaching velocities reduce the probability of coalescence.

The large number of variables involved makes it difficult to obtain a simple correlation. However, if only the high vapor flow cases are considered, it is likely that one can neglect the spectral evolution effects since the transport time of the droplets is reduced. When less time is available for the motion, the droplets would have less chance to collide during the transport. Moreover, since the approaching velocities of

is the specific heat, hjg is the latent heat of vaporization, and pg is the vapor density. It is postulated that for high flow, the pressure drop is proportional to the interaction parameter, AP = Cq. Note that this satisfies the limiting condition for the correlation that a zero pressure drop will result from the absence of any liquid in the column, or from lack of slip between the droplets and the vapor.

The data in Table 2 were scanned to select the high flow runs with AP, =2AP2. This ensured that equal amounts of work were done in each half-column. It was found that over 90 percent of the data with V,, 2 20 m/s did satisfy this requirement, which indicates that for most cases the work done was uniform throughout the lift column. The plot on Fig. 3. is the resulting correlation. It is accurate to f 50 percent for these runs, except for Run 24.

Finally, no instabilities of the two-phase flow were ob- served in these experiments which would cause a rainout. Large variations in the injection pressure, which cause large changes in the flow rate, did not seem to affect the stability of the flow. Typically in these experiments the injection pressure was varied from Yi to 2 atmospheres and vice versa over a time period of a few seconds. The lower bound for the in- jection pressure was about 50 kPa below which rainout would occur. This value is dependent on the injection temperature. For example (Run 28), when the injection temperature was 38.9"C, the observed lower bound was 40 kPa; and for Run 71, when the injection temperatuare was 46.1 'C, the lower bound was 30 kPa.

Experimental confirmation of the inferred exit velocity using equation (7) was obtained by suspending weights at the top and observing their liftoff by the momentum flux of the flow. These measurements verified equation (7) to within & 5 percent. The error in the calculated effective lift height is, therefore, no more than a few percent.

The Equivalent Power Plant Using the present results, a power plant is designed based

on a 4-m coupling section where the vapor/droplet interaction takes place, and a long section for the coasting of the high velocity droplets. The design parameters are: A = 0.0871 m2 (area of present test section), h = 4.0m., P, = 480 kPa, T, = 25"C, T, = 9°C.

The calculated quantities neglecting wall effects are: G = 2.41 g/cm2s, Vi = 29.4m/s, V, = 46.0m/s, V,; = 41.9m/s, Vge = 72.5 m/s, = 1.53, 6 = 0.0006, X = 0.0244, Vs = 19.8 m/s, AP, = 425 Pa (equation (6)). Le equals 108.0 m (this is height of coasting section); net height equals 63 m; gross power equals 1.30 kW, or 15 kW/mz of mist generator area. The expected losses expressed in meters of lift are: filter

Journal of Solar Energy Engineering MAY1983,Vol. 1051185

loss = 2 m, exit loss = 3 m, cold water pump = 18 m, and vacuum pump = 5 m, giving a total of 28 m of losses, or 44 percent of the net height. The net power is 0.73 kW, or 8.5 kW/m2 of mist generator area.

Extrapolation to a Larger Plant Concept In actual design, one is not limited to an acceleration zone 4

m in height that demands substantial acceleration ( - 10 to 20 g) over a short distance in order to exercise the full ther- modynamic work of the cycle on the droplets. For an im- proved power plant design, it is better to operate at about 5-g mist acceleration over a longer distance. An improvement in the energy coupling results because a smaller slip ratio is used (see equation (9)).

A design based on these considerations is shown in Fig. 4. The central structure is the large evacuated duct in which the water is lifted a distance of about 100 m by the conversion of its heat energy into work. The warm ocean surface water enters through the filter at the left of the diagram, and then descends to the water turbine. Most of the pressure is removed from this water by the turbine to produce power. With the remaining pressure the warm water is then sprayed upward into the bottom of the duct.

The bottom 20 m of the duct comprises the mist ac- celeration zone. Cold water is introduced into the accelerated mist in the form of a circumferential converging sheet in the coast zone which is also the condenser. A vacuum pump removes noncondensibles at the top. The pressure difference between the start and the end of the acceleration zone drives the mist to a velocity of nearly 50 m/s. The converging cold water sheet merges with the accelerated mist to form a single jet which coasts upwards against gravity almost to a stop, and then overflows into a basin from which it then drains into the ocean. Note that coalescence of droplets in the coast zone does not change their upward momentum.

The accelerated mist is also used as a jet pump for the cold water. The heights of the acceleration and the coast sections are suitably chosen so that the momentum transfer from the mist to the cold water supplies the kinetic energy needed to carry the cold water to the barometric level, from which it is able to drain back into the ocean against atmospheric pressure. The use of the accelerated mist as a jet pump shortens the lift height by -20 m, which is less than the amount of turbine head required to drive a mechanical cold water pump, so that the overall efficiency is increased. Moreover, some cost reductions should result from the replacement of the cold water pump by the jet pump and the shortening of the column relative to previous mist flow plant designs.

Conclusion The major finding in the present experimental study is that

a mist of droplets ( - 200-pm dia.) can be lifted to substantial heights (> 50 m) against gravity by their own vapor generated from flashing. Considerations of the momentum balance indicate that over 90 percent of the total pressure drop is

invested in accelerating the droplets. The efficiency of the energy coupling is theoretically inversely proportional to the slip ratio. For the present experimental conditions, the energy coupling efficiency ranged from 50 to 90 percent.

A correlation for the pressure difference, which is a direct measure of the momentum transfer from the vapor to the droplets, is

based on the parameter (v), which is a measure of the amount of interaction between the vapor and the droplets. Comparing with the data the correlation is accurate to within +50 per- cent. It should be cautioned that the correlation would be expected to show a different proportionality constant if the initial droplet size or liquid fraction, i.e., the design of the mist generator, had been chosen differently.

These results imply that one could design a power plant based on the following conditions: (z] a short coupling section followed by a long coasting section, (ii) a high droplet transport velocity, and (iiz] a high vapor flow. The equivalent power plant and an extrapolation to a larger plant concept have been presented.

AP= 45011 Pa (1 1)

Acknowledgment This work was supported by the U.S. Department of

Energy Subcontract No. 7613 monitored by Dr. Fang Chen and Dr. John Michel at Oak Ridge National Laboratory. The authors are indebted to the following individuals for their contribution to the experiments: Dr. Phil Hammond, Mr. John Ridgway, Mr. Alex Ridgway, and Mr. Min Kong Lau. The assistance of the personnel at Dynamics Technology is gratefully acknowledged.

References 1 D’Arsonval, J. A., RevueScientifique, Sept. 1881, p. 17. 2 Claude, G., “Method and Apparatus for Obtaining Power from Sea

Water,” U.S. Patent No. 2,006,985, July 1935. 3 Beck, E. J . , “Ocean Thermal Gradient Hydraulic Power Plant,” Science,

Vol. 189, 1975, p. 293. 4 Zener, C., and Fetkovich, J . , “Foam Solar Sea Power Plant,” Science,

Vol. 189, 1975, p. 294. 5 Ridgway, S. L., “The Mist Flow Ocean Thermal Energy Conversion

Plant,” Proceedings of the Fourth Ocean Thermal Energy Conversion Con- ference, New Orleans, 1977.

6 Wallis, G. B., One-Dimensional Two-PhaseFlow, McCraw-Hill, 1969. 7 Lee, C. K. B., and S . L. Ridgway, “Vapor/Droplet Coupling in Flashing

Mist-Flow,” Report No. RDA-TR-110902-001, R&D Associates, Marina del Rey, Calif., Feb. 1981.

8 Ridgway, S . L., Hammond, R. P., and C. K. B. Lee, Mist-Flow Ocean Thermal Energy Process, Final Report, Oak Ridge National Laboratory, ORNL-7613/1, Apr. 1980.

9 Ridgway, S . L., Lee, C. K. B., and R. P. Hammond, “Experimental Demonstration of the Feasibility of the Mist Flow Ocean Thermal Energy Process,” paper presented at the 8th Ocean Energy Conference, Washington, D. C., June7-11, 1981.

10 Ridgway, S . L., Hammond, R. P., and C. K. B. Lee, “Experimental Demonstration of the Feasibility of the Mist Flow Ocean Thermal Energy Process,” paper presented at the AIAA Second Terrestrial Energy Systems Conference, Colorado Springs, Colo., Dec. 1981.

11 Davenport, R., “Mist Lift Analysis Summary Report,” SERI/TR-631- 627, Solar Energy Research Institute, Golden, Colo. 1982.

186 I Vol. 105, MAY 1983 Transactions of the ASME